The power-law mathematical model for blood damage prediction: analytical developments and physical inconsistencies

Blood trauma caused by medical devices is a major concern. Complications following the implantation/application of devices such as prosthetic heart valves, cannulae, blood pumps, tubing, and throttles lead to sublethal and lethal damage to platelets and erythrocytes. This damage is provided by the alterations in fluid dynamics, providing a mechanical load on the blood corpuscle's membrane by means of the shear stress. An appropriate quantification of the shear-induced hemolysis of artificial organs is thought to be useful in the design and development of such devices in order to minimize device-induced blood trauma. To date, a power-law mathematical relationship using the time of exposure of a blood corpuscle to a certain mechanical load and the shear stress itself (derived under the peculiar condition of uniform shear stress) has served as a basic model for the estimation of the damage to blood, investigated by means of numerical and/or experimental fluid dynamical techniques. The aim of the present article is to highlight the effect of a time-varying mechanical loading acting on blood cells based on the usual power-law model; furthermore, the effect of the loading history of a blood particle is discussed, showing how the past history of the shear acting on a blood corpuscle is not taken into account, as researchers have done until now. The need for a reassessment of the power-law model for potential blood trauma assessment is discussed by using a mathematical formulation based on the hypotheses of the existence of damage accumulation for blood with respect to time and with respect to shear stress, to be applied in complex flow fields such as the ones established in the presence of artificial organs.