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Control of Cardiovascular System
Mikhail Rudenko, Olga Voronova, Vladimir Zernov,
Konstantin Mamberger, Dmitry Makedonsky,
Sergey Rudenko and Sergey Kolmakov
Russian New University,
Russia
1. Introduction
The main method of cognition of the performance of biological systems is their
mathematical modeling. The essence of this method should reflect the principle of
optimization in biology[9]. Any biosystem cannot function if its energy consumption is
inadequately high.
The same is applicable to the blood circulatory system. Its main function is to transport
blood throughout the body in order to maintain the proper gaseous exchange, deliver
important substances to viscera and tissues in living body and remove decay products. It is
impossible to study this function without due consideration of hemodynamic features. But
how is the blood circulation provided? It is a question of principle, and so far no
unambiguous answer has been given thereto.
The conventional interpretation of blood circulation is that blood flows through blood
vessels under laminar flow conditions to which Poiseuille's law is applicable. But it is a
matter of fact that this conventional interpretation concept is inadequate because it is not in
compliance with the above principle of optimization in biology, according to which all
processes in bio systems show their best performance, i.e., their highest efficiency. It is just
the compliance with this principle that is the major criterion to be used for evaluation of
adequacy of any theoretical models describing various systems in living body and their
interactions both with each other and their external environment.
Significant progress in understanding of such phenomena is made after G. Poyedintsev and
O.Voronova discovered the so called mode of elevated fluidity, i.e., the third flow conditions
that show lesser losses of energy to overcome friction and that is noted for lesser friction
losses and specific pattern of the flow[4].
It has been proved that the blood flow through the blood vessels is provided in “the third”
flow mode that is the most efficient and therefore fully in compliance with the said principle
of optimization.
The theory of the third mode is a foundation for the development of new mathematical
models describing the performance of the blood circulation system. In addition, new
methods of quantitative determination of a number of hemodynamic parameters and
The Cardiovascular System – Physiology, Diagnostics and Clinical Implications
4
qualitative evaluation of some processes occurring in the system have been elaborated. The
application of these methods in practice allows filling a lot of gaps in theoretical cardiology
and creates at the same time a system of analysis of the functions of the cardiovascular
system taking into account the relevant cause-effect relationship.
The detailed description of this theory is given in our book “Theoretical Principles of Heart
Cycle Phase Analysis”[3]. Our intention is to outline herein the general principles of the
performance of the cardiovascular system only.
2. Biophysical processes of formation of hemodynamic mechanism
2.1 Special features of hemodynamics and its regulation. Hemodynamic volumetric
parameters
There two types of liquid flow conditions described in the classical fluid mechanics: the first
type is the laminar flow, and the second one is the turbulent flow mode. In the 80th last
century, a new theory of a specific liquid flow mode was developed by G.M. Poyedinstev
and O.K. Voronova that was defined by them as the “elevated fluidity mode”[4]. Another
name “the third flow mode” was given by the above discoverers to differ it from the two
other modes well-known before. Being experts in solving technical problems of fluid
mechanics, the authors succeeded in modeling the above elevated fluidity mode in a rigid
pipe. For this purpose, hydraulic pulsators of specific design were used. It was established
that the energy used to transport liquid in the third flow mode is several times less than it is
the case under the laminar flow conditions[3]. Moreover, an efficiency of this process could
be considerably increased when liquid is pumped under certain conditions through an
elastic piping. The subsequent researches demonstrated that the physical processes
producing the elevated fluidity mode and those in the blood circulation are identical. The
mathematical tools used to describe “the third” flow mode was applied to describe the
hemodynamic processes.
It was established by the authors that there are processes which are always observed in a
rigid pipe at the initiation of a liquid flow from a quiescent state, as mentioned below.
Whilst particles of liquid are starting their moving in the rigid pipe due to a difference in the
static pressure, there a set of concentric waves of friction in the boundary layer is generating,
the front of propagation of which is directed towards the pipe axis[3] (Fig. 1). Amplitudes of
these waves depend on the diameter of the pipe, acoustic velocity in liquid and an initial
difference in pressures at the pipe ends. The length of these traveling waves during this
complex process continuously increases. The waves travel towards the axis of the pipe and
degenerate. Finally, there a single wave remains only close to the pipe wall, the profile of
which becomes parabolic that is typical for the laminar flow (s. Fig. 2 herein).
