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Mathematical Medicine and Biology: a Journal of the IMA

J E F Green, J P Whiteley, J M Oliver, H M Byrne, S L Waters
We develop a continuum model for the aggregation of cells cultured in a nutrient-rich medium in a culture well. We consider a 2D geometry, representing a vertical slice through the culture well, and assume that the cell layer depth is small compared with the typical lengthscale of the culture well. We adopt a continuum mechanics approach, treating the cells and culture medium as a two-phase mixture. Specifically, the cells and culture medium are treated as fluids. Additionally, the cell phase can generate forces in response to environmental cues, which include the concentration of a chemoattractant that is produced by the cells within the culture medium...
May 16, 2017: Mathematical Medicine and Biology: a Journal of the IMA
Benjamin Engelhardt, Janine Holze, Christina Elliott, George S Baillie, Maik Kschischo, Holger Fröhlich
The muscarinic M$_{2}$ receptor is a prominent member of the GPCR family and strongly involved in heart diseases. Recently published experimental work explored the cellular response to iperoxo-induced M$_{2}$ receptor stimulation in Chinese hamster ovary (CHO) cells. To better understand these responses, we modelled and analysed the muscarinic M$_{2}$ receptor-dependent signalling pathway combined with relevant secondary messenger molecules using mass action. In our literature-based joint signalling and secondary messenger model, all binding and phosphorylation events are explicitly taken into account in order to enable subsequent stoichiometric matrix analysis...
May 15, 2017: Mathematical Medicine and Biology: a Journal of the IMA
Leszek Pstras, Karl Thomaseth, Jacek Waniewski, Italo Balzani, Federico Bellavere
The Valsalva manoeuvre (VM) used for clinical autonomic testing results in a complex cardiovascular response with a concomitant action of several regulatory mechanisms whose nonlinear interactions are difficult to analyse without the aid of a mathematical model. The article presents a new non-pulsatile compartmental model of the human cardiovascular system with a variable intrathoracic pressure enabling the simulation of the haemodynamic response to the VM. The model is based on physiological data and includes three baroreflex mechanisms acting on heart rate, systemic resistance and venous unstressed volume...
June 1, 2017: Mathematical Medicine and Biology: a Journal of the IMA
Daozhou Gao, Thomas M Lietman, Chao-Ping Dong, Travis C Porco
Mass drug administration, a strategy in which all individuals in a population are subject to treatment without individual diagnosis, has been recommended by the World Health Organization for controlling and eliminating several neglected tropical diseases, including trachoma and soil-transmitted helminths. In this article, we derive effective reproduction numbers and average post-treatment disease prevalences of a simple susceptible-infectious-susceptible epidemic model with constant, impulsive synchronized and non-synchronized drug administration strategies...
June 1, 2017: Mathematical Medicine and Biology: a Journal of the IMA
Federico Frascoli, Emelie Flood, Peter S Kim
We present a three-dimensional model simulating the dynamics of an anti-cancer T-cell response against a small, avascular, early-stage tumour. Interactions at the tumour site are accounted for using an agent-based model (ABM), while immune cell dynamics in the lymph node are modelled as a system of delay differential equations (DDEs). We combine these separate approaches into a two-compartment hybrid ABM-DDE system to capture the T-cell response against the tumour. In the ABM at the tumour site, movement of tumour cells is modelled using effective physical forces with a specific focus on cell-to-cell adhesion properties and varying levels of tumour cell motility, thus taking into account the ability of cancer cells to spread and form clusters...
June 1, 2017: Mathematical Medicine and Biology: a Journal of the IMA
Michiel Bertsch, Bruno Franchi, Norina Marcello, Maria Carla Tesi, Andrea Tosin
In this article we propose a mathematical model for the onset and progression of Alzheimer's disease based on transport and diffusion equations. We regard brain neurons as a continuous medium and structure them by their degree of malfunctioning. Two different mechanisms are assumed to be relevant for the temporal evolution of the disease: i) diffusion and agglomeration of soluble polymers of amyloid, produced by damaged neurons and ii) neuron-to-neuron prion-like transmission. We model these two processes by a system of Smoluchowski equations for the amyloid concentration, coupled to a kinetic-type transport equation for the distribution function of the degree of malfunctioning of neurons...
