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A continuum model for the development of tissue-engineered cartilage around a chondrocyteEmail this article to a colleague. Save this article to My Clippings. Discuss or comment on this article.
The limited ability of cartilage to repair when damaged has led to the investigation of tissue engineering as a method for reconstructing cartilage. We propose a continuum multispecies model for the development of cartilage around a single chondrocyte. As in healthy cartilage, the model predicts a balance between synthesis, transport, binding and decay of matrix components. Two mechanisms are investigated for the transport of soluble matrix components: diffusion and advection, caused by displacement of the scaffold medium. Numerical results indicate that a parameter defined by the ratio of the flux of soluble components ou...
Source: Mathematical Medicine and Biology - September 6, 2009 Category: Biomedical Science Authors: Trewenack, A. J., Please, C. P., Landman, K. A. Tags: Articles Source Type: journals

Global asymptotic properties of virus dynamics models with dose-dependent parasite reproduction and virulence and non-linear incidence rateEmail this article to a colleague. Save this article to My Clippings. Discuss or comment on this article.
We consider two models for the spread of an infection with a free-living infective stage, where parasite reproduction and virulence (parasite-induced mortality) depend on the parasite dose to which the host is exposed and are given by unspecified non-linear functions of the number of the free pathogen particles, and the incidence rate is non-linear. We study the impact of these non-linearities with the focus on the global properties of these models. We consider a very general form of the non-linearities: we assume that the virulence and the parasite reproduction rates are given by unspecified non-linear functions of the nu...
Source: Mathematical Medicine and Biology - September 6, 2009 Category: Biomedical Science Authors: Korobeinikov, A. Tags: Articles Source Type: journals

A multiscale approach to modelling electrochemical processes occurring across the cell membrane with application to transmission of action potentialsEmail this article to a colleague. Save this article to My Clippings. Discuss or comment on this article.
By application of matched asymptotic expansions, a simplified partial differential equation (PDE) model for the dynamic electrochemical processes occurring in the vicinity of a membrane, as ions selectively permeate across it, is formally derived from the Poisson–Nernst–Planck equations of electrochemistry. It is demonstrated that this simplified model reduces itself, in the limit of a long thin axon, to the cable equation used by Hodgkin and Huxley to describe the propagation of action potentials in the unmyelinated squid giant axon. The asymptotic reduction from the simplified PDE model to the cable equation ...
Source: Mathematical Medicine and Biology - September 6, 2009 Category: Biomedical Science Authors: Richardson, G. Tags: Articles Source Type: journals

Analytical thermal-optic model for laser heating of biological tissue using the hyperbolic heat transfer equationEmail this article to a colleague. Save this article to My Clippings. Discuss or comment on this article.
In this paper, we solve in an analytical way the thermal-optic coupled problem associated with a 1D model of non-perfused homogeneous biological tissue irradiated by a laser beam. We consider a laser pulse duration of 200 µs and study the temperatures of areas very close to the point of laser beam application. We consider that these values of the temporal and spatial variables mean that the problem has to be solved by means of the hyperbolic heat conduction model instead of the classic or parabolic model. We therefore obtain the solution using both models and apply the temperature profiles obtained to a specific biol...
Source: Mathematical Medicine and Biology - September 6, 2009 Category: Biomedical Science Authors: Trujillo, M., Rivera, M. J., Lopez Molina, J. A., Berjano, E. J. Tags: Articles Source Type: journals

A mathematical model for the deformation of the eyeball by an elastic bandEmail this article to a colleague. Save this article to My Clippings. Discuss or comment on this article.
This article presents a mathematical model for the mechanics of the combined eye/band structure along with an algorithm to compute the model solutions. These predict the immediate and the lasting indentation of the eyeball. The model is derived from basic physical principles by minimizing a potential energy subject to a volume constraint. Assuming spherical symmetry, this leads to a two-point boundary-value problem for a non-linear second-order ordinary differential equation that describes the minimizing static equilibrium. By comparison with laboratory data, a preliminary validation of the model is given. (Source: Mathema...
Source: Mathematical Medicine and Biology - June 2, 2009 Category: Biomedical Science Authors: Keeling, S. L., Propst, G., Stadler, G., Wackernagel, W. Tags: Articles Source Type: journals

Modelling the growth and stabilization of cerebral aneurysmsEmail this article to a colleague. Save this article to My Clippings. Discuss or comment on this article.
Experimental and theoretical guidance is needed to understand how the collagen fabric evolves during the development of aneurysms. In this paper, we model the development of an aneurysm as a cylindrical/spherical membrane subject to 1D enlargement; these conceptual models reflect the development of fusiform and saccular cerebral aneurysms. The mechanical response is attributed to the elastin and collagen. We introduce variables which define the elastin and collagen fibre concentration; these evolve to simulate growth/atrophy of the constituents. A hypothetical aneurysm model is analysed: collagen stretch is constant, elast...
Source: Mathematical Medicine and Biology - June 2, 2009 Category: Biomedical Science Authors: Watton, P. N., Ventikos, Y., Holzapfel, G. A. Tags: Articles Source Type: journals

