A mathematical model for pressure-based organs behaving as biological pressure vessels

Abstract

We introduce a mathematical model that describes the allometry of physical characteristics of hollow organs behaving as pressure vessels based on the physics of ideal pressure vessels. The model was validated by studying parameters such as body and organ mass, systolic and diastolic pressures, internal and external dimensions, pressurization energy and organ energy output measurements of pressure-based organs in a wide range of mammals and birds. Seven rules were derived that govern amongst others, lack of size efficiency on scaling to larger organ sizes, matching organ size in the same species, equal relative efficiency in pressurization energy across species and direct size matching between organ mass and mass of contents. The lung, heart and bladder follow these predicted theoretical relationships with a similar relative efficiency across various mammalian and avian species; an exception is cardiac output in mammals with a mass exceeding 10 kg. This may limit massive body size in mammals, breaking Cope's rule that populations evolve to increase in body size over time. Such a limit was not found in large flightless birds exceeding 100 kg, leading to speculation about unlimited dinosaur size should dinosaurs carry avian-like cardiac characteristics.