Showing papers in "Bellman Prize in Mathematical Biosciences in 2016"

Modeling the spread and control of dengue with limited public health resources.

Abstract: A deterministic model for the transmission dynamics of dengue fever is formulated to study, with a nonlinear recovery rate, the impact of available resources of the health system on the spread and control of the disease. Model results indicate the existence of multiple endemic equilibria, as well as coexistence of an endemic equilibrium with a periodic solution. Additionally, our model exhibits the phenomenon of backward bifurcation. The results of this study could be helpful for public health authorities in their planning of a proper resource allocation for the control of dengue transmission.

Pattern formation--A missing link in the study of ecosystem response to environmental changes.

Abstract: Environmental changes can affect the functioning of an ecosystem directly, through the response of individual life forms, or indirectly, through interspecific interactions and community dynamics. The feasibility of a community-level response has motivated numerous studies aimed at understanding the mutual relationships between three elements of ecosystem dynamics: the abiotic environment, biodiversity and ecosystem function. Since ecosystems are inherently nonlinear and spatially extended, environmental changes can also induce pattern-forming instabilities that result in spatial self-organization of life forms and resources. This, in turn, can affect the relationships between these three elements, and make the response of ecosystems to environmental changes far more complex. Responses of this kind can be expected in dryland ecosystems, which show a variety of self-organizing vegetation patterns along the rainfall gradient. This paper describes the progress that has been made in understanding vegetation patterning in dryland ecosystems, and the roles it plays in ecosystem response to environmental variability. The progress has been achieved by modeling pattern-forming feedbacks at small spatial scales and up-scaling their effects to large scales through model studies. This approach sets the basis for integrating pattern formation theory into the study of ecosystem dynamics and addressing ecologically significant questions such as the dynamics of desertification, restoration of degraded landscapes, biodiversity changes along environmental gradients, and shrubland-grassland transitions.

On the relationship between sloppiness and identifiability.

Abstract: Dynamic models of biochemical networks are often formulated as sets of non-linear ordinary differential equations, whose states are the concentrations or abundances of the network components. They typically have a large number of kinetic parameters, which must be determined by calibrating the model with experimental data. In recent years it has been suggested that dynamic systems biology models are universally sloppy, meaning that the values of some parameters can be perturbed by several orders of magnitude without causing significant changes in the model output. This observation has prompted calls for focusing on model predictions rather than on parameters. In this work we examine the concept of sloppiness, investigating its links with the long-established notions of structural and practical identifiability. By analysing a set of case studies we show that sloppiness is not equivalent to lack of identifiability, and that sloppy models can be identifiable. Thus, using sloppiness to draw conclusions about the possibility of estimating parameter values can be misleading. Instead, structural and practical identifiability analyses are better tools for assessing the confidence in parameter estimates. Furthermore, we show that, when designing new experiments to decrease parametric uncertainty, designs that optimize practical identifiability criteria are more informative than those that minimize sloppiness.

Competition in the chemostat: A stochastic multi-species model and its asymptotic behavior.

Abstract: In this paper, a stochastic chemostat model in which n -species compete for a single growth-limiting substrate is considered. We first prove that the stochastic model has an unique global positive solution by using the comparison theorem for stochastic differential equations. Then we show that when the noise intensities are small, the competition outcome in the chemostat is completely determined by the species’ stochastic break-even concentrations: the species with the lowest stochastic break-even concentration survives and all other species will go to extinction in the chemostat. In other words, the competitive exclusion principle holds for stochastic competition chemostat model when the noise intensities are small. Moreover, we find that noise may change the destiny of the species. Numerical simulations illustrate the obtained results.

Vector-borne diseases models with residence times - A Lagrangian perspective.

Abstract: A multi-patch and multi-group modeling framework describing the dynamics of a class of diseases driven by the interactions between vectors and hosts structured by groups is formulated. Hosts' dispersal is modeled in terms of patch-residence times with the nonlinear dynamics taking into account the effective patch-host size. The residence times basic reproduction number R0 is computed and shown to depend on the relative environmental risk of infection. The model is robust, that is, the disease free equilibrium is globally asymptotically stable (GAS) if R0≤1 and a unique interior endemic equilibrium is shown to exist that is GAS whenever R0>1 whenever the configuration of host-vector interactions is irreducible. The effects of patchiness and groupness, a measure of host-vector heterogeneous structure, on the basic reproduction number R0, are explored. Numerical simulations are carried out to highlight the effects of residence times on disease prevalence.