A bistable genetic switch which does not require high co-operativity at the promoter: a two-timescale model for the PU.1-GATA-1 interactionEmail this article to a colleague. Save this article to My Clippings. Discuss or comment on this article.
The transcription factors PU.1 and GATA-1 antagonize each other in common myeloid progenitors and their relative abundance is thought to decide whether the cell follows the erythrocyte/megakaryocyte lineage or the granulocyte/macrophage lineage. We propose a kinetic model for the PU.1–GATA-1 interaction, analyse its phase space and interpret the results of our analysis. The conclusions have broader implications for the modelling of cell-fate selection. (Source: Mathematical Medicine and Biology)
Source: Mathematical Medicine and Biology - June 2, 2009 Category: Biomedical Science Authors: Bokes, P., King, J. R., Loose, M. Tags: Articles Source Type: journals

Pest management of a prey-predator model with sexual favoritismEmail this article to a colleague. Save this article to My Clippings. Discuss or comment on this article.
Although sex of prey is an important factor for the risk of predating, few articles consider the consequences of sexual favoritism and the corresponding effects on the impulsive predator–prey dynamics and its utility in biological control. This paper investigates the pest management strategy of a prey–predator system model with sexual favoritism. An impulsive differential equation which models the process of periodically releasing natural enemies and spraying pesticides at different fixed time for pest control is proposed and investigated. It is proved that the pest-eradication periodic solution is globally asy...
Source: Mathematical Medicine and Biology - June 2, 2009 Category: Biomedical Science Authors: Pei, Y., Yang, Y., Li, C., Chen, L. Tags: Articles Source Type: journals

A family of models of angiogenesis and anti-angiogenesis anti-cancer therapyEmail this article to a colleague. Save this article to My Clippings. Discuss or comment on this article.
In this paper we propose a class of models that describe the mutual interaction between tumour growth and the development of tumour vasculature and that generalize existing models. The study is mainly focused on the effect of a therapy that induces tumour vessel loss (anti-angiogenic therapy), with the aim of finding conditions that asymptotically guarantee the eradication of the disease under constant infusion or periodic administration of the drug. Furthermore, if tumour and/or vessel dynamics exhibit time delays, we derive conditions for the existence of Hopf bifurcations. The destabilizing effect of delays on achieving...
Source: Mathematical Medicine and Biology - February 26, 2009 Category: Biomedical Science Authors: D'Onofrio, A., Gandolfi, A. Tags: Articles Source Type: journals

Analytic solution during an infusion test of the linear unsteady poroelastic equations in a spherically symmetric model of the brainEmail this article to a colleague. Save this article to My Clippings. Discuss or comment on this article.
This work determines the spatial and temporal distribution of cerebrospinal fluid (CSF) pressure and brain displacement during an infusion test in a spherically symmetric model of the brain. The response of CSF pressure and parenchymal displacement to blood pressure pulsations is determined in the solution. We use a spherically symmetric, three-component poroelastic model of the brain, differentiating between the solid elastic matrix, the CSF and the arterial blood compartments. The governing equations are linearized with quasi-constant poroelastic parameters. The solution does reproduce the average intracranial pressure i...
Source: Mathematical Medicine and Biology - February 26, 2009 Category: Biomedical Science Authors: Wirth, B., Sobey, I. Tags: Articles Source Type: journals

Flow dynamics in a stented ureterEmail this article to a colleague. Save this article to My Clippings. Discuss or comment on this article.
Vesicorenal reflux is a major side effect associated with ureteric stent placement. In a stented upper urinary tract when the bladder pressure rises, such as during bladder spasms (due to irritation caused by the stent) or voiding of the bladder, it drives urine reflux up the ureter, which, in turn, may be a contributory factor for infections in the renal pelvis. We develop a mathematical model to examine urine flow in a stented ureter, assuming that it remains axisymmetric and treating the wall as a non-linear elastic membrane. The stent is modelled as a rigid, permeable, hollow, circular cylinder lying coaxially inside t...
Source: Mathematical Medicine and Biology - February 26, 2009 Category: Biomedical Science Authors: Siggers, J. H., Waters, S., Wattis, J., Cummings, L. Tags: Articles Source Type: journals

Evaluating the effectiveness of antiviral treatment in models for influenza pandemicEmail this article to a colleague. Save this article to My Clippings. Discuss or comment on this article.
We study the effectiveness of antiviral treatment in simple susceptible–exposed–infectious–removed models that are at the base of models used for influenza pandemic. The strategy is assessed in terms of the value of the reproductive ratio R0. We consider a general framework and analyse six different specific cases. The same antiviral strategy is simulated in all models, but they slightly differ in the compartmental structure. These differences correspond to different underlying assumptions concerning the timing of the intervention and the selection of individuals who receive treatment. It is shown that th...
Source: Mathematical Medicine and Biology - November 27, 2008 Category: Biomedical Science Authors: Lunelli, A., Pugliese, A. Tags: Articles Source Type: journals

