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Fluorescence optical diffusion tomography using multiple-frequency data
Journal of the Optical Society of America A
Abstract
A method is presented for fluorescence optical diffusion tomography in turbid media using multiple-frequency data. The method uses a frequency-domain diffusion equation model to reconstruct the fluorescent yield and lifetime by means of a Bayesian framework and an efficient, nonlinear optimizer. The method is demonstrated by using simulations and laboratory experiments to show that reconstruction quality can be improved in certain problems through the use of more than one frequency. A broadly applicable mutual information performance metric is also presented and used to investigate the advantages of using multiple modulation frequencies compared with using only one.
... A coupled diffusion model was used to simulate fluorescence propagation in a diffusive media. 35 The propagation of excitation light is modeled by Eq. (1); the transport of excited fluorescence by Eq. (2). ...
... Quantum efficiency, absorption coefficient, and lifetime of fluorophore are represented by η, μ fl , and τ , respectively, and c is the velocity of light in the medium. 35 We employed the software package NIRFAST to model photon propagation using a finite element model (FEM) for the forward model and to perform reconstructions. 36 The inverse model was performed with the following Tikhonov minimization function equation: 23 ...
... Moreover, the depth of scattering and absorption changes in the tissue can be derived from time-resolved data [14,25,26,40]. The advantage of time-resolved detection is obvious if fluorescence is to be detected [11,15,17,30,37,39]. The fluorescence lifetime of a fluorophore is, to a first approximation, independent of its concentration, but depends on the local environment and the binding state [24]. ...
... Clinical applications of optical tomography techniques are currently at the stage of tests on human subjects [19,22,27,41]. Frequency-domain instruments using modulation techniques [10,29,30] and time-domain instruments using time-correlated single-photon counting (TCSPC) [18,34,38,42] are both being evaluated. It is commonly believed that frequency-domain techniques achieve shorter acquisition times, whereas time-domain techniques deliver a better absolute accuracy of optical tissue properties. ...
We present a multi-dimensional TCSPC technique that combines multi-detector and multiplexing capability, and records fast and virtually unlimited sequences of time-of-flight distributions. The system consists of four fully parallel TCSPC channels. Each channel records simultaneously in up to eight detection channels. Up to four lasers and 32 source positions can be multiplexed. The total count rate is up to 4 x 107 photons per second. Time-of-flight sequences can be recorded with a resolution of 50 to 100 ms per curve. The system is operated within a single personal computer.
... is referred to as the TD fluorescence diffuse optical tomography (FDOT). [9][10][11] In addition to the TD measurement, measurements for continuous waves (CW) 12,13 and frequency domain (FD) [14][15][16] are known. The TD measurement often measures the temporal point-spread function (TPSF). ...
Light propagation through diffusive media can be described by the diffusion equation in a space–time domain. Furthermore, fluorescence can be described by a system of coupled diffusion equations. This paper analyzes time-domain measurements. In particular, the temporal point-spread function is measured at the boundary of a diffusive medium. Moreover, the temporal profile of fluorescence is considered. In both cases, we refer to the maximum temporal position of measured light as the peak time. In this paper, we provide proofs of the existence and uniqueness of the peak time and give explicit expressions of the peak time. The relationship between the peak time and the object position in a medium is clarified.
... We understand the concept of measurements as a function of known translated position from mutual information (see, for the example, the appendix of [10]). If we know the background optical arrangement, i.e., the cavity and source (wavelength), and measurements are made at a known set of positions (perhaps just the relative change in position), then useful information about the object (the film) can be obtained. ...
A set of power measurements as a function of controlled nanopositioner movement of a planar film arrangement in a standing wave field is presented as a means to obtain the thicknesses and the dielectric constants to a precision dictated by noise in an exciting laser beam and the positioning and detector process, all of which can be refined with averaging. From a mutual information perspective, knowing the set of positions at which measurements are performed adds information. While applicable to any arrangement of planar films, the implementation considered involves thin transmissive membranes, as are employed in applications such as optomechanics. We show that measured power data as a function of object position provides sensitivity to the film refractive index and far-subwavelength thickness. Use of a cost function allows iterative retrieval of the film parameters, and a multi-resolution framework is described as a computationally efficient procedure. The approach is complementary to ellipsometry and could play an important role in routine film characterization studies for fields involving solid state material processing, as is common in the semiconductor device field.
... FDDOT imaging method was studied in literature (Doulgerakis et al. 2019;Brian et al. 1997;Pogue et al. 1997;Ko et al. 2007;Ren et al. 2006;Kazanci 2021). Multi-frequency technique was first mentioned and used early in optical diffusion tomography (Milstein et al. 2004). In that work, basically three different modulation frequencies were used, modeled in simulations and tested with experimental method. ...
Diffuse optical tomography (DOT) modality uses diffusion equation solution of low power laser distribution in the imaging tissue. DOT method has three main running mode and three geometric subbranches. Run modes are: Continuous Wave (CW), Time Resolved (TR) and Frequency Domain (FD) modes. These run modes might have transmission-through, back-reflected or ring geometry depend on the source and detector placements on tissue surface. In this work, we tested our novel imaging method on the frequency-domain back-reflected DOT simulation model. Our novelty is: selecting a great number of multi-frequency data in the wide frequency spectrum which was not tested before in the literature. Most of the literature works consist of narrow frequency band with the limited number of frequencies such as maximum 12 multi-frequency-data which cover from 100 up to 700 MHz. In our work, we tested and compared reconstructed inclusion images generated by our 500 wide spectrum multi-frequency data versus reconstructed inclusion images generated by 20 narrow band multi-frequency data which was generally used in FD DOT studies. We observed that our novel imaging method which used wide spectrum multi-frequency data is superior to the traditionally used narrow-band multi-frequency method based on the reconstructed inclusion image localization errors. Since most of the homogenous geometry consists of fat tissue, we selected background absorption coefficient µa = 0.2 cm−1 and tissue scattering coefficient \({\upmu }\)s = 80 cm−1 for 800 nm laser source wavelength. Three-dimensional cubic imaging simulation media has 75-mm grid sizes in each direction. Two different imaging scenarios were tested. In the first scenario, one inclusion with absorption coefficient µa = 0.7 cm−1 was put inside the three-dimensional imaging geometry at 27 mm depth. In the second scenario one inclusion with absorption coefficient µa = 0.7 cm−1 was embedded in 48 mm depth location. Inclusions are cubic and they have 6 mm xyz length at each direction.
... A similar approach was published in [24] to retrieve the fluorescence lifetime distribution. A related idea is to directly use frequency-domain technology [25][26][27] to retrieve optical properties or fluorescence lifetime [28,29]. These reconstruction approaches based on solving the inverse problem in frequency domain are a good alternative to temporal windows but are not equivalent since only MHz order frequencies are used. ...
Time-resolved diffuse optical tomography is a technique used to recover the optical properties of an unknown diffusive medium by solving an ill-posed inverse problem. In time-domain, reconstructions based on datatypes are used for their computational efficiency. In practice, most used datatypes are temporal windows and Fourier transform. Nevertheless, neither theoretical nor numerical studies assessing different datatypes have been clearly expressed. In this paper, we propose an overview and a new process to compute efficiently a long set of temporal windows in order to perform diffuse optical tomography. We did a theoretical comparison of these large set of temporal windows. We also did simulations in a reflectance geometry with a spherical inclusion at different depths. The results are presented in terms of inclusion localization and its absorption coefficient recovery. We show that (1) the new windows computed with the developed method improve inclusion localization for inclusions at deep layers, (2) inclusion absorption quantification is improved at all depths and, (3) in some cases these windows can be equivalent to frequency based reconstruction at GHz order.
... A similar approach was published in [208] to retrieve the fluorescence lifetime distribution. A related idea is to directly use frequency-domain technology [55,175,89] to retrieve optical properties or fluorescence lifetime [207,148]. These reconstruction approaches based on solving the inverse problem in frequency domain are a good alternative to temporal windows but are not equivalent since only MHz order frequencies are used. ...
In this thesis I developed new techniques for diffuse optical tomography. In the first part, I developed a novel method to compute datatypes for diffuse optical tomography. With this new method a larger set of datatypes can be computed and noise is less correlated. Results show that better resolution in depth is obtained in comparison with the state-of-the-art. Moreover, quantification of absorption is improved significantly. In the second part, I developed total variation regularization method for diffuse optical tomography in irregular meshes. After, I performed brain motor cortex activation experiments in adult subjects with the collaboration of Politecnico di Milano. Previously developed algorithms were applied to that measurements obtaining time-series hemodynamic reconstructions of motor cortex. Finally, I coordinated the largest open dataset in diffuse optics composed by the measurements done within the BitMap network.
... For the inverse problem, the FDOT scheme for each type of the measurement are proposed such as CW [12,35,9,44], FD [32,22,7,26] and TD [10,21,46,13,29,37]. We can refer to [2,38] for the choice of data types in time-resolved FDOT. ...
The time-domain fluorescence diffuse optical tomography (FDOT) is theoretically and numerically investigated based on analytic expressions for a three space dimensional diffusion model. The emission light is analytically calculated by an initial boundary value problem for coupled diffusion equations in the half space. The inverse problem of FDOT is to recover the distribution of fluorophores in biological tissue, which is solved using the time-resolved measurement data on the boundary surface. We identify the location of a fluorescence target by assuming that it has a cuboidal shape. The aim of this paper is to propose a strategy which is a combination of of theoretical arguments and numerical arguments for a inversion, which enables to obtain a stable inversion and accelerate the speed of convergence. Its effectivity and performance are tested numerically using simulated data and experimental data obtained from an ex vivo beef phantom.
