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Mathematical Medicine and Biology: a Journal of the IMA

Jake P Taylor-King, Etienne Baratchart, Andrew Dhawan, Elizabeth A Coker, Inga Hansine Rye, Hege Russnes, S Jon Chapman, David Basanta, Andriy Marusyk
Intra-tumour phenotypic heterogeneity limits accuracy of clinical diagnostics and hampers the efficiency of anti-cancer therapies. Dealing with this cellular heterogeneity requires adequate understanding of its sources, which is extremely difficult, as phenotypes of tumour cells integrate hardwired (epi)mutational differences with the dynamic responses to microenvironmental cues. The later comes in form of both direct physical interactions, as well as inputs from gradients of secreted signalling molecules. Furthermore, tumour cells can not only receive microenvironmental cues, but also produce them...
February 14, 2018: Mathematical Medicine and Biology: a Journal of the IMA
L Zhong, C F Ketelaar, R J Braun, C G Begley, P E King-Smith
Evaporation is a recognized contributor to tear film thinning and tear breakup (TBU). Recently, a different type of TBU is observed, where TBU happens under or around a thick area of lipid within a second after a blink. The thick lipid corresponds to a glob. Evaporation alone is too slow to offer a complete explanation of this breakup. It has been argued that the major reason of this rapid tear film thinning is divergent flow driven by a lower surface tension of the glob (via the Marangoni effect). We examine the glob-driven TBU hypothesis in a 1D streak model and axisymmetric spot model...
January 30, 2018: Mathematical Medicine and Biology: a Journal of the IMA
C Bruni, F Conte, F Papa, C Sinisgalli
We address a non-linear programming problem to find the optimal scheme of dose fractionation in cancer radiotherapy. Using the LQ model to represent the response to radiation of tumour and normal tissues, we formulate a constrained non-linear optimization problem in terms of the variables number and sizes of the dose fractions. Quadratic constraints are imposed to guarantee that the damages to the early and late responding normal tissues do not exceed assigned tolerable levels. Linear constraints are set to limit the size of the daily doses...
January 15, 2018: Mathematical Medicine and Biology: a Journal of the IMA
Vasiliki Bitsouni, Dumitru Trucu, Mark A J Chaplain, Raluca Eftimie
Cells adhere to each other and to the extracellular matrix (ECM) through protein molecules on the surface of the cells. The breaking and forming of adhesive bonds, a process critical in cancer invasion and metastasis, can be influenced by the mutation of cancer cells. In this paper, we develop a nonlocal mathematical model describing cancer cell invasion and movement as a result of integrin-controlled cell-cell adhesion and cell-matrix adhesion, for two cancer cell populations with different levels of mutation...
January 15, 2018: Mathematical Medicine and Biology: a Journal of the IMA
Fazeleh S Mohseni-Salehi, Fatemeh Zare-Mirakabad, Soudeh Ghafouri-Fard, Mehdi Sadeghi
DNA double strand breaks (DSBs) are the most lethal lesions of DNA induced by ionizing radiation, industrial chemicals and a wide variety of drugs used in chemotherapy. In the context of DNA damage response system modelling, uncertainty may arise in several ways such as number of induced DSBs, kinetic rates and measurement error in observable quantities. Therefore, using the stochastic approaches is imperative to gain further insight into the dynamic behaviour of DSBs repair process. In this article, a continuous-time Markov chain (CTMC) model of the non-homologous end joining (NHEJ) mechanism is formulated according to the DSB complexity...
December 8, 2017: Mathematical Medicine and Biology: a Journal of the IMA
Nicholas A Battista, Andrea N Lane, Jiandong Liu, Laura A Miller
Recent in vivo experiments have illustrated the importance of understanding the haemodynamics of heart morphogenesis. In particular, ventricular trabeculation is governed by a delicate interaction between haemodynamic forces, myocardial activity, and morphogen gradients, all of which are coupled to genetic regulatory networks. The underlying haemodynamics at the stage of development in which the trabeculae form is particularly complex, given the balance between inertial and viscous forces. Small perturbations in the geometry, scale, and steadiness of the flow can lead to changes in the overall flow structures and chemical morphogen gradients, including the local direction of flow, the transport of morphogens, and the formation of vortices...
November 16, 2017: Mathematical Medicine and Biology: a Journal of the IMA
Shi Chen, Suzanne Lenhart, Judy D Day, Chihoon Lee, Michael Dulin, Cristina Lanzas
Queueing theory studies the properties of waiting queues and has been applied to investigate direct host-to-host transmitted disease dynamics, but its potential in modelling environmentally transmitted pathogens has not been fully explored. In this study, we provide a flexible and customizable queueing theory modelling framework with three major subroutines to study the in-hospital contact processes between environments and hosts and potential nosocomial pathogen transfer, where environments are servers and hosts are customers...
November 2, 2017: Mathematical Medicine and Biology: a Journal of the IMA
Dmitry Gromov, Ingo Bulla, Oana Silvia Serea, Ethan O Romero-Severson
This article is about numerical control of HIV propagation. The contribution of the article is threefold: first, a novel model of HIV propagation is proposed; second, the methods from numerical optimal control are successfully applied to the developed model to compute optimal control profiles; finally, the computed results are applied to the real problem yielding important and practically relevant results.
