Diffuse optical tomography has demonstrated significant potential for clinical utility in the diagnosis and prognosis of breast cancer, and its use in combination with other structural imaging modalities improves lesion localization and the quantification of functional tissue properties. Here, we introduce a hybrid diffuse optical imaging system that operates concurrently with magnetic resonance imaging (MRI) in the imaging suite, utilizing commercially available MR surface coils. The instrument acquires both continuous-wave and time-domain diffuse optical data in the parallel-plate geometry, permitting both absolute assignment of tissue optical properties and three-dimensional tomography; moreover, the instrument is designed to incorporate diffuse correlation spectroscopic measurements for probing tissue blood flow. The instrument is described in detail here. Image reconstructions of a tissue phantom are presented as an initial indicator of the system’s ability to accurately reconstruct optical properties and the concrete benefits of the spatial constraints provided by concurrent MRI. Last, we briefly discuss how various data combinations that the instrument could facilitate, including tissue perfusion, can enable more comprehensive assessment of lesion physiology.
We present high spatial density, multi-modal, parallel-plate Diffuse Optical Tomography (DOT) imaging systems for the purpose of breast tumor detection. One hybrid instrument provides time domain (TD) and continuous wave (CW) DOT at 64 source fiber positions. The TD diffuse optical spectroscopy with PMT- detection produces low-resolution images of absolute tissue scattering and absorption while the spatially dense array of CCD-coupled detector fibers (108 detectors) provides higher-resolution CW images of relative tissue optical properties. Reconstruction of the tissue optical properties, along with total hemoglobin concentration and tissue oxygen saturation, is performed using the TOAST software suite. Comparison of the spatially-dense DOT images and MR images allows for a robust validation of DOT against an accepted clinical modality. Additionally, the structural information from co-registered MR images is used as a spatial prior to improve the quality of the functional optical images and provide more accurate quantification of the optical and hemodynamic properties of tumors. We also present an optical-only imaging system that provides frequency domain (FD) DOT at 209 source positions with full CCD detection and incorporates optical fringe projection profilometry to determine the breast boundary. This profilometry serves as a spatial constraint, improving the quality of the DOT reconstructions while retaining the benefits of an optical-only device. We present initial images from both human subjects and phantoms to display the utility of high spatial density data and multi-modal information in DOT reconstruction with the two systems.
We present the Toast++ open-source software environment for solving the forward and inverse problems in diffuse optical tomography (DOT). The software suite consists of a set of libraries to simulate near-infrared light propagation in highly scattering media with complex boundaries and heterogeneous internal parameter distribution, based on a finite-element solver. Steady-state, time- and frequency-domain data acquisition systems can be modeled. The forward solver is implemented in C++ and supports performance acceleration with parallelization for shared and distributed memory architectures, as well as graphics processing computation. Building on the numerical forward solver, Toast++ contains model-based iterative inverse solvers for reconstructing the volume distribution of absorption and scattering parameters from boundary measurements of light transmission. A range of regularization methods are provided, including the possibility of incorporating prior knowledge of internal structure. The user can link to the Toast++ libraries either directly to compile application programs for DOT, or make use of the included MATLAB and PYTHON bindings to generate script-based solutions. This approach allows rapid prototyping and provides a rich toolset in both environments for debugging, testing, and visualization.
The optical properties of the human head in the range from 600 nm to 1100 nm have been non-invasively in-vivo investigated by various research groups using different diffuse optics techniques and data analysis methods.
Reconstruction algorithms for imaging fluorescence in near infrared ranges usually normalize fluorescence light with respect to excitation light. Using this approach, we investigated the influence of absorption and scattering heterogeneities on quantification accuracy when assuming a homogeneous model and explored possible reconstruction improvements by using a heterogeneous model. To do so, we created several computer-simulated phantoms: a homogeneous slab phantom (P1), slab phantoms including a region with a two- to six-fold increase in scattering (P2) and in absorption (P3), and an atlas-based mouse phantom that modeled different liver and lung scattering (P4). For P1, reconstruction with the wrong optical properties yielded quantification errors that increased almost linearly with the scattering coefficient while they were mostly negligible regarding the absorption coefficient. This observation agreed with the theoretical results. Taking the quantification of a homogeneous phantom as a reference, relative quantification errors obtained when wrongly assuming homogeneous media were in the range +41 to +94% (P2), 0.1 to −7% (P3), and −39 to +44% (P4). Using a heterogeneous model, the overall error ranged from −7 to 7%. In conclusion, this work demonstrates that assuming homogeneous media leads to noticeable quantification errors that can be improved by adopting heterogeneous models.