... The optical parameters (photon absorption coefficient and scattering coefficient) of each node in imaging space are the key factors that affect the reconstruction effect of FMT, and are the sufficient conditions that affect the photon propagation model and the accuracy of the reconstruction method [86][87][88][89]. The classical FMT method assumes imaging space as homogeneous space, that is, the optical parameters of each point in imaging space are the same. ...
Abstract Molecular imaging (MI) is a novel imaging discipline that has been continuously developed in recent years. It combines biochemistry, multimodal imaging, biomathematics, bioinformatics, cell & molecular physiology, biophysics, and pharmacology, and it provides a new technology platform for the early diagnosis and quantitative analysis of diseases, treatment monitoring and evaluation, and the development of comprehensive physiology. Fluorescence Molecular Tomography (FMT) is a type of optical imaging modality in MI that captures the three-dimensional distribution of fluorescence within a biological tissue generated by a specific molecule of fluorescent material within a biological tissue. Compared with other optical molecular imaging methods, FMT has the characteristics of high sensitivity, low cost, and safety and reliability. It has become the research frontier and research hotspot of optical molecular imaging technology. This paper took an overview of the recent methodology advances in FMT, mainly focused on the photon propagation model of FMT based on the radiative transfer equation (RTE), and the reconstruction problem solution consist of forward problem and inverse problem. We introduce the detailed technologies utilized in reconstruction of FMT. Finally, the challenges in FMT were discussed. This survey aims at summarizing current research hotspots in methodology of FMT, from which future research may benefit.
... Le contenu informationnel de cette modalité permet de séparer les contributions d'absorption et de diffusion en réduisant la diaphonie (nous la présenterons par la suite dans notre étude) dans les images optiques [62]. Généralement, les mesures fréquentielles sont acquises avec des systèmes à multiples fréquences de modulation [65,66,67,68]. L'acquisition à plusieurs fréquences sur une certaine bande spectrale permet de bénéficier de tous les avantages de ce régime [67]. ...
Diffuse Optical Tomography (DOT) is a new medical imaging technique used to reconstruct the optical properties of biological tissues in order to detect cancerous tumors. However, this is an ill-posed and under-determined inverse problem. The work of this thesis deals with the resolution of this problem using the radiative transfer equation as a forward model of light propagation. The sensitivity analysis showed that the anisotropy factor g of the Henyey-Greenstein phase function is the most sensitive parameter of the forward model followed by the scattering coefficient μs and then the absorption coefficient μa . In a first step, a Gauss-Newton algorithm was implemented using the sensitivity functions. However, this algorithm allows to estimate a very limited number of the optical parameters (assumed to be constant in space). In a second step, a Quasi-Newton algorithm was developed to
reconstruct the spatial distributions of the optical properties. The gradient of the objective function was efficiently computed by the adjoint method through the Lagrangian formalism with a Multi-frequency approach. The reconstructed images was obtained from simulated boundary data. The g factor was reconstructed as a new optical contrast agent in DOT and the crosstalk problem between this factor and μ s has been studied. The results showed that the algorithm is efficient to reconstruct in 2D and 3D one or several tumor inclusions having different shapes. The quality of the reconstructed images was examined according to several parameters : the number of frequencies, the crosstalk, the contrast level (Inclusion / Background), the noise level and finally the tumor inclusions positions.
Keywords: Diffuse optical tomography ; radiative transfer ; inverse problem ; adjoint method ; reconstruction algorithm ; optical properties.
... In the diffuse optics community, theoretical performance prediction for system design or optimization is usually accomplished with Monte Carlo simulation [6,9,10] or with singular value decomposition (SVD) [11][12][13][14]. The former can be very time-and resource-intensive, and the results are valid only for the particular inversion algorithm simulated. ...
Spatial frequency domain imaging (SFDI) is a wide-field diffuse optical imaging modality that has attracted considerable interest in recent years. Typically, diffuse reflectance measurements of spatially modulated light are used to quantify the optical absorption and reduced scattering coefficients of tissue, and with these, chromophore concentrations are extracted. However, uncertainties in estimated absorption and reduced scattering coefficients are rarely reported, and we know of no method capable of providing these when look-up table (LUT) algorithms are used to recover the optical properties. We present a method to generate optical property uncertainty estimates from knowledge of diffuse reflectance measurement errors. By employing the Cramér-Rao bound, we can quickly and efficiently explore theoretical SFDI performance as a function of spatial frequencies and sample optical properties, allowing us to optimize spatial frequency selection for a given application. In practice, we can also obtain useful uncertainty estimates for optical properties recovered with a two-frequency LUT algorithm, as we demonstrate with tissue-simulating phantom and in vivo experiments. Finally, we illustrate how absorption coefficient uncertainties can be propagated forward to yield uncertainties for chromophore concentrations, which could significantly impact the interpretation of experimental results.
... Four kinds of materials were used to represent lungs, heart, bone and muscle. The optical parameters for each kind of material are presented in the reference 8, while the excitation and emission wavelength corresponding to the optical parameters are 780nm and 830nm, respectively 20 . The red dots in Fig. 1(b) denote different locations of the excitation light sources. ...
... Four kinds of materials were used to represent lungs (L), heart (H), bone (B) and muscle (M). The optical parameters for each kind of material are presented in Table 2, while the excitation and emission wavelength corresponding to the optical parameters are 780nm and 830nm, respectively [37]. The black dots in Fig. 2(b) denote different locations of the excitation light sources. ...
Fluorescence molecular tomography (FMT) is a promising tomographic method in preclinical research, which enables noninvasive real-time three-dimensional (3-D) visualization for in vivo studies. The ill-posedness of the FMT reconstruction problem is one of the many challenges in the studies of FMT. In this paper, we propose a l2,1-norm optimization method using a priori information, mainly the structured sparsity of the fluorescent regions for FMT reconstruction. Compared to standard sparsity methods, the structured sparsity methods are often superior in reconstruction accuracy since the structured sparsity utilizes correlations or structures of the reconstructed image. To solve the problem effectively, the Nesterov’s method was used to accelerate the computation. To evaluate the performance of the proposed l2,1-norm method, numerical phantom experiments and in vivo mouse experiments are conducted. The results show that the proposed method not only achieves accurate and desirable fluorescent source reconstruction, but also demonstrates enhanced robustness to noise.
... EKF framework was previously used to address the reconstruction of optical parameters [146][147][148]. In [146], Eppstein et al. utilized [88,89]. The reconstruction of pharmacokinetic-rate images is addressed based on maximum a posteriori (MAP) estimation together with a parametric iterative coordinate descent optimization technique similar to the approach in [149]. ...
... ii) Separation of optical properties can be achieved by frequency domain measurements, where amplitudemodulated laser sources at a single [91] or at multiple frequencies [92] are used and the amplitude demodulation and the phase shift caused by the tissue are measured. ...
... The application of multiple frequency information was further extended to other fields where it has enhanced the quality of estimation. Simulation results for reconstructing two small objects showed improvement because of the incorporation of multiple frequency data in the tomography imaging test (Milstein et al., 2004). ...
... The phantom was a cylinder, which was 20mm in diameter and 20mm in height, consisting of four kinds of materials to represent muscle (M), lungs (L), heart (H), and bone (B). The optical parameters of each kind of materials for both the excitation and emission wavelength are listed in Table 1 [27][28][29]. Figure 1(a) demonstrates a 3D view of the phantom which was discretized into 3756 nodes and 21715 tetrahedral elements using the finite-element method and Fig. 1(b) demonstrates the cross-section of the phantom in the z = 0 plane. The black dots in Fig. 1(b) represent the excitation light sources, which were modeled as isotropic point sources placed at a depth of one transport mean free path beneath the surface in the z = 0 plane. ...
Fluorescence molecular tomography (FMT), which is a promising tomographic method for in vivo small animal imaging, has many successful applications. However, FMT reconstruction is usually an ill-posed problem because only the photon distribution over the body surface is measurable. The Lp-norm regularization is generally adopted to stabilize the solution, which can be regarded as a type of a priori information of the fluorescent probe bio-distribution. When FMT is used for the early detection of tumors, an important feature is the sparsity of the fluorescent sources because tumors are usually very small and sparse at early stage. Considering this, we propose a fast and effective method with L1-norm based on sparsity adaptive subspace pursuit to solve the FMT problem in this paper. Our proposed method treats FMT problem with sparsity-promoting L1-norm as the basis pursuit problem. At each iteration, a sparsity factor that indicates the number of unknowns is estimated and updated adaptively. Then our method seeks a small index set which indicates atoms exhibiting highest correlation with the current residual, and updates the current supporting set by merging the newly selected index set. It can be regarded as a kind of sparse approximation reconstruction strategy. To evaluate our proposed method, we compare it to the iterated-shrinkage-based method with L1-norm regularization in numerical experiments. The results demonstrate that the proposed algorithm is able to obtain satisfactory reconstruction results. In addition, the proposed method is about two orders of magnitude faster compared to the iterated-shrinkage-based method. Our method is a practical and effective FMT reconstruction method.
