Joshua C. Chang

Biphasic direct current shift, haemoglobin desaturation and neurovascular uncoupling in cortical spreading depression.

Cortical spreading depression is a propagating wave of depolarization that plays important roles in migraine, stroke, subarachnoid haemorrhage and brain injury. Cortical spreading depression is associated with profound vascular changes that may be a significant factor in the clinical response to cortical spreading depression events. We used a combination of optical intrinsic signal imaging, electro-physiology, potassium sensitive electrodes and spectroscopy to investigate neurovascular changes associated with cortical spreading depression in the mouse. We identified two distinct phases of altered neurovascular function, one during the propagating cortical spreading depression wave and a second much longer phase after passage of the wave. The direct current shift associated with the cortical spreading depression wave was accompanied by marked arterial constriction and desaturation of cortical haemoglobin. After recovery from the initial cortical spreading depression wave, we observed a second phase of prolonged, negative direct current shift, arterial constriction and haemoglobin desaturation, lasting at least an hour. Persistent disruption of neurovascular coupling was demonstrated by a loss of coherence between electro-physiological activity and perfusion. Extracellular potassium concentration increased during the cortical spreading depression wave, but recovered and remained at baseline after passage of the wave, consistent with different mechanisms underlying the first and second phases of neurovascular dysfunction. These findings indicate that cortical spreading depression is associated with a multiphasic alteration in neurovascular function, including a novel second direct current shift accompanied by arterial constriction and decrease in tissue oxygen supply, that is temporally and mechanistically distinct from the initial propagated cortical spreading depression wave. Vascular/metabolic uncoupling with cortical spreading depression may have important clinical consequences, and the different phases of dysfunction may represent separate therapeutic targets in the disorders where cortical spreading depression occurs.

A Mathematical Model of the Metabolic and Perfusion Effects on Cortical Spreading Depression

Cortical spreading depression (CSD) is a slow-moving ionic and metabolic disturbance that propagates in cortical brain tissue. In addition to massive cellular depolarizations, CSD also involves significant changes in perfusion and metabolism—aspects of CSD that had not been modeled and are important to traumatic brain injury, subarachnoid hemorrhage, stroke, and migraine. In this study, we develop a mathematical model for CSD where we focus on modeling the features essential to understanding the implications of neurovascular coupling during CSD. In our model, the sodium-potassium–ATPase, mainly responsible for ionic homeostasis and active during CSD, operates at a rate that is dependent on the supply of oxygen. The supply of oxygen is determined by modeling blood flow through a lumped vascular tree with an effective local vessel radius that is controlled by the extracellular potassium concentration. We show that during CSD, the metabolic demands of the cortex exceed the physiological limits placed on oxygen delivery, regardless of vascular constriction or dilation. However, vasoconstriction and vasodilation play important roles in the propagation of CSD and its recovery. Our model replicates the qualitative and quantitative behavior of CSD—vasoconstriction, oxygen depletion, extracellular potassium elevation, prolonged depolarization—found in experimental studies. We predict faster, longer duration CSD in vivo than in vitro due to the contribution of the vasculature. Our results also help explain some of the variability of CSD between species and even within the same animal. These results have clinical and translational implications, as they allow for more precise in vitro, in vivo, and in silico exploration of a phenomenon broadly relevant to neurological disease.

A path-integral approach to Bayesian inference for inverse problems using the semiclassical approximation

We demonstrate how path integrals often used in problems of theoretical physics can be adapted to provide a machinery for performing Bayesian inference in function spaces. Such inference comes about naturally in the study of inverse problems of recovering continuous (infinite dimensional) coefficient functions from ordinary or partial differential equations, a problem which is typically ill-posed. Regularization of these problems using

Iterative Graph Cuts for Image Segmentation with a Nonlinear Statistical Shape Prior

L^2

High-resolution reconstruction of cellular traction-force distributions: the role of physically motivated constraints and compressive regularization

L2 function spaces (Tikhonov regularization) is equivalent to Bayesian probabilistic inference, using a Gaussian prior. The Bayesian interpretation of inverse problem regularization is useful since it allows one to quantify and characterize error and degree of precision in the solution of inverse problems, as well as examine assumptions made in solving the problem—namely whether the subjective choice of regularization is compatible with prior knowledge. Using path-integral formalism, Bayesian inference can be explored through various perturbative techniques, such as the semiclassical approximation, which we use in this manuscript. Perturbative path-integral approaches, while offering alternatives to computational approaches like Markov-Chain-Monte-Carlo (MCMC), also provide natural starting points for MCMC methods that can be used to refine approximations. In this manuscript, we illustrate a path-integral formulation for inverse problems and demonstrate it on an inverse problem in membrane biophysics as well as inverse problems in potential theories involving the Poisson equation.

Regulation of calcium phosphate sedimentation in biological fluids through post-nucleation shielding

Dynamic single-molecule force spectroscopy is often used to distort bonds. The resulting responses, in the form of rupture forces, work applied, and trajectories of displacements, are used to reconstruct bond potentials. Such approaches often rely on simple parameterizations of one-dimensional bond potentials, assumptions on equilibrium starting states, and/or large amounts of trajectory data. Parametric approaches typically fail at inferring complicated bond potentials with multiple minima, while piecewise estimation may not guarantee smooth results with the appropriate behavior at large distances. Existing techniques, particularly those based on work theorems, also do not address spatial variations in the diffusivity that may arise from spatially inhomogeneous coupling to other degrees of freedom in the macromolecule. To address these challenges, we develop a comprehensive empirical Bayesian approach that incorporates data and regularization terms directly into a path integral. All experimental and statistical parameters in our method are estimated directly from the data. Upon testing our method on simulated data, our regularized approach requires less data and allows simultaneous inference of both complex bond potentials and diffusivity profiles. Crucially, we show that the accuracy of the reconstructed bond potential is sensitive to the spatially varying diffusivity and accurate reconstruction can be expected only when both are simultaneously inferred. Moreover, after providing a means for self-consistently choosing regularization parameters from data, we derive posterior probability distributions, allowing for uncertainty quantification.

Regulation of biological tissue mineralization through post-nucleation shielding

Shape-based regularization has proven to be a useful method for delineating objects within noisy images where one has prior knowledge of the shape of the targeted object. When a collection of possible shapes is available, the specification of a shape prior using kernel density estimation is a natural technique. Unfortunately, energy functionals arising from kernel density estimation are of a form that makes them impossible to directly minimize using efficient optimization algorithms such as graph cuts. Our main contribution is to show how one may recast the energy functional into a form that is minimizable iteratively and efficiently using graph cuts.

A path-integral approach to Bayesian inference for inverse problems

We introduce a probabilistic computer vision technique to track monotonically advancing boundaries of objects within image sequences. Our method incorporates a novel technique for including statistical prior shape information into graph-cut based segmentation, with the aid of a majorization-minimization algorithm. Extension of segmentation from single images to image sequences then follows naturally using sequential Bayesian estimation. Our methodology is applied to two unrelated sets of real biomedical imaging data, and a set of synthetic images. Our results are shown to be superior to manual segmentation.