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MATHEMATICAL METHODS FOR CARDIOVASCULAR STENTING

MATHEMATICAL METHODS FOR CARDIOVASCULAR STENTING. Suncica Canic Department of Mathematics University of Houston. COLLABORATORS Prof. Josip Tambaca (U of Zagreb, CRO) Dr. Craig Hartley (Baylor), Dr. David Paniagua ( THI&St.Luke’s )

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MATHEMATICAL METHODS FOR CARDIOVASCULAR STENTING

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  1. MATHEMATICAL METHODS FOR CARDIOVASCULAR STENTING Suncica Canic Department of Mathematics University of Houston COLLABORATORS Prof. JosipTambaca (U of Zagreb, CRO) Dr. Craig Hartley (Baylor), Dr. David Paniagua (THI&St.Luke’s) Mate Kosor (grad student UH & U Zagreb)

  2. COMPREHENSIVE STUDY OF FLUID-STRUCTURE INTERACTION IN BLOOD FLOW(with O. Boiarkine, R. Glowinski, G. Guidoboni, D. Kuzmin, A. Mikelic, J. Tambaca, A. Quaini) ANALYSIS • Fundamental properties of the interaction and of the solution • Derivation of new closed, effective FSI models (existence,uniqueness&stability)(thin,thick,elastic,viscoelastic structure) • Effective model for Taylor dispersion in compliant/excited vessels (intravascular drug delivery) • Derivation of reduced, effective models for endovascular stent modeling COMPUTATION • FSI: monolithic scheme vs.design of a novel loosely coupled scheme (“kinematicallycoupled scheme”) with a novel operator splitting approach exhibiting superb stability properties. • Models allowing two different structures • Fluid-cell-structure interaction and adhesion algorithm for cell coating of coronary stents EXPERIMENTAL VALIDATION AND TREATMENT (WITH TEXAS MED. CENTER) with Drs. Zoghbi, Little, Hartley, Fish, Paniagua, Rosenenstrauch • Coronary angioplasty with stenting • AAA repair • Echocardiographic assessment of mitral valve regurgitation flow chamber experiment numerics

  3. STENT • MESH TUBE THAT IS INSERTED INTO A NATURAL CONDUIT • OF THE BODY TO PREVENT OR COUNTERACT A DISEASE-INDUCED • LOCALIZED FLOW CONSTRICTION • USED IN THE CARDIOVASCULAR SYSTEM, TRACHEOBRONCHIAL, • BILIARY AND UROGENITAL SYSTEM • STENTS PLAY A CRUCIAL ROLE IN THE TREATMENT OF CORONARY • ARTERY DISEASE

  4. MANY OPEN QUESTIONS • WHICH STENT IS APPROPRIATE FOR A GIVEN LESION? • WHICH STENTS ARE APPROPRIATE FOR TORTUOUS GEOMETRIES? • WHAT IS THE OPTIMAL STENT DESIGN FOR THE AORTIC VALVE • STENT PLACEMENT? • WHAT IS THE STENT’S LONGITUDINAL STRAIGHTENING (BENDING • RIGIDITY) AND HOW DOES IT DEPEND ON ITS GEOMETRY? • LONGITUDINAL EXTENSION/SHORTENING DURING PULSATION? • BIOCOMPATIBILITY and RESTENOSIS STUDY MECHANICAL PROPERTIES OF STENTS BIOCOMPATIBILITY and RESTENOSIS

