ISRN Biomathematics http://www.hindawi.com The latest articles from Hindawi Publishing Corporation © 2014 , Hindawi Publishing Corporation . All rights reserved. A Mathematical Model for the Transmission and Spread of Drug Sensitive and Resistant Malaria Strains within a Human Population Wed, 16 Apr 2014 11:02:23 +0000 http://www.hindawi.com/journals/isrn.biomathematics/2014/636973/ Malaria remains by far the world's most important tropical disease, killing more people than any other communicable disease. A number of preventive and control measures have been put in place and most importantly drug treatment. The emergence of drug resistance against the most common and affordable antimalarials is widespread and poses a key obstacle to malaria control. A mathematical model that incorporates evolution of drug resistance and treatment as a preventive strategy is formulated and analyzed. The qualitative analysis of the model is given in terms of the effective reproduction number, . The existence and stability of the disease-free and endemic equilibria of the model are studied. We establish the threshold parameters below which the burden due to malaria can be brought under control. Numerical simulations are done to determine the role played by key parameters in the model. The public health implications of the results are twofold; firstly every effort should be taken to minimize the evolution of drug resistance due to treatment failure and secondly high levels of treatment and development of immunity are essential in reducing the malaria burden. Julius Tumwiine, Senelani D. Hove-Musekwa, and Farai Nyabadza Copyright © 2014 Julius Tumwiine et al. All rights reserved. Computational Simulations of Flow and Oxygen/Drug Delivery in a Three-Dimensional Capillary Network Tue, 15 Apr 2014 09:41:29 +0000 http://www.hindawi.com/journals/isrn.biomathematics/2014/359327/ A computational fluid dynamics (CFD) model is developed to simulate the flow and delivery of oxygen and other substances in a capillary network. A three-dimensional capillary network has been constructed to replicate the one studied by Secomb et al. (2000), and the computational framework features a non-Newtonian viscosity model of blood and the oxygen transport model including in-stream oxygen-hemoglobin dissociation and wall flux due to tissue absorption, as well as an ability to study delivery of drugs and other materials in the capillary streams. The model is first run to compute the volumetric flow rates from the velocity profiles in the segments and compared with Secomb’s work with good agreement. Effects of abnormal pressure and stenosis conditions, as well as those arising from different capillary configurations, on the flow and oxygen delivery are investigated, along with a brief look at the unsteady effects and drug dispersion in the capillary network. The current approach allows for inclusion of oxygen and other material transports, including drugs, nutrients, or contaminants based on the flow simulations. Also, three-dimensional models of complex circulatory systems ranging in scale from macro- to microvascular vessels, in principle, can be constructed and analyzed in detail using the current method. T.-W. Lee, K.-S. Bae, Heung S. Choi, and Ming-Jyh Chern Copyright © 2014 T.-W. Lee et al. All rights reserved. A Note on Hypertension Classification Scheme and Soft Computing Decision Making System Mon, 23 Dec 2013 09:41:14 +0000 http://www.hindawi.com/journals/isrn.biomathematics/2013/342970/ Nowadays young professionals are a soft target of hypertension due to the increased work pressure and poor tolerance. Many people have high blood pressure for years without knowing it. Most of the time, there are no symptoms, but when this condition goes untreated it damages arteries and vital organs throughout the body and that is why it is also termed as the silent killer. Complications arising from hypertension could lead to stroke and heart failure. Soft computing approach provides a sharper conclusion from vague, ambiguous, and imprecise data (generally found in medical field) using linguistic variables. In this study, a soft computing diagnostic support system for the risk assessment of hypertension is proposed. Pankaj Srivastava, Amit Srivastava, Anjali Burande, and Amit Khandelwal Copyright © 2013 Pankaj Srivastava et al. All rights reserved. Total Variation Filtered Demons for Improved Registration of Sliding Organs Tue, 10 Dec 2013 18:06:25 +0000 http://www.hindawi.com/journals/isrn.biomathematics/2013/534891/ We present a new approach to regularize the displacement field of the accelerated Demons registration algorithm. The accelerated Demons algorithm uses Gaussian smoothing to penalize oscillatory motion in the displacement fields during registration. This regularization approach is often applied and ensures a smooth deformation field. However, when registering images with discontinuities in their