Constructal law prediction of cardiomyocyte membrane architecture in physiology and disease

Since its inception, the constructal law has described flows of natural and man-made systems in accordance with the foundational assertion that living systems must evolve to increase access to their constituent flow material. This paper applies the constructal law to theoretically predict the optimal geometry of the transverse tubule (t-tubule) network in cardiac muscle cells (cardiomyocytes) across species. Mathematical analysis predicts the t-tubule architecture develops an intricate branching pattern to maximize calcium delivery from the membrane to the sarcomere in response to increased contractile demand throughout development. Our model predicts that, across mammalian species, higher heart rates necessitate greater t-tubule branching consistent with the need for more rapid calcium cycling under the constraint of the thermodynamics of diffusion. In heart failure, the t-tubule network deviates from the predicted optimal architecture, correlating with contractile dysfunction severity. A novel constructal law paradigm is proposed where biological systems typically develop constructal architectures, and disease represents failure to maintain optimal architectures in response to pathological stimuli. Applying thermodynamic principles like the constructal law may elucidate key structure-function relationships and rational therapeutic targets for treating cardiac disease.