Model Development and Decomposition in Physiology

Model Development and Decomposition in Physiology

Isabel Reinecke (Zuse Institute Berlin, Germany) and Peter Deuflhard (Zuse Institute Berlin, Germany)
Copyright: © 2009 |Pages: 39
DOI: 10.4018/978-1-60566-076-9.ch042
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Abstract

In this chapter some model development concepts can be used for the mathematical modeling in physiology as well as a graph theoretical approach for a decomposition technique in order to simplify parameter estimation are presented. This is based on the human menstrual cycle. First some modeling fundamentals are introduced that are applied to the model development of the human menstrual cycle. Then it is shown how a complex mathematical model can be handled if a large number of parameters are used where the parameter values are not known for the most part. A method is presented to divide the model into smaller, disjoint model parts. At the same time, it is shown how this technique works in the case of the human menstrual cycle. The principles for model development and decomposition can be used for other physiological models as well.
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Background

First, some principle modeling concepts are introduced that could be useful in the modeling of physiological processes and that are used to construct the complex mathematical model of the human menstrual cycle. The concept of compartmentalization of the considered body parts and how the connections between the compartments can be modeled, for example, via receptor binding and feedback mechanisms, is described. If the biochemical mechanisms are known, simple reaction kinetics can be used and if enzymes catalyze the reaction, simple enzyme kinetics are applied. Taking into account the fact that the different elements of the system influence each other with a certain delay, delay differential equations instead of ordinary differential equations are used.

Compartmentalization of the Human Body

The human body is not a closed homogeneous system; it consists of organs and tissues etc. in which different processes take place. In order to reduce biological complexity, the body parts that are essential in the processes are extracted and divided into discrete body elements, referred to as compartments (Andersen, 1991) that are interconnected via the shared blood system (Luecke & Wosilait, 1979), here called transport compartment. The characteristics of compartments are that isolated processes take place, but at the same time they can interact with each other. The model formulating the relations between these compartments is called compartmental model (Takeuchi et al., 2007) and this process of organizing the human body in compartments is referred to as compartmentalization which is the concept of pharmacokinetic modeling (Andersen, 1991). More precisely, physiological based compartments are used in this context since the compartments are based on the actual anatomy and physiology (Andersen, 1991).

Key Terms in this Chapter

Positive and Negative Feedback: If substrates are regulated by other substrates that inhibit or stimulate, we speak of positive and negative feedback, respectively.

Pulse Generator: There are substances that are not released at a constant rate but in pulses. In the hypothalamus there is the GnRH pulse generator responsible for the pulsatile release of GnRH. It is appropriate to choose a stochastic approach for the mathematical model.

Delay Differential Equation: The dynamics are not only dependent on the time point t but on time points that lie in the past.

Compartmentalization: The human body is divided into compartments, open systems that are interconnected.

Michaelis-Menten Mechanism: If reactions are catalyzed by enzymes, then the simplest approach for the mathematical modeling is the Michaelis-Menten mechanism.

Receptor Recycling: The unbound receptors are not active. They become activated when reacting with its ligand. After having accomplished its objective it is not degraded but returns first in an inactivatable state and then in the unbound, activatable state.

Model Decomposition: That is the partition of the mathematical model into disjoint model parts in order to simplify the parameter estimation.

Biphasic Hill Function: At low values the biphasic Hill function is decreasing and at high values increasing.

