To better understand the mechanisms leading to the formation and growth of mural thrombi on biomaterials, we have developed a two-dimensional computational model of platelet deposition and activation in flowing blood. The basic formulation is derived from prior work by others, with additional levels of complexity added where appropriate. It is comprised of a series of convection-diffusion-reaction equations which simulate platelet-surface and platelet-platelet adhesion, platelet activation by a weighted linear combination of agonist concentrations, agonist release and synthesis by activated platelets, platelet-phospholipid-dependent thrombin generation, and thrombin inhibition by heparin. The model requires estimation of four parameters to fit it to experimental data: shear-dependent platelet diffusivity and resting and activated platelet-surface and platelet-platelet reaction rate constants. The model is formulated to simulate a wide range of biomaterials and complex flows. In this article we present the basic model and its properties; in Part II (Sorensen et al., Ann. Biomed. Eng. 27:449-458, 1999) we apply the model to experimental results for platelet deposition onto collagen.

Experimental and computational studies were performed to elucidate the role of turbulent stresses in mechanical blood damage (hemolysis). A suspension of bovine red blood cells (RBC) was driven through a closed circulating loop by a centrifugal pump. A small capillary tube (inner diameter 1 mm and length 70 mm) was incorporated into the circulating loop via tapered connectors. The suspension of RBCs was diluted with saline to achieve an asymptotic apparent viscosity of 2.0 +/- 0.1 cP at 23 degrees C to produce turbulent flow at nominal flow rate and pressure. To study laminar flow at the identical wall shear stresses in the same capillary tube, the apparent viscosity of the RBC suspension was increased to 6.3 +/- 0.1 cP (at 23 degrees C) by addition of Dextran-40. Using various combinations of driving pressure and Dextran mediated adjustments in dynamic viscosity Reynolds numbers ranging from 300-5,000 were generated, and rates of hemolysis were measured. Pilot studies were performed to verify that the suspension media did not affect mechanical fragility of the RBCs. The results of these bench studies demonstrated that, at the same wall shear stress in a capillary tube, the level of hemolysis was significantly greater (p < 0.05) for turbulent flow as compared with laminar flow. This confirmed that turbulent stresses contribute strongly to blood mechanical trauma. Numerical predictions of hemolysis obtained by computational fluid dynamic modeling were in good agreement with these experimental data.

The time-varying history of stress exposure within a rotary blood pump makes it difficult to arrive at a quantifiable design criterion for predicting cell traumatization. Constant stress experiments have revealed that there is a threshold stress level above which damage to blood cells occurs depending upon the time of exposure. The shear stress history experienced by cells within a rotary blood pump, however, is highly unsteady. In order to better predict cell trauma under these realistic conditions, a mathematical damage model based on a concept of "damage accumulation" has been developed. This model is evaluated within the context of red cell trauma. Experimental results support the hypothesis that the rate of damage accumulation increases nonlinearly with the stress level as well as the age of the cell.

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