Mesh-based enhancement schemes in diffuse optical tomography

Combined multi-scale mesh and full-matrix inversion for enhancing time-domain breast diffuse optical tomography

Time-domain diffuse optical tomography can efficiently reconstruct both absorption and reduced scattering coefficients but is heavily limited by the ill-posedness in its inverse problem and low spatial resolution. To deal with these adversities, the truncated singular value decomposition (TSVD)-based whole-weighting-matrix inversion scheme can be a particularly suitable implementation. Unfortunately, TSVD is subject to a storage challenge for three-dimensional imaging of a bulk region, such as breast. In this paper, a multi-scale mesh strategy based on computed tomography (CT) anatomical geometry is adopted to solve the storage challenge, where a fine mesh is used in forward calculation to ensure accuracy, and a coarse mesh in the inversion process to enable TSVD-based inversion of the whole-weighting matrix. We validate the proposed strategy using simulated data for a single lesion model from clinical positron emission tomography images of a breast cancer patient, and further, for a complex model that is constructed by setting dual lesions at different separations in the CT breast geometry.

Data-specific mask-guided image reconstruction for diffuse optical tomography

Conventional approaches in diffuse optical tomography (DOT) image reconstruction often address the ill-posed inverse problem via regularization with a constant penalty parameter, which uniformly smooths out the solution. In this study, we present a data-specific mask-guided scheme that incorporates a prior mask constraint into the image reconstruction framework. The prior mask was created from the DOT data itself by exploiting the multi-measurement vector formulation. We accordingly propose two methods to integrate the prior mask into the reconstruction process. First, as a soft prior by exploiting a spatially varying regularization. Second, as a hard prior by imposing a region-of-interest-limited reconstruction. Furthermore, the latter method iterates between discrete and continuous steps to update the mask and optical parameters, respectively. The proposed methods showed enhanced optical contrast accuracy, improved spatial resolution, and reduced noise level in DOT reconstructed images compared with the conventional approaches such as the modified Levenberg-Marquardt approach and the l₁-regularization based sparse recovery approach.

Comparative study of one-step and two-step quantitative fluorescence photoacoustic tomography

Fluorescence optical tomography (FOT) is a well-known imaging technique, where fluorescent biological markers are injected to tag targeted tissues (tumors, proteins), and the absorption coefficient of fluorophore is reconstructed to provide contrast-enhanced images. Conventional FOT is known to have lack of stability to noise and shallow imaging depth due to strong optical scattering in biological tissue. Photoacoustic tomography (PAT) has been previously proposed to combine with FOT to resolve this issue. We propose a fully nonlinear one-step reconstruction in a diffuse-approximation modeled fluorescence photoacoustic tomographic (FPAT) setting, where the absorption coefficient of exogenous fluorophore is recovered directly from the photoacoustic data. Computational validations in two dimensions in single- and dual-grid reconstruction settings using full as well as partial data have been provided in support of the proposed algorithm. One-step schemes are particularly useful with respect to dual representations of field (optical and pressure) variables and optical parameters, especially in limited-data settings, which effectively help in constraining the optimization search space. We have compared the results of one- and two-step FPAT schemes and concluded that the one-step reconstructions are superior as compared with the corresponding two-step reconstructions. To the best of our knowledge, these are the first comparisons of one-step and two-step reconstructions in FPAT.

Thermoacoustic elastography: recovery of bulk elastic modulus of heterogeneous media using tomographically measured thermoacoustic measurements

Background

Tissue mechanical parameters such as elasticity are of great significance for the assessment of biological histopathological and physiological characteristics. Here, we propose a new approach called thermoacoustic elastography (TAE) for imaging tissue elastic modulus.

Methods

Central to TAE is an image reconstruction algorithm that allows the recovery of both microwave energy loss and elastic modulus distributions. The algorithm is first evaluated using simulated data under various practical scenarios, including a varied range of microwave energy loss and elastic modulus between the heterogeneity and background region, different noise levels, and multiple targets. The feasibility of the proposed TAE was then validated by imaging the elastic modulus distribution of agar phantoms with various elastic modulus and microwave energy loss.

Results

The results from both the simulated and phantom experiments show that the recovered elastic modulus by TAE agree well with the exact values, having an average error of less than 12.74%.

Conclusions

The findings from this study suggest that TAE provides a new addition to the family of elasticity imaging and may have broad application prospects, such as cirrhosis and atherosclerosis detection.

