Mathematical modeling of the impact of RBC aggregation and deformation parameters on blood rheological properties
Authors: Sniadovskyi Vladyslav 
Published: December 2024

The subject of the research is mathematical modeling of the rheological properties of blood, in particular the influence of basic parameters such as hematocrit, erythrocyte aggregation force, shear modulus and bending stiffness, on changes in blood viscosity. In particular, the relationship between the aggregation and deformation properties of erythrocytes and the rheological behavior of blood under shear flow conditions is analyzed. The purpose of the work is mathematical modeling of the influence of the main physical and biological parameters on the rheological properties of blood using the Dissipative Particle Dynamics (DPD) method and the MS-RBC model. Modeling makes it possible to investigate how changes in the characteristics of erythrocytes affect the viscosity of blood at different shear rates, as well as to develop predictive models for accurate determination of the rheological properties of blood, which is important for the diagnosis and treatment of vascular diseases. Task: description of a mathematical model for the rheological properties of blood, which takes into account changes in hematocrit, erythrocyte aggregation, erythrocyte deformation and shear modulus, use the Dissipative Particle Dynamics method to model the behavior of erythrocytes in blood flow and to study the effect of parameters on blood viscosity at different shear rates . Conduct a sensitivity analysis of key model parameters, such as hematocrit and erythrocyte aggregation force, and determine how changes in these parameters affect the rheological behavior of blood. Methods: Dissipative Particle Dynamics (DPD): Used to model the movement of particles (erythrocytes) in shear flow conditions and to take into account the non-Newtonian behavior of blood. This method allows for a detailed description of the interaction between individual blood components, taking into account their physical and biological characteristics. MS-RBC (Multi-Scale Red Blood Cell) Model is a multi-scale model for describing the mechanical and rheological properties of erythrocytes in the blood flow, which enables the calculation of blood viscosity depending on the shear rate, aggregation of erythrocytes and their deformation. The main results reflect that mathematical modeling of the rheological behavior of blood, which demonstrated that the viscosity of blood largely depends on the mechanical properties of erythrocytes, in particular on the shear modulus and the force of erythrocyte aggregation. The dependence of viscosity on the shear modulus was expressed by a linear equation, which showed an increase in viscosity with an increase in the shear modulus. In addition, the simulation results confirmed that at low shear rates, blood viscosity significantly depends on erythrocyte aggregation, while at high shear rates, the deformation characteristics of erythrocytes are more important. Additionally, the relationship between the model parameter  and the clinical parameter describing the properties of the erythrocyte membrane was considered. The results showed that stiffer erythrocyte membranes lead to increased blood viscosity at high shear rates. Conclusion: Modeling of erythrocyte aggregation and blood viscosity makes it possible to more accurately predict the rheological properties of blood, taking into account the mechanical characteristics of erythrocytes. Developed linear relationships between model parameters and clinical outcomes allow models to be adapted. This makes it possible to more accurately assess the rheological properties of blood, which is important for the diagnosis and treatment of various vascular diseases associated with erythrocyte aggregation disorders.