motion field such as from organs sliding along the chest wall, the assumption of a smooth deformation field is invalid. In this work, we propose using total variation based smoothing that is known to better retain the discontinuities in the deformation field. The proposed approach is a first step towards automatically recovering breathing induced organ motion with good accuracy. Damir Demirović, Amira Šerifović-Trbalić, Naser Prljača, and Philippe C. Cattin Copyright © 2013 Damir Demirović et al. All rights reserved. Thermal Distribution of Ultrasound Waves in Prostate Tumor: Comparison of Computational Modeling with In Vivo Experiments Sun, 20 Oct 2013 13:24:24 +0000 http://www.hindawi.com/journals/isrn.biomathematics/2013/428659/ Ultrasound irradiation to a certain site of the body affects the efficacy of drug delivery through changes in the permeability of cell membrane. Temperature increase in irradiated area may be affected by frequency, intensity, period of ultrasound, and blood perfusion. The aim of present study is to use computer simulation and offer an appropriate model for thermal distribution profile in prostate tumor. Moreover, computer model was validated by in vivo experiments. Method. Computer simulation was performed with COMSOL software. Experiments were carried out on prostate tumor induced in nude mice (DU145 cell line originated from human prostate cancer) at frequency of 3 MHz and intensities of 0.3, 0.5, and 1 w/cm2 for 300 seconds. Results. Computer simulations showed a temperature rise of the tumor for the applied intensities of 0.3, 0.5 and 1 w/cm2 of 0.8, 0.9, and 1.1°C, respectively. The experimental data carried out at the same frequency demonstrated that temperature increase was 0.5, 0.9, and 1.4°C for the above intensities. It was noticed that temperature rise was very sharp for the first few seconds of ultrasound irradiation and then increased moderately. Conclusion. Obtained data holds great promise to develop a model which is able to predict temperature distribution profile in vivo condition. Forough Jafarian Dehkordi, Ali Shakeri-Zadeh, Samideh Khoei, Hossein Ghadiri, and Mohammad-Bagher Shiran Copyright © 2013 Forough Jafarian Dehkordi et al. All rights reserved. Confidence Intervals for the Mean Based on Exponential Type Inequalities and Empirical Likelihood Tue, 08 Oct 2013 11:48:16 +0000 http://www.hindawi.com/journals/isrn.biomathematics/2013/765752/ For independent observations, recently, it has been proposed to construct the confidence intervals for the mean using exponential type inequalities. Although this method requires much weaker assumptions than those required by the classical methods, the resulting intervals are usually too large. Still in special cases, one can find some advantage of using bounded and unbounded Bernstein inequalities. In this paper, we discuss the applicability of this approach for dependent data. Moreover, we propose to use the empirical likelihood method both in the case of independent and dependent observations for inference regarding the mean. The advantage of empirical likelihood is its Bartlett correctability and a rather simple extension to the dependent case. Finally, we provide some simulation results comparing these methods with respect to their empirical coverage accuracy and average interval length. At the end, we apply the above described methods for the serial analysis of a gene expression (SAGE) data example. Sandra Vucane, Janis Valeinis, and George Luta Copyright © 2013 Sandra Vucane et al. All rights reserved. Global Dynamics of an Exploited Prey-Predator Model with Constant Prey Refuge Sun, 15 Sep 2013 08:07:06 +0000 http://www.hindawi.com/journals/isrn.biomathematics/2013/637640/ This paper describes a prey-predator model with Holling type II functional response incorporating constant prey refuge and harvesting to both prey and predator species. We have analyzed the boundedness of the system and existence of all possible feasible equilibria and discussed local as well as global stabilities at interior equilibrium of the system. The occurrence of Hopf bifurcation of the system is examined, and it was observed that the bifurcation is either supercritical or subcritical. Influences of prey refuge and harvesting efforts are also discussed. Some numerical simulations are carried out for the validity of theoretical results. Uttam Das, T. K. Kar, and U. K. Pahari Copyright © 2013 Uttam Das et al. All rights reserved. Fluctuations Analysis of Finite Discrete Birth and Death Chains with Emphasis on Moran Models with Mutations Wed, 11 Sep 2013 10:45:03 +0000 http://www.hindawi.com/journals/isrn.biomathematics/2013/939308/ The Moran model is a discrete-time birth and death Markov chain describing the evolution of the number of type 1 alleles in a haploid population with two alleles whose total size is preserved during the course of evolution. Bias mechanisms such as mutations or selection