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Chamber properties from transmitral flow: Prediction of average and passive left ventricular diastolic stiffness
Abstract
A chamber stiffness (K(LV))-transmitral flow (E-wave) deceleration time relation has been invasively validated in dogs with the use of average stiffness [(DeltaP/DeltaV)(avg)]. K(LV) is equivalent to k(E), the (E-wave) stiffness of the parameterized diastolic filling model. Prediction and validation of 1) (DeltaP/DeltaV)(avg) in terms of k(E), 2) early rapid-filling stiffness [(DeltaP/DeltaV)(E)] in terms of k(E), and 3) passive (postdiastasis) chamber stiffness [(DeltaP/DeltaV)(PD)] from A waves in terms of the stiffness parameter for the Doppler A wave (k(A)) have not been achieved. Simultaneous micromanometric left ventricular (LV) pressure (LVP) and transmitral flow from 131 subjects were analyzed. (DeltaP)(avg) and (DeltaV)(avg) utilized the minimum LVP-LV end-diastolic pressure interval. (DeltaP/DeltaV)(E) utilized DeltaP and DeltaV from minimum LVP to E-wave termination. (DeltaP/DeltaV)(PD) utilized atrial systolic DeltaP and DeltaV. E- and A-wave analysis generated k(E) and k(A). For all subjects, noninvasive-invasive relations yielded the following equations: k(E) = 1,401. (DeltaP/DeltaV)(avg) + 59.2 (r = 0.84) and k(E) = 229.0. (DeltaP/DeltaV)(E) + 112 (r = 0.80). For subjects with diastasis (n = 113), k(A) = 1,640. (DeltaP/DeltaV)(PD) - 8.40 (r = 0.89). As predicted, k(A) showed excellent correlation with (DeltaP/DeltaV)(PD); k(E) correlated highly with (DeltaP/DeltaV)(avg). In vivo validation of average, early, and passive chamber stiffness facilitates quantitative, noninvasive diastolic function assessment from transmitral flow.
... The high fidelity, simultaneous echocardiographic transmitral flow and pressure-volume (P-V) data recording method has been previously described [17,[20][21][22][23][24]. Briefly, immediately prior to arterial access a complete 2-D echo-Doppler study in a supine position using a Philips (Andover, MA.) iE33 system is performed according to American Society of Echocardiography (ASE) criteria. ...
... Each E-wave was also analyzed via the Parametrized Diastolic Filling (PDF) formalism (see Appendix 1) to yield, mathematically unique PDF parameters for each E-wave (stiffness parameter (k), chamber viscoelasticity/relaxation parameter (c), load parameter (x o )). 23,29,30 Stiffness (DT s ) and relaxation (DT r ) components of DT were computed via the fractionation method employed previously 19 (see Appendix 2) such that DT=DT s +DT r . By determining DT s and DT r of each E-wave, the total DT can be expressed as the fraction due to stiffness (S=DT s /DT) and the fraction of DT due to relaxation (R=DT r /DT) for each E-wave analyzed. ...
... The quantitative ventriculography was used to determine end-systolic and end-diastolic volumes which defined the limits of volume tracing of conductance catheter has been previously detailed. 23,24,31,32 After calibration of conductance volume, LV pressure and volume at diastasis were measured beatby-beat using a custom MATLAB program. End-diastasis points were defined by ECG P wave onset. ...
Although the electrophysiologic derangement responsible for atrial fibrillation (AF) has been elucidated, how AF remodels the ventricular chamber and affects diastolic function (DF) has not been fully characterized. The previously validated Parametrized Diastolic Filling (PDF) formalism models suction-initiated filling kinematically and generates error-minimized fits to E-wave contours using unique load (xo), relaxation (c), and stiffness (k) parameters. It predicts that E-wave deceleration time (DT) is a function of both stiffness and relaxation. Ascribing DTs to stiffness and DTr to relaxation such that DT=DTs+DTr is legitimate because of causality and their predicted and observed high correlation (r=0.82 and r=0.94) with simultaneous (diastatic) chamber stiffness (dP/dV) and isovolumic relaxation (tau), respectively. We analyzed simultaneous echocardiography-cardiac catheterization data and compared 16 age matched, chronic AF subjects to 16, normal sinus rhythm (NSR) subjects (650 beats). All subjects had diastatic intervals. Conventional DF parameters (DT, AT, Epeak, Edur, E-VTI, E/E’) and E-wave derived PDF parameters (c, k, DTs, DTr) were compared. Total DT and DTs, DTr in AF were shorter than in NSR (p
... With progressive impairment of relaxation, the E′ peak is reduced and delayed. 20 Thus, pseudonormal can be distinguished from normal by a reduced and delayed E′ and increase in the E/E′ ratio or by respiratory maneuvers (straining) that transiently alter load. 7,9 In this work, we test 2 hypotheses: (1) that PDF-based E-wave analysis suffices to differentiate pseudonormal from normal filling in unblinded groups, that is, where E′ is known in advance, and (2) that PDF analysis can differentiate pseudonormal from normal filling in blinded groups, when E′ is not known in advance. ...
... The database is a repository of high fidelity, simultaneous echocardiographic transmitral flow and pressure-volume data using standard recording methods that have been previously detailed. 11,13,14,20,21,26 Briefly, immediately before arterial access, a complete 2D echo-Doppler study is performed with subjects in supine position using a Philips (Andover, MA) iE33 system according to American Society of Echocardiography criteria. 9,27 ...
... Each E-wave was also analyzed via the PDF formalism (see Appendix 1 in the Data Supplement) to yield mathematically unique PDF parameters (x 0 , c, k) for each E-wave. 15,20,30,31 Stiffness (DT s ) and relaxation (DT r ) components of DT were computed via the previously validated fractionation method 18 (see Appendix 2 in the Data Supplement) such that DT=DT s +DT r (Figure 1), where total DT was determined using the conventional method. Alternatively, DT can be determined via the PDF method solely as detailed in Ref. [18]. ...
Background:
Pseudonormal Doppler E-wave filling patterns indicate diastolic dysfunction but are indistinguishable from the normal filling pattern. For accurate classification, maneuvers to alter load or to additionally measure peak E' are required. E-wave deceleration time (DT) has been fractionated into its stiffness (DTs) and relaxation (DTr) components (DT=DTs+DTr) by analyzing E-waves via the parametrized diastolic filling formalism. The method has been validated with DTs and DTr correlating with simultaneous catheterization-derived stiffness (dP/dV) and relaxation (τ) with r=0.82 and r=0.94, respectively. We hypothesize that DT fractionation can (1) distinguish between unblinded (E' known) normal versus pseudonormal age-matched groups with normal left ventricular ejection fraction, and (2) distinguish between blinded (E' unknown) normal versus pseudonormal groups, based solely on E-wave analysis.
Methods and results:
Data (763 E-waves) from 15 age-matched, pseudonormal (elevated E/E') and 15 normal subjects were analyzed. Conventional echocardiographic and parametrized diastolic filling stiffness (k) and relaxation (c) parameters and DTs and DTr were compared. Conventional diastolic function parameters did not differentiate between unblinded groups, whereas k, c (P<0.001) and DTs, DTr (P<0.001) did. Independent, blinded (E' not provided) analysis of 42 subjects (30 subjects from unblinded training set and 12 additional subjects from validation set, 581 E-waves) showed that R (=DTr/DT) had high sensitivity (0.90) and specificity (0.86) in differentiating pseudonormal from normal once E' revealed actual classification.
Conclusions:
arametrized diastolic filling-based E-wave analysis (k, c or DTs and DTr) can differentiate normal versus pseudonormal filling patterns without requiring knowledge of E'.
... The high fidelity, simultaneous echocardiographic transmitral flow and pressure-volume (P-V) data recording method has been previously described [17,[20][21][22][23][24]. Briefly, immediately prior to arterial access a complete 2-D echo-Doppler study in a supine position using a Philips (Andover, MA.) iE33 system is performed according to American Society of Echocardiography (ASE) criteria. ...
... The stiffness (DT s ) component of DT in AF, unique PDF parameters for each E-wave (stiffness parameter (k), chamber viscoelasticity/relaxation parameter (c), load parameter (x o )). 23,29,30 Stiffness (DT s ) and relaxation (DT r ) components of DT were computed via the fractionation method employed previously 19 (see Appendix 2) such that DT=DT s +DT r . By determining DT s and DT r of each E-wave, the total DT can be expressed as the fraction due to stiffness (S=DT s /DT) and the fraction of DT due to relaxation (R=DT r /DT) for each E-wave analyzed. ...
... The quantitative ventriculography was used to determine end-systolic and end-diastolic volumes which defined the limits of volume tracing of conductance catheter has been previously detailed. 23,24,31,32 After calibration of conductance volume, LV pressure and volume at diastasis were measured beatby-beat using a custom MATLAB program. End-diastasis points were defined by ECG P wave onset. ...
Although the electrophysiologic derangement responsible for atrial fibrillation (AF) has been elucidated, how AF remodels the ventricular chamber and affects diastolic function (DF) has not been fully characterized. The previously validated Parametrized Diastolic Filling (PDF) formalism models suction-initiated filling kinematically and generates error-minimized fits to E-wave contours using unique load (xo), relaxation (c), and stiffness (k) parameters. It predicts that E-wave deceleration time (DT) is a function of both stiffness and relaxation. Ascribing DTs to stiffness and DTr to relaxation such that DT=DTs+DTr is legitimate because of causality and their predicted and observed high correlation (r=0.82 and r=0.94) with simultaneous (diastatic) chamber stiffness (dP/dV) and isovolumic relaxation (tau), respectively. We analyzed simultaneous echocardiography- cardiac catheterization data and compared 16 age matched, chronic AF subjects to 16, normal sinus rhythm (NSR) subjects (650 beats). All subjects had diastatic intervals. Conventional DF parameters (DT, AT, Epeak, E dur, E-VTI, E/E′) and E-wave derived PDF parameters (c, k, DTs, DTr) were compared. Total DT and DTs, DTr in AF were shorter than in NSR (p<0.005), chamber stiffness, (k) in AF was higher than in NSR (p<0.001). For NSR, 75% of DT was due to stiffness and 25% was due to relaxation whereas for AF 81% of DT was due to stiffness and 19% was due to relaxation (p<0.005). We conclude that compared to NSR, increased chamber stiffness is one measurable consequence of chamber remodeling in chronic, rate controlled AF. A larger fraction of E-wave DT in AF is due to stiffness compared to NSR. By trending individual subjects, this method can elucidate and characterize the beneficial or adverse long-term effects on chamber remodeling due to alternative therapies in terms of chamber stiffness and relaxation.
... 15,32,47,48 Conventionally, chamber stiffness has been computed from DP avg / DV avg using invasive methods. 11,21,22,25,31,39 Although obtaining chamber stiffness, DP avg /DV avg itself usually involves an ''absolute'' measurement of LV pressure requiring catheterization, chamber stiffness, being the ratio of two derivatives, is a ''relative'' index and can be determined using ''relative measurement'' methodology, such as echocardiography, which is the preferred method of quantitative DF characterization. Hence, Doppler E-wave contours can only provide relative, rather than absolute, pressure information. ...
... Diastatic (passive) stiffness is the slope of the diastatic pressurevolume relationship, inscribed by the locus of load varying P-V points achieved at the end of each diastatic interval after E-wave termination, after the chamber has fully relaxed. 6,21,22,34,44 During diastasis, LV and left atrial pressures are equal, the pressure gradient across the mitral valve is zero, 6 there is no transmitral flow, hence the resultant forces generated by and acting on the ventricle are balanced (but not zero). 35 Accordingly, diastasis comprises the static equilibrium state of the passive LV. ...
... Datasets from 24 patients (mean age 61, 16 men) were selected from our cardiovascular biophysics laboratory database of simultaneous echocardiography-high fidelity hemodynamic (Millar conductance catheter) recordings. 5,21 Subjects underwent elective cardiac catheterization to determine presence of suspected coronary artery disease at the request of their referring physicians. Prior to data acquisition, subjects provided signed, IRB approved informed consent for participation in accordance with Washington University Human Research Protection Office (HRPO) criteria. ...
The mechanical suction-pump feature of the left ventricle aspirates atrial blood and generates a rapid rise and fall in transmitral flow (Doppler E-wave). Initially, E-wave deceleration time (DT), a routine index of clinical diastolic function, was thought to be determined only by chamber stiffness. Kinematic modeling of filling, in analogy to damped oscillatory motion [Parametrized Diastolic Filling (PDF) formalism], has been extensively validated and accurately predicts clinically observed E-wave contours while, revealing that DT is actually an algebraic function of both stiffness (PDF parameter k) and relaxation (PDF parameter c). We hypothesize that kinematic modeling based E-wave analysis accurately predicts the stiffness (DTs) and relaxation (DTr) components of DT such that DT = DTs + DTr. For validation, pressure–volume (P–V) and E-wave data from 12 control (DT < 220 ms) and 12 delayed-relaxation (DT > 220 ms) subjects, 738 beats total, were analyzed. For each E-wave, DTs and DTr was compared to simultaneous, gold-standard, high fidelity (Millar catheter) determined, chamber stiffness (K = ΔP/ΔV) and chamber relaxation (time-constant of isovolumic relaxation—τ), respectively. For the group linear regression yielded DTs = α
K + β (R = 0.82) with α = −0.38 and β = 0.20, and DTr = m
τ + b (R = 0.94) with m = 2.88 and b = −0.12. We conclude that PDF-based E-wave analysis provides the DTs and DTr components of DT with simultaneous chamber stiffness (K) and relaxation (τ) respectively, as primary determinants. This kinematic modeling based method of E-wave analysis is immediately translatable clinically and can assess the effects of pathology and pharmacotherapy as causal determinants of DT.
... Datasets from 20 patients (mean age 57 years, 13 men) were selected from our cardiovascular biophysics laboratory database of simultaneous echocardiography-high fidelity hemodynamic (Millar conductance catheter) recordings (Lisauskas et al. 2001a;Chung and Kov acs 2008). Subjects were referred by their personal physician for elective diagnostic cardiac catheterization to determine the possibility of coronary artery disease. ...
... Our simultaneous high-fidelity, P-V, and echocardiographic transmitral flow data recording method has been previously detailed (Kov acs et al. 1997(Kov acs et al. , 2000Lisauskas et al. 2001a;Chung et al. 2006;Mossahebi et al. 2011). Briefly, LV pressure was acquired using a micromanometric conductance catheter (SPC-560, SPC-562, or SSD-1043, Millar Instruments, Houston, TX) at the commencement of elective cardiac catheterization, prior to the administration of iodinated contrast agents. ...
... The PDF formalism models suction initiated early rapid filling (E-wave). The relation between catheterizationdetermined chamber stiffness (dP/dV) and k, and the viscoelasticity/ relaxation parameter c and the time-constant of IVR s have been previously established (Lakshminarayan K and SJ 1993;Hall and Kov acs 1994;Kov acs et al. 1997;Lisauskas et al. 2001a;Mossahebi et al. 2011). ...
Although catheterization is the gold standard, Doppler echocardiography is the preferred diastolic function (DF) characterization method. The physiology of diastole requires continuity of left ventricular pressure (LVP)‐generating forces before and after mitral valve opening (MVO). Correlations between isovolumic relaxation (IVR) indexes such as tau (time‐constant of IVR) and noninvasive, Doppler E‐wave‐derived metrics, such as peak A‐V gradient or deceleration time (DT), have been established. However, what has been missing is the model‐predicted causal link that connects isovolumic relaxation (IVR) to suction‐initiated filling (E‐wave). The physiology requires that model‐predicted terminal force of IVR (Ft
IVR) and model‐predicted initial force of early rapid filling (Fi E‐wave) after MVO be correlated. For validation, simultaneous (conductance catheter) P‐V and E‐wave data from 20 subjects (mean age 57 years, 13 men) having normal LV ejection fraction (LVEF>50%) and a physiologic range of LV end‐diastolic pressure (LVEDP) were analyzed. For each cardiac cycle, the previously validated kinematic (Chung) model for isovolumic pressure decay and the Parametrized Diastolic Filling (PDF) kinematic model for the subsequent E‐wave provided Ft
IVR and Fi E‐wave respectively. For all 20 subjects (15 beats/subject, 308 beats), linear regression yielded Ft
IVR= α Fi E‐wave + b (R = 0.80), where α = 1.62 and b = 1.32. We conclude that model‐based analysis of IVR and of the E‐wave elucidates DF mechanisms common to both. The observed in vivo relationship provides novel insight into diastole itself and the model‐based causal mechanistic relationship that couples IVR to early rapid filling.