It should be noted that it is just within this short period of time, i.e., starting from the
moment of the motion initiation from a quiescent state till the moment of formation of the
laminar flow (s. positions E and F in Fig. 2 herein), when liquid flows in its optimum mode
of elevated fluidity, considering it from the point of view of energy consumption (s.
positions A, B, C, D in Fig 2 herein). The energy consumption under the laminar flow
conditions to transport liquid in the pipe is significantly higher due to increase in the flow
resistance.
Control of Cardiovascular System
5
Fig. 1. Formation of concentric waves of friction at initiation of flow in a pipe (according to
G.M. Poyedintsev and O.K.Voronova); t1 - moment of pressure difference formation; V1 -
velocity of plasma in stagnated layers; V2 – velocity of blood elements in accelerated layers
There is another phenomenon typical for the “third” flow mode. If liquid contains
suspended particles similar to those in blood, during the development of the above
mentioned wave process the particles are concentrated at the wave maxima, and the
particle-free liquid is delivered to their minima, correspondingly[3]. When the liquid,
patterned in such a way, flows along the pipe axis, the velocity of the concentric particle-
loaded layers is twice what the liquid pattern-free layers reach. Vectors of velocity are
parallel to the axis of the flow. And it is just a prerequisite to elevated fluidity of liquid with
reduced friction between the liquid layers and the pipe wall. Figure 2 herein shows the
locations of erythrocytes in the blood flow referring to each flow formation stage as
mentioned above. At the beginning of the formation of the “third” flow mode, there ring-
shaped alternating layers of the blood elements and plasma are available, while in the
laminar mode all elements are accumulated in the center of the flow. In this case they are
located very close to each other forming a thick mass. This process may result in an
aggregation of erythrocytes and hemolysis. In order to avoid such pathological
consequences, it is a must to manage the blood transportation in the “third” mode of flow,
avoiding its transformation into a laminar one.
The theory gives a clue that it can be obtained when transporting liquid in a pulsating mode
through an elastic pipe. According to this theory, the pipe clear width and the liquid flow
velocity should be changed with every impulse under certain laws[3]. The laws of
increasing in the pipe clear width and decreasing in the flow velocity with every impulse
take the form as follows[4].
The Cardiovascular System – Physiology, Diagnostics and Clinical Implications
6
Fig. 2. Formation of two-phase pattern at the initiation of the flow from a quiescent state
(according to G.M. Poyedintsev and O.K. Voronova), A-F – flow structure in corresponding
sections
51
0
0
=tt
rrt
(1)
52
0
0
=t
t
WWt
(2)
where rt – current radius of the pipe increasing;
r0 – initial radius (at t = t0 );
t - current time (t ≥ t0);
t0 – time of acceleration of flow velocity up to maximum velocity in an impulse;
Wt – current value of liquid flow velocity;
W0 – maximum value of velocity in an impulse (at t = t0).
It is proved by the authors of this theory that the above conditions are met in the blood
circulation system.
This is provided by changing in the clear width of blood vessels in every cardiac cycle and
arterial pressure pulsating. The shape of the arterial pressure wave is given herein in Fig. 3
below.
Control of Cardiovascular System
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Fig. 3. Arterial pressure wave shape reography-recorded. ECG recorded simultaneously
with Rheogram.
The foundation of hemodynamics is the phase mode of the heart performance. In one beat
the heart changes its shape ten times that corresponds to the heart cycle phases[4].
The most efficient way is to evaluate the status of hemodynamics not only by values of
integral parameters, i.e., stroke and minute volumes, but also phase-related volumes of
blood entering or leaving the heart in the respective phase in a cardiac cycle.