can affect its neutral dynamics. For the ergodic Moran model with mutations, we get interested in the fixation probabilities of a mutant, the growth rate of fluctuations, the first hitting time of the equilibrium state starting from state , the first return time to the equilibrium state, and the first hitting time of starting from , together with the time needed for the walker to reach its invariant measure, again starting from . For the last point, an appeal to the notion of Siegmund duality is necessary, and a cutoff phenomenon will be made explicit. We are interested in these problems in the large population size limit . The Moran model with mutations includes the heat exchange models of Ehrenfest and Bernoulli-Laplace as particular cases; these were studied from the point of view of the controversy concerning irreversibility (-theorem) and the recurrence of states. Thierry E. Huillet Copyright © 2013 Thierry E. Huillet. All rights reserved. An Overview of Multiple Sequence Alignments and Cloud Computing in Bioinformatics Wed, 14 Aug 2013 11:04:07 +0000 http://www.hindawi.com/journals/isrn.biomathematics/2013/615630/ Multiple sequence alignment (MSA) of DNA, RNA, and protein sequences is one of the most essential techniques in the fields of molecular biology, computational biology, and bioinformatics. Next-generation sequencing technologies are changing the biology landscape, flooding the databases with massive amounts of raw sequence data. MSA of ever-increasing sequence data sets is becoming a significant bottleneck. In order to realise the promise of MSA for large-scale sequence data sets, it is necessary for existing MSA algorithms to be run in a parallelised fashion with the sequence data distributed over a computing cluster or server farm. Combining MSA algorithms with cloud computing technologies is therefore likely to improve the speed, quality, and capability for MSA to handle large numbers of sequences. In this review, multiple sequence alignments are discussed, with a specific focus on the ClustalW and Clustal Omega algorithms. Cloud computing technologies and concepts are outlined, and the next generation of cloud base MSA algorithms is introduced. Jurate Daugelaite, Aisling O' Driscoll, and Roy D. Sleator Copyright © 2013 Jurate Daugelaite et al. All rights reserved. Optimal Control of an SIR Model with Delay in State and Control Variables Tue, 13 Aug 2013 13:57:30 +0000 http://www.hindawi.com/journals/isrn.biomathematics/2013/403549/ We will investigate the optimal control strategy of an SIR epidemic model with time delay in state and control variables. We use a vaccination program to minimize the number of susceptible and infected individuals and to maximize the number of recovered individuals. Existence for the optimal control is established; Pontryagin’s maximum principle is used to characterize this optimal control, and the optimality system is solved by a discretization method based on the forward and backward difference approximations. The numerical simulation is carried out using data regarding the course of influenza A (H1N1) in Morocco. The obtained results confirm the performance of the optimization strategy. Mohamed Elhia, Mostafa Rachik, and Elhabib Benlahmar Copyright © 2013 Mohamed Elhia et al. All rights reserved. Optimal Antiviral Treatment Strategies of HBV Infection Model with Logistic Hepatocyte Growth Wed, 26 Jun 2013 08:03:39 +0000 http://www.hindawi.com/journals/isrn.biomathematics/2013/912835/ This study considers an optimal therapy strategy for HBV infection by incorporating two controls laws into a previous hepatitis B viral infection model with logistic hepatocyte growth. Our goal is to maximize the number of healthy cells and to minimize the cost of the therapy. In this context, the existence of an optimal control is proved. The optimal control is obtained by solving the optimality system which was composed of three nonlinear ODEs with initial conditions and three nonlinear adjoint ODEs with transversality conditions. The results were analysed and interpreted numerically using MATLAB. Hassan Laarabi, Abdelhadi Abta, Mostafa Rachik, and Jamal Bouyaghroumni Copyright © 2013 Hassan Laarabi et al. All rights reserved. Finite Time Blowup in a Realistic Food-Chain Model Thu, 13 Jun 2013 18:06:31 +0000 http://www.hindawi.com/journals/isrn.biomathematics/2013/424062/ We investigate a realistic three-species food-chain model, with generalist top predator. The model based on a modified version of the Leslie-Gower scheme incorporates mutual interference in all the three populations and generalizes several other known models in the ecological literature. We show that the model exhibits finite time blowup in certain parameter range and for large enough initial data. This result implies that finite time blowup is possible in a large class of such three-species food-chain models. We propose a modification to the model and