MedWorm.com provides a medical RSS filtering service. Over 6000 RSS medical sources are combined and output via different filters. This feed contains the latest items from the 'Mathematical Medicine and Biology' source. Sun, 21 Mar 2010 16:59:25 +0100 http://www.medworm.com/index.php?rid=3334622&cid=s_36514_61_f&fid=36514&url=http%3A%2F%2Fimammb.oxfordjournals.org%2Fcgi%2Fcontent%2Fshort%2F27%2F1%2F75%3Frss%3D1 In this paper we study a predator–prey model with logistic growth in the prey population, where a disease spreads among the prey according to an susceptible-infected-susceptible (SIS) epidemic model. The predators do not consume infected prey. After a review of the literature we formulate the basic mathematical model. For simplicity, we work initially with a model involving the fractions of prey susceptible and infected and then translate the results back to the model with absolute numbers. Both local and global stability results are examined. For the model working with absolute numbers, we find six possible equilibria and three important threshold values determining the behaviour of the system. There is always a unique locally stable equilibrium. We make conjectures concerning the g... Mathematical Medicine and Biology journals http://www.medworm.com/rss/comments.php?id=3334622 Fri, 05 Mar 2010 13:45:33 +0100 3334622 http://www.medworm.com/index.php?rid=3334621&cid=s_36514_61_f&fid=36514&url=http%3A%2F%2Fimammb.oxfordjournals.org%2Fcgi%2Fcontent%2Fshort%2F27%2F1%2F39%3Frss%3D1 This work examines a 1D individual-based model (IBM) for a system of tightly adherent cells, such as an epithelial monolayer. Each cell occupies a bounded region, defined by the location of its endpoints, has both elastic and viscous mechanical properties and is subject to drag generated by adhesion to the substrate. Differential-algebraic equations governing the evolution of the system are obtained from energy considerations. This IBM is then approximated by continuum models (systems of partial differential equations) in the limit of a large number of cells, N, when the cell parameters vary slowly in space or are spatially periodic (and so may be heterogeneous, with substantial variation between adjacent cells). For spatially periodic cell properties with significant cell viscosity, the r... Mathematical Medicine and Biology journals http://www.medworm.com/rss/comments.php?id=3334621 Fri, 05 Mar 2010 13:45:33 +0100 3334621 http://www.medworm.com/index.php?rid=3334620&cid=s_36514_61_f&fid=36514&url=http%3A%2F%2Fimammb.oxfordjournals.org%2Fcgi%2Fcontent%2Fshort%2F27%2F1%2F21%3Frss%3D1 A serious problem in emergency medicine is the correct evaluation of skin burn depth to make the appropriate choice of treatment. In clinical practice, there is no difficulty in classifying first- and third-degree burns correctly. However, differentiation between the IIa (superficial dermal) and IIb (deep dermal) wounds is problematic even for experienced practitioners. In this work, the use of surface skin temperature for the determination of the depth of second-degree burns is explored. An analytical solution of the 3D Pennes steady-state equation is obtained assuming that the ratio between burn depth and the burn size is small. The inverse problem is posed in a search space consisting of geometrical parameters associated with the burned region. This space is searched to minimize the err... Mathematical Medicine and Biology journals http://www.medworm.com/rss/comments.php?id=3334620 Fri, 05 Mar 2010 13:45:33 +0100 3334620 http://www.medworm.com/index.php?rid=3334619&cid=s_36514_61_f&fid=36514&url=http%3A%2F%2Fimammb.oxfordjournals.org%2Fcgi%2Fcontent%2Fshort%2F27%2F1%2F1%3Frss%3D1 To quantify the effects of changes in risk factors for chronic diseases on morbidity and mortality, Markov-type multi-state models are used. However, with multiple risk factors and many diseases relating to these risk factors, these models contain a large number of states. In this paper, we present an alternative modelling methodology implemented in the National Institute for Public Health and the Environment chronic disease model. This model includes multiple states based on risk factor levels and disease stages but only keeps track of the marginal probability values. Starting from the multi-state model, differential equations are derived that describe the change of the marginal distribution for each risk factor class and disease stage, taking into account population heterogeneity and com... Mathematical Medicine and Biology journals http://www.medworm.com/rss/comments.php?id=3334619 Fri, 05 Mar 2010 13:45:33 +0100 3334619 http://www.medworm.com/index.php?rid=3092162&cid=s_36514_61_f&fid=36514&url=http%3A%2F%2Fimammb.oxfordjournals.org%2Fcgi%2Fcontent%2Fshort%2F26%2F4%2F337%3Frss%3D1 The cell cycle is one of the best studied cellular mechanisms at the experimental and theoretical levels. Although most of the important biochemical components and reactions of the cell cycle are probably known, the precise way the cell cycle dynamics are driven is still under debate. This phenomenon is not atypical to many other biological systems where the knowledge of the molecular building blocks and the interactions between them does not lead to a coherent picture of the appropriate dynamics. We here propose a methodology to develop plausible