So, the final formulae for calculation the volumes of blood in the phase of rapid and slow
ejection, symbolized as PV3 and PV4, respectively, are as follows:
PV3=S· (QR+RS)2· f1(
α
)· [f2(
α
)+f3(
α
,
δ
γ
β
,, )] (ml); (3)
PV4=S· (QR+RS)2· f1(
α
)· f4(
α
,
δ
γ
β
,, ) (ml), (4)
where S - cross-section of ascending aorta;
QR – phase duration according to ECG curve;
RS – phase duration according to ECG curve;
f1(
α
)= 243)25( ]27)25[(5,22072 5
3
−−
−−
α
α
;
f2(α)= ;
21
5−
α
f3(
α
,
δ
γ
β
,, )= )];(2)(5))(4(
3
10
[
8
1552443322
αβχαβχδαβδα
−−−+−−
The Cardiovascular System – Physiology, Diagnostics and Clinical Implications
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f4(
α
,
δ
γ
β
,, )= )];(3)(5,7))(
3
8
(5[
8
1552443322
αβχαβχδαβαδ
−+−+−−
;)1( 2,0
RSQR
Em
+
+=
α
;)1( 2,0
RSQR ErEm
+
+
+=
β
;
)1(2
αβ
α
χ
−
−
=
)2(
χ
α
δ
+= .
Stroke volume SV is calculated by an equation as given below:
SV = PV3+ PV4=S· (QR+RS)2· f1(
α
)· [f2(
α
)+f3(
α
,
δ
γ
β
,, )+f4(
α
,
δ
γ
β
,, )] (ml) (5)
The minute stroke is computed as follows:
МV = SV· HR (l/min) (6)
In similar way calculated are other phase-related volumes of blood as listed below:
PV1 – volume of blood entering the ventricle in premature diastole;
PV2 – volume of blood entering the ventricle in atrial systole;
PV5 – volume of blood pumped by ascending aorta as peristaltic pump.
So, the main parameters in hemodynamics are 7 volumes of blood entering or leaving the
heart in different heart cycle phases. They are as follows: stroke volume SV, minute volume
MV, two diastolic phase-related volumes PV1 and PV2, two systolic phase-related volumes
PV3 and PV4, and PV5 as volume of blood pumped by the aorta.
The authors of this theory in their researches utilized relative phase volumes denoted by
RV. Each relative phase volume is that expressed as a percentage of stroke volume SV.
These relative parameters demonstrate contributions of each phase process to the formation
of the stroke volume in general.
The above hemodynamic parameters should be used mainly in order to evaluate eventual
deviations from their normal values, if any. The limits of normal values of hemodynamic
parameters are not conditional, and they have their respective calculated values.
With respect to the normal values (the required parameters) in hemodynamics, they have
been taken on the basis of the known data on ECG waves, intervals and segments for adults
from the literature sources as given below:
1. The upper and lower limit of the QRS complex values:
Control of Cardiovascular System
9
QRSmax = 0.1 s. ; QRSmin = 0.08 s.
2. The upper and lower limit of the RS complex values:
RSmax = 0.05 s. ; RSmin = 0.035 s.
3. The normal value of interval QT in every specific cardiac cycle is determined from the
Bazett formula as follows:
QT = 0.37 RR0.5 , s (male); (7)
QT = 0.4 RR0.5 , s (female) . (8)
4. Normal value PQсег. is calculated from a formula as indicated below:
PQсег. = 1 / (10-6 638,44 HR2 + 9,0787) s (9)
This equation has been produced according to the method of approximation of normal
values PQсег., as known from the sources, considering their dependence on heart rate (HR).
These values are used as initial values for calculations of an individual range of normal
values of volumetric parameters in hemodynamics considering individual patient cases. In
practice, for a better visualization of the data, it should be recommended to present them
not only numerically but also graphically, as bar charts, as shown in Figure 4 herein. In the
latter case, it is convenient to indicate the deviations from the normal value limits of the
actually calculated values of hemodynamic parameters as percentage.
For example. On Figure 4 a), b), c) the result of hemodynamic parameters PV2 measuring -
volume of blood entering the ventricle in atrial systole- is displayed as follows. Figure 4 a)
in column "Blood volumes" shows the result of measuring 18,31 (ml). The second column "%
of stroke volume" shows the deviation from the norm. It is 0% here. For quick associative
perception of both these values and rapid highlighting of going beyond the bounds of norm
parameter, there exists a dark green field with red light indicator to the right of this number
in the column "indicators of measurement results". On the left and right sides of the dark
green field we see the values of individual range of this hemodynamic parameter, calculated
using equation 7, 8, 9. In this case, it is from 15.26 to 35,13 ml. Measured parameter of 18,31
ml is in the middle of the range, which corresponds to the 0% deviation from the norm. And
the red light indicator that corresponds to this value is on the dark green background. Light
green field - is a bound of "norm - pathology". Sides of this field correspond to excess or
deficiency of more than 30% of norm. More than 30% excess requires special attention to the
patient. As a rule, such patients needs hospital care. Figure 4 b) shows another patient’s
result, PV2 = 12,85 ml, and this result goes 15.84% beyond patient’s individual norm 15,26 ...