Disease dynamics of honeybees with Varroa destructor as parasite and virus vector.

Abstract: The worldwide decline in honeybee colonies during the past 50 years has often been linked to the spread of the parasitic mite Varroa destructor and its interaction with certain honeybee viruses carried by Varroa mites. In this paper, we propose a honeybee-mite-virus model that incorporates (1) parasitic interactions between honeybees and the Varroa mites; (2) five virus transmission terms between honeybees and mites at different stages of Varroa mites: from honeybees to honeybees, from adult honeybees to the phoretic mites, from brood to the reproductive mites, from the reproductive mites to brood, and from adult honeybees to the phoretic mites; and (3) Allee effects in the honeybee population generated by its internal organization such as division of labor. We provide completed local and global analysis for the full system and its subsystems. Our analytical and numerical results allow us have a better understanding of the synergistic effects of parasitism and virus infections on honeybee population dynamics and its persistence. Interesting findings from our work include: (a) due to Allee effects experienced by the honeybee population, initial conditions are essential for the survival of the colony. (b) Low adult honeybees to brood ratios have destabilizing effects on the system which generate fluctuating dynamics that lead to a catastrophic event where both honeybees and mites suddenly become extinct. This catastrophic event could be potentially linked to Colony Collapse Disorder (CCD) of honeybee colonies. (c) Virus infections may have stabilizing effects on the system, and parasitic mites could make disease more persistent. Our model illustrates how the synergy between the parasitic mites and virus infections consequently generates rich dynamics including multiple attractors where all species can coexist or go extinct depending on initial conditions. Our findings may provide important insights on honeybee viruses and parasites and how to best control them.

Cu-blood flow model through a catheterized mild stenotic artery with a thrombosis

Abstract: Copper nanoparticles blood flow analysis through a catheterized mild stenotic artery with a thrombosis is presented. The system of coupled governing equations are prescribed and then simplified under mild stenosis assumptions. The governing equations are solved exactly, and then expressions for temperature, axial velocity, stream function, wall shear stress and resistance impedance are obtained generally for metallic nanoparticles blood flow. Due to the importance of copper nanoparticles in biomedicine, the results for Cu-blood flow model are introduced. The effect of various pertinent flow and geometric parameters on copper-blood flow features in the stenotic region are illustrated and discussed through graphs for catheter and tube models. Blood trapping is introduced graphically for numerous flow parameters.

Ecoepidemic predator-prey model with feeding satiation, prey herd behavior and abandoned infected prey

Abstract: In this paper we analyse a predator–prey model where the prey population shows group defense and the prey individuals are affected by a transmissible disease. The resulting model is of the Rosenzweig–MacArthur predator–prey type with an SI (susceptible-infected) disease in the prey. Modeling prey group defense leads to a square root dependence in the Holling type II functional for the predator–prey interaction term. The system dynamics is investigated using simulations, classical existence and asymptotic stability analysis and numerical bifurcation analysis. A number of bifurcations, such as transcritical and Hopf bifurcations which occur commonly in predator–prey systems will be found. Because of the square root interaction term there is non-uniqueness of the solution and a singularity where the prey population goes extinct in a finite time. This results in a collapse initiated by extinction of the healthy or susceptible prey and thereafter the other population(s). When also a positive attractor exists this leads to bistability similar to what is found in predator–prey models with a strong Allee effect. For the two-dimensional disease-free (i.e. the purely demographic) system the region in the parameter space where bistability occurs is marked by a global bifurcation. At this bifurcation a heteroclinic connection exists between saddle prey-only equilibrium points where a stable limit cycle together with its basin of attraction, are destructed. In a companion paper (Gimmelli et al., 2015) the same model was formulated and analysed in which the disease was not in the prey but in the predator. There we also observed this phenomenon. Here we extend its analysis using a phase portrait analysis. For the three-dimensional ecoepidemic predator–prey system where the prey is affected by the disease, also tangent bifurcations including a cusp bifurcation and a torus bifurcation of limit cycles occur. This leads to new complex dynamics. Continuation by varying one parameter of the emerging quasi-periodic dynamics from a torus bifurcation can lead to its destruction by a collision with a saddle-cycle. Under other conditions the quasi-periodic dynamics changes gradually in a trajectory that lands on a boundary point where the prey go extinct in finite time after which a total collapse of the three-dimensional system occurs.