models for the driving mechanisms of embryonic and cancerous cell cycles. We first define a key property of the system (a cyclic behaviour in the case of the embryonic cell cycle) and set mathematical constraints on the types of two variable simp... Mathematical Medicine and Biology journals http://www.medworm.com/rss/comments.php?id=3092162 Wed, 16 Dec 2009 13:55:20 +0100 3092162 http://www.medworm.com/index.php?rid=3092161&cid=s_36514_61_f&fid=36514&url=http%3A%2F%2Fimammb.oxfordjournals.org%2Fcgi%2Fcontent%2Fshort%2F26%2F4%2F323%3Frss%3D1 Deterministic mathematical models of biochemical processes operate as if the empirically derived rate constants governing the dynamics are known with certainty. Our objective in this study was to explore the sensitivity of a deterministic model of blood coagulation to variations in the values of its 44 rate constants. This was accomplished for each rate constant at a given time by defining a normalized ensemble standard deviation (wkif(t)) that accounted for the sensitivity of the predicted concentration of each protein species to variation in that rate constant (from 10 to 1000% of the accepted value). A mean coefficient of variation derived from (wkif(t)) values for all protein species was defined to quantify the overall variation introduced into the model's predictive capacity at that t... Mathematical Medicine and Biology journals http://www.medworm.com/rss/comments.php?id=3092161 Wed, 16 Dec 2009 13:55:20 +0100 3092161 http://www.medworm.com/index.php?rid=3092160&cid=s_36514_61_f&fid=36514&url=http%3A%2F%2Fimammb.oxfordjournals.org%2Fcgi%2Fcontent%2Fshort%2F26%2F4%2F309%3Frss%3D1 Establishing the conditions for the stability of ecosystems and for stable coexistence of interacting populations is a problem of the highest priority in mathematical biology. This problem is usually considered under specific assumptions made regarding the functional forms of non-linear feedbacks. However, there is growing understanding that this approach has a number of major deficiencies. The most important of these is that the precise forms of the functional responses involved in the model are unknown in detail, and we can hardly expect that these will be known in feasible future. In this paper, we consider the dynamics of two species with interaction of consumer–supplier (prey–predator) type. This model generalizes a variety of models of population dynamics, including a ran... Mathematical Medicine and Biology journals http://www.medworm.com/rss/comments.php?id=3092160 Wed, 16 Dec 2009 13:55:20 +0100 3092160 http://www.medworm.com/index.php?rid=3092159&cid=s_36514_61_f&fid=36514&url=http%3A%2F%2Fimammb.oxfordjournals.org%2Fcgi%2Fcontent%2Fshort%2F26%2F4%2F297%3Frss%3D1 A dynamical system model for tumour–immune system interaction together with a method to mimic radiation therapy are proposed. A large population of virtual patients is simulated following an ideal radiation treatment. A characteristic parameter, the immune system–tumor efficiency ratio (ISTER) is introduced. ISTER dependence of treatment success and other features are studied. Radiotherapy treatment dose optimization, following ALARA (As Low As Reasonably Achievable) criterion, as well as a patient classification are drawn from the statistics results. (Source: Mathematical Medicine and Biology) Mathematical Medicine and Biology journals http://www.medworm.com/rss/comments.php?id=3092159 Wed, 16 Dec 2009 13:55:20 +0100 3092159 http://www.medworm.com/index.php?rid=3092158&cid=s_36514_61_f&fid=36514&url=http%3A%2F%2Fimammb.oxfordjournals.org%2Fcgi%2Fcontent%2Fshort%2F26%2F4%2F263%3Frss%3D1 Mass transfer in tissues is typically studied by multiple indicator dilution (MID) studies. Several of these studies have shown that drug concentrations can be modelled by axially distributed models. In this paper, we determine the Taylor dispersion coefficient that describes the degree of axial mixing for the MID models, while accounting for the presence of red blood cells in the capillaries. The capillaries are treated as well mixed with no radial concentration gradients. The concentration in tissue is treated as position and time dependent and the partial differential equations for mass transport are averaged using the method of multiple timescales. The calculated values of the dispersion coefficient are in reasonable agreement with the values reported in literature, suggesting that Tay... Mathematical Medicine and Biology journals http://www.medworm.com/rss/comments.php?id=3092158 Wed, 16 Dec 2009 13:55:20 +0100 3092158 http://www.medworm.com/index.php?rid=2771981&cid=s_36514_61_f&fid=36514&url=http%3A%2F%2Fimammb.oxfordjournals.org%2Fcgi%2Fcontent%2Fshort%2F26%2F3%2F241%3Frss%3D1 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 out of the chondrocyte and its diffusive flux determines which of these mechanisms is dominant. We investigate the diffusion-dominated and advection-dominated limiting case... Mathematical Medicine and Biology journals http://www.medworm.com/rss/comments.php?id=2771981 Sun, 06 Sep 2009 23:00:00 +0100 2771981 http://www.medworm.com/index.php?rid=2771980&cid=s_36514_61_f&fid=36514&url=http%3A%2F%2Fimammb.oxfordjournals.org%2Fcgi%2Fcontent%2Fshort%2F26%2F3%2F225%3Frss%3D1 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 number of the free pathogen particles and