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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
George Dassios, Vasiliki Christina Panagiotopoulou
The mathematical analysis of the tumour growth attracted a lot of interest in the last two decades. However, as of today no generally accepted model for tumour growth exists. This is due partially to the incomplete understanding of the related pathology as well as the extremely complicated procedure that guides the evolution of a tumour. In the present work, we analyse the stability of a spherical tumour for four continuous models of an avascular tumour. Conditions for the stability are stated and the results are implemented numerically...
September 2016: Mathematical Medicine and Biology: a Journal of the IMA
Víctor M Pérez-García, Luis A Pérez-Romasanta
Grade II gliomas are slowly growing primary brain tumours that affect mostly young patients and become fatal after a variable time period. Current clinical handling includes surgery as first-line treatment. Cytotoxic therapies (radiotherapy RT or chemotherapy QT) are used initially only for patients having a bad prognosis. Therapies are administered following the 'maximum dose in minimum time' principle, which is the same schedule used for high-grade brain tumours. Using mathematical models describing the growth of these tumours in response to radiotherapy, we find that an extreme protraction therapeutical strategy, i...
September 2016: Mathematical Medicine and Biology: a Journal of the IMA
Qiyong Chen, Sinan Müftü, Faik Can Meral, Kemal Tuncali, Murat Akçakaya
This article presents a model-based pre-treatment optimal planning framework for hepatic tumour radiofrequency (RF) ablation. Conventional hepatic radiofrequency (RF) ablation methods rely on pre-specified input voltage and treatment length based on the tumour size. Using these experimentally obtained pre-specified treatment parameters in RF ablation is not optimal to achieve the expected level of cell death and usually results in more healthy tissue damage than desired. In this study we present a pre-treatment planning framework that provides tools to control the levels of both the healthy tissue preservation and tumour cell death...
July 19, 2016: Mathematical Medicine and Biology: a Journal of the IMA
Georgina E Lang, Dominic Vella, Sarah L Waters, Alain Goriely
Injuries such as traumatic brain injury and stroke can result in increased blood-brain barrier (BBB) permeability. This increase may lead to water accumulation in the brain tissue resulting in vasogenic oedema. Although the initial injury may be localized, the resulting oedema causes mechanical damage and compression of the vasculature beyond the original injury site. We employ a biphasic mixture model to investigate the consequences of BBB permeability changes within a region of brain tissue and the onset of vasogenic oedema...
June 15, 2016: Mathematical Medicine and Biology: a Journal of the IMA
John P Ward, Joanne L Dunster, Gianne Derks, Pratibha Mistry, José D Salazar
Nitisinone or 2-(2-nitro-4-trifluoromethylbenzoyl)cyclohexane-1,3-dione is a reversible inhibitor of 4-hydroxyphenylpyruvate dioxygenase (HPPD), an enzyme important in tyrosine catabolism. Today, nitisinone is successfully used to treat Hereditary Tyrosinaemia type 1, although its original expected role was as a herbicide. In laboratory animals, treatment with nitisinone leads to the elevation of plasma tyrosine (tyrosinaemia). In rats and Beagle dogs, repeat low-dose exposure to nitisinone leads to corneal opacities whilst similar studies in the mouse and Rhesus monkey showed no comparable toxicities or other treatment related findings...
June 15, 2016: Mathematical Medicine and Biology: a Journal of the IMA
Ioannis Sgouralis, Roger G Evans, Anita T Layton
Renal hypoxia could result from a mismatch in renal oxygen supply and demand, particularly in the renal medulla. Medullary hypoxic damage is believed to give rise to acute kidney injury, which is a prevalent complication of cardiac surgery performed on cardiopulmonary bypass (CPB). To determine the mechanisms that could lead to medullary hypoxia during CPB in the rat kidney, we developed a mathematical model which incorporates (i) autoregulation of renal blood flow and glomerular filtration rate, (ii) detailed oxygen transport and utilization in the renal medulla and (iii) oxygen transport along the ureter...
June 8, 2016: Mathematical Medicine and Biology: a Journal of the IMA
Fatemeh Saberian, Archis Ghate, Minsun Kim
The goal in radiotherapy is to maximize the biological effect (BE) of radiation on the tumour while limiting its toxic effects on healthy anatomies. Treatment is administered over several sessions to give the normal tissue time to recover as it has better damage-repair capabilities than tumour cells. This is termed fractionation. A key problem in radiotherapy involves finding an optimal number of treatment sessions (fractions) and the corresponding dosing schedule. A major limitation of existing mathematically rigorous work on this problem is that it includes only a single normal tissue...
June 2016: Mathematical Medicine and Biology: a Journal of the IMA
S P Showa, F Nyabadza, S D Hove-Musekwa, G Magombedze
The role of antibodies in HIV-1 infection is investigated using a discrete-time mathematical model that considers cell-free and cell-associated transmission of the virus. Model analysis shows that the effect of each type of antibody is dependent on the stage of the infection. Neutralizing antibodies are efficient in controlling the viral levels in the early days after seroconversion and antibodies that coat HIV-1-infected cells and recruit effector cells to either kill the HIV-1-infected cells or inhibit viral replication are efficient when the infection becomes established...
June 2016: Mathematical Medicine and Biology: a Journal of the IMA
Svetlana Bunimovich-Mendrazitsky, Sarel Halachmi, Natalie Kronik
One of the treatments offered to non-invasive bladder cancer patients is BCG instillations, using a well-established, time-honoured protocol. Some of the patients, however, do not respond to this protocol. To examine possible changes in the protocol, we provide a platform for in silico testing of alternative protocols for BCG instillations and combinations with IL-2, to be used by urologists in planning new treatment strategies for subpopulations of bladder cancer patients who may benefit from a personalized protocol...
June 2016: Mathematical Medicine and Biology: a Journal of the IMA
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