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Mathematical Medicine and Biology: a Journal of the IMA

Ezio Di Costanzo, Alessandro Giacomello, Elisa Messina, Roberto Natalini, Giuseppe Pontrelli, Fabrizio Rossi, Robert Smits, Monika Twarogowska
We propose a discrete in continuous mathematical model describing the in vitro growth process of biophsy-derived mammalian cardiac progenitor cells growing as clusters in the form of spheres (Cardiospheres). The approach is hybrid: discrete at cellular scale and continuous at molecular level. In the present model, cells are subject to the self-organizing collective dynamics mechanism and, additionally, they can proliferate and differentiate, also depending on stochastic processes The two latter processes are triggered and regulated by chemical signals present in the environment...
January 23, 2017: Mathematical Medicine and Biology: a Journal of the IMA
N Eymard, V Volpert, P Kurbatova, V Volpert, N Bessonov, K Ogungbenro, L Aarons, P Janiaud, P Nony, A Bajard, S Chabaud, Y Bertrand, B Kassaï, C Cornu, P Nony
T lymphoblastic lymphoma (T-LBL) is a rare type of lymphoma with a good prognosis with a remission rate of 85%. Patients can be completely cured or can relapse during or after a 2-year treatment. Relapses usually occur early after the remission of the acute phase. The median time of relapse is equal to 1 year, after the occurrence of complete remission (range 0.2-5.9 years) (Uyttebroeck et al., 2008). It can be assumed that patients may be treated longer than necessary with undue toxicity.The aim of our model was to investigate whether the duration of the maintenance therapy could be reduced without increasing the risk of relapses and to determine the minimum treatment duration that could be tested in a future clinical trial...
January 12, 2017: Mathematical Medicine and Biology: a Journal of the IMA
Eva Kaslik, Mihaela Neamtu
This article generalizes the existing minimal model of the hypothalamic-pituitary-adrenal (HPA) axis in a realistic way, by including memory terms: distributed time delays, on one hand and fractional-order derivatives, on the other hand. The existence of a unique equilibrium point of the mathematical models is proved and a local stability analysis is undertaken for the system with general distributed delays. A thorough bifurcation analysis for the distributed delay model with several types of delay kernels is provided...
December 26, 2016: Mathematical Medicine and Biology: a Journal of the IMA
Timothy W Secomb
A novel theoretical method is presented for simulating the spatially resolved convective and diffusive transport of reacting solutes between microvascular networks and the surrounding tissues. The method allows for efficient computational solution of problems involving convection and non-linear binding of solutes in blood flowing through microvascular networks with realistic 3D geometries, coupled with transvascular exchange and diffusion and reaction in the surrounding tissue space. The method is based on a Green's function approach, in which the solute concentration distribution in the tissue is expressed as a sum of fields generated by time-varying distributions of discrete sources and sinks...
December 2016: Mathematical Medicine and Biology: a Journal of the IMA
Michel Iskin da S Costa, Lucas Dos Anjos
Release of natural enemies to control pest populations is a common strategy in biological control. However, its effectiveness is supposed to be impaired, among other factors, by Allee effects in the biological control agent and by the fact that introduced pest natural enemies interact with some native species of the ecosystem. In this work, we devise a tritrophic food chain model where the assumptions previously raised are proved correct when a hyperpredator attacks the introduced pest natural enemy by a functional response type 2 or 3...
December 2016: Mathematical Medicine and Biology: a Journal of the IMA
Christian Engwer, Alexander Hunt, Christina Surulescu
Glioma is a common type of primary brain tumour, with a strongly invasive potential, often exhibiting non-uniform, highly irregular growth. This makes it difficult to assess the degree of extent of the tumour, hence bringing about a supplementary challenge for the treatment. It is therefore necessary to understand the migratory behaviour of glioma in greater detail. In this paper, we propose a multiscale model for glioma growth and migration. Our model couples the microscale dynamics (reduced to the binding of surface receptors to the surrounding tissue) with a kinetic transport equation for the cell density on the mesoscopic level of individual cells...
December 2016: Mathematical Medicine and Biology: a Journal of the IMA
Peinan Ge, William J Bottega, Jonathan L Prenner, Howard F Fine
A mechanics-based mathematical model of an eye possessing a posterior retinal detachment is presented for the case where an encircling scleral buckle (a cerclage) is sutured around the equator of the eye. The mechanical behaviour of the retina and the globe, both before and after applying the cerclage, is studied. An energy formulation yields the self-consistent equations of equilibrium and boundary conditions of the ocular system, and analytical solutions are established for the scleral buckle, for the globe and for the detached segment of the retina...