that the incidence rate is an unspecified function of the number of susceptible hosts and free pathogen particles; all these funct... Mathematical Medicine and Biology journals http://www.medworm.com/rss/comments.php?id=2771980 Sun, 06 Sep 2009 23:00:00 +0100 2771980 http://www.medworm.com/index.php?rid=2771979&cid=s_36514_61_f&fid=36514&url=http%3A%2F%2Fimammb.oxfordjournals.org%2Fcgi%2Fcontent%2Fshort%2F26%2F3%2F201%3Frss%3D1 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 leads to insights that are not otherwise apparent; these include an explanation of why the squid giant axon attains a diameter in the region of 1 mm. The simplified PDE m... Mathematical Medicine and Biology journals http://www.medworm.com/rss/comments.php?id=2771979 Sun, 06 Sep 2009 23:00:00 +0100 2771979 http://www.medworm.com/index.php?rid=2771978&cid=s_36514_61_f&fid=36514&url=http%3A%2F%2Fimammb.oxfordjournals.org%2Fcgi%2Fcontent%2Fshort%2F26%2F3%2F187%3Frss%3D1 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 biological tissue for comparison. Finally, we theoretically study the effect of the thermal relaxation time on the temperature profiles in the tissue for both heating and coo... Mathematical Medicine and Biology journals http://www.medworm.com/rss/comments.php?id=2771978 Sun, 06 Sep 2009 23:00:00 +0100 2771978 http://www.medworm.com/index.php?rid=2455935&cid=s_36514_61_f&fid=36514&url=http%3A%2F%2Fimammb.oxfordjournals.org%2Fcgi%2Fcontent%2Fshort%2F26%2F2%2F165%3Frss%3D1 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: Mathematical Medicine and Biology) Mathematical Medicine and Biology journals http://www.medworm.com/rss/comments.php?id=2455935 Tue, 02 Jun 2009 04:00:00 +0100 2455935 http://www.medworm.com/index.php?rid=2455934&cid=s_36514_61_f&fid=36514&url=http%3A%2F%2Fimammb.oxfordjournals.org%2Fcgi%2Fcontent%2Fshort%2F26%2F2%2F133%3Frss%3D1 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, elastin degrades and collagen fibre concentration can adapt to maintain mechanical equilibrium. An analytic expression for the rate of evolution of the fibre concentration is ... Mathematical Medicine and Biology journals http://www.medworm.com/rss/comments.php?id=2455934 Tue, 02 Jun 2009 04:00:00 +0100 2455934 http://www.medworm.com/index.php?rid=2455933&cid=s_36514_61_f&fid=36514&url=http%3A%2F%2Fimammb.oxfordjournals.org%2Fcgi%2Fcontent%2Fshort%2F26%2F2%2F117%3Frss%3D1 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) Mathematical Medicine and Biology journals http://www.medworm.com/rss/comments.php?id=2455933 Tue, 02 Jun 2009 04:00:00 +0100 2455933 http://www.medworm.com/index.php?rid=2455932&cid=s_36514_61_f&fid=36514&url=http%3A%2F%2Fimammb.oxfordjournals.org%2Fcgi%2Fcontent%2Fshort%2F26%2F2%2F97%3Frss%3D1 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 asymptotically stable under the assumption that the release amount of the predator is greater than some critical value. Permanent conditions are established under the assump... Mathematical Medicine and Biology journals http://www.medworm.com/rss/comments.php?id=2455932 Tue, 02 Jun 2009 04:00:00 +0100 2455932 http://www.medworm.com/index.php?rid=2217489&cid=s_36514_61_f&fid=36514&url=http%3A%2F%2Fimammb.oxfordjournals.org%2Fcgi%2Fcontent%2Fshort%2F26%2F1%2F63%3Frss%3D1 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 the tumour eradication is also investigated. Finally, global conditions for stability and eradication in the presence of delays are given for some particular cases. (Sou... Mathematical Medicine and Biology journals http://www.medworm.com/rss/comments.php?id=2217489 Thu, 26 Feb 2009 05:00:00 +0100 2217489 http://www.medworm.com/index.php?rid=2217488&cid=s_36514_61_f&fid=36514&url=http%3A%2F%2Fimammb.oxfordjournals.org%2Fcgi%2Fcontent%2Fshort%2F26%2F1%2F25%3Frss%3D1 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 increase during the test as well as the rise in CSF pressure pulsation amplitude due to transmission of blood pressure oscillations. In addition, the CSF flux into and out... Mathematical Medicine and Biology journals http://www.medworm.com/rss/comments.php?id=2217488 Thu, 26 Feb 2009 05:00:00 +0100 2217488 http://www.medworm.com/index.php?rid=2217487&cid=s_36514_61_f&fid=36514&url=http%3A%2F%2Fimammb.oxfordjournals.org%2Fcgi%2Fcontent%2Fshort%2F26%2F1%2F1%3Frss%3D1 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 the ureter. The renal pelvis is treated as an elastic bag, whose volume increases in response to an increased internal pressure. Fluid enters the renal pelvis from the kid... Mathematical Medicine and Biology journals http://www.medworm.com/rss/comments.php?id=2217487 Thu, 26 Feb 2009 05:00:00 +0100 2217487 http://www.medworm.com/index.php?rid=1997090&cid=s_36514_61_f&fid=36514&url=http%3A%2F%2Fimammb.oxfordjournals.org%2Fcgi%2Fcontent%2Fshort%2F25%2F4%2F359%3Frss%3D1 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 these details can have a strong influence on the predicted effectiveness of the strategy: for instance, with R0 = 1.8 in absence of treatment, different models predict that... Mathematical Medicine and Biology journals http://www.medworm.com/rss/comments.php?id=1997090 Thu, 27 Nov 2008 05:00:00 +0100 1997090 http://www.medworm.com/index.php?rid=1997089&cid=s_36514_61_f&fid=36514&url=http%3A%2F%2Fimammb.oxfordjournals.org%2Fcgi%2Fcontent%2Fshort%2F25%2F4%2F337%3Frss%3D1 