Моделирование транспорта кислорода в организме человека

This work offers a three-dimensional model of erythrocyte motion in the capillary with an account for erythrocyte rolling, volume and e surface area. This model was used to study the motion of red blood cells in the capillary, considering membrane mobility, erythrocyte’s shape and position in the capillary, as well as stability of the cell’s volume and surface area. The study became a basis for numerical estimates and approximation formulas of the resistance exerted by erythrocytes while moving along the vessel, depending on microhemodynamical parameters (blood vessel diameter, plasma viscosity and erythrocyte content, Young’s modulus, speed, cell’s volume and surface area). We have developed a model of a red blood cell aggregation moving through capillary fragments, obtained numerical estimates of the blood flow and vascular resistance of the capillary network, estimated the approximation expression of pressure difference allowing for the blood flow and depending on the hematocrit, plasma viscosity, vessel diameter and length, intervals between red cells arriving in the capillary network, erythrocyte speed, volume, surface area and elastic characteristics. Another model that we have offered is the model for regulating the blood flow and transporting oxygen by vasoactive metabolic products. In this model, we made allowances for the rate of metabolic products produced in body tissues and their physical and chemical properties (such as diffusion coefficients, solubility and permeability); as oxygen transport (metabolic products) between a tissue and red blood cells (capillaries); red blood cells’ motion along the capillaries; blood vessel diameter and length (arteries, arterioles, capillaries, venules, veins); architecture of the vascular net; hematocrit; transport of metabolic products between post-capillary venules and precapillary arterioles; changes in arteriolar diameter when smooth arteriole muscles are affected by vasoactive metabolic products; veno-arterial difference at the ends of the vascular net; hemodynamics in the blood flow. This model allowed us to study the regulation of blood flow and oxygen transport in the tissues, and to consider, along with the oxygen released by red blood cells and absorbed by body tissues, such parameters as vasoactive metabolic products released by body tissues, transport of such metabolic products to the venous net and further on to precapillary arterioles, where they affect arteriolar muscles and lead to changes in the cross-sectional area of arterioles, which, in its turn, affects hemodynamics in the blood flow, and hence the oxygen transport in the body tissues. Based on these studies, we have obtained numerical estimates and approximation formulas of the time required by the oxygen transport system (OTS) to go from one steady state to another, as well as estimated for blood flow velocity depending on the veno-arterial pressure difference at the ends of the vascular net and the rate of oxygen consumption. This paper also decribes an algorithm for assessing the state of the OTS in the human body judging from the heart rhythm. We have obtained numerical evaluation for the state of OTS of healthy volunteers and introduced an index of OTS state, which can be used to assess general physical working capacity (with an average load) for industrial and other employees. The paper offeres an algorithm for assessing OTS in the body allowing us to evaluate OTS in the case we lack certain data, which is particularly important in the case when we deal with patients rather than with healthy volunteers. In addition, this approach allows us to identify the ways to correct OTS considering the resources available.