BIOMED 2013 Abstracts

Full Papers Short Papers
Full Papers
Paper Nr: 1
Title:

Computational Biology Modeling across Different Scales
Authors:

Filippo Castiglione and Francesco Pappalardo
Abstract: One of the most formidable challenges in modern biology is to get a unified view of the various mechanisms governing the behavior and of the causal relationships among different parts of a living system. It is coming clearer nowadays that to get such comprehensive picture computational models embracing different observation levels in space and time have to be formulated to explain the enormous amount of data deriving from -omic high throughput measurements methods. In this article we aim at giving a meaning to the concept of multi-scale modeling in the framework of studies of biological systems with particular interest in understanding human physiology in disease conditions.
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Paper Nr: 6
Title:

Flux through a Time-periodic Gate - Monte Carlo Test of a Homogenization Result
Authors:

Daniele Andreucci, Dario Bellaveglia, Emilio N. M. Cirillo and Silvia Marconi
Abstract: We investigate via Monte Carlo numerical simulations and theoretical considerations the outflux of random walkers moving in an interval bounded by an interface exhibiting channels (pores, doors) which undergo an open/close cycle according to a periodic schedule. We examine the onset of a limiting boundary behavior characterized by a constant ratio between the outflux and the local density, in the thermodynamic limit. We compare such a limit with the predictions of a theoretical model already obtained in the literature as the homogenization limit of a suitable diffusion problem.
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Short Papers
Paper Nr: 4
Title:

Impact of Pericardial Effusion on Cardiac Mechanics in Patients with Dilated Cardiomyopathy
Authors:

Francesco Scardulla, Antonino Rinaudo, Cesare Scardulla and Salvatore Pasta
Abstract: Dilated cardiomyopathy (CDM) is a degenerative disease of the myocardium accompanied by left ventricular (LV) remodeling, resulting in an impaired pump performance. Differently, pericardial effusion (PE) is a liquid accumulation in the pericardial cavity, which may inhibit blood filling of heart chambers. Clinical evidence show that PE may improve pump performance in patients with CDM. Therefore, this study aims to assess wall stress and global function of patients with CDM, PE as compared to healthy patient. These findings suggests that CDM has an important implication in the mechanical changes of LV and right ventricle by increasing wall stress and reducing pump function. Conversely, PE determines lowering myocardial fiber stress and improves global function as compared to those of CDM.
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Paper Nr: 5
Title:

Modelling Transdermal Drug Delivery through a Two-layered System
Authors:

Giuseppe Pontrelli, Andrea Di Mascio and Filippo de Monte
Abstract: One of the most promising frontiers of bioengineering is the controlled release of a therapeutic drug from a vehicle across the skin (transdermal drug delivery). In order to study the complete process, a multiphase mathematical model describing the dynamics of a substance between two porous coupled media of different properties and extents is presented. A system of partial differential equation describes the diffusion and the reversible binding and unbinding processes in both layers. Additional flux continuity at the interface and clearance conditions into systemic circulation are imposed. A Sturm-Liouville problem is solved and an analytical solution is given in the form of an infinite series expansion. The model points out the role of the diffusion and reaction parameters, which control the complex transfer mechanism and the drug kinetics across the two layers. Drug mass are given and their dependence on the physical parameters are discussed.
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Paper Nr: 7
Title:

On the Implementation of a Non-linear Viscoelastic Model into Coupled Blood Flow-biochemistry Model
Authors:

Tomas Bodnár and Adelia Sequeira
Abstract: This paper presents selected numerical results obtained using a macroscopic blood coagulation model coupled with a non-linear viscoelastic model for blood flow. The governing system is solved using a central finitevolume scheme employing an explicit Runge-Kutta time-integration. An artificial compressibility method is used to resolve the pressure. A non-linear TVD filter is applied for stabilization. A simple test case of blood flow over a clotting surface in a straight 3D vessel is solved. This work merges and significantly extends our previous studies (Bodnár and Sequeira, 2008) and (Bodnár et al., 2011a).
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Paper Nr: 9
Title:

Patient Specific Modelling in Diagnosing Depression - Combining Mixture and Non-linear Mixed Effect Modelling
Authors:

Johnny T. Ottesen
Abstract: Depression is a very common disease. Approximately 10% of people in the Western world experience severe depression during their lifetime and many more experience a mild form of depression. It is commonly believed that depression is caused by malfunctions in the biological system constituted by the hypothalamus-pituitaryadrenal (HPA) axis. We pose a novel model capable of showing both circardian as well as ultradian oscillations of hormone concentrations. We show that these patterns imitate those observed in the corresponding data. We demonstrate that patient-specific modelling shows its ability to make diagnoses more precise and to offer individual treatment plans and drug design. Efficient and reliable methods for parameter estimation are crucial. Presently we are examine how well the shuffled complex evolution algorithm do in estimating parameters. The next step is to investigate which parameters there are responsible for which pathologies by non-linear mixed effect modelling and statistical hypothesis testing. Preliminary results are promising. Finally, we plan to investigate how well the Metropolis-Hastings Algorithm of the Bayesian Markov Chain Monte Carlo method for estimating the parameters is working and we are about to do the same using iteratively refined principal differential analysis or the approximated maximum likelihood estimate.
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Paper Nr: 10
Title:

Simulating Drug-eluting Stents - Progress Made and the Way Forward
Authors:

Sean McGinty, Christopher McCormick, Sean McKee, Marcus Wheel, Simon Kennedy and Keith Oldroyd
Abstract: Drug-eluting stents have significantly improved the treatment of coronary artery disease. Compared with their bare metal predecessors, they offer reduced rates of restenosis and thus represent the current gold standard in percutaneous coronary interventions. Drug-eluting stents have been around for over a decade, and while progress is continually being made, they are not suitable in all patients and lesion types. Furthermore there are still real concerns over incomplete healing and late stent thrombosis. In this paper, some modelling approaches are reviewed and the future of modelling and simulation in this field is discussed.
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Paper Nr: 11
Title:

Cardiovascular Dynamics during Head-up Tilt assessed Via a Pulsatile and Non-pulsatile Model
Authors:

N. Williams, H. T. Tran and M. S. Olufsen
Abstract: This study compares a pulsatile and a non-pulsatile model for prediction of head-up tilt dynamics for healthy young adults. Many people suffering from dizziness or light-headedness are often exposed to the head-up tilt test to explore potential deficits within the autonomic control system, which is supposed to maintain the cardiovascular system at homeostasis. However, this system is complex and difficult to study in vivo. This study shows how mathematical modeling can be used to extract features of the system that cannot be measured experimentally. More specifically, we show that it is possible to develop a mathematical model that can predict changes in cardiac contractility and vascular resistance, quantities that cannot be measured directly, but which can be useful to assess the state of the system. The cardiovascular system is pulsatile, yet predicting control in response to head-up tilt for the complete system is computationally challenging, and limits the applicability of the model. In this study we show how to develop a simpler non- pulsatile model that can be interchanged with the pulsatile model, which is significantly easier to compute, yet it still is able to predict internal variables. The models are validated using head-up tilt data from healthy young adults.
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Paper Nr: 12
Title:

Chemical Master Equations - A Mathematical Scheme for the Multi-site Phosphorylation Case
Authors:

Alessandro Borri, Francesco Carravetta, Gabriella Mavelli and Pasquale Palumbo
Abstract: The Chemical Master Equation (CME) provides a fruitful approach for the stochastic description of complex biochemical processes, because it is able to cope with random fluctuations of the chemical agents and to fit the experimental behavior in a more accurate way than deterministic concentration equations. In this work, our attention is focused on modeling and simulation of multisite phosphorylation/dephosphorylation cycles, by using the quasi-steady state approximation of enzymatic kinetics. The CME dynamics is written from the coefficients of the deterministic reaction-rate equations and the stationary distribution is computed explicitly, according to a recently developed realization scheme. Simulations are included to provide a comparison with Monte Carlo methods in terms of computational complexity.
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Paper Nr: 13
Title:

A Viscoelastic Model for Glioma Growth
Authors:

J. R. Branco, J. A. Ferreira and P. de Oliveira
Abstract: In this paper we propose a mathematical model to describe the evolution of glioma cells in the brain taking into account the viscoelastic properties of brain tissue. The mathematical model is established considering that the glioma cells are of two phenotypes: migratory and proliferative. The evolution of the migratory cells is described by a diffusion-reaction equation of non Fickian type deduced considering a mass conservation law with a non Fickian migratory mass flux. The evolution of the proliferation cells is described by a reaction equation. Numerical simulations that illustrate the behaviour of the mathematical model are included.
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Paper Nr: 14
Title:

Electrical Conduction in Biological Tissues - Homogenization Techniques and Asymptotic Decay for Linear and Nonlinear Problems
Authors:

M. Amar, D. Andreucci, P. Bisegna and R. Gianni
Abstract: We collect some results concerning electrical conduction problems in biological tissues. These problems are set in a finely mixed periodic medium and the unknown electric potentials solve standard elliptic equations set in different conductive regions (the intracellular and extracellular spaces), separated by an interface (the cell membrane), which exhibits both a capacitive and a conductive behavior. As the spatial period of the medium goes to zero, the problems approach a homogenization limit. The macroscopic models are obtained by using the technique of asymptotic expansions, in the case where the conductive behavior of the cell membrane is linear, and by means of two-scale convergence, in the case where, due to its biochemical structure, the cell membrane performs a strongly nonlinear conductive behavior. The asymptotic behavior of the macroscopic potential for large times is investigated, too.
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Paper Nr: 15
Title:

A Splitting Algorithm for Medical Image Denoising
Authors:

Adérito Araújo
Abstract: In this work we consider a stable algorithm for integrating a mathematical model based on mean curvature motion equation proposed in (Alvarez, Lions, Morel 1992) for image denoising. The scheme is constructed using a finite difference space discretisation and semi-implicit time discretisation and is considered with a splitting algorithm that can be implemented in parallel. We apply this algorithm to the problem of denoising optical coherence tomograms from the human retina while preserving image features.
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