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 and the risk of death by the disease. In particular, we illustrate the onset of the long cycles caused by rational exemption when vaccination decisions are based on delayed... Mathematical Medicine and Biology journals http://www.medworm.com/rss/comments.php?id=1997089 Thu, 27 Nov 2008 05:00:00 +0100 1997089 http://www.medworm.com/index.php?rid=1997088&cid=s_36514_61_f&fid=36514&url=http%3A%2F%2Fimammb.oxfordjournals.org%2Fcgi%2Fcontent%2Fshort%2F25%2F4%2F323%3Frss%3D1 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 cooling and re-warming procedure during surgery are in qualitative agreement with experimental data in producing the afterdrop effect and the observed dynamical variation in... Mathematical Medicine and Biology journals http://www.medworm.com/rss/comments.php?id=1997088 Thu, 27 Nov 2008 05:00:00 +0100 1997088 http://www.medworm.com/index.php?rid=1997087&cid=s_36514_61_f&fid=36514&url=http%3A%2F%2Fimammb.oxfordjournals.org%2Fcgi%2Fcontent%2Fshort%2F25%2F4%2F285%3Frss%3D1 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) Mathematical Medicine and Biology journals http://www.medworm.com/rss/comments.php?id=1997087 Thu, 27 Nov 2008 05:00:00 +0100 1997087 http://www.medworm.com/index.php?rid=1743069&cid=s_36514_61_f&fid=36514&url=http%3A%2F%2Fimammb.oxfordjournals.org%2Fcgi%2Fcontent%2Fshort%2F25%2F3%2F267%3Frss%3D1 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 women consistently show an immune system's average activity level of about a = 2.8596 for the women. Fortunately, an optimum time-varying therapy program a(t) is found t... Mathematical Medicine and Biology journals http://www.medworm.com/rss/comments.php?id=1743069 Fri, 29 Aug 2008 04:00:00 +0100 1743069 http://www.medworm.com/index.php?rid=1743068&cid=s_36514_61_f&fid=36514&url=http%3A%2F%2Fimammb.oxfordjournals.org%2Fcgi%2Fcontent%2Fshort%2F25%2F3%2F247%3Frss%3D1 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 reproduction number, dictates whether the disease will become endemic in the ecosystem. Under one combination of these coupled conditions, a highly infectious disease could d... Mathematical Medicine and Biology journals http://www.medworm.com/rss/comments.php?id=1743068 Fri, 29 Aug 2008 04:00:00 +0100 1743068 http://www.medworm.com/index.php?rid=1743067&cid=s_36514_61_f&fid=36514&url=http%3A%2F%2Fimammb.oxfordjournals.org%2Fcgi%2Fcontent%2Fshort%2F25%2F3%2F233%3Frss%3D1 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) Mathematical Medicine and Biology journals http://www.medworm.com/rss/comments.php?id=1743067 Fri, 29 Aug 2008 04:00:00 +0100 1743067 http://www.medworm.com/index.php?rid=1743066&cid=s_36514_61_f&fid=36514&url=http%3A%2F%2Fimammb.oxfordjournals.org%2Fcgi%2Fcontent%2Fshort%2F25%2F3%2F215%3Frss%3D1 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 regularization is investigated and appropriate convergence results are obtained. Numerical results of concentration-dependent chemotactic terms are explored. (Source: Mathematical... Mathematical Medicine and Biology journals http://www.medworm.com/rss/comments.php?id=1743066 Fri, 29 Aug 2008 04:00:00 +0100 1743066 http://www.medworm.com/index.php?rid=1743065&cid=s_36514_61_f&fid=36514&url=http%3A%2F%2Fimammb.oxfordjournals.org%2Fcgi%2Fcontent%2Fshort%2F25%2F3%2F187%3Frss%3D1 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 remaining domain. Numerical studies are performed on a non-linear test problem to confirm the accuracy and convergence of the scheme. The computations on the tear film m... Mathematical Medicine and Biology journals http://www.medworm.com/rss/comments.php?id=1743065 Fri, 29 Aug 2008 04:00:00 +0100 1743065 http://www.medworm.com/index.php?rid=1500593&cid=s_36514_61_f&fid=36514&url=http%3A%2F%2Fimammb.oxfordjournals.org%2Fcgi%2Fcontent%2Fshort%2F25%2F2%2F185%3Frss%3D1 (Source: Mathematical Medicine and Biology) Mathematical Medicine and Biology journals http://www.medworm.com/rss/comments.php?id=1500593 Fri, 06 Jun 2008 04:00:00 +0100 1500593 http://www.medworm.com/index.php?rid=1500592&cid=s_36514_61_f&fid=36514&url=http%3A%2F%2Fimammb.oxfordjournals.org%2Fcgi%2Fcontent%2Fshort%2F25%2F2%2F171%3Frss%3D1 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 for inhomogeneous doses is applied to different uniform dose TCP models. As expected, the TCP takes into account the whole dose distribution over the target volume, but i... Mathematical Medicine and Biology journals http://www.medworm.com/rss/comments.php?id=1500592 Fri, 06 Jun 2008 04:00:00 +0100 1500592 http://www.medworm.com/index.php?rid=1500591&cid=s_36514_61_f&fid=36514&url=http%3A%2F%2Fimammb.oxfordjournals.org%2Fcgi%2Fcontent%2Fshort%2F25%2F2%2F157%3Frss%3D1 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 of the corresponding adjoint system. Numerical results are given for various scenarios. The optimal waveforms confirm the previously discovered positive effects of active... Mathematical Medicine and Biology journals http://www.medworm.com/rss/comments.php?id=1500591 Fri, 06 Jun 2008 04:00:00 +0100 1500591 http://www.medworm.com/index.php?rid=1500590&cid=s_36514_61_f&fid=36514&url=http%3A%2F%2Fimammb.oxfordjournals.org%2Fcgi%2Fcontent%2Fshort%2F25%2F2%2F141%3Frss%3D1 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 hyperinsulinemic