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Seminars

The PHYSIOMATH seminar takes place usually at the Department of Mathematics
Instituto Superior Técnico
Room 3.10, 3rd floor
Av. Rovisco Pais, 1
1049-001
Lisboa

See the annoucement for the detailed program and for the eventual changes of the place

- 12.07.2013

- Jevgenija Pavlova CEMAT, Instituto Superior Técnico, Lisbon
- Modeling the Coagulation Dynamics in Human Blood
*Abstract:*Blood coagulation is an extremely complex biological process in which blood forms clots to prevent bleeding, following by their dissolution and the subsequent repair of the injured tissue. The process involves different interactions between the plasma, the vessel wall and platelets having a huge impact of the flowing blood on the thrombus growth regularization. The blood coagulation model we are working on consists of a system of reaction-advection-diffusion equations, describing the cascade of biochemical reactions, coupled with rheological models for the blood flow (Newtonian, shear-thinning and viscoelastic models). We introduce the effect of blood slip at the vessel wall emphasizing an extra supply of activated platelets to the clotting site. We expect that such contribution could be dominant, resulting in the acceleration of thrombin production and eventually of the whole clot progression. Such model will have the capacity to predict effects of specific perturbations in the hemostatic system that can’t be done by laboratory tests, and will assist in clinical diagnosis and therapies of blood coagulation diseases. A mathematical model and numerical results for thrombus development will be presented. The chain of biochemical reactions interacting with the platelets, resulting in a fibrin-platelets clot formation and the additional blood flow influence on thrombus development will be discussed.

- 00.00.2012 00.00.2012 12:30

- 04.09.2013

- Kazuaki Nakane Division of Health Sciences, Osaka University, Japan
- A Homology-based Algorithm for the Analysis of Structures
*Abstract:*Observations of the microstructure of objects by means of a microscope are carried out in different technical fields. The state organization of iron with quenching-annealing and the human tissue by biopsy are typical examples. Since the results of such observations depend on the skills of the technician, objective methods are required for the quantification of structures. When the observed structures are very complex, the performance of pattern recognition and Fourier methods is not satisfactory. In this talk, I will introduce an algorithm based on the concept of homology. By applying this method, we obtain rigorous quantitative estimates of a structure. Several examples of its application will be presented.

- 00.00.2012 00.00.2012 17:00

- 13.11.2013

- Andrey Tsyganov Ulyanovsk State Pedagogical University, Ulyanovsk, Russia
- Parallel Algorithms for NFA State Minimization Problem
*Abstract:*This talk will start with an introduction, where we present the Laboratory of Mathematical Modeling which was recently established in Ulyanovsk State Pedagogical University. The report will cover its hardware and software facilities and main areas of conducted research: cosmology, molecular biology, combinatorial optimization, parameter identification. Then we will switch to the main subject of the talk. We consider the state minimization problem for nondeterministic finite automata (NFA) which is known to be computationally hard (PSPACE-complete) and introduce ReFaM – a software tool for its solution. This software tool provides a number of parallel algorithms: parallel versions of exact Kameda- Weiner and Melnikov methods as well as their hybrids with popular metaheurstics (genetic algorithm, simulated annealing, etc.). All parallel algorithms are implemented using MPI and OpenMP techniques. We discuss the implementation details and provide the results of numerical experiments.

- 00.00.2012 00.00.2012 15:30

- Julia Tsyganova Ulyanovsk State University, Ulyanovsk, Russia
- Parameter Identification in Stochastic Dynamic Systems based on API Approach (with applications in Biology)
*Abstract:*In this talk, we discuss the following two problems. First, we present the Auxiliary Performance Functional (API) developed by Prof. I.V. Semushin and study its role in the state and parameter estimation of linear discrete-time stochastic systems. The minimization procedure of the API with respect to parameters of the Data Model is then considered. Our approach differs from what has been done earlier in the adaptive filtering theory. We may mention that the minimization with respect to the parameters of the Adaptive Filter instead of the Data Model was considered previously. Second, we concern with robust array adaptive filters grounded in SR and UD covariance matrix factorizations used for the API gradient evaluation in identification algorithms. As a reallife example, we consider an application of the API approach to linear time-invariant statespace stochastic MIMO filter systems arising in human body temperature daily variation adaptive stochastic modeling. Simulation results and conclusions are also provided. Key words: linear stochastic system, parameter estimation, model identification, Auxiliary Performance Functional (API) approach, state sensitivity evaluation methods, stochastic modeling, homeostasis, thermoregulation.