Accelerating nonlinear reconstruction in laminar optical tomography by use of recursive SVD inversion

Image reconstruction in the most model-based biophotonic imaging modalities essentially poses an ill-posed nonlinear inverse problem, which has been effectively tackled in the diffusion-approximation-satisfied scenarios such as diffuse optical tomography. Nevertheless, a nonlinear implementation in high-resolution laminar optical tomography (LOT) is normally computationally-costly due to its strong dependency on a dense source-detector configuration and a physically-rigorous photon-transport model. To circumvent the adversity, we herein propose a practical nonlinear LOT approach to the absorption reconstruction. The scheme takes advantage of the numerical stability of the singular value decomposition (SVD) for the ill-posed linear inversion, and is accelerated by adopting an explicitly recursive strategy for the time-consuming repeated SVD inversion, which is based on a scaled expression of the sensitivity matrix. Experiments demonstrate that the proposed methodology can perform as well as the traditional nonlinear one, while the computation time of the former is merely 26.27% of the later on average.

GPU-based acceleration and mesh optimization of finite-element-method-based quantitative photoacoustic tomography: a step towards clinical applications

Finite element method (FEM)-based time-domain quantitative photoacoustic tomography (TD-qPAT) is a powerful approach, as it provides highly accurate quantitative imaging capability by recovering absolute tissue absorption coefficients for functional imaging. However, this approach is extremely computationally demanding, and requires days for the reconstruction of one set of images, making it impractical to be used in clinical applications, where a large amount of data needs to be processed in a limited time scale. To address this challenge, here we present a graphic processing unit (GPU)-based parallelization method to accelerate the image reconstruction using FEM-based TD-qPAT. In addition, to further optimize FEM-based TD-qPAT reconstruction, an adaptive meshing technique, along with mesh density optimization, is adopted. Phantom experimental data are used in our study to evaluate the GPU-based TD-qPAT algorithm, as well as the adaptive meshing technique. The results show that our new approach can considerably reduce the computation time by at least 136-fold over the current central processing unit (CPU)-based algorithm. The quality of image reconstruction is also improved significantly when adaptive meshing and mesh density optimization are applied.

Reconstruction for Limited-Projection Fluorescence Molecular Tomography Based on a Double-Mesh Strategy

Limited-projection fluorescence molecular tomography (FMT) has short data acquisition time that allows fast resolving of the three-dimensional visualization of fluorophore within small animal in vivo. However, limited-projection FMT reconstruction suffers from severe ill-posedness because only limited projections are used for reconstruction. To alleviate the ill-posedness, a feasible region extraction strategy based on a double mesh is presented for limited-projection FMT. First, an initial result is rapidly recovered using a coarse discretization mesh. Then, the reconstructed fluorophore area in the initial result is selected as a feasible region to guide the reconstruction using a fine discretization mesh. Simulation experiments on a digital mouse and small animal experiment in vivo are performed to validate the proposed strategy. It demonstrates that the presented strategy provides a good distribution of fluorophore with limited projections of fluorescence measurements. Hence, it is suitable for reconstruction of limited-projection FMT.

Fast multislice fluorescence molecular tomography using sparsity-inducing regularization

Fluorescence molecular tomography (FMT) is a rapidly growing imaging method that facilitates the recovery of small fluorescent targets within biological tissue. The major challenge facing the FMT reconstruction method is the ill-posed nature of the inverse problem. In order to overcome this problem, the acquisition of large FMT datasets and the utilization of a fast FMT reconstruction algorithm with sparsity regularization have been suggested recently. Therefore, the use of a joint L1/total-variation (TV) regularization as a means of solving the ill-posed FMT inverse problem is proposed. A comparative quantified analysis of regularization methods based on L1-norm and TV are performed using simulated datasets, and the results show that the fast composite splitting algorithm regularization method can ensure the accuracy and robustness of the FMT reconstruction. The feasibility of the proposed method is evaluated in an in vivo scenario for the subcutaneous implantation of a fluorescent-dye-filled capillary tube in a mouse, and also using hybrid FMT and x-ray computed tomography data. The results show that the proposed regularization overcomes the difficulties created by the ill-posed inverse problem.

Mesh Optimization for Monte Carlo-Based Optical Tomography

Mesh-based Monte Carlo techniques for optical imaging allow for accurate modeling of light propagation in complex biological tissues. Recently, they have been developed within an efficient computational framework to be used as a forward model in optical tomography. However, commonly employed adaptive mesh discretization techniques have not yet been implemented for Monte Carlo based tomography. Herein, we propose a methodology to optimize the mesh discretization and analytically rescale the associated Jacobian based on the characteristics of the forward model. We demonstrate that this method maintains the accuracy of the forward model even in the case of temporal data sets while allowing for significant coarsening or refinement of the mesh.

