ENGINEERING MECHANICS OF THROMBOLYSIS

Objective: The objective of this research is to investigate the mechanical deformation of a thrombus (blood clot), as well as analyze its detachment from the vessel walls using Fluid Structure Interaction module in 3-dimensional modeling software, COMSOL Multiphysics®. Figure 1: Platelets + Fibrin + RBC (Denoble) 4

Background: Blood coagulation is the regulatory mechanism for preventing excessive blood loss at the site of an injury4. However without an extensive clear out of the clot build up in the arteries, this mechanism becomes one of the leading causes of cardiovascular diseases. Blood clots that develop inside the blood vessels can cause heart attacks and strokes. Therefore, the prediction of mechanical properties of blood clots can help enhancing the fractionation of the clot tissues. Based on existing clinical procedures for thrombolysis (breaking of blood clots), are limited due to the inefficiency caused by significant risks of excessive bleeding. There is an intense need for a widespread research on the blood clot deformation modeling, which could possibly enhance the efficiency of the thrombolytic techniques3.

Figure 2: Blood Clot (Michael) 5

Numerical Modeling: COMSOL Multiphysics® (a general-purpose software platform, fashioned for advanced numerical modeling and simulating physics based problems, especially accounting for the coupled or multiphysics phenomena) 1 will be used to develop a model for this study. The FSI (Fluid-Structure Interaction) module will illustrate deformation of the clot attached to the vessel wall by the blood flow. This module assists in solving for the flow patterns in a continuously deforming geometry using the arbitrary Lagrangian-Eulerian technique. The ALE method will set the fundamental framework for the clot deforming analysis and the moving boundaries with the moving grid. COMSOL Multiphysics® devises new mesh coordinates on the vessel area, based on the movement of clot’s boundaries. The Navier-Stokes equations responsible for solving the blood flow will be calculated for the moving coordinates1. Below are given some 3-dimensional models created with fluid-structure interaction modules, for different problems. The basic framework of the model for this study will have visual similarity with the models given below:

Figure 3: FSI Model (Application Gallery) 1 Figure 4: FSI Model (Application Gallery) 2 Figure 5: FSI Model (Wick, 2013) 6

Methods: Using the fluid-structure interaction module, the blood fluid dynamics and structural mechanics will be coupled. Fixed blood vessel width, height and along with steady state inlet mean velocity will be applied to model a horizontal blood flow. Blood clot will be attached to the inner bottom of the vessel. Mesh will be applied to the blood. The initial and final mesh will be compared, before and after the interaction with the blood clot. The clot and the vessel will be modeled as incompressible, wheras the blood flow is described by the Navier-Stokes equations1,2 ; Equation 1: Navier-Stokes Equation (Application Gallery)1 𝜌 !𝒖

!"− ∇. [−𝑝𝑰 + 𝜂 ∇𝒖 + ∇𝒖 𝑇 + 𝜌 𝒖 − 𝒖𝒎 .∇ 𝒖 = 𝑭      

−∇.𝒖 = 0 Expected Results: Since blood vessels are smaller in dimensions, the blood flow will be assumed laminar with (Re << 100). The eddy movements around the blood clot will be restricted to the smaller areas1. In order to analyze the deformation pattern of clot, different shear modulus values will be applied for the blood clot, whereas a constant value will be used for the vessel wall. The blood fluid and the clot are expected to experience the same deformation pattern. The simulation framework developed in this study will assist in increasing the effeciency of “Engineering Mechanics of Thrombolysis”.

References: 1.    Application  Gallery.  Fluid-­‐Structure  Interaction.  http://www.comsol.com/model/fluid-structure-interaction- 361  2.  Application  Gallery.  Fluid-­‐Structure  Interaction  In  a  Network  of  Blood  Vessels.  http://www.comsol.com/model/fluid-structure-interaction-in-a-network-of-blood    3.  Adam  D.  M.,  Charles,  A.  C.,  Alexander,  P.  D.,  Linggian,  Y.,  Hitinder,  S.  G.,  and  Zhen,  X.  Noninvasive  Thrombolysis  using  Pulsed  Ultrasound  Cavitation  Therapy        

Histotripsy.  Vol.  35,  Issue  12,  Pages  1982-­‐1994,  (2009).  4.  Denoble,P.,  Deep  Vein  Thrombosis,  The  Dive  Laboratory,  DAN.  (2014).  https://thedivelab.wordpress.com/2014/03/07/deep-vein-thrombosis-dvt/  5.  Michael,  B.,  Darwin's  Black  Box,  A  System  without  room  for  error:  Blood  Clotting,  P.p.  79-­‐97.  www.designanduniverse.com  6. Wick,  T.,  Solving  Monolithic  Fluid-­‐Structure  Interaction  Problems  in  Arbitrary  Lagrangian  Eulerian  Coordinates  with  the  deal.II  Library.  (2013)  Retrieved  

August  2015,  from  http://media.archnumsoft.org/10305/