35.13 ml. In this case red light indicates lack of blood volume, rather than redundancy.
Lower (upper) than 30% value, but lower (upper) than normal value corridor, denotes
further out-patient treatment for this patient. Fig. 4 c) shows a third patient with PV2 = 47,00
ml value, which goes 76.91% beyond his individual norm 10,72 ... 26.13 ml. Red light
indicates the redundancy of blood volume. This patient should be examined by cardiac cycle
phase analysis to identify the root causes of the disease. It’s possible to identify these causes
using ECG and RHEO for phase compensation mechanism of the cardio-vascular system
determination.
The Cardiovascular System – Physiology, Diagnostics and Clinical Implications
10
а) b) c)
Fig. 4. Displayed measured phase-related values and their qualitative representation as bar
charts, with reference to normal values. This figure gives three different measuring cases
The values of phase-related blood volumes are influenced by the mechanism of
compensation existing in the cardiovascular system[6]. This mechanism is responsible for
the maintenance of the hemodynamic parameters within their respective norms. If any
parameter goes far beyond its norm, it means that it is an indication of physiological
problems of the respective phase process. In this case, the function in the next phase
compensates for the changes in the functioning of the problematic phase[6]. It is the just the
case with sportsmen whose cardiovascular system shows the proper performance.
Physical exercise may cause a deficiency in diastolic volumes of blood by more than 500
%.[4] Under the circumstances, the systolic phases undertake to compensate for the above
deficiency. For this purpose, the mechanisms may be involved, the manifestations of which
cannot be found even in a pathology case. Upon stress relieving, 1 minute later, all phase-
related volumes are normalized again. This kind of the performance of the cardiovascular
system hinders an identification of the cause of pathology at early stages for those who are
not professional athletes.
As a rule, deviations due to pathology exceed the norm by more than 30 %. Patients, who
receive their treatment at cardiology hospital, show sometimes deviations of 50 % and over.
The only way to find the primary cause of any pathology, based on the manifestation of the
compensation mechanism, can be a thorough analysis of the actual cause-relationship in
every individual case.
The phase-related volumetric parameters in hemodynamics are the most informative
characteristics of the performance of the cardiovascular system since they are capable of
Control of Cardiovascular System
11
reflecting the coordinated operation of the heart and the associated blood vessels. Knowing
their ratios and considering the actual anatomic and functional status of the heart and the
blood vessels in every phase, we can produce very reliably a diagnosis of the actual status of
the blood circulation system, reveal pathology and control the efficiency of therapy, if
required.
The above mentioned evidence is really of fundamental importance. It should be taken into
account when making diagnosis.
2.2 Mechanism of regulation of systolic pressure
The above mentioned main volumetric parameters should be complemented by another
one: it is arterial pressure (AP). The cardiovascular system has its own mechanism to
provide separate regulation of the systolic and diastolic pressures (AP)[8]. A narrowing in
sectional areas of the blood vessels in total leads to a displacement of a certain volume of
blood that is symbolized by ΔV. The displacement volume enters the ventricles in premature
diastole phase T – P. During myocardium contraction phase R – S, the same volume is
displaced via the closed aortic valve into the aorta. Actually, before the ejection of stroke
volume SV into aorta, the total of displacement volume ΔV enters the aorta. Therefore, it is
that the R – S phase, when ΔV can be ejected into the aorta, is preceded by that phase when
the motion of the entire mass of blood is actuated, and this preceding phase is the Q – R
interval, when the contraction of the septum occurs. It is just the phase when the blood flow
becomes its directed vortex motion within the ventricle. Displacement volume ΔV
contributes to moving against the total increased resistance of the blood vessels in the next
phase which shows rapid blood ejection.
