Mathematical Medicine and Biology (Math Med Biol)

Publications in this journal

• Article: Mathematical Tools for Understanding Infectious Disease Dynamics by O. Diekmann, H. Heesterbeek and T. Britton Princeton University Press, pp. 516, ISBN 978-0-691-15539-5.

  Philip D O'Neill
  Mathematical Medicine and Biology 05/2013;
• Article: A patient-specific model of the negative-feedback control of the hypothalamus-pituitary-thyroid (HPT) axis in autoimmune (Hashimoto's) thyroiditis.

  Balamurugan Pandiyan, Stephen J Merrill, Salvatore Benvenga
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  ABSTRACT: The purpose of modelling the negative-feedback control mechanism of the hypothalamus-pituitary-thyroid (HPT) axis in autoimmune (Hashimoto's) thyroiditis is to describe the clinical course of euthyroidism, subclinical hypothyroidism and overt hypothyroidism for patients. Thyroid hormone thyroxine (T4) and triiodothyronine (T3) levels are controlled by negative-feedback control through thyroid-stimulating hormone (TSH). T4, like other hormones, can be bound or unbound; the unbound T4 (FT4) is used as a marker for hypothyroidism. Autoimmune thyroiditis is a disease in which the thyroid-infiltrating lymphocytes attack autoantigens in follicle cells, destroying them over a long time. To describe the operation of the feedback control, we developed a mathematical model involving four clinical variables: TSH, FT4, anti-thyroid peroxidase antibodies and the thyroid gland's functional size. The first three variables are regularly measured while the last variable is determined through relationships between the other three variables. The problem of two different time scales for circulating hormones and thyroid damage is addressed using singular perturbation theory. Analysis of the mathematical model establishes stability and conditions under which the diseased state can maintain the slow movement toward diseased state equilibrium. Although we have used four variables in modelling the feedback control through the HPT axis, the predicted clinical course given any set of parameters is shown to depend on the steady-state levels of TSH and FT4. This observation makes possible the development of the clinical charts based only on the levels of TSH, time and potential steady-state values. To validate the model predictions, a dataset obtained from a Sicilian adult population has been employed.
  Mathematical Medicine and Biology 05/2013;
• Article: Bifurcation analysis of an existing mathematical model reveals novel treatment strategies and suggests potential cure for type 1 diabetes.

  Kenneth H M Nielsen, Flemming M Pociot, Johnny T Ottesen
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  ABSTRACT: Type 1 diabetes is a disease with serious personal and socioeconomic consequences that has attracted the attention of modellers recently. But as models of this disease tend to be complicated, there has been only limited mathematical analysis to date. Here we address this problem by providing a bifurcation analysis of a previously published mathematical model for the early stages of type 1 diabetes in diabetes-prone NOD mice, which is based on the data available in the literature. We also show positivity and the existence of a family of attracting trapping regions in the positive 5D cone, converging towards a smaller trapping region, which is the intersection over the family. All these trapping regions are compact sets, and thus, practical weak persistence is guaranteed. We conclude our analysis by proposing 4 novel treatment strategies: increasing the phagocytic ability of resting macrophages or activated macrophages, increasing the phagocytic ability of resting and activated macrophages simultaneously and lastly, adding additional macrophages to the site of inflammation. The latter seems counter-intuitive at first glance, but nevertheless it appears to be the most promising, as evidenced by recent results.
  Mathematical Medicine and Biology 04/2013;
• Article: Mathematical modelling of Pseudomonas aeruginosa biofilm growth and treatment in the cystic fibrosis lung.

  J K Miller, Justin S Brantner, Curtis Clemons, K L Kreider, Amy Milsted, Pat Wilber, Yang H Yun, Wiley J Youngs, Gerald Young, Hope T Badawy, Patrick O Wagers
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  ABSTRACT: Lung failure due to chronic bacterial infection is the leading cause of death for patients with cystic fibrosis (CF). It is thought that the chronic nature of these infections is, in part, due to the increased tolerance and recalcitrant behaviour of bacteria growing as biofilms. Inhalation of silver carbene complex (SCC) antimicrobial, either encased in polymeric biodegradable particles or in aqueous form, has been proposed as a treatment. Through a coordinated experimental and mathematical modelling effort, we examine this proposed treatment of lung biofilms. Pseudomonas aeruginosa biofilms grown in a flow-cell apparatus irrigated with an artificial CF sputum medium are analysed as an in vitro model of CF lung infection. A 2D mathematical model of biofilm growth within the flow-cell is developed. Numerical simulations demonstrate that SCC inactivation by the environment is critical in aqueous SCC, but not SCC-polymer, based treatments. Polymer particle degradation rate is shown to be an important parameter that can be chosen optimally, based on environmental conditions and bacterial susceptibility.
  Mathematical Medicine and Biology 03/2013;
• Article: A model for the spatial transmission of dengue with daily movement between villages and a city.