Kinetics of the formation of a protein corona around nanoparticles

Abstract: Interaction of metal or oxide nanoparticles (NPs) with biological soft matter is one of the central phenomena in basic and applied biology-oriented nanoscience. Often, this interaction includes adsorption of suspended proteins on the NP surface, resulting in the formation of the protein corona around NPs. Structurally, the corona contains a "hard" monolayer shell directly contacting a NP and a more distant weakly associated "soft" shell. Chemically, the corona is typically composed of a mixture of distinct proteins. The corresponding experimental and theoretical studies have already clarified many aspects of the corona formation. The process is, however, complex, and its understanding is still incomplete. Herein, we present a kinetic mean-field model of the formation of the "hard" corona with emphasis on the role of (i) protein-diffusion limitations and (ii) interplay between competitive adsorption of distinct proteins and irreversible reconfiguration of their native structure. The former factor is demonstrated to be significant only in the very beginning of the corona formation. The latter factor is predicted to be more important. It may determine the composition of the corona on the time scales comparable or longer than a few hours.

Biological control via "ecological" damping: An approach that attenuates non-target effects.

Abstract: In this work we develop and analyze a mathematical model of biological control to prevent or attenuate the explosive increase of an invasive species population, that functions as a top predator, in a three-species food chain. We allow for finite time blow-up in the model as a mathematical construct to mimic the explosive increase in population, enabling the species to reach "disastrous", and uncontrollable population levels, in a finite time. We next improve the mathematical model and incorporate controls that are shown to drive down the invasive population growth and, in certain cases, eliminate blow-up. Hence, the population does not reach an uncontrollable level. The controls avoid chemical treatments and/or natural enemy introduction, thus eliminating various non-target effects associated with such classical methods. We refer to these new controls as "ecological damping", as their inclusion dampens the invasive species population growth. Further, we improve prior results on the regularity and Turing instability of the three-species model that were derived in Parshad et al. (2014). Lastly, we confirm the existence of spatiotemporal chaos.

A Cellular Potts Model of single cell migration in presence of durotaxis.

Abstract: Cell migration is a fundamental biological phenomenon during which cells sense their surroundings and respond to different types of signals. In presence of durotaxis, cells preferentially crawl from soft to stiff substrates by reorganizing their cytoskeleton from an isotropic to an anisotropic distribution of actin filaments. In the present paper, we propose a Cellular Potts Model to simulate single cell migration over flat substrates with variable stiffness. We have tested five configurations: (i) a substrate including a soft and a stiff region, (ii) a soft substrate including two parallel stiff stripes, (iii) a substrate made of successive stripes with increasing stiffness to create a gradient and (iv) a stiff substrate with four embedded soft squares. For each simulation, we have evaluated the morphology of the cell, the distance covered, the spreading area and the migration speed. We have then compared the numerical results to specific experimental observations showing a consistent agreement.

Z-type control of populations for Lotka-Volterra model with exponential convergence.

Abstract: The population control of the Lotka-Volterra model is one of the most important and widely investigated issues in mathematical ecology. In this study, assuming that birth rate is controllable and using the Z-type dynamic method, we develop Z-type control laws to drive the prey population and/or predator population to a desired state to keep species away from extinction and to improve ecosystem stability. A direct controller group is initially designed to control the prey and predator populations simultaneously. Two indirect controllers are then proposed for prey population control and predator population control by exerting exogenous measure on another species. All three control laws possess exponential convergence performances. Finally, the corresponding numerical simulations are performed. Results substantiate the theoretical analysis and effectiveness of such Z-type control laws for the population control of the Lotka-Volterra model.

Parasite sources and sinks in a patched Ross-Macdonald malaria model with human and mosquito movement: Implications for control.