Fatal SIR diseases and rational exemption to vaccinationEmail this article to a colleague. Save this article to My Clippings. Discuss or comment on this article.
A challenge to disease control in modern societies is the spread of rational exemption to vaccination as a consequence of the rational comparison between the steadily declining risk of infection and the risk of side effects from the vaccine. Here, we consider rational exemption in an susceptible-infectious-removed (SIR) model with information-dependent vaccination where individuals use information on the disease's mortality as their information set. Using suitable assumptions on the dynamics of the population, we show the dynamic implications of the interaction between rational exemption, current and delayed information an...
Source: Mathematical Medicine and Biology - November 27, 2008 Category: Biomedical Science Authors: d'Onofrio, A., Manfredi, P., Salinelli, E. Tags: Articles Source Type: journals

Understanding post-operative temperature drop in cardiac surgery: a mathematical modelEmail this article to a colleague. Save this article to My Clippings. Discuss or comment on this article.
A mathematical model is presented to understand heat transfer processes during the cooling and re-warming of patients during cardiac surgery. Our compartmental model is able to account for many of the qualitative features observed in the cooling of various regions of the body including the central core containing the majority of organs, the rectal region containing the intestines and the outer peripheral region of skin and muscle. In particular, we focus on the issue of afterdrop: a drop in core temperature following patient re-warming, which can lead to serious post-operative complications. Model results for a typical coo...
Source: Mathematical Medicine and Biology - November 27, 2008 Category: Biomedical Science Authors: Tindall, M. J., Peletier, M. A., Severens, N. M. W., Veldman, D. J., de Mol, B. A. J. M. Tags: Articles Source Type: journals

Multistrain virus dynamics with mutations: a global analysisEmail this article to a colleague. Save this article to My Clippings. Discuss or comment on this article.
We consider within-host virus models with n ≥ 2 strains and allow mutation between the strains. If there is no mutation, a Lyapunov function establishes global stability of the steady state corresponding to the fittest strain. For small perturbations, this steady state persists, perhaps with small concentrations of some or all other strains, depending on the connectivity of the graph describing all possible mutations. Moreover, using a perturbation result due to Smith & Waltman (1999), we show that this steady state also preserves global stability. (Source: Mathematical Medicine and Biology)
Source: Mathematical Medicine and Biology - November 27, 2008 Category: Biomedical Science Authors: De Leenheer, P., Pilyugin, S. S. Tags: Articles Source Type: journals

Inducing catastrophe in malignant growthEmail this article to a colleague. Save this article to My Clippings. Discuss or comment on this article.
Mathematical catastrophe theory is used to describe cancer growth during any time-dependent program a(t) of therapeutic activity. The program may be actively imposed, e.g. as chemotherapy, or occur passively as an immune response. With constant therapy a(t), the theory predicts that cancer mass p(t) grows in time t as a cosine-modulated power law, with power = 1.618···, the Fibonacci constant. The cosine modulation predicts the familiar relapses and remissions of cancer growth. These fairly well agree with clinical data on breast cancer recurrences following mastectomy. Two such studies of 3183 Italian...
Source: Mathematical Medicine and Biology - August 29, 2008 Category: Biomedical Science Authors: Gatenby, R. A., Frieden, B. R. Tags: Articles Source Type: journals

Predator-prey model with disease infection in both populationsEmail this article to a colleague. Save this article to My Clippings. Discuss or comment on this article.
A predator–prey model with disease infection in both populations is proposed to account for the possibility of a contagious disease crossing species barrier from prey to predator. We obtain several threshold parameters from local analysis of various equilibria of the proposed system as well as coupled conditions on these threshold parameters which determine the stability of these equilibria. One of the coupled conditions, in the form of an ecological threshold number for the predator–prey ecosystem, always determines the coexistence of predators and prey. The other condition, in the form of a disease basic repr...
Source: Mathematical Medicine and Biology - August 29, 2008 Category: Biomedical Science Authors: Hsieh, Y.-H., Hsiao, C.-K. Tags: Articles Source Type: journals

An enzyme kinetic model of blood island formationEmail this article to a colleague. Save this article to My Clippings. Discuss or comment on this article.
Blood islands are conglomerations of prevascular stem cells that form during vasculogenesis, a function critical to early vascular and hematopoietic development. In this paper, a model of blood island formation is proposed employing the approach of classical enzyme kinetics. Deterministic simulations of the model show the formation of blood island-like structures. These are compared to murine blood islands. (Source: Mathematical Medicine and Biology)
Source: Mathematical Medicine and Biology - August 29, 2008 Category: Biomedical Science Authors: Matteson, A. Tags: Articles Source Type: journals

Identification of a chemotactic sensitivity in a coupled systemEmail this article to a colleague. Save this article to My Clippings. Discuss or comment on this article.
Chemotaxis is the process by which cells behave in a way that follows the chemical gradient. Applications to bacteria growth, tissue inflammation and vascular tumours provide a focus on optimization strategies. Experiments can characterize the form of possible chemotactic sensitivities. This paper addresses the recovery of the chemotactic sensitivity from these experiments while allowing for non-linear dependence of the parameter on the state variables. The existence of solutions to the forward problem is analysed. The identification of a chemotactic parameter is determined by inverse problem techniques. Tikhonov regulariz...
Source: Mathematical Medicine and Biology - August 29, 2008 Category: Biomedical Science Authors: Fister, K. R., McCarthy, M. L. Tags: Articles Source Type: journals