  Andrew L Nevai, Edy Soewono
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  ABSTRACT: Dengue is a re-emergent vector-borne disease affecting large portions of the world's population living in the tropics and subtropics. The virus is transmitted through the bites of female Aedes aegypti mosquitoes, and it is widely believed that these bites occur primarily in the daytime. The transmission of dengue is a complicated process, and one of the main sources of this complexity is due to the movement of people, e.g. between home and their places of work. Hence, the mechanics of disease progression may also differ between day and night. A discrete-time multi-patch dengue transmission model which takes into account the mobility of people as well as processes of infection, recovery, recruitment, mortality, and outbound and return movements is considered here. One patch (the city) is connected to all other patches (the villages) in a spoke-like network. We obtain here the basic reproductive ratio (0) of the transmission model which represents a threshold for an epidemic to occur. Dynamical analysis for vector control, human treatment and vaccination, and different kinds of mobility are performed. It is shown that changes in human movement patterns can, in some situations, affect the ability of the disease to persist in a predictable manner. We conclude with biological implications for the prevention and control of dengue virus transmission.
  Mathematical Medicine and Biology 03/2013;
• Article: Deterministic modelling for transmission of Human Papillomavirus 6/11: impact of vaccination.

  Laureen Ribassin-Majed, Rachid Lounes, Stephan Clemençon
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  ABSTRACT: This paper is devoted to assess the impact of quadrivalent human papillomavirus (HPV) vaccine on the prevalence of non-oncogenic HPV 6/11 types in French males and females. For this purpose, a non-linear dynamic model of heterosexual transmission for HPV 6/11 types infection is developed, which accounts for immunity due to vaccination, in particular. The vaccinated reproduction number Rv is derived using the approach described by Diekmann et al. (2010) called the next generation operator approach. The model proposed is analysed, with regard to existence and uniqueness of the solution, steady-state stability. Precisely, the stability of the model is investigated depending on the sign of Rv-1. Prevalence data are used to fit a numerical HPV model, so as to assess infection rates. Our approach suggests that 10 years after introducing vaccination, the prevalence of HPV 6/11 types in females will be halved and that in males will be reduced by one-quarter, assuming a sustained vaccine coverage of 30% among females. Using the formula, we derived for the vaccinated reproduction number, we show that the non-oncogenic HPV 6/11 types would be eradicated if vaccine coverage in females is kept above 12%.
  Mathematical Medicine and Biology 03/2013;
• Article: The role of contractile unit reorganization in force generation in airway smooth muscle.

  B S Brook, O E Jensen
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  ABSTRACT: Airway smooth muscle (ASM) cells undergo remodelling and reside in a tissue structure that is subject to heterogenous stress distributions that change dynamically during the breathing cycle. In this paper, we develop a structural model of an ASM cell that consists of contractile units (actin and myosin filaments) in series and parallel, anchored to a nonlinearly elastic cytoskeleton. We mimic a typical experimental protocol that involves isometric force generation through triggering of the contractile machinery, followed by oscillatory length fluctuation of the cell. We use the model to predict the effect of a single instance of rearrangement of the contractile machinery, combined with strain-stiffening of the cytoskeleton, on the force generated by the sarcomeres, and the total force generated by the cell. By linking intra-cellular events to whole-cell behaviour, the model reveals mechanistic relationships between structural properties and cell-level force-length loops. We show how contractile force, shortening velocity and sarcomere operating lengths vary as the internal cell architecture is altered. Additionally, we show how interactions between the internal contractile machinery and cytoskeletal structure play a role in the regulation of force generation and hysteresis of the cell.
  Mathematical Medicine and Biology 01/2013;
• Article: A mathematical model for the human menstrual cycle.