Abstract: We consider the dynamics of a mosquito-transmitted pathogen in a multi-patch Ross–Macdonald malaria model with mobile human hosts, mobile vectors, and a heterogeneous environment. We show the existence of a globally stable steady state, and a threshold that determines whether a pathogen is either absent from all patches, or endemic and present at some level in all patches. Each patch is characterized by a local basic reproduction number, whose value predicts whether the disease is cleared or not when the patch is isolated: patches are known as “demographic sinks” if they have a local basic reproduction number less than one, and hence would clear the disease if isolated; patches with a basic reproduction number above one would sustain endemic infection in isolation, and become “demographic sources” of parasites when connected to other patches. Sources are also considered focal areas of transmission for the larger landscape, as they export excess parasites to other areas and can sustain parasite populations. We show how to determine the various basic reproduction numbers from steady state estimates in the patched network and knowledge of additional model parameters, hereby identifying parasite sources in the process. This is useful in the context of control of the infection on natural landscapes, because a commonly suggested strategy is to target focal areas, in order to make their corresponding basic reproduction numbers less than one, effectively turning them into sinks. We show that this is indeed a successful control strategy—albeit a conservative and possibly expensive one—in case either the human host, or the vector does not move. However, we also show that when both humans and vectors move, this strategy may fail, depending on the specific movement patterns exhibited by hosts and vectors.

Theoretical study and control optimization of an integrated pest management predator-prey model with power growth rate.

Abstract: This work presents a pest control predator–prey model, where rate of change in prey density follows a scaling law with exponent less than one and the control is by an integrated management strategy. The aim is to investigate the change in system dynamics and determine a pest control level with minimum control price. First, the dynamics of the proposed model without control is investigated by taking the exponent as an index parameter. And then, to determine the frequency of spraying chemical pesticide and yield releases of the predator, the existence of the order-1 periodic orbit of the control system is discussed in cases. Furthermore, to ensure a certain robustness of the adopted control, i.e., for an inaccurately detected species density or a deviation, the control system could be stabilized at the order-1 periodic orbit, the stability of the order-1 periodic orbit is verified by an stability criterion for a general semi-continuous dynamical system. In addition, to minimize the total cost input in pest control, an optimization problem is formulated and the optimum pest control level is obtained. At last, the numerical simulations with a specific model are carried out to complement the theoretical results.

Stability of genetic regulatory networks based on switched systems and mixed time-delays.

Abstract: In this paper, the switched genetic regulatory networks (GRNs) are modeled from a real biological system, based on switched systems, noise and mixed time-delays. Global asymptotical stability for the proposed switched GRNs are studied by the Lyapunov method and the matrix inequality techniques. Some new sufficient conditions are obtained to ensure the global asymptotical stability of the proposed switched GRNs. Furthermore, the proposed LMI results are computationally efficient as it can be solved numerically with standard commercial software. Finally, an example is provided to illustrate the usefulness of the results.

Reproduction numbers for epidemic models with households and other social structures II: Comparisons and implications for vaccination

Abstract: In this paper we consider epidemic models of directly transmissible SIR (susceptible → infective → recovered) and SEIR (with an additional latent class) infections in fully-susceptible populations with a social structure, consisting either of households or of households and workplaces. We review most reproduction numbers defined in the literature for these models, including the basic reproduction number R0 introduced in the companion paper of this, for which we provide a simpler, more elegant derivation. Extending previous work, we provide a complete overview of the inequalities among these reproduction numbers and resolve some open questions. Special focus is put on the exponential-growth-associated reproduction number Rr, which is loosely defined as the estimate of R0 based on the observed exponential growth of an emerging epidemic obtained when the social structure is ignored. We show that for the vast majority of the models considered in the literature Rr ≥ R0 when R0 ≥ 1 and Rr ≤ R0 when R0 ≤ 1. We show that, in contrast to models without social structure, vaccination of a fraction 1-1/R0 of the population, chosen uniformly at random, with a perfect vaccine is usually insufficient to prevent large epidemics. In addition, we provide significantly sharper bounds than the existing ones for bracketing the critical vaccination coverage between two analytically tractable quantities, which we illustrate by means of extensive numerical examples.

