Mathematical Modeling and Validation in Physiology: Applications to the Cardiovascular and Respiratory Systems (Lecture Notes in Mathematics Book 2064)

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 Front Matter....Pages i-xx Front Matter....Pages 1-1 Merging Mathematical and Physiological Knowledge: Dimensions and Challenges....Pages 3-19 Mathematical Modeling of Physiological Systems....Pages 21-41 Parameter Selection Methods in Inverse Problem Formulation....Pages 43-73 Application of the Unscented Kalman Filtering to Parameter Estimation....Pages 75-88 Integrative and Reductionist Approaches to Modeling of Control of Breathing....Pages 89-103 Parameter Identification in a Respiratory Control System Model with Delay....Pages 105-118 Front Matter....Pages 119-119 Experimental Studies of Respiration and Apnea....Pages 121-132 Model Validation and Control Issues in the Respiratory System....Pages 133-162 Experimental Studies of the Baroreflex....Pages 163-176 Development of Patient Specific Cardiovascular Models Predicting Dynamics in Response to Orthostatic Stress Challenges....Pages 177-213 Parameter Estimation of a Model for Baroreflex Control of Unstressed Volume....Pages 215-246 Back Matter....Pages 247-254