- 00.00.2012 00.00.2012 16:30

- 11.12.2013

- Marco Leite UCL Institute of Neurology and Instituto de Sistemas e Robótica, IST
- Modelling populations of integrate and fire neurons: a Fokker-Planck approach to population density dynamics
*Abstract:*Much of the phenomenology of interest in the field of neuroscience arises from the interaction of large populations of densely interconnected neurons (~105 neurons per mm3 of mammal cortex, averaging 104 connections per neuron). Different levels of abstraction may be adopted when modelling such systems, and these need to be well suited with regards to the phenomena one is interested in studying. Here we aim at the study of the (sparse) synchronization of neurons observed during electrophysiologically recorded fast oscillatory behavior of networks of large populations. For that we use a ubiquitous simplified neuronal model - the conductance based leaky integrate and fire neuron. This model may be described by a one dimensional stochastic differential equation. Under mean field assumptions we may describe, using a linear Fokker-Planck equation, the behavior of a single population of uncoupled neurons with a PDE. The coupling of different populations will render this Fokker-Planck equation strongly non-linear. In this presentation I will also explore some details of such modelling approaches, namely: the non-natural boundary conditions generated by the neuronal firing mechanism and the numerical scheme used to deal with the brittleness from there ensued. I will also present results on the types of behavior, data, and statistics that such modelling approach is able to predict, e.g. neuronal (a)synchrony, neuronal input currents, firing rates, inter spike intervals, etc... This type of approach allows for a computationally tractable and scalable study of networks of populations of neurons. In the future we plan to implement parameter estimation algorithms to this family of models.

- 00.00.2012 00.00.2012 16:00

- 13.03.2014

- Elias Gudino CMUC, Universidade de Coimbra, Portugal
- A 3D model for mechanistic control of drug release
*Abstract:*A 3D mathematical model for sorption/desorption by a cylindrical polymeric matrix with dispersed drug is proposed. The model is based on a system of partial differential equations coupled with boundary conditions over a moving boundary. We assume that the penetrant diffuses into a swelling matrix and causes a deformation which induces a stress driven diffusion and consequently a non-Fickian mass flux. A physically sound non linear dependence between strain and penetrant concentration is considered and introduced in a Boltzmann integral with a kernel computed from a Maxwell-Wiechert model. Numerical simulations show how the mechanistic behavior can have a role in drug delivery design.

- 00.00.2012 00.00.2012 15:30

- 15.05.2014

- Jahed Naghipoor CMUC, Universidade de Coimbra, Portugal
- A non-Fickian reaction diffusion equation for polymeric stent embedded in the arterial wall
*Abstract:*In recent years, mathematical modeling of cardiovascular drug delivery systems has become an effective tool to gain deeper insights in the cardiovascular diseases like atherosclerosis.. In the case of coronary biodegradable stent which is a tiny expandable biocompatible metallic mesh tube covered by biodegradable polymer, it leads to a deeper understanding of the drug release mechanisms from polymeric stent into the arterial wall. A coupled non-Fickian model of a cardiovascular drug delivery system using a biodegradable drug eluting stent is proposed in this talk. Energy estimates are used to study the qualitative behavior of the model. The numerical results are obtained using an IMEX finite element method. The influence of arterial stiffness in the sorption of drug eluted from the stent is analyzed. The results presented in this talk open new perspectives to adapt the drug delivery profile to the needs of the patient.