Backward bifurcation and control in transmission dynamics of arboviral diseases

Abstract: In this paper, we derive and analyze a compartmental model for the control of arboviral diseases which takes into account an imperfect vaccine combined with individual protection and some vector control strategies already studied in the literature. After the formulation of the model, a qualitative study based on stability analysis and bifurcation theory reveals that the phenomenon of backward bifurcation may occur. The stable disease-free equilibrium of the model coexists with a stable endemic equilibrium when the reproduction number, R 0 , is less than unity. Using Lyapunov function theory, we prove that the trivial equilibrium is globally asymptotically stable. When the disease–induced death is not considered, or/and, when the standard incidence is replaced by the mass action incidence, the backward bifurcation does not occur. Under a certain condition, we establish the global asymptotic stability of the disease–free equilibrium of the principal model. Through sensitivity analysis, we determine the relative importance of model parameters for disease transmission. Numerical simulations show that the combination of several control mechanisms would significantly reduce the spread of the disease, if we maintain the level of each control high, and this, over a long period.

Determination of critical nucleation number for a single nucleation amyloid-β aggregation model.

Abstract: Aggregates of amyloid-β (Aβ) peptide are known to be the key pathological agents in Alzheimer disease (AD). Aβ aggregates to form large, insoluble fibrils that deposit as senile plaques in AD brains. The process of aggregation is nucleation–dependent in which the formation of a nucleus is the rate–limiting step, and controls the physiochemical fate of the aggregates formed. Therefore, understanding the properties of nucleus and pre-nucleation events will be significant in reducing the existing knowledge–gap in AD pathogenesis. In this report, we have determined the plausible range of critical nucleation number ( n * ), the number of monomers associated within the nucleus for a homogenous aggregation model with single unique nucleation event, by two independent methods: A reduced-order stability analysis and ordinary differential equation based numerical analysis, supported by experimental biophysics. The results establish that the most likely range of n * is between 7 and 14 and within, this range, n * = 12 closely supports the experimental data. These numbers are in agreement with those previously reported, and importantly, the report establishes a new modeling framework using two independent approaches towards a convergent solution in modeling complex aggregation reactions. Our model also suggests that the formation of large protofibrils is dependent on the nature of n * , further supporting the idea that pre-nucleation events are significant in controlling the fate of larger aggregates formed. This report has re-opened an old problem with a new perspective and holds promise towards revealing the molecular events in amyloid pathologies in the future.

Epidemic outbreak for an SIS model in multiplex networks with immunization.

Abstract: With the aim of understanding epidemic spreading in a general multiplex network and designing optimal immunization strategies, a mathematical model based on multiple degree is built to analyze the threshold condition for epidemic outbreak. Two kinds of strategies, the multiplex node-based immunization and the layer node-based immunization, are examined. Theoretical results show that the general framework proposed here can illustrate the effect of diverse correlations and immunizations on the outbreak condition in multiplex networks. Under a set of conditions on uncorrelated coefficients, the specific epidemic thresholds are shown to be only dependent on the respective degree distribution in each layer.

On the effect of mucus rheology on the muco-ciliary transport

Abstract: A two dimensional numerical model is used to study the muco-ciliary transport process in human respiratory tract. Here, hybrid finite difference-lattice Boltzmann method is used to model the flow physics of the transport of mucus and periciliary liquid (PCL) layer in the airway surface liquid. The immersed boundary method is also used to implement the propulsive effect of the cilia and also the effects of the interface between the mucus and PCL layers. The main contribution of this study is on elucidating the role of the viscoelastic behavior of mucus on the muco-ciliary transport and for this purpose an Oldroyd-B model is used as the constitutive equation of mucus for the first time. Results show that the viscosity and viscosity ratio of mucus have an enormous effect on the muco-ciliary transport process. It is also seen that the mucus velocity is affected by mucus relaxation time when its value is less than 0.002 s. Results also indicate that the variation of these properties on the mucus velocity at lower values of viscosity ratio is more significant.

A mathematical model of syphilis transmission in an MSM population.

Abstract: Syphilis is caused by the bacterium Treponema pallidum subspecies pallidum, and is a sexually transmitted disease with multiple stages. A model of transmission of syphilis in an MSM population (there has recently been a resurgence of syphilis in such populations) that includes infection stages and treatment is formulated as a system of ordinary differential equations. The control reproduction number is calculated, and it is proved that if this threshold parameter is below one, syphilis dies out; otherwise, if it is greater than one, it is shown that there exists a unique endemic equilibrium and that for certain special cases, this equilibrium is globally asymptotically stable. Using data from the literature on MSM populations, numerical methods are used to determine the variation and robustness of the control reproduction number with respect to the model parameters, and to determine adequate treatment rates for syphilis eradication. By assuming a closed population and no return to susceptibility, an epidemic model is obtained. Final outbreak sizes are numerically determined for various parameter values, and its variation and robustness to parameter value changes is also investigated. Results quantify the importance of early treatment for syphilis control.

