A Model-Based Iterative Learning Approach for Diffuse Optical Tomography.

Diffuse optical tomography (DOT) utilises near-infrared light for imaging spatially distributed optical parameters, typically the absorption and scattering coefficients. The image reconstruction problem of DOT is an ill-posed inverse problem, due to the non-linear light propagation in tissues and limited boundary measurements. The ill-posedness means that the image reconstruction is sensitive to measurement and modelling errors. The Bayesian approach for the inverse problem of DOT offers the possibility of incorporating prior information about the unknowns, rendering the problem less ill-posed. It also allows marginalisation of modelling errors utilising the so-called Bayesian approximation error method. A more recent trend in image reconstruction techniques is the use of deep learning, which has shown promising results in various applications from image processing to tomographic reconstructions. In this work, we study the non-linear DOT inverse problem of estimating the (absolute) absorption and scattering coefficients utilising a 'model-based' learning approach, essentially intertwining learned components with the model equations of DOT. The proposed approach was validated with 2D simulations and 3D experimental data. We demonstrated improved absorption and scattering estimates for targets with a mix of smooth and sharp image features, implying that the proposed approach could learn image features that are difficult to model using standard Gaussian priors. Furthermore, it was shown that the approach can be utilised in compensating for modelling errors due to coarse discretisation enabling computationally efficient solutions. Overall, the approach provided improved computation times compared to a standard Gauss-Newton iteration.

Evaluation of temporal moments and Fourier transformed data in time-domain diffuse optical tomography.

Time-domain diffuse optical tomography (TD-DOT) uses near-infrared pulsed lasers as light sources to measure time-varying exitance on the boundary of the target. These are used to estimate optical properties of the imaged target. Several integral-transform-based moments of the time-resolved data have been utilized in TD-DOT, the most common being the mean time of flight and variance. Recently, it has been shown that Fourier transforming the time-domain data to frequency domain enables utilization of these data at one or several frequencies, producing equally as good estimates as the whole time-domain data. In this work, we present a systematic comparison of the usage of the temporal moments and Fourier transformed data in TD-DOT. Both absolute and difference imaging are evaluated using numerical simulations. The simulations show that utilizing temporal moments and Fourier transformed data in TD-DOT provides good quality reconstructions with a good estimation accuracy. These estimates are improved if more than one data type is used. Furthermore, the simulations show that the frequency-domain computations enable computationally cheaper and straightforward implementation of the inverse solver when compared to the temporal moments.

Perturbation Monte Carlo Method for Quantitative Photoacoustic Tomography.

Quantitative photoacoustic tomography aims at estimating optical parameters from photoacoustic images that are formed utilizing the photoacoustic effect caused by the absorption of an externally introduced light pulse. This optical parameter estimation is an ill-posed inverse problem, and thus it is sensitive to measurement and modeling errors. In this work, we propose a novel way to solve the inverse problem of quantitative photoacoustic tomography based on the perturbation Monte Carlo method. Monte Carlo method for light propagation is a stochastic approach for simulating photon trajectories in a medium with scattering particles. It is widely accepted as an accurate method to simulate light propagation in tissues. Furthermore, it is numerically robust and easy to implement. Perturbation Monte Carlo maintains this robustness and enables forming gradients for the solution of the inverse problem. We validate the method and apply it in the framework of Bayesian inverse problems. The simulations show that the perturbation Monte Carlo method can be used to estimate spatial distributions of both absorption and scattering parameters simultaneously. These estimates are qualitatively good and quantitatively accurate also in parameter scales that are realistic for biological tissues.

Time-domain diffuse optical tomography utilizing truncated Fourier series approximation.

Diffuse optical tomography (DOT) uses near infrared light for in vivo imaging of spatially varying optical parameters in biological tissues. It is known that time-resolved measurements provide the richest information on soft tissues, among other measurement types in DOT such as steady-state and intensity-modulated measurements. Therefore, several integral-transform-based moments of the time-resolved DOT measurements have been considered to estimate spatially distributed optical parameters. However, the use of such moments can result in low-contrast images and cross-talks between the reconstructed optical parameters, limiting their accuracy. In this work, we propose to utilize a truncated Fourier series approximation in time-resolved DOT. Using this approximation, we obtained optical parameter estimates with accuracy comparable to using whole time-resolved data that uses low computational time and resources. The truncated Fourier series approximation based estimates also displayed good contrast and minimal parameter cross-talk, and the estimates further improved in accuracy when multiple Fourier frequencies were used.

Histological data of axons, astrocytes, and myelin in deep subcortical white matter populations.

This immunohistochemistry dataset contains the main structures in deep subcortical white matter (axons, astrocytes, and myelinated axons) in a representative cohort of an ageing population. A set of samples from 90 subjects of the Cognitive Function and Ageing Study (CFAS) were analysed, stratified into three groups of 30 subjects each, in relation to the presence of age-associated deep subcortical lesions. High-resolution microscopy data enables the extraction of valuable information, such as volume fractions, for the construction and validation of diffusion MRI (dMRI) models. The dataset provided here was used in Coelho et al. [1].

