# Numerical Modelling of Erythrocyte Sticking Mechanics
## 2 Problem Formulation  
Thrombosis is usually caused by damage to the wall of the blood vessel, blood composition, and increased blood clotting. In this work, a part of thrombus formation was chosen for study, i.e., when the erythrocyte begins to interact with fibrin and activated platelets. The problem is related to the interaction of the erythrocyte in the process of sticking. The purpose of this study is to achieve erythrocyte adhesion in a numerical experiment based on the initial data taken from known physical experiments. At the same time, using the developed theoretical model, the work is also aimed at reproducing the dynamics of erythrocytes, showing the behavior of erythrocyte interactions over time. According to previous studies [31], an erythrocyte is not prone to adherence, even when deformed at a distance from the vessel surface. However, during the formation of a clot, its behavior should involve the adhesion process, the behavior and mechanics of which are not clear. In this work, the main attention is paid to solving the above problem using the numerical simulation method. Additionally, the mechanical parameters of the thrombus components (platelets, fibrin) taken from the known literature are presented.  
The question arises of how the behavior of cells can be different when sticking in a liquid. Mechanical parameters (Table 1) are taken from known physical experiments and used in the presented developed model. Taking into account these parameters, in this work, the interaction at a distance of a blood cell is reproduced and modeled. At the same time, different behavior of the cell during interaction was obtained, different modeling possibilities were shown, and attention was paid to the influence of the liquid. One of the objectives of the study is to obtain the sticking process, in which the erythrocyte (red blood cell) oscillates on the interacting surface. However, as further studies will show, oscillations under the action of a fluid (due to the drag force) may not occur. It is under the action of the liquid that the erythrocyte can be additionally deformed (only the process of loading occurs) when interacting with the surface, and because of which the erythrocyte stops as a result.  
The first stage of the study of the interaction of red blood cells (RBC), presented in the publication [31], concerned the question of whether a blood cell can reach the surface of a blood vessel (the case when a thrombus is not formed); such a study of cell mechanics was not found in the known literature. The revealed effects were not previously observed, namely, the deformation of the cell in the absence of contact. This has become possible for soft matter such as a cell. In the second case, the present publication took the next step. In this case, the interaction of an erythrocyte cell with a blood clot was considered. This stands out as a separate case in clot formation when RBC adhere to the clot surface. Moreover, a completely different behavior of the cell was found than the accepted idea of the process of cell adhesion in air. The sticking process (with oscillations) in the liquid did not occur; this effect was not observed in the known literature. This is manifested in the completely different behavior of cells when interacting in liquid and when interacting in air.  
The tasks are completely different, but since in both cases the object is the same--an erythrocyte, and the interaction takes place in a blood vessel, the descriptions of the simulation methodology have some similarities. The initial data are supplemented with data on the blood clot, and the additional forces required to solve the new problem are estimated. Part of the description of the methodology, i.e., a detailed description of the forces, is presented in [31] and is not repeated here.