An overset grid method for the study of reflex tearingEmail this article to a colleague. Save this article to My Clippings. Discuss or comment on this article.
We present an overset grid method to simulate the evolution of human tear film thickness subject to reflex tearing. The free-surface evolution is governed by a single fourth-order non-linear equation derived from lubrication theory with specified film thickness and volume flux at each end. The model arises from considering the limiting case where the surfactant is strongly affecting the surface tension. In numerical simulations, the overset grid is composed of fine boundary grids near the upper and lower eyelids to capture localized capillary thinning referred to as ‘black lines’ and a Cartesian grid covers the...
Source: Mathematical Medicine and Biology - August 29, 2008 Category: Biomedical Science Authors: Maki, K. L., Braun, R. J., Driscoll, T. A., King-Smith, P. E. Tags: Articles Source Type: journals

Single-cell-based models in biology and medicineEmail this article to a colleague. Save this article to My Clippings. Discuss or comment on this article.
(Source: Mathematical Medicine and Biology)
Source: Mathematical Medicine and Biology - June 6, 2008 Category: Biomedical Science Authors: Anderson, A. R. A., Chaplain, M. A. J., Rejniak, K. A., Fozard, J. A. Tags: Book Review Source Type: journals

A general tumour control probability model for non-uniform dose distributionsEmail this article to a colleague. Save this article to My Clippings. Discuss or comment on this article.
This article introduces a new approach to compute tumour control probabilities (TCPs) under inhomogeneous dose conditions. The equivalent subvolume model presented here does not assume independence between cell responses and can be derived from any homogeneous dose TCP model. To check the consistency of this model, some natural properties are shown to hold, including the so-called uniform dose theorem. In the spirit of the equivalent uniform dose (EUD) concept introduced by Niemierko (1997, Med. Phys., 24, 103–110), the probability-EUD is defined. This concept together with the methodology introduced to compute TCPs ...
Source: Mathematical Medicine and Biology - June 6, 2008 Category: Biomedical Science Authors: Gonzalez, S. J., Carando, D. G. Tags: Articles Source Type: journals

Optimal control applied to a thoraco-abdominal CPR modelEmail this article to a colleague. Save this article to My Clippings. Discuss or comment on this article.
The techniques of optimal control are applied to a validated blood circulation model of cardiopulmonary resuscitation (CPR), consisting of a system of seven difference equations. In this system, the non-homogeneous forcing terms are chest and abdominal pressures acting as the ‘controls’. We seek to maximize the blood flow, as measured by the pressure difference between the thoracic aorta and the right atrium. By applying optimal control methods, we characterize the optimal waveforms for external chest and abdominal compression during cardiac arrest and CPR in terms of the solutions of the circulation model and ...
Source: Mathematical Medicine and Biology - June 6, 2008 Category: Biomedical Science Authors: Jung, E., Lenhart, S., Protopopescu, V., Babbs, C. Tags: Articles Source Type: journals

Maximum likelihood estimation of a time-inhomogeneous stochastic differential model of glucose dynamicsEmail this article to a colleague. Save this article to My Clippings. Discuss or comment on this article.
Stochastic differential equations (SDEs) are assuming an important role in the definition of dynamical models allowing for explanation of internal variability (stochastic noise). SDE models are well established in many fields, such as investment finance, population dynamics, polymer dynamics, hydrology and neuronal models. The metabolism of glucose and insulin has not yet received much attention from SDE modellers, except from a few recent contributions, because of methodological and implementation difficulties in estimating SDE parameters. Here, we propose a new SDE model for the dynamics of glycemia during a euglycemic h...
Source: Mathematical Medicine and Biology - June 6, 2008 Category: Biomedical Science Authors: Picchini, U., Ditlevsen, S., De Gaetano, A. Tags: Articles Source Type: journals

Neuronal currents and EEG-MEG fieldsEmail this article to a colleague. Save this article to My Clippings. Discuss or comment on this article.
In a recent paper by the author, Fokas and Hadjiloizi proved that a neuronal current within a spherical homogeneous conductor can be split into two orthogonal components in such a way that one component provides the electroencephalography (EEG)-related fields and the other component provides the fields related to magnetoencephalography (MEG). Hence, in spherical geometry, the EEG and MEG measurements contain no overlapping information about the current. In the present work, we utilize a new integral representation for the magnetic potential, introduced recently by Fokas, Kariotou and the author, to prove that this elegant ...
Source: Mathematical Medicine and Biology - June 6, 2008 Category: Biomedical Science Authors: Dassios, G. Tags: Articles Source Type: journals

A model for an inverse power constitutive law for cerebral complianceEmail this article to a colleague. Save this article to My Clippings. Discuss or comment on this article.
This work provides a model that links the commonly used inverse power relationship between cerebral compliance and intracranial pressure to some mechanical properties of distal cerebral veins. The underlying model of the compliance is based on a mechanism whereby the distal cerebral blood vessels are assumed to be the main compliant part of the brain and cerebrospinal fluid volume changes are accommodated by blood displacement into or out of these vessels. This simplified model is not intended to produce a highly accurate prediction of the intracranial pressure–volume curve, which is best achieved by a numerical solu...
Source: Mathematical Medicine and Biology - June 6, 2008 Category: Biomedical Science Authors: Wirth, B., Sobey, I. Tags: Articles Source Type: journals