... It was originally used in relativistic particle physics [4], and the scalar BSE has been used to study Anderson localization [5], random lasers [6], and coherent backscattering [7]. The diffusion equation, which can be derived from either the BSE [8] or the BTE [1], can effectively model the propagation of photons deep inside tissue and other heavily scattering media [9][10][11][12]. The diffusion approximation holds for highly scattering media having sufficiently low absorption, or when the albedo, the ratio of the scattering coefficient to the extinction coefficient, is almost one [7]. ...
We present a formalism for solving the scalar Bethe–Salpeter equation (BSE) in the nondiffusive regime under the ladder approximation and for an infinite randomly scattering medium having scatterers of size on the order of or larger than the wavelength. We compare the information content in a wave transport model (the BSE) with that in energy-based transport, the Boltzmann transport equation (BTE), in the spatial frequency domain. Our results suggest that when absorption dominates scatter, the intensity Green’s function from a BTE model is similar to the field correlation Green’s function from a BSE solution. When scatter dominates loss, there are significant differences between the BTE and BSE representations, and the BTE solutions appear to be smoothed versions of those from the BSE. Therefore, field correlation measurements, perhaps extracted from intensity correlations over frequency and space, offer significantly more information than a mean-intensity measurement in the weakly scattering and nondiffusive regime. Our work provides a mathematical framework for electric field correlation-based imaging methods based on the BSE that hold promise in, for example, near-surface tissue imaging.
... The phantom was a cylinder, which was 20mm in diameter and 20mm in height, consisting of four kinds of materials to represent muscle (M), lungs (L), heart (H), and bone (B). The optical parameters of each kind of materials for both the excitation and emission wavelength are listed in Table 1 [27][28][29]. Figure 1(a) demonstrates a 3D view of the phantom which was discretized into 3756 nodes and 21715 tetrahedral elements using the finite-element method and Fig. 1(b) demonstrates the cross-section of the phantom in the z = 0 plane. The black dots in Fig. 1(b) represent the excitation light sources, which were modeled as isotropic point sources placed at a depth of one transport mean free path beneath the surface in the z = 0 plane. ...
Fluorescence molecular tomography (FMT), as a promising imaging modality, can three-dimensionally locate the specific tumor position in small animals. However, it remains challenging for effective and robust reconstruction of fluorescent probe distribution in animals. In this paper, we present a novel method based on sparsity adaptive subspace pursuit (SASP) for FMT reconstruction. Some innovative strategies including subspace projection, the bottom-up sparsity adaptive approach, and backtracking technique are associated with the SASP method, which guarantees the accuracy, efficiency, and robustness for FMT reconstruction. Three numerical experiments based on a mouse-mimicking heterogeneous phantom have been performed to validate the feasibility of the SASP method. The results show that the proposed SASP method can achieve satisfactory source localization with a bias less than 1mm; the efficiency of the method is much faster than mainstream reconstruction methods; and this approach is robust even under quite ill-posed condition. Furthermore, we have applied this method to an in vivo mouse model, and the results demonstrate the feasibility of the practical FMT application with the SASP method.
... TCSPC tomography measurements have been demonstrated in phantoms (Kepshire et al 2009, Gao et al 2010 and proposed in animals (Leblond et al 2011). As an alternative to TCSPC measurements, gated detectors operating in analogue rather than in the digital single-photon counting mode, as well as gated image intensifiers coupled to chargecoupled devices (CCDs), have been implemented to alleviate image acquisition times both in phantoms (Milstein et al 2004, Soloviev et al 2007, Kumar et al 2008 and animals (Venugopal et al 2010). After each impulse of excitation light, the gated detector collects fluorescent photons over a picosecond-wide window until sufficient SNR is obtained before moving the window to sample a different portion of the photon 'time-of-flight' distribution. ...
Emerging fluorescence and bioluminescence tomography approaches have several common, yet several distinct features from established emission tomographies of PET and SPECT. Although both nuclear and optical imaging modalities involve counting of photons, nuclear imaging techniques collect the emitted high energy (100-511 keV) photons after radioactive decay of radionuclides while optical techniques count low-energy (1.5-4.1 eV) photons that are scattered and absorbed by tissues requiring models of light transport for quantitative image reconstruction. Fluorescence imaging has been recently translated into clinic demonstrating high sensitivity, modest tissue penetration depth, and fast, millisecond image acquisition times. As a consequence, the promise of quantitative optical tomography as a complement of small animal PET and SPECT remains high. In this review, we summarize the different instrumentation, methodological approaches and schema for inverse image reconstructions for optical tomography, including luminescence and fluorescence modalities, and comment on limitations and key technological advances needed for further discovery research and translation.
... We describe optical diffusion tomography (ODT) [6][7][8] with two enabling features that result in dramatic image quality improvements. Fluorescence provides contrast [9], and fluorescent sources have been incorporated into an ODT framework (FODT) [10,11]. Imaging without a scattering background emulsion and with large data sets allows accurate images to be formed only of the subject or a region of interest. ...
Despite the broad impact in medicine that optics can bring, thus far practical approaches are limited to weak scatter or near-surface monitoring. We show a method that utilizes a laser topography scan and a diffusion equation model to describe the photon transport, together with a multiresolution unstructured grid solution to the nonlinear optimization measurement functional, that overcomes these limitations. We conclude that it is possible to achieve whole body optical imaging with a resolution suitable for finding cancer nodules within an organ during surgery, with the aid of a targeted imaging agent.
... We do not claim to compare CW and time resolved fDOT systems in general since we think that a universal answer is probably out of reach. However, the proposed methodology does not restrict to the fDOT systems evaluated here and it can be adapted to other fDOT systems like frequency domain systems [45, 42, 46, 47] or time-gating techniques [14, 9].Fig. 2. Expected counting signal in CW-fDOT (a) or in ITD-fDOT (c) obtained for a single excitation source (i.e. ...
In this communication, the intrinsic precision in the localization of a fluorescent source in a turbid medium is analyzed for various fluorescence diffuse optical tomography (fDOT) setups in reflection geometry via a rigorous statistical methodology, the Cramer-Rao bound. Firstly, a spatially and temporally resolved imaging technique (TD) is considered and the strong impact of the fluorescence life-time is revealed. Then, these performances are compared with other standard setups, namely a spatially resolved in a continuous wave setup (CW) and a single detector in a time resolved setup (ITD).
... Time domain NIR fluorescence imaging is a novel functional imaging technique whereby a region of interest is irradiated by a NIR excitation light source and the emitted fluorescence light together with the transmitted and/or reflected light at excitation is used to allow spatial distributions of fluorophores and/or other structures in tissues to be imaged [11][12][13][14][15][16][17][18][19][20] . In comparison with the technique being performed using CW and/or in frequency domain 1,18,[21][22][23][24][25][26] , the time domain technique has shown to provides a more quantitatively accurate results within image reconstruction 27 and particularly from the point of view of spatial resolution. More specifically, since time domain measurement data implicitly contains all modulation frequencies from frequency domain measurement, it should therefore provide much more information regarding the underlying optical properties 28 . ...
In this work a generalization of the approach allowing time-domain (TD)
excitation and fluorescence data to be generated using a finite element
model (FEM) is introduced. This new functionality allows simulation of
temporal point-spread functions (TPSF) for a heterogeneous scattering
and absorbing media of arbitrary geometry. In the first part of this
paper, the approach used to develop a computationally efficient model
for solving the time-dependent diffusion equation for excitation and
fluorescence data is presented. In the second part, a detailed
theoretical evaluation of the method is given by comparing the developed
FEM simulations with analytical and Monte Carlo data. The total fluence
(intensity data), shows qualitative match whereas meantime of flight is
almost identical among the three models for both excitation and emission
data. The results show that the model is reliable and warrants its use
for future TD applications where diffusion modelling can be used.
Fluorescence Molecular Tomography (FMT) is a powerful imaging modality for the research of cancer diagnosis, disease treatment and drug discovery. Via three-dimensional (3-D) imaging reconstruction, it can quantitatively and noninvasively obtain the distribution of fluorescent probes in biological tissues. Currently, photon propagation of FMT is conventionally described by the Finite Element Method (FEM), and it can obtain acceptable image quality. However, there are still some inherent inadequacies in FEM, such as time consuming, discretization error and inflexibility in mesh generation, which partly limit its imaging accuracy. To further improve the solving accuracy of photon propagation model (PPM), we propose a novel compactly supported radial basis functions (CSRBFs)-based meshless method (MM) to implement the PPM of FMT. We introduced a series of independent nodes and continuous CSRBFs to interpolate the PPM, which can avoid complicated mesh generation. To analyze the performance of the proposed MM, we carried out numerical heterogeneous mouse simulation to validate the simulated surface fluorescent measurement. Then we performed an in vivo experiment to observe the tomographic reconstruction. The experimental results confirmed that our proposed MM could obtain more similar surface fluorescence measurement with the golden standard (Monte-Carlo method), and more accurate reconstruction result was achieved via MM in in vivo application.
Emerging as an important alternative to molecular imaging, fluorescence molecular tomography (FMT) is applied to probing the distribution of fluorescence reporters associated with cellular functions [1–3]. In comparison with other molecular imaging approaches, fluorescence molecular imaging can obtain high sensitivity detection with low instrumentation expense. Such an imaging mode has attracted great attention thanks to the increasing availability of fluorescent proteins, dyes and probes that enable the non-invasive study of gene expression, protein function, protein-protein interactions and a large number of cellular processes [1]. The application of fluorescence tomography would also help bioengineering scientists investigate disease processes, evaluate therapy response and develop new drugs.
