Models for Physiological Systems

Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, 2006

Computational modelling of biological processes and systems has witnessed a remarkable development in recent years. The search-term ( modelling OR modeling ) yields over 58 000 entries in PubMed, with more than 34 000 since the year 2000: thus, almost two-thirds of papers appeared in the last 5–6 years, compared to only about one-third in the preceding 5–6 decades. The development is fuelled both by the continuously improving tools and techniques available for bio-mathematical modelling and by the increasing demand in quantitative assessment of element inter-relations in complex biological systems. This has given rise to a worldwide public domain effort to build a computational framework that provides a comprehensive theoretical representation of integrated biological function—the Physiome. The current and next issues of this journal are devoted to a small sub-set of this initiative and address biocomputation and modelling in physiology, illustrating the breadth and depth of experim...

2007

Although recent enthousiasm has emerged for Systems Biology, it is of major importance to identify the roots it has with computational (mathematical) modeling. In fact, major contributions have been made for decades with the aim to quantitatively analyze and model the function of living systems in order, ultimately, to better understand the underlying constituents and collective behaviors and use them for diagnosis and therapeutic purposes. However, the impressive evolution of technological resources and methods allows today to revisit these early attempts and to bring to light new concepts, targets, and expectations. This chapter, after a tentative definition of the generic elements behind Systems Biology and Physiology, will provide a review of current efforts devoted to multimodal, multilevel, multiresolution approaches, all being addressed from the joint observational, modeling and information processing points of view. The several theoretical frames at our disposal will also be addressed, in particular the capability to handle multiple modeling formalisms. Examples from the literature and the research conducted by the authors will exemplify these multidisciplinary developments and results. The forthcoming challenges to be faced will then be outlined.

2015

The paper gives a summary of 2014 year results in the topic of physiological modeling and control achieved by the Physiological Controls Group of the Obuda University. The presentation is integrated in the tradition established years ago at IEEE INES conferences and 2014's IEEE SACI conference summarizing the latest results obtained by the group. Four topics are presented, highlighting collaboration with our partner research institutes as well: modern robust control of diabetes, antiangiogenic model-based tumor control, biostatistical modeling methods of diabetes, control of peristaltic pumps in hemodialyisis problem. I.

2011

2018

Biological systems such as cell cycle are complex systems consisting of an enormous number of elements. These elements interact in ways that produce nonlinear and complex systems behaviour such as oscillations. A number of modelling approaches have been used to explain these kinds of systems; they are classified into four classes (continuous, discrete, stochastic and hybrid). Ordinary Differential Equations (ODEs) are used to mimic the continuous dynamic behaviour of system components, while discrete models can simulate the biological elements as straightforward binary variables providing a qualitative view of system behaviour. Stochastic models are used to model the effect of noise in biological systems. Combined methods together introduce hybrid models to cover the limitations of individual models and take advantage of their strengths. This study introduces a series of advanced models with increasing resolution from discrete to continuous in a systematic way to model the mammalian...

1998

Finite-difference numerical methods are developed for the solution of some systems in the biomedical sciences; namely, a predator-prey model and the SEIR (Susceptible/Exposed/ Infectious/Recovered) measles model. First-order methods are developed to solve the predator-prey model and one second-order method is developed to solve the SEIR measles model. The predator-prey model is extended to one-space dimension to incorporate diffusion. The SEIR measles model is extended to one-space dimension to incorporate (i) diffusion, (ii) convection and (iii) diffusion-convection. The SEIR measles model is extended further to model diffusion in two-space dimensions. The reaction terms in these systems of partial differntial equations contain nonlinear expressions. Nevetheless, it is seen that the numerical solutions are obtained by solving a linear algebraic system at each time step, as opposed to solving a nonlinear algebraic systems, which is often required when integrating non-linear partial differential equations. The development of each numerical method is made in the light of experience gained in solving the system of ordinary differential equations for each system.

2007

2 3.1. Structured population modeling 3.1.1. Structured modeling in demography and epidemiology 3.1.2. Invasion processes in fragile isolated environments 3.1.3. Indirectly transmitted diseases 3.1.4. Direct movement of population 3.2. Optimal control problems in biomathematics 3.2.1. Disease control 3.2.2. Controlling the size of a population 3.2.3. Public prevention of epidemics in an optimal economic growth model 3.2.4. Age structured population dynamics as a problem of control 3.3. Developping mathematical methods of optimal control, inverse problems and dynamical systems; software tools 3.3.1. Inverse problems : application to parameter identification and data assimilation in biomathematics 3.3.2. Dynamic programming and factorization of boundary value problems 3.3.3. Applications of the factorization method to devise new numerical methods 3.3.4. Differential equations with delay modeling cellular replication 3.3.5. Tools for modeling and control in biomathematics 3.4. Application fields and collaborations with biologists 3.4.1. Epidemiology 3.4.1.1. Brucellosis 3.4.1.2. HIV-1 Infection in tissue culture 3.4.1.3. Contamination of a trophic chain by radionuclides 3.4.2. Blood cells 3.4.2.1. Generating process for blood cells (Hematopoiesis) 3.4.2.2. Malignant proliferation of hematopoietic stem cells 3.4.2.3. Socio-biological activities of the Immune-System cells 3.4.3. Modeling in viticulture; collaboration with INRA 3.4.3.1. Integrated Pest Management in viticulture. 3.4.3.2. Spreading of a fungal disease over a vineyard 3.4.4. Modeling in neurobiology 3.4.4.1. The biological model of aplysia 3.4.4.2. MEG-EEG inverse problem 3.4.4.3. Inverse problem for Aplysia's ganglion model 3.4.4.4. Modeling of the treatment of Parkinson's disease by deep brain stimulation