Impact of delays in cell infection and virus production on HIV-1 dynamicsEmail this article to a colleague. Save this article to My Clippings. Discuss or comment on this article.
Analysed is a mathematical model for HIV-1 infection with two delays accounting, respectively, for (i) a latent period between the time target cells are contacted by the virus particles and the time the virions enter the cells and (ii) a virus production period for new virions to be produced within and released from the infected cells. For this model, the basic reproduction number is identified and its threshold property is discussed: the uninfected steady state is proved to be globally asymptotically stable if and unstable if . In the latter case, an infected steady state occurs and is proved to be locally asymptotic...
Source: Mathematical Medicine and Biology - June 6, 2008 Category: Biomedical Science Authors: Zhu, H., Zou, X. Tags: Articles Source Type: journals

Analysis of extrema of heartbeat time series in exercise testEmail this article to a colleague. Save this article to My Clippings. Discuss or comment on this article.
The heartbeat time series of the electrocardiogram recorded during exercise test clearly reflects the physiological control mechanism of the autonomic nervous system on heart rate. This series shows both decreasing and increasing trends and variability of the variance. We analyse the series of intervals between two consecutive extrema, i.e. the durations of accelerations or decelerations of heart rate. We compute the distribution of the length of these intervals and their mean in a model of stationary independent variables, where they are independent of the variables’ distribution. We use the mean length as discrimin...
Source: Mathematical Medicine and Biology - May 21, 2008 Category: Biomedical Science Authors: Cammarota, C., Curione, M. Tags: Articles Source Type: journals

Calcium release site ultrastructure and the dynamics of puffs and sparksEmail this article to a colleague. Save this article to My Clippings. Discuss or comment on this article.
When Markov chain models of intracellular Ca2+-regulated Ca2+ channels are coupled via a mathematical representation of a Ca2+ microdomain, simulated Ca2+ release sites may exhibit the phenomenon of ‘stochastic Ca2+ excitability’ reminiscent of Ca2+ puffs and sparks. Interestingly, some single-channel models that include Ca2+ inactivation are not particularly sensitive to channel density, so long as the requirement for inter-channel communication is satisfied, while other single-channel models that do not include Ca2+ inactivation open and close synchronously only when the channel density is in a prescribed ran...
Source: Mathematical Medicine and Biology - May 21, 2008 Category: Biomedical Science Authors: DeRemigio, H., Groff, J. R., Smith, G. D. Tags: Articles Source Type: journals

Variability in the secretion of corticotropin-releasing hormone, adrenocorticotropic hormone and cortisol and understandability of the hypothalamic-pituitary-adrenal axis dynamics--a mathematical study based on clinical evidenceEmail this article to a colleague. Save this article to My Clippings. Discuss or comment on this article.
In this article, we have developed a simple mathematical model that captures the vital mechanisms of the hypothalamic-pituitary-adrenal (HPA) axis self-regulatory activities. For this, a system of three-component non-linear delay differential equations has been proposed and analysed to observe the ultradian and circadian variabilities of the hormone secretion of the HPA axis in normal subjects. Our analysis reveals that a feedback mechanism is sufficient to show the ultradian variability of the hormone secretion pattern but fails to show the circadian variability. A central nervous system-driven pulse generator coupled wit...
Source: Mathematical Medicine and Biology - May 21, 2008 Category: Biomedical Science Authors: Bairagi, N., Chatterjee, S., Chattopadhyay, J. Tags: Articles Source Type: journals

Shortening of cardiac action potential duration near an insulating boundaryEmail this article to a colleague. Save this article to My Clippings. Discuss or comment on this article.
It is known, from both experiments and simulations, that cardiac action potentials are shortened near a non-conducting boundary. In the present paper, this effect is studied in a simple, two-current ionic model, with propagation restricted to a 1D fibre. An asymptotic approximation for the dependence of action potential duration on distance to the boundary is derived. This estimate agrees well with simulations. (Source: Mathematical Medicine and Biology)
Source: Mathematical Medicine and Biology - May 21, 2008 Category: Biomedical Science Authors: Cain, J. W., Schaeffer, D. G. Tags: Articles Source Type: journals

Control of invasive hosts by generalist parasitoidsEmail this article to a colleague. Save this article to My Clippings. Discuss or comment on this article.
This article was motivated by the invasion of leaf-mining microlepidopteron attacking horse chestnut trees in Europe and the need for a biological control. Following Owen & Lewis (2001, Bull. Math. Biol., 63, 655–684), we consider predation of leafminers by a generalist parasitoid with a Holling Type II functional response. We first identified six equilibrium points and discussed their stabilities in the non-spatial model. The model always predicts persistence of the parasitoid. Depending on the parameter values, the model may predict that the host persists and goes extinct or there is something like an Allee eff...
Source: Mathematical Medicine and Biology - May 21, 2008 Category: Biomedical Science Authors: Magal, C., Cosner, C., Ruan, S., Casas, J. Tags: Articles Source Type: journals

