Tomáš Bodnár (TU Prag): Areal strain in hemolysis models for viscoelastic fluids flows


Abstract:  The recent advances in in the development and application of ventricular assist devices and other mechanical aids in human circulatory system revealed the need for better understanding and estimation of mechanically introduced blood damage. Several models were developed and are currently in use, based on either Eulerian or Lagrangian [1] formulations of empiric stress dependent correlations. Some of the most recent models are however exploring the possibility to use certain intermediate variable (instead of stress) to estimate blood damage [2], [3]. These are typically based on some scalar measure of local strain (deformation). Interestingly, the corresponding tensor equations are very similar to rheological models describing the viscoelastic stress tensor [4], [5]. In the present work we are are exploring the possibility to use some of the advanced rheological models of blood for direct estimate of blood damage. This effort can be seen as a continuation of development and application of the viscoelastic fluids models presented in [4], [6], [7] in the context of strain based blood damage models described in [3].

Some initial numerical experiments testing different strain indicators were performed using an in-house developed finite-volume code previously used e.g. in. [5] and [4]. Selected simulations for an axisymmetric idealized stenosed blood vessel will be presented.


References:  [1] H. Yu, S. Engel, G. Janiga, and D. Thevenin (2017). A Review of Hemolysis Prediction Models for Computational Fluid Dynamics. Artificial Organs, 41(7):603–621.

[2] P.L. Maffettone and M. Minale (1998). Equation of change for ellipsoidal drops in viscous flow. Journal of Non-Newtonian Fluid Mechanics, 78, 227–241.

[3] D. Arora, M. Behr, and M. Pasquali (2004). A Tensor-based Measure for Estimating Blood Damage. Artificial Organs 28(11):1002–1015.

[4] A. Sequeira and T. Bodnár (2022). Analysis of the Shear-Thinning Viscosity Behavior of the Johnson-Segalman Viscoelastic Fluids. Fluids 7(1), 1–24.

[5] T. Bodnár, K.R. Rajagopal and A. Sequeira (2011) Simulation of the Three-Dimensional Flow of Blood Using a Shear-Thinning Viscoelastic Fluid Model. Mathematical Modelling of Natural Phenomena. 6(5), 1–24.

[6] T. Bodnár and A. Sequeira (2014) Blood Coagulation Simulations using a Viscoelastic Model. Mathematical Modelling of Natural Phenomena. 9(6), 34–45.

[7] T. Bodnár (2014) On the Eulerian formulation of a stress induced platelet activation function. Mathematical Biosciences, 257, 91–95.

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