Biosystems Engineering: Biofactories for Food Production in the Century XXI, 2014

Mathematics is an important tool for system modeling allows us to describe the behavior of a phenomenon or system in the real world, in particular biological systems. This chapter gives an overview of mathematical models, their construction, types of models, and examples of possible applications in biosystems models. Essential for building a model is determining its scope. In addition, the mechanistic and phenomenological mathematical models are described. Applications on fish biomass estimation, quality of fruits and crops are presented.

Texts in Applied Mathematics, 2002

2008

Annals of Biomedical Engineering, 2000

Effective modeling of nonlinear dynamic systems can be achieved by employing Laguerre expansions and feedforward artificial neural networks in the form of the Laguerre-Volterra network ͑LVN͒. This paper presents a different formulation of the LVN that can be employed to model nonlinear systems displaying complex dynamics effectively. This is achieved by using two different filter banks, instead of one as in the original definition of the LVN, in the input stage and selecting their structural parameters in an appropriate way. Results from simulated systems show that this method can yield accurate nonlinear models of Volterra systems, even when considerable noise is present, separating at the same time the fast from the slow components of these systems effectively.

2000

Since its "foundation," computational intelligence has been creating novel-high perspectives on modeling, on the other hand, the "old-fashioned" mathematics offers powerful methods that should not be forgotten or underestimated. On this paper, it is discussed a novel methodology proposed by the authors on the mathematical modeling, with emphasis in biomedical and biological modeling. The methodology comprises of an attempt to use simultaneously mathematics and computational intelligence in a single picture, using the concept of blindness of a model. The methodology proposed can be summarized into the name of "the middle-way-out principle." Besides the theory is presented and discussed, no real problem is treated, it is left to future works, due to the choice of the authors and current incipient state of the theory. The paper is concluded with some conclusions and final remarks, the main references used all over the work are presented in the end.

Proc. Second Symp. Biomed. Infor. Manag. Systems, 1987

Physiological research on many mechanisms has reached the subcellular and molecular level. While molecules have been identified for some processes, it is not yet possible to describe physiological function directly in terms of molecular structure. The state diagram, as used in chemical kinetics, is an ideal language for expressing hypotheses of physiological mechanism at the subcellular and molecular level. No only does a state diagram express a hypothesis in specific, quantitative terms, it also facilitates the inclusion of physical constraints such as conservation laws and chemical data. Approximations and graphical methods frequently used to simplify the solution of state diagrams are shown to be inaccurate and should now be replaced by direct computer solutions of the kinetic equations.

Journal of General Physiology, 2011

Readers of the current issue will find something unfamiliar, perhaps tantalizing, perhaps unsettling. I am referring to the articles by Cha et al. (see "Ionic mechanisms and Ca 2+ dynamics..." and "Time-dependent changes in membrane excitability..."). The first of these articles is less exotic; it presents computer simulations of a model for bursting electrical activity in pancreatic  cells. The second uses bifurcation diagrams to analyze the behavior of the model. I will argue that this is relevant far beyond  cells-the leading edge of a wedge driving the methods of dynamical systems theory into the heart of biology. Mathematical modeling of cell electrical activity has a long history in physiology, going back to the work of Hodgkin and Huxley (Hodgkin and Huxley, 1952; Chay and Keizer, 1983) for action potential generation and propagation in squid giant axon. The model of Cha et al. (2011a,b) is based on the Hodgkin and Huxley formalism, but augmented with mechanisms for maintaining ionic balance (pumps and exchangers for Ca 2+ , Na + , and K + , and the endoplasmic reticulum). In addition, a nod is given in the direction of metabolism, as  cells are first and foremost metabolic sensors and use ATP-dependent K + (K(ATP)) channels, to transduce the rate of glucose metabolism into intensity of electrical activity. Cha et al. (2011a,b) follow the path blazed by Chay and Keizer (1983). Their model was based on the simple idea, first proposed by Atwater et al. (1980), that bursting results from slow modulation of spiking by calcium. That is, during the active spiking phase of the burst, calcium builds up and turns on calcium-activated K + (K(Ca)) channels until membrane potential falls below the threshold level and spiking terminates. During the ensuing silent phase, calcium would be pumped out of the cell, lowering the spike threshold and allowing the next active phase to begin. Rinzel (1985) formalized this mathematically, recognizing that the key element of Chay-Keizer was a fast spiking system modulated by slow negative feedback. This led to a profusion of models, different biophysically but essentially equivalent mathematically, with alternate proposals for the source of the negative feedback. These included inactivation of the L-type Ca 2+ channel (Chay, 1990), indirect activation of K(ATP) channels by Ca 2+ via its effects on ATP consumption or production (Keizer and Magnus, 1989