We present a multi-laboratory comparison of several independent forward solvers used for photon migration
through layered media. Two main categories of forward solvers are presented: Monte Carlo procedures and
solutions of the diffusion equation for the time domain. For Monte Carlo we have included four independent
codes. For the solutions of the diffusion equation, we have presented: two semi-analytical approaches based
on the Green's function method and one solution obtained with the finite element method. The comparisons
between the different time-dependent solutions were performed for a two-layer medium.
The choice of the regularization parameter has a profound effect on the solution of ill-posed inverse problems such as optical topography. We review 11 different methods for selecting the Tikhonov regularization parameter that have been described previously in the literature. We test them on two trial problems, deblurring and optical topography, and conclude that the L-curve method is the method of choice, though in particularly ill-posed problems, generalized cross-validation may provide an alternative.
We have developed a novel parallel-plate diffuse optical tomography (DOT) system for three-dimensional in vivo imaging of human breast tumor based on large optical data sets. Images of oxy-, deoxy-, and total hemoglobin concentration as well as blood oxygen saturation and tissue scattering were reconstructed. Tumor margins were derived using the optical data with guidance from radiology reports and magnetic resonance imaging. Tumor-to-normal ratios of these endogenous physiological parameters and an optical index were computed for 51 biopsy-proven lesions from 47 subjects. Malignant cancers (N=41) showed statistically significant higher total hemoglobin, oxy-hemoglobin concentration, and scattering compared to normal tissue. Furthermore, malignant lesions exhibited a twofold average increase in optical index. The influence of core biopsy on DOT results was also explored; the difference between the malignant group measured before core biopsy and the group measured more than 1 week after core biopsy was not significant. Benign tumors (N=10) did not exhibit statistical significance in the tumor-to-normal ratios of any parameter. Optical index and tumor-to-normal ratios of total hemoglobin, oxy-hemoglobin concentration, and scattering exhibited high area under the receiver operating characteristic curve values from 0.90 to 0.99, suggesting good discriminatory power. The data demonstrate that benign and malignant lesions can be distinguished by quantitative three-dimensional DOT.
Can time-resolved, high-resolution data as acquired by an intensified gated CCD camera (ICCD) aid in the tomographic
reconstruction of fluorescence concentration? Usually it is argued that fluorescence is a linear process and thus does not
require non-linear, time-dependent reconstructions algorithms, unless absorption and scattering coefficients need to be
determined as well. Furthermore, the acquisition of a number of time frames is usually prohibitive for fluorescence
measurements, at least in small animals, due to the increased total measurement time. On the other hand, it is obvious
that diffusion is less pronounced in images at early gates, due to selective imaging of photons of lower scatter order. This
will be the case also for photons emitted by fluorescent sources. Early-gated imaging might increase the contrast in
acquired images and could possibly improve fluorescence localization. Herein, we present early gated fluorescence
images obtained from phantoms and compare them to continuously acquired data. Increased contrast between
background and signal maximum can be observed in time-gated images as compared to continuous data. To make use of
the properties exhibited by early gated frames, it is necessary to use a modified reconstruction algorithm. We propose a
variant of the well-known Born approximation to the diffusion equation that allows to take into account single time
frames. The system matrix for the time-dependent Born approach is more complex to calculate, however the complexity
of the actual inverse problem (and the acquisition times) of single-frame reconstructions remains the same as compared
to continuous mode.
The quality of phase and amplitude data from two medical optical tomography systems were compared. The two systems are a 32-channel time-domain system developed at University College London (UCL) and a 16-channel frequency-domain system developed at Helsinki University of Technology (HUT). Difference data measured from an inhomogeneous and a homogeneous phantom were compared with a finite-element method (diffusion equation) and images of scattering and absorption were reconstructed based on it. The measurements were performed at measurement times between 1 and 30 s per source. The mean rms errors in the data measured by the HUT system were 3.4% for amplitude and 0.51 deg for phase, while the corresponding values for the UCL data were 6.0% and 0.46 deg, respectively. The reproducibility of the data measured with the two systems was tested with a measurement time of 5 s per source. It was 0.4% in amplitude for the HUT system and 4% for the UCL system, and 0.08 deg in phase for both systems. The image quality of the reconstructions from the data measured with the two systems were compared with several quantitative criteria. In general a higher contrast was observed in the images calculated from the HUT data.
