Using a General Algebraic Formula to Identify the Primary Mechanical Properties Impacting Blood Loss Capacity

Abstract

The physiological response to hypovolemia is conventionally characterized in terms of clinical symptoms rather than fundamental homeostatic mechanisms. It is well understood how complex changes in the mechanical properties of the ventricles and the vasculature are coordinated to regulate arterial pressure and cardiac output. However, these mechanical properties in animal models are difficult to measure and control. Although complex mathematical models of the cardiovascular system have been developed to predict how changes in mechanical properties affect hemodynamic variables, solutions require assumption of a specific set of parameter values that characterizes each subject. Unlike complex mathematical models, however, equations characterizing simple closed-loop cardiovascular models can be solved algebraically, which provides general algebraic formulas applicable to all mammals in health and disease. Therefore, the purpose of the present work is to use a simple closed-loop model to develop an algebraic formula for maximum blood loss in terms of the mechanical properties of the cardiovascular system. First, the standard minimal closed-loop model was assumed, consisting of four vascular compartments, two ventricles, and two resistances. Second, to solve the set of eight model equations algebraically, the ventricular end-diastolic pressure-volume relationships were linearized. Third, the impact of the baroreflex was assumed to be limited by a maximum heart rate and cardiac contractility, as well as a maximum change in unstressed vascular volumes. Fourth, the blood loss capacity was assumed to be exhausted when mean arterial pressure and cardiac output have reached their minimum levels following failure of homeostatic mechanisms. For healthy adults, it was found that the mechanical properties having the greatest impact on blood loss capacity are venous compliances, ventricular diastolic stiffness, and the maximum change in vascular unstressed volume. This algebraic formula is a novel tool for clinical investigators to address challenges as diverse as comparing experimental results across mammalian species, identifying risk factors for adverse outcomes, and exploring new clinical strategies to extend blood loss capacity.