... 32 No atrioventricular blood flow 4,8,25 or tissue motion is present, 31,35 the atrium and ventricle are both relaxed, and pressure remains constant (dP=dt ffi 0). Accordingly, diastasis comprises the static equilibrium state of the passive LV. 24,39 Since LV volume, (i.e., load) changes physiologically on a beat-by-beat basis, diastasis is achieved at slightly different ventricular volumes and pressures generating a series of slightly different equilibrium states. The locus of these load-varying diastasis P-V points define the diastatic P-V relationship (D-PVR), slope of which (K CATH ) provides the passive stiffness of the LV (Fig. 1). ...
... In order to obtain the D-PVR, we fit the P-V data using a linear, rather than using an exponential fit, since a previous study 40 has shown that a linear or exponential fit to the same data yields a similar measure of goodness of fit. Importantly, for a given chamber, the in vivo equilibrium volume of the LV is diastasis, 24,39 and chamber stiffness of the diastatic P-V relation has been shown to be distinct from, and to be always lower than, chamber stiffness in the same chamber measured at end-diastole. 40 Quantification of DD has remained a challenge without direct, invasive measurement. ...
... Datasets from 30 patients (mean age 57 years, 18 men) were selected from our cardiovascular biophysics laboratory database of simultaneous echocardiography-high fidelity hemodynamic (Millar conductance catheter) recordings. 6,24 Subjects underwent elective cardiac catheterization to determine the presence of coronary artery disease at the request of their referring physicians. The data selection criteria included a broad range of LV end-diastolic pressure (LVEDP) representative of a patient population encountered clinically, normal LVEF (>50%), normal sinus rhythm, clearly discernible E-waves followed by a diastatic interval, and normal valvular function. ...
The slope of the diastatic pressure–volume relationship (D-PVR) defines passive left ventricular (LV) stiffness \( \mathcal{K}.\) Although \( \mathcal{K} \) is a relative measure, cardiac catheterization, which is an absolute measurement method, is used to obtain the former. Echocardiography, including transmitral flow velocity (Doppler E-wave) analysis, is the preferred quantitative diastolic function (DF) assessment method. However, E-wave analysis can provide only relative, rather than absolute pressure information. We hypothesized that physiologic mechanism-based modeling of E-waves allows derivation of the D-PVRE-wave whose slope, \( \mathcal{K}_{{\text{E-}}{\text{wave}}} \), provides E-wave-derived diastatic, passive chamber stiffness. Our kinematic model of filling and Bernoulli’s equation were used to derive expressions for diastatic pressure and volume on a beat-by-beat basis, thereby generating D-PVRE-wave, and \( \mathcal{K}_{{\text{E-}}{\text{wave}}} \). For validation, simultaneous (conductance catheter) P–V and echocardiographic E-wave data from 30 subjects (444 total cardiac cycles) having normal LV ejection fraction (LVEF) were analyzed. For each subject (15 beats average) model-predicted \( \mathcal{K}_{{\text{E-}}{\text{wave}}} \) was compared to experimentally measured \( \mathcal{K}_{\text{CATH}} \)
via linear regression yielding as follows: \( \mathcal{K}_{{\text{E-}}{\text{wave}}} = \alpha {\mathcal{K}}_{\text{CATH}} + b\;(R^{2} = 0.92), \) where, α = 0.995 and b = 0.02. We conclude that echocardiographically determined diastatic passive chamber stiffness, \( \mathcal{K}_{{\text{E-}}{\text{wave}}} \), provides an excellent estimate of simultaneous, gold standard (P–V)-defined diastatic stiffness, \( \mathcal{K}_{\text{CATH}} \). Hence, in chambers at diastasis, passive LV stiffness can be accurately determined by means of suitable analysis of Doppler E-waves (transmitral flow).
... Compared to the low DD grade cohort, the high DD group had higher stiffness (k), lower time-constant of isovolumic relaxation (tau), and shorter deceleration time. Prior work has shown patients with normal LVEF can have increased invasively determined end-diastatic chamber dP/dV stiffness [15], and it is known that stiffness by the PDF method correlates strongly with the average ΔP/ΔV measure of stiffness as determined by invasive measurements [27]. Given that viscoelasticity was similarly impaired in both groups in the current study, it stands to reason that chamber stiffness and not viscoelasticity is the main determinant of increased left atrial pressure in the setting of reduced LVEF. ...
... The current study has several limitations that deserve to be acknowledged. Though our measurements were not directly compared to invasively derived data, these PDF methods have been validated in prior studies [19,26,27]. The sample size in the current study is relatively small, and could be underpowered to demonstrate differences for some parameters. ...
Background
The American Society for Echocardiography/European Association of Cardiovascular Imaging (ASE/EACVI) 2016 guidelines for assessment of diastolic dysfunction (DD) are based primarily on the effects of diastolic dysfunction on left ventricular filling hemodynamics. However, these measures do not provide quantifiable mechanistic information about diastolic function. The Parameterized Diastolic Filling (PDF) formalism is a validated theoretical framework that describes DD in terms of the physical properties of left ventricular filling.
Aims
We hypothesized that PDF analysis can provide mechanistic insight into the mechanical properties governing higher grade DD.
Methods
Patients referred for echocardiography showing reduced left ventricular ejection fraction (< 45%) were prospectively classified into DD grade according to 2016 ASE/EACVI guidelines. Serial E-waves acquired during free breathing using pulsed wave Doppler of transmitral blood flow were analyzed using the PDF formalism.
Results
Higher DD grade (grade 2 or 3, n = 20 vs grade 1, n = 30) was associated with increased chamber stiffness (261 ± 71 vs 169 ± 61 g/s ² , p < 0.001), increased filling energy (2.0 ± 0.9 vs 1.0 ± 0.5 mJ, p < 0.001) and greater peak forces resisting filling (median [interquartile range], 18 [15–24] vs 11 [8–14] mN, p < 0.001). DD grade was unrelated to chamber viscoelasticity (21 ± 4 vs 20 ± 6 g/s, p = 0.32). Stiffness was inversely correlated with ejection fraction ( r = − 0.39, p = 0.005).
Conclusions
Higher grade DD was associated with changes in the mechanical properties that determine the physics of poorer left ventricular filling. These findings provide mechanistic insight into, and independent validation of the appropriateness of the 2016 guidelines for assessment of DD.
... The gold-standard methods (simultaneous micromanometric hemodynamics and echocardiography) have been extensively used to validate the physiological interpretation. Results have shown these parameters are causally related to the chamber properties that determine diastolic function (14,(28)(29)(30). Physiological conditions can additionally be determined from the damped harmonic oscillator derived parameters such as kx0, which is the peak force in the spring that corresponds to the peak atrioventricular pressure gradient that generates the E-wave (14, 15) ; 1/2kx0 2 , which indicates the stored potential elastic energy that is capable of generating the recoil (14) ; the peak resistive force (cE-peak), which is the force that resists filling at the peak flow ; and c 2 -4k, which indicates the balance between the factors both driving and resisting the ventricular filling (14)(15)(16). ...
... In the echocardiographic study, the parameter k represents the chamber stiffness/elastic recoil property. As described above, chamber stiffness (dP/dV) as evaluated by invasive cardiac catheterization, has been shown to be linearly related to the spring constant k (g/s 2 ) (28)(29)(30). It has been shown that PDF analysis of the Doppler E-wave can accurately determine the LV diastatic passive chamber stiffness (41). ...
Right ventricle (RV) has frequently been described as the forgotten ventricle in the circulation. However, its importance in various cardiac diseases is now unquestioned. This recognition has led to improved risk stratification and development of algorithms for intervention, which incorporate measurements of RV function as key components of the assessment of many conditions. The diastolic function plays an important role in determining ventricular filling and stroke volume. Abnormal left ventricular (LV) diastolic function has been recognized in many cardiovascular diseases and is associated with worse outcomes, including total mortality and hospitalizations due to heart failure. In this review, we define what global RV diastolic function is, and how to measure it. This article indicates the validation of kinematic model parameters for assessing RV diastolic function. J. Med. Invest. 67 : 11-20, February, 2020
... Previous studies modeled filling in kinematic terms via the parameterized diastolic filling formalism. 36,37 This model characterizes transmitral blood flow velocity in terms of elastic, inertial, and damping forces. During filling, the elastic driving force generates both inertial forces, causing acceleration, and resistive (damping) forces, opposing acceleration. ...
... The 3 mathematically independent model parameters-spring constant, damping constant, and initial spring displacement-fully characterize the velocity of the E-wave. 36,37 The transmitral flow-based load-independent index of diastolic function can be derived and validated for the LV. 38 In the present study, it was, therefore, demonstrated that the kinematic model parameters have high reproducibility and can be determined independent of volume. ...
Background:
The rate of left ventricular pressure decrease during isovolumic relaxation is traditionally assessed algebraically via 2 empirical indices: the monoexponential and logistic time constants (τE and τL). Since the pattern of right ventricular (RV) pressure decrease is quite different from that of the left ventricular, we hypothesized that novel kinematic model parameters are more appropriate and useful to evaluate RV diastolic dysfunction.
Methods and results:
Eight patients with pulmonary arterial hypertension (age 12.5±4.8 years) and 20 normal subjects (control group; age 12.3±4.4 years) were enrolled. The kinematic model was parametrized by stiffness/restoring Ek and damping/relaxation μ. The model predicts isovolumic relaxation pressure as a function of time as the solution of d2P/dt2+(1/μ)dP/dt+EkP=0, based on the theory that the pressure decay is determined by the interplay of inertial, stiffness/restoring, and damping/relaxation forces. In the assessment of RV diastolic function, τE and τL did not show significant differences between the pulmonary arterial hypertension and control groups (46.8±15.5 ms versus 32.5±14.6 ms, and 19.6±5.9 ms versus 14.5±7.2 ms, respectively). The pulmonary arterial hypertension group had a significantly higher Ek than the control group (915.9±84.2 s-2 versus 487.0±99.6 s-2, P<0.0001) and a significantly lower μ than the control group (16.5±4.3 ms versus 41.1±10.4 ms, P<0.0001). These results show that the RV has higher stiffness/elastic recoil and lower cross-bridge relaxation in pulmonary arterial hypertension.
Conclusions:
The present findings indicate the feasibility and utility of kinematic model parameters for assessing RV diastolic function.
... Moreover, the velocity of transmitral inflow is modulated by numerous factors. Changes in preload alter the peak velocity of the left ventricular filling pattern of transmitral flow, with a clear dependency between heart rate with both the peak velocity of rapid filling and atrial contraction in humans [57][58][59][60]. ...
... This fits with our results, where bradycardia was associated with an increase in DT. Thus, according to literature [57][58][59][60], we assume, that in our study the significant bradycardia after hyperoxia had led to a prolonged inflow during early diastole, which caused lengthened DT. ...
Objective:
Hyperoxia is known to influence cardiovascular and endothelial function, but it is unknown if there are differences between younger and older persons. The aim of this study was to monitor changes in myocardial diastolic function and flow-mediated dilatation (FMD) in younger and elderly volunteers, before and after exposure to relevant hyperbaric hyperoxia.
Methods:
51 male patients were separated into two groups for this study. Volunteers in Group 1 (n=28, mean age 26 ±6, "juniors") and Group 2 (n=23, mean age 53 ±9, "seniors") received standard HBO₂ protocol (240kPa oxygen). Directly before and after hyperoxic exposure in a hyperbaric chamber we took blood samples (BNP, hs-troponin-t), assessed the FMD and echocardiographic parameters with focus on diastolic function.
Results:
After hyperoxia we observed a high significant decrease in heart rate and systolic/diastolic FMD. Diastolic function varied in both groups: E/A ratio showed a statistically significant increase in Group 1 and remained unchanged in Group 2. E/e' ratio showed a slight but significant increase in Group 1, whereas e'/a' ratio increased in both groups. Deceleration time increased significantly in all volunteers. Isovolumetric relaxation time remained unchanged and ejection fraction showed a decrease only in Group 2. There were no changes in levels of BNP and hs-troponin-t in either group.
Conclusion:
Hyperoxia seems to influence endothelial function differently in juniors and seniors: FMD decreases more in seniors, possibly attributable to pre-existing reduced vascular compliance. Hyperoxia-induced bradycardia induced a more pronounced improvement in diastolic function in juniors. The ability of Group 1 to cope with hyperoxia-induced effects did not work in the same manner as with Group 2.
... The theoretical framework describing LV filling in this manner has been termed the parameterized diastolic filling (PDF) formalism [2]. Using gold standard high fidelity invasive hemodynamic measurements, the stiffness constant k has been shown to have a close linear relationship with LV diastolic stiffness [3]. In the same manner, it has been shown that the influence of the damping constant c can be used to formulate an accurate estimate of the invasively determined time constant of isovolumic pressure decay, tau [4]. ...
... k Stiffness g/s 2 (N/m) LV rigidity, or the extent to which the LV resists deformation in response to an applied force. Linearly related to chamber stiffness [3] (dP/dV), and thus influences the restoring force that drives early diastolic filling. Increased in hypertension [8]. ...
Background
Early diastolic left ventricular (LV) filling can be accurately described using the same methods used in classical mechanics to describe the motion of a loaded spring as it recoils, a validated method also referred to as the Parameterized Diastolic Filling (PDF) formalism. With this method, each E-wave recorded by pulsed wave (PW) Doppler can be mathematically described in terms of three constants: LV stiffness (k), viscoelasticity (c), and load (x0). Also, additional parameters of physiological and diagnostic interest can be derived. An efficient software application for PDF analysis has not been available. We aim to describe the structure, feasibility, time efficiency and intra-and interobserver variability for use of such a solution, implemented in Echo E-waves, a freely available software application (www.echoewaves.org).
Results
An application was developed, with the ability to open DICOM files from different vendors, as well as rapid semi-automatic analysis and export of results. E-waves from 20 patients were analyzed by two investigators. Analysis time for a median of 34 (interquartile range (IQR) 29–42) E-waves per patient (representing 63 %, IQR 56–79 % of the recorded E-waves per patient) was 4.3 min (IQR 4.0–4.6 min). Intra-and intraobserver variability was good or excellent for 12 out of 14 parameters (coefficient of variation 2.5–18.7 %, intraclass correlation coefficient 0.80–0.99).
Conclusion
Kinematic analysis of diastolic function using the PDF method for Doppler echocardiography implemented in freely available semiautomatic software is highly feasible, time efficient, and has good to excellent intra-and interobserver variability.
... We assessed E-wave derived chamber stiffness (DT, k) 8,19,20 in NSR and AF groups. To validate E-wave predicted stiffness we used chamber stiffness from simultaneous catheterization-derived multiple beat P-V data. ...
... The conductance catheter method of volume determination has known limitations related to noise, saturation and calibration that we have previously acknowledged. 14,15,16,19 Only physiologically consistent P-V loops were selected and averaged. If the two absolute measures (ESV, EDV) have slight systematic differences, resulting in a systematic volume calibration offset, the absolute values of the slopes could be innacurate. ...
Echocardiographic diastolic function (DF) assessment remains a challenge in atrial fibrillation (AF), because indexes such as E/A cannot be used and because chronic, rate controlled AF causes chamber remodeling. To determine if echocardiography can accurately characterize diastolic chamber properties we compared 15 chronic AF subjects to 15, age matched normal sinus rhythm (NSR) subjects using simultaneous echocardiography-cardiac catheterization (391 beats analyzed). Conventional DF parameters (DT, Epeak, AT, Edur, E-VTI, E/E\') and validated, E-wave derived, kinematic modeling based chamber stiffness parameter (k), were compared. For validation, chamber stiffness (dP/dV) was independently determined from simultaneous, multi-beat P-V loop data. Results show that neither AT, Epeak nor E-VTI differentiated between groups. Although DT, Edur and E/E’ did differentiate between groups (DTNSR vs. DTAF p < 0.001, EdurNSR vs. EdurAF p < 0.001, E/E\'NSR vs. E/E\'AF p < 0.05), the model derived chamber stiffness parameter k was the only parameter specific for chamber stiffness, (kNSR vs. kAF p < 0.005). The invasive gold standard determined end-diastolic stiffness in NSR was indistinguishable from end-diastolic (i.e. diastatic) stiffness in AF (p = 0.84). Importantly, the analysis provided mechanistic insight by showing that diastatic stiffness in AF was significantly greater than diastatic stiffness in NSR (p < 0.05). We conclude that passive (diastatic) chamber stiffness is increased in normal LVEF chronic, rate controlled AF hearts relative to normal LVEF NSR controls and that in addition to DT, the E-wave derived, chamber stiffness specific index k, differentiates between AF vs. NSR groups, even when invasively determined end-diastolic chamber stiffness fails to do so.