  C Y Chen, J P Ward
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  ABSTRACT: A simple mathematical model framework is developed to describe the hormonal interactions of the human menstrual cycle along the hypothalamus-pituitary-ovaries axis. The framework is designed so that it can be readily extended to model processes that disrupt the normal functioning cycle. The model in its most basic formulation exhibits multiple periodic solutions, one of which shows the key characteristics of a menstrual cycle, while the others indicate possible abnormalities sometimes observed in women of reproductive age. The basic model is extended to encompass receptor down-regulation as a mechanism to describe the desensitization of the pituitary to continuous stimulation of hypothalamic hormone, a hormonal therapy that is commonly prescribed prior to the surgical procedure for the removal of uterine myomas. Though the mechanisms for desensitization are likely to be more complex, the model results are in good qualitative agreement with physiological observations.
  Mathematical Medicine and Biology 01/2013;
• Article: Modelling fibrinolysis: 1D continuum models.

  Brittany E Bannish, James P Keener, Michael Woodbury, John W Weisel, Aaron L Fogelson
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  ABSTRACT: Fibrinolysis is the enzymatic degradation of the fibrin mesh that stabilizes blood clots. Experiments have shown that coarse clots made of thick fibres sometimes lyse more quickly than fine clots made of thin fibres, despite the fact that individual thick fibres lyse more slowly than individual thin fibres. This paper aims at using a 1D continuum reaction-diffusion model of fibrinolysis to elucidate the mechanism by which coarse clots lyse more quickly than fine clots. Reaction-diffusion models have been the standard tool for investigating fibrinolysis, and have been successful in capturing the wave-like behaviour of lysis seen in experiments. These previous models treat the distribution of fibrin within a clot as homogeneous, and therefore cannot be used directly to study the lysis of fine and coarse clots. In our model, we include a spatially heterogeneous fibrin concentration, as well as a more accurate description of the role of fibrin as a cofactor in the activation of the lytic enzyme. Our model predicts spatio-temporal protein distributions in reasonable quantitative agreement with experimental data. The model also predicts observed behaviour such as a front of lysis moving through the clot with an accumulation of lytic proteins at the front. In spite of the model improvements, however, we find that 1D continuum models are unable to accurately describe the observed differences in lysis behaviour between fine and coarse clots. Features of the problems that lead to the inaccuracy of 1D continuum models are discussed. We conclude that higher-dimensional, multiscale models are required to investigate the effect of clot structure on lysis behaviour.
  Mathematical Medicine and Biology 12/2012;
• Article: Modelling fibrinolysis: a 3D stochastic multiscale model.

  Brittany E Bannish, James P Keener, Aaron L Fogelson
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  ABSTRACT: Fibrinolysis, the proteolytic degradation of the fibrin fibres that stabilize blood clots, is initiated when tissue-type plasminogen activator (tPA) activates plasminogen to plasmin, the main fibrinolytic enzyme. Many experiments have shown that coarse clots made of thick fibres lyse more quickly than fine clots made of thin fibres, despite the fact that individual thick fibres lyse more slowly than individual thin fibres. The generally accepted explanation for this is that a coarse clot with fewer fibres to transect will be degraded faster than a fine clot with a higher fibre density. Other experiments show the opposite result. The standard mathematical tool for investigating fibrinolysis has been deterministic reaction-diffusion models, but due to low tPA concentrations, stochastic models may be more appropriate. We develop a 3D stochastic multiscale model of fibrinolysis. A microscale model representing a fibre cross section and containing detailed biochemical reactions provides information about single fibre lysis times, the number of plasmin molecules that can be activated by a single tPA molecule and the length of time tPA stays bound to a given fibre cross section. Data from the microscale model are used in a macroscale model of the full fibrin clot, from which we obtain lysis front velocities and tPA distributions. We find that the fibre number impacts lysis speed, but so does the number of tPA molecules relative to the surface area of the clot exposed to those molecules. Depending on the values of these two quantities (tPA number and surface area), for given kinetic parameters, the model predicts coarse clots lyse faster or slower than fine clots, thus providing a possible explanation for the divergent experimental observations.
  Mathematical Medicine and Biology 12/2012;
• Article: Minimizing the passive release of heparin-binding growth factors from an affinity-based delivery system.

