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International Workshop "Mathematical and Statistical Modelling of Biomedical Systems" Aula Magna Pietro Gismondi, Facoltà di Scienze MFN, Università di Roma Tor Vergata, |
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Abstracts
Nicola Bellomo and Guido Forni
Department of Mathematics, Politecnico di Torino and Department of Clinical and Biological Sciences, Ospedale San Luigi Gonzaga Università degli Studi di Torino Looking for New Paradigms Towards a Biological-Mathematical Theory of Complex Multicellular Systems This lecture deals with the development of new paradigms based on the methods of the mathematical kinetic theory for active particles to model the dynamics of large systems of interacting cells. Interactions are ruled, not only by laws of classical mechanics, but also by biological functions which are able to modify the above laws. It is technically shown, also by reasoning on specific examples, how the theory can be applied to model large complex systems in biology. A challenging, however difficult, objective is the development of a mathematical theory of biological systems. This means not simply designing mathematical models, but deriving a self-consistent robust mathematical description of a sufficiently large variety of biological phenomena. The above target may need years to be properly developed for a large variety of biological systems. On the other hand it is a fascinating perspective which is worth to be pursued, while some conceptual frameworks can be already designed at least for some specific systems. Here we aim to propose the guiding lines towards a mathematical theory for multicellular systems in vertebrates with special attention to the competition between tumor and immune cells. Camillo Cammarota Linguistic analysis of heart beat time series The heart beat time series is the sequence of time intervals between two consecutive main peaks of the ECG. This series is modeled as a non stationary sequence of random variables. Short sequences of consecutive values are coded into words over an alphabet of two or three symbols. The observed probability distribution of the words is used to characterize different states (normality, atrial fibrillation, aging), responses to stress, time reversal. State space models and the universality property of binary words distribution under theassumption of independence are used.
The genetic variability of HIV and its consequences During
their spread among humans, HIV-1 viruses have developed an
extraordinary degree of genetic diversity, and most can be
sub-classified into nine pure subtypes (A, B, C, D, F, G, H, J, and
K) and 16 major circulating recombinant forms. Several factors are
known to contribute to the generation of new viral variants and to
influence the speed with which these viruses evolve. Modelling the Dynamics of West Nile Virus Infection West Nile Virus (WNV) Infection is an arboviral infection which is endemic in West Africa, West Asia and parts of Europe.
In 1999 it was detected for the first time in North America and since then it has traveled rapidly across the continent causing mortality in humans, horses and birds, although only birds transmit the desease. In this talk we formulate and analize a mathematical model of this infection. We find the Basic Reproductive Number Ro in terms of measurable epidemiological and demographic parameters. Using experimental and field data we estimate Ro for several species of birds. Numerical simulations of the temporal course of the infection show that for some parameters new outbreaks can appear from the endemic state due to the coupling between the seasonal oscillations and the natural oscillations of the system through a mechanism of parametric resonance. Andreas Deutsch Cellular automaton modelling of spatio-temporal pattern formation in interacting cell systems Examples of spatio-temporal
pattern formation are life cycles of bacteria and social amoebae,
embryonic tissue formation, wound healing or
tumour growth. Thereby, development of a particular spatio-temporal ''multi-cellular'' pattern may be interpreted as cooperative phenomenon emerging from an intricate interplay of local (e.g. by adhesion) and non-local (e.g. via diffusing signals) cell interactions. What are cooperative phenomena in interacting cell systems and how can they be studied? Mathematical models are required for the analysis of cooperative phenomena. Typical modeling attempts focus on a macroscopic perspective, i.e. the models (e.g. partial differential equations) describe the spatio-temporal dynamics of cell concentrations. More recently, cell-based models have been suggested in which the fate of each individual cell can be tracked. Cellular automata are discrete dynamical systems and may be utilized as cell-based models. Here, we analyze spatio-temporal pattern formation in cellular automaton models of interacting discrete cells. We introduce lattice-gas cellular automata and a cellular automaton based on an extended Potts model that allows to consider cell shapes. Model applications are bacterial pattern formation and tumour growth. Alessio Farcomeni Design issues and new modelling strategies for DNA Micro and Macro arrays The seminar reviews the different
issues in analyzing and modelling data arising from microarrays, in
which thousands of genes are spotted,
Livio Finos, Luigi Salmaso and Fortunato Pesarin Application of a data-driven procedure controlling the False Discovery Rate (FDR) to functional magnetic resonance imaging (fMRI) The data of the functional magnetic
resonance (fMRI) studies are characterized by an increasing quality in
the definition of the images.
Mimmo Iannelli The complex dynamics of age-structured population models Modeling of age-structured populations is governed by the Gurtin-MacCamy system that takes into account age-structure and nonlinear effects on the vital rates.The framework of this problem allows to treat ecological mechanisms for the intra-specific interaction such as juvenile-adult competition, Allee effect, cannibalism. It is known that the models that take into account age-structure are related to delay equations (distributed delay, but also concentrated delay) and that stability of steady states is governed by transcendental characteristic equations that are not easy to analyze analytically. Thus numerical methods for the analysis of such characteristic equations are a powerful tool for exploring the behavior of the models, tracing asymptotical stability, Hopf bifurcations and possible chaos. Recent numerical approaches for characteristic roots of delay differential are based on the discretization of either the associated solution operator semigroup or its infinitesimal generator whose spectra are related to the characteristic roots. The idea is to turn the characteristic roots approximation problem into a corresponding eigenvalue problem for a suitable matrix. This approach has been applied to the specific case of the Gurtin-MacCamy model in order to explore its behaviour versus some significant parameters. In this talk we present the complex dynamics of the Gurtin-MacCamy model, the numerical method set up to locate the characteristic roots, the results we can draw on the behaviour of specific models.
