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This volume synthesizes theoretical and practical aspects of both
the mathematical and life science viewpoints needed for modeling of
the cardiovascular-respiratory system specifically and
physiological systems generally. Theoretical points include model
design, model complexity and validation in the light of available
data, as well as control theory approaches to feedback delay and
Kalman filter applications to parameter identification. State of
the art approaches using parameter sensitivity are discussed for
enhancing model identifiability through joint analysis of model
structure and data. Practical examples illustrate model development
at various levels of complexity based on given physiological
information. The sensitivity-based approaches for examining model
identifiability are illustrated by means of specific modeling
examples. The themes presented address the current problem of
patient-specific model adaptation in the clinical setting, where
data is typically limited.
Stochastic biomathematical models are becoming increasingly
important as new light is shed on the role of noise in living
systems. In certain biological systems, stochastic effects may even
enhance a signal, thus providing a biological motivation for the
noise observed in living systems. Recent advances in stochastic
analysis and increasing computing power facilitate the analysis of
more biophysically realistic models, and this book provides
researchers in computational neuroscience and stochastic systems
with an overview of recent developments. Key concepts are developed
in chapters written by experts in their respective fields. Topics
include: one-dimensional homogeneous diffusions and their boundary
behavior, large deviation theory and its application in stochastic
neurobiological models, a review of mathematical methods for
stochastic neuronal integrate-and-fire models, stochastic partial
differential equation models in neurobiology, and stochastic
modeling of spreading cortical depression.
The human cardiovascular and respiratory control systems represent
an important focal point for developing physiological control
theory because of the complexity of the control mechanisms
involved, the interaction between cardiovascular and respiratory
func--tion, and the importance of this interaction in many clinical
situations. This volume brings together the range of control
processes involved in the effective regulation of these systems and
develops modeling themes, strategies, and key clinical applications
using contemporary mathematical and control methodologies. The
reader will gain an appreciation of how analytical techniques and
ideas from optimal control theory, systems theory, and numerical
analysis can be utilized to better understand the regulation
processes in human cardiovascular and respiratory systems.
Cardiovascular and Respiratory Systems uses a principle-based
modeling approach and analysis of feedback control regulation to
elucidate the physiological relationships. Models are arranged
around specific questions or conditions, such as exercise or sleep
transition, and are generally based on physiological mechanisms
rather than on formal descriptions of input-output behavior. The
authors ask open questions relevant to medical and clinical
applications and clarify underlying themes of physiological control
organization. Current problems, key issues, developing trends, and
unresolved questions are highlighted.
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