Implementation of a computationally efficient least-squares algorithm for highly under-determined three-dimensional diffuse optical tomography problems

Direct approach to compute Jacobians for diffuse optical tomography using perturbation Monte Carlo-based photon "replay"

Perturbation Monte Carlo (pMC) has been previously proposed to rapidly recompute optical measurements when small perturbations of optical properties are considered, but it was largely restricted to changes associated with prior tissue segments or regions-of-interest. In this work, we expand pMC to compute spatially and temporally resolved sensitivity profiles, i.e. the Jacobians, for diffuse optical tomography (DOT) applications. By recording the pseudo random number generator (PRNG) seeds of each detected photon, we are able to "replay" all detected photons to directly create the 3D sensitivity profiles for both absorption and scattering coefficients. We validate the replay-based Jacobians against the traditional adjoint Monte Carlo (aMC) method, and demonstrate the feasibility of using this approach for efficient 3D image reconstructions using in vitro hyperspectral wide-field DOT measurements. The strengths and limitations of the replay approach regarding its computational efficiency and accuracy are discussed, in comparison with aMC, for point-detector systems as well as wide-field pattern-based and hyperspectral imaging systems. The replay approach has been implemented in both of our open-source MC simulators - MCX and MMC (http://mcx.space).

Model-resolution-based basis pursuit deconvolution improves diffuse optical tomographic imaging

The image reconstruction problem encountered in diffuse optical tomographic imaging is ill-posed in nature, necessitating the usage of regularization to result in stable solutions. This regularization also results in loss of resolution in the reconstructed images. A frame work, that is attributed by model-resolution, to improve the reconstructed image characteristics using the basis pursuit deconvolution method is proposed here. The proposed method performs this deconvolution as an additional step in the image reconstruction scheme. It is shown, both in numerical and experimental gelatin phantom cases, that the proposed method yields better recovery of the target shapes compared to traditional method, without the loss of quantitativeness of the results.

Data-resolution based optimization of the data-collection strategy for near infrared diffuse optical tomography

PURPOSE

To optimize the data-collection strategy for diffuse optical tomography and to obtain a set of independent measurements among the total measurements using the model based data-resolution matrix characteristics.

METHODS

The data-resolution matrix is computed based on the sensitivity matrix and the regularization scheme used in the reconstruction procedure by matching the predicted data with the actual one. The diagonal values of data-resolution matrix show the importance of a particular measurement and the magnitude of off-diagonal entries shows the dependence among measurements. Based on the closeness of diagonal value magnitude to off-diagonal entries, the independent measurements choice is made. The reconstruction results obtained using all measurements were compared to the ones obtained using only independent measurements in both numerical and experimental phantom cases. The traditional singular value analysis was also performed to compare the results obtained using the proposed method.

RESULTS

The results indicate that choosing only independent measurements based on data-resolution matrix characteristics for the image reconstruction does not compromise the reconstructed image quality significantly, in turn reduces the data-collection time associated with the procedure. When the same number of measurements (equivalent to independent ones) are chosen at random, the reconstruction results were having poor quality with major boundary artifacts. The number of independent measurements obtained using data-resolution matrix analysis is much higher compared to that obtained using the singular value analysis.

CONCLUSIONS

The data-resolution matrix analysis is able to provide the high level of optimization needed for effective data-collection in diffuse optical imaging. The analysis itself is independent of noise characteristics in the data, resulting in an universal framework to characterize and optimize a given data-collection strategy.

Mesh-based Monte Carlo method in time-domain widefield fluorescence molecular tomography

We evaluated the potential of mesh-based Monte Carlo (MC) method for widefield time-gated fluorescence molecular tomography, aiming to improve accuracy in both shape discretization and photon transport modeling in preclinical settings. An optimized software platform was developed utilizing multithreading and distributed parallel computing to achieve efficient calculation. We validated the proposed algorithm and software by both simulations and in vivo studies. The results establish that the optimized mesh-based Monte Carlo (mMC) method is a computationally efficient solution for optical tomography studies in terms of both calculation time and memory utilization. The open source code, as part of a new release of mMC, is publicly available at http://mcx.sourceforge.net/mmc/.

Optical imaging in cancer research: basic principles, tumor detection, and therapeutic monitoring

Accurate and rapid detection of diseases is of great importance for assessing the molecular basis of pathogenesis, preventing the onset of complications, and implementing a tailored therapeutic regimen. The ability of optical imaging to transcend wide spatial imaging scales ranging from cells to organ systems has rejuvenated interest in using this technology for medical imaging. Moreover, optical imaging has at its disposal diverse contrast mechanisms for distinguishing normal from pathologic processes and tissues. To accommodate these signaling strategies, an array of imaging techniques has been developed. Importantly, light absorption, and emission methods, as well as hybrid optical imaging approaches are amenable to both small animal and human studies. Typically, complex methods are needed to extract quantitative data from deep tissues. This review focuses on the development of optical imaging platforms, image processing techniques, and molecular probes, as well as their applications in cancer diagnosis, staging, and monitoring therapeutic response.