clamp experiment, introducing system noise in tissue glucose uptake and apply for its estimation a closed-form Hermite expansion of the transition densiti... Mathematical Medicine and Biology journals http://www.medworm.com/rss/comments.php?id=1500590 Fri, 06 Jun 2008 04:00:00 +0100 1500590 http://www.medworm.com/index.php?rid=1500589&cid=s_36514_61_f&fid=36514&url=http%3A%2F%2Fimammb.oxfordjournals.org%2Fcgi%2Fcontent%2Fshort%2F25%2F2%2F133%3Frss%3D1 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 property is not true once the highly symmetric spherical environment is abandoned. It seems that any ambiguity concerning overlapping information coming from EEG and MEG ... Mathematical Medicine and Biology journals http://www.medworm.com/rss/comments.php?id=1500589 Fri, 06 Jun 2008 04:00:00 +0100 1500589 http://www.medworm.com/index.php?rid=1500588&cid=s_36514_61_f&fid=36514&url=http%3A%2F%2Fimammb.oxfordjournals.org%2Fcgi%2Fcontent%2Fshort%2F25%2F2%2F113%3Frss%3D1 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 solution of more complicated models, but rather to justify the phenomenological inverse power law and to provide a basic interpretation of cerebral elasticity, reference pres... Mathematical Medicine and Biology journals http://www.medworm.com/rss/comments.php?id=1500588 Fri, 06 Jun 2008 04:00:00 +0100 1500588 http://www.medworm.com/index.php?rid=1500587&cid=s_36514_61_f&fid=36514&url=http%3A%2F%2Fimammb.oxfordjournals.org%2Fcgi%2Fcontent%2Fshort%2F25%2F2%2F99%3Frss%3D1 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 asymptotically stable. The formula for shows that increasing either of the two delays will decrease . This may suggest a new direction for new drugs—drugs that can prolong t... Mathematical Medicine and Biology journals http://www.medworm.com/rss/comments.php?id=1500587 Fri, 06 Jun 2008 04:00:00 +0100 1500587 http://www.medworm.com/index.php?rid=1459095&cid=s_36514_61_f&fid=36514&url=http%3A%2F%2Fimammb.oxfordjournals.org%2Fcgi%2Fcontent%2Fshort%2F25%2F1%2F87%3Frss%3D1 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 discriminant statistics to compare stress and recovery phases. Data analysis performed over the heartbeat series of 14 healthy subjects shows significant difference between stress... Mathematical Medicine and Biology journals http://www.medworm.com/rss/comments.php?id=1459095 Wed, 21 May 2008 04:00:00 +0100 1459095 http://www.medworm.com/index.php?rid=1459094&cid=s_36514_61_f&fid=36514&url=http%3A%2F%2Fimammb.oxfordjournals.org%2Fcgi%2Fcontent%2Fshort%2F25%2F1%2F65%3Frss%3D1 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 range. This observation led us to hypothesize that single-channel models with Ca2+ inactivation would be less sensitive to the details of release site ultrastructure than mo... Mathematical Medicine and Biology journals http://www.medworm.com/rss/comments.php?id=1459094 Wed, 21 May 2008 04:00:00 +0100 1459094 http://www.medworm.com/index.php?rid=1459093&cid=s_36514_61_f&fid=36514&url=http%3A%2F%2Fimammb.oxfordjournals.org%2Fcgi%2Fcontent%2Fshort%2F25%2F1%2F37%3Frss%3D1 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 with the primary feedback mechanism can exhibit the ultradian as well as circadian variability in the hormone secretion of the HPA axis. The model can also predict different... Mathematical Medicine and Biology journals http://www.medworm.com/rss/comments.php?id=1459093 Wed, 21 May 2008 04:00:00 +0100 1459093 http://www.medworm.com/index.php?rid=1459092&cid=s_36514_61_f&fid=36514&url=http%3A%2F%2Fimammb.oxfordjournals.org%2Fcgi%2Fcontent%2Fshort%2F25%2F1%2F21%3Frss%3D1 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) Mathematical Medicine and Biology journals http://www.medworm.com/rss/comments.php?id=1459092 Wed, 21 May 2008 04:00:00 +0100 1459092 http://www.medworm.com/index.php?rid=1459091&cid=s_36514_61_f&fid=36514&url=http%3A%2F%2Fimammb.oxfordjournals.org%2Fcgi%2Fcontent%2Fshort%2F25%2F1%2F1%3Frss%3D1 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 effect where the outcome depends on the initial host density. Special cases were also studied for small carrying capacities leading to complex dynamical behaviours. Then, nu... Mathematical Medicine and Biology journals http://www.medworm.com/rss/comments.php?id=1459091 Wed, 21 May 2008 04:00:00 +0100 1459091 http://www.medworm.com/index.php?rid=1295032&cid=s_36514_61_f&fid=36514&url=http%3A%2F%2Fimammb.oxfordjournals.org%2Fcgi%2Fcontent%2Fshort%2F24%2F4%2F413-a%3Frss%3D1 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 large numbers of features. The ACA is an optimization algorithm capable of incorporating prior information, allowing it to search the sample space more efficiently than ot... Mathematical Medicine and Biology journals http://www.medworm.com/rss/comments.php?id=1295032 Tue, 11 Mar 2008 04:00:00 +0100 1295032 http://www.medworm.com/index.php?rid=1295031&cid=s_36514_61_f&fid=36514&url=http%3A%2F%2Fimammb.oxfordjournals.org%2Fcgi%2Fcontent%2Fshort%2F24%2F4%2F401%3Frss%3D1 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 distribution. The heuristic arguments are supported in a simulation study evaluating different steps in the argument. (Source: Mathematical Medicine and Biology) Mathematical Medicine and Biology journals http://www.medworm.com/rss/comments.php?id=1295031 Tue, 11 Mar 2008 04:00:00 +0100 1295031 http://www.medworm.com/index.php?rid=1295030&cid=s_36514_61_f&fid=36514&url=http%3A%2F%2Fimammb.oxfordjournals.org%2Fcgi%2Fcontent%2Fshort%2F24%2F4%2F379%3Frss%3D1 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-established empirical descriptions of these rheological effects, accounting in particular for spatially varying haematocrit distributions; we solved the PDE system using a characte... Mathematical Medicine and Biology journals http://www.medworm.com/rss/comments.php?id=1295030 Tue, 11 Mar 2008 04:00:00 +0100 1295030 http://www.medworm.com/index.php?rid=1295029&cid=s_36514_61_f&fid=36514&url=http%3A%2F%2Fimammb.oxfordjournals.org%2Fcgi%2Fcontent%2Fshort%2F24%2F4%2F347%3Frss%3D1 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. Realistic lid motion from observed blinks is included in the model with end fluxes specified to more closely match the blink cycle than those previously reported. Numeric... Mathematical Medicine and Biology journals http://www.medworm.com/rss/comments.php?id=1295029 Tue, 11 Mar 2008 04:00:00 +0100 1295029 http://www.medworm.com/index.php?rid=1009710&cid=s_36514_61_f&fid=36514&url=http%3A%2F%2Fimammb.oxfordjournals.org%2Fcgi%2Fcontent%2Fshort%2F24%2F3%2F327%3Frss%3D1 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 formulated each model and related the coefficients between the models, numerical simulations are performed on a block of incompressible material. These demonstrate that the si... Mathematical Medicine and Biology journals http://www.medworm.com/rss/comments.php?id=1009710 Tue, 06 Nov 2007 05:00:00 +0100 1009710 http://www.medworm.com/index.php?rid=1009709&cid=s_36514_61_f&fid=36514&url=http%3A%2F%2Fimammb.oxfordjournals.org%2Fcgi%2Fcontent%2Fshort%2F24%2F3%2F301%3Frss%3D1 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 incidence law. (Source: Mathematical Medicine and Biology) Mathematical Medicine and Biology journals http://www.medworm.com/rss/comments.php?id=1009709 Tue, 06 Nov 2007 05:00:00 +0100 1009709 http://www.medworm.com/index.php?rid=1009708&cid=s_36514_61_f&fid=36514&url=http%3A%2F%2Fimammb.oxfordjournals.org%2Fcgi%2Fcontent%2Fshort%2F24%2F3%2F287%3Frss%3D1 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) Mathematical Medicine and Biology journals http://www.medworm.com/rss/comments.php?id=1009708 Tue, 06 Nov 2007 05:00:00 +0100 1009708 http://www.medworm.com/index.php?rid=1009707&cid=s_36514_61_f&fid=36514&url=http%3A%2F%2Fimammb.oxfordjournals.org%2Fcgi%2Fcontent%2Fshort%2F24%2F3%2F271%3Frss%3D1 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) Mathematical Medicine and Biology journals http://www.medworm.com/rss/comments.php?id=1009707 Tue, 06 Nov 2007 05:00:00 +0100 1009707 http://www.medworm.com/index.php?rid=1009706&cid=s_36514_61_f&fid=36514&url=http%3A%2F%2Fimammb.oxfordjournals.org%2Fcgi%2Fcontent%2Fshort%2F24%2F3%2F251%3Frss%3D1 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 literature. The asymmetric nature of the protein molecules due to various reasons such as tilting is the primary cause for the dimple formation. We discuss the effects of spont... Mathematical Medicine and Biology journals http://www.medworm.com/rss/comments.php?id=1009706 Tue, 06 Nov 2007 05:00:00 +0100 1009706 http://www.medworm.com/index.php?rid=949459&cid=s_36514_61_f&fid=36514&url=http%3A%2F%2Fimammb.oxfordjournals.org%2Fcgi%2Fcontent%2Fshort%2F24%2F2%2F225%3Frss%3D1 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 subjects. The results show that it is possible to gain insight into the behaviour of the rather complex physiological system using only a few noninvasive measurements and tracta... Mathematical Medicine and Biology journals http://www.medworm.com/rss/comments.php?id=949459 Wed, 23 May 2007 04:00:00 +0100 949459 http://www.medworm.com/index.php?rid=949458&cid=s_36514_61_f&fid=36514&url=http%3A%2F%2Fimammb.oxfordjournals.org%2Fcgi%2Fcontent%2Fshort%2F24%2F2%2F209%3Frss%3D1 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 so-called dispersion relations, predicting that a certain representative length dominates in this model. As the analytical analysis is restricted to travelling waves, we... Mathematical Medicine and Biology journals http://www.medworm.com/rss/comments.php?id=949458 Wed, 23 May 2007 04:00:00 +0100 949458 http://www.medworm.com/index.php?rid=949457&cid=s_36514_61_f&fid=36514&url=http%3A%2F%2Fimammb.oxfordjournals.org%2Fcgi%2Fcontent%2Fshort%2F24%2F2%2F169%3Frss%3D1 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 averaged across the axial direction. The leading-order fluid flow is then of Hele–Shaw type, and may be solved for explicitly. The trajectory of the tissue constru... Mathematical Medicine and Biology journals http://www.medworm.com/rss/comments.php?id=949457 Wed, 23 May 2007 04:00:00 +0100 949457 http://www.medworm.com/index.php?rid=949456&cid=s_36514_61_f&fid=36514&url=http%3A%2F%2Fimammb.oxfordjournals.org%2Fcgi%2Fcontent%2Fshort%2F24%2F2%2F149%3Frss%3D1 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 distribution of carriers in Japan. (Source: Mathematical Medicine and Biology) Mathematical Medicine and Biology journals http://www.medworm.com/rss/comments.php?id=949456 Wed, 23 May 2007 04:00:00 +0100 949456 http://www.medworm.com/index.php?rid=949455&cid=s_36514_61_f&fid=36514&url=http%3A%2F%2Fimammb.oxfordjournals.org%2Fcgi%2Fcontent%2Fshort%2F24%2F2%2F131%3Frss%3D1 