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Window Proper Orthogonal Decomposition: Application to Continuum and Atomistic Data
Proper Orthogonal Decomposition (POD) is a powerful tool for analyzing multidimensional data, especially of vector fields in large-scale simulations....
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Quantifying and Reducing Uncertainty about Causality in Improving Public Health and Safety
Effectively managing uncertain health, safety, and environmental risks requires quantitative methods for quantifying uncertain risks, answering the...
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Controlling Chaos in the Heart: Some Mathematics Behind Terminating Cardiac Arrhythmias
Precisely coordinated rhythmic contraction of heart muscle tissue is essential for the effective pum** of blood, and abnormal cardiac rhythms...
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Pulsatile blood flow in large arteries: comparative study of Burton’s and McDonald’s models
To get a clear picture of the pulsatile nature of blood flow and its role in the pathogenesis of atherosclerosis, a comparative study of blood flow...
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Mathematical Models of Cellular Bioelectrical Activity
In this chapter, we briefly review the main mathematical models used in cellular electrophysiology, and we refer to [212, 273] for a more complete...
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Mathematical Models of Cardiac Cells Arrangements: The Bidomain Model
We model an excitable cell as a long cylindrical cable and assume the so-called core conduction assumption, stating that the potential along the...
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Influence of random uncertainties of anisotropic fibrous model parameters on arterial pressure estimation
This paper deals with a stochastic approach based on the principle of the maximum entropy to investigate the effect of the parameter random...
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Predicting the risk factors of coronary tortuosity
The risk factors of coronary tortuosity are identified using binary logistic regression and discriminant analysis methods. The qualities of the...
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Other Distances
In this chapter we group together distances and distance paradigms which do not fit in the previous chapters, being either too practical (as in...
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Mathematical modeling of lactate metabolism with applications to sports
Based on a mathematical model of the blood circulatory system, we construct a mathematical model for lactate metabolism in a human body. We pose the...
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Fluid–Structure Interaction in Hemodynamics: Modeling, Analysis, and Numerical Simulation
Fluid–structure interaction (FSI) problems arise in many applications. They include multi-physics problems in engineering such as aeroelasticity and...
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Parameter Estimation of a Model for Baroreflex Control of Unstressed Volume
The baroreflex involves a number of control pathways. In this chapter we consider in greater detail the role of the control of unstressed volume...
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Merging Mathematical and Physiological Knowledge: Dimensions and Challenges
This chapter introduces the main theoretical and practical topics which arise in the mathematical modeling of the human cardiovascular–respiratory...
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Development of Patient Specific Cardiovascular Models Predicting Dynamics in Response to Orthostatic Stress Challenges
Physiological realistic models of the controlled cardiovascular system are constructed and validated against clinical data. Special attention is paid...
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Semi-classical signal analysis
This study introduces a new signal analysis method, based on a semi-classical approach. The main idea in this method is to interpret a pulse-shaped...
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Probability Distributions
This first chapter on probability is narrowly focused on probability distributions. The initial section presents the basics of descriptive statistics...
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Working with Probability
Chapter 3 was a coherent presentation of material on descriptive statistics and probability distributions, which are viewed as theoretical...
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Physical determining factors of the arterial pulse waveform: theoretical analysis and calculation using the 1-D formulation
The shape of the arterial pulse waveform is intimately related to the physical properties of the cardiovascular system. It is clinically relevant to...
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Other Distances
In this chapter we group together distances and distance paradigms which do not fit in the previous chapters, being either too practical (as in...
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Recursive Partitioning and Tree-Based Methods
An algorithm known as recursive partitioning is the key to the nonpara- metric statistical method of classification and regression trees (CART)...