- 00.00.2012 00.00.2012 16:00

- 23.07.2014

- Willi Jäger, Maria Neuss-Radu , University of Heidelberg, University of Erlangen-Nuremberg (resp.)
- Interactions of the fluid and solid phases in complex media — coupling reactive flows, transport and mechanics, and applications to medical processes.
*Abstract:*Modelling reactive flows, diffusion, transport and mechanical interactions in media consisting of multiple phases, e.g. of a fluid and a solid phase in a porous medium, is giving rise to many open problems for (multi-scale) analysis and simulation. In this lecture, the following processes are studied:

diffusion, transport, and reaction of substances in the fluid and the solid phases, mechanical interactions of the fluid and solid phases, change of the mechanical properties of the solid phase by chemical reactions, volume changes (“growth”) of the solid phase.

These processes occur for instance in soil and in porous materials, but also in biological membranes, tissues and in bones. The model equations consist of systems of nonlinear partial differential equations, with initial-boundary conditions and transmission conditions on fixed or free boundaries, mainly in complex domains. The coupling of processes on different scales is posing challenges to the mathematical analysis as well as to computing. In order to reduce the complexity, effective macroscopic equations have to be derived, including the relevant information from the micro-scale.

In case of processes in tissues, a homogenization limit leads to an effective, mechanical system, containing a pressure gradient, which satisfies a generalized, time-dependent Darcy law, a Biot-law, where the chemical substances satisfy diffusion-transport-reaction equations and are influencing the mechanical parameters.

The interaction of the fluid and the material transported in a vessel with its flexible wall, incorporating material and changing its structure and mechanical behavior, is a process important e.g. in the vascular system (plaque-formation) or in porous media.

The modeling and analytic aspects addressed in our talk are also highly relevant for the study of inflammatory processes.

The lecture is based on recent results obtained in cooperation with A. Mikelic, F. Weller and Y. Yang.

- 00.00.2012 00.00.2012 13:00

- 09.09.2014

- Maria Specovius-Neugebauer University of Kassel, Germany
- The time periodic Stokes system in a layer: asymptotic behavior at infinity
*Abstract:*While there are numerous papers on the time decay of solutions to the Stokes and Navier-Stokes initial boundary value in various types of domains only few results are devoted to the spatial decay. In this talk we consider the solutions to the time periodic Stokes problem in a layer where the data are also time periodic and smooth with bounded support for simplicity. The results were obtained in a joint work with Konstantin Pileckas,Vilnius.

- 00.00.2012 00.00.2012 12:30

- 09.10.2014

- Sílvia Barbeiro CMUC, Department of Mathematics, University of Coimbra, Portugal
- Modeling electromagnetic wave’s propagation in human eye’s structure
*Abstract:*In this talk we will discuss the a mathematical model that describes the electromagnetic wave’s propagation through the eye’s structures in order to create a virtual OCT scan. Our model is based on time-dependent Maxwell’s equations. We use the discontinuous Galerkin method for the integration in space and a low-storage Runge-Kutta method for the integration in time. In the model we consider anisotropic permittivity tensors which arise naturally in our application of interest. We illustrate the performance of the method with some numerical experiments.

- 00.00.2012 00.00.2012 15:30

- 06.11.2014

- Anca-Maria Toader CMAF and Faculdade de Ciências da Universidade de Lisboa, Portugal
- The Adjoint Method in Optimization of Eigenvalues and Eigenmodes
*Abstract:*The Adjoint Method goes back to the works of Pontryagin in the framework of Ordinary Differential Equations. In the eighties, J. Cea employed the Adjoint Method in a practical way, from the perspective of Lagrange multipliers. Since then, applications of the Adjoint Method were successfully used in Shape Optimization, Topology Optimization and very recently to optimize eigenvalues and eigenmodes (eigenvectors).

The main contribution of this study is to show how the Adjoint Method is applied to the optimization of eigenvalues and eigenmodes. The general case of an arbitrary cost function will be detailed. In this framework, the direct problem does not involve a bilinear form and a linear form as usual in other applications. However, it is possible to follow the spirit of the method and deduce N adjoint problems and obtain N adjoint states, where N is the number of eigenmodes taken into account for optimization.