The ant colony algorithm for feature selection in high-dimension gene expression data for disease classificationEmail this article to a colleague. Save this article to My Clippings. Discuss or comment on this article.
The use of gene expression data to diagnose complex diseases represents an exciting area of medicine; however, such data sets are often noisy, requiring the selection of feature subsets to obtain maximum classification accuracy. Due to the high dimensions of many expression data sets, filter-based methods are commonly used, but often yield inconsistent results. Optimization algorithms can outperform filter methods, but often require preselection of features to achieve good results. To address the problems of many commonly used feature selection methods, the ant colony algorithm (ACA) is proposed for use on data sets with l...
Source: Mathematical Medicine and Biology - March 11, 2008 Category: Biomedical Science Authors: Robbins, K. R., Zhang, W., Bertrand, J. K., Rekaya, R. Tags: Articles Source Type: journals

Bayesian support is larger than bootstrap support in phylogenetic inference: a mathematical argumentEmail this article to a colleague. Save this article to My Clippings. Discuss or comment on this article.
In phylogenetic inference, the support of an estimated phylogenetic tree topology and its interior branches is usually measured either with non-parametric bootstrap support (BS) values or with Bayesian posterior probabilities (BPPs). Extensive empirical evidence indicates that BPP values are systematically larger than BS when measured on the same data set, but there are no theoretical results supporting such a systematic difference. In the present note, we give a heuristic mathematical argument supporting the empirically observed phenomenon. The argument uses properties of the marginal and profile likelihoods of the normal...
Source: Mathematical Medicine and Biology - March 11, 2008 Category: Biomedical Science Authors: Britton, T., Svennblad, B., Erixon, P., Oxelman, B. Tags: Articles Source Type: journals

Shock formation and non-linear dispersion in a microvascular capillary networkEmail this article to a colleague. Save this article to My Clippings. Discuss or comment on this article.
Temporal and spatial fluctuations are a common feature of blood flow in microvascular networks. Among many possible causes, previous authors have suggested that the non-linear rheological properties of capillary blood flow (notably the Fåhræus effect, the Fåhræus–Lindqvist effect and the phase-separation effect at bifurcations) may be sufficient to generate temporal fluctuations even in very simple networks. We have simulated blood flow driven by a fixed pressure drop through a simple arcade network using coupled hyperbolic partial differential equations (PDEs) that incorporate well-establishe...
Source: Mathematical Medicine and Biology - March 11, 2008 Category: Biomedical Science Authors: Pop, S. R., Richardson, G., Waters, S. L., Jensen, O. E. Tags: Articles Source Type: journals

Single-equation models for the tear film in a blink cycle: realistic lid motionEmail this article to a colleague. Save this article to My Clippings. Discuss or comment on this article.
We consider model problems for the tear film over multiple blink cycles that utilize a single equation for the tear film; the single non-linear partial differential equation that governs the film thickness arises from lubrication theory. The two models that we consider arise from considering the absence of naturally occurring surfactant and the case when the surfactant is strongly affecting the surface tension. The film is considered on a time-varying domain length with specified film thickness and volume flux at each end; only one end of the domain is moving, which is analogous to the upper eyelid moving with each blink. ...
Source: Mathematical Medicine and Biology - March 11, 2008 Category: Biomedical Science Authors: Heryudono, A., Braun, R. J., Driscoll, T. A., Maki, K. L., Cook, L. P., King-Smith, P. E. Tags: Articles Source Type: journals

Non-linear modelling of breast tissueEmail this article to a colleague. Save this article to My Clippings. Discuss or comment on this article.
Previous approaches to modelling the large deformation of breast tissue, as occurs, e.g. in imaging using magnetic resonance imaging or mammography, include using linear elasticity and pseudo-non-linear elasticity, in which case the non-linear deformation is approximated by a series of small linear isotropic deformations, with the (constant) Young's modulus of each linear deformation an exponential function of the total non-linear strain. In this paper, these two approaches are compared to the solution of the full non-linear elastic problem for tissue with an exponential relationship between stress and strain. Having formu...
Source: Mathematical Medicine and Biology - November 6, 2007 Category: Biomedical Science Authors: Whiteley, J. P., Gavaghan, D. J., Chapman, S. J., Brady, J. M. Tags: Articles Source Type: journals

Role of horizontal incidence in the occurrence and control of chaos in an eco-epidemiological systemEmail this article to a colleague. Save this article to My Clippings. Discuss or comment on this article.
A predator–prey model with disease in the prey population is proposed and analysed. The mode of disease transmission plays an important role in such dynamics. Keeping this factor in mind, we observe the dynamics of such a system for simple mass action incidence and standard incidence. Our observations indicate that the phenomenon of rarity or non-occurrence of chaos in our proposed model is well defined if the mode of disease transmission follows standard incidence. Moreover, using the method of Latin hypercube sampling, we show that the region of stability increases if the disease transmission follows the standard i...
Source: Mathematical Medicine and Biology - November 6, 2007 Category: Biomedical Science Authors: Chatterjee, S., Kundu, K., Chattopadhyay, J. Tags: Articles Source Type: journals