Stochastic descriptors in an SIR epidemic model for heterogeneous individuals in small networks.

Abstract: We continue here the work initiated in [13], and analyse an SIR epidemic model for the spread of an epidemic among the members of a small population of N individuals, defined in terms of a continuous-time Markov chain X. We propose a structure by levels and sub-levels of the state space of the process X, and present two different orders, Orders A and B, for states within each sub-level, which are related to a matrix and a scalar formalism, respectively, when developing our analysis. Stochastic descriptors regarding the length and size of an outbreak, the maximum number of individuals simultaneously infected during an outbreak, the fate of a particular individual within the population, and the number of secondary cases caused by a certain individual until he recovers, are deeply analysed. Our approach is illustrated by carrying out a set of numerical results regarding the spread of the nosocomial pathogen Methicillin-resistant Staphylococcus Aureus among the patients within an intensive care unit. In this application, our interest is in analysing the effectiveness of control strategies (the isolation of the patient initiating the outbreak and the proper room configuration of the intensive care unit) that intrinsically introduce heterogeneities among the members of the population.

Analysis of a growth model inspired by Gompertz and Korf laws, and an analogous birth-death process.

Abstract: We propose a new deterministic growth model which captures certain features of both the Gompertz and Korf laws. We investigate its main properties, with special attention to the correction factor, the relative growth rate, the inflection point, the maximum specific growth rate, the lag time and the threshold crossing problem. Some data analytic examples and their performance are also considered. Furthermore, we study a stochastic counterpart of the proposed model, that is a linear time-inhomogeneous birth-death process whose mean behaves as the deterministic one. We obtain the transition probabilities, the moments and the population ultimate extinction probability for this process. We finally treat the special case of a simple birth process, which better mimics the proposed growth model.

Modeling the evolution of winner and loser effects: A survey and prospectus.

Abstract: The evolution of winner or loser effects—higher probabilities of winning after winning or of losing after losing—has received remarkably little attention from theoreticians, even though such effects are widespread across the animal kingdom. We review game-theoretic models that regard such winner and loser effects as outcomes of a strategic response. We show that these models have been well supported by the empirical literature in the past, but are not designed to address some recent observations. In the light of this recent progress on the empirical front, we identify factors that newer theory must be developed to explore.

Complex dynamics in an alcoholism model with the impact of Twitter

Abstract: A novel alcoholism model which involves impact of Twitter is formulated. It is shown that the model has multiple equilibria. Stability of all the equilibria are obtained in terms of the basic reproductive number R0. Using the center manifold theory, the occurrence of backward and forward bifurcation for a certain defined range of R0 are established. Furthermore, the existence of Hopf bifurcation is also established by regarding the transmission coefficient β as the bifurcation parameter. Numerical simulations and sensitivity analysis on a few parameters are also carried out. Our results show that Twitter can serve as a good indicator of alcoholism model and affect the spread of the drinking.

Pressure and wall shear stress in blood hammer - Analytical theory.

Abstract: We describe an analytical theory of blood hammer in a long and stiffened artery due to sudden blockage. Based on the model of a viscous fluid in laminar flow, we derive explicit expressions of oscillatory pressure and wall shear stress. To examine the effects on local plaque formation we also allow the blood vessel radius to be slightly nonuniform. Without resorting to discrete computation, the asymptotic method of multiple scales is utilized to deal with the sharp contrast of time scales. The effects of plaque and blocking time on blood pressure and wall shear stress are studied. The theory is validated by comparison with existing water hammer experiments.

A model of a syntrophic relationship between two microbial species in a chemostat including maintenance.