Optical tomography is a medical imaging technique which can provide images of haemodynamic parameters and oxygenation at the bedside. Here, we examine two approaches to optical tomography which are intended to provide information about perinatal brain injury. First, we reconstruct static 3D images showing the increase in blood volume and decrease in oxygenation associated with intra-ventricular haemorrhage. Second, we present the first 3D optical tomography images of the whole head during motor evoked responses and show that the peak of activation can be localised to within 11 mm of the estimated position of the motor cortex.
In this paper the solution to the transport equation will be considered using the Pn Method. Although this technique has been applied to two and three dimensional problems it can be computationally expensive when a high order of approximation is required for convergence of the problem. In this paper results will be presented that indicate a potential solution to this problem by utilising an adaptive Pn approach where the order of angular basis is varied according to the local complexity of the domain. This substantially reduces the computational cost of assembly and solution of the linear system. Results for a two-dimensional circular test problem are presented and compared to a standard solution with uniform order of angular basis.
This paper develops and analyzes the performance of an adaptive
diffusion regularization method with a specific algorithm
reconstruction method called the Lagged Diffusivity Newton-Krylov
method for Diffuse Optical Tomography inverse problem.
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.
We present the Radiosity-Diffusion model in three dimensions(3D), as an extension to previous work in 2D. It is a method for handling non-scattering spaces in optically participating media. We present the extension of the model to 3D including an extension to the model to cope with increased complexity of the 3D domain. We show that in 3D more careful consideration must be given to the issues of meshing and visibility to model the transport of light within reasonable computational bounds. We demonstrate the model to be comparable to Monte-Carlo simulations for selected geometries, and show preliminary results of comparisons to measured time-resolved data acquired on resin phantoms.
Absolute dual-parameter image reconstruction in optical tomography (OT) is a nonlinear and ill-posed problem, requiring a model-based iterative approach and an accurate and fully three-dimensional light transport forward model. These factors make OT a computationally expensive problem, resulting in reconstruction times that range from several minutes to hours, which is not acceptable in most clinical applications. In order to reduce reconstruction times we propose a coarse-grain parallel implementation of the inverse algorithm using a shared-memory threaded approach. Unlike most conventional parallelization strategies which operate on the level of the linear algebra subsystem our approach uses a parallelization at the application level, thereby leaving the underlying linear matrix solution routines untouched. This allows to exploit the inherently parallel structure of the problem, while at the same time utilizing fast direct or efficiently preconditioned iterative serial linear solvers, which in most cases can not be efficiently parallelized. We compare the performance of the coarse-grain parallel approach with a low-level parallelization of the linear conjugate gradient solver and show that the proposed method achieves significant performance improvements, thereby bringing reconstruction times within a clinically acceptable range.
KEYWORDS: 3D modeling, Data modeling, 3D image processing, Head, 3D image reconstruction, Image restoration, Absorption, Brain, 3D metrology, Optical tomography
The head is inherently a heterogenous 3 dimensional (3D) domain and any useful image reconstruction algorithm in optical tomography should be based on the true shape and dimensions of the domain to be imaged. However due to the computational complexity of the problem, most reconstruction algorithms have been based on either 2 dimensional (2D) domains or simple 3D homogenous models. In this work we use a complex multi-layered model of the head to generate data in the presence of known changes of absorption within the brain. In order to evaluate the reconstruction of images from 3D data, we use either a 2D mesh based on the outline of a single measurement plane, or a 3D mesh based on the forward model itself. We show that the use of a 2D model for the reconstruction of images from a complex heterogenous 3D model is not successful for absolute imaging of internal optical property. In 3D, image reconstruction using meantime data only from a 3D domain is not successful when reconstructing for absorption only while keeping background scatter constant and homogenous. Image reconstruction in 3D is greatly improved when a-priori structural knowledge is used. Reconstruction of internal absorption only, from difference data (data after a change in absorption minus data before a change) works both in 2D and 3D, however in 2D, any depth information available from the data is lost.