The blood circulation scheme is shown in Figure 5 herein. The anatomy of the heart is
designed in such a way so that the displacement blood can penetrate without hindrance
through the closed arteric valve into the aorta. It is determined not only by the configuration
of the valves but also the mechanism of the contraction of the heart chambers that consists of
three phases. Phase one among them is the contraction of the septum. Phase two provides
for the contraction of the ventricle walls. Phase three is the phase of tension. The processes
occurring therein are responsible for spinning the blood flows so that the penetration of the
displacement blood through the closed valves into the aorta is assisted. Under normal
conditions, when there is no displacement volume ΔV available, and, as a consequence, no
penetration is required, upon completion of the phase of tension, stroke volume SV residing
in the heart is supplied into the aorta. In this case, volume SV added to the volume of blood
residing in the aorta creates the systolic pressure that produces a difference in pressures
between the aorta and the periphery. Such mechanism required to overcome an increased
blood flow resistance operates cyclically till the cause of blood vessel constriction
disappears. The processes described above are typical for the mechanism of regulation of
the diastolic arterial pressure. Various Rheogram curve shapes reflect this mechanism.
The anatomy design of the heart is determined by the phase mechanism of hemodynamics,
i.e., the mechanism of the regulation of the diastolic pressure. This mechanism is responsible
for elimination of general vasoconstriction difficulties in blood circulation. Causes of the
said vasoconstriction cannot be diagnostically identified in this case.
The Cardiovascular System – Physiology, Diagnostics and Clinical Implications
12
Fig. 5. а) Blood circulation scheme considering changes in blood vessel resistance. b) AP
changes in aorta; c) Changes in AP identifiable on Rheo curve in phase of tension S-L, in
proportion to displacement volume ∆V in blood vessel constriction
With synchronous recording of an ECG and a Rheo from the ascending aorta, provided that
they are synchronized at wave point S on the ECG curve, the process of the regulation of
diastolic pressure may manifest itself as an early AP rise on the respective Rheo curve in
phases R – S and S – L.
2.3 Mechanism of regulation of systolic pressure
The mechanism of regulation of the systolic pressure differs significantly from that
responsible for the regulation of the diastolic pressure. It has the function to provide a pre-
requisite to the blood circulation in the blood vessels due to a difference in pressures
between the aorta and veins and manage the transportation of an oxygen quantity as
required by tissues and cells. For these purposes, several biophysical processes are engaged.
First and foremost, we should mention the process of myocardium contraction in tension
phase S – L. The tension created in this phase presets the velocity of the blood flow during
the blood ejection phase. Therefore, the initial velocity of the blood flow in the aorta
depends on the degree of the myocardium tension.
The second important process is the phenomenon of an increase in the systolic pressure
during the propagation of the AP wave throughout the arteries[1]. The systolic pressure in
the aorta and that in the brachial artery may considerably differ from each other. On the
Control of Cardiovascular System
13
normal conditions, the pressure increase is provided by the pumping function of the blood
vessels and their increasing resistance.
An additional point to emphasize is that there is another biophysical phenomenon
connected with hemodynamics. It is cavitation in blood that promotes blood volume
expansion[2]. It may spread over very quickly within one heart cycle and is capable of
considerably expanding the blood volume.
The cause of the systolic pressure buildup is a reduction in blood supply of some viscera. The
pressure buildup is aimed at elimination of hindrances in blood supply in order to maintain
the proper blood circulation. The blood supply mechanism of some viscera provides for
protection from arterial overpressures. In the first place, the protection of the cerebral blood
supply system should be mentioned. The cerebral blood vessels are anatomically connected
with veins. During an increase in AP, the venous drainage is hindered, affecting the blood
vessel constriction and limiting in such a way an excessive AP increase.
If for some reason a viscus is not sufficiently supplied with blood, it leads to a systolic AP
growth. The venous drainage will be hindered. The first symptoms of this problem could be
edema of legs. To solve this problem, required should be elimination of the cause of the
improper blood supply to the affected viscus that should decrease the AP and,
subsequently, normalize the venous drainage.
3. Phase structure of heart cycle according to ECG curve
Every heart cycle consists of 10 phases. Each phase undertakes its own functions[7].
The complete phase structure of an ECG is shown in Figure 6 herein.