... We assessed E-wave derived chamber stiffness (DT, k) 8,19,20 in NSR and AF groups. To validate E-wave predicted stiffness we used chamber stiffness from simultaneous catheterization-derived multiple beat P-V data. ...
... The conductance catheter method of volume determination has known limitations related to noise, saturation and calibration that we have previously acknowledged. 14,15,16,19 Only physiologically consistent P-V loops were selected and averaged. If the two absolute measures (ESV, EDV) have slight systematic differences, resulting in a systematic volume calibration offset, the absolute values of the slopes could be innacurate. ...
Echocardiographic diastolic function (DF) assessment remains a challenge in atrial fibrillation (AF), because indexes such as E/A cannot be used and because chronic, rate controlled AF causes chamber remodeling. To determine if echocardiography can accurately characterize diastolic chamber properties we compared 15 chronic AF subjects to 15, age matched normal sinus rhythm (NSR) subjects using simultaneous echocardiography-cardiac catheterization (391 beats analyzed). Conventional DF parameters (DT, Epeak, AT, Edur, E-VTI, E/E') and validated, E-wave derived, kinematic modeling based chamber stiffness parameter (k), were compared. For validation, chamber stiffness (dP/dV) was independently determined from simultaneous, multi-beat P-V loop data. Results show that neither AT, Epeak nor E-VTI differentiated between groups. Although DT, Edur and E/E' did differentiate between groups (DTNSR vs. DTAF p < 0.001, EdurNSR vs. EdurAF p < 0.001, E/E'NSR vs. E/E'AF p < 0.05), the model derived chamber stiffness parameter k was the only parameter specific for chamber stiffness, (kNSR vs. kAF p < 0.005). The invasive gold standard determined end-diastolic stiffness in NSR was indistinguishable from end-diastolic (i.e. diastatic) stiffness in AF (p = 0.84). Importantly, the analysis provided mechanistic insight by showing that diastatic stiffness in AF was significantly greater than diastatic stiffness in NSR (p < 0.05). We conclude that passive (diastatic) chamber stiffness is increased in normal LVEF chronic, rate controlled AF hearts relative to normal LVEF NSR controls and that in addition to DT, the E-wave derived, chamber stiffness specific index k, differentiates between AF vs. NSR groups, even when invasively determined end-diastolic chamber stiffness fails to do so.
... In this construct, model-based analysis of Doppler mitral inflow velocity (E-wave) contours yields passive/stiffness (k: spring constant), relaxation/viscoelastic (c: damping constant), and load (x o : initial spring displacement) indices that can be used to generate several indices such as available potential energy (ergs) for filling (1/2 kx o 2 ). The PDF formalism has been extensively validated using invasive (high fidelity) hemodynamic methods, [20][21][22] and is highly reproducible in patients with normal left ventricular ejection fraction and elevated filling pressures. 23,24 The Sphygmocor radial artery tonometer uses an invasively validated general transfer function to generate central aortic pressures and waveforms. ...
... However, the PDF formalism method has been extensively invasively validated and provides several potential advantages over the E/e' ratio. [20][21][22][23]27 A recent study challenged the E/e' ratio as a measure of diastolic function in the setting of normal left ventricular ejection fraction, finding poor correlation between E/e' and invasive pulmonary capillary wedge pressure measurements and low discrimination for E/e' as a predictor of elevated wedge pressure. 43 In contrast, the PDF approach accurately predicts elevated ventricular filling pressures in patients with normal ejection fraction and diastolic dysfunction. ...
-Heart failure with preserved ejection fraction (HFPEF) involves failure of cardiovascular reserve in multiple domains. In HFPEF animal models, dietary sodium restriction improves ventricular and vascular stiffness and function. We hypothesized that the sodium-restricted Dietary Approaches to Stop Hypertension diet (DASH/SRD) would improve left ventricular diastolic function, arterial elastance, and ventricular-arterial (V-A) coupling in hypertensive HFPEF.
-Thirteen patients with treated hypertension and compensated HFPEF consumed the DASH/SRD (target sodium 50 mmol/2100 kcal) for 21 days. We measured baseline and post-DASH/SRD brachial and central BP (via radial arterial tonometry), and cardiovascular function with echocardiographic measures (all previously invasively validated). Diastolic function was quantified via the Parametrized Diastolic Filling formalism, which yields relaxation/viscoelastic (c) and passive/stiffness (k) constants through analysis of Doppler mitral inflow velocity (E-wave) contours. Effective arterial elastance (Ea) end-systolic elastance (Ees), and V-A coupling (defined as the ratio Ees:Ea) were determined using previously published techniques. Wilcoxon matched-pairs signed rank tests were used for pre-post comparisons. The DASH/SRD reduced clinic and 24-hour brachial systolic pressure (155±35 to 138±30 and 130±16 to 123±18 mmHg, both p=.02) and central end-systolic pressure trended lower (116±18 to 111±16 mmHg,p=.12). In conjunction, diastolic function improved (c, 24.3±5.3 to 22.7±8.1 s(-1);p=.03; k, 252±115 to 170±37 1/s(2);p=.03), Ea decreased (2.0±0.4 to 1.7±0.4 mmHg/ml;p=.007), and V-A coupling improved (Ees:Ea, 1.5±0.3 to 1.7±0.4;p=.04).
-In hypertensive HFPEF patients, the sodium-restricted DASH diet was associated with favorable changes in ventricular diastolic function, arterial elastance, and V-A coupling. Clinical Trial Registration-URL: http://www.clinicaltrials.gov. Unique identifier: NCT00939640.
... Before data acquisition, subjects provided signed Institutional Review Board-approved informed consent for participation in accordance with Washington University Human Research Protection Office-approved criteria. The method of simultaneous echocardiographic transmitral flow and P-V data recording is well established and has been previously detailed (3,21,23). Among the 12 data sets, 5 data sets had LVEDP Ͻ 15 mmHg, 4 data sets had 15 mmHg Ͻ LVEDP Ͻ 20 mmHg, and 3 data sets had LVEDP Ͼ 20 mmHg. ...
... The simultaneous high-fidelity, P-V, and echocardiographic transmitral flow data recording method has been previously detailed (3,21,23). Briefly, LV pressure and volume were acquired using micromanometric conductance catheter (SPC-560, SPC-562, or SSD-1043, Millar Instruments, Houston, TX) at the commencement of elective cardiac catheterization before the administration of iodinated contrast agents. Pressure signals from the transducers were fed into a clinical amplifier system (Quinton Diagnostics, Bothell, WA, and General Electric). ...
Pressure-volume (P-V) loop-based analysis facilitates thermodynamic assessment of left ventricular function in terms of work and energy. Typically these quantities are calculated for a cardiac cycle using the entire P-V loop, although thermodynamic analysis may be applied to a selected phase of the cardiac cycle, specifically, diastole. Diastolic function is routinely quantified by analysis of transmitral Doppler E-wave contours. The first law of thermodynamics requires that energy (ε) computed from the Doppler E-wave (εE-wave) and the same portion of the P-V loop (εP-V E-wave) be equivalent. These energies have not been previously derived nor have their predicted equivalence been experimentally validated. To test the hypothesis that εP-V E-wave and εE-wave are equivalent, we used a validated kinematic model of filling to derive εE-wave in terms of chamber stiffness, relaxation/viscoelasticity, and load. For validation, simultaneous (conductance catheter) P-V and echocadiographic data from 12 subjects (205 total cardiac cycles) having a range of diastolic function were analyzed. For each E-wave, εE-wave was compared with εP-V E-wave calculated from simultaneous P-V data. Linear regression yielded the following: εP-V E-wave=αεE-wave+b (R2=0.67), where α=0.95 and b=6e(-5). We conclude that E-wave-derived energy for suction-initiated early rapid filling εE-wave, quantitated via kinematic modeling, is equivalent to invasive P-V-defined filling energy. Hence, the thermodynamics of diastole via εE-wave generate a novel mechanism-based index of diastolic function suitable for in vivo phenotypic characterization.
... Twenty-five datasets were selected from the Cardiovascular Biophysics Laboratory database of simultaneous micromanometric catheter-recorded left ventricular (LV) pressure and echocardiographic data (21). The subjects were scheduled for an elective diagnostic cardiac catheterization at the request of their referring physicians to rule out the presence of coronary artery disease. ...
... Our method of high-fidelity, in vivo pressure-volume recording has been previously detailed (2,7,21) . Briefly, after arterial access and placement of a 64-cm sheath (Arrow, Reading, PA), a 6-Fr micromanometer-tipped pigtail (triple pressure transducer) pressure-volume, conductance catheter (SSD-1034, Millar Instruments, Houston, TX) was directed into the mid-LV in a retrograde fashion across the aortic valve under fluoroscopic control. ...
In current practice, empirical parameters such as the monoexponential time constant tau or the logistic model time constant tauL are used to quantitate isovolumic relaxation. Previous work indicates that tau and tauL are load dependent. A load-independent index of isovolumic pressure decline (LIIIVPD) does not exist. In this study, we derive and validate a LIIIVPD. Recently, we have derived and validated a kinematic model of isovolumic pressure decay (IVPD), where IVPD is accurately predicted by the solution to an equation of motion parameterized by stiffness (Ek), relaxation (tauc), and pressure asymptote (Pinfinity) parameters. In this study, we use this kinematic model to predict, derive, and validate the load-independent index MLIIIVPD. We predict that the plot of lumped recoil effects [Ek.(P*max-Pinfinity)] versus resistance effects [tauc.(dP/dtmin)], defined by a set of load-varying IVPD contours, where P*max is maximum pressure and dP/dtmin is the minimum first derivative of pressure, yields a linear relation with a constant (i.e., load independent) slope MLIIIVPD. To validate the load independence, we analyzed an average of 107 IVPD contours in 25 subjects (2,669 beats total) undergoing diagnostic catheterization. For the group as a whole, we found the Ek.(P*max-Pinfinity) versus tauc.(dP/dtmin) relation to be highly linear, with the average slope MLIIIVPD=1.107+/-0.044 and the average r2=0.993+/-0.006. For all subjects, MLIIIVPD was found to be linearly correlated to the subject averaged tau (r2=0.65), tauL(r2=0.50), and dP/dtmin (r2=0.63), as well as to ejection fraction (r2=0.52). We conclude that MLIIIVPD is a LIIIVPD because it is load independent and correlates with conventional IVPD parameters. Further validation of MLIIIVPD in selected pathophysiological settings is warranted.
... The deceleration time (DT) of early diastolic filling measured by Doppler mitral inflow velocity provides a potential method to do this. Theoretic considerations indicate that the DT is determined by the sum of left atrial (LA) and LV chamber stifness (K LA ϩ K LV ) (8,13). Little et al. (14) proposed that K LA could be ignored because, during the time of DT, the atrium behaves as a conduit, and there is little change in LA volume or pressure (14). ...
... This might reflect the limited ability of reliably computing LV chamber stiffness from E waves, which have an inflection point in their deceleration portion (12). However, in a large population of 131 subjects with normal ejection fraction, in vivo validation of Little et al.'s (14) average chamber stiffness K LV as assessed by a cosine (linear) function from DT compared with that assessed using a modelbased image-processing parameterized formalism using a damped, simple harmonic oscillator has shown a highly significant correlation (13). ...
Left ventricular (LV) filling deceleration time (DT) is determined by the sum of atrial and ventricular stiffnesses (KLA + KLV). If KLA, however, is close to zero, then DT would reflect KLV only. The purpose of this study was to quantify KLA during DT. In 15 patients, KLV was assessed, immediately after cardiopulmonary bypass, from E wave DT as derived from mitral tracings obtained by transesophageal echocardiography and computed according to a validated formula. In each patient, a left atrial (LA) volume curve was also obtained combining mitral and pulmonary vein (PV) cumulative flow plus LA volume measured at end diastole. Time-adjusted LA pressure was measured simultaneously with Doppler data in all patients. KLA was then calculated during the ascending limb of the V loop and during DT. LA volume decreased by 7.3 +/- 6.5 ml/m2 during the first of mitral DT, whereas LV volume increased 9.4 +/- 8.4 ml/m2 (both P < 0.001). There was a small amount of blood coming from the PV during the same time interval, with the cumulative flow averaging 3.2 +/- 2.4 ml/m(2) (P < 0.001). Mean LA pressure was 10.0 +/- 5.1 mmHg, and it did not change during DT [from 7.8 +/- 4.3 to 8.0 +/- 4.3 mmHg, not significant (NS)], making KLA, which averaged 0.46 +/- 0.39 mmHg/ml during the V loop, close to zero during DT [KLA(DT): from -0.002 +/- 0.08 to -0.001 +/- 0.031 mmHg/ml, NS]. KLV, as assessed noninvasively from DT, averaged 0.25 +/- 0.32 mmHg/ml. In conclusion, notwithstanding the significant decrement in LA volume, KLA does not change and can be considered not different from zero during DT. Thus KLA does not affect the estimation of KLV from Doppler parameters.
... A study done by Hamlin et al. [5] concluded that in patients with heart failure, the decreased ability to augment the diastolic relaxation is responsible for the inability to accommodate the increase in estimated preload during exercise, resulting in higher filling pressure. Patients with heart failure have a stiffer heart with inability to relax and accept the large volume of blood in shorter period of diastole at high heart rate [32,33]. A recent meta-analysis of 14 trials that included 812 heart failure patients with reduced ejection fraction, those in exercise training groups tended to maintain their left ventricular function (ejection fraction and end-systolic and end-diastolic value) better than patients in the control arm of these studies. ...
Chronic heart failure (CHF) is a complex syndrome characterized by progressive decline in left ventricular function, low exercise tolerance and raised mortality and morbidity. Left ventric-ular diastolic dysfunction plays a major role in CHF and progression of most cardiac diseases. The current recommended goals can theoretically be accomplished via exercise and pharmacological therapy so the aim of the present study was to evaluate the impact of cardiac rehabilitation program on diastolic dysfunction and health related quality of life and to determine the correlation between changes in left ventricular diastolic dysfunction and domains of health-related quality of life (HRQoL). Forty patients with chronic heart failure were diagnosed as having dilated cardiomyop-athy (DCM) with systolic and diastolic dysfunction. The patients were equally and randomly divided into training and control groups. Only 30 of them completed the study duration. The training group participated in rehabilitation program in the form of circuit-interval aerobic training adjusted according to 55-80% of heart rate reserve for a period of 7 months. Circuit training improved both diastolic and systolic dysfunction in the training group. On the other hand, only a significant correlation was found between improvement in diastolic dysfunction and health related quality of life measured by Kansas City Cardiomyopathy Questionnaire. It was concluded that improvement in diastolic dysfunction as a result of rehabilitation program is one of the important underlying mechanisms responsible for improvement in health-related quality of life in DCM patients.
... In the PDF method, the Ewave velocity data is fitted to a mathematical function describing the resulting recoil velocities of any combination of x 0 , k and c; thus each E-wave analyzed yields the constants x 0 , k and c, describing the properties of the LV during that episode of diastolic filling. The PDF method has been extensively validated, [5,6], and a software program facilitating the application of the method has been described and made freely available [7]. In this study, as a secondary aim, we sought to explore the value of retrospective analysis of a single Ewave per patient. ...
Background
Diastolic dysfunction can be caused by hypertension or diabetes mellitus, and it is also often found with increasing age. In a given patient, the cause of diastolic dysfunction is therefore not always obvious. We sought to study the interplay of these risk factors for diastolic dysfunction in an outpatient population with a low likelihood of ischemic heart disease.
Methods
Consecutive patients referred for stress echocardiography were included retrospectively. Exclusion criteria included pathological stress response, atrial arrhythmia, left ventricular ejection fraction < 55%, and more than mild valvular disease. Standard diastolic parameters were recorded in all patients. In a subset of patients, mechanistic analysis of early filling was performed using the parameterized diastolic filling (PDF) method.
Results
We included 726 patients (median [interquartile range] age 56 (44–65) years, 57% male). The prevalence of diabetes and hypertension was 43 and 49%, respectively. In multiple linear regression modeling, the presence of diabetes, hypertension, sex and increasing age explained a moderate amount of the variance in e’ velocities, E/A ratio and E/e’ (R² = 0.31–0.48, p < 0.001), and a low amount of the variance in left atrial volume index (LAVI) and the PDF parameters (n = 446, R² = 0.05–0.17, p < 0.001). Sex was only related to LAVI and E/e’ for the conventional parameters (beta − 0.94, p = 0.04, and beta − 0.91, p < 0.001, respectively).