Image reconstruction and data collection in optical tomography can be achieved in a number of different ways. This paper explores the limitations of using assumptions of linearity, particularly in the case where image data is acquired before and after a change in optical properties within an object with heterogeneous optical properties. The effects of using a 2 dimensional (2D) reconstruction scheme for changes in 3D measurements are also demonstrated. Problems are a direct result of the inherent non-linearity of optical tomographic image reconstruction. We show how these assumptions affect images of changes in absorption in the presence of a) heterogeneous background scatter, and b) heterogeneous background absorption using both simulations and time-resolved experimental data. Comparisons of results using non-linear and linear image reconstruction techniques are included throughout. The origin and dependence of the error are investigated. Methods to improve results by using estimates of background structure from baseline images are shown to improve quantitation and object localization in simple images. The potential significance of this error is discussed in relation to successful, reliable clinical imaging of the neonatal brain.
Multi-channel NIR system can obtain the topographic image of brain activity. Since the image is reconstructed from the change in optical density measured with the source-detector pairs, it is important to reveal the volume of tissue sampled by each source-detector pair. In this study, the light propagation in three-dimensional adult head model is calculated by hybrid radiosity-diffusion method. The model is a layered slab which mimics the extra cerebral tissue (skin, skull), CSF and brain. The change in optical density caused by the absorption change in a small cylindrical region of 10 mm in diameter at various positions in the brain is calculated. The greatest change in optical density can be observed when the absorber is located in the middle of the source and detector. When the absorber is located just below the source or detector, the change in optical density is almost half of that caused by the same absorber in the midpoint. The light propagation in the brain is strongly affected by the presence of non-scattering layer and consequently sensitive region is broadly distributed on the brain surface.
The effect of the layered surface tissues of the head on the measurement of brain oxygenation by near infrared spectroscopy (NIRS) has been investigated by both time-of-flight measurement and Monte Carlo simulation on models consisting of three or four separate layered homogeneous media. The clear cerebrospinal fluid (CSF) layer surrounding the brain has previously been shown to significantly affect light distribution, and in the head the brain surface is deeply folded with many CSF filled sulci. Therefore the most sophisticated model has four layers including a clear 'CSF' layer containing slots imitating sulci on the brain. Simpler models are also used and the light distributions in each are compared to examine the effect of the CSF layer. The mean optical pathlength of each model calculated from the temporal point spread function (TPSF) of the time-of-flight measurement agrees well with the Monte Carlo prediction. The fractional pathlength in each of the layers and the spatial sensitivity profile, which indicates the volume of tissue interrogated, are calculated by the Monte Carlo method. Results show that the light distribution in the head is highly affected by the existence of the clear CSF layer, and the optical pathlength and spatial sensitivity profile in the models with a clear layer are quite different from those without. However the presence of the sulci hardly affect the light distribution, the results from the sophisticated brain model with sulci being almost the same as those of the model with a simple CSF layer.
KEYWORDS: Tissue optics, Scattering, Absorption, Monte Carlo methods, Near infrared spectroscopy, Tissues, Finite element methods, Optical properties, Brain, Head
Determination of the optical pathlength of light in tissue is important to quantitate NIRS data. However, the inhomogeneity of the illuminated tissues increases the difficulty of determining the relevant optical pathlength in the tissue. For instance, in the head, the contribution of the tissues overlying the brain to the total optical pathlength cannot be ignored in the monitoring of cerebral oxygenation with NIRS. In this study, time-of-flight measurements of an inhomogeneous phantom are carried out in the laboratory to examine the contribution of the overlying tissue to the optical pathlength. The phantom consists of two homogeneous components, the boundaries of which are two concentric cylinders. The TPSF is measured with a picosecond laser and a streak camera, and the change of TPSF with the distance between source and detection fibers is examined. The experimental TPSF and mean time of flight are compared with the results of a Monto Carlo simulation and a finite element model based on the diffusion equation. A comparison of the accuracy of prediction of the pathlength by each model is presented as a function of the spacing between source and detection fibers. The intensity photon measurement density functions in each of the cylinders were estimated from the Monte Carlo simulations. The results provide estimates for the amount of the NIRS signal arising from overlying tissues in the head.
