Development of a radiative transport based, fluorescence-enhanced, frequency-domain small animal imaging system

Herein we present the development of a fluorescence-enhanced, frequency-domain radiative transport reconstruction system designed for small animal optical tomography. The system includes a time-dependent data acquisition instrument, a radiative transport based forward model for prediction of time-dependent propagation of photons in small, non-diffuse volumes, and an algorithm which utilizes the forward model to reconstruct fluorescent yields from air/tissue boundary measurements. The major components of the instrumentation include a charge coupled device camera, an image intensifier, signal generators, and an optical switch. Time-dependent data were obtained in the frequency-domain using homodyne techniques on phantoms with 0.2% to 3% intralipid solutions. Through collaboration with Transpire, Inc., a fluorescence-enhanced, frequency-domain, radiative transport equation (RTE) solver was developed. This solver incorporates the discrete ordinates, source iteration with diffusion synthetic acceleration, and linear discontinuous finite element differencing schemes, to predict accurately the fluence of excitation and emission photons in diffuse and transport limited systems. Additional techniques such as the first scattered distributed source method and integral transport theory are used to model the numerical apertures of fiber optic sources and detectors. The accuracy of the RTE solver was validated against diffusion and Monte Carlo predictions and experimental data. The comparisons were favorable in both the diffusion and transport limits, with average errors of the RTE predictions, as compared to experimental data, typically being less than 8% in amplitude and 7% in phase. These average errors are similar to those of the Monte Carlo and diffusion predictions. Synthetic data from a virtual mouse were used to demonstrate the feasibility of using the RTE solver for reconstructing fluorescent heterogeneities in small, non-diffuse volumes. The current version of the RTE solver limits the reconstruction to one iteration and the reconstruction of marginally diffuse, frequency-domain experimental data using RTE was not successful. Multiple iterations using a diffusion solver successfully reconstructed the fluorescent heterogeneities, indicating that, when available, multiple iterations of the RTE based solver should also reconstruct the heterogeneities

Quantitative susceptibility mapping and susceptibility-based distortion correction of echo planar images

Thesis (Ph. D. in Medical Engineering)--Harvard-MIT Program in Health Sciences and Technology, 2012.Cataloged from PDF version of thesis.Includes bibliographical references (p. 143-153).The field of medical image analysis continues to expand as magnetic resonance imaging (MRI) technology advances through increases in field strength and the development of new image acquisition and reconstruction methods. The advent of echo planar imaging (EPI) has allowed volumetric data sets to be obtained in a few seconds, making it possible to image dynamic physiological processes in the brain. In order to extract meaningful information from functional and diffusion data, clinicians and neuroscientists typically combine EPI data with high resolution structural images. Image registration is the process of determining the correct correspondence. Registration of EPI and structural images is difficult due to distortions in EPI data. These distortions are caused by magnetic field perturbations that arise from changes in magnetic susceptibility throughout the object of interest. Distortion is typically corrected by acquiring an additional scan called a fieldmap. A fieldmap provides a direct measure of the magnetic perturbations, allowing distortions to be easily computed and corrected. Fieldmaps, however, require additional scan time, may not be reliable in the presence of significant motion or respiration effects, and are often omitted from clinical protocols. In this thesis, we develop a novel method for correcting distortions in EPI data and registering the EPI to structural MRI. A synthetic fieldmap is computed from a tissue/air segmentation of a structural image using a perturbation method and subsequently used to unwarp the EPI data. Shim and other missing parameters are estimated by registration. We obtain results that are similar to those obtained using fieldmnaps, however, neither fieldmaps nor knowledge of shim coefficients is required. In addition, we describe a method for atlas-based segmentation of structural images for calculation of synthetic fieldmaps. CT data sets are used to construct a probabilistic atlas of the head and corresponding MRI is used to train a classifier that segments soft tissue, air, and bone. Synthetic fieldmap results agree well with acquired fieldmaps: 90% of voxel shifts show subvoxel disagreement with those computed from acquired fieldmaps. In addition, synthetic fieldmaps show statistically significant improvement following inclusion of the atlas. In the second part of this thesis, we focus on the inverse problem of reconstructing quantitative magnetic susceptibility maps from acquired fieldmaps. Iron deposits change the susceptibility of tissue, resulting in magnetic perturbations that are detectable with high resolution fieldmaps. Excessive iron deposition in specific regions of the brain is associated with neurodegenerative disorders such as Alzheimer's and Parkinson's disease. In addition, iron is known to accumulate at varying rates throughout the brain in normal aging. Developing a non-invasive method to calculate iron concentration may provide insight into the role of iron in the pathophysiology of neurodegenerative disease. Calculating susceptibility maps from measured fieldmaps is difficult, however, since iron-related field inhomogeneity may be obscured by larger field perturbations, or 'biasfields', arising from adjacent tissue/air boundaries. In addition, the inverse problem is ill-posed, and fieldmap measurements are only valid in limited anatomical regions. In this dissertation, we develop a novel atlas-based susceptibility mapping (ASM) technique that requires only a single fieldmap acquisition and successfully inverts a spatial formulation of the forward field model. We derive an inhomogeneous wave equation that relates the Laplacian of the observed field to the D'Alembertian of susceptibility, and eliminates confounding biasfields. The tissue/air atlas we constructed for susceptibility-based distortion correction is applied to resolve ambiquity in the forward model arising from the ill-posed inversion. We include fourier-based modeling of external susceptibility sources and the associated biasfield in a variational approach, allowing for simultaneous susceptibility estimation and biasfield elimination. Results show qualitative improvement over two methods commonly used to infer underlying susceptibility values and quantitative susceptibility estimates show stronger correlation with postmortem iron concentrations than competing methods.by Clare Poynton.Ph.D.in Medical Engineerin

