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Register a new userStudy of conduction, block and reflection at the excitable tissues boundary in terms of the interval model of action potential
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Authors
Sergii Kovalchuk
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Some mechanisms of cardiac arrhythmias can be presented as a composition of elementary acts of block and reflection on the contacts of homogeneous areas of the conducting tissue. For study this phenomena we use an axiomatic one-dimensional model of interaction of cells of excitable tissue. The model has four functional parameters that determine the functional states durations of the cell. We show that the cells of a homogeneous excitable tissue, depending on the ratio of the durations of the functional intervals, can operate in the mode of solitary waves conduction or in one of three modes of selfgeneration. It is proved that the propagation of a solitary wave through the boundary of homogeneous conducting tissues can be accompanied by a block or multiplex reflection. Block and reflection are unidirectional phenomena, and there are not compatible on the same boundary. Systematized rules of transmitting, block and reflection waves at the boundary of homogeneous conducting tissues open up new possibilities for design mechanisms of generation and analyzing complex heart rate patterns.
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The electrical coupling between myocytes and fibroblasts and the spacial distribution of fibroblasts within myocardial tissues are significant factors in triggering and sustaining cardiac arrhythmias but their roles are poorly understood. This article describes both direct numerical simulations and an asymptotic theory of propagation and block of electrical excitation in a model of atrial tissue with myocyte-fibroblast coupling. In particular, three idealised fibroblast distributions are introduced: uniform distribution, fibroblast barrier and myocyte strait, all believed to be constituent blocks of realistic fibroblast distributions. Primary action potential biomarkers including conduction velocity, peak potential and triangulation index are estimated from direct simulations in all cases. Propagation block is found to occur at certain critical values of the parameters defining each idealised fibroblast distribution and these critical values are accurately determined. An asymptotic theory proposed earlier is extended and applied to the case of a uniform fibroblast distribution. Biomarker values are obtained from hybrid analytical-numerical solutions of coupled fast-time and slow-time periodic boundary value problems and compare well to direct numerical simulations. The boundary of absolute refractoriness is determined solely by the fast-time problem and is found to depend on the values of the myocyte potential and on the slow inactivation variable of the sodium current ahead of the propagating pulse. In turn, these quantities are estimated from the slow-time problem using a regular perturbation expansion to find the steady state of the coupled myocyte-fibroblast kinetics. The asymptotic theory gives a simple analytical expression that captures with remarkable accuracy the block of propagation in the presence of fibroblasts.
The analytical theory of our earlier study (Mortensen et al. (2021), Mathematical Medicine and Biology, 38(1), pp. 106-131) is extended to address the outstanding cases of fibroblast barrier distribution and myocyte strait distribution. In particular, closed-form approximations to the resting membrane potential and to the critical parameter values for propagation are derived for these two non-uniform fibroblast distributions and are in good agreement with numerical estimates.
Coordination in circular and longitudinal muscle motions are of crucial importance in the motor function of gastrointestinal (GI) tract. Intestinal wall motions depend on myogenic-active properties of smooth muscles layers of intestinal wall, which is the ability to create active contractile forces in response to distension. Considering the stress in the circular and longitudinal smooth muscles as a sum of passive, depending on muscle deformations, and active, depending on muscle tone, components, and also assuming that the change in the muscle tone depends on the current stress-strain condition, the system of four ordinary differential equations (ODE) is obtained, which describes filling-emptying cycle of intestinal segment as a process of coordinated activities of circular and longitudinal muscles of intestinal wall. A general approach in formulating the modelling conditions is based on the previously described model restricted to the circularly distensible reservoir of constant length. Obtained results illustrate the character of coordinated activities of two orthogonal muscle layers, which are alternating phases of reciprocally and uniformly changing modalities such as stretching of the wall and muscle tone. The results also contribute to the existing understanding of the roles of Auerbachs and Meisners intermuscular and submucous neural plexuses in regulations of autonomous intestinal motility, as well as clarify functional mechanisms of the interstitial cells of Cajal (ICC) in triggering of smooth muscle contractions.
Background: The global spread of the severe acute respiratory syndrome (SARS) epidemic has clearly shown the importance of considering the long-range transportation networks in the understanding of emerging diseases outbreaks. The introduction of extensive transportation data sets is therefore an important step in order to develop epidemic models endowed with realism. Methods: We develop a general stochastic meta-population model that incorporates actual travel and census data among 3 100 urban areas in 220 countries. The model allows probabilistic predictions on the likelihood of country outbreaks and their magnitude. The level of predictability offered by the model can be quantitatively analyzed and related to the appearance of robust epidemic pathways that represent the most probable routes for the spread of the disease. Results: In order to assess the predictive power of the model, the case study of the global spread of SARS is considered. The disease parameter values and initial conditions used in the model are evaluated from empirical data for Hong Kong. The outbreak likelihood for specific countries is evaluated along with the emerging epidemic pathways. Simulation results are in agreement with the empirical data of the SARS worldwide epidemic. Conclusions: The presented computational approach shows that the integration of long-range mobility and demographic data provides epidemic models with a predictive power that can be consistently tested and theoretically motivated. This computational strategy can be therefore considered as a general tool in the analysis and forecast of the global spreading of emerging diseases and in the definition of containment policies aimed at reducing the effects of potentially catastrophic outbreaks.
Compressive sensing (CS) is a signal processing technique that enables sub-Nyquist sampling and near lossless reconstruction of a sparse signal. The technique is particularly appealing for neural signal processing since it avoids the issues relevant to high sampling rate and large data storage. In this project, different CS reconstruction algorithms were tested on raw action potential signals recorded in our lab. Two numerical criteria were set to evaluate the performance of different CS algorithms: Compression Ratio (CR) and Signal-to-Noise Ratio (SNR). In order to do this, individual CS algorithm testing platforms for the EEG data were constructed within MATLAB scheme. The main considerations for the project were the following. 1) Feasibility of the dictionary 2) Tolerance to non-sparsity 3) Applicability of thresholding or interpolation.
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