Carson Ingo

On random walks and entropy in diffusion-weighted magnetic resonance imaging studies of neural tissue.

In diffusion‐weighted MRI studies of neural tissue, the classical model assumes the statistical mechanics of Brownian motion and predicts a monoexponential signal decay. However, there have been numerous reports of signal decays that are not monoexponential, particularly in the white matter.

A multimodal MRI approach to identify and characterize microstructural brain changes in neuropsychiatric systemic lupus erythematosus

Systemic lupus erythematosus (SLE) is an autoimmune disease with multi-organ involvement and results in neurological and psychiatric (NP) symptoms in up to 40% of the patients. To date, the diagnosis of neuropsychiatric systemic lupus erythematosus (NPSLE) poses a challenge due to the lack of neuroradiological gold standards. In this study, we aimed to better localize and characterize normal appearing white matter (NAWM) changes in NPSLE by combining data from two quantitative MRI techniques, diffusion tensor imaging (DTI) and magnetization transfer imaging (MTI). 9 active NPSLE patients (37 ± 13 years, all females), 9 SLE patients without NP symptoms (44 ± 11 years, all females), and 14 healthy controls (HC) (40 ± 9 years, all females) were included in the study. MTI, DTI and fluid attenuated inversion recovery (FLAIR) images were collected from all subjects on a 3 T MRI scanner. Magnetization transfer ratio (MTR), mean diffusivity (MD), fractional anisotropy (FA), radial diffusivity (RD), axial diffusivity (AD) maps and white matter lesion maps based on the FLAIR images were created for each subject. MTR and DTI data were then co-analyzed using tract-based spatial statistics and a cumulative lesion map to exclude lesions. Significantly lower MTR and FA and significantly higher AD, RD and MD were found in NPSLE compared to HC in NAWM regions. The differences in DTI measures and in MTR, however, were only moderately co-localized. Additionally, significant differences in DTI measures, but not in MTR, were found between NPSLE and SLE patients, suggesting that the underlying microstructural changes detected by MD are linked to the onset of NPSLE. The co-analysis of the anatomical distribution of MTI and DTI measures can potentially improve the diagnosis of NPSLE and contribute to the understanding of the underlying microstructural damage.

New Insights into the Fractional Order Diffusion Equation Using Entropy and Kurtosis

Fractional order derivative operators offer a concise description to model multi-scale, heterogeneous and non-local systems. Specifically, in magnetic resonance imaging, there has been recent work to apply fractional order derivatives to model the non-Gaussian diffusion signal, which is ubiquitous in the movement of water protons within biological tissue. To provide a new perspective for establishing the utility of fractional order models, we apply entropy for the case of anomalous diffusion governed by a fractional order diffusion equation generalized in space and in time. This fractional order representation, in the form of the Mittag–Leffler function, gives an entropy minimum for the integer case of Gaussian diffusion and greater values of spectral entropy for non-integer values of the space and time derivatives. Furthermore, we consider kurtosis, defined as the normalized fourth moment, as another probabilistic description of the fractional time derivative. Finally, we demonstrate the implementation of anomalous diffusion, entropy and kurtosis measurements in diffusion weighted magnetic resonance imaging in the brain of a chronic ischemic stroke patient.

Entropy and information in a fractional order model of anomalous diffusion

Abstract Fractional order dynamic models (e.g., systems of ordinary and partial differential equations of non-integer order in time and space) are becoming more popular for characterizing the behavior of complex systems. Justification for such models is typically based on improved fits to experimental data or a reduced mean squared error for models with the same number of fitting parameters. This rationale, however, is relative to the form of the selected fitting function, and is dependent on the order of the derivatives. Nevertheless, there seems to be a recognition that fractional order models work better than integer order models in describing the electrical and mechanical properties of multi-scale, heterogeneous materials. In order to address this issue and to offer a new approach for establishing the utility of fractional order models, we calculate the total Shannon spectral entropy for the case of anomalous diffusion governed by a fractional order diffusion equation generalized in space and in time. This fractional order representation of the continuous time, random walk model of diffusion gives a spectral entropy minimum for normal (i.e., Gaussian) diffusion with surrounding values leading to greater values of spectral entropy.

Upper Extremity Motor Impairments and Microstructural Changes in Bulbospinal Pathways in Chronic Hemiparetic Stroke

Following hemiparetic stroke, precise, individuated control of single joints is often replaced by highly stereotyped patterns of multi-joint movement, or abnormal limb synergies, which can negatively impact functional use of the paretic arm. One hypothesis for the expression of these synergies is an increased dependence on bulbospinal pathways such as the rubrospinal (RubST) tract and especially the reticulospinal (RetST) tracts, which co-activate multiple muscles of the shoulder, elbow, wrist, and fingers. Despite indirect evidence supporting this hypothesis in humans poststroke, it still remains unclear whether it is correct. Therefore, we used high-resolution diffusion tensor imaging (DTI) to quantify white matter microstructure in relation to severity of arm synergy and hand-related motor impairments. DTI was performed on 19 moderately to severely impaired chronic stroke individuals and 15 healthy, age-matched controls. In stroke individuals, compared to controls, there was significantly decreased fractional anisotropy (FA) and significantly increased axial and radial diffusivity in bilateral corona radiata and body of the corpus callosum. Furthermore, poststroke, the contralesional (CL) RetST FA correlated significantly with both upper extremity (UE) synergy severity (r = −0.606, p = 0.003) and hand impairment (r = −0.609, p = 0.003). FA in the ipsilesional RubST significantly correlated with hand impairment severity (r = −0.590, p = 0.004). For the first time, we separately evaluate RetST and RubST microstructure in chronic stroke individuals with UE motor impairment. We demonstrate that individuals with the greatest UE synergy severity and hand impairments poststroke have the highest FA in the CL RetST a pattern consistent with increased myelination and suggestive of neuroplastic reorganization. Since the RetST pathway microstructure, in particular, is sensitive to abnormal joint coupling and hand-related motor impairment in chronic stroke, it could help test the effects of specific, and novel, anti-synergy neurorehabilitation interventions for recovery from hemiparesis.