Biomechanical imaging techniques based on acoustic radiation force (ARF) have been developed to characterize the viscoelasticity of soft tissue by measuring the motion excited by ARF noninvasively. The unknown stress distribution in the region of excitation (ROE) limits an accurate inverse characterization of soft tissue viscoelasticity, and single degree-of-freedom (SDF) simplified models have been applied to solve the inverse problem approximately. In this study, the ARF induced creep imaging is employed to estimate the time constant of a Voigt viscoelastic tissue model, and an inverse finite element (FE) characterization procedure based on a Bayesian formulation is presented. The Bayesian approach aims to estimate a reasonable quantification of the probability distributions of soft tissue mechanical properties in the presence of measurement noise and model parameter uncertainty. Gaussian process (GP) metamodeling is applied to provide a fast statistical approximation based on a small number of computationally expensive FE-model runs. Numerical simulation results demonstrate that the Bayesian approach provides an efficient and practical estimation of the probability distributions of time constant in the ARF induced creep imaging. In a comparison study with the SDF models, the Bayesian approach with FE models improves the estimation results even in the presence of large uncertainty levels of the model parameters. This article is protected by copyright. All rights reserved.
This article is protected by copyright. All rights reserved.
Use of multi-frequency DOT for reconstruction of optical properties is investigated. Choosing appropriate frequency values by considering system noise and using multi-parameter Tikhonov regularization, improvement is demonstrated using phantom data with multi-frequency reconstruction.
Fluorescence molecular tomography (FMT) is a promising imaging technique in preclinical research, enabling three-dimensional location of the specific tumor position for small animal imaging. However, FMT presents a challenging inverse problem that is quite ill-posed and ill-conditioned. Thus, the reconstruction of FMT faces various challenges in its robustness and efficiency. We present an FMT reconstruction method based on nonmonotone spectral projected gradient pursuit (NSPGP) with l(1)-norm optimization. At each iteration, a spectral gradient-projection method approximately minimizes a least-squares problem with an explicit onenorm constraint. A nonmonotone line search strategy is utilized to get the appropriate updating direction, which guarantees global convergence. Additionally, the Barzilai-Borwein step length is applied to build the optimal step length, further improving the convergence speed of the proposed method. Several numerical simulation studies, including multisource cases as well as comparative analyses, have been performed to evaluate the performance of the proposed method. The results indicate that the proposed NSPGP method is able to ensure the accuracy, robustness, and efficiency of FMT reconstruction. Furthermore, an in vivo experiment based on a heterogeneous mouse model was conducted, and the results demonstrated that the proposed method held the potential for practical applications of FMT. (C) 2014 Society of Photo-Optical Instrumentation Engineers (SPIE)
Fluorescence Photo-Acoustic Tomography (FPAT) is a multimodality biomedical imaging technique that combines high-resolution ultrasound imaging with high-contrast fluorescence optical tomography. In the first step of FPAT, one utilizes the photo-acoustic effect to recover the total absorbed energy map inside the media with ultrasound tomography. In the second step, called Quantitative FPAT (QFPAT), one uses interior absorbed energy data to recover either the quantum efficiency or the concentration distribution or both of the fluorophores inside the media. The objective of this work is to derive the mathematical model for QFPAT and to study the corresponding inverse problems. We derive some uniqueness and stability results on these inverse problems and propose a few (often explicit) reconstruction algorithms. Numerical simulations based on synthetic data are presented to verify the theory and algorithms proposed.
Practical imaging constraints restrict the number of wavelengths that can be measured in a single Biolumines- cence Tomography imaging session, but it is unclear which set of measurement wavelengths is optimal, in the sense of providing the most information about the bioluminescent source. Mutual Information was used to integrate knowledge of the type of bioluminescent source likely to be present, the optical properties of tissue and physics of light propagation, and the noise characteristics of the imaging system, in order to quantify the information contained in measurements at different sets of wavelengths. The approach was applied to a two-dimensional simulation of Bioluminescence Tomography imaging of a mouse, and the results indicate that different wavelengths and sets of wavelengths contain different amounts of information. When imaging at a single wavelength, 580nm was found to be optimal, and when imaging at two wavelengths, 570nm and 580nm were found to be optimal. Examination of the dispersion of the posterior distributions for single wavelengths suggests that information regarding the location of the centre of the bioluminescence distribution is relatively independent of wavelength, whilst information regarding the width of the bioluminescence distribution is relatively wavelength specific.
Optical Signal Recording.- Overview of Photon Counting Techniques.- Multidimensional TCSPC Techniques.- Building Blocks of Advanced TCSPC Devices.- Application of Modern TCSPC Techniques.- Detectors for Photon Counting.- Practice of TCSPC Experiments.- Final Remarks.- References.
We evaluated the potential of the Cramér-Rao lower bound (CRLB) to serve as a design metric for diffuse optical imaging systems. The CRLB defines the best achievable precision of any estimator for a given data model; it is often used in the statistical signal processing community for feasibility studies and system design. Computing the CRLB requires inverting the Fisher information matrix (FIM), however, which is usually ill-conditioned (and often underdetermined) in the case of diffuse optical tomography (DOT). We regularized the FIM by assuming that the inhomogeneity to be imaged was a point target and assessed the ability of point-target CRLBs to predict system performance in a typical DOT setting in silico. Our reconstructions, obtained with a common iterative algebraic technique, revealed that these bounds are not good predictors of imaging performance across different system configurations, even in a relative sense. This study demonstrates that agreement between the trends predicted by the CRLBs and imaging performance obtained with reconstruction algorithms that rely on a different regularization approach cannot be assumed a priori. Moreover, it underscores the importance of taking into account the intended regularization method when attempting to optimize source-detector configurations.
Light propagation in tissue is known to be favored in the near infrared
spectral range. Capitalizing on this fact, new classes of molecular
contrast agents are engineered to fluoresce in the NIR. The potential of
these new agents is vast as it allows tracking non-invasively and
quantitatively specific molecular events in-vivo. However, to monitor
the bio-distribution of such compounds in thick tissue proper physical
models of light propagation are necessary. To recover 3D concentrations
of the compound distribution, it is necessary to perform a model based
inverse problem: Diffuse Optical tomography. In this work, we focus on
fluorescent diffuse optical tomography expressed within the normalized
Born approach. More precisely, we investigate the performances of
Fluorescence Molecular Tomography (FMT) in the case of time resolved
measurements. The different moments of the time point spread function
(TPSF) were analytically derived to construct the forward model. The
derivation was performed from the zero order moment to the second
moment. This new forward model approach was validated with simulations
based on relevant parameters. Enhanced performance of FMT was achieved
using these new analytical solutions when compared to the current
formulations.
The importance of cellular pH has been shown clearly in the study of
cell activity, pathological feature, drug metabolism, etc. Monitoring pH
changes of living cells and imaging the regions with abnormal pH values
in vivo could provide the physiologic and pathologic information for the
research of the cell biology, pharmacokinetics, diagnostics and
therapeutics of certain diseases such as cancer. Thus, pH-sensitive
fluorescence imaging of bulk tissues has been attracting great attention
in the regime of near-infrared diffuse fluorescence tomography (DFT), an
efficient small-animal imaging tool. In this paper, the feasibility of
quantifying pH-sensitive fluorescence targets in turbid medium is
investigated using both time-domain and steady-state DFT methods. By use
of the specifically designed time-domain and continuous-wave systems and
the previously proposed image reconstruction scheme, we validate the
method through 2-dimensional imaging experiments on a small-animal-sized
phantom with multiply targets of distinct pH values. The results show
that the approach can localize the targets with reasonable accuracy and
achieve quantitative reconstruction of the pH-sensitive fluorescent
yield.
Fluorescence diffuse optical tomography (FT) is an emerging molecular
imaging technique that can spatially resolve both fluorophore
concentration and lifetime parameters. In this study, we investigated
the performance of a frequency domain FT system for inclusions with
various sizes and contrast levels. Due to the ill-posedness of the FT
problem, the fluorescence parameters can not be recovered accurately.
The reconstructed fluorescence parameters depend on the signal to
background contrast and size of the compartments containing the
fluorophores. Recently, imaging with multiple modalities has become a
popular trend. Different modalities give different information on the
subject under investigation. Here, we evaluated the improvement in FT
reconstruction when structural a priori information from a second
imaging modality was incorporated. The results demonstrated that the
structural a priori information was crucial to be able to recover both
parameters with high accuracy. Without such a priori information, the
same fluorophore concentration for different object sizes could not be
recovered to the same value. On the other hand, when the structural a
priori information was available, both fluorescence parameters could be
recovered within 15% error for all the cases.
Analysis of the quasi-sinusoidal temporal signals measured by a Diffuse Optical Tomography (DOT) instrument can be used to determine both quantitative and qualitative characteristics of functional brain activities arising from visual and auditory simulations, motor activities, and cognitive tasks performances. Once the activated regions in the brain are resolved using DOT, the temporal resolution of this modality is such that one can track the spatial evolution (both the location and morphology) of these regions with time. In this paper, we explore a state-estimation approach using Extended Kalman Filters to track the dynamics of functionally activated brain regions. We develop a model to determine the size, shape, location and contrast of an area of activity as a function of time. Under the assumption that previously acquired MRI data has provided us with a segmentation of the brain, we restrict the location of the area of functional activity to the thin, cortical sheet. To describe the geometry of the region, we employ a mathematical model in which the projection of the area of activity onto the plane of the sensors is assumed to be describable by a low dimensional algebraic curve. In this study, we consider in detail the case where the perturbations in optical absorption parameters arising due to activation are confined to independent regions in the cortex layer. We estimate the geometric parameters (axis lengths, rotation angle, center positions) defining the best fit ellipse for the activation area's projection onto the source-detector plane. At a single point in time, an adjoint field-based nonlinear inversion routine is used to extract the activated area's information. Examples of the utility of the method will be shown using synthetic data.
