Heterogeneous anisotropic magnetic susceptibility of the myelin-water layers causes local magnetic field perturbations in axons.

One goal of MRI is to determine the myelin water fraction in neural tissue. One approach is to measure the reduction in T * arising from microscopic perturbations in the magnetic field caused by heterogeneities in the magnetic susceptibility of myelin. In this paper, analytic expressions for the induced magnetic field distribution are derived within and around an axon, assuming that the myelin susceptibility is anisotropic.

The movement of a nerve in a magnetic field: application to MRI Lorentz effect imaging.

Direct detection of neural activity with MRI would be a breakthrough innovation in brain imaging. A Lorentz force method has been proposed to image nerve activity using MRI; a force between the action currents and the static MRI magnetic field causes the nerve to move. In the presence of a magnetic field gradient, this will cause the spins to precess at a different frequency, affecting the MRI signal.

T1ρ magnetic resonance imaging for detection of early cartilage changes in knees of asymptomatic collegiate female impact and nonimpact athletes.

Objective: To determine if T1ρ magnetic resonance imaging (T1ρ MRI) could assess early articular cartilage changes in knees of asymptomatic female collegiate athletes. It was hypothesized that impact cohort would demonstrate greater changes than nonimpact cohort.

Design: An institutional review board-approved prospective cohort study.

Two-domain mechanics of a spherical, single chamber heart with applications to specific cardiac pathologies.

Continuum approximations of tissue consider responses averaged over many cells in a region. This simplified approach allows consideration of macroscopic effects, such as deformation or action potential propagation. A bidomain (sometimes known as biphasic) approach retains the macroscopic character of a continuum approximation while allowing one to consider microscopic effects; novel behavior arising from interactions between the intracellular and extracellular spaces can also be noted.

Monodomain shear wave propagation and bidomain shear wave dispersion in an elastic model of cardiac tissue.

Cardiac tissue elastically deforms under an applied stress, permitting shear waves to propagate through the heart. Traditionally, this behavior has been modeled with a monodomain approach, in which the mechanical properties of the intracellular and extracellular spaces are averaged together. We consider a mechanical bidomain model of cardiac tissue in which the mechanics of the intracellular and extracellular spaces are considered individually with the two spaces coupled by a spring constant.

Fourier analysis in Magnetic Induction Tomography: Mapping of anisotropic, inhomogeneous resistivity.

Magnetic Induction Tomography is an electromagnetic-based technique for mapping the passive electromagnetic properties of conductors and has the potential for applications in biomedical imaging. In a previous analysis we approached the inverse problem of determining isotropic resistivity with a Fourier-based analysis. Here, we extend that analysis to anisotropic media.

Fourier-based magnetic induction tomography for mapping resistivity.

Magnetic induction tomography is used as an experimental tool for mapping the passive electromagnetic properties of conductors, with the potential for imaging biological tissues. Our numerical approach to solving the inverse problem is to obtain a Fourier expansion of the resistivity and the stream functions of the magnetic fields and eddy current density. Thus, we are able to solve the inverse problem of determining the resistivity from the applied and measured magnetic fields for a two-dimensional conducting plane.

Mechanical bidomain model of cardiac tissue.

Intracellular and extracellular spaces are separately considered in an electrical bidomain model of tissue. We propose a mechanical bidomain model separately considering the intracellular and extracellular spaces, coupled through a linear restoring force proportional to the displacement difference of the two spaces. We consider a mechanically passive model of heart fibers (no tension) with an action potential, and an electrically passive model (no action potential) in tissue with an ischemic boundary.

Spherical topology in cardiac simulations.

Computational simulations of the electrodynamics of cardiac fibrillation yield a great deal of useful data and provide a framework for theoretical explanations of heart behavior. Extending the application of these mathematical models to defibrillation studies requires that a simulation should sustain fibrillation without defibrillation intervention. In accordance with the critical mass hypothesis, the simulated tissue should be of a large enough size.

Optimization of feedback pacing for defibrillation.

A mathematical model of multisite feedback pacing for defibrillation is optimized for electrode spacing and stimulus period. For four electrodes, the defibrillation success rate is highest at 88% when the electrodes are spaced as far apart as possible. For a single electrode, the optimum success rate was 26%.

Forward Euler stability of the bidomain model of cardiac tissue.

The bidomain model describes the anisotropic electrical properties of cardiac tissue. One common numerical technique for solving the bidomain equations is the explicit forward Euler method. In this communication we derive a relationship between the time and space steps that ensures the stability of this numerical method.

A model for multi-site pacing of fibrillation using nonlinear dynamics feedback.

Traditionally, cardiac defibrillation requires a strong electric shock. Many unwanted side effects of this shock could be eliminated if defibrillation were performed using weak stimuli applied to several locations throughout the heart. Such multi-site pacing algorithms have been shown to defibrillate both experimentally (Pak et al.

Automating phase singularity localization in mathematical models of cardiac tissue dynamics.

Electrical wave-fronts are responsible for contraction in heart tissue. Rotary wave-fronts break up into daughter waves and it is this break up that is believed to underlie ventricular fibrillation. Mathematical methods abound for simulation of fibrillation, and localizing the core of rotary wave-fronts (the phase singularities) is key to characterizing the state of fibrillation and effectiveness of defibrillation in these models.