prove that the modified model has globally existing classical solutions, as well as a global attractor. We reconstruct the attractor using nonlinear time series analysis and show that it pssesses rich dynamics, including chaos in certain parameter regime, whilst avoiding blowup in any parameter regime. We also provide estimates on its fractal dimension as well as provide numerical simulations to visualise the spatiotemporal chaos. Rana D. Parshad, Hamid Ait Abderrahmane, Ranjit Kumar Upadhyay, and Nitu Kumari Copyright © 2013 Rana D. Parshad et al. All rights reserved. Models for the Study of Whole-Body Glucose Kinetics: A Mathematical Synthesis Tue, 28 May 2013 08:43:42 +0000 http://www.hindawi.com/journals/isrn.biomathematics/2013/120974/ The maintenance of blood glucose homeostasis is complex and involves several key tissues. Most of these tissues are not easily accessible, making direct measurement of the physiological parameters involved in glucose metabolism difficult. The use of isotope tracer methodology and mathematical modeling allows indirect estimates of in vivo glucose metabolism through relatively noninvasive means. The purpose of this paper was to provide a mathematical synthesis of the models developed for describing glucose kinetics. As many of the models were developed using dogs, example data from the canine literature are presented. However, examples from the human and feline literature are also given in the absence of dog data. The glucose system is considered in both the steady and nonsteady states, and the models are examined by grouping them into schemes consisting of one, two, and three glucose compartments. Noncompartmental schemes are also considered briefly. Leslie L. McKnight, Secundino Lopez, Anna Kate Shoveller, and James France Copyright © 2013 Leslie L. McKnight et al. All rights reserved. Stochastic Model for In-Host HIV Dynamics with Therapeutic Intervention Mon, 29 Apr 2013 15:12:24 +0000 http://www.hindawi.com/journals/isrn.biomathematics/2013/103708/ Untangling the dynamics between HIV and CD4 cellular populations and molecular interactions can be used to investigate the effective points of interventions in the HIV life cycle. With that in mind, we propose and show the usefulness of a stochastic approach towards modeling HIV and CD4 cells’ dynamics in vivo by obtaining probability generating function, the moment structures of the healthy CD4 cell and the virus particles at any time t, and the probability of HIV clearance. The unique feature is that both therapy and the intracellular delay are incorporated into the model. Our analysis shows that, when it is assumed that the drug is not completely effective as is the case of HIV in vivo, the probability of HIV clearance depends on two factors: the combination of drug efficacy and length of the intracellular delay and also the education of the infected patients. Comparing simulated data before and after treatment indicates the importance of combined therapeutic intervention and intracellular delay in having low, undetectable viral load in HIV-infected person. Waema R. Mbogo, Livingstone S. Luboobi, and John W. Odhiambo Copyright © 2013 Waema R. Mbogo et al. All rights reserved. The Problem of Antigen Affinity Discrimination in B-Cell Immunology Sun, 21 Apr 2013 09:49:29 +0000 http://www.hindawi.com/journals/isrn.biomathematics/2013/845918/ B and T lymphocytes activate the humoral and cellular arms of the adaptive immune system. The adaptive strategy works because receptors of adaptive immune cells can mount an immune response based on their affinity for antigens. Thus, affinity discrimination is central to adaptive immunity and has important biomedical ramifications. Due to its intricate connection to the affinity maturation process, affinity discrimination has a special significance in B-cell-mediated immune response. The role of affinity-matured high-affinity antibodies is increasingly recognized in vaccine development. In this paper, we discuss the recent progress made in mathematical and computational studies to explore the cellular and molecular mechanisms of B-cell affinity discrimination. Formation of B-cell receptor (BCR) oligomers and BCR-lipid rafts, upon antigenic stimulation, emerge to be key factors in B-cell affinity discrimination (at the level of single cells). It also provides a new way of thinking about kinetic proofreading and serial triggering, concepts that have been widely utilized to understand affinity discrimination in adaptive immune cells. Potential future applications of mathematical and computational modeling of affinity discrimination are discussed in the context of autoimmune disorders and vaccine design. Subhadip Raychaudhuri Copyright © 2013 Subhadip Raychaudhuri. All rights reserved. Phase-Coupled Oscillations in the Brain: Nonlinear Phenomena in Cellular Signalling Wed, 27 Mar 2013 15:36:49 +0000 http://www.hindawi.com/journals/isrn.biomathematics/2013/194239/ We report the existence of phase-coupled oscillations in a model neural system. The model consists of a group of excitatory principal cells in interaction with local inhibitory interneurons. The voltages across the membranes of excitatory cells are governed primarily by calcium and potassium ion conductivities. The number of potassium channels open at any given instant changes in accordance with a deterministic law. The time scale of this change is set by a constant which depends on midpoint potentials at which potassium and calcium currents are half-activated. The growth of mean membrane potential of excitatory principal cells is controlled by that of the inhibitory interneurons. Nonlinear oscillatory system associated with these limit cycles starting from two different initial conditions maintain a definite phase relationship. The phase-coupled oscillations in electrical activity of the neuronal cells carry together amplitude, phase, and time information for cellular signaling. This mechanism supports an energy efficient way of information processing in the central nervous system. The information content is encoded as persistent periodic oscillations represented by stable limit cycles in the phase space. Vikas Rai, Sreenivasan Rajamoni Nadar, and Riaz A. Khan Copyright © 2013 Vikas Rai et al. All rights reserved. Pattern Formation in Spatially Extended Tritrophic Food Chain Model Systems: Generalist versus Specialist Top Predator Wed, 13 Mar 2013 09:44:45 +0000 http://www.hindawi.com/journals/isrn.biomathematics/2013/198185/ The complex dynamics of two types of tritrophic food chain model systems when the species undergo spatial movements, modeling two real situations of marine ecosystem, are investigated in this study analytically and using numerical simulations. The study has been carried out with the objective to explore and compare the competitive effects of fish and molluscs species being the top predators, when phytoplankton and zooplankton species are undergoing spatial movements in the subsurface water. Reaction diffusion systems have been used to represent temporal evolution and spatial interaction among the species. The two model systems differ in an essential way that the top predators are generalist and specialist, respectively, in two models. “Wave of Chaos” mechanism is found to be the responsible factor for the pattern (non-Turing) formation in one dimension seen in the food chain ending with top generalist predator. In the present work we have reported WOC phenomenon, for the first time in the literature, in a three-species spatially extended food chain model system. The numerical simulation leads to spontaneous and interesting pattern formation in two dimensions. Constraints on different parameters under which Turing and non-Turing patterns may be observed are obtained analytically. Diffusion-driven analysis is carried out, and the effect of diffusion on the chaotic dynamics of the model systems is studied. The existence of chaotic attractor and long-term chaotic behavior demonstrate the effect of diffusion on the dynamics of the model systems. It is observed from numerical study that food chain model system with top predator as generalist has very rich dynamics and shows very interesting patterns. An ecosystem having top predator as specialist leads to the stability of the system. Nitu Kumari Copyright © 2013 Nitu Kumari. All rights reserved. Modeling Neural Activity Thu, 07 Mar 2013 11:33:12 +0000 http://www.hindawi.com/journals/isrn.biomathematics/2013/871472/ This paper provides an overview of different types of models for studying activity of nerve cells and their networks with a special emphasis on neural oscillations. One part describes the neuronal models based on the Hodgkin and Huxley formalism first described in the 1950s. It is discussed how further simplifications of this formalism enable mathematical analysis of the process of neural excitability. The focus of the paper’s second component is on network activity. Understanding network function is one of the important frontiers remaining in neuroscience. At present, experimental techniques can only provide global recordings or samples of the activity of the huge networks that form the nervous system. Models in neuroscience can therefore play a critical role by providing a framework for integration of necessarily incomplete datasets, thereby providing insight into the mechanisms of neural function. Network models can either explicitly contain individual network nodes that model the neurons, or they can be based on representations of compound population activity. The latter approach was pioneered by Wilson and Cowan in the 1970s. Finally I provide an overview and discuss how network models are employed in the study of neuronal network pathology such as epilepsy. Wim van Drongelen Copyright © 2013 Wim van Drongelen. All rights reserved. Macroscopic Modelling of