  Tuoi T N Vo, Martin G Meere
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  ABSTRACT: We consider a mathematical model that describes the leakage of heparin-binding growth factors from an affinity-based delivery system. In the delivery system, heparin binds to a peptide which has been covalently cross-linked to a fibrin matrix. Growth factor in turn binds to the heparin, and growth factor release is governed by both binding and diffusion mechanisms, the purpose of the binding being to slow growth factor release. The governing mathematical model, which in its original formulation consists of six partial differential equations, is reduced to a system of just two equations. It is usually desirable that there be no passive release of growth factor from a device, with all of the growth factor being held in place via binding until such time as it is actively released by invading cells. However, there will inevitably be some passive release, and so it is of interest to identify conditions that will make this release as slow as possible. In this paper, we identify a parameter regime that ensures that at least a fraction of the growth factor will release slowly. It is found that slow release is assured if the matrix is prepared with the concentration of cross-linked peptide greatly exceeding the dissociation constant of heparin from the peptide, and with the concentration of heparin greatly exceeding the dissociation constant of the growth factor from heparin. Also, for the first time, in vitro experimental release data are directly compared with the theoretical release profiles generated by the model. We propose that the two stage release behaviour frequently seen in experiments is due to an initial rapid out-diffusion of free growth factor over a diffusion time scale (typically days), followed by a much slower release of the bound fraction over a time scale depending on both diffusion and binding parameters (frequently months).
  Mathematical Medicine and Biology 10/2012;
• Article: A fluid mechanical explanation of the spontaneous reattachment of a previously detached Descemet membrane.

  Z Ismail, A D Fitt, C P Please
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  ABSTRACT: Descemet membrane detachment (DMD) is a rare but potentially serious surgical complication that arises most often during cataract surgery. A recent study (Couch, S. M. & Baratz, K. H. (2009) Cornea, 28, 1160-1163) cited the case of a patient with DMDs in both eyes, noting that though one detachment was surgically repaired, the other spontaneously reattached and needed no further treatment. A fluid mechanical model of buoyancy-driven aqueous humour flow in the anterior chamber around a DMD is developed to explain this phenomenon. The analytical model is based on the lubrication theory limit of the Navier-Stokes equations. The flow is determined for a fixed geometry and the possible motion of the DMD is then analysed. Numerical calculations are also carried out (using COMSOL© Multiphysics) to confirm the lubrication theory results. The analytical and numerical results both show that, under the correct conditions, either spontaneous reattachment or worsening of the tear may occur. We conclude that it is possible that clinical outcomes for DMDs may be controlled by adjusting the temperature difference across the eye and/or the orientation of the patient.
  Mathematical Medicine and Biology 10/2012;
• Article: A mathematical model of intestinal oedema formation.

  Jennifer Young, Béatrice Rivière, Charles S Cox, Karen Uray
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  ABSTRACT: Intestinal oedema is a medical condition referring to the build-up of excess fluid in the interstitial spaces of the intestinal wall tissue. Intestinal oedema is known to produce a decrease in intestinal transit caused by a decrease in smooth muscle contractility, which can lead to numerous medical problems for the patient. Interstitial volume regulation has thus far been modelled with ordinary differential equations, or with a partial differential equation system where volume changes depend only on the current pressure and not on updated tissue stress. In this work, we present a computational, partial differential equation model of intestinal oedema formation that overcomes the limitations of past work to present a comprehensive model of the phenomenon. This model includes mass and momentum balance equations which give a time evolution of the interstitial pressure, intestinal volume changes and stress. The model also accounts for the spatially varying mechanical properties of the intestinal tissue and the inhomogeneous distribution of fluid-leaking capillaries that create oedema. The intestinal wall is modelled as a multi-layered, deforming, poroelastic medium, and the system of equations is solved using a discontinuous Galerkin method. To validate the model, simulation results are compared with results from four experimental scenarios. A sensitivity analysis is also provided. The model is able to capture the final submucosal interstitial pressure and total fluid volume change for all four experimental cases, and provide further insight into the distribution of these quantities across the intestinal wall.
  Mathematical Medicine and Biology 10/2012;
• Article: On the mechanics of a detaching retina.