Phase of atrial systole Pн – Pк;
Phase of closing of atrioventricular valve Pк – Q;
Phase of contraction of septum Q – R;
Phase of contraction of ventricle walls R – S;
Phase of tension of myocardium S – L;
Phase of rapid ejection L – j;
Phase of slow ejection j - Tн ;
Phase of buildup of maximum systolic pressure in aorta Tн - Tк,;
Phase of closing of aortic valve Tк - Uн;
Phase of premature diastole of ventricles Uн - Pн .
Each phase serves its purpose. But the phases may be grouped in a manner as follows:
Group of diastol4ic phases which are responsible for blood supply to the ventricles:
Phase of premature diastole of ventricles Uн - Pн;
Phase of atrial systole Pн – Pк;
Phase of closing of atrioventricular valve Pк – Q.
The phase of premature diastole contains a period of time equal to the duration of wave U
which reflects an intensive filling of the coronary vessels with blood. It occurs in
synchronism with filling of the ventricles.
The diastolic phases are described as hemodynamic values PV1 and PV2.
The Cardiovascular System – Physiology, Diagnostics and Clinical Implications
14
Fig. 6. Phase structure of ECG recorded from ascending aorta; Phase of atrial systole Pн – Pк;
Phase of closing of atrioventricular valve Pк – Q; Phase of contraction of septum Q – R;
Phase of contraction of ventricle walls R – S; Phase of tension of myocardium S – L; Phase of
rapid ejection L – j; Phase of slow ejection j - Tн ; Phase of buildup of maximum systolic
pressure in aorta Tн - Tк,; Phase of closing of aortic valve Tк - Uн; Phase of premature diastole
of ventricles Uн - Pн
Group of systolic phases which provide for the conditions for the proper blood circulation.
They can be divided into subgroups undertaking certain functions as given below:
Subgroup responsible for diastolic AP regulation:
Phase of contraction of septum Q – R;
Phase of contraction of ventricle walls R – S;
Phase of tension of myocardium S – L (partially).
Subgroup responsible for systolic AP regulation:
Phase of tension of myocardium S – L,
Phase of rapid ejection L – j.
Subgroup responsible for aorta pumping function control:
Phase of slow ejection j - Tн ;
Phase of buildup of maximum systolic pressure in aorta Tн - Tк,;
Control of Cardiovascular System
15
Phase of closing of aortic valve Tк - Uн;
The given systolic phases are characterized by hemodynamic values PV3, PV4 and SV.
Hemodynamic value MV is an indication of a blood flow rate.
Hemodynamic parameter PV5 shows what share of blood is pumped by the aorta operating
as a peristaltic pump during the ejection of blood from the ventricles.
It should be noted that phase of slow ejection j - Tн is a time when the stroke volume of
blood is distributed throughout the large blood vessel, i.e., the time of the aorta expansion.
As our investigations demonstrate, in case of improper elasticity of the aorta this period of
time is prolonged.
4. Phase structure of heart cycle on RHEO curve
An electrocardiogram reflects the most important hemodynamic processes. According to an
ECG curve, it is possible to identify an intensity of the contraction of the muscles of the
respective segment in the cardiovascular system by analyzing inflection points in the
respective heart cycle phase and considering the respective phase amplitudes. However, it is
required to understand how the flow of blood changes. For this purpose, rheography should
be used. A rheogram shows changes in the arterial pressure. An ECG and a RHEO are
produced by using signals of different nature. To record an ECG used is electric potential,
and for RHEOgraphy employed are changes in amplitudes of high-frequency AC under the
influence of changing blood volumes in blood circulation, which produce changes in the
conductivity within the space between the recording electrodes.
There is no AP increase in myocardium tension phase S – L. The aortic valve opens at the
moment denoted as L. The slope ratio of RHEO in phase of rapid ejection L – j is descriptive
of the velocity of stroke volume travel, and, finally, decisive in governing the systolic AP.