A theoretical framework is presented that allows a lifetime based analysis of the entire temporal diffuse fluorescence response curve from a turbid medium. Optimization studies using singular value decomposition analysis show that direct time domain fluorescence reconstructions are optimally performed using a few points near the peak and rise portions of the temporal response. It is also shown that the initial portion of the fluorescent response curve offers superior contrast-to-noise performance, while the late decay portions offer minimal cross-talk between multiple lifetime components.
We present preliminary results of the frequency domain fluorescent diffuse tomography (FD FDT) method in application to fluorescent proteins. For first step in the experimental setup we utilized light-emitting diode (530 nm wavelength) modulated with low frequency (18 kHz). A model experiments with capsules containing DsRed suspension in scattering medium has been conducted. The results of post mortem experiments with capsules containing DsRed, introduced into abdominal cavity of mice to simulate tumors inside animal body, are presented. An algorithm of processing fluorescent image based on calculating zero of maximum curvature has been applied to detect fluorescent inclusions boundaries on the image.
In this study, time-domain fluorescence diffuse optical tomography (FDOT) in biological tissue is investigated by solving the inverse problem using a convolution and deconvolution of the zero-lifetime emission light intensity and the exponential function for a finite lifetime, respectively. We firstly formulate the fundamental equations in time-domain assuming that the fluorescence lifetime is equal to zero, and then the solution including the lifetime is obtained by convolving the emission light intensity and the lifetime function. The model is a 2-D 10 mm-radius circle with the optical properties simulating biological tissue for the near infrared light, and contains some regions with fluorophores. Temporal and spatial profiles of excitation and emission light intensities are calculated and discussed for several models. The inverse problem of fluorescence diffuse optical tomography is solved using simulated measurement emission intensities for reconstructing fluorophore concentration. A time-domain measurement system uses ultra-short pulsed laser for excitation and measures the temporal and spatial distributions of fluorescence emitting from the tissue surface. To improve image quality, we propose implementation of a FDOT algorithm using full time-resolved (TR) data.
The inverse problem of fluorescence diffusse optical tomography (FDOT) is often highly ill-posed, which needs regularization techniques. In this paper, we propose a combined l1l2-norm regularization method to address the ill-posed FDOT inverse problem. Compared with the traditional Tikhonov regularization, the proposed method is able to effectively remove the noise in the reconstructed image without much over-smoothness. The performance of the proposed method is demonstrated in 3D numerical simulation.
We present experiments and simulations that show the microscopic fluorescence resonance energy transfer (FRET) donor-acceptor distance can be determined using a diffusion model. The approach could lead to deep tissue in vivo FRET imaging.
Strong light scattering and absorption limit visualization of the internal structure of biological tissue. Only special tools for turbid media imaging, such as optical diffuse tomography, enable noninvasive investigation of the internal biological tissues, including visualization and intravital monitoring of deep tumors. In this work the preliminary results of fluorescence diffuse tomography (FDT) of small animals are presented. Using of exogenous fluorophores, targeted specifically at tumor cells, and fluorescent proteins expressed endogenously can significantly increase the contrast of obtained images. Fluorescent compounds of different nature, such as sulphonated aluminium phthalocyanine (Photosens), red fluorescing proteins and CdTe/CdSe-core/shell nanocrystals (quantum dots) were applied. The animal was scanned in the transilluminative configuration by low-frequency modulated light (1 kHz) from Nd:YAG laser with second harmonic generation at the wavelength of 532 nm or semiconductor laser at the wavelength of 655 nm. Photosens was injected intravenously into linear mice with metastazing Lewis lung carcinoma in dose 4 mg/kg. Quantum dots (5x10-11 M) or protein DsRed2 (1-5x10-6 M) in glass capsules (inner diameter 2-3 mm) were placed inside the esophagus of 7-day-old hairless rats (18-20 g) to simulate marked tumors. Cells of HEK-293 Phoenix line, transitory transfected with Turbo-RFP protein gene, were injected hypodermically to immunodeficient mice. This work demonstrates potential capabilities of FDT method for detection and monitoring of deep fluorescent-labeled tumors in animal models. Strong advantages of fluorescent proteins and quantum dots over the traditional photosensitizer for FDT imaging are shown.
Standards are important for calibration procedures in fluorescence imaging and overall for enabling
accurate quantification. However, due to the strong nonlinear dependence of the fluorescence signal on
tissue scattering, tissue absorption and activity depth, the construction of standards becomes challenging.
So far, most fluorescent standards for diffusive imaging have been based on laboratory solutions that mix
scattering, absorbing and fluorescence materials to construct substances of known and stable optical properties.
Herein we review the most common characteristics of diffusive imaging and outline strategies to produce
materials that can serve as standards in whole body imaging applications.
The primary objective of this research program is to investigate concurrent near infrared (NIR) optical and magnetic resonance (MR) imaging for breast cancer diagnosis. The NIR diffuse optical imaging offers novel criteria for cancer differentiation with the ability to measure (in vivo) oxygenation and vascularization state, the uptake and release of contrast agents and chromophore concentrations with high sensitivity. However, NIR diffuse optical tomography is inherently a low spatial resolution imaging modality due to diffuse nature of light photons. Alternatively, MR provides high spatial resolution with excellent tissue discrimination, but has limited ability to monitor hemoglobin dynamics and other contrast mechanisms that optical imaging provides. Therefore, concurrent MRl-NlR optical imaging brings together the most advantageous aspects of the two imaging modalities for breast cancer diagnosis.
The importance of cellular pH has been shown clearly in the study of cell activity, pathological feature, and drug metabolism. Monitoring pH changes of living cells and imaging the regions with abnormal pH-values, in vivo, could provide invaluable physiological and pathological information for the research of the cell biology, pharmacokinetics, diagnostics, and therapeutics of certain diseases such as cancer. Naturally, pH-sensitive fluorescence imaging of bulk tissues has been attracting great attentions from the realm of near infrared diffuse fluorescence tomography (DFT). Herein, the feasibility of quantifying pH-induced fluorescence changes in turbid medium is investigated using a continuous-wave difference-DFT technique that is based on the specifically designed computed tomography-analogous photon counting system and the Born normalized difference image reconstruction scheme. We have validated the methodology using two-dimensional imaging experiments on a small-animal-sized phantom, embedding an inclusion with varying pH-values. The results show that the proposed approach can accurately localize the target with a quantitative resolution to pH-sensitive variation of the fluorescent yield, and might provide a promising alternative method of pH-sensitive fluorescence imaging in addition to the fluorescence-lifetime imaging.
We report here the in vivo diagnostic use of a peptide-dye conjugate consisting of a cyanine dye and the somatostatin analog octreotate as a contrast agent for optical tumor imaging. When used in whole-body in vivo imaging of mouse xenografts, indotricarbocyanine-octreotate accumulated in tumor tissue. Tumor fluorescence rapidly increased and was more than threefold higher than that of normal tissue from 3 to 24 h after application. The targeting conjugate was also specifically internalized by primary human neuroendocrine tumor cells. This imaging approach, combining the specificity of ligand/receptor interaction with near-infrared fluorescence detection, may be applied in various other fields of cancer diagnosis.
In general it is not possible to write an analytic expression for the fluorescence signal generated by a fluorophore distributed in a scattering medium such as tissue. However, by assuming that the scattering properties of the tissue are the same at the excitation and emission wavelengths, we have derived a simple relation between the fluorescence and the scatter signals. Along with diffusion theory, this was used to write expressions for the fluorescence signal detected at the tissue surface in both the time and the frequency domains. Experiments using the fluorophore aluminum chlorosulfonated phthalocyanine in tissue-simulating materials confirmed the accuracy of the model. Applications to in vivo spectroscopy are discussed.
Using the method of images, we examine the three boundary conditions commonly applied to the surface of a semi-infinite turbid medium. We find that the image-charge configurations of the partial-current and extrapolated-boundary conditions have the same dipole and quadrupole moments and that the two corresponding solutions to the diffusion equation are approximately equal. In the application of diffusion theory to frequency-domain photon-migration (FDPM) data, these two approaches yield values for the scattering and absorption coefficients that are equal to within 3%. Moreover, the two boundary conditions can be combined to yield a remarkably simple, accurate, and computationally fast method for extracting values for optical parameters from FDPM data. FDPM data were taken both at the surface and deep inside tissue phantoms, and the difference in data between the two geometries is striking. If one analyzes the surface data without accounting for the boundary, values deduced for the optical coefficients are in error by 50% or more. As expected, when aluminum foil was placed on the surface of a tissue phantom, phase and modulation data were closer to the results for an infinite-medium geometry. Raising the reflectivity of a tissue surface can, in principle, eliminate the effect of the boundary. However, we find that phase and modulation data are highly sensitive to the reflectivity in the range of 80-100%, and a minimum value of 98% is needed to mimic an infinite-medium geometry reliably. We conclude that noninvasive measurements of optically thick tissue require a rigorous treatment of the tissue boundary, and we suggest a unified partial-current--extrapolated boundary approach.
