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A Diffusion Model of Platelet Derived Growth Factor (PDGF) for Hybrid Modeling of Intimal Hyperplasia

A Diffusion Model of Platelet Derived Growth Factor (PDGF) for Hybrid Modeling of Intimal Hyperplasia. Presented by Katelyn Swift-Spong Research Alliance in Math and Science Computational Sciences and Engineering Division Mentor: Dr. Richard Ward August 13, 2008 Oak Ridge, Tennessee.

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A Diffusion Model of Platelet Derived Growth Factor (PDGF) for Hybrid Modeling of Intimal Hyperplasia

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  1. A Diffusion Model of Platelet Derived Growth Factor (PDGF) for Hybrid Modeling of Intimal Hyperplasia Presented by Katelyn Swift-SpongResearch Alliance in Math and ScienceComputational Sciences and Engineering Division Mentor: Dr. Richard Ward August 13, 2008 Oak Ridge, Tennessee

  2. Intimal Hyperplasia • Occurs in arterial wall as response to injury such as balloon angioplasty • Smooth muscle cells (SMCs) migrate from media to intima layer of the arterial wall • Migration due to presence of the chemoattractant PDGF and breakdown of collagen by matrix metalloproteinase (MMP) enzyme kinetics • Results in restenosis (re-narrowing) of the artery Diagram of Artery Intima Lumen Endothelial cell layer Media Internal elastic lamina Adventitia

  3. Images of rat carotid arteries from UT Medical Center IH present Normal Artery Intimal Hyperplasia Lumen Lumen

  4. Output of simple migration model Hybrid Intimal Hyperplasia Model • Needed for a greater understanding of the process • Use for prediction of restenosis • Cell movement modeled with discrete event simulation • Chemical diffusion of Platelet Derived Growth Factor (PDGF) is continuous

  5. Three Dimensional Diffusion Model of PDGF • Developed using C++ • Visualization with Matlab and VisIT • Used finite difference method to solve the diffusion equation • Applied no flux boundary conditions

  6. Finite Difference Method • An explicit method used to solve the diffusion equation in three dimensions • Continuous partial differential equation solved using discrete space and time steps • Forward time and central space discretization • Concentration at previous time step used to compute concentration at next time step Diffusion equation Finite difference approximation

  7. Stability • Time step must be small enough to satisfy this condition • Diffusion coefficient for PDGF in a solution is around 10-6 cm2/s

  8. Constant Zero 2D initial conditions Model Results • Began with one dimensional model and expanded it to two and three dimensions • Used visualization for model validation • Used initial conditions of constant concentration of one in top half and zero in bottom • Applied no flux boundary conditions

  9. Integration of 3D Diffusion Model • Previously developed cell migration model was recently extended to 3D • Needed 3D diffusion model • Incorporate into discrete event simulation of cell migration • Leads to hybrid modeling environment

  10. Trilinear Interpolation • Concentration within grid needed for cell migration model • Computes PDGF concentration, C(x,y,z), at specified time • Uses linear interpolation method seven times Image from Wikipedia

  11. Lagrange Interpolating Polynomial • Used to determine partial derivative of concentration at point within grid • Computes • Interpolates a polynomial of degree n-1 that passes through n points • Partials used by cell migration model

  12. © RCSB MMP-2 MMP2 kinetics model developed by Alicia Weber using SBW Future Work • Incorporate matrix metalloproteinase (MMP) 2 enzyme kinetics model developed with JSim and Systems Biology Workbench (SBW) into IH model • Develop collagen degradation model based on MMP-2 kinetics • Include effects of hormones from hormone replacement therapy

  13. SBW COR JSim Model Interoperability • Tested capabilities of extensible markup language (XML) based programs • Cellular Open Resource (COR), SBW, and JSim do not support three dimensional partial differential equations • Not all CellML and Systems Biology Markup Language (SBML) files could be used with these programs • Easy to use without programming background Screen shots of JSim, SBW, and COR user interfaces

  14. Conclusions • Achieved successful integration of diffusion model into cell migration model • Need an integrated modeling language that extends beyond the present capability • Capable of integrating the kinetics models described using the XML formats, such as CellML and SBML, with the diffusion models for biochemicals and cells • Still needed in hybrid IH model • Collagen breakdown by MMP2 • Effect of hormones from hormone replacement therapy on cell migration

  15. Acknowledgments Special thanks to Richard Ward, Kara Kruse, and Jim Nutaro for their help and guidance. The Research Alliance in Math and Science program is sponsored by the Office of Advanced Scientific Computing Research, U.S. Department of Energy. The work was performed at the Oak Ridge National Laboratory, which is managed by UT-Battelle, LLC under Contract No. De-AC05-00OR22725. This work has been authored by a contractor of the U.S. Government, accordingly, the U.S. Government retains a non-exclusive, royalty-free license to publish or reproduce the published form of this contribution, or allow others to do so, for U.S. Government purposes.

  16. Questions 16 Managed by UT-Battellefor the Department of Energy UTBOG_Computing_0801

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