Three-dimensional photoacoustic tomography based on graphics-processing-unit-accelerated finite element method

Compared with commonly used analytical reconstruction methods, the frequency-domain finite element method (FEM) based approach has proven to be an accurate and flexible algorithm for photoacoustic tomography. However, the FEM-based algorithm is computationally demanding, especially for three-dimensional cases. To enhance the algorithm's efficiency, in this work a parallel computational strategy is implemented in the framework of the FEM-based reconstruction algorithm using a graphic-processing-unit parallel frame named the "compute unified device architecture." A series of simulation experiments is carried out to test the accuracy and accelerating effect of the improved method. The results obtained indicate that the parallel calculation does not change the accuracy of the reconstruction algorithm, while its computational cost is significantly reduced by a factor of 38.9 with a GTX 580 graphics card using the improved method.

Design and evaluation of a miniature probe integrating diffuse optical tomography and electroencephalographic source localization

We present a dual-modality three-dimensional imaging approach that integrates diffuse optical tomography (DOT) and electroencephalographic source localization (ESL). This dual-modal DOT/ESL approach is evaluated using solid tissue-like phantoms where targets having both optical and electrical contrasts relative to the background phantom are included. The results obtained from extensive phantom experiments show that this dual-modal approach is suitable for imaging seizure focus in the study of epilepsy.

Discretization error analysis and adaptive meshing algorithms for fluorescence diffuse optical tomography: part II

In the first part of this work, we analyze the effect of discretization on the accuracy of fluorescence diffuse optical tomography (FDOT). Our error analysis provides two new error estimates which present a direct relationship between the error in the reconstructed fluorophore concentration and the discretization of the forward and inverse problems. In this paper, based on these error estimates, we develop two new adaptive mesh generation algorithms for the numerical solutions of the forward and inverse problems in FDOT, with the objective of error reduction in the reconstructed optical images due to discretization while keeping the size of the discretized forward and inverse problems within the allowable limits. We present three-dimensional numerical simulations to demonstrate the improvements in accuracy, resolution and detectability of small heterogeneities in reconstructed images provided by the use of the new adaptive mesh generation algorithms. Finally, we compare our algorithms both analytically and numerically with the existing conventional adaptive mesh generation algorithms.

Fast tomographic reconstruction strategy for diffuse optical tomography

Diffuse Optical Tomography (DOT) has been growing significantly in the past two decades as a promising tool for in-vivo and non-invasive imaging of tissues using near-infrared light. It can improve our ability to probe complex biologic interactions dynamically and to study disease and treatment responses over time in near real time. Recent advances on the transfer of techniques from laboratory to clinics have led to the development of various diagnostic applications such as imaging of the female breast and infant brain. The potential value of the promising tool, however, can be limited by the reconstruction time for tomographically imaging tissue optical properties. The current solution procedure in DOT consumes a considerable amount of time due to discretization of the problem domain and nonlinear nature of tissue optical properties. It is becoming ever more important to develop faster imaging tools as measurement data sets increase in size as a result of the application of newer generation instruments. Here we provide a fast solution strategy that significantly reduces imaging effort for DOT. The fast imaging strategy adopts advanced model-order reduction (MOR) techniques for reducing system complexity, while preserving (to the greatest possible extent) system input-output behavior for the forward problem. Our results demonstrate that the MOR-based imaging method can be an order of magnitude faster than the conventional approach while maintaining a relatively small error tolerance. The goal is to develop inexpensive, noninvasive imaging system that can run at patient's bedside in real time and produce data continuously over a long period of time.

Non-invasive imaging of epileptic seizures in vivo using photoacoustic tomography

Non-invasive laser-induced photoacoustic tomography (PAT) is an emerging imaging modality that has the potential to image the dynamic function of the brain due to its unique ability of imaging biological tissues with high optical contrast and ultrasound resolution. Here we report the first application of our finite-element-based PAT for imaging of epileptic seizures in an animal model. In vivo photoacoustic images were obtained in rats with focal seizures induced by microinjection of bicuculline, a GABA(A) antagonist, into the neocortex. The seizure focus was accurately localized by PAT as confirmed with gold-standard electroencephalogram (EEG). Compared to the existing neuroimaging modalities, PAT not only has the unprecedented advantage of high spatial and temporal resolution in a single imaging modality, but also is portable and low in cost, making it possible to bring brain imaging to the bedside.