An optimization algorithm based on the derivative of the cost function is developed. This derivative depends on the derivatives of the eigenmodes and the Adjoint Method allows one to express it in terms of the the adjoint states and of the solutions of the direct eigenvalue problem.

This method was applied in [1] for material identification purposes in the framework of free material design. In [2] this study is applied to optimization of microstructures, modeled by Bloch wave techniques.

References:

S. Oliveira, A.-M. Toader, P. Vieira, Damage identification in a concrete dam by fitting measured modal parameters. Nonlinear Analysis: Real World Applications, 13, Issue 6, 2888-2899, 2012.

C. Barbarosie, A.-M. Toader, The Adjoint Method in the framework of Bloch Waves (in preparation).

- 00.00.2012 00.00.2012 16:00

- 20.11.2014

- Javad Hatami IBB-Institute for Biotechnology and Biosciences, IST, Univ Lisbon
- A Mathematical Approach To Model Human Megakaryopoiesis Process in vitro
*Abstract:*Megakaryopoiesis is a complex process, which is commenced with the proliferation and the differentiation of hematopoietic stem cells (HSC) into megakaryocytes (Mk), followed by maturation and polyploidy of Mk and ended by platelet biogenesis. An in vitro two-stage protocol including HSC expansion and Mk lineage commitment of human umbilical cord blood cells (hUCB) were established [1]. In the first stage, hUCB CD34+-enriched cells were expanded in co-culture with bone marrow human mesenchymal stem cells (BM hMSC) in a cytokines cocktail pre-optimized for CD34+ expansion. In the second stage, expanded cells were differentiated toward Mk lineage using a cocktail containing TPO and IL-3 in a serum-free medium. Phenotypic characterization of cells was performed by Flow cytometry. In order to describe the fate of HSC during the megakaryopoiesis, a mathematical approach was used based on kinetic modeling of cell expansion and differentiation. This kind of modeling, which computes the concentration of each subset during the time, can provide significant insight into the limiting step involved in the protocol and how the interaction of different factors can affect the outcome of megakaryopoiesis process. A set of ordinary differentiation equation (ODE) were used to analyze the proliferation and differentiation of UCB CD34+ cells, as evaluated by the number of HSC (CD34+ cells), Mk (CD41+ cells) and platelets (CD42b+ cells). These ODEs were solved and a general solution for each subset was fitted to the experimental result, using least square method, to determine the unknown coefficient factors. The establishment of such reliable kinetic model will be useful for development of an efficient bioreactor system devoted for production of specific hematopoietic product.

References:

1. Hatami J, Andrade PZ, Bacalhau D, Cirurgião F, Ferreira FC, et al. (2014) Proliferation extent of CD34+ cells as a key parameter to maximize megakaryocytic differentiation of umbilical cord blood-derived hematopoietic stem/progenitor cells in a two-stage culture protocol. Biotechnology Reports 4: 50-55.

- 00.00.2012 00.00.2012 16:00

- 12.02.2015

- Paolo Falsaperla Dipartimento di Matematica e Informatica, Università di Catania, Catania, Italy
- A mathematical model of anorexia and bulimia
*Abstract:*Time evolution of pathological and harmful behaviors (such as binge drinking or drug consumption [1, 2]) can be modeled in the context of epidemiological models [3]. In this paper we propose a mathematical model to study the dynamics of anorexic and bulimic populations inspired by the model of Gonzalez et al. [4].

The model proposed takes into account, among other things, the eftects of peers' influence, media influence, and education. We prove the existence of three possible equilibria, that without media influences are disease-free, bulimic-endemic, and endemic. Neglecting media and education eftects we investigate the stability of such equilibria, and we prove that under the influence of media, only one of such equilibria persists and becomes a global attractor. Which of the three equilibria becomes global attractor depends on the other parameters.

