Mathematical model of blunt injury to the vascular wall via formation of rouleaux and changes in local hemodynamic and rheological factors. Implications for the mechanism of traumatic myocardial infarction

BACKGROUND: Blood viscosity is fundamentally important in clinical practice yet the apparent viscosity at very low shear rates is not well understood. Various conditions such as blunt trauma may lead to the appearance of zones inside the vessel where shear stress equals zero. The aim of this research was to determine the blood viscosity and quantitative aspects of rouleau formation from erythrocytes at yield velocity (and therefore shear stress) equal to zero. Various fundamental differential equations and aspects of multiphase medium theory have been used. The equations were solved by a method of approximation. Experiments were conducted in an aerodynamic tube. RESULTS: The following were determined: (1) The dependence of the viscosity of a mixture on volume fraction during sedimentation of a group of particles (forming no aggregates), confirmed by published experimental data on the volume fractions of the second phase (f(2)) up to 0.6; (2) The dependence of the viscosity of the mixture on the volume fraction of erythrocytes during sedimentation of rouleaux when yield velocity is zero; (3) The increase in the viscosity of a mixture with an increasing erythrocyte concentration when yield velocity is zero; (4) The dependence of the quantity of rouleaux on shear stress (the higher the shear stress, the fewer the rouleaux) and on erythrocyte concentration (the more erythrocytes, the more rouleaux are formed). CONCLUSIONS: This work represents one of few attempts to estimate extreme values of viscosity at low shear rate. It may further our understanding of the mechanism of blunt trauma to the vessel wall and therefore of conditions such as traumatic acute myocardial infarction. Such estimates are also clinically significant, since abnormal values of blood viscosity have been observed in many pathological conditions such as traumatic crush syndrome, cancer, acute myocardial infarction and peripheral vascular disease.