Digital mouse phantom for optical imaging

We present a method for design and use of a digital mouse phantom for small animal optical imaging. We map the boundary of a mouse model from magnetic resonance imaging (MRI) data through image processing algorithms and discretize the geometry by a finite element (FE) descriptor. We use a validated FE implementation of the three-dimensional (3-D) diffusion equation to model transport of near infrared (NIR) light in the phantom with a mesh resolution optimized for representative tissue optical properties on a computing system with 8-GB RAM. Our simulations demonstrate that a section of the mouse near the light source is adequate for optical system design and that the variation of intensity of light on the boundary is well within typical noise levels for up to 20% variation in optical properties and nodes used to model the boundary of the phantom. We illustrate the use of the phantom in setting goals for specific binding of targeted exogenous fluorescent contrasts based on anatomical location by simulating a nearly tenfold change in the detectability of a 2-mm-deep target depending on its placement. The methodology described is sufficiently general and may be extended to generate digital phantoms for designing clinical optical imaging systems.

Image correction algorithm for functional three-dimensional diffuse optical tomography brain imaging

We outline a computationally efficient image correction algorithm, which we have applied to diffuse optical tomography (DOT) image time series derived from a magnetic resonance imaging (MRI)-based brain model. Results show that the algorithm increases spatial resolution, decreases spatial bias, and only modestly reduces temporal accuracy for noise levels typically seen in experiment, and produces results comparable to image reconstructions that incorporate information from MRI priors. We demonstrate that this algorithm has robust performance in the presence of noise, background heterogeneity, irregular external and internal boundaries, and error in the initial guess. However, the algorithm introduces artifacts when the absorption and scattering coefficients of the reference medium are overestimated--a situation that is easily avoided in practice. The considered algorithm offers a practical approach to improving the quality of images from time-series DOT, even without the use of MRI priors.

Mesh adaptation technique for Fourier-domain fluorescence lifetime imaging

A novel adaptive mesh technique in the Fourier domain is introduced for problems in fluorescence lifetime imaging. A dynamical adaptation of the three-dimensional scheme based on the finite volume formulation reduces computational time and balances the ill-posed nature of the inverse problem. Light propagation in the medium is modeled by the telegraph equation, while the lifetime reconstruction algorithm is derived from the Fredholm integral equation of the first kind. Stability and computational efficiency of the method are demonstrated by image reconstruction of two spherical fluorescent objects embedded in a tissue phantom.

Finite-element-based photoacoustic tomography: phantom and chicken bone experiments

We describe a photoacoustic image reconstruction algorithm that is based on the finite-element solution to the photoacoustic wave equation in the frequency domain. Our reconstruction approach is an iterative Newton method coupled with combined Marquardt and Tikhonov regularizations that can extract the spatial distribution of optical-absorption property in heterogeneous media. We demonstrate this algorithm by using phantom and chicken bone measurements from a circular scanning photoacoustic tomography system. The results obtained show that millimeter-sized phantom objects and chicken bones and/or joints can be clearly detected using our finite-element-based photoacoustic tomography method.

Dynamically adaptive mesh refinement technique for image reconstruction in optical tomography

A novel adaptive mesh technique is introduced for problems of image reconstruction in luminescence optical tomography. A dynamical adaptation of the three-dimensional scheme based on the finite-volume formulation reduces computational time and balances the ill-posed nature of the inverse problem. The arbitrary shape of the bounding surface is handled by an additional refinement of computational cells on the boundary. Dynamical shrinking of the search volume is introduced to improve computational performance and accuracy while locating the luminescence target. Light propagation in the medium is modeled by the telegraph equation, and the image-reconstruction algorithm is derived from the Fredholm integral equation of the first kind. Stability and computational efficiency of the introduced method are demonstrated for image reconstruction of one and two spherical luminescent objects embedded within a breastlike tissue phantom. Experimental measurements are simulated by the solution of the forward problem on a grid of 5x5 light guides attached to the surface of the phantom.

Spatially varying optical and acoustic property reconstruction using finite-element-based photoacoustic tomography

A finite-element reconstruction algorithm for simultaneous reconstruction of both optical and acoustic properties of heterogeneous media is presented. The algorithm is based on the Helmholtz-like photoacoustic wave equation in the frequency domain. A dual meshing scheme is described and an adjoint sensitivity method is adopted for efficient inverse computation. The algorithm is implemented with the second-order absorbing boundary conditions and with a multireceiving and multifrequency strategy. The algorithm is evaluated using simulated data under various practical cases including different noise levels, varied range of receiving frequency, different contrast levels between the heterogeneity and background region, and multiple targets. The effect of acoustic heterogeneity on conventional pure optical absorption reconstruction is also studied.