Environmental Influence on Growth and Form of Sponges and Corals Using the Accretive Growth Model Sun, 24 Feb 2013 15:14:20 +0000 http://www.hindawi.com/journals/isrn.biomathematics/2013/159170/ We discuss a macroscopical growth model which can be used to simulate growth forms of complex-shaped branching organisms with radiate accretive growth. This type of growth processes can be found in many different marine sessile organisms. We use scleractinian corals and a branching sponge as an example. With the radiate accretive growth model a wide range of morphologies and the influence of the physical environment (light and nutrient distribution by advection-diffusion) can be modelled. We show an (preliminary) example of how the accretive growth model can be coupled with a model of gene regulation and body plan formation in a branching sponge. Jaap A. Kaandorp Copyright © 2013 Jaap A. Kaandorp. All rights reserved. Dinucleotide Circular Codes Tue, 12 Feb 2013 08:36:09 +0000 http://www.hindawi.com/journals/isrn.biomathematics/2013/538631/ We begin here a combinatorial study of dinucleotide circular codes. A word written on a circle is called circular. A set of dinucleotides is a circular code if all circular words constructed with this set have a unique decomposition. Propositions based on a letter necklace allow to determine the 24 maximum dinucleotide circular codes (of 6 elements). A partition property is also identified with eight self-complementary maximum dinucleotide circular codes and two classes of eight maximum dinucleotide circular codes in bijective correspondence by the complementarity map. Christian J. Michel and Giuseppe Pirillo Copyright © 2013 Christian J. Michel and Giuseppe Pirillo. All rights reserved. New Cancer Stochastic Models Involving Both Hereditary and Nonhereditary Cancer Cases: A New Approach Tue, 29 Jan 2013 12:41:06 +0000 http://www.hindawi.com/journals/isrn.biomathematics/2013/954912/ To incorporate biologically observed epidemics into multistage models of carcinogenesis, in this paper we have developed new stochastic models for human cancers. We have further incorporated genetic segregation of cancer genes into these models to derive generalized mixture models for cancer incidence. Based on these models we have developed a generalized Bayesian approach to estimate the parameters and to predict cancer incidence via Gibbs sampling procedures. We have applied these models to fit and analyze the SEER data of human eye cancers from NCI/NIH. Our results indicate that the models not only provide a logical avenue to incorporate biological information but also fit the data much better than other models. These models would not only provide more insights into human cancers but also would provide useful guidance for its prevention and control and for prediction of future cancer cases. Wai-Yuan Tan and Hong Zhou Copyright © 2013 Wai-Yuan Tan and Hong Zhou. All rights reserved. Biochemical Systems Theory: A Review Wed, 16 Jan 2013 08:16:11 +0000 http://www.hindawi.com/journals/isrn.biomathematics/2013/897658/ Biochemical systems theory (BST) is the foundation for a set of analytical andmodeling tools that facilitate the analysis of dynamic biological systems. This paper depicts major developments in BST up to the current state of the art in 2012. It discusses its rationale, describes the typical strategies and methods of designing, diagnosing, analyzing, and utilizing BST models, and reviews areas of application. The paper is intended as a guide for investigators entering the fascinating field of biological systems analysis and as a resource for practitioners and experts. Eberhard O. Voit Copyright © 2013 Eberhard O. Voit. All rights reserved. Integrating Imaging Data into Predictive Biomathematical and Biophysical Models of Cancer Wed, 26 Dec 2012 09:20:14 +0000 http://www.hindawi.com/journals/isrn.biomathematics/2012/287394/ While there is a mature literature on biomathematical and biophysical modeling in cancer, many of the existing approaches are not of clinical utility, as they require input data that are extremely difficult to obtain in an intact organism, and/or require a large number of assumptions on the free parameters included in the models. Thus, there has only been very limited application of such models to solve problems of clinical import. More recently, however, there has been increased activity at the interface of quantitative, noninvasive imaging data, and tumor mathematical modeling. In addition to reporting on bulk tumor morphology and volume, emerging imaging techniques can quantitatively report on for example tumor vascularity, glucose metabolism, cell density and proliferation, and hypoxia. In this paper, we first motivate the problem of predicting therapy response by highlighting some (acknowledged) shortcomings in existing methods. We then provide introductions to a number of representative quantitative imaging methods