  5. MECHANICAL PROPERTIES OF STENTS • LARGE CARDIOVASCULAR LITERATURE • CASE REPORTS • Zarins, Mehta, Gyongyosi, Rieu, Sainsous,Ormiston, Webster, Dixon, Post, Kuntz, Mirkovitch, • Sigwart, Garasic, Edelman, Rogers, Kastrati, Sigwart, Dyet, Watts, Ettles, Schomig, Rogers, • Tseng, Edelman, Squire, Gruntzig, Mayler, Hanna,… • MODERATLY LARGE ENGINEERING LITERATURE • SIMULATIONS USE 3D COMMERCIAL SOFTWARE • Moore, Timmins, Berry, Dumoulin, Taylor, Bedoya, Schmidt, Behrens, Cochelin, Holzapfel, Gasser, • Stadler, Magliavacca, Petrini, Colombo, Auricchio, Hoang, … HELPED UNDERSTAND MANY STENT PERFORMANCE FEATURES!!! • DRAWBACKS: • 3D simulation of each stent strut is computationally very expensive • thin and long structure: need extremely fine mesh to achieve • reasonable accuracy • commercial software uses “black box” approach: do not know which models are used • computationally prohibitive to include dynamic 3D stent modeling in a fluid-structure interaction solver

  6. OUR APPROACH: DIMENSION REDUCTION • AND MULTI-SCALE MODELING • STENT STRUTS MATHEMATICAL THEORY OF 1D CURVED RODS* • STENT3D MESH OF 1D CURVED RODS SATISFYING CERTAIN • GEOMETRIC AND CONTACT CONDITIONS AT VERTICES • SPEEDS UP CALCULATION BY SEVERAL ORDERS OF MAGNITUDE • STENT DESIGN OPTIMIZATION AND COUPLING WITH FLUID • EFFECTIVE PRESSURE-DISPLACEMENT RELATIONSHIP FROM • LEADING-ORDER ENERGY FORMULATION • CAN BE USED IN NUMERICAL FLUID-STRUCTURE INTERACT. STUDIES

  7. COMPARISON WITH 3D MODEL 3D simulation: freeFEM++, P2 elements, computational mesh (h=1/10,…,1/40) 1D SIMULATION 30x displacement magnification 3D SIMULATION 3D simulations converge with mesh refinement to 1D solution with #3D nodes: 211337 v.s. #1D nodes: 474 for 2.7% diff. QUANTITATIVE DIFFERENCE BETWEEN 1D and 3D DISPLACEMENT FOR 2 ZIG-ZAGS

  8. APPLICATION (with Drs. Paniagua (THI and VA Hospital), Fish (THI & St. Luke’s Hospital)) • MAXIMALLY EXPANDED STENTS ARE STIFFER: Stent expanded radius R; max displ=15% Stent expanded radius 0.8 R; max displ=23.5% THIS INDICATES THAT POST-DILATATION PRACTICE IS HIGHLY ADVISABLE • NON-UNIFORM GEOMETRY INFLUENCES STENTS’MECHANICAL RESPONSE: SMALLER DIAMONDSIMPLY HIGHER STIFFNESS USED IN OPTIMAL STENT DESIGNFOR PERCUTANEOUS AORTICVALVE REPLACEMENT (PRODUCED BY A PRIVATE CONSORTIUM IN HOUSTON with A FACTORY IN NJ) Max dipl=0.8cm Max dipl=0.56cm

  9. CORONARY STENT RESPONSE TOCOMPRESSION AND TO BENDING STENTS CONSIDERED: Palmaz by Cordis Palmaz-like stent mesh Express by Boston Sci. Express-like stent mesh Cypher-like stent mesh Cypher by Cordis Xience by Abbott Xience-like stent mesh

  10. Movie Gallery of Coronary Stents Exposed to Compression and Bending Compression Bending Uniform (Palmaz-like) stent (strut thickness 80 microns) Xience-like stent; open cell design (strut thickness 80 microns; CoCr) Cypher-like stent (strut thickness 140 m & 140/3 m) Express-like stent; open cell design (strut thickness 132 m)

