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Similar Journals
 Mathematical Medicine and Biology: A Journal of the IMAJournal Prestige (SJR): 0.517 Citation Impact (citeScore): 1Number of Followers: 2      Hybrid journal (It can contain Open Access articles) ISSN (Print) 1477-8599 - ISSN (Online) 1477-8602 Published by Oxford University Press  [415 journals]
• Action potential propagation and block in a model of atrial tissue with
myocyte–fibroblast coupling

Authors: Mortensen P; Gao H, Smith G, et al.
Abstract: 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 idealized 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 idealized 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.
PubDate: Fri, 08 Jan 2021 00:00:00 GMT

• Stability of a non-local kinetic model for cell migration with
density-dependent speed

Authors: Loy N; Preziosi L.
Abstract: The aim of this article is to study the stability of a non-local kinetic model proposed by Loy & Preziosi (2020a) in which the cell speed is affected by the cell population density non-locally measured and weighted according to a sensing kernel in the direction of polarization and motion. We perform the analysis in a $d$-dimensional setting. We study the dispersion relation in the one-dimensional case and we show that the stability depends on two dimensionless parameters: the first one represents the stiffness of the system related to the cell turning rate, to the mean speed at equilibrium and to the sensing radius, while the second one relates to the derivative of the mean speed with respect to the density evaluated at the equilibrium. It is proved that for Dirac delta sensing kernels centered at a finite distance, corresponding to sensing limited to a given distance from the cell center, the homogeneous configuration is linearly unstable to short waves. On the other hand, for a uniform sensing kernel, corresponding to uniformly weighting the information collected up to a given distance, the most unstable wavelength is identified and consistently matches the numerical solution of the kinetic equation.
PubDate: Sat, 19 Dec 2020 00:00:00 GMT

• Simple model of atherosclerosis in cylindrical arteries: impact of
anisotropic growth on Glagov remodeling

Authors: Mohammad Mirzaei N; Fok P.
Abstract: In 1987, Seymour Glagov observed that arteries went through a two-stage remodeling process as a result of plaque growth: first, a compensatory phase where the lumen area remains approximately constant and second, an encroachment phase where the lumen area decreases over time. In this paper, we investigate the effect of growth anisotropy on Glagov remodeling in five different cases: pure radial, pure circumferential, pure axial, isotropic and general anisotropic growth where the elements of the growth tensor are chosen to minimize the total energy. We suggest that the nature of anisotropy is inclined towards the growth direction that requires the least amount of energy. Our framework is the theory of morphoelasticity on an axisymmetric arterial domain. For each case, we explore their specific effect on the Glagov curves. For the latter two cases, we also provide the changes in collagen fiber orientation and length in the intima, media and adventitia. In addition, we compare the total energy produced by growth in radial, circumferential and axial direction and deduce that using a radially dominant anisotropic growth leads to lower strain energy than isotropic growth.
PubDate: Wed, 19 Aug 2020 00:00:00 GMT

• Corrigendum: A proposed fractional order Gompertz model, and its
application to tumour growth data

Authors: Bolton L; Cloot A, Schoombie S, et al.
Abstract: Correction wishes to be made by L. Bolton11, in consultation with Professor A. Atangana to the following aspects formerly published in A proposed fractional order Gompertz model, and its application to tumour growth data; Larisse Bolton; Alain H.J.J. Cloot; Schalk W. Schoombie; Jacobus P. Slabbert, Mathematical Medicine and Biology 2014; doi: http://dx.10.1093/imammb/dqt024
PubDate: Mon, 10 Aug 2020 00:00:00 GMT

• Bifurcation analysis of a phage-bacteria interaction model with prophage
induction

Authors: Ndongmo Teytsa H; Tsanou B, Bowong S, et al.
Abstract: A predator-prey model is used to investigate the interactions between phages and bacteria by considering the lytic and lysogenic life cycles of phages and the prophage induction. We provide answers to the following conflictual research questions: (1) what are conditions under which the presence of phages can purify a bacterial infected environment' (2) Can the presence of phages triggers virulent bacterial outbreaks' We derive the basic offspring number $\mathcal N_0$ that serves as a threshold and the bifurcation parameter to study the dynamics and bifurcation of the system. The model exhibits three equilibria: an unstable environment-free equilibrium, a globally asymptotically stable (GAS) phage-free equilibrium (PFE) whenever $\mathcal N_0<1$, and a locally asymptotically stable environment-persistent equilibrium (EPE) when $\mathcal N_0>1$. The Lyapunov–LaSalle techniques are used to prove the GAS of the PFE and estimate the EPE basin of attraction. Through the center manifold approximation, topological types of the PFE are precised. Existence of transcritical and Hopf bifurcations are established. Precisely, when $\mathcal N_0>1$, the EPE loses its stability and periodic solutions arise. Furthermore, increasing $\mathcal N_0$ can purify an environment where bacteriophages are introduced. Purposely, we prove that for large values of $\mathcal N_0$, the overall bacterial population asymptotically approaches zero, while the phage population sustains. Ecologically, our results show that for small values of $\mathcal N_0$, the existence of periodic solutions could explain the occurrence of repetitive bacteria-borne disease outbreaks, while large value of $\mathcal N_0$ clears bacteria from the environment. Numerical simulations support our theoretical results.
PubDate: Tue, 28 Jul 2020 00:00:00 GMT

• The optimal age of vaccination against dengue in Brazil based on
serotype-specific forces of infection derived from serological data

Authors: Maier S; Massad E, Amaku M, et al.
PubDate: Thu, 16 Jul 2020 00:00:00 GMT

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