Analitical and numerical simulation of platelets in microchannels and their stress history

Microfluidic systems are emerging as potential novel flow-based assays for monitoring platelet response under controlled shear stress conditions. Current approaches for microfluidic channel design are currently based on computing basic fluid dynamic quantities (e.g. wall shear stress) from simplified formulas. However, accurate designing approaches should take into account the variability of shear stress and related physical quantities experienced by a population of platelets flowing in a channel. 3D computational fluid dynamic (CFD) models could provide accurate estimation of distributions of shear stress and related quantities in a channel, although requiring iterative and computationally demanding analyses. Thus, approximated analytical and semi-analytical models may be used to allow a fast preliminary dimensioning phase of microfluidic channels. In this work, we present the formulation of analytical models able to describe statistical distributions of shear stress and related physical quantities among a population of platelets flowing in a microfluidic channel. We also evaluate the accuracy of the models by comparing them to 3D multiphase CFD analyses of straight microfluidic channels with flowing platelets. Two analytical models were proposed based on two different approximations: a parallel plate model and a circular channel model. Good agreement was found for both models in terms of cumulative distributions of shear stress, stress accumulation and residence time among a population of platelets. In terms of probability density functions, accuracy is dependent on the aspect ratio of the channel considered. Analytical models described in this study can be also used to solve the problem of shaping a microfluidic channel so that platelets flowing therein are subjected to specific and more complex shear stress patterns with respect to time, thus providing a useful tool for the pre-dimensioning phase of microfluidic channels for controlled and dynamic shear stress exposure of platelets.