NUMERICAL IMPLEMENTATION OF A CONTINUUM PLATELET AGGREGATION MODEL

Open Access
- Author:
- Samra, Stefan Basil
- Graduate Program:
- Mechanical Engineering
- Degree:
- Master of Science
- Document Type:
- Master Thesis
- Date of Defense:
- None
- Committee Members:
- Eric G Paterson, Thesis Advisor/Co-Advisor
Eric G Paterson, Thesis Advisor/Co-Advisor - Keywords:
- openfoam
platelet aggregation
thrombosis
numerical - Abstract:
- A continuum stress transport model of platelet aggregation from the literature [14], [16], [15], and [18] is presented and solved numerically. The model is a single-scale reduction of a multi-scale model and utilizes the incompressible Navier-Stokes equations with a Newtonian constituative relationship to govern blood ow. Other eld variables including platelet and chemical activator concentrations exist with partial dierential equations governing their transport. The platelet aggregation model is closely related to the model of the viscoelastic Oldroyd-B uid, which is discussed. The focus of this thesis is on the numerical solution of the Oldroyd-B equations and the equations comprising the platelet aggregation model using a nite volume formulation within an existing open source Computational Fluid Dynamics platform. Pressure-velocity coupling is achieved using the PISO Algorithm while the remaining model equations are solved sequentially. In the rst class of simulations, the ow of an Oldroyd-B uid is solved within a two dimen- sional planar domain. The viscous and elastic properties of the uid are varied in an eort to observe the model's resulting behavior. Exact solutions for the transient and steady-state ow of an Oldroyd-B uid are used for the purpose of validating the numerical approach. Numerical solutions are observed to correspond well with exact solutions for a range of parameter sets. Solution divergence is observed under certain conditions, specically for uids with high Weis- senberg numbers and elastic moduli. In the second class of simulations, the platelet aggregation model is solved within the same domain as the Oldroyd-B simulations. Clot growth is observed but solution divergence occurs in the presence of growth of the model's stress tensor eld. By limiting certain model parameters it is shown that numerical stability can be improved. Using this approach, the sensitivity of results to various model parameters is investigated. Finally, a preliminary investigation of the application of the model to the clinically important case of clot growth within stagnant and recirculating ows is presented.