and describe how they are currently (and potentially can be) used to initialize and constrain patient specific mathematical and biophysical models of tumor growth and treatment response, thereby increasing the clinical utility of such approaches. We conclude by highlighting some of the exciting research directions when one integrates quantitative imaging and tumor modeling. Thomas E. Yankeelov Copyright © 2012 Thomas E. Yankeelov. All rights reserved. A Mathematical Model for Assessing the Impact of Intravenous Drug Misuse on the Dynamics of HIV and HCV within Correctional Institutions Mon, 17 Dec 2012 14:54:12 +0000 http://www.hindawi.com/journals/isrn.biomathematics/2012/919502/ Unsafe injecting practices, blood exchange, the use of nonsterile needles, and other cutting instruments for tattooing are common in correctional institutions, resulting in a number of blood transmitted infections. A mathematical model for assessing the dynamics of HCV and HIV coinfection within correctional institutions is proposed and comprehensively analyzed. The HCV-only and HIV-only submodels are first considered. Analytical expressions for the threshold parameter in each submodel and the cointeraction are derived. Global dynamics of this coinfection shows that whenever the threshold parameter for the respective submodels and the coinfection model is less than unity, then the epidemics die out, the reverse condition implies disease persistence within correctional institutions. Numerical simulations using a set of plausible parameter values are provided to support analytical findings. S. Mushayabasa, Claver P. Bhunu, and Alexander G. R. Stewart Copyright © 2012 S. Mushayabasa et al. All rights reserved. Mathematical Modeling and Computational Simulation of a New Biomedical Instrument Design Mon, 10 Dec 2012 11:09:23 +0000 http://www.hindawi.com/journals/isrn.biomathematics/2012/256741/ Endo surgiclip instrument is the biomedical instrument that can be applied for endoscopic surgery to assist surgeons in homeostasis and secure mucosal gap surfaces during surgical operations. Since some clinic feedbacks show the surgiclip drop-off incidents which can potentially sever organ and tissue, the improvement of endo surgiclip instrument has been made in these years. Since few research papers were involved in the study of endo surgiclip instrument performance via mathematical modeling and computational simulation, currently some instrumental modifications are mainly based on clinic lab tests which prolong the improvement cycle and increase additional manufacturing cost. This paper introduces a new biomedical surgiclip instrument based on mathematical modeling, computer-aided simulation, and prototype testing. The analytic methodology proposed in this paper can help engineers in biomedical industry develop and improve biomedical instrument. Compared to the current conventional surgiclip instruments, this new surgiclip instrument can properly assist surgeon in surgical procedure with less operational force and no surgiclip drop-off incident. The prototype has also been built and tested. Both computational simulation and prototype testing show close results which validate the feasibility of this newly developed endo surgiclip instrument and the methodologies of mathematical modeling based computational simulation proposed in this paper. Zheng Jeremy Li Copyright © 2012 Zheng Jeremy Li. All rights reserved. Assessing the Impact of Increasing Antimicrobial Resistance of Vibrio cholerae on the Future Trends of Cholera Epidemic Tue, 04 Dec 2012 14:06:12 +0000 http://www.hindawi.com/journals/isrn.biomathematics/2012/127492/ Cholera, an acute intestinal infection caused by the bacterium Vibrio cholerae, remains a major public health problem in many parts of Africa, Asia, and Latin America. A mathematical model is developed, to assess the impact of increasing antimicrobial resistance of Vibrio cholerae on the future trends of the cholera epidemic. Equilibrium states of the model are determined and their stabilities have been examined. The impacts of increasing antimicrobial resistance of Vibrio cholerae on the future trends of cholera epidemic have been investigated through the reproductive number. Numerical results are provided to support analytical findings. Steady Mushayabasa and Claver P. Bhunu Copyright © 2012 Steady Mushayabasa and Claver P. Bhunu. All rights reserved. Optimal Control of a Delayed HIV Infection Model with Immune Response Using an Efficient Numerical Method Thu, 29 Nov 2012 08:40:40 +0000 http://www.hindawi.com/journals/isrn.biomathematics/2012/215124/ We present a delay-differential equation model with optimal control that describes the interactions between human immunodeficiency virus (HIV), CD4+ T cells, and cell-mediated immune response. Both the treatment and the intracellular delay are incorporated into the model in order to improve therapies to cure HIV infection. The