June 1, 2017: Mathematical Medicine and Biology: a Journal of the IMA
Till D Frank, Anatoly Kiyatkin, Alex Cheong, Boris N Kholodenko
Signal integration determines cell fate on the cellular level, affects cognitive processes and affective responses on the behavioural level, and is likely to be involved in psychoneurobiological processes underlying mood disorders. Interactions between stimuli may subjected to time effects. Time-dependencies of interactions between stimuli typically lead to complex cell responses and complex responses on the behavioural level. We show that both three-factor models and time series models can be used to uncover such time-dependencies...
June 1, 2017: Mathematical Medicine and Biology: a Journal of the IMA
Guillaume Lefebvre, François Cornelis, Patricio Cumsille, Thierry Colin, Clair Poignard, Olivier Saut
This work is devoted to modelling gastrointestinal stromal tumour metastases to the liver, their growth and resistance to therapies. More precisely, resistance to two standard treatments based on tyrosine kinase inhibitors (imatinib and sunitinib) is observed clinically. Using observations from medical images (CT scans), we build a spatial model consisting in a set of non-linear partial differential equations. After calibration of its parameters with clinical data, this model reproduces qualitatively and quantitatively the spatial tumour evolution of one specific patient...
June 1, 2017: Mathematical Medicine and Biology: a Journal of the IMA
Alfonso Sepúlveda-Gálvez, Jesús Agustín Badillo-Corona, Isaac Chairez
Mathematical modelling applied to biological systems allows for the inferring of changes in the dynamic behaviour of organisms associated with variations in the environment. Models based on ordinary differential equations are most commonly used because of their ability to describe the mechanisms of biological systems such as transcription. The disadvantage of using this approach is that there is a large number of parameters involved and that it is difficult to obtain them experimentally. This study presents an algorithm to obtain a finite-time parameter characterization of the model used to describe changes in the metabolic behaviour of Escherichia coli associated with environmental changes...
March 17, 2017: Mathematical Medicine and Biology: a Journal of the IMA
I A Kuznetsov, A V Kuznetsov
In tauopathies, such as Alzheimer's disease (AD), microtubule (MT)-associated protein tau detaches from MTs and aggregates, eventually forming insoluble neurofibrillary tangles. In a healthy axon, the tau concentration increases toward the axon terminal, but in a degenerating axon, the tau concentration gradient is inverted and the highest tau concentration is in the soma. In this article, we developed a mathematical model of tau transport in axons. We calibrated and tested the model by using published distributions of tau concentration and tau average velocity in a healthy axon...
March 1, 2017: Mathematical Medicine and Biology: a Journal of the IMA
Richard C Barnard, Martin Frank, Kai Krycki
In this paper, we study the sensitivities of electron dose calculations with respect to stopping power and transport coefficients. We focus on the application to radiotherapy simulations. We use a Fokker-Planck approximation to the Boltzmann transport equation. Equations for the sensitivities are derived by the adjoint method. The Fokker-Planck equation and its adjoint are solved numerically in slab geometry using the spherical harmonics expansion ($P_N$) and an Harten-Lax-van Leer finite volume method. Our method is verified by comparison to finite difference approximations of the sensitivities...
March 1, 2017: Mathematical Medicine and Biology: a Journal of the IMA
Pak-Wing Fok, Rebecca Sanft
In this paper, we investigate an axisymmetric model of intimal thickening using hyperelasticity theory. Our model describes the growth of the arterial intima due to cell proliferation which, in turn, is driven by the release of a cytokine such as platelet-derived growth factor (PDGF). With the growth rate tied to both local stress and the local concentration of PDGF, we derive a quadruple free boundary problem with different regions of the vessel wall characterized by different homeostatic stress. We compare our model predictions to rabbit and rodent models of atherosclerosis and find that in order to achieve the growth rates reported in the experiments, growth must be mainly cytokine induced rather than stress induced...
March 1, 2017: Mathematical Medicine and Biology: a Journal of the IMA
I Borsi, A Fasano, M Primicerio, T Hillen
The tumour growth paradox refers to the observation that incomplete treatment of cancers can enhance their growth. As shown here and elsewhere, the existence of cancer stem cells (CSCs) can explain this effect. CSC are less sensitive to treatments, hence any stress applied to the tumour selects for CSC, thereby increasing the fitness of the tumour. In this paper, we use a mathematical model to understand the role of CSC in the progression of cancer. Our model is a rather general system of integro-differential equations for tumour growth and tumour spread...