Using a set of coupled radiation transport equations, we derive image operators for luminescence optical tomography with which it is possible to reconstruct concentration and mean lifetime distribution from information obtained from dc and time-harmonic optical sources. Weight functions and detector readings were computed from analytic solutions of the diffusion equation and from numerical solutions of the transport equation by Monte Carlo methods. Detector readings were also obtained from experiments on vessels containing a balloon filled with dye embedded in an Intralipid suspension with dye in the background. Image reconstructions were performed by the conjugate gradient descent method and the simultaneous algebraic reconstruction technique with a positivity constraint. A concentration correction was developed in which the reconstructed concentration information is used in the mean-lifetime reconstruction. The results show that the target can be accurately located in both the simulated and the experimental cases, but quantitative inaccuracies are present. Observed errors include a shadowing effect in regions that have the lowest weight within the inclusion. Application of the concentration correction can significantly improve computational efficiency and reduce error in the mean-lifetime reconstructions.
We have designed, synthesized, and evaluated the efficacy of novel dye-peptide conjugates that are receptor specific. Contrary to the traditional approach of conjugating dyes to large proteins and antibodies, we used small peptide-dye conjugates that target over-expressed receptors on tumors. Despite the fact that the peptide and the dye probe have similar molecular mass, our results demonstrate that the affinity of the peptide for its receptor and the dye fluorescence properties are both retained. The use of small peptides has several advantages over large biomolecules, including ease of synthesis of a variety of compounds for potential combinatorial screening of new targets, reproducibility of high purity compounds, diffusiveness to solid tumors, and the ability to incorporate a variety of functional groups that modify the pharmacokinetics of the peptide-dye conjugates. The efficacy of these new fluorescent optical contrast agents was evaluated in vivo in well-characterized rat tumor lines expressing somatostatin (sst(2)) and bombesin receptors. A simple continuous wave optical imaging system was employed. The resulting optical images clearly show that successful specific tumor targeting was achieved. Thus, we have demonstrated that small peptide-dye conjugates are effective as contrast agents for optical imaging of tumors.
Although diffuse optical tomography is a highly promising technique used to noninvasively image blood volume and oxygenation, the reconstructed data are sensitive to systemic difference between the forward model and the actual experimental conditions. In particular, small changes in optode location or in the optode-tissue coupling coefficient significantly degrade the quality of the reconstruction images. Accurate system calibration therefore is an essential part of any experimental protocol. We present a technique for simultaneously calibrating optode positions and reconstructing images that significantly improves image quality, as we demonstrate with simulations and phantom experiments.
A nonlinear, Bayesian optimization scheme is presented for reconstructing fluorescent yield and lifetime, the absorption coefficient, and the diffusion coefficient in turbid media, such as biological tissue. The method utilizes measurements at both the excitation and the emission wavelengths to reconstruct all unknown parameters. The effectiveness of the reconstruction algorithm is demonstrated by simulation and by application to experimental data from a tissue phantom containing the fluorescent agent Indocyanine Green.
We develope a method to optimize the resolution of diffuse optical tomographic instruments. Singular-value analysis of the tomographic weight matrix associated with specific data types, geometries, and optode arrangements is shown to provide a measure of image resolution. We achieve optimization of device configuration by monitoring the resolution measure described. We introduce this idea and demonstrate its utility by optimizing the spatial sampling interval and field-of-view parameters in the parallel-plane transmission geometry employed for diffuse optical breast imaging. We also compare resolution in transmission and remission geometries.
The theoretical information content, defined by C.E. Shannon (1948), is proposed as an objective measure of MR (magnetic resonance) image quality. This measure takes into account the contrast-to-noise ratio (CNR), scan resolution, and field of view. It is used to derive an optimum in the tradeoff problem between image resolution and CNR, and as a criterion to assess the usefulness of high-resolution (512(2)) MR images. The result tells that for a given total acquisition time, an optimum value of the resolution can be found. This optimum is very broad. To apply Shannon's theory on information constant to MR images, a model for the spatial spectral power density of these images is required. Such a model has been derived from experimental observations of ordinary MR images, as well as from theoretical considerations.
Given either a finite number of time gates or a small number of RF frequencies, we examine which system design yields the maximum usable information for diffusive optical tomography in both transmissive and reflective geometries.
© 2000 Optical Society of America
© 2002 Optical Society of America
Bell System Technical Journal, also pp. 623-656 (October)
We present a review of methods for the forward and inverse problems in optical tomography. We limit ourselves to the highly scattering case found in applications in medical imaging, and to the problem of absorption and scattering reconstruction. We discuss the derivation of the diffusion approximation and other simplifications of the full transport problem. We develop sensitivity relations in both the continuous and discrete case with special concentration on the use of the finite element method. A classification of algorithms is presented, and some suggestions for open problems to be addressed in future research are made.
Frequency-domain diffusion imaging uses the magnitude and phase of modulated light propagating through a highly scattering medium to reconstruct an image of the spatially dependent scattering or absorption coeffi-cients in the medium. An inversion algorithm is formulated in a Bayesian framework and an efficient opti-mization technique is presented for calculating the maximum a posteriori image. In this framework the data are modeled as a complex Gaussian random vector with shot-noise statistics, and the unknown image is mod-eled as a generalized Gaussian Markov random field. The shot-noise statistics provide correct weighting for the measurement, and the generalized Gaussian Markov random field prior enhances the reconstruc-tion quality and retains edges in the reconstruction. A localized relaxation algorithm, the iterative-coordinate-descent algorithm, is employed as a computationally efficient optimization technique. Numerical results for two-dimensional images show that the Bayesian framework with the new optimization scheme outperforms conventional approaches in both speed and reconstruction quality. © 1999 Optical Society of America [S0740-3232(99)01410-6] OCIS codes: 100.
Tumor detection has been carried out in mice sensitized with hematoporphyrin derivative (HpD) by measuring the spatial distribution of the fluorescence lifetime of the exogenous compound. This result has been achieved using a time-gated video camera and a suitable mathematical processing that led to the so-called “lifetime images.” Extensive experimental tests have been performed on mice bearing the MS-2 fibrosarcoma or the L1210 leukemia. Lifetime images of mice show that the fluorescence decay of HpD is appreciably slower in the tumor than in healthy tissues nearby, allowing a reliable detection of the neoplasia. The lengthening of the lifetime in tumors depends little on the drug dose, which in our experiments could be lowered down to 0.1 mg/kg body weight, still allowing a definite tumor detection. In order to ascertain the results achieved with the imaging apparatus, high-resolution spectroscopy, based on a time-correlated single photon counting system, has also been performed to measure the fluorescence lifetime of the drug inside the tumor and outside. The outcomes obtained with two techniques are in good agreement.
Optical tomography is a novel imaging modality that is employed to reconstruct cross-sectional images of the optical properties of highly scattering media given measurements performed on the surface of the medium. Recent advances in this field have mainly been driven by biomedical applications in which near-infrared light is used for transillumination and reflectance measurements of highly scattering biological tissues. Many of the reconstruction algorithms currently utilized for optical tomography make use of model-based iterative image reconstruction (MOBIIR) schemes. The imaging problem is formulated as an optimization problem, in which an objective function is minimized. In the simplest case the objective function is a normalized-squared error between measured and predicted data. The predicted data are obtained by using a forward model that describes light propagation in the scattering medium given a certain distribution of optical properties.
The lifetime of a f luorophore generally varies in different environments, making the molecule a sensitive indicator of tissue oxygenation, pH, and glucose. However, lifetime measurements are complicated when the f luorophore is embedded in an optically thick, highly scattering medium such as human tissue. We formulate the inverse problem for f luorescence lifetime tomography using diffuse photon density waves, and we demonstrate the technique by deriving spatial images of heterogeneous f luorophore distribution and lifetime, using simulated measurements in heterogeneous turbid media.
We present for the first time experimental images of fluorescence lifetime distribution using model-based reconstruction. The lifetime distribution in our phantom experiments was realized through using an oxygen-sensitive dye [Sn(IV)Chlorin-e6-Cl2-3Na (SCCN)] whose lifetime varied with the oxygen concentration provided in the target and background media. The fluorescence tomographic data was obtained using our multichannel frequency-domain system. Spatial maps of fluorescence lifetime were achieved with a finite element based reconstruction algorithm.
In order for diffuse optical tomography to realize its potential of obtaining quantitative images of spatially varying optical properties within random media, several potential experimental systematic errors must be overcome. One of these errors is the calibration of the emitter strength and detector efficiency/gain. While in principle these parameters can be determined accurately prior to an imaging experiment, slight fluctuations will cause significant image artifacts. For this reason, it is necessary to consider including their calibration as part of the inverse problem for image reconstruction. In this paper, we show that this can be done successfully in a linear reconstruction model with simulated continuous-wave data. The technique is general for frequency and time domain data.
The imaging process has two fundamental stages: detection and display. The detection stage can be quantified rigourously using Shannon's information theory. This requires the contrast scale (CS), modulation transfer function (MTF), and noise power spectrum [N(f)] to be combined into a signal-to-noise ratio (SNR). This results in two fundamental summary figures of merit: the density of noise equivalent quanta (NEQ) in the image and the information bandwidth integral (IBWI). These algorithm-independent measures are used to quantify the recording stage. The display stage is less well understood since it couples to an external observer. Several types of decision makers are treated. Examples are drawn from first and second generation CT, demonstrating that thye are nearly quantum limited for large signals, indicating how their algorithms are matched or mismatched to the geometry, and calculating the contrast-detail diagrams for those decision makers.