optimal controls represent the efficiency of drug treatment in inhibiting viral production and preventing new infections. Existence for the optimal control pair is established, Pontryagin’s maximum principle is used to characterize these optimal controls, and the optimality system is derived. For the numerical simulation, we propose a new algorithm based on the forward and backward difference approximation. Khalid Hattaf and Noura Yousfi Copyright © 2012 Khalid Hattaf and Noura Yousfi. All rights reserved. Effect of Pulsatile Flow Waveform and Womersley Number on the Flow in Stenosed Arterial Geometry Sun, 25 Nov 2012 11:55:46 +0000 http://www.hindawi.com/journals/isrn.biomathematics/2012/853056/ The salient hemodynamic flow features in a stenosed artery depend not only on the degree of stenosis, but also on its location in the circulatory system and the physiological condition of the body. The nature of pulsatile flow waveform and local Womersley number vary in different regions of the arterial system and at different physiological state, which affects the local hemodynamic wall parameters, for example, the wall shear stress (WSS) and oscillatory shear index (OSI). Herein, we have numerically investigated the effects of different waveforms and Womersley numbers on the flow pattern and hemodynamic parameters in an axisymmetric stenosed arterial geometry with 50% diametral occlusion. Temporal evolution of the streamlines and hemodynamic parameters are investigated, and the time-averaged hemodynamic wall parameters are compared. Presence of the stenosis is found to increase the OSI of the flow even at the far-downstream side of the artery. At larger Womersley numbers, the instantaneous flow field in the stenosed region is found to have a stronger influence on the flow profiles of the previous time levels. The study delineates how an approximation in the assumption of inlet pulsatility profile may lead to significantly different prediction of hemodynamic wall parameters. Moloy Kumar Banerjee, Ranjan Ganguly, and Amitava Datta Copyright © 2012 Moloy Kumar Banerjee et al. All rights reserved. Bayesian Models of Brain and Behaviour Tue, 23 Oct 2012 15:47:27 +0000 http://www.hindawi.com/journals/isrn.biomathematics/2012/785791/ This paper presents a review of Bayesian models of brain and behaviour. We first review the basic principles of Bayesian inference. This is followed by descriptions of sampling and variational methods for approximate inference, and forward and backward recursions in time for inference in dynamical models. The review of behavioural models covers work in visual processing, sensory integration, sensorimotor integration, and collective decision making. The review of brain models covers a range of spatial scales from synapses to neurons and population codes, but with an emphasis on models of cortical hierarchies. We describe a simple hierarchical model which provides a mathematical framework relating constructs in Bayesian inference to those in neural computation. We close by reviewing recent theoretical developments in Bayesian inference for planning and control. William Penny Copyright © 2012 William Penny. All rights reserved. Spatially Explicit Nonlinear Models for Explaining the Occurrence of Infectious Zoonotic Diseases Tue, 23 Oct 2012 13:49:29 +0000 http://www.hindawi.com/journals/isrn.biomathematics/2012/132342/ Zoonotic diseases can be transmitted via an arthropod vector, and disease risk maps are often created based on underlying associative factors within the surrounding landscape of known occurrences. A limitation however is the ability to map disease risk at a meaningful geographic scale, and traditional regression modeling approaches may not always be appropriate. Our objective was to determine if nonlinear modeling could improve explanatory power in describing the occurrence of 2 tick-borne diseases (Lyme disease (LD) and Rocky Mountain spotted fever (RMSF)) known to occur in Tennessee. Medically diagnosed cases of LD (ICD-9: 088.81) and RMSF (ICD-9: 082.0) were extracted from a managed care organization data warehouse for the 2000–2009 time period. Four separate modeling techniques were constructed (logistic regression, classification and regression tree (CART), gradient boosted tree (GBT), and neural network (NNET)) and compared for accuracy. Results suggest that areas higher in disease prevalence were not necessarily the same areas having high predicted disease risk. GBT best explained LD occurrence (misclassification rate: 0.232; ROC: 0.789). RMSF prevalence was best explained with an NNET algorithm (misclassification rate: 0.288; ROC: 0.696). Covariates explaining disease risk included forested wetlands, urbanization, and median income. Nonlinear modeling may provide better results than traditional regression-based approaches. Stephen Jones, William Conner, and Bo Song Copyright © 2012 Stephen Jones et al. All rights reserved.