Conclusions
Diabetes, hypertension, increasing age, and to a lesser extent sex, explain a moderate amount of the variance in conventional diastolic parameters related to myocardial tissue velocities and E/A ratio in a healthy outpatient population. The effect of these risk factors was substantially less pronounced on left atrial volume index and the PDF parameters.
... Thirteen datasets were selected from our Cardiovascular Biophysics Laboratory database of simultaneous echocardiographic and high fidelity hemodynamic recordings (Lisauskas et al. 2001). Clinical characteristics are listed inTable 1. ...
Left ventricular (LV) pressure?volume (P?V) loop analysis is the gold standard for chamber function assessment. To advance beyond traditional P?V and pressure phase plane (dP/dt-P) analysis in the quest for novel load-independent chamber properties, we introduce the normalized P?V loop. High-fidelity LV pressure and volume data (161 P-V loops) from 13 normal control subjects were analyzed. Normalized LV pressure (PN) was defined by 0?? P(t) ? 1. Normalized LV volume (VN) was defined as VN=V(t)/Vdiastasis, since the LV volume at diastasis (Vdiastasis) is the in-vivo equilibrium volume relative to which the LV volume oscillates. Plotting PN versus VN for each cardiac cycle generates normalized P-V loops. LV volume at the peak LV ejection rate and at the peak LV filling rate (peak ?dV/dt and peak +dV/dt, respectively) were determined for conventional and normalized loops. VN at peak +dV/dt was inscribed at 64???5% of normalized equilibrium (diastatic) volume with an inter-subject variation of 8%, and had a reduced intra-subject (beat-to-beat) variation compared to conventional P-V loops (9% vs. 13%, respectively; P?<?0.005), thereby demonstrating load-independent attributes. In contrast, VN at peak ?dV/dt was inscribed at 81???9% with an inter-subject variation of 11%, and had no significant change in intra-subject (beat-to-beat) variation compared to conventional P-V loops (17% vs. 17%, respectively; P?=?0.56), therefore failing to demonstrate load-independent tendencies. Thus, the normalized P-V loop advances the quest for load-independent LV chamber properties. VN at the peak LV filling rate (?sarcomere length at the peak sarcomere lengthening rate) manifests load-independent properties. This novel method may help to elucidate and quantify new attributes of cardiac and cellular function. It merits further application in additional human and animal physiologic and pathophysiologic datasets.
... These parameters (x o ,c,and k) are determined directly from the clinical E-wave contour. Their physiologic interpretation has been extensively validated using gold-standard (simultaneous micromanometric hemodynamics and echocardiography) methods that causally relate these parameters to chamber properties that determine DF. 23,26,45,46 Its applications in physiology include: generation of the third 47 and fourth heart sounds, 48 constant-volume attribute of the four-chambered heart, 49 physiologic and clinical significance of mitral annular oscillations or longitudinal ringing of the ventricle in diastole, 50,51 decomposition of Ewave deceleration time into its stiffness and relaxation components, 52 and determination of the in-vivo equilibrium volume of the LV as the volume at diastasis. 53 ...
Athletic training can result in increased left ventricular (LV) wall thickness, termed physiologic hypertrophy (PhH). By contrast, pathologic hypertrophy (PaH) can be due to hypertension, aortic stenosis, or genetic mutation causing hypertrophic cardiomyopathy (HCM). Because morphologic (LV dimension, wall thickness, mass, etc.) and functional index similarities (LV ejection fraction, cardiac output, peak filling rate, etc.) limit diagnostic specificity, ability to differentiate between PhH and PaH is important. Conventional echocardiographic diastolic function (DF) indexes have limited ability to differentiate between PhH and PaH and cannot provide information on chamber property (stiffness and relaxation). We hypothesized that kinematic model-based DF assessment can differentiate between PhH and PaH and, by providing chamber properties, has even greater value compared with conventional metrics. For validation, we assessed DF in the following three age-matched groups: pathologic (HCM) hypertrophy (PaH, n = 14), PhH (Olympic rowers, PhH, n = 21), and controls (n = 21). Magnetic resonance imaging confirmed presence of both types of hypertrophy and determined LV mass and chamber size. Model-based indexes, chamber stiffness (k), relaxation/viscoelasticity (c), and load (xo) and conventional indexes, Epeak (peak of E-wave), ratio of Epeak to Apeak (E/A), E-wave acceleration time (AT), and E-wave deceleration time (DT) were computed. We analyzed 1588 E waves distributed as follows: 328 (PaH), 672 (athletes), and 588 (controls). Among conventional indexes, Epeak and E-wave DT were similar between PaH and PhH, whereas E/A and E-wave AT were lower in PaH. Model-based analysis showed that PaH had significantly higher relaxation/viscoelasticity (c) and chamber stiffness (k) than PhH. The physiologic equation of motion for filling-based derivation of the model provides a mechanistic understanding of the differences between PhH and PaH.
... The PDF formalism has been validated in a broad range of normal and pathophysiologic settings (in humans and animals). The PDF parameters and indexes derived from them have been rigorously shown to have direct clinical relevance (Dent et al. 2001; Lisauskas et al. 2001a,b; Riordan and Kov acs 2006; Shmuylovich and Kov acs 2006). The PDF formalism has been automated (Hall and Kov acs 1994; Hall et al. 1998) and solves the " inverse problem of diastole " (Hall and Kov acs 1993) by providing a unique set of PDF parameters for each analyzed E-wave. ...
In early diastole, the suction pump feature of the left ventricle opens the mitral valve and aspirates atrial blood. The ventricle fills via a blunt profiled cylindrical jet of blood that forms an asymmetric toroidal vortex ring inside the ventricle whose growth has been quantified by the standard (dimensionless) expression for vortex formation time, VFTstandard = {transmitral velocity time integral}/{mitral orifice diameter}. It can differentiate between hearts having distinguishable early transmitral (Doppler E-wave) filling patterns. An alternative validated expression, VFTkinematic reexpresses VFTstandard by incorporating left heart, near "constant-volume pump" physiology thereby revealing VFTkinematic's explicit dependence on maximum rate of longitudinal chamber expansion (E'). In this work, we show that VFTkinematic can differentiate between hearts having indistinguishable E-wave patterns, such as pseudonormal (PN; 0.75 < E/A < 1.5 and E/E' > 8) versus normal. Thirteen age-matched normal and 12 PN data sets (738 total cardiac cycles), all having normal LVEF, were selected from our Cardiovascular Biophysics Laboratory database. Doppler E-, lateral annular E'-waves, and M-mode data (mitral leaflet separation, chamber dimension) was used to compute VFTstandard and VFTkinematic. VFTstandard did not differentiate between groups (normal [3.58 ± 1.06] vs. PN [4.18 ± 0.79], P = 0.13). In comparison, VFTkinematic for normal (3.15 ± 1.28) versus PN (4.75 ± 1.35) yielded P = 0.006. Hence, the applicability of VFTkinematic for diastolic function quantitation has been broadened to include analysis of PN filling patterns in age-matched groups.
... ns of the aorta and pulmonary artery with the left and right ventricles, respectively. (The appearance of flow through an aortic leaflet is a graphics artifact; those streaklines are actually behind the leaflet but were drawn last, giving the impression that they are in front.) to LVEDP) as noted by Kovács et al . (1997), Garcia et al . (2001) and Lisauskas et al . (2001b); ...
Two complementary mathematical modelling approaches are covered. They contrast the degree of mathematical and computationa sophistication that can be applied to cardiovascular physiology problems and they highlight the differences between a flui dynamic versus kinematic (lumped parameter) approach. McQueen & Peskin model cardiovascular tissue as being incompressible having essentially uniform mass density, and apply a modified form of the Navier–Stokes equations to the four chambered hear and great vessels. Using a supercomputer their solution provides fluid, wall and valve motion as a function of space and time.
Their computed results are consistent with flow attributes observed in vivo via cardiac MRI. Kovács focuses on the physiology of diastole. The suction pump attribute of the filling ventricle is modelle as a damped harmonic oscillator. The model predicts transmitral flow–velocity as a function of time. Using the contour o the clinical Doppler echocardiographic Eand A–wave as input, unique solution of Newton's Law allows solution of the ‘invers problem’ of diastole. The model quantifies diastolic function in terms of model parameters accounting for (lumped) chambe stiffness, chamber viscoelasticity and filling volume. The model permits derivation of novel (thermodynamic) indexes of diastoli function, facilitates non–invasive quantitation of diastolic function and can predict ‘new’ physiology from first principles.
... The lower k value in the athlete group indicates lower resting chamber stiffness (DP/DV). 26 This indicates that, for the same change in volume (DV), the increase in the LV pressure is lower in athletes. The peak AV gradient, kx o , interestingly remained indistinguishable between the groups, as anticipated. ...
Physiologic hypertrophy of the athlete heart, compared to the heart of nonathletic controls, is characterized by an increase in the left ventricular (LV) chamber dimension, mass, and wall thickness. Comparisons of the diastolic function (DF) between athletes and controls have employed conventional echocardiographic transmitral flow (Doppler E-wave)-derived indexes such as the peak flow velocity and deceleration time (which are load-dependent) and obscure the mechanistic determinants (e.g., stiffness, relaxation, load) of E-wave. With a focus on stiffness and relaxation chamber properties, conventional kinematic model-derived and load-independent indexes of the DF were compared between athletes and controls in this study. Echocardiographic and magnetic resonance imaging (MRI) data from 22 master athletes (whose sport was canoeing) and 21 sedentary controls were analyzed (1290 Doppler E-waves; 702 from athletes and 588 from the controls; on average, there were 30 pieces of data per subject). The LV mass and chamber size were determined from the MRI data. Quantitative DF assessment utilized an established kinematic model of filling that used the digitized Doppler E-wave contour as the input and characterized the DF on the basis of the chamber stiffness (k), relaxation/viscoelasticity (c), load (xo). We observed significant chamber stiffness (k), load (xo), and E-wave duration differences between the two groups. Concordant with the findings of previous studies, we also noted significant group differences in LV mass and dimension. These results indicated that physiological LV remodeling of the athlete heart at rest generates numerically quantifiable alterations in specific chamber properties. Assessment of the DF by using these methods during exercise will further elucidate the dynamic interplay between relaxation and stiffness as DF determinants.
... A study done by Hamlin et al. [5] concluded that in patients with heart failure, the decreased ability to augment the diastolic relaxation is responsible for the inability to accommodate the increase in estimated preload during exercise, resulting in higher filling pressure. Patients with heart failure have a stiffer heart with inability to relax and accept the large volume of blood in shorter period of diastole at high heart rate [32,33] associated with resistance exercise training negatively counter balances the favorable adaptations associated with exercise training [34]. The work of Belardinelli et al. [35,36] showed improvement in diastolic dysfunction represented in early and late diastolic filling after 2-month exercise training study of heart failure patients with moderate to severe systolic dysfunction . ...
Chronic heart failure (CHF) is a complex syndrome characterized by progressive decline in left ventricular function, low exercise tolerance and raised mortality and morbidity. Left ventricular diastolic dysfunction plays a major role in CHF and progression of most cardiac diseases. The current recommended goals can theoretically be accomplished via exercise and pharmacological therapy so the aim of the present study was to evaluate the impact of cardiac rehabilitation program on diastolic dysfunction and health related quality of life and to determine the correlation between changes in left ventricular diastolic dysfunction and domains of health-related quality of life (HRQoL). Forty patients with chronic heart failure were diagnosed as having dilated cardiomyopathy (DCM) with systolic and diastolic dysfunction. The patients were equally and randomly divided into training and control groups. Only 30 of them completed the study duration. The training group participated in rehabilitation program in the form of circuit-interval aerobic training adjusted according to 55–80% of heart rate reserve for a period of 7 months. Circuit training improved both diastolic and systolic dysfunction in the training group. On the other hand, only a significant correlation was found between improvement in diastolic dysfunction and health related quality of life measured by Kansas City Cardiomyopathy Questionnaire. It was concluded that improvement in diastolic dysfunction as a result of rehabilitation program is one of the important underlying mechanisms responsible for improvement in health-related quality of life in DCM patients.
... The increases in TDI Am velocities and other measures of late LV filling may also, in part, reflect increases in LV end-diastolic pressures because of increased passive stiffness that would require augmented LA transport function. 29 Alternations in passive LV stiffness may result from increased myocardial collagen formation, which has been suggested by studies using ultrasonic integrated backscatter to characterize the myocardium of T1DM patients. 8 ...
... For the noninvasive assessment of K LV , a number of Doppler indexes have been used, one of the most useful being the deceleration time of the early mitral filling wave (DT). 6,8 The theoretic analysis and experimental study of Little el al 12 predicted that if left atrial pressure remains relatively constant during early filling deceleration, then deceleration time will be proportional to the inverse square root of In chronic heart failure, a tight relationship may exist between diastolic dysfunction, progressive ventricular remodelling, and the unwarranted neurohormonal activation that may be revealed, among its many markers, by high levels of circulating brain natriuretic peptide (BNP) and N-terminal proBNP. 14e17 Physical exercise in heart failure patients strongly affects autonomic and neurohormonal regulation 18e21 and has also been shown to improve LV diastolic filling. ...
Diastolic dysfunction in long-term heart failure is accompanied by abnormal neurohormonal control and ventricular stiffness. The diastolic phase is determined by a balance between pressure gradients and intrinsic ventricular wall properties: according to a mathematical model, the latter (ie, left ventricular [LV] elastance, K(LV)) may be calculated by the formula: K(LV) = (70/[DT-20])(2) mm Hg/mL, where DT is the transmitral Doppler deceleration time.
In 54 patients with chronic systolic heart failure (39 men, 15 women; age 65 +/- 10 years; New York Heart Association [NYHA], 2.3 +/- 0.9; ejection fraction [EF], 32% +/- 5%), we analyzed the relationship between K(LV) and an index of neurohormonal derangement (levels of brain natriuretic peptide [BNP]), and investigated whether 3 months of physical training could modulate diastolic operating stiffness. Patients were randomized to physical training (n = 27) or to a control group (n = 27). Before and after training, patients underwent Doppler echocardiogram and cardiopulmonary stress test. At baseline, ventricular stiffness was related to BNP levels (P < .01). Training improved NYHA class, exercise performance, and estimated pulmonary pressure. BNP was reduced. Ventricular volumes, mean blood pressure, and EF remained unchanged. A 27% reduction of elastance was observed (K(LV), 0.111 +/- 0.044 from 0.195 +/- 0.089 mm Hg/mL; P < .01), whose magnitude was related to changes in BNP (P < .05) and to K(LV) at baseline (P < .01). No changes in K(LV) were observed in controls after 3 months (0.192 +/- 0.115 from 0.195 +/- 0.121 mm Hg/mL).
In heart failure, left ventricular diastolic stiffness is related to neurohormonal derangement and is modified by physical training. This improvement in LV compliance could result from a combination of hemodynamic improvement and regression of the fibrotic process.
... Garcia et al. (7) and others (12,13) have demonstrated that pulsed Doppler early filling deceleration time relates to the LV operating stiffness. In this study population, however, deceleration time did not change after ESR. ...
We sought to validate measurement of intraventricular pressure gradients (IVPG) and analyze their change in patients with hypertrophic obstructive cardiomyopathy (HOCM) after ethanol septal reduction (ESR). Quantitative analysis of color M-mode Doppler (CMM) images may be used to estimate diastolic IVPG noninvasively. Noninvasive IVPG measurement was validated in 10 patients undergoing surgical myectomy. Echocardiograms were then analyzed in 19 patients at baseline and after ESR. Pulsed Doppler data through the mitral valve and pulmonary venous flow were obtained. CMM was used to obtain the flow propagation velocity (Vp) and to calculate IVPG off-line. Left atrial pressure was estimated with the use of previously validated Doppler equations. Data were compared before and after ESR. CMM-derived IVPG correlated well with invasive measurements obtained before and after surgical myectomy [r = 0.8, P < 0.01, Delta(CMM - invasive IVPG) = 0.09 +/- 0.45 mmHg]. ESR resulted in a decrease of resting LVOT systolic gradient from 62 +/- 10 to 29 +/- 5 mmHg (P < 0.001). There was a significant increase in the Vp and IVPG (from 48 +/- 5to 74 +/- 7 cm/s and from 1.5 +/- 0.2 to 2.6 +/- 0.3 mmHg, respectively, P < 0.001 for both). Estimated left atrial pressure decreased from 16.2 +/- 1.1 to 11.5 +/- 0.9 mmHg (P < 0.001). The increase in IVPG correlated with the reduction in the LVOT gradient (r = 0.6, P < 0.01). Reduction of LVOT obstruction after ESR is associated with an improvement in diastolic suction force. Noninvasive measurements of IVPG may be used as an indicator of diastolic function improvement in HOCM.
