Insight into the fundamental trade-offs of diffusion MRI from polarization-sensitive optical coherence tomography in ex vivo human brain

In the first study comparing high angular resolution diffusion MRI (dMRI) in the human brain to axonal orientation measurements from polarization-sensitive optical coherence tomography (PSOCT), we compare the accuracy of orientation estimates from various dMRI sampling schemes and reconstruction methods. We find that, if the reconstruction approach is chosen carefully, single-shell dMRI data can yield the same accuracy as multi-shell data, and only moderately lower accuracy than a full Cartesian-grid sampling scheme. Our results suggest that current dMRI reconstruction approaches do not benefit substantially from ultra-high b-values or from very large numbers of diffusion-encoding directions. We also show that accuracy remains stable across dMRI voxel sizes of 1 ​mm or smaller but degrades at 2 ​mm, particularly in areas of complex white-matter architecture. We also show that, as the spatial resolution is reduced, axonal configurations in a dMRI voxel can no longer be modeled as a small set of distinct axon populations, violating an assumption that is sometimes made by dMRI reconstruction techniques. Our findings have implications for in vivo studies and illustrate the value of PSOCT as a source of ground-truth measurements of white-matter organization that does not suffer from the distortions typical of histological techniques.Published versio

Accelerated Diffusion Spectrum Imaging with Compressed Sensing Using Adaptive Dictionaries

Diffusion Spectrum Imaging (DSI) offers detailed information on complex distributions of intravoxel fiber orientations at the expense of extremely long imaging times (~1 hour). It is possible to accelerate DSI by sub-Nyquist sampling of the q-space followed by nonlinear reconstruction to estimate the diffusion probability density functions (pdfs). Recent work by Menzel et al. imposed sparsity constraints on the pdfs under wavelet and Total Variation (TV) transforms. As the performance of Compressed Sensing (CS) reconstruction depends strongly on the level of sparsity in the selected transform space, a dictionary specifically tailored for sparse representation of diffusion pdfs can yield higher fidelity results. To our knowledge, this work is the first application of adaptive dictionaries in DSI, whereby we reduce the scan time of whole brain DSI acquisition from 50 to 17 min while retaining high image quality. In vivo experiments were conducted with the novel 3T Connectome MRI, whose strong gradients are particularly suited for DSI. The RMSE from the proposed reconstruction is up to 2 times lower than that of Menzel et al.’s method, and is actually comparable to that of the fully-sampled 50 minute scan. Further, we demonstrate that a dictionary trained using pdfs from a single slice of a particular subject generalizes well to other slices from the same subject, as well as to slices from another subject.National Institutes of Health (U.S.) (NIH R01 EB007942)National Institute for Biomedical Imaging and Bioengineering (U.S.) (NIBIB K99EB012107)National Institute for Biomedical Imaging and Bioengineering (U.S.) (NIBIB R01EB006847)National Institute for Biomedical Imaging and Bioengineering (U.S.) (K99/R00 EB008129)National Center for Research Resources (U.S.) (NCRR P41RR14075)National Institutes of Health (U.S.) (NIH Blueprint for Neuroscience Research U01MH093765)National Institutes of Health (U.S.) (The Human Connectome project)Siemens Aktiengesellschaft (Siemens-MIT Alliance)Center for Integration of Medicine and Innovative Technology (MIT-CIMIT Medical Engineering Fellowship

Analytical Approach to Channelized Hotelling Observer Performance for Regularized Tomographic Image Reconstruction

Our goal is to analyze regularized image reconstruction methods such as penalized likelihood with respect to the performance of the channelized Hotelling observer (CHO) in the task of detecting a small target signal in the reconstructed images, in the presence of a correlated random background. We derive here an approximation to the performance of the CHO by working entirely with continuous-space formulations and then discretizing the final result. This approach leads to an extension and a refinement of approximations that we previously derived in the discrete space.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/85962/1/Fessler196.pd

Analysis of Observer Performance in Known-Location Tasks for Tomographic Image Reconstruction

We consider the task of detecting a statistically varying signal of known location on a statistically varying background in a reconstructed tomographic image. We analyze the performance of linear observer models in this task. We show that, if one chooses a suitable reconstruction method, a broad family of linear observers can exactly achieve the optimal detection performance attainable with any combination of a linear observer and linear reconstructor. This conclusion encompasses several well-known observer models from the literature, including models with a frequency-selective channel mechanism and certain types of internal noise. Interestingly, the "optimal" reconstruction methods are unregularized and in some cases quite unconventional. These results suggest that, for the purposes of designing regularized reconstruction methods that optimize lesion detectability, known-location tasks are of limited use.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/85959/1/Fessler48.pd

Analysis of Unknown-Location Signal Detectability for Regularized Tomographic Image Reconstruction

Our goal is to optimize regularized image reconstruction methods for emission tomography with respect to the task of detecting small lesions of unknown location in the reconstructed images. We consider model observers whose decisions are based on finding the maximum value of a local test statistic over all possible lesion locations. We use tail probability approximations by Adler (AAP 2000) and Siegmund and Worsley (AS 1995) to evaluate the probabilities of false alarm and detection respectively for the observers of interest. We illustrate how these analytical tools can be used to optimize regularization with respect to the performance (at low probability of false alarm operating points) of a maximum channelized non-prewhitening observer.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/85961/1/Fessler221.pd

Channelized Hotelling Observer Performance for Penalized-Likelihood Image Reconstruction