Brain Microstructure: Impact of the Permeability on Diffusion MRI

Diffusion Magnetic Resonance Imaging (dMRI) enables a non invasive in-vivo characterization of the brain tissue. The disentanglement of each microstructural property reflected on the total dMRI signal is one of the hottest topics in the field. The dMRI reconstruction techniques ground on assumptions on the signal model and consider the neurons axons as impermeable cylinders. Nevertheless, interactions with the environment is characteristic of the biological life and diffusional water exchange takes place through cell membranes. Myelin wraps axons with multiple layers constitute a barrier modulating exchange between the axon and the extracellular tissue. Due to the short transverse relaxation time (T2) of water trapped between sheets, myelin contribution to the diffusion signal is often neglected. This thesis aims to explore how the exchange influences the dMRI signal and how this can be informative on myelin structure. We also aimed to explore how recent dMRI signal reconstruction techniques could be applied in clinics proposing a strategy for investigating the potential as biomarkers of the derived tissue descriptors. The first goal of the thesis was addressed performing Monte Carlo simulations of a system with three compartments: intra-axonal, spiraling myelin and extra-axonal. The experiments showed that the exchange time between intra- and extra-axonal compartments was on the sub-second level (and thus possibly observable) for geometries with small axon diameter and low number of wraps such as in the infant brain and in demyelinating diseases. The second goal of the thesis was reached by assessing the indices derived from three dimensional simple harmonics oscillator-based reconstruction and estimation (3D-SHORE) in stroke disease. The tract-based analysis involving motor networks and the region-based analysis in grey matter (GM) were performed. 3D-SHORE indices proved to be sensitive to plasticity in both white matter (WM) and GM, highlighting their viability as biomarkers in ischemic stroke. The overall study could be considered the starting point for a future investigation of the interdependence of different phenomena like exchange and relaxation related to the established dMRI indices. This is valuable for the accurate dMRI data interpretation in heterogeneous tissues and different physiological conditions

Uncertainty quantification in virtual surgery hemodynamics predictions for single ventricle palliation.

International audienceThe adoption of simulation tools to predict surgical outcomes is increasingly leading to questions about the variability of these predictions in the presence of uncertainty associated with the input clinical data. In the present study, we propose a methodology for full propagation of uncertainty from clinical data to model results that, unlike deterministic simulation, enables estimation of the confidence associated with model predictions.We illustrate this problem in a virtual stage II single ventricle palliation surgery example. First, probability density functions (PDFs) of right pulmonary artery (PA) flow split ratio and average pulmonary pressure are determined from clinical measurements, complemented by literature data. Starting from a zero dimensional semi-empirical approximation, Bayesian parameter estimation is used to find the distributions of boundary conditions that produce the expected PA flow split and average pressure PDFs as pre-operative model results. To reduce computational cost, this inverse problem is solved using a Kriging approximant. Second, uncertainties in the boundary conditions are propagated to simulation predictions. Sparse grid stochastic collocation is employed to statistically characterize model predictions of post-operative hemodynamics in models with and without PA stenosis. The results quantify the statistical variability in virtual surgery predictions, allowing for placement of confidence intervals on simulation outputs

Uncertainty quantification in virtual surgery hemodynamics predictions for single ventricle palliation.