Model-based ultrasound tomography: Tissue phantom experiments

We present a detailed experimental study to evaluate our finite element based nonlinear reconstruction algorithm for recovery of acoustic properties in heterogeneous scattering media. Using a circularly scanning ultrasound system at 500 KHz, tissue phantom experiments were performed to study spatial resolution and contrast issues in model-based ultrasound tomography. Our results show that both acoustic attenuation and speed images can be quantitatively reconstructed in terms of the location, size, shape, and acoustic property value of the target when different contrast levels between the target and background were used. We also demonstrate that a high contrast target as small as 3 mm in diameter can be quantitatively resolved with our acoustic speed and attenuation images.

Looking and listening to light: the evolution of whole-body photonic imaging

Optical imaging of live animals has grown into an important tool in biomedical research as advances in photonic technology and reporter strategies have led to widespread exploration of biological processes in vivo. Although much attention has been paid to microscopy, macroscopic imaging has allowed small-animal imaging with larger fields of view (from several millimeters to several centimeters depending on implementation). Photographic methods have been the mainstay for fluorescence and bioluminescence macroscopy in whole animals, but emphasis is shifting to photonic methods that use tomographic principles to noninvasively image optical contrast at depths of several millimeters to centimeters with high sensitivity and sub-millimeter to millimeter resolution. Recent theoretical and instrumentation advances allow the use of large data sets and multiple projections and offer practical systems for quantitative, three-dimensional whole-body images. For photonic imaging to fully realize its potential, however, further progress will be needed in refining optical inversion methods and data acquisition techniques.

Measurement of particle-size distribution and concentration in heterogeneous turbid media with multispectral diffuse optical tomography

We present a method that is capable of extracting particle-size distribution (PSD) and concentration in heterogeneous turbid media by use of multispectral diffuse optical tomography (MSDOT). After the spectroscopic scattering images of the heterogeneous turbid media are obtained with MSDOT, the morphologic information of particles in the heterogeneities is recovered with an iterative regularized reconstruction algorithm based on Mie scattering theory when a particular form of PSD is assumed (Gaussian distribution is used in this study). The method described is tested and evaluated with both simulated and experimental data. The simulations are intended to test the sensitivity of the overall approach to noise effect. A series of phantom experiments are conducted with our newly developed ten-wavelength MSDOT system. Polystyrene microsphere suspensions contain particles of varying size from 2 to 6 microm as targets are embedded in a scattering background medium in these experiments. To achieve optimized results from experimental data, we developed a data preprocessing method for MSDOT as well as a scheme for calibrating scattering spectra. The results from both simulations and experiments show that the particle mean size and concentration can be reconstructed with acceptable accuracy, whereas the recovery of the standard deviation is sensitive to noise effect and can be as large as 86% from the experimental data.

Differentiation of cysts from solid tumors in the breast with diffuse optical tomography

RATIONALE AND OBJECTIVES

Near-infrared diffuse optical tomography (DOT) is an emerging imaging technology that has the potential to offer enhanced contrast resolution over the existing technologies for detection and diagnosis of breast cancer. Thus far, the clinical evaluation of DOT has been largely limited to solid tumors. A pilot clinical study focused on DOT imaging of breasts with cysts is presented.

MATERIALS AND METHODS

Six cases were studied using the recently developed compact, parallel-detection DOT system. Images characterizing the tissue absorption and scattering were obtained with a finite element-based reconstruction algorithm. The optical images were compared with the mammograms and sonograms. In one case, in vitro measurements of optical properties were conducted for the fluid obtained from needle aspiration.

RESULTS

Substantial contrast between cyst and adjacent parenchyma is observed. For the six cases evaluated, the locations and sizes of cysts imaged optically are accurate and consistent with the mammographic and sonographic findings. For the case that aspiration was performed, the absorption and scattering coefficients imaged in the cyst region are quantitatively accurate compared with that measured in vitro from the fluid aspirated.

CONCLUSION

This pilot study shows that cysts ranging from 1-4 cm in diameter can be quantitatively imaged. They can be differentiated from solid breast tumors because cysts generally demonstrate lower absorption and scattering coefficients compared with the surrounding normal tissue, whereas solid tumors show concurrent higher absorption and scattering related to the normal tissue.