This is a joint work with C. Ciarcia, A. Giacobbe, G. Mulone.

[1] Mulone G, Straughan: Modeling binge drinking, Int. J. Biomath., 5(1), 1250005 (2012)

[2] Mulone G, Straughan B: A note on heroin epidemics, Math. Biosci. 218, 118{141 (2009)

[3] Hethcote HW: The mathematics of infectious diseases, SIAM Rev. 42, 599{653 (2000).

[4] Gonzalez B et al.: Am I too fat? Bulimia as an epidemic, J. Math. Psych. 47, 515{526 (2003).

- 00.00.2012 00.00.2012 15:30

- 23.04.2015

- Pedro Serranho Universidade Aberta
- Applied mathematics to the imaging of the human retina
*Abstract:*In this talk we will focus on mathematical problems arising in the field of medical imaging and their possible numerical solutions, namely in the imaging of the human retina. We will focus on how mathematical methods (for classification and solving partial differential equations) applied to real medical imaging data can provide additional information and simulations with the potential to be an aid to the early diagnosis of diseases affecting the retina, as for instance diabetes.

- 00.00.2012 00.00.2012 16:00

- 27.05.2015

- Vincenzo Coscia Department of Mathematics, University of Ferrara, Italy
- Modeling complexity: From vascular biomechanics to social systems
*Abstract:*In this talk I will give insight on the activity of the research center Mathematics for Technology, Medicine & Biosciences of the University of Ferrara. I'll report on the studies concerning the mechanics of the human venous system as well as on the mathematical modeling of social systems, such as pedestrian dynamics and vehicular traffic, with the common paradigm of complexity modeling.

- 00.00.2012 00.00.2012 15:30

- Room P3.10, Department of Mathematics

- 16.07.2015

- Nuno Lopes ISEL–Instituto Superior de Engenharia de Lisboa
- Analytical and Numerical Methods of the type FEM-C/D for Improved Boussinesq Models
*Abstract:*In this talk, some analytical and numerical models are developed for the generation and propagation of surface water waves. These problems are solved using asymptotic and numerical methods. Regarding the numerical methods, we consider the continuous and continuous/discontinuous Galerkin finite element methods (FEM-C/D) with penalty terms.

In the first problem, the model of Zhao et al. (2004) is extended in order to include some effects like dissipation and absorption of the energy of the surface water waves. We show that this model is robust with respect to the instabilities related to steep bottom gradients of the bathymetry. A new class of nonlinear Boussinesq-type systems is derived in the second problem. A CFL type condition is obtained for the linearized problem with constant bathymetry. The consistency of the dispersion relation as well as the good stability properties of this model are verified. From the numerical tests, we can conclude that the proposed numerical model is appropriate to model surface water waves. In the third problem, a class of Korteweg, de Vries–Benjamin, Bona and Mahony (KdV-BBM) type equations is deduced. The Nwogu’s parameter is determined in order to optimise the velocity potential of the linearized KdV-BBM model. Moreover, a numerical analysis of the proposed model is performed. We conclude that the KdV-BBM model is less prone to instabilities than the KdV model. Finally, a new Boussinesq-type differential equation of sixth-order to model bidirectional waves is derived and exact travelling wave solutions are obtained. A new analytical travelling wave solution is found. This is a joint work with P. J. S. Pereira and L. Trabucho.

- 00.00.2012 00.00.2012 16:00

- 16.12.2015

- Annie Raoult Université Paris Descartes, France
- Effective behavior of lattices with angular interactions
*Abstract:*Angular interactions are of primary importance in mechanical trusses that they stabilize as well as in atomistic lattices, see Allinger and Tersoff-Brenner potentials. Graphenes are nowadays the best known example of hexagonal lattices. We will concentrate on the behavior of 2d-lattices undergoing deformations in the 3d-space, where major difficulties are already present when seeking for an equivalent behavior. We will give an example where homogenization is not required in the formulation of an equivalent continuous problem. We will show that for hexagonal lattices, on the contrary, homogenization is required even when only bond energy is taken into account. When angular interactions are added, we characterize the equivalent behavior by an alternate method. We will discuss the practical interest of the representation formulas.