Quantitative histomorphometry of capillary microstructure in deep white matter.

White matter lesions represent a major risk factor for dementia in elderly people. Magnetic Resonance Imaging (MRI) studies have demonstrated cerebral blood flow reduction in age-related white matter lesions, indicating that vascular alterations are involved in developing white matter lesions. Hypoperfusion and changes in capillary morphology are generally linked to dementia. However, a quantitative study describing these microvascular alterations in white matter lesions is missing in the literature; most previous microvascular studies being on the cortex. The aim of this work is to identify and quantify capillary microstructural changes involved in the appearance of deep subcortical lesions (DSCL). We characterize the distribution of capillary diameter, thickness, and density in the deep white matter in a population of 75 elderly subjects, stratified into three equal groups according to DSCL: Control (subject without DSCL), Lesion (sample presenting DSCL), and Normal Appearing White Matter (NAWM, the subject presented DSCL but not at the sampled tissue location). Tissue samples were selected from the Cognitive Function and Aging Study (CFAS), a cohort representative of an aging population, from which immunohistochemically-labeled histological images were acquired. To accurately estimate capillary diameters and thicknesses from the 2D histological images, we also introduce a novel semi-automatic method robust to non-perpendicular incidence angle of capillaries into the imaging plane, and to non-circular deformations of capillary cross sections. Subjects with DSCL presented a significant increase in capillary wall thickness, a decrease in the diameter intra-subject variability (but not in the mean), and a decrease in capillary density. No significant difference was observed between controls and NAWM. Both capillary wall thickening and reduction in capillary density contribute to the reduction of cerebral blood flow previously reported for white matter lesions. The obtained distributions provide reliable statistics of capillary microstructure useful to inform the modeling of human cerebral blood flow, for instance to define microcirculation models for their estimation from MRI or to perform realistic cerebral blood flow simulations.

Population-based Bayesian regularization for microstructural diffusion MRI with NODDIDA.

PURPOSE: Information on the brain microstructure can be probed by Diffusion Magnetic Resonance Imaging (dMRI). Neurite Orientation Dispersion and Density Imaging with Diffusivities Assessment (NODDIDA) is one of the simplest microstructural model proposed. However, the estimation of the NODDIDA parameters from clinically plausible dMRI acquisition is ill-posed, and different parameter sets can describe the same measurements equally well. A few approaches to resolve this problem focused on developing better optimization strategies for this non-convex optimization. However, this fundamentally does not resolve ill-posedness. This article introduces a Bayesian estimation framework, which is regularized through knowledge from an extensive dMRI measurement set on a population of healthy adults (henceforth population-based prior). METHODS: We reformulate the problem as a Bayesian maximum a posteriori estimation, which includes as a special case previous approach using non-informative uniform priors. A population-based prior is estimated from 35 subjects of the MGH Adult Diffusion data (Human Connectome Project), acquired with an extensive acquisition protocol including high b-values. The accuracy and robustness of different approaches with and without the population-based prior is tested on subsets of the MGH dataset, and an independent dataset from a clinically comparable scanner, with only clinically plausible dMRI measurements. RESULTS: The population-based prior produced substantially more accurate and robust parameter estimates, compared to the conventional uniform priors, for clinically feasible protocols, without introducing any evident bias. CONCLUSIONS: The use of the proposed Bayesian population-based prior can lead to clinically feasible and robust estimation of NODDIDA parameters without changing the acquisition protocol.

Iba-1-/CD68+ microglia are a prominent feature of age-associated deep subcortical white matter lesions.

Deep subcortical lesions (DSCL) of the brain, are present in ~60% of the ageing population, and are linked to cognitive decline and depression. DSCL are associated with demyelination, blood brain barrier (BBB) dysfunction, and microgliosis. Microglia are the main immune cell of the brain. Under physiological conditions microglia have a ramified morphology, and react to pathology with a change to a more rounded morphology as well as showing protein expression alterations. This study builds on previous characterisations of DSCL and radiologically 'normal-appearing' white matter (NAWM) by performing a detailed characterisation of a range of microglial markers in addition to markers of vascular integrity. The Cognitive Function and Ageing Study (CFAS) provided control white matter (WM), NAWM and DSCL human post mortem tissue for immunohistochemistry using microglial markers (Iba-1, CD68 and MHCII), a vascular basement membrane marker (collagen IV) and markers of BBB integrity (fibrinogen and aquaporin 4). The immunoreactive profile of CD68 increased in a stepwise manner from control WM to NAWM to DSCL. This correlated with a shift from small, ramified cells, to larger, more rounded microglia. While there was greater Iba-1 immunoreactivity in NAWM compared to controls, in DSCL, Iba-1 levels were reduced to control levels. A prominent feature of these DSCL was a population of Iba-1-/CD68+ microglia. There were increases in collagen IV, but no change in BBB integrity. Overall the study shows significant differences in the immunoreactive profile of microglial markers. Whether this is a cause or effect of lesion development remains to be elucidated. Identifying microglia subpopulations based on their morphology and molecular markers may ultimately help decipher their function and role in neurodegeneration. Furthermore, this study demonstrates that Iba-1 is not a pan-microglial marker, and that a combination of several microglial markers is required to fully characterise the microglial phenotype.