Background:
Chronic heart failure (CHF) is a complex syndrome characterized by a progressive reduction of the left ventricular (LV) contractility, low exercise tolerance, and increased mortality and morbidity. Diastolic dysfunction (DD) of the LV, is a keystone in the pathophysiology of CHF and plays a major role in the progression of most cardiac diseases. Also, it is well estimated that exercise training induces several beneficial effects on patients with CHF.
Aim:
To evaluate the impact of a cardiac rehabilitation program on the DD and LV ejection fraction (EF) in patients with CHF.
Methods:
Thirty-two stable patients with CHF (age: 56 ± 10 years, EF: 32% ± 8%, 88% men) participated in an exercise rehabilitation program. They were randomly assigned to aerobic exercise (AER) or combined aerobic and strength training (COM), based on age and peak oxygen uptake, as stratified randomization criteria. Before and after the program, they underwent a symptom-limited maximal cardiopulmonary exercise testing (CPET) and serial echocardiography evaluation to evaluate peak oxygen uptake (VO2peak), peak workload (Wpeak), DD grade, right ventricular systolic pressure (RVSP), and EF.
Results:
The whole cohort improved VO2peak, and Wpeak, as well as DD grade (P < 0.05). Overall, 9 patients (28.1%) improved DD grade, while 23 (71.9%) remained at the same DD grade; this was a significant difference, considering DD grade at baseline (P < 0.05). In addition, the whole cohort improved RVSP and EF (P < 0.05). Not any between-group differences were observed in the variables assessed (P > 0.05).
Conclusion:
Exercise rehabilitation improves indices of diastolic and systolic dysfunction. Exercise protocol was not observed to affect outcomes. These results need to be further investigated in larger samples.
The spatiotemporal features of normal in vivo cardiac motion are well established. Longitudinal velocity has become a focus of diastolic function (DF) characterization, particularly the tissue Doppler e'-wave, manifesting in early diastole when the left ventricle (LV) is a mechanical suction pump (dP/dV < 0). To characterize DF and elucidate mechanistic features, several models have been proposed and have been previously compared algebraically, numerically, and in their ability to fit physiological velocity data. We analyze two previously noncompared models of early rapid-filling lengthening velocity (Doppler e'-wave): parametrized diastolic filling (PDF) and force balance model (FBM). Our initial numerical experiments sampled FBM-generated e'(t) contours as input to determine PDF model predicted fit. The resulting exact numerical agreement [standard error of regression (SER) = 9.06 × 10-16] was not anticipated. Therefore, we analyzed all published FBM-generated e'(t) contours and observed identical agreement. We re-expressed FBM's algebraic expressions for e'(t) and observed for the first time that model-based predictions for lengthening velocity by the FBM and the PDF model are mathematically identical: e'(t) = γe-α
t
sinh(βt), thereby providing exact algebraic relations between the three PDF parameters and the six FBM parameters. Previous pioneering experiments have independently established the unique determinants of e'(t) to be LV relaxation, restoring forces (stiffness), and load. In light of the exact intermodel agreement, we conclude that the three PDF parameters, relaxation, stiffness (restoring forces), and load, are unique determinants of DF and e'(t). Thus, we show that only the PDF formalism can compute the three unique, independent, physiological determinants of long-axis LV myocardial velocity from e'(t).NEW & NOTEWORTHY We show that two separate, independently derived physiological (kinematic) models predict mathematically identical expressions for LV-lengthening velocity (Doppler e'-wave), indicating that damped harmonic oscillatory motion is a physiologically accurate model of diastolic function. Although both models predict the same "overdamped" velocity contour, only one model solves the "inverse problem" and generates unique, lumped parameters of relaxation, stiffness (restoring force), and load from the e'-wave.
We hypothesized that the kinematic model-based parameters obtained from the transtricuspid E-wave would be useful for evaluating the right ventricular diastolic property in pediatric pulmonary arterial hypertension (PAH)patients. The model was parametrized by stiffness/elastic recoil k, relaxation/damping c and load x. These parameters were determined as the solution of m⋅d ² x/dt ² + c⋅dx/dt + kx = 0, which is based on the theory that the E-wave contour is determined by the interplay of stiffness/restoring force, damping/relaxation force and load. The PAH group had a significantly higher k and c compared with the control group (182.5 ± 72.4 g/s vs. 135.7 ± 49.5 g/s ² , p = 0.0232, and 21.9 ± 6.5 g/s vs. 10.6 ± 5.2 g/s, p <0.0001, respectively). These results indicate that in the PAH group, the right ventricle had higher stiffness/elastic recoil and inferior cross-bridge relaxation. The present findings indicate the feasibility and utility of using kinematic model parameters to assess right ventricular diastolic function.
The parameterized diastolic filling (PDF) method can be used to study the mechanics of early diastolic left ventricular (LV) filling. However, there are no publications describing the reference ranges of the PDF parameters. This study retrospectively recruited patients with normal results on rest and stress echocardiography and no diabetes or hypertension (n=138, 45% female). DICOM images of the resting E-wave from transmitral pulsed wave Doppler flow velocities were analyzed using freely available software. Viscoelastic energy loss (c) and stiffness (k) were higher in males compared to females (p≤0.001 for both). There were no correlations between any of the PDF parameters and age (p>0.05 for all). In males, stiffness was correlated with systolic blood pressure (r=0.24, p=0.04), and load and filling energy were correlated with diastolic blood pressure (r=-0.27, p=0.02, and r=-0.29, p=0.01, respectively). Sex-specific normal 95% reference limits for PDF analysis of early LV filling are presented for clinical use.
New Findings
What is the topic of this review?
This review focuses on how in vivo and molecular measurements of cardiac passive stiffness can predict exercise tolerance and how exercise training can reduce cardiac passive stiffness.
What advances does it highlight?
This review highlights advances in understanding the relationship between molecular (titin‐based) and in vivo (left ventricular) passive stiffness, how passive stiffness modifies exercise tolerance, and how exercise training may be therapeutic for cardiac diseases with increased passive stiffness.
Exercise can help alleviate the negative effects of cardiovascular disease and cardiovascular co‐morbidities associated with sedentary behaviour; this may be especially true in diseases that are associated with increased left ventricular passive stiffness. In this review, we discuss the inverse relationship between exercise tolerance and cardiac passive stiffness. Passive stiffness is the physical property of cardiac muscle to produce a resistive force when stretched, which, in vivo , is measured using the left ventricular end diastolic pressure–volume relationship or is estimated using echocardiography. The giant elastic protein titin is the major contributor to passive stiffness at physiological muscle (sarcomere) lengths. Passive stiffness can be modified by altering titin isoform size or by post‐translational modifications. In both human and animal models, increased left ventricular passive stiffness is associated with reduced exercise tolerance due to impaired diastolic filling, suggesting that increased passive stiffness predicts reduced exercise tolerance. At the same time, exercise training itself may induce both short‐ and long‐term changes in titin‐based passive stiffness, suggesting that exercise may be a treatment for diseases associated with increased passive stiffness. Direct modification of passive stiffness to improve exercise tolerance is a potential therapeutic approach. Titin passive stiffness itself may be a treatment target based on the recent discovery of RNA binding motif 20, which modifies titin isoform size and passive stiffness. Translating these discoveries that link exercise and left ventricular passive stiffness may provide new methods to enhance exercise tolerance and treat patients with cardiovascular disease.
Several mathematical expressions (linear, logarithmic, exponential, power law) have been proposed for the diastolic pressure-volume (P-V) relation. The P-V relation is a major component of the atrioventricular pressure gradient that determines transmitral flow. Which P-V relation applies in the in-vivo setting has not been determined by analysis of echocardiographic transmitral flow data. We sought to determine if alternative P-V relations are distinguishable via transmitral echocardiographic Doppler E-wave analysis. One-dimensional force-displacement analogues of the alternative P-V relations were used in a lumped parameter kinematic model for transmitral flow. E-waves of 17 subjects were analyzed using model-based image processing (MBIP). Root-mean-square-error determined fits of model predicted flow velocity to E-wave contours were similar regardless of the force-displacement relation used. We conclude that the simplest (linear) force-displacement relation is suitable for MBIP of transmitral Doppler flow and quantitative diastolic function assessment.
Background:
Heart failure with preserved ejection fraction (HFpEF) is increasingly recognized as a distinct entity with unique pathophysiology. In the Dietary Approaches to Stop Hypertension in Diastolic Heart Failure (DASH-DHF) study, the sodium-restricted Dietary Approaches to Stop Hypertension (DASH/SRD) diet was associated with improved blood pressure and cardiovascular function in 13 hypertensive patients with HFpEF. Using targeted metabolomics, we explored metabolite changes and their relationship with energy-dependent measures of cardiac function in DASH-DHF.
Methods and results:
Using chromatography and mass spectrometry, 152 metabolites including amino acids, free fatty acids, phospholipids, diglycerides, triglycerides, cholesterol esters and acyl carnitines were measured. Comparison of baseline and post-DASH/SRD samples revealed increases in short-chain acetyl, butryl and propionyl carnitines (p=0.02, 0.03, 0.03 respectively). Increases in propionyl carnitine correlated with ventricular-arterial coupling ratio (Ees:Ea; r=0.78; p =0.005) and ventricular contractility (maximum rate of change of pressure-normalized stress dσ*/dtmax; r=0.66; p=0.03). Changes in L-carnitine also correlated with Ees:Ea (r=0.62; p=0.04), dσ*/dtmax (r=0.60; p=0.05) and inversely with ventricular stiffness (k; r=-0.63, p=0.03).
Conclusions:
Metabolite profile changes of patients with HFpEF during dietary modification with DASH/SRD suggest improved energy substrate utilization. Additional studies are needed to clarify connections between diet, metabolic changes, and myocardial function in HFpEF.
Despite Leonardo da Vinci's observation (circa 1511) that "the atria or filling chambers contract together while the pumping chambers or ventricles are relaxing and vice versa", the dynamics of four-chamber heart function, and of diastolic function in particular, are not generally appreciated. We view diastolic function (DF) from a global perspective while characterizing it in terms of causality and clinical relevance. Our models derive from the insight that global diastolic function is ultimately a result of forces generated by elastic recoil, modulated by cross-bridge relaxation, and load. The interaction between recoil and relaxation results in physical wall motion that generates pressure gradients that drive fluid flow, while epicardial wall motion is constrained by the pericardial sac. Traditional DF indexes (τ, E/E', etc.) are not derived from causal mechanisms and are interpreted as approximating either stiffness or relaxation, but not both, thereby limiting the accuracy of DF quantification. Our derived kinematic models of isovolumic relaxation and suction-initiated filling are extensively validated, quantify the balance between stiffness and relaxation, and provide novel mechanistic physiologic insight. For example, causality based modeling provides load-independent indexes of DF and reveals that both stiffness and relaxation modify traditional DF indexes. The method has revealed that the in-vivo LV equilibrium volume occurs at diastasis, predicted novel relationships between filling and wall motion, and quantified causal relationships between ventricular and atrial function. In summary, by using governing physiologic principles as a guide, we define what global diastolic function is, what it is not, and how to measure it.
Copyright © 2015, American Journal of Physiology - Heart and Circulatory Physiology.
The normal cardiovascular system is a finely tuned pump and delivery system functioning together, with optimal efficiency, to match cardiac output to the integrated metabolic demands of the entire corpus. The inherent physical properties of the two systems contribute to the efficiency, and the physiological coordination of central and local control mechanisms assure that all tissues are supplied with appropriate blood supply. Under normal circumstances, local demands for blood flow are met by locally controlled adjustments and diversion of flow to metabolically active tissues without the need to increase pump function. When metabolic demands increase significantly, cardiac output must increase to meet the demand. If the heart is unable to meet the demand, the corpus is, by definition, in heart failure. The problem for the physician treating patients and for the researcher studying the mechanisms and/or the treatment of cardiovascular disease is to be able to understand and quantify changes in or loss of function.
Model-based image processing (MBIP) of Doppler echocardiographic transmitral flow (E-waves) has been validated as a method of quantitative diastolic function (DF) assessment. MBIP incorporates the mechanical suction-pump role of the heart, uses the E-wave as input, solves the 'inverse problem' of diastole and generates three unique parameters (xo, c, k) for each E-wave. The model's spring constant k is the analogue of (average) chamber stiffness (ΔP/ΔV). Exercising subjects with chronic heart failure (CHF) attaining an oxygen consumption peak VO2 ≤ 14 ml/kg/min are likely to benefit from transplantation whereas those attaining peak VO2 > 14 ml/kg/min do not. The relationship between peak VO2 and DF has not been determined in CHF. Doppler E-waves of 31 pre-transplant subjects were analyzed using MBIP. Least squares linear best tit determined the k vs. peak VO2 relation. For subjects with VO2 ≤ 14 ml/kg/min (n = 12) k was linearly proportional to peak VO2 with r = 0.57. We conclude that: k is inversely correlated with peak VO2; a clear delineation exists for k at a VO2 ≤ or > 14 ml/kg/min. These results show that the stiffer the chamber the worse the exercise tolerance, and MBIP facilitates quantitative DF determination in subjects with CHF.
Acoustic radiation force impulse (ARFI) imaging has been shown to be capable of imaging local myocardial stiffness changes throughout the cardiac cycle. Expanding on these results, the authors present experiments using cardiac ARFI imaging to visualize and quantify the propagation of mechanical stiffness during ventricular systole. In vivo ARFI images of the left ventricular free wall of two exposed canine hearts were acquired. Images were formed while the heart was externally paced by one of two electrodes positioned on the epicardial surface and either side of the imaging plane. Two-line M-mode ARFI images were acquired at a sampling frequency of 120 Hz while the heart was paced from an external stimulating electrode. Two-dimensional ARFI images were also acquired, and an average propagation velocity across the lateral field of view was calculated. Directions and speeds of myocardial stiffness propagation were measured and compared with the propagations derived from the local electrocardiogram (ECG), strain, and tissue velocity measurements estimated during systole. In all ARFI images, the direction of myocardial stiffness propagation was seen to be away from the stimulating electrode and occurred with similar velocity magnitudes in either direction. When compared with the local epicardial ECG, the mechanical stiffness waves were observed to travel in the same direction as the propagating electrical wave and with similar propagation velocities. In a comparison between ARFI, strain, and tissue velocity imaging, the three methods also yielded similar propagation velocities.
Several expressions have been considered for the diastolic pressure–volume (P–V) relation whose mechanical analogue is the force–length relation. How alternative P–V relations modify transmitral flow (Doppler E-wave) velocity contours has not been explored. The linear force–length term of a previously validated lumped parameter transmitral flow model was replaced by a logarithmic, exponential, or power law term for E-wave prediction. Model-based image processing (MBIP) was used for model-predicted flow vs. clinical E-wave comparison using root-mean-square-error (RSME) as an index of goodness-of-fit. RMSE of fits to 100 cm/s amplitude E-waves for linear, logarithmic, power law, and exponential relations were indistinguishable [RMSE: 4.1 1.2%, 4.9 1.4%, 5.1 2.0%, and 5.3 1.6% (mean SD), respectively]. We conclude that the linear force–length relation is suitable for E-wave based quantitative diastolic function assessment with the added benefit of closed form solutions to the inverse problem of diastole. Conversely, it is not possible to distinguish whether a ventricle obeys a linear, power law, exponential, or logarithmic P–V relation by MBIP of E-waves.
Myocardial tissue characterization represents an extension of currently available echocardiographic imaging. The systematic variation of backscattered energy during the cardiac cycle (the "cyclic variation" of backscatter) has been employed to characterize cardiac function in a wide range of investigations. However, the mechanisms responsible for observed cyclic variation remain incompletely understood. As a step toward determining the features of cardiac structure and function that are responsible for the observed cyclic variation, the present study makes use of a kinematic approach of diastolic function quantitation to identify diastolic function determinants that influence the magnitude and timing of cyclic variation. Echocardiographic measurements of 32 subjects provided data for determination of the cyclic variation of backscatter to diastolic function relation characterized in terms of E-wave determined, kinematic model-based parameters of chamber stiffness, viscosity/relaxation and load. The normalized time delay of cyclic variation appears to be related to the relative viscoelasticity of the chamber and predictive of the kinematic filling dynamics as determined using the parameterized diastolic filling formalism (with r-values ranging from .44 to .59). The magnitude of cyclic variation does not appear to be strongly related to the kinematic parameters.