Accelerating frequency-domain diffuse optical tomographic image reconstruction using graphics processing units

Diffuse optical tomographic image reconstruction uses advanced numerical models that are computationally costly to be implemented in the real time. The graphics processing units (GPUs) offer desktop massive parallelization that can accelerate these computations. An open-source GPU-accelerated linear algebra library package is used to compute the most intensive matrix-matrix calculations and matrix decompositions that are used in solving the system of linear equations. These open-source functions were integrated into the existing frequency-domain diffuse optical image reconstruction algorithms to evaluate the acceleration capability of the GPUs (NVIDIA Tesla C 1060) with increasing reconstruction problem sizes. These studies indicate that single precision computations are sufficient for diffuse optical tomographic image reconstruction. The acceleration per iteration can be up to 40, using GPUs compared to traditional CPUs in case of three-dimensional reconstruction, where the reconstruction problem is more underdetermined, making the GPUs more attractive in the clinical settings. The current limitation of these GPUs in the available onboard memory (4 GB) that restricts the reconstruction of a large set of optical parameters, more than 13,377.

A coupled finite element-boundary element method for modeling Diffusion equation in 3D multi-modality optical imaging

Three dimensional image reconstruction for multi-modality optical spectroscopy systems needs computationally efficient forward solvers with minimum meshing complexity, while allowing the flexibility to apply spatial constraints. Existing models based on the finite element method (FEM) require full 3D volume meshing to incorporate constraints related to anatomical structure via techniques such as regularization. Alternate approaches such as the boundary element method (BEM) require only surface discretization but assume homogeneous or piece-wise constant domains that can be limiting. Here, a coupled finite element-boundary element method (coupled FE-BEM) approach is demonstrated for modeling light diffusion in 3D, which uses surfaces to model exterior tissues with BEM and a small number of volume nodes to model interior tissues with FEM. Such a coupled FE-BEM technique combines strengths of FEM and BEM by assuming homogeneous outer tissue regions and heterogeneous inner tissue regions. Results with FE-BEM show agreement with existing numerical models, having RMS differences of less than 0.5 for the logarithm of intensity and 2.5 degrees for phase of frequency domain boundary data. The coupled FE-BEM approach can model heterogeneity using a fraction of the volume nodes (4-22%) required by conventional FEM techniques. Comparisons of computational times showed that the coupled FE-BEM was faster than stand-alone FEM when the ratio of the number of surface to volume nodes in the mesh (N(s)/N(v)) was less than 20% and was comparable to stand-alone BEM ( ± 10%).

Compositional-prior-guided image reconstruction algorithm for multi-modality imaging

The development of effective multi-modality imaging methods typically requires an efficient information fusion model, particularly when combining structural images with a complementary imaging modality that provides functional information. We propose a composition-based image segmentation method for X-ray digital breast tomosynthesis (DBT) and a structural-prior-guided image reconstruction for a combined DBT and diffuse optical tomography (DOT) breast imaging system. Using the 3D DBT images from 31 clinically measured healthy breasts, we create an empirical relationship between the X-ray intensities for adipose and fibroglandular tissue. We use this relationship to then segment another 58 healthy breast DBT images from 29 subjects into compositional maps of different tissue types. For each breast, we build a weighted-graph in the compositional space and construct a regularization matrix to incorporate the structural priors into a finite-element-based DOT image reconstruction. Use of the compositional priors enables us to fuse tissue anatomy into optical images with less restriction than when using a binary segmentation. This allows us to recover the image contrast captured by DOT but not by DBT. We show that it is possible to fine-tune the strength of the structural priors by changing a single regularization parameter. By estimating the optical properties for adipose and fibroglandular tissue using the proposed algorithm, we found the results are comparable or superior to those estimated with expert-segmentations, but does not involve the time-consuming manual selection of regions-of-interest.

Parametric Diffuse Optical Imaging in Reflectance Geometry

Diffuse optical imaging (DOI) is a model-based technique used for noninvasive characterization of subsurface tissue function and structure. Compared to more common transmission geometries, reflectance DOI has the advantage of being portable and easily implemented in a clinical setting. However, reflectance measurements are generally not compatible with conventional DOI image reconstruction methods because they typically provide a limited number of unique tissue views. In this paper, we describe a fast and reliable DOI image reconstruction method based on parameterization of tissue and tumor optical contrast, using physiological a priori knowledge. The reconstruction method is formulated within the general Bayesian inversion framework and is capable of handling both model and measurement errors. Simulations are carried out to illustrate the application of this approach, using a limited number of source-detector combinations. It is also shown that parametric reflectance DOI is robust to model misspecifications and measurement noise.

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.

Image-guided near infrared spectroscopy using boundary element method: phantom validation

Image-guided near infrared spectroscopy (IG-NIRS) can provide high-resolution vascular, metabolic and molecular characterization of localized tissue volumes in-vivo. The approach for IG-NIRS uses hybrid systems where the spatial anatomical structure of tissue obtained from standard imaging modalities (such as MRI) is combined with tissue information from diffuse optical imaging spectroscopy. There is need to optimize these hybrid systems for large-scale clinical trials anticipated in the near future in order to evaluate the feasibility of this technology across a larger population. However, existing computational methods such as the finite element method mesh arbitrary image volumes, which inhibit automation, especially with large numbers of datasets. Circumventing this issue, a boundary element method (BEM) for IG-NIRS systems in 3-D is presented here using only surface rendering and discretization. The process of surface creation and meshing is faster, more reliable, and is easily generated automatically as compared to full volume meshing. The proposed method has been implemented here for multi-spectral non-invasive characterization of tissue. In phantom experiments, 3-D spectral BEM-based spectroscopy recovered the oxygen dissociation curve with mean error of 6.6% and tracked variation in total hemoglobin linearly.