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Table of Contents
Foreword
Ralf Herwig
Preface
Andriani Daskalaki
Acknowledgment
Andriani Daskalaki
Chapter 1
Peter Ghazal
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Chapter 2
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In this chapter the authors describe systems and control theory concepts for systems biology and the corresponding implications for medicine. The... Sample PDF
Systems and Control Theory for Medical Systems Biology
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Chapter 3
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In this chapter we investigate how the inclusion of time delay alters the dynamic properties of (a) delayed protein cross talk model, (b) time delay... Sample PDF
Mathematical Description of Time Delays in Pathways Cross Talk
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Chapter 4
Elisabeth Maschke-Dutz
In this chapter basic mathematical methods for the deterministic kinetic modeling of biochemical systems are described. Mathematical analysis... Sample PDF
Deterministic Modeling in Medicine
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Chapter 5
Andrew Kuznetsov
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Synthetic Biology as a Proof of Systems Biology
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Chapter 6
Tuan D. Pham
Computational models have been playing a significant role for the computer-based analysis of biological and biomedical data. Given the recent... Sample PDF
Computational Models for the Analysis of Modern Biological Data
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Chapter 7
Vanathi Gopalakrishnan
This chapter provides a perspective on 3 important collaborative areas in systems biology research. These areas represent biological problems of... Sample PDF
Computer Aided Knowledge Discovery in Biomedicine
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Chapter 8
Thomas Meinel
The function of proteins is a main subject of research in systems biology. Inference of function is now, more than ever, required by the upcoming of... Sample PDF
Function and Homology of Proteins Similar in Sequence: Phylogenetic Profiling
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Chapter 9
Nikolaos G. Sgourakis, Pantelis G. Bagos, Stavros J. Hamodrakas
GPCRs comprise a wide and diverse class of eukaryotic transmembrane proteins with well-established pharmacological significance. As a consequence of... Sample PDF
Computational Methods for the Prediction of GPCRs Coupling Selectivity
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Chapter 10
Pantelis G. Bagos, Stavros J. Hamodrakas
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Bacterial ß-Barrel Outer Membrane Proteins: A Common Structural Theme Implicated in a Wide Variety of Functional Roles
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Chapter 11
L.K. Flack
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Clustering Methods for Gene-Expression Data
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Chapter 12
George Sakellaropoulos, Antonis Daskalakis, George Nikiforidis, Christos Argyropoulos
The presentation and interpretation of microarray-based genome-wide gene expression profiles as complex biological entities are considered to be... Sample PDF
Uncovering Fine Structure in Gene Expression Profile by Maximum Entropy Modeling of cDNA Microarray Images and Kernel Density Methods
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Chapter 13
Wasco Wruck
This chapter describes the application of the BeadArrayTM technology for gene expression profiling. It introduces the BeadArrayTM technology, shows... Sample PDF
Gene Expression Profiling with the BeadArrayTM Platform
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Chapter 14
Djork-Arné Clevert, Axel Rasche
Readers shall find a quick introduction with recommendations into the preprocessing of Affymetrix GeneChip® microarrays. In the rapidly growing... Sample PDF
The Affymetrix GeneChip® Microarray Platform
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Chapter 15
Jacek Majewski
Eukaryotic genes have the ability to produce several distinct products from a single genomic locus. Recent developments in microarray technology... Sample PDF
Alternative Isoform Detection Using Exon Arrays
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Chapter 16
Prerak Desai
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Gene Expression in Microbial Systems for Growth and Metabolism
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Chapter 17
Heike Stier
Alternative splicing is an important part of the regular process of gene expression. It controls time and tissue dependent expression of specific... Sample PDF
Alternative Splicing and Disease
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Chapter 18
Axel Kowald
Aging is a complex biological phenomenon that practically affects all multicellular eukaryotes. It is manifested by an ever increasing mortality... Sample PDF
Mathematical Modeling of the Aging Process
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Chapter 19
Evgenia Makrantonaki
This chapter introduces an in vitro model as a means of studying human hormonal aging. For this purpose, human sebaceous gland cells were maintained... Sample PDF
The Sebaceous Gland: A Model of Hormonal Aging
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Chapter 20
R. Seigneuric, N.A.W. van Riel, M.H.W. Starmans, A. van Erk
Complex diseases such as cancer have multiple origins and are therefore difficult to understand and cure. Highly parallel technologies such as DNA... Sample PDF
Systems Biology Applied to Cancer Research
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Chapter 21