During early rapid filling, blood aspirated by the left ventricle (LV) generates an asymmetric toroidal vortex whose development has been quantified using vortex formation time (VFT), a dimensionless index defined by the length-to-diameter ratio of the aspirated (equivalent cylindrical) fluid column. Since LV wall motion generates the atrioventricular pressure gradient resulting in the early transmitral flow (Doppler E-wave) and associated vortex formation, we hypothesized that the causal relation between VFT and diastolic function (DF), parametrized by stiffness, relaxation, and load, can be elucidated via kinematic modeling. Gharib et al. (Gharib M, Rambod E, Kheradvar A, Sahn DJ, Dabiri JO. Proc Natl Acad Sci USA 103: 6305-6308, 2006) approximated E-wave shape as a triangle and calculated VFT(Gharib) as triangle (E-wave) area (cm) divided by peak (Doppler M-mode derived) mitral orifice diameter (cm). We used a validated kinematic model of filling for the E-wave as a function of time, parametrized by stiffness, viscoelasticity, and load. To calculate VFT(kinematic), we computed the curvilinear E-wave area (using the kinematic model) and divided it by peak effective orifice diameter. The derived VFT-to-LV early rapid filling relation predicts VFT to be a function of peak E-wave-to-peak mitral annular tissue velocity (Doppler E'-wave) ratio as (E/E')(3/2). Validation utilized 262 cardiac cycles of simultaneous echocardiographic high-fidelity hemodynamic data from 12 subjects. VFT(Gharib) and VFT(kinematic) were calculated for each subject and were well-correlated (R(2) = 0.66). In accordance with prediction, VFT(kinematic) to (E/E')(3/2) relationship was validated (R(2) = 0.63). We conclude that VFT(kinematic) is a DF index computable in terms of global kinematic filling parameters of stiffness, viscoelasticity, and load. Validation of the fluid mechanics-to-chamber kinematics relation unites previously unassociated DF assessment methods and elucidates the mechanistic basis of the strong correlation between VFT and (E/E')(3/2).
Diastolic dysfunction in patients with heart failure has prognostic relevance, possibly because of its relationship with worsening haemodynamic status. In the quest for simpler indexes of haemodynamic status in patients, brain natriuretic peptide (BNP) levels have been proposed as a surrogate of diastolic function. To date, the value of combining BNP levels with non-invasive haemodynamic monitoring by transthoracic electric bioimpedance (TEB) for the prediction of diastolic function has not been evaluated.
We compared left ventricular diastolic function measured by tissue Doppler imaging (TDI) with TEB results and BNP levels in 120 patients with chronic advanced systolic heart failure on optimal treatment (70 +/- 9 years, NYHA 2.4 +/- 0.8, ejection fraction 31 +/- 5%). Of the TEB variables measured, we only considered thoracic fluid content (TFC). To describe diastolic function, we used the TDI of the velocity of displacement of the mitral annulus (E') and the ratio E/E'. In all patients, E/E' was significantly related to TFC and to BNP levels (P < 0.001). Moreover, the combination of BNP > or = 350 pg/mL and TFC > or = 35/kOmega identified patients with diastolic dysfunction (defined as E/E' > or = 15) with high sensitivity and specificity (95 and 94%, respectively).
The combination of transthoracic bioimpedance monitoring and BNP measurement accurately indicated the presence of diastolic dysfunction in most patients. These user-friendly and operator-independent tools may be useful as a screening assessment for diastolic dysfunction, and consequently abnormal central haemodynamic status, either in ambulatory patients or when an adequate echocardiographic evaluation is not readily available.
The transmitral Doppler E-wave "delayed relaxation" (DR) pattern is an established sign of diastolic dysfunction (DD). Furthermore, chambers exhibiting a DR filling pattern are also expected to have a prolonged time-constant of isovolumic relaxation (τ). The simultaneous observation of a DR pattern and normal τ in the same heart is not uncommon, however. The simultaneous hemodynamic equivalent of the DR pattern has not been proposed. To determine the feature of the left ventricular (LV) pressure contour during the E-wave that is causally related to its DR pattern we applied kinematic and fluid mechanics based arguments to derive the pressure recovery ratio (PRR). The PRR is dimensionless and is defined by the left ventricular pressure difference between diastasis and minimum pressure, normalized to the pressure difference between a fiducial diastolic filling pressure and minimum pressure [PRR=(PDiastasis-PMin)/(PFiducial-PMin)]. We analyzed 354 cardiac cycles from 40 normal sinus rhythm (NSR) subjects and 113 beats from nine atrial fibrillation (AF) subjects from our database of simultaneous transmitral flow-micromanometric LV pressure recordings. The fiducial pressure is defined by the end diastolic pressure in NSR and by the pressure at dP/dtMIN in the setting of AF. Consistent with derivation, PRR was linearly related to a DR pattern related, model-based relaxation parameter (R2 = 0.77, 0.83 in NSR and AF, respectively). Furthermore, the PRR successfully differentiated subjects with a DR pattern from subjects with partial DR or normal E-wave pattern (p < 0.05). We conclude that the PRR may differentiate between subjects having a DR pattern and subjects with normal E-waves, even when τ cannot. (E-mail: [email protected]
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One and a half ventricle repair (1.5VR) is a surgical option for hypoplastic right ventricle (RV). The benefits of this procedure compared to biventricular repair (2VR) or Fontan operation remain unsettled. To compare postoperative hemodynamics, we performed a theoretical analysis using a computational model based on lumped-parameter state-variable equations. We varied the RV stiffness constant (B
RV) to simulate the various RV hypoplasia, and estimated hemodynamics for a given B
RV. With B
RV < 150% of normal, cardiac output was the largest in 2VR. With B
RV > 150%, cardiac output became larger in 1.5VR than in 2VR. With B
RV > 250%, RV end-diastolic volume was almost the same between 1.5VR and 2VR, and a rapid increase in atrial pressure precluded the use of 1.5VR. These results indicate that the beneficial effect of 1.5VR depends on the RV stiffness constant. Determination of management strategy should not only be based on the morphologic parameters but also on the physiological properties of RV.
Dissertation
Cardiovascular disease is the leading cause of death for developed countries, including the United States. In order to diagnose and detect certain cardiac diseases, it is necessary to assess myocardial performance and function. One mechanical property that has been shown to reflect myocardial performance is myocardial stiffness. Acoustic radiation force impulse (ARFI) imaging has been demonstrated to be capable of visualizing variations in local stiffness within soft tissue.
In this thesis, the initial investigations into the visualization of myocardial performance with ARFI imaging are presented. In vivo ARFI images were acquired with a linear array placed on exposed canine hearts. When co-registered with the electrocardiogram (ECG), ARFI images of the heart reflected the expected changes in myocardial stiffness through the cardiac cycle. With the implementation of a quadratic motion filter, motion artifacts within the ARFI images were reduced to below 1.5 &mu m at all points of the cardiac cycle. The inclusion of pre-excitation displacement estimates in the quadratic motion filter further reduced physiological motion artifacts at all points of the cardiac cycle to below 0.5 &mu m.
In order for cardiac ARFI imaging to more quantitatively assess myocardial performance, novel ARFI imaging sequences and methods were developed to address challenges specifically related to cardiac imaging. These improvements provided finer sampling and improved spatial and temporal resolution within the ARFI images. In vivo epicardial ARFI images of an ovine heart were formed using these sequences, and the quality and utility of the resultant ARFI-induced displacement curves were examined.
In vivo cardiac ARFI images were formed of canine left ventricular free walls while the hearts were externally paced by one of two electrodes positioned epicardially on either side of the imaging plane. Directions and speeds of myocardial stiffness propagation were measured within the ARFI imaging field of view. In all images, the myocardial stiffness waves were seen to be traveling away from the stimulating electrode. The stiffness propagation velocities were also shown to be consistent with propagation velocities measured from elastography and tissue velocity imaging as well as the local epicardial ECG.
ARFI-induced displacement curves of an ovine heart were formed and temporally registered with left ventricular pressure and volume measurements. From these plots, the synchronization of myocardial stiffening and relaxation with the four phases (isovolumic contraction, ejection, isovolumic relaxation, and filling) of the cardiac cycle was determined. These ARFI imaging sequences were also used to correlate changes in left ventricular performance with changes in myocardial stiffness. These preliminary results indicated that changes in the ARFI imaging-derived stiffnesses were consistent with those predicted by current, clinically accepted theories of myocardial performance and function.
These results demonstrate the ability of ARFI imaging to visualize changes in myocardial stiffness through the cardiac cycle and its feasibility to provide clinically useful insight into myocardial performance.
Quantification of left ventricular (LV) diastolic function is necessary to diagnose heart failure (HF) when LV systolic function is normal.1–4 Furthermore, repetitive assessment of LV filling pressures is an important guide for titration of diuretic treatment and can predict survival of HF patients.5 Because of patient discomfort and the risks involved in invasive procedures, a noninvasive estimate of diastolic LV function and pressures is highly desirable. In current cardiological practice, noninvasive evaluation of diastolic LV function is based on Doppler echocardiographic visualization of LV inflow and/or LV tissue reextension. LV inflow and LV tissue reextension, however, are only indirectly related to LV filling pressures through laws of physics such as the Bernoulli principle and Laplace law. Noninvasive estimates of LV filling pressures can therefore be offset not only by limitations of the imaging technique but also by shortcomings inherent to derivation of pressures from inflow or reextension signals. As a result of these problems with noninvasive estimates of LV diastolic function and pressures, the cardiological community has witnessed over the past 20 years repetitive cycles in which a Doppler echocardiographic index was first proposed as robust and shortly thereafter discredited by contradictory evidence. The latest of such cycles involved the ratio of early transmitral velocity to tissue Doppler mitral annular early diastolic velocity (E/E′). The value of the E/E′ ratio as a reliable estimate of LV filling pressures was demonstrated in a variety of cardiac diseases6–10 and endorsed by European and American consensus statements on diastolic HF4 and diastolic LV dysfunction11 before being seriously questioned both in hypertrophic12 and dilated cardiomyopathy.13 This continuing uncertainty14 surrounding the value of noninvasive estimates of LV filling pressures and diastolic LV dysfunction asks for a reappraisal of physiological assumptions linking LV filling pressures to myocardial reextension …
For normal cardiac performance, the left ventricle (LV) must be able to eject an adequate stroke volume at arterial pressure (systolic function) and fill without requiring an elevated left atrial (LA) pressure (diastolic function). These systolic and diastolic functions must be adequate to meet the needs of the body both at rest and during stress.
Response by Tschope and Paulus on p 809
Systolic function is conveniently (although not always accurately) measured as the ejection fraction (EF), calculated as stroke volume divided by end-diastolic volume.1 The LV EF is easily interpreted. The lower limit of normal is ≈50%. The lower the EF is, the greater the reduction in systolic function. Diastolic function has been more difficult to evaluate.2 Traditionally, invasive measures of LV diastolic pressure-volume relations and the rate of LV pressure fall during isovolumetric relaxation have been used. However, these methods are not practical for routine clinical use and do not adequately evaluate all aspects of diastolic filling.3
Comprehensive echocardiographic evaluation of the dynamics of LV filling using blood pool and tissue Doppler has now progressed so that it provides clinically important information that can be used to direct patient care. We present data that support the use of echocardiographic evaluation of diastolic function to recognize cardiac dysfunction in patients with heart failure, especially those with preserved EF; to guide the management of patients by identifying those with and without elevated left filling pressures regardless of underlying EF; and to determine prognosis in a wide variety of patient populations.
Although the LV end-diastolic pressure-volume relation describes the passive properties of the LV, LV filling is not a passive or slow process.3 In fact, the peak flow rate across the mitral valve is equal to or greater than the peak flow rate across the aortic valve. …
Echocardiography has emerged as the preferred modality by which diastolic function (DF) is assessed for clinical or research purposes. Echocardiographic indexes and parameters of DF such as E/A, DT, E/E', etc., deteriorate with advancing age. Whether the efficiency of filling depends on age is unknown. To better characterize the filling process and DF in causal rather than correlative terms, we have previously modeled diastole kinematically. We introduced and validated a dimensionless measure of DF termed the kinematic filling efficiency index (KFEI). In the present study, we determined the effect of aging on DF in terms of KFEI in 72 control subjects without cardiovascular-related diseases or pathologies. We also evaluated the age dependence of other conventional parameters of DF. In concordance with other noninvasive DF measures known to decrease with age, KFEI decreases and correlates very strongly with age (R2 = 0.80). Multivariate analysis showed that age is the single most important contributor to KFEI (p = 0.003). We conclude that KFEI provides novel insight into DF impairment mechanisms because of aging. These results support the clinical value of KFEI and advance our ability to characterize DF in mechanistic and quantitative terms based on the efficiency of filling. (E-mail: [email protected]
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Left ventricular (LV) diastolic pressure-volume (P-V) relations arise from a complex interplay of active decay of force (i.e., relaxation), passive elastic myocardial properties, and time-varying inflow across the mitral orifice. This study was designed to quantify the passive properties of the intact ventricle and the effects of elastic recoil by separating filling from relaxation with a method of LV volume clamping with a remote-controlled mitral valve. Eleven open-chest fentanyl-anesthetized dogs were instrumented with aortic and mitral flow probes, LV and left atrium micromanometers, and a remote-controlled mitral valve. We prevented complete (end-systolic volume clamping) or partial filling at different times in diastole. The ventricle thus relaxed completely at different volumes, and we generated P-V coordinates for the passive ventricle that included negative, as well as positive, values of pressure. We then estimated ventricular volumes from ventricular weight in eight dogs, using regression equations based on data in the literature, to determine the equilibrium volume (V0), that is, volume at zero transmural pressure, in the working ventricle. We abandoned the traditional exponential approach and characterized by the P-V relation with a logarithmic approach that included maximum LV volume (Vm), minimum volume (Vd), and stiffness parameters (Sp and Sn) for the positive (p) and negative (n) phases: Pp = -Sp In[(Vm - V)/(Vm - V0)] and Pn = Sn In[(V - Vd)/(V0 - Vd)]. With this formulation, the chamber compliance, dP/dV, is normalized by the LV operating volume, and Sp and Sn are size-independent chamber stiffness parameters with the units of stress. In eight ventricles with LV weight = 131 +/- 20 g, Vm = 116 +/- 18 ml, V0 = 37 +/- 6 ml, and Vd = 13 +/- 2 ml, stiffness Sp = 14.6 mm Hg and Sn = 5.1 mm Hg were determined from the slopes of the log-linearized equations. Also, the duration of LV relaxation is increased by the process of ventricular filling (161 +/- 31 msec, filling versus 108 +/- 36 msec, nonfilling, measured from dP/dtmin, p less than 0.0001). We conclude that volume clamping is a useful method of studying restoring forces and that the logarithmic approach is conceptually and quantitatively useful in characterizing the passive properties of the intact ventricle.
The transmitral and pulmonary venous flow velocity (TMFV and PVFV, respectively) patterns are related to the physiological state of the left heart by use of an electrical analog model. Filling of left ventricle (LV) through the mitral valve is characterized by a quadratic Bernoulli's resistance in series with an inertance. Filling of the left atrium (LA) through the pulmonary veins is represented by a lumped network of linear resistance, capacitance, and inertance. LV and LA are each represented by a time-varying elastance. A volume dependency is incorporated into the LV model to produce physiological pressure-volume loops and Starling curves. The state-space representation of the analog model consists of 10 simultaneous differential equations, which are solved by numerical integration. Model validity is supported by the following. First, the expected effects of aging and decreasing LV compliance on TMFV and PVFV are accurately represented by the model. Second, the model-generated TMFV and PVFV waveforms fit well to pulsed-Doppler recordings in normal and postinfarct patients. It is shown that the TMFV deceleration time is prolonged by the increase in LV compliance and, to a lesser extent, by the increase in LA compliance. A shift from diastolic dominance to systolic dominance in PVFV occurs when LA compliance or pulmonary perfusion pressure increases or when LV compliance or mitral valve area decreases. The present model should serve as a useful theoretical basis for echocardiographic evaluation of LV and LA functions.
