Introduction

Abstract

The human body is an intricate network of multiple functioning sub-systems. Many unobserved processes quietly keep running within the body even while we remain largely unconscious of them. For decades, scientists have sought to understand how different physiological systems work and how they can be mathematically modeled. Mathematical models of biological systems provide key scientific insights and also help guide the development of technologies for treating disorders when proper functioning no longer occurs. One of the challenges encountered with physiological systems is that, in a number of instances, the quantities we are interested in are difficult to observe directly or remain completely inaccessible. This could be either because they are located deep within the body or simply because they are more abstract (e.g., emotion). Consider the heart, for instance. The left ventricle pumps out blood through the aorta to the rest of the body. Blood pressure inside the aorta (known as central aortic pressure) has been considered a useful predictor of the future risk of developing cardiovascular disease, perhaps even more useful than the conventional blood pressure measurements taken from the upper arm (McEniery et al. (Eur Heart J 35(26):1719–1725, 2014)). However, measuring blood pressure inside the aorta is difficult. Consequently, researchers have had to rely on developing mathematical models with which to estimate central aortic pressure using other peripheral measurements (e.g., Ghasemi et al. (J Dyn Syst Measur Control 139(6):061003, 2017)). The same could be said regarding the recovery of CRH (corticotropin-releasing hormone) secretion timings within the hypothalamus—a largely inaccessible structure deep within the brain—using cortisol measurements in the blood based on mathematical relationships (Faghih (System identification of cortisol secretion: Characterizing pulsatile dynamics, Ph.D. dissertation, Massachusetts Institute of Technology, 2014)). Emotions could also be placed in this same category. They are difficult to measure because of their inherently abstract nature. Emotions, however, do cause changes in heart rate, sweating, and blood pressure that can be measured and with which someone’s feelings can be estimated. What we have described so far, in a sense, captures the big picture underlying this book. We have physiological quantities that are difficult to observe directly, we have measurements that are easier to acquire, and we have the ability to build mathematical models to estimate those inaccessible quantities.