- 00.00.2012 00.00.2012 18:00

- 17.03.2016

- Cristiana Silva CIDMA - Universidade de Aveiro
- Optimal control of epidemiological models
*Abstract:*We apply optimal control theory to a Tuberculosis (TB) and a TB-HIV/AIDS co-infection models. The models are given by systems of ordinary differential equations.

For the TB model, optimal control strategies are proposed to minimize the number of active infectious and persistent latent individuals, as well as the cost of interventions. A cost-effectiveness analysis is done, to compare the application of each one of the control measures, separately or in combination.

We introduce delays in the TB model, representing the time delay on the diagnosis and commencement of treatment of individuals with active TB infection. The stability of the disease free and endemic equilibriums is investigated for any time delay. Corresponding optimal control problems, with time delays in both state and control variables, are formulated and studied.

We propose a model for TB-HIV/AIDS coinfection transmission dynamics. We analyze separately the HIV-only, TB-only and TB-HIV/AIDS models. The respective basic reproduction numbers are computed, equilibria and stability are studied. Optimal control theory is applied to the TB-HIV/AIDS model and optimal treatment strategies for co-infected individuals with HIV and TB are derived. Numerical simulations to the optimal control problem show that non intuitive measures can lead to the reduction of the number of individuals with active TB and AIDS.

- 00.00.2012 00.00.2012 15:30

- 19.03.2016

- Alfio Quarteroni École Polytechnique Fédérale de Lausanne, Switzerland
- Mathematical models and their impact on our daily life
*Abstract:*Mathematical and numerical models describe and simulate various aspects of the real world, their interaction and their dynamics. Thanks to the impetuous progress of computers power and the development of powerful and accurate algorithms, nowadays we can use mathematics to improve our basic understanding of natural and biological processes, enhance social communications and technological innovation, provide medical doctors with quantitative and rigorous tools in clinical practice.

This presentation will introduce the basic concepts behind mathematical and numerical models, and illustrate their use in different fields of science and engineering, including sports, life sciences and the environment.

- 00.00.2012 00.00.2012 13:30

- 30.03.2016

- Kathleen Curran University College Dublin
- FibReGen: Modelling Myofibre Regeneration
*Abstract:*In young individuals, myofibres are capable of altering their profile in response to perturbation, but plasticity of ageing skeletal muscle is less clearly understood. The age-related loss of muscle mass in sarcopenia is mediated by a reduction in the total number of myofibres, a decrease in size of fast-twitch myosin heavy chain fibres and altered morphology. These maladaptations create negative metabolic and functional implications that impede healthy ageing.

Despite modern advances, Duchenne muscular dystrophy (DMD) remains fatal and incurable. Muscle is extensively replaced by adipose tissue, and heart failure often results. We propose to model for the molecular pathogenesis centred around the increased susceptibility of glycolytic fibres to degeneration in DMD and connect the histological findings of hypercontracted fibres, segmental necrosis and grouped necrosis to glycolytic fibres and investigate recent evidence from animal models suggesting that oxidative fibre type switching may ameliorate the effects of the disease.

Early physiological changes often start at the cellular or fascicular level, which is beyond the capabilities of conventional MRI. Histology, requiring invasive biopsies, is necessary to assess early treatment and training effects. Diffusion tensor imaging (DTI) provides a sensitive noninvasive readout of early physiological changes in tissue microstructure. DTI can also be applied for in vivo quantification and 3D visualisation of the macroscopic muscle fibre architecture.

The aim of FibReGen is to develop subject-specific and patient-specific computational models of skeletal and cardiac muscle entirely from MRI data. These computational models will integrate anatomical, functional, metabolic and mechanical data, and will characterise fibre type proportion and interconversion in a wide-ranging spectrum of subjects including elite athletes, those with age-related sarcopenia and patients with DMD.

- 00.00.2012 00.00.2012 16:00