Left ventricular (LV) diastolic pressure-volume (P-V) relations arise from a complex interplay of active decay of force (i.e., relaxation), passive elastic myocardial properties, and time-varying inflow across the mitral orifice. This study was designed to quantify the passive properties of the intact ventricle and the effects of elastic recoil by separating filling from relaxation with a method of LV volume clamping with a remote-controlled mitral valve. Eleven open-chest fentanyl-anesthetized dogs were instrumented with aortic and mitral flow probes, LV and left atrium micromanometers, and a remote-controlled mitral valve. We prevented complete (end-systolic volume clamping) or partial filling at different times in diastole. The ventricle thus relaxed completely at different volumes, and we generated P-V coordinates for the passive ventricle that included negative, as well as positive, values of pressure. We then estimated ventricular volumes from ventricular weight in eight dogs, using regression equations based on data in the literature, to determine the equilibrium volume (V0), that is, volume at zero transmural pressure, in the working ventricle. We abandoned the traditional exponential approach and characterized by the P-V relation with a logarithmic approach that included maximum LV volume (Vm), minimum volume (Vd), and stiffness parameters (Sp and Sn) for the positive (p) and negative (n) phases: Pp = -Sp In[(Vm - V)/(Vm - V0)] and Pn = Sn In[(V - Vd)/(V0 - Vd)]. With this formulation, the chamber compliance, dP/dV, is normalized by the LV operating volume, and Sp and Sn are size-independent chamber stiffness parameters with the units of stress. In eight ventricles with LV weight = 131 +/- 20 g, Vm = 116 +/- 18 ml, V0 = 37 +/- 6 ml, and Vd = 13 +/- 2 ml, stiffness Sp = 14.6 mm Hg and Sn = 5.1 mm Hg were determined from the slopes of the log-linearized equations. Also, the duration of LV relaxation is increased by the process of ventricular filling (161 +/- 31 msec, filling versus 108 +/- 36 msec, nonfilling, measured from dP/dtmin, p less than 0.0001). We conclude that volume clamping is a useful method of studying restoring forces and that the logarithmic approach is conceptually and quantitatively useful in characterizing the passive properties of the intact ventricle.
The Doppler transmitral velocity curve is commonly used to assess left ventricular diastolic function. Recent investigations, however, relating Doppler mitral indexes to ventricular compliance, relaxation, and preload have been inconclusive and at times contradictory. We used a mathematical formulation to study the physical and physiological determinants of the transmitral velocity pattern for exponential chamber pressure-volume relationships with active ventricular relaxation (2,187 combinations investigated). We showed that transmitral velocity is fundamentally affected by two principal physical determinants, the transmitral pressure difference and the net atrioventricular compliance, as well as the impedance characteristics of the mitral valve. These physical determinants in turn are specified by the compliance and relaxation parameters of physiological interest. We found that the peak mitral velocity is most strongly related to initial left atrial pressure but lowered by prolonged relaxation, low atrial and ventricular compliance, and systolic dysfunction. Peak acceleration varies directly with atrial pressure and inversely with the time constant of isovolumic relaxation, with little influence of compliance, whereas the mitral deceleration rate is approximately valve area divided by atrioventricular compliance. We then used these data to suggest possible strategies for improved analysis of noninvasive data (Doppler indexes, planimetered valve area, and isovolumic relaxation time) to estimate ventricular compliance and relaxation and atrial pressure.
Residual stress in an organ is defined as the stress that remains when all external loads are removed. Residual stress has generally been ignored in published papers on left ventricular wall stress. To take residual stress into account in the analysis of stress distributions in a beating heart, one must first measure the residual strain in the no-load state of the heart. Residual strains in equatorial cross-sectional rings (2-3 mm thick) of five potassium-arrested rat left ventricles were measured. The effects of friction and external loading were reduced by submersing the specimen in fluid, and a hypothermic, hyperkalemic arresting solution containing nifedipine and EGTA was used to delay the onset of ischemic contracture. Stainless steel microspheres (60-100 microns) were lightly imbedded on the surface of the slices, and the coordinates of the microspheres were digitized from photographs taken before and after a radial cut was made through the left ventricular free wall. Two-dimensional strains computed from the deformation of a slice after one radial cut were defined as the residual strains in that slice. It was found that the distributions of the principal residual stretch ratios were asymmetric with respect to the radial cut: in areas where substantial transmural strain gradients existed, the distributions of strain components were different on the two sides of the radial cut. A second radial cut produced deformations significantly smaller than those produced from the first radial cut. Hence, a slice with one radial cut may be considered stress free.(ABSTRACT TRUNCATED AT 250 WORDS)
Isovolumic relaxation time (IVRT) and events of early transmitral flow measured by Doppler echocardiography were validated against the time constant of left ventricular relaxation (tau) in open-chest dogs. During increased inotropy (by isoproterenol infusion) at constant preload, enhancement of relaxation was indicated by a decrease in tau from 48 +/- 12 (mean +/- SD) to 33 +/- 5 msec (p = 0.04) with a concomitant decrease in IVRT from 74 +/- 18 to 38 +/- 8 msec (p = 0.03). During decreased inotropy (by propranolol infusion) at constant preload, slowing of relaxation was indicated by an increase in tau from 40 +/- 8 to 51 +/- 13 msec (p = 0.02) with a concomitant increase in IVRT from 71 +/- 15 to 83 +/- 21 msec (p less than 0.05). A significant correlation between changes in tau and changes in IVRT was found (r = 0.66, p less than 0.001). In contrast, when left ventricular end-diastolic pressure was increased from 7 +/- 2 to 24 +/- 4 mm Hg at constant inotropy, tau increased from 47 +/- 14 to 64 +/- 25 msec (p = 0.03), whereas no change in IVRT was observed (76 +/- 19 and 71 +/- 19 msec, respectively). Aortic pressure was not significantly changed during any intervention, and heart rate was kept constant by pacing. Peak early transmitral velocity was unchanged by propranolol but increased during isoproterenol and saline infusion (p less than 0.001 and p less than 0.01, respectively).(ABSTRACT TRUNCATED AT 250 WORDS)
Diastole can be divided into four phases: isovolumic relaxation, early filling, diastasis, and atrial systole. The amount of LV filling that occurs during each of these phases depends on myocardial relaxation, the passive characteristics of the LV, the characteristics of the left atrium, pulmonary veins, and mitral valve, and the heart rate. When diastolic function is normal, the net effect of these factors results in an LV filling sufficient to produce an adequate cardiac output, while mean pulmonary venous pressure is maintained below 12 mm Hg. In the absence of systolic dysfunction, abnormal diastolic performance is usually due to abnormal relaxation and/or changes in the passive LV characteristics. Invasive studies can quantitate the rate of myocardial relaxation and the LV diastolic pressure-volume relation. More recently, RNA and Doppler echocardiography have been used to noninvasively evaluate diastolic performance by determining the pattern of LV diastolic filling. At rest, most LV filling occurs early in diastole. Conditions that produce diastolic dysfunction, such as LV hypertrophy and ischemia, are associated with reduced early diastolic filling and an augmented importance of atrial systole. It is important to recognize that such patterns can occur in patients who do not have clinically apparent diastolic dysfunction and in normals. Furthermore, a normal pattern can occur in patients who have severe diastolic dysfunction. A reduced early diastolic filling, in the absence of pulmonary congestion, indicates the loss of diastolic reserve, since the left atrium is being used as a booster pump. This pattern of diastolic filling in a patient who has symptoms of pulmonary congestion may suggest diastolic dysfunction, even if the systolic LV performance is normal. Since diastolic filling of the LV results from a complex interplay of factors, it is unlikely that a single, easily interpreted index of LV diastolic performance will ever be developed. However, the recent development of a noninvasive evaluation of the pattern of LV diastolic filling by RNA or Doppler echocardiography is an important advance. When interpreted with an understanding of the determinants of LV filling and the patient's clinical status, these noninvasive tests can contribute to the rational assessment of LV diastolic performance.
A new parametrized diastolic filling (PDF) formalism for evaluation of holodiastolic (left and right) ventricular function via Doppler echocardiography is presented. It is motivated by the empiric observation that during diastole the heart behaves as a suction pump whose dynamics, in certain respects, are those of a damped harmonic oscillator. An expression for elastic recoil (suction) initiated ventricular diastolic fluid inflow velocity v(t) is obtained by differentiation from the solution x(t) of the linear differential equation that describes the motion of a forced, damped harmonic oscillator. It is solved for "over-damped" motion, for zero initial velocity and initial displacement = xo cm. An explicit forcing term F(t) = Fosin(omega t) is included to account for late diastolic (atrial) filling. The quantitative parameters of the model include inertia (mass; m), viscosity (damping constant; c), source of stored energy for suction (spring constant; k), and its initial displacement xo, the amplitude and frequency of the (atrial) forcing term Fo, omega. The mathematical behavior of the solution v(t) and its dependence on the parameters xo, c, and k, which characterize the contour of the Doppler velocity profile (DVP), is discussed. When clinical examples of normal and abnormal transmitral DVPs are compared with v(t) calculated using the harmonic oscillator model, excellent agreement [DVP-v(t)]/v(t) approximately 0.05 is obtained throughout diastole. Thus the model allows accurate qualitative and quantitative characterization of global ventricular diastolic behavior by noninvasive means in a variety of normal and abnormal stiffness-compliance states. In addition, it may serve as a prototype for a class of mathematical models that can encompass the essential dynamic elements of ventricular diastolic function that couple to flow and further enhance the role of the heart as a suction pump.
We studied left ventricular relaxation in the filling and transiently nonfilling working hearts of seven open-chest pentobarbital-anesthetized dogs by totally occluding the mitral annulus during one systole. In the completely isovolumic nonfilling cycle, the ventricle relaxes to a lower pressure minimum (usually negative) than in the normal filling cycle. By clamping the ventricle at end systole, we determined the pressure asymptote (Poo) under dynamic conditions. With this information, we evaluated the validity of a monoexponential characterization of relaxation. P = (P0 - Poo) exp(-t/T) + Poo (T, time constant, P0, pressure at t = 0). Plots of In(P-Poo) versus t are nonlinear and concave to the origin, thereby revealing that late relaxation is more rapid than predicted by a monoexponential relation. Nevertheless, the monoexponential T remains a useful index of relaxation and correlates well with other temporal indexes (isovolumic relaxation time and relaxation half-time). When T is calculated from a filling cycle by assuming a zero pressure asymptote, i.e., the conventional way, there is no significant difference with the true value based on the nonfilling cycle.
The third heart sound (S3) occurs shortly after the early (E-wave) peak of the transmitral diastolic Doppler velocity profile (DVP). It is thought to be due to cardiohemic vibrations powered by rapid deceleration of transmitral blood flow. Although the presence, timing, and clinical correlates of the S3 have been extensively characterized, derivation and validation of a causal, mathematical relation between transmitral flow velocity and the S3 are lacking.
To characterize the kinematics and physiological mechanisms of S3 production, we modeled the cardiohemic system as a forced, damped, nonlinear harmonic oscillator. The forcing term used a closed-form mathematical expression for the deceleration portion of the DVP. We tested the hypothesis that our model's predictions for amplitude, timing, and frequency of S3 accurately predict the transthoracic phonocardiogram, using the simultaneously recorded transmitral Doppler E wave as input, in three subject groups: those with audible pathological S3, those with audible physiological S3, and those with inaudible S3.
We found excellent agreement between model prediction and the observed data for all three subject groups. We conclude that, in the presence of a normal mitral valve, the kinematics of filling requires that all hearts have oscillations of the cardiohemic system during E-wave deceleration. However, the oscillations may not have high enough amplitude or frequency to be heard as an S3 unless there is sufficiently rapid fluid deceleration (of the Doppler E-wave contour) with sufficient cardiohemic coupling.
A noninvasive measure of left ventricular (LV) chamber stiffness (KLV) would be clinically useful. Our theoretical analysis predicts that KLV can be calculated from the time for deceleration of LV early filling (tdec) by [formula: see text] where p = density of blood, L = effective mitral length, and A = mitral area.
We tested this hypothesis in eight conscious dogs instrumented for measurement of LV pressure (P) with use of a micromanometer and volume (V) with use of sonomicrometers. KLV was determined as the slope of the late diastolic portion of the LV P-V loop. KLV was varied from 0.99 +/- 0.35 to 2.58 +/- 0.92 mm Hg/mL with use of three graded doses of phenylephrine. We assumed that p = 1.0 and that L/A = 3.4. Thus, we predicted that KLV = (0.08/tdec)2. The LV filling pattern was determined from the derivative of LV volume (dV/dt). tdec was measured from peak early filling to the end of early filling. Predicted KLV and actual KLV were closely correlated (r = .94, SEE = 0.06 mm Hg/mL, P < .05). The regression line was close to the line of identity (slope = 0.95, intercept = 0.13 mm Hg/mL). Dobutamine did not alter the relation between tdec and KLV.tdec determined from the mitral valve flow velocity measured with Doppler echocardiography correlated well with that measured by dV/dt (r = .89, P < .01) but was 0.02 seconds longer. KLV-calculated tdec from the corrected Doppler tdec provided a good estimate of measured KLV (r = .75, SEE = 0.5 mm Hg/mL, P < .01).
LV chamber stiffness can be determined from the time for deceleration of LV early filling, which can be measured noninvasively.
We develop an automated method of characterizing the late atrial filling phase of diastole by fitting a kinematic model for diastolic filling to the clinical Doppler A-wave contour. The result is a set of model parameters which completely characterizes the contour. We have previously derived a parameterized diastolic filling (PDF) model, which predicts the time-dependent transmitral blood flow velocity obtained by Doppler echocardiography. An automated method to determine the PDF model parameters for early rapid filling from the clinical Doppler E-wave has also been developed and validated. The method consists of digitizing the acoustic Doppler waveform, recreating the Doppler velocity profile, extracting the maximum velocity envelope, and fitting the PDF model for early filling to the envelope. In the current work, we apply the same general approach for PDF parameter determination for the late atrial filling phase of diastole. To assess the presence and significance of near-degeneracies in the model parameter set, numerical experiments (consisting of fitting the model to a model-generated contour to which Gaussian noise was added) were performed. These revealed a two-dimensional degeneracy in four-dimensional parameter space which could be removed by using two kinematic simplifications: critical damping and resonant forcing. We show that these degeneracy-eliminating approximations do not limit the ability of the model to predict clinical A-wave contours.
Doppler echocardiographic studies of transmitral flow have become a routine clinical tool for the assessment and characterization of ventricular diastolic (filling) function. We have previously derived a parametrized diastolic filling (PDF) formalism for the purpose of diastolic function assessment using Doppler echocardiography. The model accommodates the mechanical "suction" feature of early diastolic filling of the heart by using a simple harmonic oscillator (SHO) as a paradigm for the kinematics of filling. PDF model predictions of transmitral flow velocity have shown excellent agreement with human echocardiographic Doppler contours (temporal profiles) when a visual, transparency overlay method of model fit to clinical Doppler contour comparison was used. The determination of PDF model parameters from the clinical Doppler contour is equivalent to the solution of the "inverse problem" of diastole. Previously, this determination consisted of a manual, iterative method of graphical overlay, in which model predicted contours were visually compared with the echocardiography machine generated Doppler contour using transparencies. To automate the process of model parameter estimation (i.e., solution of the "inverse problem") for the early or "rapid filling" phase of diastole (known in cardiology as the E-wave of the clinical Doppler velocity profile [DVP]) we recorded the acoustic pulsed Doppler signal using the forward channel of a commercial echocardiography machine. The Doppler spectrogram for a particular E-wave was recreated using short-time Fourier transform processing. The maximum velocity envelope (MVE) was extracted from the spectrogram. The PDF model was fit to the E-wave MVE using a Levenberg-Marquardt (iterative) algorithm by the requirement that the mean-square error between the clinical data (MVE) and the model be minimized. Because the model is linear, all of the PDF parameters for the Doppler E-wave can be uniquely determined. We show that: (1) solution of the "inverse problem of diastole" is possible; (2) clinical Doppler E-wave contours can be accurately reproduced and quantified using the PDF formalism and its parameters; and (3) our proposed, automated method of PDF parameter determination for the E-wave is robust.
Anatomic/physiologic and kinematic mathematical models of diastolic filling which employ (lumped) parameters of diastolic function have been used to predict or characterize transmitral flow. The ability to determine model parameters from clinical transmitral flow, the Doppler velocity profile (DVP), is equivalent to solving the "inverse problem" of diastole. Systematic model-to-model and model-to-data comparison has never been carried out, in part due to the requirement that DVPs be digitized by hand. We developed, tested and verified a computerized method of DVP acquisition and reproduction, and carried out numerical determination of model-to-model and model-to-data goodness-of-fit. The transmitral flow velocity of two anatomic/physiologic models and one kinematic model were compared. Each model's ability to fit computer-acquired and reproduced transmitral DVPs was assessed. Results indicate that transmitral flow velocities generated by the three models are 'graphically indistinguishable and are able to fit the E-wave of clinical DVPs with comparable mean-square errors. Nonunique invertibility of the anatomic/physiologic models was verified, i.e., multiple sets of model parameters could be found that fit a single DVP with comparable mean-square error. The kinematic formulation permitted automated, unique, model-parameter determination, solving the "inverse problem" for the Doppler E-wave. We conclude that automated, quantitative characterization of clinical Doppler E-wave contours using this method is feasible. The relation of kinematic parameters to physiologic variables is a subject of current investigation.