KEYWORDS: Photons, Monte Carlo methods, Diffusion, Error analysis, Data modeling, Stochastic processes, Analog electronics, Statistical analysis, Image restoration, Absorption
Models of light propagation in tissue fall into two general categories: stochastic such as Monte Carlo, or Random Walk, or deterministic, such as the diffusion approximation. The former attempts to model the discrete, particle, nature of light, and inherently includes noise via the random numbers used to generate steps. The latter models the continuous, wave nature of light via a partial differential equation. Considerable effort has gone into showing that the mean of a deterministic model equates to, and the mean of a stochastic model converges to, the mean of experimental data. Efficiency considerations lead to a Monte Carlo model that has reduced variance in the sense that sample mean more quickly converges to the expectation value. When considering image reconstruction problems it is vital to be able to predict the standard errors of data from any given measure. Unfortunately, variance reduction Monte Carlo models greatly underestimate the standard errors, and 'analog' Monte Carlo methods that give correct estimates are very inefficient. In this paper we derive standard error estimations from a deterministic model that is very much faster, and demostrate the equivalence of these estimates with stochastic methods. The application of reliable error-estimates to image reconstruction is shown.
Near-infrared spectroscopy is increasingly being used for monitoring cerebral oxygenation and haemodynamics. One current concern is the effect of the cerebrospinal fluid upon the distribution of light in the head. There are difficulties in modeling clear layers in scattering systems. The Monte Carlo model should handle clear regions accurately, but is too slow to be used for realistic geometries. The diffusion equation can be solved quickly for realistic geometries, but is only valid in scattering regions. In this paper we describe experiments carried out on a solid slab phantom to investigate the effect of clear regions. These experiments were used to examine the accuracy with which the different models described propagation through a clear layer inside a scattering object. We found that the presence of a clear layer had a significant effect upon the light distribution, which was modeled correctly by Monto Carlo techniques, but not by diffusion theory.
The performance of reconstruction algorithms for near-IR optical tomography depends critically on the accuracy of the forward model used to evaluate the closeness of a given solution to that most consistent with the data (Maximum A-Posteriori criterion). Statistical photon noise can be accounted for theoretically, but there are also problems with inaccurate geometry, refractive index mismatching, and boundary effects. Sensitivity to such effects depends extensively on what measures are being used (time-varying intensity, integrated intensity, mean time, etc.). Although reconstructions have been obtained with a variety of data measures, including noise, they are often derived under strict assumptions about the accuracy of the model. In this paper we discuss the robustness of data measures and image reconstruction in the presence of model inaccuracies. In particular we consider robustness with respect to geometric errors in the modeling of the support of the solution and to the initial estimates for the starting solution vector.
We introduce photon measurement density functions (PMDF) as a generalization of photon sampling volumes in near-IR transillumination of scattering tissue. For a given source-detector pair, the PMDF identifies the regions within the tissue contributing to the measurement signal. The knowledge of these regions of sensitivity is important for both spectroscopic applications where the penetration depth of the probing light must be known, and for imaging applications where the PMDF can be used to select the measurement types best suited for the reconstruction of a given tissue parameter. We have developed analytical models which allows to calculate PMDFs for certain geometries and a variety of measurement types in 3D, and a finite element model (FEM) which can be applied to arbitrarily complex and inhomogeneous 2D cases. As an example, we present calculations performed on a FEM mesh generated from an MRI image of a human head.
KEYWORDS: Data modeling, 3D modeling, Tissues, Scattering, Modulation, Data conversion, Finite element methods, Phase shifts, Diffusion, Light scattering
We present a finite element (FE) model for calculation of photon propagation in highly scattering tissues. The model can either be used for time domain measurements, where the temporal distribution of transmitted light after an ultra short input pulse is measured, or for frequency domain measurements, where the input is a frequency modulated light source, and the phase shift and modulation depth between the input and output signal are measured. The FE model is used on inhomogeneous objects to investigate the effect of scattering and absorbing inhomogeneities on boundary measurements in both the time and frequency domain. The time and frequency versions are validated by comparing the results with data from analytical calculations and from a Monte-Carlo model. By comparing data from a two- dimensional and a three-dimensional FE model we derive a conversion factor for integrated intensity and mean time of flight that will permit the reconstruction of 3D data from a cylinder using a 2D FE model. The reconstruction is demonstrated on data generated with the FE forward model.