Nonlinear Sciences and interdisciplinarity FENOMEC (Fenomenos nolineales y mecanica) is an interdisciplinary group based in 10 departments of UNAM, with 32 members.
The group has organized, in its more than 10 years, different activities ranging from research to workshops and conferences, around nonlinear sciences. The talk will describe some of the results of the members of FENOMEC and some of the benefits and problems of interdiscipline.
Analysis of spontaneous fluctuation of heart rate and arterial pressure * Several
methods for studying the temporal series of systolic arterial pressure
and RR interval have been proposed both in the time and in the The
study of the spontaneous fluctuations of heart beat allows to
investigate the modulation of the autonomic nervous system on the
cardiovascular system. Many indexes calculated by different mathematical approaches have been used to extrapolate from the time series of heart rate and arterial pressure different information which give some insights for the cardiovascular autonomic modulation. Due to the growing number of these indexes their physiological meaning not always has been directly tested. We have set up an animal models in which we can easily tested the physiological relevance of different mathematical indexes by performing autonomic blockades in awake and freely moving rats by continuously monitoring arterial pressure and heart rate.
The nested-epidemic model for the spread of hepatitis C among injecting drug users The illicit use of drugs
represents an important social, criminal and public health problem. In
particular, injecting is probably the main cause of health damage
related to illegal drug use today. It is therefore important for policy
makers not only to examine the possibilities for preventing the further
spread of illicit drug use and injecting, but also to think carefully
about the most efficient and acceptable approach to meeting the current
and future health and social care needs of users and addicts, including
those exposed to the risk of becoming infected with human
immunodeficiency virus (HIV), hepatitis B virus (HBV), or hepatitis C
virus (HCV). Mathematical modelling can be of major help in order to
obtain qualitative and quantitative evaluation of the costs and the
possible impact of the various interventions and to produce forecasts
of both injecting use and health consequences, such as infectious
diseases. In a recent paper s an epidemic Mover-Stayer type model for
the spread of drug use has been proposed and used to make qualitative
and quantitative scenario analyses. Such model has been extended in
order to mirror the spread of an infectious disease, in particular
hepatitis C, among the injecting drug user population.
In order to model the spread of a disease (HCV) among a population evolving following a different epidemic (injecting drug use) all the compartments of the “external epidemic” (injecting drug use) should be subdivided into two sub-compartments: the first one comprising individuals who are not affected by HCV and the second one comprising individuals affected. The two compartments may be identified by a dichotomous variable taking, for example, value 1 for individuals affected and 0 for the others. Then the transitions within any compartment may be properly modelled allowing to pass from sub-compartment 0 to sub-compartment 1 according to some epidemic behaviour. The resulting model may be defined the “two epidemics” or, better, the “nested epidemics” model. It must be observed that the model, is a Mover-Stayer model for what concerns the “external epidemic” (injecting drug use) but is a homogeneous epidemic model for HCV (all individuals are at risk of HCV the same). The corresponding equations, either deterministic or stochastic, can be easily written and a suitable simulation program can produce numerical results highly valuable for policy making. Let us consider, as an example, the effect of harm reduction interventions on the external and on the internal epidemic. Harm reduction is a public health approach, which gives priority on reducing the adverse consequences of drug use for the individual, the community and society, rather than on eliminating drug use or ensuring abstinence. Although the aim is still to reduce drug use in general, the emphasis is placed on the prevention of potential harmful effects of drug-taking behaviour. With regard to HIV or hepatitis, for example, a harm reduction strategy will first try to reduce the transmission infections by means of cleaning of injecting equipment that has been previously used by others or by means of the cessation of sharing of injecting equipment, rather than by means of promoting abstention from drug use. Achieving those immediate and realistic goals is usually viewed as first steps towards risk-free use. Abstinence may be considered a final aim. With respect to this definition it follows immediately that a harm reduction intervention aimed at reducing the transmission of infections can be viewed as a secondary intervention with respect to the external epidemic, but it is completely equivalent to a primary prevention intervention with respect to the internal epidemic. Thus, such kind of interventions is of high impact with respect to the external epidemic (onset incidence of injecting drug use) when the prevalence of injecting drug users is high, but it is significant to prevent the spread of the internal epidemic (onset incidence of infectious diseases) only if applied at the very beginning of the injecting drug use epidemic.
Alberto Tesei On an ill-posed parabolic equation of population dynamics It is well known that modelling of diffusing populations gives rise to quasilinear parabolic equations, if crowding effects Bruno De Finetti
(1906-1985) gave important contributions to Probability,
Statistics and their applications to human life: on the
centenary of his birth, his work will be recalled in the conclusion of this Workshop. |
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