Local volume fraction distributions of axons, astrocytes, and myelin in deep subcortical white matter.

This study aims to statistically describe histologically stained white matter brain sections to subsequently inform and validate diffusion MRI techniques. For the first time, we characterise volume fraction distributions of three of the main structures in deep subcortical white matter (axons, astrocytes, and myelinated axons) in a representative cohort of an ageing population for which well-characterized neuropathology data is available. We analysed a set of samples from 90 subjects of the Cognitive Function and Ageing Study (CFAS), stratified into three groups of 30 subjects each, in relation to the presence of age-associated deep subcortical lesions. This provides volume fraction distributions in different scenarios relevant to brain diffusion MRI in dementia. We also assess statistically significant differences found between these groups. In agreement with previous literature, our results indicate that white matter lesions are related with a decrease in the myelinated axons fraction and an increase in astrocytic fraction, while no statistically significant changes occur in axonal mean fraction. In addition, we introduced a framework to quantify volume fraction distributions from 2D immunohistochemistry images, which is validated against in silico simulations. Since a trade-off between precision and resolution emerged, we also performed an assessment of the optimal scale for computing such distributions.

Simultaneous magnetic resonance diffusion and pseudo-diffusion tensor imaging.

PURPOSE: An emerging topic in diffusion magnetic resonance is imaging blood microcirculation alongside water diffusion using the intravoxel incoherent motion (IVIM) model. Recently, a combined IVIM diffusion tensor imaging (IVIM-DTI) model was proposed, which accounts for both anisotropic pseudo-diffusion due to blood microcirculation and anisotropic diffusion due to tissue microstructures. In this article, we propose a robust IVIM-DTI approach for simultaneous diffusion and pseudo-diffusion tensor imaging. METHODS: Conventional IVIM estimation methods can be broadly divided into two-step (diffusion and pseudo-diffusion estimated separately) and one-step (diffusion and pseudo-diffusion estimated simultaneously) methods. Here, both methods were applied on the IVIM-DTI model. An improved one-step method based on damped Gauss-Newton algorithm and a Gaussian prior for the model parameters was also introduced. The sensitivities of these methods to different parameter initializations were tested with realistic in silico simulations and experimental in vivo data. RESULTS: The one-step damped Gauss-Newton method with a Gaussian prior was less sensitive to noise and the choice of initial parameters and delivered more accurate estimates of IVIM-DTI parameters compared to the other methods. CONCLUSION: One-step estimation using damped Gauss-Newton and a Gaussian prior is a robust method for simultaneous diffusion and pseudo-diffusion tensor imaging using IVIM-DTI model. Magn Reson Med 79:2367-2378, 2018. © 2017 The Authors Magnetic Resonance in Medicine published by Wiley Periodicals, Inc. on behalf of International Society for Magnetic Resonance in Medicine. This is an open access article under the terms of the Creative Commons Attribution License, which permits use, distribution and reproduction in any medium, provided the original work is properly cited.

Nonlinear approach to difference imaging in diffuse optical tomography.

Difference imaging aims at recovery of the change in the optical properties of a body based on measurements before and after the change. Conventionally, the image reconstruction is based on using difference of the measurements and a linear approximation of the observation model. One of the main benefits of the linearized difference reconstruction is that the approach has a good tolerance to modeling errors, which cancel out partially in the subtraction of the measurements. However, a drawback of the approach is that the difference images are usually only qualitative in nature and their spatial resolution can be weak because they rely on the global linearization of the nonlinear observation model. To overcome the limitations of the linear approach, we investigate a nonlinear approach for difference imaging where the images of the optical parameters before and after the change are reconstructed simultaneously based on the two datasets. We tested the feasibility of the method with simulations and experimental data from a phantom and studied how the approach tolerates modeling errors like domain truncation, optode coupling errors, and domain shape errors.

Compensation of modeling errors due to unknown domain boundary in diffuse optical tomography.

Diffuse optical tomography is a highly unstable problem with respect to modeling and measurement errors. During clinical measurements, the body shape is not always known, and an approximate model domain has to be employed. The use of an incorrect model domain can, however, lead to significant artifacts in the reconstructed images. Recently, the Bayesian approximation error theory has been proposed to handle model-based errors. In this work, the feasibility of the Bayesian approximation error approach to compensate for modeling errors due to unknown body shape is investigated. The approach is tested with simulations. The results show that the Bayesian approximation error method can be used to reduce artifacts in reconstructed images due to unknown domain shape.

Compensation of optode sensitivity and position errors in diffuse optical tomography using the approximation error approach.

Diffuse optical tomography is highly sensitive to measurement and modeling errors. Errors in the source and detector coupling and positions can cause significant artifacts in the reconstructed images. Recently the approximation error theory has been proposed to handle modeling errors. In this article, we investigate the feasibility of the approximation error approach to compensate for modeling errors due to inaccurately known optode locations and coupling coefficients. The approach is evaluated with simulations. The results show that the approximation error method can be used to recover from artifacts in reconstructed images due to optode coupling and position errors.