Modeling the Circulatory System By Considering the Effects of Heart Rate Variability and Fluid Pressure Dynamics

The purpose of the cardiovascular system is to deliver metabolic substrate and remove heat and other metabolic byproducts from the tissues of the body.  Optimal function of the cardiovascular system requires operation as a constant-pressure system such that peripheral organs/tissues are treated as resistors aligned in a parallel circuit (following Ohm’s Law).  The heart is a rhythmical pump that generates a force that gives rise to the system’s fluid pressure. This pressure is ultimately modified by blood flow and system resistance resulting in an exit pressure that determines the facility of metabolic balance. Recently, much has been made about the importance of rhythm variability in biological systems in optimizing function and reducing system fatigue.  Heart rate rhythm variability, Traube-Hering waves, aortic reflective waves, body water minute waves, and arterial and venous wall elasticity are non-constant variables key in regulating pressure and cardiovascular function.  Interestingly, computational models of the cardiovascular system have not placed a high degree of consideration towards an understanding of how these phenomena can be represented mathematically to more completely understand cardiovascular regulation. Therefore, the purpose of the present analysis is to begin to develop a model of the cardiovascular system based on fluid dynamics that considers the described characteristics of heart rate variability and fluid pressure dynamics in order to create a more authentic computational model.  For this purpose, our proposed model treats the cardiovascular system as a motor-generator system designed to provide a relatively constant system pressure.  In this model, the heart is a constant rhythm pump (motor) and the autonomic nervous system is a variable rhythm generator which has the unique ability to alter pump rhythm and system conduit resistance while achieving constant pressure.  Variability of system resistance is modeled by a series of nozzles acting as a simple Windkessel in concert with flow wave harmonics which dissipate pressure as flow is propagated through the system.   Return of fluid to the pump is modeled as a turbine providing a secondary pressure generator facilitating fluid return to the pump. System resistance due to fluid viscosity and vessel elasticity are modeled as effects of non-conservative forces. An initial attempt to diagram this model will be presented based on published data. Further, initial experiments to test our model have focused on the effect of changes in heart rate and autonomic balance. Data analysis of the performance of various intensities of physical activity and the change in sympathetic and parasympathetic balance from 0530 to 1730 show that the sympathetic nervous system actually reduces heart rate variability and that sympathetic balance decreases significantly in the afternoon hours. These results will allow us to set limits of the generator on regulating pump rhythm.