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Development of a computational model for macroscopic predictions of device-induced thrombosis

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Abstract

While cardiovascular device-induced thrombosis is associated with negative patient outcomes, the convoluted nature of the processes resulting in a thrombus makes the full thrombotic network too computationally expensive to simulate in the complex geometries and flow fields associated with devices. A macroscopic, continuum computational model is developed based on a simplified network, which includes terms for platelet activation (chemical and mechanical) and thrombus deposition and growth in regions of low wall shear stress (WSS). Laminar simulations are performed in a two-dimensional asymmetric sudden expansion geometry and compared with in vitro thrombus size data collected using whole bovine blood. Additionally, the predictive power of the model is tested in a flow cell containing a series of symmetric sudden expansions and contractions. Thrombi form in the low WSS area downstream of the asymmetric expansion and grow into the nearby recirculation region, and thrombus height and length largely remain within 95 % confidence intervals calculated from the in vitro data for 30 min of blood flow. After 30 min, predicted thrombus height and length are 0.94 and 4.32 (normalized by the 2.5 mm step height). Importantly, the model also correctly predicts locations of thrombus deposition observed in the in vitro flow cell of expansions and contractions. As the simulation results, which rely on a greatly reduced model of the thrombotic network, are still able to capture the macroscopic behavior of the full network, the model shows promise for timely predictions of device-induced thrombosis toward optimizing and expediting the device development process.

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Abbreviations

\({\varvec{u}}\) :

Velocity

p :

Pressure

t :

Time

\(\nu \) :

Kinematic viscosity

\(\rho \) :

Density

F :

Modified Brinkman function

\(\varepsilon \) :

Aggregation intensity

\(\varepsilon _\mathrm{t}\) :

Aggregation intensity threshold

k :

Thrombus permeability

Q :

Arbitrary scalar quantity

D :

Diffusivity

R :

Sources and sinks

\(\phi _\mathrm{n}\) :

Non-activated platelet concentration

\(\phi _\mathrm{a}\) :

Activated platelet concentration

\(D_\mathrm{n}\) :

Diffusion coefficient for non-activated platelets

\(D_\mathrm{a}\) :

Diffusion coefficient for activated platelets

\(A_\mathrm{C}\) :

Chemical platelet activation rate

ADP:

Adenosine diphosphate (ADP) concentration

\(\mathrm{ADP}_\mathrm{t}\) :

ADP threshold for chemical activation

\(t_\mathrm{ADP}\) :

Characteristic time for chemical activation

\(A_\mathrm{M}\) :

Mechanical platelet activation rate

\(\tau \) :

Scalar shear stress

\(\bar{{\bar{\varvec{\sigma }}}}\) :

Viscous stress tensor

\(\phi _\mathrm{f}\) :

Activated platelet fraction

C :

Power law coefficient

\(\alpha \) :

Power law coefficient

\(\beta \) :

Power law coefficient

\(D_\mathrm{ADP}\) :

Diffusion coefficient for ADP

\(R_\mathrm{ADP}\) :

Amount of ADP in a platelet

\(\alpha _\varepsilon \) :

Thrombus volumetric growth rate

\(\tau _\mathrm{w}\) :

Wall shear stress (WSS)

\(P_\mathrm{TSP}\) :

Weighting function for thrombus deposition /growth

\(\tau _\mathrm{low,wall}\) :

Low WSS threshold for thrombus deposition

\(\tau _\mathrm{high,wall}\) :

High WSS threshold for thrombus deposition

\(\tau _\mathrm{low,thrombus}\) :

Low WSS threshold for thrombus growth

\(\tau _\mathrm{high,thrombus}\) :

High WSS threshold for thrombus growth

\(\beta _\varepsilon \) :

Thrombus breakdown function

B :

Thrombus breakdown rate

\(\tau _\mathrm{breakdown,wall}\) :

WSS threshold for thrombus breakdown at a wall

\(\tau _\mathrm{breakdown,thrombus}\) :

WSS threshold for thrombus breakdown at a thrombus surface

U :

Average inlet velocity

h :

Step height

\(\phi _{\mathrm{a},i}\) :

Initial (background) concentration of activated platelets

\(\phi _{\mathrm{n},i}\) :

Initial concentration of non-activated platelets

\(t_{\mathrm{G}}\) :

Characteristic thrombus growth time

H :

Thrombus height

L :

Thrombus length

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Acknowledgments

A Walker Graduate Assistantship from the Applied Research Laboratory at the Pennsylvania State University and a Penn State Grace Woodward Foundation grant supported this work.

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Authors and Affiliations

  1. Department of Biomedical Engineering, The Pennsylvania State University, 205 Hallowell Building, University Park, PA, 16802, USA

    Joshua O. Taylor & Keefe B. Manning

  2. Applied Research Laboratory, The Pennsylvania State University, State College, PA, USA

    Joshua O. Taylor, Richard S. Meyer & Steven Deutsch

  3. Department of Surgery, Penn State Hershey Medical Center, Hershey, PA, USA

    Keefe B. Manning

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  1. Joshua O. Taylor
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  4. Keefe B. Manning
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Correspondence to Keefe B. Manning.

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Taylor, J.O., Meyer, R.S., Deutsch, S. et al. Development of a computational model for macroscopic predictions of device-induced thrombosis. Biomech Model Mechanobiol 15, 1713–1731 (2016). https://doi.org/10.1007/s10237-016-0793-2

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