Assessment of cancer immunotherapy outcome in terms of the immune response time featuresEmail this article to a colleague. Save this article to My Clippings. Discuss or comment on this article.
A cytokine-based periodic immunotherapy treatment is included in a model of tumour growth with a delay. The effects of dose schedule are studied in the case of a weak immune system and a growing tumour. We find the existence of ‘metastable’ states (that may last for tens of years) induced by the treatment and also potentially adverse effects of the dosage frequency on the stabilization of the tumour. These two effects depend on the delay between the tumour growth and the immune system response, the cytokine dose burden, and other parameters considered in the model. (Source: Mathematical Medicine and Biology)
Source: Mathematical Medicine and Biology - November 6, 2007 Category: Biomedical Science Authors: Rodriguez-Perez, D., Sotolongo-Grau, O., Espinosa Riquelme, R., Sotolongo-Costa, O., Santos Miranda, J. A., Antoranz, J. C. Tags: Articles Source Type: journals

Modelling the geometric features and investigating electrical properties of dendrites in a fish thalamic neuronEmail this article to a colleague. Save this article to My Clippings. Discuss or comment on this article.
A certain pacific fish has a thalamic nerve cell with a unique dendritic geometry. Instead of the cell having a branching dendritic structure, the large cell of the corpus glomerulosum has, generally, a single dendritic stalk with a large bulbous tip. We formulate a cable-theory model that incorporates the geometry, and then, we solve the problem for a single, localized synaptic current source at the bulb. From the solution representation, we numerically examine the characteristics of the postsynaptic potential due to the presence of the bulbous tip. (Source: Mathematical Medicine and Biology)
Source: Mathematical Medicine and Biology - November 6, 2007 Category: Biomedical Science Authors: Krzyzanski, W., Bell, J. Tags: Articles Source Type: journals

Modelling HA protein-mediated interaction between an influenza virus and a healthy cell: pre-fusion membrane deformationEmail this article to a colleague. Save this article to My Clippings. Discuss or comment on this article.
We present a mathematical model for pre-fusion interaction between an influenza virus and a healthy cell. Our model describes the role played by hemagglutinin (HA) protein clusters in bringing the viral membrane into close contact with the host cell membrane as a first step of the fusion process between the two membranes. The viral membrane is modelled as a lipid bilayer with bending rigidity. Using the calculus of variations, we compute the deformation of the viral membrane under the influence of HA protein clusters. Our numerical results support the hypothesis of dimple formation in the fusion site proposed in the litera...
Source: Mathematical Medicine and Biology - November 6, 2007 Category: Biomedical Science Authors: Vaidya, N. K., Huang, H., Takagi, S. Tags: Articles Source Type: journals

Parameter estimation of a respiratory control model from noninvasive carbon dioxide measurements during sleepEmail this article to a colleague. Save this article to My Clippings. Discuss or comment on this article.
A new method for estimating the parameters of a human gas exchange model is presented. Sensitivity analysis is used both to inspect the relative importance of the model parameters and to speed up the par-ameter estimation process. Multistart optimization is used to compensate for the effects of partial and noisy measurements. The validity of the method is first investigated with a test problem for which par-ameter identifiability is shown. The method is then applied to the estimation of sleep-related changes in the respiratory control system from the end-tidal and transcutaneous carbon dioxide measurements on human subject...
Source: Mathematical Medicine and Biology - May 23, 2007 Category: Biomedical Science Authors: Aittokallio, T., Gyllenberg, M., Polo, O., Virkki, A. Tags: Articles Source Type: journals

Mathematical analysis of a free-boundary model for lung branching morphogenesisEmail this article to a colleague. Save this article to My Clippings. Discuss or comment on this article.
Lung branching morphogenesis has been widely studied in the field of developmental biology. Lung airway trees consist of relatively regular-sized distal branches, but how this regular branched pattern is formed is not well understood. In the present study, we undertake a detailed mathematical analysis of the model proposed in (Hartmann & Miura (2006), which numerically captures branching morphogenesis of the simplest possible experimental system in vitro. We investigate analytically the stability of 1D travelling waves with respect to periodic perturbations in two dimensions. This linear stability analysis leads to the...
Source: Mathematical Medicine and Biology - May 23, 2007 Category: Biomedical Science Authors: Hartmann, D., Miura, T. Tags: Articles Source Type: journals

Tissue growth in a rotating bioreactor. Part II: fluid flow and nutrient transport problemsEmail this article to a colleague. Save this article to My Clippings. Discuss or comment on this article.
Fluid flow and nutrient transport around a growing tissue construct within a cylindrical bioreactor of circular cross-section are considered. The bioreactor is filled with nutrient-rich culture medium, and the growing tissue construct is modelled as a cylindrical obstacle, also of circular cross-section, at a given (moving) position within the nutrient solution. The bioreactor rotates about its cylindrical axis, and its axial length is small relative to its radius (the high-aspect ratio vessel bioreactor). This small-aspect ratio means that a simple idealized model may be considered, in which (leading order) quantities are...
Source: Mathematical Medicine and Biology - May 23, 2007 Category: Biomedical Science Authors: Cummings, L. J., Waters, S. L. Tags: Articles Source Type: journals

