The Mathematics of the Living Body, Volume 1: Cardiovascular Physiology
Zachariah Sinkala - Zachariah Sinkala Publishing
This is a physiology book written in equations - but the physiology always comes first. Every equation emerges from a named protein, a measurable cellular event, or a conservation law that the biology makes necessary.
The central argument is that the cardiovascular system is a control architecture. It is not a collection of organs with properties to memorise. It is a set of coupled feedback loops - a pressure-controlled pump regulated by a proportional-integral controller in the brainstem, a hormonal cascade in the kidney, and local autoregulation in every organ. Once you see it this way, the pharmacology, the pathology, and the clinical decision-making all follow from the same mathematical framework.
Nineteen chapters, 280 pages, 27 original figures. The book moves from physical foundations (Poiseuille flow, Windkessel compliance, pressure-volume loops) through cardiac dynamics (Frank-Starling, Hodgkin-Huxley, arrhythmia as bifurcation) and regulatory systems (baroreflex as PI controller, RAAS as enzyme cascade, cerebral autoregulation) to clinical disease states (heart failure, hypertension, shock, atherosclerosis, drug mathematics) and finally to a patient-specific digital twin framework and a full case study applying every major equation to a single real clinical scenario.
Each chapter opens with the molecular biology - named genes, named proteins, named mechanisms - before any equation appears. Each carries an explicit Model Assumptions box distinguishing core physical principles from useful approximations from empirical fits. Worked examples report ranges, not single numbers.
The reader is a medical student who already knows basic physiology and wants to know why, a biomedical engineering student who wants clinical grounding, or a quantitatively minded clinician who prefers mechanism-first explanations. It is a companion text, not a primary medical textbook - strongest for readers who want the first-principles framework underneath the clinical vocabulary they already have.
Where physiology ends, mathematics begins.