December 2016: Mathematical Medicine and Biology: a Journal of the IMA
Leonid Hanin, Jason Rose
We develop a mathematical and statistical methodology for estimation of important unobservable characteristics of the individual natural history of cancer from a sample of cross-sectional diameters of liver metastases measured at autopsy. Estimation of the natural history of cancer is based on a previously proposed stochastic model of cancer progression tailored to this type of observations. The model accounts for primary tumour growth, shedding of metastases, their selection, latency and growth in a given secondary site...
December 2016: Mathematical Medicine and Biology: a Journal of the IMA
F Clarelli, C Di Russo, R Natalini, M Ribot
In this article, we study in detail the fluid dynamics system proposed in Clarelli et al. (2013, J. Math. Biol., 66, 1387-1408) to model the formation of cyanobacteria biofilms. After analysing the linear stability of the unique non-trivial equilibrium of the system, we introduce in the model the influence of light and temperature, which are two important factors for the development of a cyanobacteria biofilm. Since the values of the coefficients we use for our simulations are estimated through information found in the literature, some sensitivity and robustness analyses on these parameters are performed...
December 2016: Mathematical Medicine and Biology: a Journal of the IMA
Matthew R Myers, Prasanna Hariharan, Suvajyoti Guha, Jing Yan
Respiratory protective devices (RPDs) are critical for reducing the spread of infection via inhalable droplets. In determining the type of RPD to deploy, it is important to know the reduction in the infection rate that the RPD enables for the given pathogen and population. This paper extends a previously developed susceptible-infected-recovered (SIR) epidemic model to analyse the effect of a protection strategy. An approximate solution to the modified SIR equations, which compares well with a full numerical solution to the equations, was used to derive a simple threshold equation for predicting when growth of the infected population will occur for a given protection strategy...
October 25, 2016: Mathematical Medicine and Biology: a Journal of the IMA
Iftah Nudel, Luis Dorfmann, Gal deBotton
Compartment syndrome (CS) occurs when the pressure in an enclosed compartment increases due to tissue swelling or internal bleeding. As the intra-compartmental pressure (ICP) builds up, the blood flow to the tissue or the organ is compromised, resulting in ischemia, necrosis and damage to the nerves and other tissues. At the present there are no established diagnostic procedures, and clinical observations such as pain, paralysis and even compartment pressure monitoring are an unreliable determinant of the presence of the syndrome...
October 18, 2016: Mathematical Medicine and Biology: a Journal of the IMA
Giuseppe Pontrelli, Marco Lauricella, José A Ferreira, Gonçalo Pena
We present a multi-layer mathematical model to describe the transdermal drug release from an iontophoretic system. The Nernst-Planck equation describes the basic convection-diffusion process, with the electric potential obtained by solving the Laplace's equation. These equations are complemented with suitable interface and boundary conditions in a multi-domain. The stability of the mathematical problem is discussed in different scenarios and a finite-difference method is used to solve the coupled system. Numerical experiments are included to illustrate the drug dynamics under different conditions...
October 13, 2016: Mathematical Medicine and Biology: a Journal of the IMA
N J Malunguza, S D Hove-Musekwa, S Dube, Z Mukandavire
Super-infection by multiple HIV-1 subtypes, previously thought restricted to high risk groups, has now been reported in the general heterosexual populations at relatively the same incidence rate as in high risk groups. We present a simple deterministic HIV model with super-infection by two HIV-1 subtypes. Mathematical characteristics including the basic reproductive number [Formula: see text], invasion threshold [Formula: see text] and conditions for asymptotic stability are derived. In the absence of super-infection the model exhibits competitive exclusion, and all equilibria are globally attracting if they exist except for the disease free which is a saddle for [Formula: see text] The results show that the subtype with the dominant reproductive number exceeding unity dominates the weaker subtype forcing it to extinction regardless of the size of the reproductive number...