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 problem and then relaxing to the continuous realm. We prove that in the case where the data have an inherent ‘checkerboard’ sign pattern, the algorithm will auto... Mathematical Medicine and Biology journals http://www.medworm.com/rss/comments.php?id=949455 Wed, 23 May 2007 04:00:00 +0100 949455 http://www.medworm.com/index.php?rid=949465&cid=s_36514_61_f&fid=36514&url=http%3A%2F%2Fimammb.oxfordjournals.org%2Fcgi%2Fcontent%2Fshort%2F24%2F1%2F111%3Frss%3D1 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. The results show that the thrombin inhibition rate, the gel permeability and the shear rate are key parameters in regulating the height of the fibrin gel. (Source: Math... Mathematical Medicine and Biology journals http://www.medworm.com/rss/comments.php?id=949465 Thu, 22 Feb 2007 05:00:00 +0100 949465 http://www.medworm.com/index.php?rid=949464&cid=s_36514_61_f&fid=36514&url=http%3A%2F%2Fimammb.oxfordjournals.org%2Fcgi%2Fcontent%2Fshort%2F24%2F1%2F85%3Frss%3D1 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 sufficiently collapsible transverse sinus, but it is also possible that a stenosed sinus may persist following resolution of significant intracranial hypertension. (Source: Mathem... Mathematical Medicine and Biology journals http://www.medworm.com/rss/comments.php?id=949464 Thu, 22 Feb 2007 05:00:00 +0100 949464 http://www.medworm.com/index.php?rid=949463&cid=s_36514_61_f&fid=36514&url=http%3A%2F%2Fimammb.oxfordjournals.org%2Fcgi%2Fcontent%2Fshort%2F24%2F1%2F57%3Frss%3D1 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 solutions are presented for the limiting cases in which the coefficient of drag between the cells and the scaffold is very large or zero. In the limit of large time, sol... Mathematical Medicine and Biology journals http://www.medworm.com/rss/comments.php?id=949463 Thu, 22 Feb 2007 05:00:00 +0100 949463 http://www.medworm.com/index.php?rid=949462&cid=s_36514_61_f&fid=36514&url=http%3A%2F%2Fimammb.oxfordjournals.org%2Fcgi%2Fcontent%2Fshort%2F24%2F1%2F35%3Frss%3D1 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 characteristic of latent TB and for small reduction in an immune response, the use of a single drug is capable of curing the infection before the appearance of drug resistance. H... Mathematical Medicine and Biology journals http://www.medworm.com/rss/comments.php?id=949462 Thu, 22 Feb 2007 05:00:00 +0100 949462 http://www.medworm.com/index.php?rid=949461&cid=s_36514_61_f&fid=36514&url=http%3A%2F%2Fimammb.oxfordjournals.org%2Fcgi%2Fcontent%2Fshort%2F24%2F1%2F17%3Frss%3D1 Most pathogens are capable of infecting multiple hosts. These multiple hosts provide many avenues for the disease to emerge. In this investigation, we formulate and analyse multi-host epidemic models and determine conditions under which the disease can emerge. In particular, SIS and SIR epidemic models are formulated for a pathogen that can infect n different hosts. The basic reproduction number is computed and shown to increase with n, the number of hosts that can be infected. Therefore, the possibility of disease emergence increases with the number of hosts infected. The SIS model for two hosts is studied in detail. Necessary and sufficient conditions are derived for the global stability of an endemic equilibrium. Numerical examples illustrate the dynamics of the two- and three-host epid... Mathematical Medicine and Biology journals http://www.medworm.com/rss/comments.php?id=949461 Thu, 22 Feb 2007 05:00:00 +0100 949461 http://www.medworm.com/index.php?rid=949460&cid=s_36514_61_f&fid=36514&url=http%3A%2F%2Fimammb.oxfordjournals.org%2Fcgi%2Fcontent%2Fshort%2F24%2F1%2F1%3Frss%3D1 This paper studies two classes of epidemic models. These models are the standard SIR and SEIR models with time-varying periodic contact rate. The importance of the latent period is our target. When the latent period can be ignored and when it must be taken into account are the main points of our simulation. The comparison of the simulation results of our two models shows that the latent period is affecting the pattern of the dynamics of the disease. This paper addresses how model predictions are affected by the assumed form of the seasonally varying transmission rate and whether or not a latent class is included. Moreover, for some infectious diseases, using latent period leads to appearance or disappearance of some periodic solutions for the same parameter set. A key parameter for our mod... Mathematical Medicine and Biology journals http://www.medworm.com/rss/comments.php?id=949460 Thu, 22 Feb 2007 05:00:00 +0100 949460 http://www.medworm.com/index.php?rid=949472&cid=s_36514_61_f&fid=36514&url=http%3A%2F%2Fimammb.oxfordjournals.org%2Fcgi%2Fcontent%2Fshort%2F23%2F4%2F391%3Frss%3D1 (Source: Mathematical Medicine and Biology) Mathematical Medicine and Biology journals http://www.medworm.com/rss/comments.php?id=949472 Tue, 28 Nov 2006 05:00:00 +0100 949472 http://www.medworm.com/index.php?rid=949471&cid=s_36514_61_f&fid=36514&url=http%3A%2F%2Fimammb.oxfordjournals.org%2Fcgi%2Fcontent%2Fshort%2F23%2F4%2F389%3Frss%3D1 (Source: Mathematical Medicine and Biology) Mathematical Medicine and Biology journals http://www.medworm.com/rss/comments.php?id=949471 Tue, 28 Nov 2006 05:00:00 +0100 949471 http://www.medworm.com/index.php?rid=949470&cid=s_36514_61_f&fid=36514&url=http%3A%2F%2Fimammb.oxfordjournals.org%2Fcgi%2Fcontent%2Fshort%2F23%2F4%2F363%3Frss%3D1 We formulate in general terms the equations for axisymmetric and fully 3D models of a hydrocephalic brain. The model is developed using small strain poroelasticity that includes non-linear permeability. The axisymmetric model is solved for four ventricle shapes, an ellipsoid, a ‘peanut’ shape, a ‘cross’ shape and a ‘bone’ shape. The distribution of fluid pressure, velocity and content in the deformed parenchyma for a blocked aqueduct provides new qualitative insight into hydrocepahlus. Some observations are offered for two forms of cerebrospinal fluid flow abnormality, normal pressure hydrocephalus and idiopathic intracranial hypertension. The model is extended to include a gravitational term in the governing equations and the effect of hydrostatic press... Mathematical Medicine and Biology journals http://www.medworm.com/rss/comments.php?id=949470 Tue, 28 Nov 2006 05:00:00 +0100 949470 http://www.medworm.com/index.php?rid=949469&cid=s_36514_61_f&fid=36514&url=http%3A%2F%2Fimammb.oxfordjournals.org%2Fcgi%2Fcontent%2Fshort%2F23%2F4%2F339%3Frss%3D1 We examine a spherically symmetric model of the brain and apply non-linear permeability in a small strain poroelastic framework. Numerical solutions to the model show that non-linear effects tend to improve predictions of ventricle wall displacement and pressure increase in acute hydrocephalus in comparison with a constant permeability model. Our model is used to study different mechanisms for hydrocephalus: complete blockage of the aqueduct and normal pressure hydrocephalus (NPH), as well as offering observations on mechanical effects in idiopathic intracranial hypertension. In each situation it is possible to apply different parameter conditions to quantify mechanical effects that correspond to some observed symptoms. The results support and quantify ideas from Levine (2000, Ventricle si... Mathematical Medicine and Biology journals http://www.medworm.com/rss/comments.php?id=949469 Tue, 28 Nov 2006 05:00:00 +0100 949469 http://www.medworm.com/index.php?rid=949468&cid=s_36514_61_f&fid=36514&url=http%3A%2F%2Fimammb.oxfordjournals.org%2Fcgi%2Fcontent%2Fshort%2F23%2F4%2F311%3Frss%3D1 We develop mathematical models to provide insights into the morphology of a tissue construct formed from a single-cell suspension in culture media, within a rotating bioreactor. The bioreactor consists of a cylindrical vessel of circular cross-section rotating about its longitudinal axis with constant angular speed. Experimental studies show that at rotation rates below a critical value, the cells ‘self-assemble’ to form smooth ‘nodules’ that are approximately cylindrical with elliptical cross-section; however, at rotation rates above a critical value, an amorphous construct forms with a highly irregular boundary. The construct is denser than the surrounding culture media and histological studies indicate that the interior of the construct, which is a mix of apoptot... Mathematical Medicine and Biology journals http://www.medworm.com/rss/comments.php?id=949468 Tue, 28 Nov 2006 05:00:00 +0100 949468 http://www.medworm.com/index.php?rid=949467&cid=s_36514_61_f&fid=36514&url=http%3A%2F%2Fimammb.oxfordjournals.org%2Fcgi%2Fcontent%2Fshort%2F23%2F4%2F297%3Frss%3D1 In this work, we consider a delay differential equations model for bacteriophage infection and discuss the robustness of the positive equilibrium with respect to stochastic perturbations of the environment using two different approaches. First, we provide analytical estimates of the population intensities of fluctuations by Fourier transform methods. Next, we simulate the strong solutions of the arising stochastic delay differential equations by numerical methods of order 1. Extensive numerical experiments suggest that a noisy environment for the bacteria population is much more destabilizing on the concentrations at the equilibrium point than a noisy environment for the phage. (Source: Mathematical Medicine and Biology) Mathematical Medicine and Biology journals http://www.medworm.com/rss/comments.php?id=949467 Tue, 28 Nov 2006 05:00:00 +0100 949467 http://www.medworm.com/index.php?rid=949466&cid=s_36514_61_f&fid=36514&url=http%3A%2F%2Fimammb.oxfordjournals.org%2Fcgi%2Fcontent%2Fshort%2F23%2F4%2F279%3Frss%3D1 We find accurate approximations for the expected number of three-cycles and unchorded four-cycles under a stochastic distribution for graphs that has been proposed for modelling yeast two-hybrid protein–protein interaction networks. We show that unchorded four-cycles are characteristic motifs under this model and that the count of unchorded four-cycles in the graph is a reliable statistic on which to base parameter estimation. Finally, we test our model against a range of experimental data, obtain parameter estimates from these data and investigate possible improvements in the model. Characterization of this model lays the foundation for its use as a prior distribution in a Bayesian analysis of yeast two-hybrid networks that can potentially aid in identifying false-positive and false... Mathematical Medicine and Biology journals http://www.medworm.com/rss/comments.php?id=949466 Tue, 28 Nov 2006 05:00:00 +0100 949466