the Mathematics of Living Body

The Mathematics of the Living Body, Volume 1: Cardiovascular PhysiologyZachariah Sinkala - Zachariah Sinkala PublishingThis 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.

Pagina's: 282, Paperback, Zachariah Sinkala