  William J Bottega, Peter L Bishay, Jonathan L Prenner, Howard F Fine
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  ABSTRACT: A mechanics-based mathematical model for retinal detachment is developed, incorporating an energy-based criterion for propagation. Retinas with and without central tears are considered and contraction of the vitreous and extension of its fibrils, along with a pressure difference across the retina, are taken as the stimuli for detachment propagation. In addition to the equations of motion, boundary and matching conditions, the variational formulation yields the self-consistent energy release rate that governs detachment, and formulae for critical stress and critical deflections that provide a rational basis for measuring critical parameters. Exact analytical solutions are established for axisymmetric detachment of retinas with and without tears, and numerical simulations are performed based on these solutions. The results yield characteristic behaviour, including threshold levels and stability of detachment, 'dimpling' of the detaching retina, the effects of changes in material and geometric parameters, and the influence of the presence and size of the retinal tear on detachment propagation. The model predicts that once detachment ensues it does so in an unstable manner and is extensive in scope. This is in agreement with clinical observation. Results also suggest that, under appropriate conditions, the presence and size of a retinal tear or hole can have a 'stabilizing' effect with regard to detachment propagation.
  Mathematical Medicine and Biology 07/2012;
• Article: Multiple travelling-wave solutions in a minimal model for cell motility.

  L S Kimpton, J P Whiteley, S L Waters, J R King, J M Oliver
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  ABSTRACT: Two-phase flow models have been used previously to model cell motility. In order to reduce the complexity inherent with describing the many physical processes, we formulate a minimal model. Here we demonstrate that even the simplest 1D, two-phase, poroviscous, reactive flow model displays various types of behaviour relevant to cell crawling. We present stability analyses that show that an asymmetric perturbation is required to cause a spatially uniform, stationary strip of cytoplasm to move, which is relevant to cell polarization. Our numerical simulations identify qualitatively distinct families of travelling-wave solutions that coexist at certain parameter values. Within each family, the crawling speed of the strip has a bell-shaped dependence on the adhesion strength. The model captures the experimentally observed behaviour that cells crawl quickest at intermediate adhesion strengths, when the substrate is neither too sticky nor too slippy.
  Mathematical Medicine and Biology 07/2012;
• Article: Modelling of axonal cargo rerouting in a dendrite.

  A V Kuznetsov
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  ABSTRACT: This paper develops a model of axonal cargo transport in and out of a dendrite en route to the axon. The entrance of axonal cargos into a dendrite is explained by a mixed orientation of microtubules (MTs) in a dendrite. Using the simplest hypothesis explaining cargo targeting to axons and dendrites (this hypothesis postulates that axonal cargos are driven by kinesin motors and that dendritic cargos are driven by dynein motors), it is assumed that axonal cargos can enter a dendrite using MTs whose plus-ends are directed outward. Later, as kinesin motors detach from these MTs and reattach to oppositely directed MTs, the axonal cargos are transported out of the dendrite and are rerouted to the axon. The developed model makes it possible to investigate the dynamics of axonal cargo trafficking in a dendrite and study how it is affected by various input parameters, such as the kinesin velocity distribution.
  Mathematical Medicine and Biology 06/2012;
• Article: Measurement of chondrocyte chemotaxis using a Boyden chamber: a model of receptor-mediated cell migration combined with cell sedimentation.

  Chih-Yuan Chen, Kuan-Chih Hsiau, C A Chung
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  ABSTRACT: The Boyden chamber assay measures the coefficients of cell motility by fitting the experiments with theoretical calculations. Under the circumstance of rapid receptor kinetics, the distribution of chemical-receptor complexes on the cell surface can be treated as being quasi-steady and chemotaxis is directly related to the biochemical concentration, leading to the celebrated Keller-Segel model, which has been shown to be an approximation to the full receptor-mediated form. No matter approximate or full, these approaches have ignored cell sedimentation in the upper chamber, assuming that all the cells have already resided on the filter top at the beginning of the test. However, the time required for all the cells to settle through the suspension can be close to the entire incubation time of just several hours. In order to amend such a deficiency, the present work combines the receptor-based model with cell sedimentation for modeling the chemotaxis assay using the Boyden chamber. Simulations were performed to fit the experimental data in the literature, which tested the chondrocyte chemotactic motility in response to collagen. Results show that once cell sedimentation is involved, the assumption of quasi-steady receptor distribution may be invalid for the Boyden assay. This is because the formation of the chemical-receptor complexes is profoundly retarded by the process of cell sedimentation. To estimate the parameters of cell motility and receptor kinetics, cell sedimentation should be incorporated in modeling the chemotaxis assay using the Boyden chamber.
  Mathematical Medicine and Biology 06/2012;
• Article: Effect of tubular inhomogeneities on feedback-mediated dynamics of a model of a thick ascending limb.

