Browsing Mathematical Modelling in Biosciences by Title
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Key aspects for effective mathematical modelling of fractionaldiffusion in cardiac electrophysiology: A quantitative study
(Communications in Nonlinear Science and Numerical Simulation, 202005)Microscopic structural features of cardiac tissue play a fundamental role in determining complex spatiotemporal excitation dynamics at the macroscopic level. Recent efforts have been devoted to the development of mathematical ... 
Lagged and instantaneous dynamical influences related to brain structural connectivity
(Frontiers in Psychology, 20151231)Contemporary neuroimaging methods can shed light on the basis of human neural and cognitive specializations, with important implications for neuroscience and medicine. Indeed, different MRI acquisitions provide different ... 
Largescale simulations of synthetic markets
(Communications in Applied and Industrial Mathematics, 20151008)Highfrequency trading has been experiencing an increase of interest both for practical purposes within nancial institutions and within academic research; recently, the UK Government O ce for Science reviewed the state ... 
A leastsquares implicit RBFFD closest point method and applications to PDEs on moving surfaces
(Journal of Computational Physics, 201810)The closest point method (Ruuth and Merriman, J. Comput. Phys. 227(3):19431961, [2008]) is an embedding method developed to solve a variety of partial differential equations (PDEs) on smooth surfaces, using a closest point ... 
Longitudinal variations of brain functional connectivity: A case report study based on a mouse model of epilepsy
(F1000Research, 20151231)Brain Functional Connectivity (FC) quantifies statistical dependencies between areas of the brain. FC has been widely used to address altered function of brain circuits in control conditions compared to different pathological ... 
Metamodeling on detailed geography for accurate prediction of invasive alien species dispersal
(Scientific Reports, 20191107)Invasive species are recognized as a significant threat to biodiversity. The mathematical modeling of their spatiotemporal dynamics can provide significant help to environmental managers in devising suitable control ... 
Modeling cardiac structural heterogeneity via spacefractional differential equations
(Computational and Mathematical Biomedical Engineering (CMBE2017) Proceedings, 2017)We discuss here the use of nonlocal models in space and fractional order operators in the characterisation of structural complexity and the modeling of propagation in heterogeneous biological tissues. In the specific, we ... 
Modelling Cortical Spreading Depression by a computational algorithm of distributed neural excitability: correlation with clinical features in single migraine with aura patients
(Journal of Headache and Pain 18 (Suppl. 1), 2017) 
Numerical approximations for fractional elliptic equations via the method of semigroups
(ESAIM: Mathematical Modelling and Numerical Analysis, 2020)We provide a novel approach to the numerical solution of the family of nonlocal elliptic equations $(\Delta)^su=f$ in $\Omega$, subject to some homogeneous boundary conditions $\mathcal{B}(u)=0$ on $\partial \Omega$, where ... 
Numerical simulation of a susceptibleexposedinfectious spacecontinuous model for the spread of rabies in raccoons across a realistic landscape
(Journal of Biological Dynamics, 20131231)We introduce a numerical model for the spread of a lethal infectious disease in wildlife. The reference model is a SusceptibleExposedInfectious system where the spatial component of the dynamics is modelled by a diffusion ... 
Optimized schwarz methods and model adaptivity in electrocardiology simulations
(Lecture Notes in Computational Science and Engineering, 20141231)[No abstract available] 
Optimized schwarz methods for the bidomain system in electrocardiology
(Mathematical Modelling and Numerical Analysis, 20131231)The propagation of the action potential in the heart chambers is accurately described by the Bidomain model, which is commonly accepted and used in the specialistic literature. However, its mathematical structure of a ... 
Optimized Schwarz Methods in the StokesDarcy Coupling
(IMA J. Num. Analysis 38 (4), 20181016)This article studies optimized Schwarz methods for the Stokes–Darcy problem. Robin transmission conditions are introduced, and the coupled problem is reduced to a suitable interface system that can be solved using Krylov ... 
Parallelizing the KolmogorovFokkerPlanck Equation
(ESAIM M2AN: Mathematical Modelling and Numerical Analysis, 20151231)We design two parallel schemes, based on Schwarz Waveform Relaxation (SWR) procedures, for the numerical solution of the Kolmogorov equation. The latter is a simplified version of the FokkerPlanck equation describing the ... 
Patientspecific computational modeling of Cortical Spreading Depression via Diffusion Tensor Imaging
(International Journal for Numerical Methods in Biomedical Engineering, 20160629)Cortical Spreading Depression (CSD), a depolarization wave originat ing in the visual cortex and traveling towards the frontal lobe, is com monly accepted as a correlate of migraine visual aura. As of today, little is ... 
Patientspecific modelling of cortical spreading depression applied to migraine studies
(20190617)Migraine is a common neurological disorder and onethird of migraine patients suffer from migraine aura, a perceptual disturbance preceding the typically unilateral headache. Cortical spreading depression (CSD), a ... 
Qualitative analysis of kineticbased models for tumorimmune system interaction
(Discrete and Continuous Dynamical Systems  Series B, 201808)A mathematical model, based on a mesoscopic approach, describing the competition between tumor cells and immune system in terms of kinetic integrodifferential equations is presented. Four interacting populations are ... 
An RBFFD closest point method for solving PDEs on surfaces
(Journal of Computational Physics, 2018)Partial differential equations (PDEs) on surfaces appear in many applications throughout the natural and applied sciences. The classical closest point method (Ruuth and Merriman, J. Comput. Phys. 227(3):19431961, ... 
SDEdriven modeling of phenotypically heterogeneous tumors: The influence of cancer cell stemness
(Discrete and Continuous Dynamical Systems  Series B, 2019)We deduce cell population models describing the evolution of a tumor (possibly interacting with its environment of healthy cells) with the aid of differential equations. Thereby, different subpopulations of cancer cells ... 
A spacefractional Monodomain model for cardiac electrophysiology combining anisotropy and heterogeneity on realistic geometries
(20171004)Classical models of electrophysiology do not typically account for the effects of high structural heterogeneity in the spatiotemporal description of excitation waves propagation. We consider a modification of the Monodomain ...