March 1, 2017: Mathematical Medicine and Biology: a Journal of the IMA
T Ruck, S Bittner, S G Meuth, M Herty
The migration of immune cells from peripheral immune organs into the central nervous system (CNS) through the blood-brain barrier (BBB) is a tightly regulated process. The complex interplay between cells of the BBB and immune cells coordinates cell migration as a part of normal immune surveillance while its dysregulation is critically involved in the pathogenesis of various CNS diseases. To develop tools for a deeper understanding of distribution and migratory pattern of immune cells regulated by the BBB, we made use of a mathematical modelling approach derived from Markov chain theory...
March 1, 2017: Mathematical Medicine and Biology: a Journal of the IMA
Marc Artzrouni, Vasiliy N Leonenko, Thierry A Mara
A system of two differential equations is used to model the transmission dynamics of human immunodeficiency virus between 'persons who inject drugs' (PWIDs) and their syringes. Our vector-borne disease model hinges on a metaphorical urn from which PWIDs draw syringes at random which may or may not be infected and may or may not result in one of the two agents becoming infected. The model's parameters are estimated with data mostly from the city of Omsk in Western Siberia. A linear trend in PWID prevalence in Omsk could only be fitted by considering a time-dependent version of the model captured through a secular decrease in the probability that PWIDs decide to share a syringe...
March 1, 2017: Mathematical Medicine and Biology: a Journal of the IMA
Lydia Hill, Mark A J Chaplain, Roland Wolf, Yury Kapelyukh
The Cytochrome P450 (CYP) system is involved in 90% of the human body's interactions with xenobiotics and due to this, it has become an area of avid research including the creation of transgenic mice. This paper proposes a three-compartment model which is used to explain the drug metabolism in the Hepatic Reductase Null (HRN) mouse developed by the University of Dundee (Henderson, C. J., Otto, D. M. E., Carrie, D., Magnuson, M. A., McLaren, A. W., Rosewell, I. and Wolf, C. R. (2003) Inactivation of the hepatic cytochrome p450 system by conditional deletion of hepatic cytochrome p450 reductase...
March 1, 2017: Mathematical Medicine and Biology: a Journal of the IMA
Ryan Nikin-Beers, Stanca M Ciupe
Cross-reactive T cell responses induced by a primary dengue virus infection may contribute to increased disease severity following heterologous infections with a different virus serotype in a phenomenon known as the original antigenic sin. In this study, we developed and analyzed in-host models of T cell responses to primary and secondary dengue virus infections that considered the effect of T cell cross-reactivity in disease enhancement. We fitted the models to published patient data and showed that the overall infected cell killing is similar in dengue heterologous infections, resulting in dengue fever and dengue hemorrhagic fever...
February 27, 2017: Mathematical Medicine and Biology: a Journal of the IMA
Ana Victoria Ponce Bobadilla, Philip K Maini, Helen Byrne
The tumour control probability (TCP) is the probability that a treatment regimen of radiation therapy (RT) eradicates all tumour cells in a given tissue. To decrease the toxic effects on healthy cells, RT is usually delivered over a period of weeks in a series of fractions. This allows tumour cells to repair sublethal damage (RSD) caused by radiation. In this article, we introduce a stochastic model for tumour response to radiotherapy which accounts for the effects of RSD. The tumour is subdivided into two cell types: 'affected' cells which have been damaged by RT and 'unaffected' cells which have not...
February 26, 2017: Mathematical Medicine and Biology: a Journal of the IMA
Jian Du, Aaron L Fogelson
We present a two-phase model of platelet aggregation in coronary-artery-sized blood vessels. The model tracks the number densities of three platelet populations as well as the concentration of a platelet activating chemical. Through the formation of elastic bonds, activated platelets can cohere with one another to form a platelet thrombus. Bound platelets in a thrombus move in a velocity field different from that of the bulk fluid. Stresses produced by the elastic bonds act on the bound platelet material. Movement of the bound platelet material and that of the background fluid are coupled through an interphase drag and an incompressibility constraint...
February 20, 2017: Mathematical Medicine and Biology: a Journal of the IMA
Ryan S Waters, Justin S A Perry, SunPil Han, Bibiana Bielekova, Tomas Gedeon
The immune system has many adaptive and dynamic components that are regulated to ensure appropriate, precise and rapid response to a foreign pathogen. A delayed or inadequate immune response can lead to prolonged disease, while an excessive or under-regulated response can lead to autoimmunity. The cytokine, interleukin-2 (IL-2) and its receptor IL-2R play an important role in maintaining this balance.The IL-2 receptor transduces pSTAT5 signal through both the intermediate and high affinity receptors, which differ from each other by the presence of CD25 chain in IL-2 receptor...
February 20, 2017: Mathematical Medicine and Biology: a Journal of the IMA
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