High-Frequency Stimulation of Excitable Cells and Networks

High-frequency (HF) stimulation has been shown to block conduction in excitable cells including neurons and cardiac myocytes. However, the precise mechanisms underlying conduction block are unclear. Using a multi-scale method, the influence of HF stimulation is investigated in the simplified FitzhHugh-Nagumo and biophysically-detailed Hodgkin-Huxley models. In both models, HF stimulation alters the amplitude and frequency of repetitive firing in response to a constant applied current and increases the threshold to evoke a single action potential in response to a brief applied current pulse. Further, the excitable cells cannot evoke a single action potential or fire repetitively above critical values for the HF stimulation amplitude. Analytical expressions for the critical values and thresholds are determined in the FitzHugh-Nagumo model. In the Hodgkin-Huxley model, it is shown that HF stimulation alters the dynamics of ionic current gating, shifting the steady-state activation, inactivation, and time constant curves, suggesting several possible mechanisms for conduction block. Finally, we demonstrate that HF stimulation of a network of neurons reduces the electrical activity firing rate, increases network synchronization, and for a sufficiently large HF stimulation, leads to complete electrical quiescence. In this study, we demonstrate a novel approach to investigate HF stimulation in biophysically-detailed ionic models of excitable cells, demonstrate possible mechanisms for HF stimulation conduction block in neurons, and provide insight into the influence of HF stimulation on neural networks

Three-Dimensional Morphometric Analysis of the Craniofacial Complex in the Unaffected Relatives of Individuals with Nonsyndromic Orofacial Clefts

Numerous studies have described altered patterns of craniofacial form in the unaffected relatives of individuals with nonsyndromic oral clefts. Unfortunately, results from these studies have been highly variable and have failed to provide a reliable method for discriminating at-risk relatives from controls. In the present study, we compared craniofacial shape between a sample of unaffected relatives (33 females; 14 males) from CL/P multiplex families and an equal number of age/sex/ethnicity-matched controls. A total of 16 x,y,z facial landmark coordinates derived from 3D photogrammetry were analyzed via Euclidean Distance Matrix Analysis (EDMA), while 14 additional linear distances from direct anthropometry were analyzed via t-tests. Variables identified as significantly different (p ≤ 0.10 from EDMA; 0.05 from t-tests) were then entered into a two-group discriminant function analysis. All analyses were carried out for each sex separately. Compared to controls, female unaffected relatives demonstrated increased upper facial width, midface reduction and lateral displacement of the alar cartilage. A single discriminant function was derived (canonical correlation = 0.43; p = 0.01) which correctly classified 70% of female unaffected relatives and 73% of female controls. Male unaffected relatives demonstrated increased upper facial and cranial base width, increased lower facial height and decreased upper facial height. Again, a single discriminant function was derived (canonical correlation = 0.79; p < 0.001) which correctly classified 86% of male unaffected relatives and 93% of male controls. In both males and females, upper facial width contributed most to group discrimination. Based on the discriminant function results, unaffected relatives were classified into risk/liability classes (high risk or low risk) based on the degree of phenotypic divergence from controls. Results suggest that the craniofacial shape differences characterizing unaffected relatives are partly sex-specific and perhaps more pronounced in males. The pattern of relative-control differences observed in both sexes is in broad agreement with previous findings from both humans and animal models. Although preliminary, these results suggest that a quantitative assessment of the craniofacial phenotype may allow for the identification of at-risk individuals within CL/P multiplex families. Importantly, the identification of such individuals could lead to improvements in recurrence risk estimation and gene mapping

Matroid prophet inequalities and Bayesian mechanism design

Thesis (S.M.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 2012.Cataloged from PDF version of thesis.Includes bibliographical references (p. 42-44).Consider a gambler who observes a sequence of independent, non-negative random numbers and is allowed to stop the sequence at any time, claiming a reward equal to the most recent observation. The famous prophet inequality of Krengel, Sucheston, and Garling asserts that a gambler who knows the distribution of each random variable can achieve at least half as much reward, in expectation, as a "prophet" who knows the sampled values of each random variable and can choose the largest one. We generalize this result to the setting in which the gambler and the prophet are allowed to make more than one selection, subject to a matroid constraint. We show that the gambler can still achieve at least half as much reward as the prophet; this result is the best possible, since it is known that the ratio cannot be improved even in the original prophet inequality, which corresponds to the special case of rank-one matroids. Generalizing the result still further, we show that under an intersection of p matroid constraints, the prophet's reward exceeds the gambler's by a factor of at most 0(p), and this factor is also tight. Beyond their interest as theorems about pure online algoritms or optimal stopping rules, these results also have applications to mechanism design. Our results imply improved bounds on the ability of sequential posted-price mechanisms to approximate optimal mechanisms in both single-parameter and multi-parameter Bayesian settings. In particular, our results imply the first efficiently computable constant-factor approximations to the Bayesian optimal revenue in certain multi-parameter settings. This work was done in collaboration with Robert Kleinberg.by S. Matthew Weinberg.S.M

Analysis of Heterogeneous Cardiac Pacemaker Tissue Models and Traveling Wave Dynamics

The sinoatrial-node (SAN) is a complex heterogeneous tissue that generates a stable rhythm in healthy hearts, yet a general mechanistic explanation for when and how this tissue remains stable is lacking. Although computational and theoretical analyses could elucidate these phenomena, such methods have rarely been used in realistic (large-dimensional) gap-junction coupled heterogeneous pacemaker tissue models. In this study, we adapt a recent model of pacemaker cells (Severi et al. 2012), incorporating biophysical representations of ion channel and intracellular calcium dynamics, to capture physiological features of a heterogeneous population of pacemaker cells, in particular "center" and "peripheral" cells with distinct intrinsic frequencies and action potential morphology. Large-scale simulations of the SAN tissue, represented by a heterogeneous tissue structure of pacemaker cells, exhibit a rich repertoire of behaviors, including complete synchrony, traveling waves of activity originating from periphery to center, and transient traveling waves originating from the center. We use phase reduction methods that do not require fully simulating the large-scale model to capture these observations. Moreover, the phase reduced models accurately predict key properties of the tissue electrical dynamics, including wave frequencies when synchronization occurs, and wave propagation direction in a variety of tissue models. With the reduced phase models, we analyze the relationship between cell distributions and coupling strengths and the resulting transient dynamics. Further, the reduced phase model predicts parameter regimes of irregular electrical dynamics. Thus, we demonstrate that phase reduced oscillator models applied to realistic pacemaker tissue is a useful tool for investigating the spatial-temporal dynamics of cardiac pacemaker activity.Comment: 34 pages, 11 figure