Parsimonious continuous time random walk models and kurtosis for diffusion in magnetic resonance of biological tissue

In this paper, we provide a context for the modeling approaches that have been developed to describe non-Gaussian diffusion behavior, which is ubiquitous in diffusion weighted magnetic resonance imaging of water in biological tissue. Subsequently, we focus on the formalism of the continuous time random walk theory to extract properties of subdiffusion and superdiffusion through novel simplifications of the Mittag-Leffler function. For the case of time-fractional subdiffusion, we compute the kurtosis for the Mittag-Leffler function, which provides both a connection and physical context to the much-used approach of diffusional kurtosis imaging. We provide Monte Carlo simulations to illustrate the concepts of anomalous diffusion as stochastic processes of the random walk. Finally, we demonstrate the clinical utility of the Mittag-Leffler function as a model to describe tissue microstructure through estimations of subdiffusion and kurtosis with diffusion MRI measurements in the brain of a chronic ischemic stroke patient.

Comparison of perfusion signal acquired by arterial spin labeling–prepared intravoxel incoherent motion (IVIM) MRI and conventional IVIM MRI to unravel the origin of the IVIM signal

Applications of intravoxel incoherent motion (IVIM) imaging in the brain are scarce, whereas it has been successfully applied in other organs with promising results. To better understand the cerebral IVIM signal, the diffusion properties of the arterial blood flow within different parts of the cerebral vascular tree (i.e., different generations of the branching pattern) were isolated and measured by employing an arterial spin labeling (ASL) preparation module before an IVIM readout.

Neural Plasticity in Moderate to Severe Chronic Stroke Following a Device-Assisted Task-Specific Arm/Hand Intervention

Currently, hand rehabilitation following stroke tends to focus on mildly impaired individuals, partially due to the inability for severely impaired subjects to sufficiently use the paretic hand. Device-assisted interventions offer a means to include this more severe population and show promising behavioral results. However, the ability for this population to demonstrate neural plasticity, a crucial factor in functional recovery following effective post-stroke interventions, remains unclear. This study aimed to investigate neural changes related to hand function induced by a device-assisted task-specific intervention in individuals with moderate to severe chronic stroke (upper extremity Fugl-Meyer < 30). We examined functional cortical reorganization related to paretic hand opening and gray matter (GM) structural changes using a multimodal imaging approach. Individuals demonstrated a shift in cortical activity related to hand opening from the contralesional to the ipsilesional hemisphere following the intervention. This was driven by decreased activity in contralesional primary sensorimotor cortex and increased activity in ipsilesional secondary motor cortex. Additionally, subjects displayed increased GM density in ipsilesional primary sensorimotor cortex and decreased GM density in contralesional primary sensorimotor cortex. These findings suggest that despite moderate to severe chronic impairments, post-stroke participants maintain ability to show cortical reorganization and GM structural changes following a device-assisted task-specific arm/hand intervention. These changes are similar as those reported in post-stroke individuals with mild impairment, suggesting that residual neural plasticity in more severely impaired individuals may have the potential to support improved hand function.

Infarct location is associated with quality of life after mild ischemic stroke

Background In patients with mild ischemic stroke, small but eloquent infarcts may have devastating effects, particularly on health-related quality of life. Aim This study investigates the association between acute infarct location and three-month health-related quality of life in patients with mild ischemic stroke. Methods We evaluated consecutively enrolled patients from a single center between August 2012 and July 2013. Our primary outcome at three months was impairment in any health-related quality of life domain (upper extremity, lower extremity, executive function, and general concerns) defined by a T-score <45. We analyzed the association between acute infarct locations and impaired health-related quality of life at three months in univariate and multivariable analysis. Results Among 229 patients (mean age 64.9 years, 55% male, 29.7% black, and median initial NIHSS score 1), impaired health-related quality of life was noted in 84 (36.2%) patients at three months. In univariate analysis, patients with subcortical infarcts (56.0% vs. 39.3%, p = 0.02) and brainstem infarcts (21.4% vs. 10.3%, p = 0.02) were more likely to have impaired health-related quality of life. In multivariable analysis, patients with subcortical and/or brainstem infarcts had increased odds of impaired health-related quality of life (adjusted OR 2.54, 95% CI 1.29–5.01, p = 0.01). Conclusions After mild ischemic stroke, subcortical and brainstem infarct locations predict impairment in health-related quality of life.

Studying neurons and glia non-invasively via anomalous subdiffusion of intracellular metabolites

Cells in the central nervous system, neurons and glia, display a wide range of structural features. Molecular diffusion properties in the intracellular space of these cells reflect this structural diversity, deviating from standard Gaussian dynamics and resulting in anomalous subdiffusion. By tracking the displacement of intracellular metabolites, diffusion-weighted magnetic resonance spectroscopy allows for in vivo compartment-specific and cell-preferential morphological analysis of neurons and glia in the human brain. Suggestive of different intracellular environments between tissue type, the neuronal and glial intracellular space in gray matter is significantly more subdiffusive than in white matter. An important difference is found between the subdiffusion of choline, a predominantly glial metabolite, in gray and white matter, potentially reflecting differences in structural complexity between fibrous and protoplasmic astrocytes. The exclusively intracellular metabolite subdiffusive dynamics, taken together with water intra- and extracellular displacement, provide new insight of differing extracellular gray and white matter properties and exchange between tissue compartments.