  11. CONCLUSIONS • Palmaz-like stent is by far the hardest stent with respect to both • compression and bending (should not be clinically applied in tortuous geometries [*]) • open-cell design provides more flexibility to bending • (important since longitudinal straightening effect of rigid stent has been clinically • associated with increased incidence of major adverse cardiovascular events [*]) • Express-like stent has high flexibility (bending) while keeping • high radial strength(radial displacement: 0.24%) • (important to avoid buckling of bent stents) • Xience-like stent has the smallest longitudinal extension • under cyclic loading (“in phase” circumferential rings; not “opposing”) • (clinically important when landing a stent in an “angle” area formed by a native artery) • New design: more flexibility than Express with higher • radial strength: Cypher-like stent with open-cell design Xience-like Express-like pre post Cypher-like *Gyongyosi et al. Longitudinal straightening effect of stents is an additional predictor for major adverse cardiac events. J American College of Cardiology 35 (2000) Computer-generated Cypher-like stent with open cell design

  12. STENT BIOCOMPATIBILITY • re-stonosis; development of neo-intimal hyperplasia = scar tissue in response to mechanical intervention • with material of poor biocompatibility movie

  13. Day 3 100x 200x 400x SOLUTION METHODS • endothelial cells (optimal lining but not easily accessible, harvested or isolated) • genetically engineered smooth muscle cells (similar) • genetically engineered auricular chondrocytes (Dr. Doreen Rosenstrauch THI) • - genetically engineered to produce NO • - easily accessible: minimally invasive harvesting • - superior adhearance (collagen) • - good results with LVADs Scott-Burdent, Rosenstrauch et al.) STENT COATING • Cardiovascular Surgery Research Lab– Texas Heart Institute (Marie Ng, Boniface Magesa, Doreen Rosenstrauch, ArashTadbiri)

  14. CELL COATING OF ARTIFICIAL SURFACES with J. Hao, R. Glowinski, T.W. Pan, Drs. D. Rosenstrauch, C. Hartley • OPTIMIZE INITIAL SEEDING FOR FAST COMPLETE COVERAGE • (Canic and Rosenstrauch: Use of auricular chondrocytes in lining of artificial surfaces: A mathematical model. • IEEE Transactions of NanobioscienceVol 7(3) 2008, 240-245.) • STUDY CELL LOSS, ROLLING AND ADHESION IN PRECONDITIONING • (UNDER CONTROLLED FLOW CONDITIONS IN A FLOW LOOP) • (J. Hao, T.W. Pan, S. Canic, R. Glowinski, D. Rosenstrauch. A Fluid-Cell Interaction and Adhesion Algorithm for Tissue-Coating of Cardiovascular Implants. • SIAM J Multiscale Modeling and Simulation 7(4) 1669-1694 (2009) USE MATHEMATICS AND COMPUTATION TO REDUCE THE EXTENT OF EXPERIMENTAL INVESTIGATION TO OPTIMIZE CELL COATING OF ARTIFICIALCARDIOVASCULAR SURFACES

  15. FLUID-PARTICLE INTERACTION AND ADHESION ALGORITHM J. Hao, T.W. Pan, S. Canic, R. Glowinski, D. Rosenstrauch. A Fluid-Cell Interaction and Adhesion Algorithm for Tissue-Coating of Cardiovascular Implants. SIAM J Multiscale Modeling and Simulation 7(4) 1669-1694 (2009) DYNAMIC ADHESION ALGORITHM Hammer and Apte, Biophys.J. (1992) FLUID-PARTICLE INTERACTION ALGORITHM Glowinski,Pan et al., J. Comp. Phys. (2001) Fluid velocity=const. t = 0 Periodic boundary conditions Fluid velocity=0 No-slip boundary condition Fluid velocity=const. CELL ADHESION modeled via randomly distributed adhesion molecules (Hookean springs) and stochastic bond dynamics. t > 0 Fluid velocity=0