When relaxed after contraction, isolated cardiac myocytes quickly relengthen back to their slack length. The molecular basis of the force that underlies passive relengthening, known as restoring force, is not well understood. In a previous study of titin's elasticity in cardiac myocytes, we proposed that titin/connectin develops restoring force, in addition to passive force. This study tested whether titin indeed contributes to the restoring force in cardiac myocytes. Skinned rat cardiac myocytes in suspension were shortened by approximately 20%, using Ca(2+)-independent shortening, followed by relaxation. Cells were observed to relengthen until they reached their original slack sarcomere length. However, the ability to relengthen was abolished after cells had been treated for 12 minutes with trypsin (0.25 microgram/mL, 20 degrees C). Gel electrophoresis showed that this treatment had degraded titin without clearly affecting other proteins, and immunoelectron microscopy revealed that the elastic segment of titin in the I band was missing from the sarcomere. Restoring force was also directly measured, before and after trypsin treatment. Restoring force of control cells was -61 +/- 20 micrograms (per cell) at a sarcomere length of 1.70 microns. Comparison of our results with those of activated trabeculae indicated that a large fraction of restoring force of cardiac muscle originates from within the myocyte. Restoring force of myocytes was found to be depressed after titin had been degraded with trypsin. We conclude that cardiac, titin indeed develops restoring force in shortened cardiac myocytes, in addition to passive force in stretched cells, and that titin functions as a bidirectional spring. Our work suggests that at the level of the whole heart, part of the actomyosin-based active force that is developed during systole is harnessed by titin, allowing for elastic diastolic recoil and aiding in ventricular filling.
Doppler mitral flow velocities and related variables are used to assess left (LV) and right ventricular filling and, indirectly, ventricular diastolic function. Three abnormal ventricular filling patterns (impaired relaxation and pseudonormal and restrictive physiology) are recognized in patients with various heart diseases and have been related to alterations in LV diastolic properties and filling pressures. More recently, these variables have been used to assess the hemodynamic effects of drug therapy or heart surgery and prognosis in patients with restrictive and dilated cardiomyopathies. Despite these encouraging results, widespread clinical use of these Doppler techniques has been hampered by difficulties in obtaining accurate and reproducible measurements from Doppler flow velocity recordings. This is due, in part, to an underappreciation of factors such as cardiac filling mechanics, Doppler examination principles, and ultrasound machine settings, which can markedly affect the quality of the flow velocity recordings. The purpose of this article is to provide the technical information for performing a systematic and comprehensive Doppler evaluation of LV diastolic function that can be used on a routine basis. This information includes discussing the different flow velocity recordings required for a Doppler assessment of LV diastolic function, their proper recording technique, and the common technical pitfalls.
The extracellular collagen matrix of the myocardium plays an important role in maintaining muscle fiber and cardiac alignment and ventricular shape and size. It also influences tissue and ventricle stiffness. This network consists of an organized hierarchy of collagen that is intimately associated with individual and groups of myocyte and muscle fibers, as well as the coronary vasculature. In renovascular and genetic hypertension, the hypertrophic response of the myocardium includes an increase in collagen concentration, thickening of existing fibrillar collagen, and addition of newly synthesized collagen to all of the matrix components. The consequences of this remodeling are a stiffer myocardium and left ventricular diastolic dysfunction. With removal of less than half of the normal amount of collagen the opposite occurs. That is, the ventricle dilates and there is an increase in ventricular compliance. Thus an abnormal accumulation of collagen is a major distinguishing factor between physiologic and pathologic hypertrophy while an abrupt decrease in collagen concentration results in a ventricular remodeling similar to that of a heart in failure.
Abnormalities of diastolic function have a major role in producing the signs and symptoms of heart failure. However, diastolic function of the heart is a complex sequence of multiple interrelated events, and it has been difficult to understand, diagnose and treat the various abnormalities of diastolic filling that occur in patients with heart disease. Recently, Doppler echocardiography has been used to examine the different diastolic filling patterns of the left ventricle in health and disease, but confusion about diagnosis and treatment options has arisen because of the misinterpretation of these flow velocity curves. This review presents a simplified approach to understanding the process of diastolic filling of the left ventricle and interpreting the Doppler flow velocity curves as they relate to this process. It has been hypothesized that transmitral flow velocity curves show a progression over time with diseases involving the myocardium. This concept can be applied clinically to estimate left ventricular filling pressures and to predict prognosis in selected groups of patients. Specific therapy for diastolic dysfunction based on Doppler flow velocity curves is discussed.
Model-based image processing (MBIP) of Doppler E-waves eliminates the need for digitizing waveforms by hand or determining the contour 'by eye'. Little et al. (Circulation 1995, 92:1933-1939) used pressure-volume measurements for dogs to verify the physiologic-model-derived prediction that the left ventricular chamber stiffness, KLV1 can be determined from the deceleration time tdec, when that portion of the E-wave contour is fit by a cosine function. MBIP of clinical Doppler E-wave images to determine chamber stiffness KLV has not been performed.
We sought to determine KLV by MBIP of clinical Doppler E-wave images and elucidate the physiologic meaning of the harmonic oscillator filling model's parameter k.
The unique mathematical relationship between the kinematic, harmonic oscillator model of filling and KLV predicts that the oscillator's spring constant k be linearly proportional to the chamber stiffness KLV. To verify this, digitally acquired, clinical Doppler transmitral flow velocity images from 21 subjects were analyzed. The parameter k and the stiffness KLV were computed independently for each subject and compared. In accordance with prediction, a linear relationship between k and the stiffness KLV, namely k = 1.16 [A/(rho L)]KLV+41, r = 0.96, was observed.
The oscillator parameter k is linearly proportional to the left ventricular chamber stiffness KLV. The MBIP approach allows automated computation of k and KLV, provides a robust, automated, observer independent method of Doppler transmitral flow velocity analysis, and eliminates the need for visual determination of the contour or measurement of its attributes by eye. It provides a stimulus for further validation of the relationships among K, KLV, and catheterization-based diastolic chamber properties in humans and their correlations with selected diastolic function-altering syndromes.
Physiological models of transmitral flow predict E-wave contour alteration in response to variation of model parameters (stiffness, relaxation, mass) reflecting the physiology of hypertension. Accordingly, analysis of only the E-wave (rather than the E-to-A ratio) should be able to differentiate between hypertensive subjects and control subjects. Conventional versus model-based image processing methods have never been compared in their ability to differentiate E-waves of hypertensive subjects with respect to age-matched control subjects. Digitally acquired transmitral Doppler flow images were analyzed by an automated model-based image processing method. Model-derived indexes were compared with conventional E-wave indexes in 22 subjects: 11 with hypertension and echocardiographically verified ventricular hypertrophy and 11 age-matched nonhypertensive control subjects. Conventional E-wave indexes included peak E, E, and acceleration and deceleration times. Model-based image processing-derived indexes included acceleration and deceleration times, potential energy index, and damping and kinematic constants. Intergroup comparison yielded lower probability values for model-based compared with conventional indexes. In the subjects studied, Doppler E-wave images analyzed by this automated method (which eliminates the need for hand-digitizing contours or the manual placement of cursors) demonstrate diastolic function alteration secondary to hypertension made discernible by model-based indexes. The method uses the entire E-wave contour, quantitatively differentiates between hypertensive subjects and control subjects, and has potential for automated noninvasive diastolic function evaluation in large patient populations, such as hypertension and other transmitral flow velocity-altering pathophysiological states.
We sought to define the hemodynamic determinants of pulmonary venous (PV) flow velocities to assess how these are affected by respiration, heart rate and loading conditions.
Pulmonary venous flow velocity (PVFV) recorded with pulsed wave Doppler technique is currently used in the noninvasive evaluation of left ventricular (LV) diastolic function and filling pressures. Although previous studies in both animals and humans have shown that PV flow is pulsatile, the hemodynamic determinants of the individual components of this flow remain controversial. Understanding the physiologic mechanisms should help to better define the clinical utility of these Doppler techniques.
PV flow velocities obtained with transesophageal pulsed wave Doppler imaging were recorded together with PV, left atrial (LA) and LV pressures in 10 sedated, spontaneously breathing normal dogs. PVFV and hemodynamic data were analyzed during apnea, inspiration and expiration, at atrial paced heart rates of 60, 80, 100 and 120 beats/min and mean LA pressures of 6, 12, 18 and 24 mm Hg.
The data showed that 1) PV pressure varied depending on recording site, resembling pulmonary artery pressure closer to the pulmonary capillary bed and LA pressure closer to the venoatrial junction; 2) PVFV qualitatively followed changes in the PV-LA pressure gradient; 3) four PVFV components exist under normal conditions-three of which follow phasic changes in LA pressure and one of which (the late systolic component) is more influenced by RV stroke volume and the compliance of the pulmonary veins and left atrium; 4) normal respiration and changes in heart rate significantly alter PVFV variables--in particular, reverse flow velocity at atrial contraction; and 5) increasing LA pressure results in larger PV A wave and PV early systolic flow velocities, as well as an earlier peak in PV late systolic flow velocity and a more prominent velocity minimum before PV diastolic flow.
Using transesophageal pulsed wave Doppler technique, four PVFV components are identifiable and determined by PV-LA hemodynamic pressure gradients. These gradients appear to be influenced by a combination of physiologic events that include RV stroke volume, the compliance of the pulmonary vasculature and left atrium and phasic changes in LA pressure. PV flow velocity components are significantly influenced by heart rate, respiration and LA pressure. These findings have implications for the interpretation of LV diastolic function and filling pressures by current Doppler echocardiographic techniques but require further clinical investigation.
In an effort to characterize more fully diastolic function using Doppler echocardiography, we have previously developed an automated method of model-based image processing for spectral Doppler images of transmitral blood flow. In this method, maximum velocity envelopes (MVEs) extracted from individual Doppler images are aligned and averaged over several cardiac cycles. The averaged waveform is fit by the solution of a kinematic model of diastolic filling. The results are estimates of the model parameters. As expected, the mean and standard deviation of the model parameter estimates depend on many factors such as noise, the number of cardiac cycles averaged, beat-to-beat variation, waveform shape, observation time and the processing methods used, among others. A comprehensive evaluation of these effects has not been performed to date. A simulation was developed to evaluate the performance of three automated processing methods and to measure the influence of noise, beat-to-beat variation and observation time on the model parameter estimates. The simulation's design and a description and analysis of the three automated processing methods are presented. Of the three methods evaluated, using the inflection point in the acceleration portion of the velocity contour as the first data point to be fit was found to be the most robust method for processing averaged E-wave MVE waveforms. Using this method under nominal conditions, the average bias was measured to be < 3% for each of the model parameters. As expected, the biases and standard deviations of the estimates increased as a result of increased noise levels, increased beat-to-beat variation and decreased observation time. Another important finding was that the effects of noise, beat-to-beat variation and waveform observation time on the parameter estimates are dependent on the location in model parameter space.
To characterize diastolic function from transmitral Doppler data, the image's maximum velocity envelope (MVE) is fit by a model for flow velocity. To reduce the physiologic beat-to-beat variability of best-fit determined model parameters, averaging of multiple cardiac cycles is indicated. To assess variability mathematically, we modeled physiologic noise as a random (normally-distributed) process and evaluated three methods of averaging (1, averaging model parameters from single images; 2, averaging images; and 3, averaging MVEs) using clinical datasets (50 continuous beats from 5 subjects). Method 2 generates a positive bias because low-velocity beats will not contribute to the composite MVE. The difference between Methods 3 and 1 is less than 2.0 E-5 (m/s)2 for uncorrelated model parameters. Input having 10% beat-to-beat variation yields a bias of <4% for model parameter mean. Hence, Method 1 was, in general, more robust than Method 3.
Conventional echocardiographic characterization of diastolic function requires manual analysis of Doppler E-and A-wave amplitudes, deceleration times, isovolumic relaxation times, and pulmonary venous flow patterns. Mathematic modeling of the suction pump activity of the heart permits characterization of diastolic function through model-based image processing, which relies solely on transmitral Doppler images. This automated method uniquely specifies the entire E-wave contour using 3 parameters (x(o), k, and c) that determine E-wave amplitude, width, and rate of decay. Moreover, the index beta = c2 - 4k, reflecting the balance between chamber viscosity and stiffness/recoil, represents a novel parameter for characterizing diastolic function. We analyzed Doppler E waves from 39 patients (mean age 79 years, 61% women, mean ejection fraction 47%) using the model-based image processing technique. A value of beta <-900 was selected as indicative of severe diastolic dysfunction. Of 17 subjects with beta <-900, 8 (47%) were no longer alive at 1 year. Of 22 subjects with beta >-900, all were alive (p = 0.001). The index beta, dichotomized at <-900, had a predictive accuracy of 0.769 (30 of 39), a negative predictive value of 1.0 (22 of 22 alive), and a positive predictive value of 0.471 (8 of 17 deceased) for 1-year vital status. Of 14 subjects with deceleration time < or =160 ms, 5 (36%) were deceased at 1 year, whereas for deceleration time >160 ms, 22 of 25 patients were alive (p = NS). Of 16 subjects with ejection fraction <45%, 6 (38%) were deceased at 1 year. Of 23 subjects with ejection fraction >45%, 21 were alive at 1 year (p = 0.074). On multivariate analysis, beta dichotomized at -900 was the strongest independent predictor of 1-year mortality. We conclude that evaluation of diastolic function using model-based image processing provides valuable prognostic information in elderly patients with heart failure.
The role of left ventricular (LV) diastolic function in health and disease is still incompletely understood and under appreciated by most primary care physicians and many cardiologists. Physical examination, electrocardiogram, and chest radiographs are unreliable in making the diagnosis of LV diastolic dysfunction in most individuals, and invasive measurements of cardiac pressures, rates of LV relaxation, and LV compliance are costly, clinically impracticable as they carry increased risk, and require special catheters and software analysis programs. The authors address the definition of LV diastolic dysfunction, history of diastole, LV filling patterns, pulmonary venous flow velocity variables, additional ancillary data, practical echo-Doppler evaluation of LV diastolic function, and limitations.
Modeling methods have been employed to further characterize the physical and physiologic processes of filling and diastolic function. They have led to more detailed understanding of the effect of alteration of physiologic parameters on the Doppler E-wave contour as well as pulmonary vein flow. Depending on the modeling approach, different aspects of the filling process have been considered from AV gradient and net compliance to atrial appendage function to the mechanical suction pump attribute of the heart. The models have been applied for further characterization of diastolic function and elucidation of novel basic physiologic relations. We trust that readers recognize that this article could not serve as a comprehensive and global review of the state-of-the-art in physiologic modeling, but rather as a selective overview, with emphasis on the main modeling principles and options currently in use. Modeling of systems physiology, especially as it relates to the function of the four-chamber heart, remains a fertile area of investigation. Future progress is likely to have profound influence on (noninvasive) diagnosis and quantitation of the effect of therapy and lead to continued discovery of "new" (macroscopic, cellular, and molecular biologic) physiology.
Shortened early transmitral deceleration times (E(DT)) have been qualitatively associated with increased filling pressure and reduced survival in patients with cardiac disease and increased left ventricular operating stiffness (K(LV)). An equation relating K(LV) quantitatively to E(DT) has previously been described in a canine model but not in humans. During several varying hemodynamic conditions, we studied 18 patients undergoing open-heart surgery. Transesophageal echocardiographic two-dimensional volumes and Doppler flows were combined with high-fidelity left atrial (LA) and left ventricular (LV) pressures to determine K(LV). From digitized Doppler recordings, E(DT) was measured and compared against changes in LV and LA diastolic volumes and pressures. E(DT) (180 +/- 39 ms) was inversely associated with LV end-diastolic pressures (r = -0.56, P = 0.004) and net atrioventricular stiffness (r = -0.55, P = 0.006) but had its strongest association with K(LV) (r = -0.81, P < 0.001). K(LV) was predicted assuming a nonrestrictive orifice (K(nonrest)) from E(DT) as K(nonrest) = (0.07/E(DT))(2) with K(LV) = 1.01 K(nonrest) - 0.02; r = 0.86, P < 0.001, DeltaK (K(nonrest) - K(LV)) = 0.02 +/- 0.06 mm Hg/ml. In adults with cardiac disease, E(DT) provides an accurate estimate of LV operating stiffness and supports its application as a practical noninvasive index in the evaluation of diastolic function.
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