KEYWORDS: Data modeling, Reconstruction algorithms, Finite element methods, Scattering, Performance modeling, Inverse problems, Diffusion, Tissue optics, Absorption, Chemical elements
We have developed an iterative reconstruction algorithm for TOAST, based on a finite element method (FEM) forward model that is fast and very flexible. The algorithm can be used at present with either non-time-resolved and/or time-resolved data, and can reconstruct either (mu) a and/or (mu) s parameters. An equivalent version can be formulated in terms of phase shift and modulation frequency. The basis of the algorithm is to attempt to find the minimum error norm between the measured data and the forward model acting on the trial solution, by a `classical' non-linear search in the distribution of the (mu) a and (mu) s parameters. In principle any search strategy could be used, but the advantage of our approach is that it employs analytical results for the gradient change (partial)M/(partial)(mu) , where M is the measurement. A number of factors influence the performance of the algorithm -- sampling density of the data and solution, noise in the data, accuracy of the model, and appropriate usage of a priori information. It appears that the presence of local minima of the error norm surface cannot be ignored. This paper presents an analysis of the performance of the algorithm on data generated from the FEM model, and from an independent Monte-Carlo model.
In Time-resolved Optical Absorption and Scattering Tomography (TOAST) the imaging problem is to reconstruct the coefficients of absorption (mu)a and scattering (mu)s of light in tissue given the time-dependent photon flux at the surface of the subject, resulting from ultrafast laser input pulses. This inverse problem is mathematically similar to the Electrical Impedance problem (EIT) but presents some unique features. In particular the necessity of searching in two solution spaces requires the use of multiple data types that are maximally uncorrelated with respect to the solution spaces. We developed an algorithm for TOAST that uses an iterative non-linear gradient descent method to minimize an appropriate error norm. The algorithm can work on multiple types of data and an important topic is the choice of the best data format to use. Usually the choice is integrated intensity and mean time- of-flight for the temporal domain data. In this paper we compare these data types with the use of higher order moments of the temporal distribution (variance, skew, kurtosis). We show that reliable results must take detailed account of the confidence limits on each data point. We demonstrate how the probability distribution function for photon propagation can be calculated so that the variance of any given measurement type can be derived.
The successful development and clinical use of instruments that perform real-time near-infra red spectroscopy of transilluminated tissue has led to a widespread interest in the development of an imaging modality. The most promising approach uses picosecond laser pulses input on an object (Omega) , and measures the development of light intensity as a function of time at points on the boundary (partial)(Omega) . The imaging problem is to reconstruct the absorption and scattering coefficients inside (Omega) . We have proposed the following method for the reconstruction algorithm: A Forward model is developed in terms of the Green's Function of the Diffusion Approximation to the Radiative Transfer Equation. Given a perturbation of the image, the Jacobian of the Forward model can be derived. Inversion of the Jacobian then gives a perturbation step for a subsequent iteration. Previously we have derived an analytical expression for the Green's Function in certain simple geometries, and for a homogeneous initial image. We have now developed a Finite Element method to extend this to more general geometries and inhomogeneous images, with the inverse of the system stiffness matrix playing the role of the Green's Function. Thus it is now possible to proceed past the first iteration. The stability of the reconstruction is presented both for the time-independent case where the data is the absolute intensity on the boundary (partial)(Omega) , and for the time-dependent case where the data is the mean time of arrival of light.
Bedside instruments are now available which can transilluminate tissue with near-infrared radiation and measure the boundary flux both temporally and spatially resolved. Consequently there is an increasing demand for image processing methods that allow reconstruction of the spatial distribution of the absorption and scattering coefficient within the tissue. Iterative algorithms for solving this inverse problem require an accurate forward model. Previous attempts to simulate light propagation within a specific medium have been made either with a Monte-Carlo model or by deriving the Greens function for a given geometry, assuming diffuse light propagation. While the former requires extended computing time to achieve a certain precision, the latter is restricted to simple geometries. We present here a Finite Element model that allows the solution of the forward problem for complex geometries within a reasonable time and that could be used in real-time bedside imaging equipment. This model permits fast calculation of the integrated intensity and the mean time of flight. The model is being used to investigate perturbations imposed on the measurement data by absorbing or scattering inhomogeneities to determine the viability of the iterative reconstruction.
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