  Hwayeon Ryu, Anita T Layton
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  ABSTRACT: One of the key mechanisms that mediate renal autoregulation is the tubuloglomerular feedback (TGF) system, which is a negative feedback loop in the kidney that balances glomerular filtration with tubular reabsorptive capacity. Tubular fluid flow, NaCl concentration and other related variables are known to exhibit TGF-mediated oscillations. In this study, we used a mathematical model of the thick ascending limb (TAL) of a short loop of Henle of the rat kidney to study the effects of (i) spatially inhomogeneous TAL NaCl active transport rate, (ii) spatially inhomogeneous tubular radius and (iii) compliance of the tubular walls on TGF-mediated dynamics. A bifurcation analysis of the TGF model equations was performed by deriving a characteristic equation and finding its roots. Results of the bifurcation analysis were validated via numerical simulations of the full model equations. Model results suggest that a higher TAL NaCl active transport rate or a smaller TAL radius near the loop bend gives rise to stable oscillatory solutions at sufficiently high TGF gain values, even with zero TGF delay. In addition, when the TAL walls are assumed to be compliant, the TGF system exhibits a heightened tendency to oscillate, a result that is consistent with predictions of a previous modelling study.
  Mathematical Medicine and Biology 04/2012;
• Article: 'Go or grow': the key to the emergence of invasion in tumour progression?

  H Hatzikirou, D Basanta, M Simon, K Schaller, A Deutsch
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  ABSTRACT: Uncontrolled proliferation and abnormal cell migration are two of the main characteristics of tumour growth. Of ultimate importance is the question what are the mechanisms that trigger the progression from benign neoplasms (uncontrolled/autonomous proliferation) to malignant invasive tumours (high migration). In the following, we challenge the currently prevailing view that the emergence of invasiveness is mainly the consequence of acquired cancer cell mutations. To study this, we mainly focus on the 'glioblastoma multiforme' (GBM) tumour which is a particularly aggressive and invasive tumour. In particular, with the help of a simple growth model, we demonstrate that the short time required for the recurrence of a GBM tumour after a gross total resection cannot be deduced solely from a mutation-based theory. We propose that the transition to invasive tumour phenotypes can be explained on the basis of the microscopic 'Go or Grow' mechanism (migration/proliferation dichotomy) and the oxygen shortage, i.e. hypoxia, in the environment of a growing tumour. We test this hypothesis with the help of a lattice-gas cellular automaton. Finally, we suggest possible therapies that could help prevent the progression towards malignancy and invasiveness of benign tumours.
  Mathematical Medicine and Biology 03/2012; 29(1):49-65.
• Article: An asymptotic model of particle deposition at an airway bifurcation.

  Jennifer R Zierenberg, David Halpern, Marcel Filoche, Bernard Sapoval, James B Grotberg
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  ABSTRACT: Particle transport and deposition associated with flow over a wedge is investigated as a model for particle transport and flow at the carina of an airway bifurcation during inspiration. Using matched asymptotics, a uniformly valid solution is obtained to represent the high Reynolds number flow over a wedge that considers the viscous boundary layer near the wedge and the outer inviscid region and is then used to solve the particle transport equations. Sometimes particle impaction on the wedge is prevented due to the boundary layer. We call this boundary layer shielding (BLS). This effect can be broken down into different types: rejection, trapping and deflection that are described by what happens to the particle's initial negative velocity normal to the wall either changing sign, reaching zero, or remaining negative in the boundary layer region. The deposition efficiency depends on the critical Stokes number but exhibits a weak dependence on Reynolds number. Deposition efficiency for S(c) in the range 0 <S(c)< 0.4 yields the following relationship De ≈ (1.867S(c)(1.78) -0.016) sin(βπ/2) at large Reynolds numbers, where βπ is the wedge angle. For a specific deposition efficiency, S(c) decreases as βπ increases. The distribution of impacted particles was also computed and revealed that particles primarily impact within one airway diameter of the carina, consistent with computational fluid dynamics approaches. This work provides a new insight that the BLS inherent to the wedge component of the structure is the dominant reason for the particle distribution. This finding is important in linking aerosol deposition to the location of airway disease as well as target sites for therapeutic deposition.
  Mathematical Medicine and Biology 02/2012;