Complex Systems in Biomedicine
Complex Systems in Biomedicine
By A. Quarteroni, L. Formaggia, A. Veneziani
Publisher: Springer
Number Of Pages: 292
Publication Date: 2006-07-11
ISBN-10 / ASIN: 8847003946
ISBN-13 / EAN: 9788847003941
Binding: Hardcover
Mathematical modeling of human physiopathology is a tremendously
ambitious task. It encompasses the modeling of most diverse
compartments such as the cardiovascular, respiratory, skeletal and
nervous systems, as well as the mechanical and biochemical interaction
between blood flow and arterial walls, or electrocardiac processes and
the electric conduction into biological tissues. Mathematical models
can be set up to simulate both vasculogenesis (the aggregation and
organisation of endothelial cells dispersed in a given environment) and
angiogenesis (the formation of new vessels sprouting from an existing
vessel) that are relevant to the formation of vascular networks, and in
particular to the description of tumor growth. The integration of
models aimed at simulating the cooperation and interrelation of
different systems is an even more difficult task. It calls for the set
up of, for instance, interaction models for the integrated
cardio-vascular system and the interplay between central circulation
and peripheral compartments, models for the mid-long range
cardiovascular adjustments to pathological conditions (e.g. to account
for surgical interventions, congenital malformations, or tumor growth),
models for the integration among circulation, tissue perfusion,
biochemical and thermal regulation, models for parameter identification
and sensitivity analysis to parameter changes or data uncertainty and
many others. The heart is a complex system in itself, where electrical
phenomena are functionally related with the wall deformation. In its
turn, electrical activity is related with heart physiology. It involves
nonlinear reaction-diffusion processes and provides the activation
stimulus to the heart dynamics and eventually the blood ventricular
flow that drives the haemodynamics of the whole circulatory system. In
fact, the influence is reciprocal, since the circulatory system in
turns affects the heart dynamics and may induce an overload depending
upon the individual physiopathologies ( for instance the presence of a
stenotic artery or a vascular prosthesis).Virtually, all the fields of
mathematics have a role to play in this context. Geometry and
approximation theory provide the tools for handling clinical data
acquired by tomography or magnetic resonance, identifying meaningful
geometrical patterns and producing three-dimensional geometrical models
stemming from the original patients data. Mathematical analysis, flow
and solid dynamics, stochastic analysis are used to set up the
differential models and predict uncertainty. Numerical analysis and
high performance computing are needed to numerically solve the complex
differential models. Finally, methods from stochastic and statistical
analysis are exploited for the modeling and interpretation of
space-time patterns. Indeed, the complexity of the problems at hand
often stimulates the use of innovative mathematical techniques that are
able, for instance, to accurately catch those processes that occur at
multiple scales in time and space (like cellular and systemic effects),
and that are governed by heterogeneous physical laws.
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Complex Systems in Biomedicine
By A. Quarteroni, L. Formaggia, A. Veneziani
Publisher: Springer
Number Of Pages: 292
Publication Date: 2006-07-11
ISBN-10 / ASIN: 8847003946
ISBN-13 / EAN: 9788847003941
Binding: Hardcover
Mathematical modeling of human physiopathology is a tremendously
ambitious task. It encompasses the modeling of most diverse
compartments such as the cardiovascular, respiratory, skeletal and
nervous systems, as well as the mechanical and biochemical interaction
between blood flow and arterial walls, or electrocardiac processes and
the electric conduction into biological tissues. Mathematical models
can be set up to simulate both vasculogenesis (the aggregation and
organisation of endothelial cells dispersed in a given environment) and
angiogenesis (the formation of new vessels sprouting from an existing
vessel) that are relevant to the formation of vascular networks, and in
particular to the description of tumor growth. The integration of
models aimed at simulating the cooperation and interrelation of
different systems is an even more difficult task. It calls for the set
up of, for instance, interaction models for the integrated
cardio-vascular system and the interplay between central circulation
and peripheral compartments, models for the mid-long range
cardiovascular adjustments to pathological conditions (e.g. to account
for surgical interventions, congenital malformations, or tumor growth),
models for the integration among circulation, tissue perfusion,
biochemical and thermal regulation, models for parameter identification
and sensitivity analysis to parameter changes or data uncertainty and
many others. The heart is a complex system in itself, where electrical
phenomena are functionally related with the wall deformation. In its
turn, electrical activity is related with heart physiology. It involves
nonlinear reaction-diffusion processes and provides the activation
stimulus to the heart dynamics and eventually the blood ventricular
flow that drives the haemodynamics of the whole circulatory system. In
fact, the influence is reciprocal, since the circulatory system in
turns affects the heart dynamics and may induce an overload depending
upon the individual physiopathologies ( for instance the presence of a
stenotic artery or a vascular prosthesis).Virtually, all the fields of
mathematics have a role to play in this context. Geometry and
approximation theory provide the tools for handling clinical data
acquired by tomography or magnetic resonance, identifying meaningful
geometrical patterns and producing three-dimensional geometrical models
stemming from the original patients data. Mathematical analysis, flow
and solid dynamics, stochastic analysis are used to set up the
differential models and predict uncertainty. Numerical analysis and
high performance computing are needed to numerically solve the complex
differential models. Finally, methods from stochastic and statistical
analysis are exploited for the modeling and interpretation of
space-time patterns. Indeed, the complexity of the problems at hand
often stimulates the use of innovative mathematical techniques that are
able, for instance, to accurately catch those processes that occur at
multiple scales in time and space (like cellular and systemic effects),
and that are governed by heterogeneous physical laws.
6729 KB RAR'd PDF
pass: giga
http://rapidshare.com/files/24148492/Qua_ComSysinBioMed.rar