Matej Orešic, Antonio Vidal-Puig
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Systems Biology Strategies in Studies of Energy Homeostasis In Vivo
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Chapter 22
Axel Rasche
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Approaching Type 2 Diabetes Mellitus by Systems Biology
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Chapter 23
Alia Benkahla, Lamia Guizani-Tabbane, Ines Abdeljaoued-Tej, Slimane Ben Miled, Koussay Dellagi
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Systems Biology and Infectious Diseases
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Chapter 24
Daniela Albrecht, Reinhard Guthke
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Systems Biology of Human-Pathogenic Fungi
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Chapter 25
Jessica Ahmed
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Development of Specific Gamma Secretase Inhibitors
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Chapter 26
Paul Wrede
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In Machina Systems for the Rational De Novo Peptide Design
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Chapter 27
Ferda Mavituna, Raul Munoz-Hernandez, Ana Katerine de Carvalho Lima Lobato
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Applications of Metabolic Flux Balancing in Medicine
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Chapter 28
Roberta Alfieri, Luciano Milanesi
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Multi-Level Data Integration and Data Mining in Systems Biology
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Chapter 29
Hendrik Hache
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Methods for Reverse Engineering of Gene Regulatory Networks
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Chapter 30
Alok Mishra
This chapter introduces the techniques that have been used to identify the genetic regulatory modules by integrating data from various sources. Data... Sample PDF
Data Integration for Regulatory Gene Module Discovery
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Chapter 31
Elizabeth Santiago-Cortés
Biological systems are composed of multiple interacting elements; in particular, genetic regulatory networks are formed by genes and their... Sample PDF
Discrete Networks as a Suitable Approach for the Analysis of Genetic Regulation
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Chapter 32
A. Maffezzoli
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Chapter 33
Paolo Vicini
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The System for Population Kinetics: Open Source Software for Population Analysis
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Chapter 34
Julia Adolphs
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Photosynthesis: How Proteins Control Excitation Energy Transfer
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Chapter 35
Michael R. Hamblin
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Photodynamic Therapy: A Systems Biology Approach
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Chapter 36
Andriani Daskalaki
Photodynamic Therapy (PDT) involves administration of a photosensitizer (PS) either systemically or locally, followed by illumination of the lesion... Sample PDF
Modeling of Porphyrin Metabolism with PyBioS
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Chapter 37
Alexey R. Brazhe, Nadezda A. Brazhe, Alexey N. Pavlov, Georgy V. Maksimov
This chapter describes the application of interference microscopy and double-wavelet analysis to noninvasive study of cell structure and function.... Sample PDF
Interference Microscopy for Cellular Studies
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Chapter 38
Cathrin Dressler, Olaf Minet, Urszula Zabarylo, Jürgen Beuthan
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Fluorescence Imaging of Mitochondrial Long-Term Depolarization in Cancer Cells Exposed to Heat-Stress
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Chapter 39
Athina Theodosiou, Charalampos Moschopoulos, Marc Baumann, Sophia Kossida
In previous years, scientists have begun understanding the significance of proteins and protein interactions. The direct connection of those with... Sample PDF
Protein Interactions and Diseases
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Chapter 40
Bernard de Bono
From a genetic perspective, disease can be interpreted in terms of a variation in molecular sequence or expression (dose) that impairs normal... Sample PDF
The Breadth and Depth of BioMedical Molecular Networks: The Reactome Perspective
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Chapter 41
Jorge Numata
Thermodynamics is one of the best established notions in science. Some recent work in biomolecular modeling has sacrificed its rigor in favor of... Sample PDF
Entropy and Thermodynamics in Biomolecular Simulation
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Chapter 42
Isabel Reinecke, Peter Deuflhard
In this chapter some model development concepts can be used for the mathematical modeling in physiology as well as a graph theoretical approach for... Sample PDF
Model Development and Decomposition in Physiology
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Chapter 43
Mohamed Derouich
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Chapter 44
Mohamed Derouich
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Dengue Fever: A Mathematical Model with Immunization Program
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Chapter 45
Ross Foley
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Automated Image Analysis Approaches in Histopathology
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