5. Criteria for recording phases on ECG, Rheo and their derivatives
When considering an ECG as a complex signal, it should be pointed out that it consists of a
number of single-period in-series sinusoidal signals connected. It is referred to a re-
distribution of energy in bio systems in a not a stepwise, but sinusoidal way, showing half-
periods as follows: energy increase, retardation, attenuation and development. Transition
points of these processes should be at the same time the points of inflection of energy
functions which are shown by the first derivative at their extrema. Similar processes occur in
the cardiovascular system control. Figure 8 represents a schematic model of an ECG
comprising the said in-series single-period sinusoidal waves.
Should an ECG curve be differentiated, 10 extrema on the derivative can be identified which
correspond to the boundaries of the respective phases of the heart cycle. It should be
mentioned that each phase shall be determined by the same criterion, i.e., by the respective
local extremum on the derivative curve. Since a wavefront steepness varies, the respective
amplitudes of the derivative extrema differ. The ECG phases are equivalent to those of
energy variations responsible for the heart control. For illustration purposes, it is better to
use graphic differentiation.
The Cardiovascular System – Physiology, Diagnostics and Clinical Implications
16
Fig. 7. Phase structure of RHEO recorded from ascending aorta
Control of Cardiovascular System
17
Fig. 8. Schematic model of ECG comprising in-series single-period sinusoidal variations
It is just the graphic differentiation that is capable of clearly illustrating all specific points of
such complex signal like an ECG signal. Whereas it is practically impossible to detect
visually on an ECG curve the inflection points, they can be easy identified on the derivative
by local extrema without error. Figure 9 gives an ECG curve and its first derivative. It is
evident that point P on the ECG curve corresponds to point Р on the derivative that is found
by the respective local extremum. In the same way point T should be identified. It is of great
importance to localize point S. There are no other methods capable of identifying this point.
Fig. 9. Graphic differentiation of ECG curve. Shown are an ECG and its first derivative.
Wave points on the ECG curve are its inflection points that correspond to the local extrema
on the derivative
The Cardiovascular System – Physiology, Diagnostics and Clinical Implications
18
It is just the derivative that is capable of recognizing point S very clearly by the respective
local positive extremum. The proposed procedure of identifying the above mentioned key
points makes possible to develop a computer-assisted technology for measuring durations
of every heart cycle phase.
For the same purpose, the second derivative may be used, too, but in this case there is no
need to do it since the informative content of the heart cycle phase identifiable criteria with
utilization of the first derivative is quite sufficient.
Some real ECG curves recorded from the aorta are given in Figure 10 herein. Wave points P,
Q, S and T are marked on the curves which are reliably found according to the first
derivative.
Figure 11 herein illustrates real ECG signals and the first derivative of this ECG. The ECG
shape shown in this Figure is close to an ideal one. It is the matter of fact that in practice we
deal with such ECG curves that significantly differ from the ideal ECG type represented
herein. Therefore, it is the differentiation only that can very reliably identify the boundaries
of every phase in every heart cycle.
point P point Q
point S point T
Fig. 10. Key points P, Q, S and T on ECG curve, characterizing the respective phases of the
heart cycle and corresponding to the respective local extrema on the derivative
Control of Cardiovascular System
19
Fig. 11. Identification of phases on an ECG curve with use of the first derivative graph
6. Functions of cardiovascular system to be evaluated on the basis of heart
cycle phase analysis
The complex of the functions of the cardiovascular system is a combination of the functions
in every individual heart cycle phase. There is a certain logic design available explaining
this. Every phase has its own significance but the basis of all phases is the mechanism of
contraction or relaxation of muscles. Should metabolic disturbance in a muscle occur, its
contraction or relaxation will be diminished. In this case, every next phase will undertake to
compensate for this malfunction by enhancing its activity. The phase analysis gives us a clue
to clearly identifying such imbalances.
In this connection, the following functions of the cardiovascular system should be
mentioned:
№ Function Regulated parameter
1 Contraction of septum diastolic AP in the aorta
2 Contraction of myocardium; diastolic AP in the aorta
3 Tension of myocardium muscles systolic AP in the aorta
4 Elasticity of aorta Maintain blood flow structure
5 condition of venous flow
6 condition of pulmonary function
7 whether pre-stroke conditions
are available or not
8 problems with coronary blood
flow
Table 1. Main functions and regulated parameters of cardiovascular system
The Cardiovascular System – Physiology, Diagnostics and Clinical Implications
20
Figure 12 given below demonstrates the relations between the heart cycle phases on an ECG
& RHEO and the respective functions of the cardiovascular system. Although it seems that
the hemodynamic mechanism as a whole and the performance of the cardiovascular system
are very complicated, the heart cycle phase analysis allows establishing of cause-effect
relationship of any pathology in every individual case within the shortest time. It is very
important that it makes possible to detect the primary cause of a cardiac disease.