Abstract: Many microbial ecosystems can be seen as microbial 'food chains' where the different reaction steps can be seen as such: the waste products of the organisms at a given reaction step are consumed by organisms at the next reaction step. In the present paper we study a model of a two-step biological reaction with feedback inhibition, which was recently presented as a reduced and simplified version of the anaerobic digestion model ADM1 of the International Water Association (IWA). It is known that in the absence of maintenance (or decay) the microbial 'food chain' is stable. In a previous study, using a purely numerical approach and ADM1 consensus parameter values, it was shown that the model remains stable when decay terms are added. However, the authors could not prove in full generality that it remains true for other parameter values. In this paper we prove that introducing decay in the model preserves stability whatever its parameters values are and for a wide range of kinetics.

Numerical simulation of dual-phase-lag bioheat transfer model during thermal therapy.

Abstract: This paper theoretically investigates the thermal behavior in a living biological tissue under various coordinate systems and different non-Fourier boundary conditions with the dual-phase-lag bioheat transfer model during thermal therapy. The properties of Legendre wavelets together with the finite difference scheme are used to find an approximate analytical solution of the present problem. It has been observed that surrounding healthy tissues are less affected in second and third kind of boundary condition when applied along with spherical symmetric coordinate system. Also greater temperature rise and fast achievement of peak hyperthermia temperature is achieved when second and third kind of boundary conditions are used in combination with Cartesian coordinate system. It is observed that due to the presence of blood perfusion and temperature dependent metabolic heat generation term, the dual-phase-lag bioheat transfer model reduces to Pennes bioheat transfer model only when τq=τT=0s, not for arbitrary τq=τT. Further, in case of dual-phase-lag bioheat transfer model wave-like or diffusion-like behavior will dominate depends whether the ratio τq/τT > 1 or τq/τT < 1. Effect of temperature dependent metabolic heat generation rate, thermal conductivity and blood perfusion rate on dimensionless temperature are discussed in details. The whole analysis is presented in dimensionless form.

Atomic force microscopy indentation and inverse analysis for non-linear viscoelastic identification of breast cancer cells

Abstract: Breast cancer cells (MCF-7 and MCF-10A) are studied through indentation with spherical borosilicate glass particles in atomic force microscopy (AFM) contact mode in fluid. Their mechanical properties are obtained by analyzing the recorded reaction force–time response. The analysis is based on comparing experimental data with predictions from finite element (FE) simulation. Here, FE modeling is employed to simulate the AFM indentation experiment which is neither a displacement nor a force controlled test. This approach is expected to overcome many underlying problems of the widely used models such as Hertz contact model due to its capability to capture the contact behaviors between the spherical indentor and the cell, account for cell geometry, and incorporate with large strain theory. In this work, a non-linear viscoelastic (NLV) model in which the viscoelastic part is described by Prony series terms is used for the constitutive model of the cells. The time-dependent material parameters are extracted through an inverse analysis with the use of a surrogate model based on a Kriging estimator. The purpose is to automatically extract the NLV properties of the cells with a more efficient process compared to the iterative inverse technique that has been mostly applied in the literature. The method also allows the use of FE modeling in the analysis of a large amount of experimental data. The NLV parameters are compared between MCF-7 and MCF-10A and MCF-10A treated and untreated with the drug Cytochalasin D to examine the possibility of using relaxation properties as biomarkers for distinguishing these types of breast cancer cells. The comparisons indicate that malignant cells (MCF-7) are softer and exhibit more relaxation than benign cells (MCF-10A). Disrupting the cytoskeleton using the drug Cytochalasin D also results in a larger amount of relaxation in the cell’s response. In addition, relaxation properties indicate larger differences as compared to the elastic moduli like instantaneous shear modulus. These results may be useful for disease diagnosing purposes.

A two-variable model robust to pacemaker behaviour for the dynamics of the cardiac action potential.

Abstract: Ionic models with two state variables are routinely used in patient specific electro-physiology simulations due to the small number of parameters to be constrained and their computational tractability. Among these models, the Mitchell and Schaeffer (MS) action potential model is often used in ventricle electro-physiology due to its ability to reproduce the shape of the action potential and its restitution properties. However, for some choices of parameters characterising this ionic model, unwanted pacemaker behaviour is present. The absence of any a priori criterion to exclude unstable parameter combinations affects parameter fitting algorithms, as unphysiological solutions can only be discarded a posteriori. In this paper we propose an adaptation of the MS model that does not exhibit pacemaker behaviour for any combination of the parameters. The robustness to pacemaker behaviour makes this model suitable for inverse problem applications.