International audienceThe adoption of simulation tools to predict surgical outcomes is increasingly leading to questions about the variability of these predictions in the presence of uncertainty associated with the input clinical data. In the present study, we propose a methodology for full propagation of uncertainty from clinical data to model results that, unlike deterministic simulation, enables estimation of the confidence associated with model predictions.We illustrate this problem in a virtual stage II single ventricle palliation surgery example. First, probability density functions (PDFs) of right pulmonary artery (PA) flow split ratio and average pulmonary pressure are determined from clinical measurements, complemented by literature data. Starting from a zero dimensional semi-empirical approximation, Bayesian parameter estimation is used to find the distributions of boundary conditions that produce the expected PA flow split and average pressure PDFs as pre-operative model results. To reduce computational cost, this inverse problem is solved using a Kriging approximant. Second, uncertainties in the boundary conditions are propagated to simulation predictions. Sparse grid stochastic collocation is employed to statistically characterize model predictions of post-operative hemodynamics in models with and without PA stenosis. The results quantify the statistical variability in virtual surgery predictions, allowing for placement of confidence intervals on simulation outputs

Phase control and measurement in digital microscopy

The ongoing merger of the digital and optical components of the modern microscope is creating opportunities for new measurement techniques, along with new challenges for optical modelling. This thesis investigates several such opportunities and challenges which are particularly relevant to biomedical imaging. Fourier optics is used throughout the thesis as the underlying conceptual model, with a particular emphasis on three--dimensional Fourier optics. A new challenge for optical modelling provided by digital microscopy is the relaxation of traditional symmetry constraints on optical design. An extension of optical transfer function theory to deal with arbitrary lens pupil functions is presented in this thesis. This is used to chart the 3D vectorial structure of the spatial frequency spectrum of the intensity in the focal region of a high aperture lens when illuminated by linearly polarised beam. Wavefront coding has been used successfully in paraxial imaging systems to extend the depth of field. This is achieved by controlling the pupil phase with a cubic phase mask, and thereby balancing optical behaviour with digital processing. In this thesis I present a high aperture vectorial model for focusing with a cubic phase mask, and compare it with results calculated using the paraxial approximation. The effect of a refractive index change is also explored. High aperture measurements of the point spread function are reported, along with experimental confirmation of high aperture extended depth of field imaging of a biological specimen. Differential interference contrast is a popular method for imaging phase changes in otherwise transparent biological specimens. In this thesis I report on a new isotropic algorithm for retrieving the phase from differential interference contrast images of the phase gradient, using phase shifting, two directions of shear, and non--iterative Fourier phase integration incorporating a modified spiral phase transform. This method does not assume that the specimen has a constant amplitude. A simulation is presented which demonstrates good agreement between the retrieved phase and the phase of the simulated object, with excellent immunity to imaging noise

Phase control and measurement in digital microscopy

The ongoing merger of the digital and optical components of the modern microscope is creating opportunities for new measurement techniques, along with new challenges for optical modelling. This thesis investigates several such opportunities and challenges which are particularly relevant to biomedical imaging. Fourier optics is used throughout the thesis as the underlying conceptual model, with a particular emphasis on three--dimensional Fourier optics. A new challenge for optical modelling provided by digital microscopy is the relaxation of traditional symmetry constraints on optical design. An extension of optical transfer function theory to deal with arbitrary lens pupil functions is presented in this thesis. This is used to chart the 3D vectorial structure of the spatial frequency spectrum of the intensity in the focal region of a high aperture lens when illuminated by linearly polarised beam. Wavefront coding has been used successfully in paraxial imaging systems to extend the depth of field. This is achieved by controlling the pupil phase with a cubic phase mask, and thereby balancing optical behaviour with digital processing. In this thesis I present a high aperture vectorial model for focusing with a cubic phase mask, and compare it with results calculated using the paraxial approximation. The effect of a refractive index change is also explored. High aperture measurements of the point spread function are reported, along with experimental confirmation of high aperture extended depth of field imaging of a biological specimen. Differential interference contrast is a popular method for imaging phase changes in otherwise transparent biological specimens. In this thesis I report on a new isotropic algorithm for retrieving the phase from differential interference contrast images of the phase gradient, using phase shifting, two directions of shear, and non--iterative Fourier phase integration incorporating a modified spiral phase transform. This method does not assume that the specimen has a constant amplitude. A simulation is presented which demonstrates good agreement between the retrieved phase and the phase of the simulated object, with excellent immunity to imaging noise

Gratings: Theory and Numeric Applications

International audienceThe book containes 11 chapters written by an international team of specialist in electromagnetic theory, numerical methods for modelling of light diffraction by periodic structures having one-, two-, or three-dimensional periodicity, and aiming numerous applications in many classical domains like optical engineering, spectroscopy, and optical telecommunications, together with newly born fields such as photonics, plasmonics, photovoltaics, metamaterials studies, cloaking, negative refraction, and super-lensing. Each chapter presents in detail a specific theoretical method aiming to a direct numerical application by university and industrial researchers and engineers