Why is the distribution of HTLV-I carriers geographically biased? An answer through a mathematical epidemic modelEmail this article to a colleague. Save this article to My Clippings. Discuss or comment on this article.
Human T-cell leukemia virus type I (HTLV-I) is a retrovirus that causes adult T-cell leukemia, and the distribution of HTLV-I carriers is endemically biased, e.g. in Japan the density of carriers is high in Kyushu and Okinawa. In order to consider population dynamics over long times taking account of an increase and a decrease of a population we propose a continuous-time HTLV-I model. The model describes population dynamics of carrier numbers and that of carrier proportions, and theoretical results about an increase and a decrease of carriers are obtained. The present approach derives an explanation of the biased distribut...
Source: Mathematical Medicine and Biology - May 23, 2007 Category: Biomedical Science Authors: Eshima, N., Tabata, M., Okada, T. Tags: Articles Source Type: journals

Spectral analysis of two-signed microarray expression dataEmail this article to a colleague. Save this article to My Clippings. Discuss or comment on this article.
We give a simple and informative derivation of a spectral algorithm for clustering and reordering complementary DNA microarray expression data. Here, expression levels of a set of genes are recorded simultaneously across a number of samples, with a positive weight reflecting up-regulation and a negative weight reflecting down-regulation. We give theoretical support for the algorithm based on a biologically justified hypothesis about the structure of the data, and illustrate its use on public domain data in the context of unsupervised tumour classification. The algorithm is derived by considering a discrete optimization pro...
Source: Mathematical Medicine and Biology - May 23, 2007 Category: Biomedical Science Authors: Higham, D. J., Kalna, G., Vass, J. K. Tags: Articles Source Type: journals

Fibrin gel formation in a shear flowEmail this article to a colleague. Save this article to My Clippings. Discuss or comment on this article.
Blood clots are made up of platelets and fibrin gel, and the relative amount of fibrin is strongly influenced by the shear rate. In order to explore this phenomenon, this paper presents a model of fibrin gel formation over the surface of an injured blood vessel in a shear flow. A condition for gelation including source and sink terms of polymer is derived. A simplified model of coagulation, involving activation and inhibition of the enzyme thrombin and thrombin-mediated production of fibrin monomer, is combined with the model of gelation to explore how the shear rate and other parameters control the formation of fibrin gel...
Source: Mathematical Medicine and Biology - February 22, 2007 Category: Biomedical Science Authors: Guy, R. D., Fogelson, A. L., Keener, J. P. Tags: Articles Source Type: journals

Idiopathic intracranial hypertension and transverse sinus stenosis: a modelling studyEmail this article to a colleague. Save this article to My Clippings. Discuss or comment on this article.
Idiopathic intracranial hypertension (IIH) is a syndrome of unknown etiology characterized by elevated intracranial pressure (ICP). Although a stenosis of the transverse sinus has been observed in many IIH patients, the role this feature plays in IIH is in dispute. In this paper, a lumped-parameter model is developed for the purpose of analytically investigating the elevated pressures associated with IIH and a collapsible transverse sinus. This analysis yields practical predictions regarding the degree of elevated ICPs and the effectiveness of various treatment methods. Results suggest that IIH may be caused by a sufficien...
Source: Mathematical Medicine and Biology - February 22, 2007 Category: Biomedical Science Authors: Stevens, S. A., Previte, M., Lakin, W. D., J.Thakore, N., Penar, P. L., Hamschin, B. Tags: Articles Source Type: journals

Multiphase modelling of cell behaviour on artificial scaffolds: effects of nutrient depletion and spatially nonuniform porosityEmail this article to a colleague. Save this article to My Clippings. Discuss or comment on this article.
This paper contains analysis of a recently formulated multiphase model for the growth of biological tissue that comprises motile cells and water inside a rigid scaffold material. The model is extended here to include a term describing cell proliferation which is mediated by the supply of a diffusible nutrient and to include the case where the scaffold porosity varies in space. Numerical solutions of the model equations are presented for different values of the parameters. Comparison is drawn between the different types of growth that arise when using static or dynamic methods for seeding the scaffold with cells. Analytical...
Source: Mathematical Medicine and Biology - February 22, 2007 Category: Biomedical Science Authors: Lemon, G., King, J. R. Tags: Articles Source Type: journals

Within-host population dynamics of antibiotic-resistant M. tuberculosisEmail this article to a colleague. Save this article to My Clippings. Discuss or comment on this article.
Mathematical models for the population dynamics of de novo resistant Mycobacterium tuberculosis within individuals are studied. The models address the use of one or two antimicrobial drugs for treating latent tuberculosis (TB). They consider the effect of varying individual immune response strength on the dynamics for the appearance of resistant bacteria. From the analysis of the models, equilibria and local stabilities are determined. For assessing temporal dynamics and global stability for sensitive and drug-resistant bacteria, numerical simulations are used. Results indicate that for a low bacteria load that is characte...
Source: Mathematical Medicine and Biology - February 22, 2007 Category: Biomedical Science Authors: Alavez-Ramirez, J., Castellanos, J. R. A., Esteva, L., Flores, J. A., Fuentes-Allen, J. L., Garcia-Ramos, G., Gomez, G., Lopez-Estrada, J. Tags: Articles Source Type: journals