What type of regularization method is optimal for penalized-likelihood image reconstruction when the imaging task is signal detection based on a channelized Hotelling (CHO) observer? To answer such questions, one would like to have a simple analytical expression (even if approximate) for the performance (SNR) of the CHO observer given different reconstruction methods. Bonetto, Qi, and Leahy (IEEE T-NS, Aug. 2000) derived and validated one such expression for penalized-likelihood (aka MAP) reconstruction and the Signal Known Exactly (SKE) problem using linearizations and local shift-invariance approximations. This paper describes a further simplification of the analytical SNR expression for the more general case of a Gaussian-distributed signal. This simplification, based on frequency-domain decompositions, greatly reduces computation time and thus can facilitate analytical comparisons between reconstruction methods in the context of detection tasks. It also leads to the very interesting result that regularization is not essential in this context for a large family of linear observers.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/85971/1/Fessler177.pd

Analysis of Observer Performance in Unknown-Location Tasks for Tomographic Image Reconstruction

Our goal is to optimize regularized image reconstruction for emission tomography with respect to lesion detectability in the reconstructed images. We consider model observers whose decision variable is the maximum value of a local test statistic within a search area. Previous approaches have used simulations to evaluate the performance of such observers. We propose an alternative approach, where approximations of tail probabilities for the maximum of correlated Gaussian random fields facilitate analytical evaluation of detection performance. We illustrate how these approximations, which are reasonably accurate at low probability of false alarm operating points, can be used to optimize regularization with respect to lesion detectability.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/85914/1/Fessler33.pd

Analysis of Observer Performance in Detecting Signals with Location Uncertainty for Regularized Tomographic Image Reconstruction

Our goal is to optimize regularized image reconstruction methods for emission tomography with respect to the task of detecting small lesions in the reconstructed images. To reflect medical practice realistically, we consider the location of the lesion to be unknown. This location uncertainty significantly complicates the mathematical analysis of model observer performance. We consider model observers whose decisions are based on finding the maximum value of a local test statistic over all possible locations. Khurd and Gindi (SPIE 2004) and Qi and Huesman (SPIE 2004) described analytical approximations of the moments of the local test statistics and used Monte Carlo simulations to evaluate the localization performance of such "maximum observers". We propose here an alternative approach, where tail probability approximations developed by Adler (AAP 2000) facilitate analytical evaluation of the detection performance of these observers. We illustrate how these approximations can be used to evaluate the probability of detection (for low probability of false alarm operating points) for the maximum channelized hotelling observer. Using our analyses, one can rank and optimize image reconstruction methods without requiring time-consuming Monte Carlo simulations.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/85960/1/Fessler205.pd

Recovery of total I-131 activity within focal volumes using SPECT and 3D OSEM

We experimentally investigated the SPECT recovery of I-131 activity in multiple spheres located simultaneously at different locations within a cylindrical phantom that had an elliptical cross section. The sphere volumes ranged from 209 cc down to 4.2 cc. A Prism 3000 camera and two types of parallel-hexagonal-hole collimation were employed: high energy (HE) and ultra high energy (UHE). Using appropriately-different 3D models of the point source response function for the two types of collimation, approximately the same recovery of activity could be achieved with either collimation by 3D OSEM reconstruction. The recovery coefficient was greater with no background activity in the phantom by 0.10, on average, compared to that with background. In the HE collimation case, the activity recovery was considerably better for all volumes using 3D OSEM reconstruction than it had been in the past using 1D SAGE reconstruction. Recovery-coefficient-based correction in a simulated patient case involving spherical tumours moderately improved the activity estimates (average error reduced from 14% to 9% for UHE collimation, and from 15% to 11% for HE collimation). For a test case with HE collimation, increasing the projection-image sampling density while decreasing the image voxel size increased the recovery coefficient by 0.075 on average, and, if used in a full set of calibration measurements of recovery coefficient versus volume, might lead to further improvement in accuracy for the patient case.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/58098/2/pmb7_3_017.pd

Disrupted Topological Organization of Structural Networks revealed by Probabilistic Diffusion Tractography in Tourette Syndrome Children

Tourette syndrome (TS) is a childhood-onset neurobehavioral disorder. Although previous TS studies revealed structural abnormalities in distinct corticobasal ganglia circuits, the topological alterations of the whole-brain white matter (WM) structural networks remain poorly understood. Here, we used diffusion MRI probabilistic tractography and graph theoretical analysis to investigate the topological organization of WM networks in 44 drug-naive TS children and 41 age- and gendermatched healthy children. The WM networks were constructed by estimating inter-regional connectivity probability and the topological properties were characterized using graph theory. We found that both TS and control groups showed an efficient small-world organization in WM networks. However, compared to controls, TS children exhibited decreased global and local efficiency, increased shortest path length and small worldness, indicating a disrupted balance between local specialization and global integration in structural networks. Although both TS and control groups showed highly similar hub distributions, TS children exhibited significant decreased nodal efficiency, mainly distributed in the default mode, language, visual, and sensorimotor systems. Furthermore, two separate networks showing significantly decreased connectivity in TS group were identified using network-based statistical (NBS) analysis, primarily composed of the parieto-occipital cortex, precuneus, and paracentral lobule. Importantly, we combined support vector machine and multiple kernel learning frameworks to fuse multiple levels of network topological features for classification of individuals, achieving high accuracy of 86.47%. Together, our study revealed the disrupted topological organization of structural networks related to pathophysiology of TS, and the discriminative topological features for classification are potential quantitative neuroimaging biomarkers for clinical TS diagnosis