  16. Number of cells = 80 Mesh size h for the velocity=0.1 mm (using P1 element) Cell size (ellipsas)= 2 x 1.6 mm Mesh size h for the pressure=0.2 mm (using P1 elements) Channel length=400 mm Each cell occupies 20x16 mesh blocks. Dual core AMD Opteron 275 @ 2.2 GHz : 11h 30min 4 sec (not parallelized) • RESULTS • Cell detachment in the pre-conditioning stage (stochastic bond dynamics) Shear rate (1/s) Viscosity(g/cm s) Detachment % • observed chondrocyte sliding in simulations • (experimentally verified!!) • captured cell detachment (initial linear growth • experimentally verified) 0.01 100 0 0.01 200 25 0.05 5 0 0.05 8 10 0.05 9 30 (blood:0.03 ; 100 in dog’s coronaries) USE OF OUR COMPUTATIONAL MODEL as a start to study cell-detachment, cell adhesion, and formation of stable cartilage by varying shear rate and fluid viscosity for a given cell type J. Hao, T.W. Pan, S. Canic, R. Glowinski, D. Rosenstrauch. A Fluid-Cell Interaction and Adhesion Algorithm for Tissue-Coating of Cardiovascular Implants. SIAM J Multiscale Modeling and Simulation 7(4) 1669-1694 (2009)

  17. REFERENCES (selected) [1] J. Tambaca, M. Kosor, S. Canic, and D. Paniagua, Mathematical Modeling of Vascular Stents. SIAM J Applied Mathematics Volume 70 (6) pp. 1922-1952 (2010). [2] J. Tambaca, S. Canic and D. Paniagua, A Novel Approach to Modeling Coronary Stents using a Slender Curved Rod Model: A Comparison between Fractured Xience-like and Palmaz-like Stents. Applied and Numerical PDEs: Scientific Computing, Simulation, Optimisation and Control (eds Fitzgibbon, Kuznetov, Neittanamitski, Periaux, Pironneau). Springer pp. 41-58 (2010). [3] J. Tambaca, S. Canic, M. Kosor, D. Paniagua, and D. Fish. Mechanical Properties of Commercially Available Coronary Stents in Their Expanded State. J Am. College of Cardiology (under revision) [4] J. Hao, T.W. Pan, S. Canic, R. Glowinski, D. Rosenstrauch. A Fluid-Cell Interaction and Adhesion Algorithm for Tissue-Coating of Cardiovascular Implants. SIAM J Multiscale Modeling and Simulation 7(4) 1669-1694 (2009) [5] G. Guidoboni, R. Glowinski, N. Cavallini, S. Canic. Stable loosely-coupled-type algorithm for fluid-structure interaction in blood flow. Journal of Computational Physics Vol. 228, Issue 18 6916-6937 (2009). [6] S. Canic and D. Rosenstrauch. Use of auricular chondrocytes in lining of artificial surfaces: A mathematical model. IEEE Transactions of NanobioscienceVol 7(3) 2008, 240-245. [7] S. Canic, Z. Krajcer, and S. Lapin. Design of Optimal Prostheses Using Mathematical Modeling. Endovascular Today (Cover Story). May Issue (2006) 48-50.

  18. University of Houston, MD Anderson Library • THANKS: • The National Science Foundation • The National Institutes of Health (joint with NSF: NIGMS program) • Roderick Duncan MacDonald Research Grant at St. Luke’s Episcopal Hospital, Houston • Texas Higher Education Board (ATP Mathematics) • Kent Elastomer Products Inc. • UH Mathematics Department Summer Research Grant • Medtronic Inc.

  19. COMPARISON WITH 3D MODEL 3D simulation: freeFEM++, P2 elements, computational mesh (h=1/10,…,1/40) OVERALL DISPLACEMENT COMPARSION 1D SIMULATION 3D SIMULATION 30x displacement magnification 3D simulations converge to 1D solution for h=1/10,…,1/60 #3D nodes: TODO #1D nodes: 474 QUANTITATIVE DIFFERENCE BETWEEN 1D and 3D DISPLACEMENT

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