Figure 13 displays anatomic segments of the heart and their respective functions in every
heart cycle phase.
Fig. 12. Diagnosable heart segments with their functions and their relations to heart cycle
phases on ECG and RHEO
7. Conclusion
Making progress in research of biophysical processes of the formation of the hemodynamic
mechanism is possible only when theoretical models are tested for their compliance in
practice, i.e., a model to be validated should show in practice its compliance with the
requirements for all simulated functions. The results of many years’ researches accumulated
by our R & D team made it possible not only to develop an innovative, radically new theory
of the heart cycle phase analysis but also provide metrology for such field of medical science
as cardiology[4]. We have succeeded in solving the problem of indirect measuring
technologies for hemodynamic parameters, including phase-related volumes, by the
mathematical modeling.
Control of Cardiovascular System
21
Fig. 13. Anatomical design of the heart predetermined by the required functions in every
heart cycle
Our clinical studies offer a clearer view of how many difficult issues associated with
biochemical reactions responsible for the stable maintenance of the hemodynamic and the
entire performance of the cardiovascular system can be answered. This is a pre-requisite to
developing and validating of new high-efficient therapy methods.
Hereby the authors would like to express their hope that within the nearest future we shall
deal with a new research field, which is cardiometry. The basis of this science should create
mathematical modeling and instrumentation technology.
8. Acknowledgements
The well-known recipe for success in any work is to create a team of like-minded researches
working for the same cause. If the concept of their work is that the point of life is work, and
if the work results encourage and motivate them, then success is assured. But our life is able
to make its corrections. We regret to say that, one of the authors of our discovery, who
originated the idea of the “third” mode of flow, died. We speak about Gustav M.
Poyedintsev, a great mathematician and scientist. Our last book Theoretical Principles of Heart
Cycle Phase Analysis published in 2007 was devoted to the memory of him and his work.
The other sad news has been received by us when we were working on this Chapter: Jaana
Koponen-Kolmakova, another member of our R & D team, has departed this life. She was
really an outstanding person! She was the General Manager of the Company
CARDIOCODE-Finland. She remains in our memory for ever.
The Cardiovascular System – Physiology, Diagnostics and Clinical Implications
22
During our work we meet a lot of people who dedicate their life to science. We always enjoy
communicating with them. This is a sort of people who deserve our special recognition and
respect.
9. References
[1] Caro, C.; Padley, T.; Shroter, R. & Sid, W. (1981) Blood Circulation Mechanics. Mir. M.
(fig.12.14).
[2] Goncharenko, A. & Goncharenko, S. (2005) Extrasensory Capabilities of Heart. Magazin
“Technika Molodyozhi”, No. 5, ISSN 0320 – 331 Х Rosen, P. (1969) The Principle of
Optimization in Biology. Mir.
[3] М. Rudenko, M.; Voronova, O. & Zernov. V. (2009). Theoretical Principles of Heart Cycle
Phase Analysis. Fouqué Literaturverlag. ISBN 978-3-937909-57-8, Frankfurt a/M.
München London - New York.
[4] Voronova, O. (1995). Development of Models & Algorithms of Automated Transport Function
of The Cardiovascular System. Doctorate Thesis. Prepared by Mrs. O.K. Voronova,
Ph.D., VGTU, Voronezh.
[5] Voronova, O. & Poyedintsev, G. Patent № 94031904 (RF). Method of Determination of the
Functional Status of the Left Sections of the Heart & their Associated Large Blood Vessels.
[6] Rudenko, M.; Voronova, O. & Zernov. V. Innovation in cardiology. A new diagnostic
standard establishing criteria of quantitative & qualitative evaluation of main
parameters of the cardiac & cardiovascular system according to ECG and Rheo
based on cardiac cycle phase analysis (for concurrent single-channel recording of
cardiac signals from ascending aorta). (npre.2009.3667.1). Nature Precedings.
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