The fluorescence spectrum was measured as a function of dye concentration in human whole blood and a few other common solvents in order to determine what fluorescence properties are unique to indocyanine green in blood.
The absorption spectrum of indocyanine green depends on the nature of the solvent medium and on the dye concentration. Binding to plasma proteins causes the principal peaks in the absorption spectrum to shift about 25 nm toward the higher wavelengths. The much greater influence on the spectrum of the dye concentration results from progressive aggregate formation with increasing concentration. Indocyanine green solutions therefore do not follow Lambert-Beer's law above 15 mg-I-1 (in plasma). Indocyanine green solutions in plasma and concentrated (1,000 mg-I-1) solutions in distilled water are stable for at least 4 h. In long-term experiments the optical density of indocyanine green solutions in plasma as well as in distilled water generally diminishes, even in the dark. On the 7th day a new absorption maximum starts to appear at gamma=900 nm, possibly caused by further aggregate formation leading to much larger particles. Spectral stabilization after injection of a concentrated solution into the blood is most rapid when the dye is dissolved in distilled water. Spectral stabilization slows down with decreasing temperature. As rapid spectral stabilization is essential in quantitative dye dilution studies, the practice of adding a albumin and/or isotonic saline solution to the injectate should be discontinued. When a 10 g-1(-1) aqueous solution of indocyanine green is used, spectral stabilization takes less than 1.5 a (at 37 degrees C), which is sufficiently fast for almost any application.
To improve the detectability of tumors by light-induced fluorescence, the use of monoclonal antibodies (MoAb) as carriers of fluorescent molecules was studied. As a model for this approach, the biodistribution of an anticarcinoembryonic antigen (CEA) MoAb coupled to fluorescein was studied in mice bearing a human colon carcinoma xenograft. In vitro, such conjugates with fluorescein-MoAb molar ratios ranging from four to 19, doubly labeled with 125I, showed more than 82% binding to immobilized CEA. In vivo, conjugates with a fluorescein-MoAb molar ratio of ten or less resulted in a tumor uptake of more than 30% of the injected dose of radioactivity per gram tumor at 24 hours. Tumor to liver, kidney, and muscle ratios of 20, 30 and 72, respectively, were obtained 48 hours after injection of the 125I-MoAb-(fluorescein)10 conjugate. The highest fluorescence intensity was always obtained for the tumor with the anti-CEA MoAb conjugate; whereas in control mice injected with fluoresceinated control immunoglobulin G1, no detectable increase in tumor fluorescence was observed. To compare these results with a classically used dye, mice bearing the same xenografts received 60 micrograms of Photofrin II. The intensity of the fluorescence signal of the tumor with this amount of Photofrin II was eight times lower than that obtained after an injection of 442 ng of fluorescein coupled with 20 micrograms of MoAb, which gave an absolute amount of fluorescein localized in the tumor of up to 125 ng/g of tumor. These results illustrate the possibility of improving the specificity of in vivo tumor localization of dyes for laser-induced fluorescence photodetection and phototherapy by coupling them to MoAb directed against tumor markers.
The ability to optically image or detect diseased tissue volumes located deep within tissues depends upon the degree of contrast provided by differences in local optical properties. In this report, we show that the exogenous contrast offered by fluorescent compounds is superior to that provided by nonfluorescing, light-absorbing compounds when time-dependent measurements are employed. In addition, we show that the induced contrast is not only moderated by the preferential uptake of fluorescent agents into diseased tissue volumes of interest but also by the fluorescent optical properties and the fluorescence dynamics in the specific tissue volume. Using tissue phantom studies, we demonstrated experimentally that near-infrared-absorbing and fluorescent dyes such as indocyanine green can provide detection of diseased tissue volumes from fluorescence measurements made at the periphery of tissue when there is perfect, 100-fold and 10-fold partitioning in diseased tissues over that in surrounding normal tissues. Experimental results of common laser dyes show the contrast is also mediated by the quantum yield and lifetime parameters that may be dependent upon the local tissue environment.
Tumor localization using fluorescence has been made practical by current improvements in tumor targeting molecules, especially monoclonal antibodies and their derivatives, by the development of convenient near-infrared emitting fluorochromes and by the availability of digital cameras having high sensitivity in this spectral region. Recent studies in animals have demonstrated that fluorochrome labeling of monoclonal antibodies confers adequate sensitivity and improved resolution. Distribution and catabolism of fluorochrome-labeled and radiolabeled antibodies are similar. Simultaneous localization of multiple reagents is made possible by labeling with several different near-infrared emitting fluorochromes; thus background subtraction and differential labeling of multiple tumor-associated components can be performed. Difficulties in using the fluorochrome labels are mainly related to light scattering and absorption in tissues, but detection of small tumors at depths of several millimeters is feasible. The major medical use of this new technology is likely to be endoscopic location of tumors. Scientific uses include studies of tumor metastasis, uptake and distribution of drugs and tumor-targeting molecules by tumors, and migration patterns of near-infrared labeled cells in vivo.
The vitamin folic acid (FA) enters cells either through a carrier protein, termed the reduced folate carrier, or via receptor-mediated endocytosis facilitated by the folate receptor (FR). Because folate-drug conjugates are not substrates of the former, they penetrate cells exclusively via FR-mediated endocytosis. When FA is covalently linked via its gamma-carboxyl to a drug or imaging agent, FR binding affinity (KD approximately 10(-10)M) is not measurably compromised, and endocytosis proceeds relatively unhindered, promoting uptake of the attached drug/imaging agent by the FR-expressing cell. Because FRs are significantly overexpressed on a large fraction of human cancer cells (e.g., ovarian, lung, breast, endometrial, renal, colon, and cancers of myeloid hematopoietic cells), this methodology may allow for the selective delivery of a wide range of imaging and therapeutic agents to tumor tissue. Folate-mediated tumor targeting has been exploited to date for delivery of the following molecules and molecular complexes: (i) protein toxins, (ii) low-molecular-weight chemotherapeutic agents, (iii) radioimaging agents, (iv) MRI contrast agents, (v) radiotherapeutic agents, (vi) liposomes with entrapped drugs, (vii) genes, (viii) antisense oligonucleotides, (ix) ribozymes, and (x) immunotherapeutic agents. In virtually all cases, in vitro studies demonstrate a significant improvement in potency and/or cancer-cell specificity over the nontargeted form of the same pharmaceutical agent. Where live animal studies have been conducted, they also reveal significant promise.
We present near-infrared frequency-domain photon migration imaging for the lifetime sensitive detection and localization of exogenous fluorescent contrast agents within tissue-simulating phantoms and actual tissues. We employ intensity-modulated excitation light that is expanded and delivered to the surface of a tissue or tissue-simulating phantom. The intensity-modulated fluorescence generated from within the volume propagates to the surface and is collected using a gain-modulated image-intensified charge-coupled device camera. From the spatial values of modulation amplitude and phase of the detected fluorescent light, micromolar volumes of diethylthiatricarbocyanine iodide (tau = 1.17 ns) and indocyanine green (ICG) (tau = 0.58 ns) embedded 1.0 cm deep in a tissue phantom are localized and discriminated on the basis of their lifetime differences. To demonstrate the utility of frequency-domain fluorescent measurements for imaging disease, we image the fluorescence emitted from the surface of in vivo and ex vivo canine mammary gland tissues containing lesions with preferential uptake of ICG. Pathology confirms the ability to detect spontaneous mammary tumors and regional lymph nodes amidst normal mammary tissue and fat as deep as 1.5 cm from the tissue surface.
To build and test an optical imaging system that is sensitive to near-infrared fluorescent molecular probes activated by specific enzymes in tumor tissues in mice.
The imaging system consisted of a source that delivered 610-650-nm excitation light within a lighttight chamber, a 700-nm longpass filter for selecting near-infrared fluorescence emission photons from tissues, and a charge-coupled device (CCD) for recording images. The molecular probe was a biocompatible autoquenched near-infrared fluorescent compound that was activated by tumor-associated proteases for cathepsins B and H. Imaging experiments were performed 0-72 hours after intravenous injection of the probe in nude mice that bore human breast carcinoma (BT-20).
The imaging system had a maximal spatial resolution of 60 microns, with a field of view of 14 cm2. The detection threshold of the nonquenched near-infrared fluorescent dye was subpicomolar in the imaging phantom experiments. In tissue, 250 pmol of fluorochrome was easily detected during the 10-second image acquisition. After intravenous injection of the probe into the tumor-bearing animals, tumors as small as 1 mm became detectable because of tumor-associated enzymatic activation of the quenched compound.
Tumor proteases can be used as molecular targets, allowing visualization of millimeter-sized tumors. The development of this technology, probe design, and optical imaging systems hold promise for molecular imaging, cancer detection, and evaluation of treatment.
We present quantitative optical images of human breast in vivo. The images were obtained by using near-infrared diffuse optical tomography (DOT) after the administration of indocyanine green (ICG) for contrast enhancement. The optical examination was performed concurrently with a magnetic resonance imaging (MRI) exam on patients scheduled for excisional biopsy or surgery so that accurate image coregistration and histopathological information of the suspicious lesions was available. The ICG-enhanced optical images coregistered accurately with Gadolinium-enhanced magnetic resonance images validating the ability of DOT to image breast tissue. In contrast to simple transillumination, we found that DOT provides for localization and quantification of exogenous tissue chromophore concentrations. Additionally our use of ICG, an albumin bound absorbing dye in plasma, demonstrates the potential to differentiate disease based on the quantified enhancement of suspicious lesions.