September 25, 2016: Mathematical Medicine and Biology: a Journal of the IMA
Yichen Lu, Mei Yan Lee, Shu Zhu, Talid Sinno, Scott L Diamond
During clotting under flow, platelets bind and activate on collagen and release autocrinic factors such as ADP and thromboxane, while tissue factor (TF) on the damaged wall leads to localized thrombin generation. Towards patient-specific simulation of thrombosis, a multiscale approach was developed to account for: platelet signalling [neural network (NN) trained by pairwise agonist scanning (PAS), PAS-NN], platelet positions (lattice kinetic Monte Carlo, LKMC), wall-generated thrombin and platelet-released ADP/thromboxane convection-diffusion (partial differential equation, PDE) and flow over a growing clot (lattice Boltzmann)...
September 25, 2016: Mathematical Medicine and Biology: a Journal of the IMA
Gürsan Çoban, M Serdar Çelebi
In this work, we constructed a novel collagen fibre remodelling algorithm that incorporates the complex nature of random evolution acting on single fibres causing macroscopic fibre dispersion. The proposed framework is different from the existing remodelling algorithms, in that the microscopic random force on cellular scales causing a rotational-type Brownian motion alone is considered as an aspect of vascular tissue remodelling. A continuum mechanical framework for the evolution of local dispersion and how it could be used for modeling the evolution of internal radius of biaxially strained artery structures under constant internal blood pressure are presented...
September 10, 2016: Mathematical Medicine and Biology: a Journal of the IMA
Theresa Stocks, Thomas Hillen, Jiafen Gong, Martin Burger
The normal tissue complication probability (NTCP) is a measure for the estimated side effects of a given radiation treatment schedule. Here we use a stochastic logistic birth-death process to define an organ-specific and patient-specific NTCP. We emphasize an asymptotic simplification which relates the NTCP to the solution of a logistic differential equation. This framework is based on simple modelling assumptions and it prepares a framework for the use of the NTCP model in clinical practice. As example, we consider side effects of prostate cancer brachytherapy such as increase in urinal frequency, urinal retention and acute rectal dysfunction...
September 2, 2016: Mathematical Medicine and Biology: a Journal of the IMA
Andrei Korobeinikov, Elena Shchepakina, Vladimir Sobolev
The paradox of enrichment in a 3D model for bacteriophage dynamics, with a free infection stage of the phage and a bilinear incident rate, is considered. An application of the technique of singular perturbation theory allows us to demonstrate why the paradox arises in this 3D model despite the fact that it has a bilinear incident rate (while in 2D predator-prey models it is usually associated with the concavity of the attack rate). Our analysis demonstrates that the commonly applied approach of the model order reduction using the so-called quasi-steady-state approximation can lead to a loss of important properties of an original system...
September 2016: Mathematical Medicine and Biology: a Journal of the IMA
J A Ferreira, J Naghipoor, Paula de Oliveira
A coupled non-Fickian model of a cardiovascular drug delivery system using a biodegradable drug-eluting stent is proposed. The numerical results are obtained using an implicit-explicit finite-element method. The influence of vessel stiffness on the transport of drug eluted from the stent is analysed. The results presented in this paper suggest new perspectives to adapt the drug delivery profile to the needs of the patient.
September 2016: Mathematical Medicine and Biology: a Journal of the IMA
Subhadip Paul, Prasun Kumar Roy
The efficacy of radiation therapy, a primary modality of cancer treatment, depends in general upon the total radiation dose administered to the tumour during the course of therapy. Nevertheless, the delivered radiation also irradiates normal tissues and dose escalation procedure often increases the elimination of normal tissue as well. In this article, we have developed theoretical frameworks under the premise of linear-quadratic-linear (LQL) model using stochastic differential equation and Jensen's inequality for exploring the possibility of attending to the two therapeutic performance objectives in contraposition-increasing the elimination of prostate tumour cells and enhancing the relative sparing of normal tissue in fractionated radiation therapy, within a prescribed limit of total radiation dose...
September 2016: Mathematical Medicine and Biology: a Journal of the IMA
V M Veliov, A Widder
The paper investigates a version of a simple epidemiological model involving only susceptible and infected individuals, where the heterogeneity of the population with respect to susceptibility/infectiousness is taken into account. A comprehensive analysis of the asymptotic behaviour of the disease is given, based on an explicit aggregation of the model. The results are compared with those of a homogeneous version of the model to highlight the influence of the heterogeneity on the asymptotics. Moreover, the performed analysis reveals in which cases incomplete information about the heterogeneity of the population is sufficient in order to determine the long-run outcome of the disease...
September 2016: Mathematical Medicine and Biology: a Journal of the IMA
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