November 2, 2017: Mathematical Medicine and Biology: a Journal of the IMA
M Dvoriashyna, R Repetto, M R Romano, J H Tweedy
The anterior chamber (AC) and posterior chamber (PC) of the eye are connected through the pupil and are filled with aqueous humour. The aqueous flows from the posterior to the AC at an approximately constant rate, and the intraocular pressure is governed by this rate and the resistance to aqueous outflow. In some patients the iris and lens come into contact, leading to pressure build-up in the PC, peripheral axial shallowing of the AC and, possibly, to angle-closure glaucoma. This can lead to blindness, which may be prevented by surgically creating an iridotomy, that is a hole through the iris to facilitate the flow from the posterior to the AC...
October 30, 2017: Mathematical Medicine and Biology: a Journal of the IMA
Kazuo Yamazaki
We study the systems of partial differential equations with diffusion that model the dynamics of infectious diseases without life-time immunity, in particular the cases of cholera from Wang & Wang (2015, J. Biol. Dyn., 9, 233-261) and avian influenza from Vaidya et al. (2012, Discrete Contin. Dyn. Syst. Ser. B, 17, 2829-2848). In both works, similarly to all others in the literature on various models of infectious diseases and more, it had to be assumed for a technical reason that the diffusivity coefficients of the susceptible, infected and recovered individuals, humans or birds, had to be identical in order to prove the existence of their unique solutions for all time...
October 27, 2017: Mathematical Medicine and Biology: a Journal of the IMA
Julien Aniort, Laurent Chupin, Nicolae Cîndea
Calcium has two important roles in haemodialysis. It participates in the activation of blood coagulation and calcium intakes have a major impact on patient mineral and bone metabolism. The aim of this article is to propose a mathematical model for calcium ions concentration in a dialyzer during haemodialysis using a citrate dialysate. The model is composed of two elements. The first describes the flows of blood and dialysate in a dialyzer fibre. It was obtained by asymptotic analysis and takes into account the anisotropy of the fibres forming a dialyzer...
October 20, 2017: Mathematical Medicine and Biology: a Journal of the IMA
Alun Thomas, Karim Khader, Andrew Redd, Molly Leecaster, Yue Zhang, Makoto Jones, Tom Greene, Matthew Samore
We consider extensions to previous models for patient level nosocomial infection in several ways, provide a specification of the likelihoods for these new models, specify new update steps required for stochastic integration, and provide programs that implement these methods to obtain parameter estimates and model choice statistics. Previous susceptible-infected models are extended to allow for a latent period between initial exposure to the pathogen and the patient becoming themselves infectious, and the possibility of decolonization...
October 12, 2017: Mathematical Medicine and Biology: a Journal of the IMA
Longfei Li, R J Braun, W D Henshaw, P E King-Smith
Fluorescein is perhaps the most commonly used substance to visualize tear film thickness and dynamics; better understanding of this process aids understanding of dry eye syndrome which afflicts millions of people. We study a mathematical model for tear film flow, evaporation, solutal transport and fluorescence over the exposed ocular surface during the interblink. Transport of the fluorescein ion by fluid flow in the tear film affects the intensity of fluorescence via changes in concentration and tear film thickness...
September 27, 2017: 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...
September 1, 2017: 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...
September 1, 2017: 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...
September 1, 2017: 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...
September 1, 2017: Mathematical Medicine and Biology: a Journal of the IMA
Hamidreza Hajiani Boushehrian, Omid Abouali, Khosrow Jafarpur, Alireza Ghaffarieh, Goodarz Ahmadi
In this research, a series of numerical simulations for evaluating the effects of saccadic eye movement on the aqueous humour (AH) flow field and movement of pigment particles in the anterior chamber (AC) was performed. To predict the flow field of AH in the AC, the unsteady forms of continuity, momentum balance and conservation of energy equations were solved using the dynamic mesh technique for simulating the saccadic motions. Different orientations of the human eye including horizontal, vertical and angles of 10° and 20° were considered...
September 1, 2017: Mathematical Medicine and Biology: a Journal of the IMA
Alexander Nestor-Bergmann, Georgina Goddard, Sarah Woolner, Oliver E Jensen
Using a popular vertex-based model to describe a spatially disordered planar epithelial monolayer, we examine the relationship between cell shape and mechanical stress at the cell and tissue level. Deriving expressions for stress tensors starting from an energetic formulation of the model, we show that the principal axes of stress for an individual cell align with the principal axes of shape, and we determine the bulk effective tissue pressure when the monolayer is isotropic at the tissue level. Using simulations for a monolayer that is not under peripheral stress, we fit parameters of the model to experimental data for Xenopus embryonic tissue...
August 8, 2017: Mathematical Medicine and Biology: a Journal of the IMA
Atanaska Dobreva, Ralf Paus, N G Cogan
Alopecia areata (AA) is a CD8$^{+}$ T cell-dependent autoimmune disease that disrupts the constantly repeating cyclic transformations of hair follicles (HFs). Among the three main HF cycle stages-growth (anagen), regression (catagen) and relative quiescence (telogen)-only anagen HFs are attacked and thereby forced to prematurely enter into catagen, thus shortening active hair growth substantially. After having previously modelled the dynamics of immune system components critically involved in the disease development (Dobreva et al...
August 7, 2017: Mathematical Medicine and Biology: a Journal of the IMA
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