We have synthesized a group of glucamine and gluosamine-substituted cyanine dyes structurally related to indocyanine green (ICG) and have characterized these compounds with regard to their potential as contrast agents for biomedical optical imaging. The compounds reported herein exhibit increased hydrophilicity and less plasma protein binding (< 50%), and are thus expected to have different pharmacokinetic properties compared with ICG. Furthermore, we measured enhanced fluorescence quantum yields (7-15%) in a physiological environment with respect to ICG. For the derivative with the highest hydrophilicity (5a) the efflux from tumor and normal tissue was monitored by intensity-modulated diffuse optical spectroscopy after intravenous injection into tumor-bearing rats. In comparison with ICG, 5a exhibited a considerably enhanced tissue-efflux half-life (73 min versus less than 10 min for ICG in tumor tissue), a two-fold higher initial tissue absorption coefficient compared to ICG, and finally, it generated an elevated tumor-to-tissue concentration gradient up to 1 h after injection. In conclusion, compounds such as 5a are promising contrast agents for optical imaging, and could facilitate highly sensitive and specific detection of breast cancer or other malignancies by utilizing mechanisms similar to contrast-enhanced magnetic resonance imaging or computerized tomography.
In the field of diffuse optical tomography (DOT), it is widely accepted that time-resolved (TR) measurement can provide the richest information on photon migration in a turbid medium, such as biological tissue. However, the currently available image reconstruction algorithms for TR DOT are based mostly on the cw component or some featured data types of original temporal profiles, which are related to the solution of a time-independent diffusion equation. Although this methodology can greatly simplify the reconstruction process, it suffers from low spatial resolution and poor quantitativeness owing to the limitation of effectively applicable data types. To improve image quality, it has been argued that exploiting the full TR data is essential. We propose implementation of a DOT algorithm by using full TR data and furthermore a variant algorithm with time slices of TR data to alleviate the computational complexity and enhance noise robustness. Compared with those algorithms where the featured data types are used, our evaluations on the spatial resolution and quantitativeness show that a significant improvement in imaging quality can be achieved when full TR data are used, which convinces the DOT community of the potential advantage of the TR domain over cw and frequency domains.
Optical diffusion tomography is a method for reconstructing three-dimensional optical properties from light that passes through a highly scattering medium. Computing reconstructions from such data requires the solution of a nonlinear inverse problem. The situation is further complicated by the fact that while reconstruction algorithms typically assume exact knowledge of the optical source and detector coupling coefficients, these coupling coefficients are generally not available in practical measurement systems. A new method for estimating these unknown coupling coefficients in the three-dimensional reconstruction process is described. The joint problem of coefficient estimation and three-dimensional reconstruction is formulated in a Bayesian framework, and the resulting estimates are computed by using a variation of iterative coordinate descent optimization that is adapted for this problem. Simulations show that this approach is an accurate and efficient method for simultaneous reconstruction of absorption and diffusion coefficients as well as the coupling coefficients. A simple experimental result validates the approach.
We investigate fiber placement issues associated with a hybrid magnetic resonance imaging (MRI) near-infrared (NIR) imaging technique for small animal brain studies. Location of the optical fibers on the cranium is examined, with an emphasis on maximizing the recovered resolution and contrast in the region of interest, which in this case is the murine brain. In a series of simulation studies, singular value decomposition of the Jacobian is used in order to determine the measurement sites that provide the most information about the region of interest. The modeling results indicate that data collected using fibers arranged on one side of the head near the brain contain as much information about optical changes within the brain as those positioned equally spaced around the entire periphery of the head. Practical space limitation considerations favor the one-sided fiber array geometry in the case where the NIR acquisition is expected to occur simultaneously with MRI.
Reconstructions of a three-dimensional absorber embedded in a scattering medium by use of frequency domain measurements of the transmitted light in a single source-detector plane are presented. The reconstruction algorithm uses Bayesian regularization and iterative coordinate descent optimization, and it incorporates estimation of the detector noise level, the source-detector coupling coefficient, and the background diffusion coefficient in addition to the absorption image. The use of multiple modulation frequencies is also investigated. The results demonstrate the utility of this algorithm, the importance of a three-dimensional model, and that out-of-plane scattering permits recovery of three-dimensional features from measurements in a single plane.
We present a normalized Born expansion that facilitates fluorescence reconstructions in turbid, tissuelike media. The algorithm can be particularly useful for tissue investigations of fluorochrome distributionin vivo, since it does not require absolute photon-field measurements or measurements before contrast-agent administration. This unique advantage can be achieved only in fluorescence mode. We used this algorithm to three-dimensionally image and quantify an indocyanine fluorochrome phantom, using a novel fluorescence tomographic imager developed for animals.
An analysis is presented of the information transfer from emitter-space to detector-space in single photon emission computed tomography (SPECT) systems. The analysis takes into account the fact that count loss side information is generally not available at the detector. Side information corresponds to the number gamma-rays lost deleted due to lack of interaction with the detector data. It is shown that the information transfer depends on the structure of the likelihood function of the emitter locations associated with the detector data. This likelihood function is the average of a set of ideal-detection likelihood functions, each matched to a particular set of possible deleted gamma-ray paths. A lower bound is derived for the information gain due to incorporating the count loss side information at the detector. This is shown to be significant when the mean emission rate is small or when the gamma-ray deletion probability is strongly dependent on emitter location. Numerical evaluations of the mutual information, with and without side information, associated with information-optimal apertures and uniform parallel-hole collimators are presented.
An aperture performance criterion for single-photon-emission computed tomography (SPECT) that is based on the mutual information (MI) between the source and detector processes is proposed. The MI is a measure of the reduction in uncertainty of the emitter location, given the detector data, and it takes account of the inherent tradeoffs between the effects of sensitivity and resolution on source estimation accuracy. Specific expressions for the MI are derived for one-dimensional linear geometries and two-dimensional, parallel-slice, ring geometries under the assumptions of Poisson emission times, uniform emission angles, no scattering, and a known lost-count correction factor. For one-dimensional geometries a necessary and sufficient condition for an aperture to maximize the mutual information is given. The MI-optimal apertures are derived for various source distributions using an iterative maximization procedure. The MI is then numerically calculated for various ring apertures associated with the parallel-slice SPRINT II system.
The feasibility of employing fluorescent contrast agents to perform optical imaging in tissues and other scattering media has been examined through computational studies. Fluorescence lifetime and yield can give crucial information about local metabolite concentrations or environmental conditions within tissues. This information can be employed toward disease detection, diagnosis, and treatment if noninvasively quantitated from reemitted optical signals. However, the problem of inverse image reconstruction of fluorescence yield and lifetime is complicated because of the highly scattering nature of the tissue. Here a light propagation model employing the diffusion equation is used to account for the scattering of both the excitation and fluorescent light. Simulated measurements of frequency-domain parameters of fluorescent modulated ac amplitude and phase lag are used as inputs to an inverse image-reconstruction algorithm, which employs the diffusion model to predict frequency-domain measurements resulting from a modulated input at the phantom periphery. In the inverse image-reconstruction algorithm, a Newton-Raphson technique combined with a Marquardt algorithm is employed to converge on the fluorescent properties within the medium. The successful reconstruction of both the fluorescence yield and lifetime in the case of a heterogeneous fluorophore distribution within a scattering medium has been demonstrated without a priori information or without the necessity of obtaining absence images.
We present a straightforward procedure for frequency domain modeling of reradiation in a highly scattering medium with an arbitrary, finite three-dimensional geometry. We use a finite difference numerical solver to determine the fluence distribution at the excitation wavelength, which is then coupled to the emission wavelength with an array of equivalent reradiating sources. We then calculate the fluence distribution at the emission wavelength with a second, independent numerical simulation with new optical parameters appropriate to the emission wavelength, using the distributed reradiating sources as the excitation. We compare three-dimensional simulations of a fluorophore distributed in a scattering medium with experimental data. We also compare simulations of the Raman reradiation of small diamonds in a scattering medium with experiment.
We present a finite-element-based algorithm for reconstruction of fluorescence lifetime and yield in turbid media, using frequency-domain data. The algorithm is based on a set of coupled diffusion equations that describe the propagation of both excitation and fluorescent emission light in multiply scattering media. Centered on Newton's iterative method, we implemented our algorithm by using a synthesized scheme of Marquardt and Tikhonov regularizations. A low-pass spatial filter is also incorporated into the algorithm for enhancing image reconstruction. Simulation studies using both noise-free and noisy data have been performed with the nonzero photon density boundary conditions. Our results suggest that quantitative images can be produced in terms of fluorescent lifetime and yield values and location, size, and shape of heterogeneities within a circular background region.
The authors present a Markov random field model which allows realistic edge modeling while providing stable maximum a posterior (MAP) solutions. The model, referred to as a generalized Gaussian Markov random field (GGMRF), is named for its similarity to the generalized Gaussian distribution used in robust detection and estimation. The model satisfies several desirable analytical and computational properties for map estimation, including continuous dependence of the estimate on the data, invariance of the character of solutions to scaling of data, and a solution which lies at the unique global minimum of the a posteriori log-likelihood function. The GGMRF is demonstrated to be useful for image reconstruction in low-dosage transmission tomography.<
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