Can Continuum Mechanics Help Us Understand Physiological Frequencies?

The human body involves many repetitive processes in which fluids move periodically, such as mucus movement during coughing, milk during feeding, tears during blinking or blood flow driven by the heart rate. We present an analytical model of an elastic-vessel network that conveys viscoelastic fluids, solvable in the frequency domain. The model incorporates key physical principles: momentum and mass conservation, a Hooke-like description for the vessels, and experimental data on fluid properties. The model was validated by comparing flow and pressure waveforms with those from a fully nonlinear 3D model of the human arterial system for Newtonian fluids [1]. We report new results for the frequency that minimizes resistance to blood flow in a model of the human arterial tree with the experimental rheology of human blood [2], and for a model of the mammalian arterial vasculature [3]. Our model provides a reasonable explanation for pulsatile physiological frequencies, being the ones that minimize resistance to flow throughout the network. We find good agreement with a scaling law for species ranging from ferrets to elephants, derived from heart rate data in the literature for 95 mammals. Preliminary results on synovial fluid in the knee indicate that the model does not predict frequencies when these ones can vary continuously depending on the activity (e.g., walking and running) but are zero at rest. However, the model may help explain how fluid mechanical properties influence certain diseases.