Impact of Stent Design on Drug Transport and Vascular Re-Endothelialization

Transcription

1 Impact of Stent Design on Drug Transport and Vascular Re-Endothelialization Franz Bozsak 1, Jean-Marc Chomaz 1, Taewon Seo 2,3, and Abdul I. Barakat 1,3 1 Laboratoire d'hydrodynamique, Ecole Polytechnique, France 2 Department of Mechanical Engineering, Andong National University - Korea 3 Department of Mechanical and Aerospace Engineering, University of California, Davis, USA

2 Stent-Induced Arterial Flow Disturbance Shear Stress (dyne/cm 2 ) Re=400 Seo et al., 2005

3 Endothelial Wound Healing Dependence on WSS Level t=0h 6h 12h 24h Static 100 μm Upstream Downstream t=19 dyne/cm 2 t=3 dyne/cm 2 Flow Gojova and Barakat, 2005

4 Stent-Induced Arterial Flow Disturbance Shear Stress (dyne/cm 2 ) Re=400 Seo et al., 2005

5 Modeling Drug Transport in the Arterial Wall Models of the Arterial Wall One-layer: Wall considered as the media with the intima modeled as a boundary condition Multi-layer: Intima and media are modeled as separate layers Subendothelial space and media described as porous layers ET and IEL expressed as Kedem- Katchalsky membranes (Prosi et al., 2005)

6 Modeling Drug Transport in Arterial Wall: Reaction Model Specific Binding as proposed by Sakharov et al. (2002) and Tzafriri et al. (2009) Reaction Model Differential Equation Representation db dt Da * c 1 b forward b: Concentration of Bound Drug Da: Damköhler number= reaction/diffusion B p : Binding Potential: small for hydrophobic drugs, large for hydrophilic drugs k C S k f b B bm b c 0Bp backward

7 Baseline Model of Stented Artery: Multi-Layer Model with Reversible Binding

8 Arterial Wall Dynamics: Drug Transport Total Drug Concentration Concentration of Bound Drug

9 One-Layer vs. Multi-Layer Model

10 Example of Limitation of One-Layer Model One-Layer Model Multi-Layer Model Affects drug concentration at endothelial surface

11 Model Predictions for Different Drugs

12 Stent Optimization Objective Function: Basic Elements Primary Considerations: Efficacy (C>C min ) - percentage of therapeutic domain that has efficacious concentration levels Toxicity (C<C max ) - percentage of therapeutic domain that has toxic concentration levels Homogeneity - percentage of therapeutic domain that lies in a defined concentration region between efficacy and toxicity Secondary Considerations: Flow disturbance Thrombosis (currently being added)

13 Optimization Strategy Our issues with classical optimization strategies: No direct gradient information available Time consuming function evaluations Gradient-free optimization methods (Belitz, P. and Bewley, T., J. Global Optim., 2012, online only, 1-31): Surrogate Management Framework Two repetitive major steps: 1. Global search on a surrogate surface for a prospective minimum point and evaluate objective function 2. Local poll of the vicinity of the current prospective minimum point If poll successful (new minimum found): update surface and back to step 1 If poll unsuccessful (no new minimum found): update surface, refine grid and back to step 1

14 Optimization Example 1: Drug Diffusivity and Initial Loading Paclitaxel Stent Sirolimus Stent stent strut D, C 0 Drug Diffusivity (cm 2 /s) Drug Loading (μg/cm 2 ) Current Optimized Current Optimized Paclitaxel x Sirolimus x ~ x 10 5

15 Optimization Example 1: Drug Diffusivity and Initial Loading Paclitaxel Stent Sirolimus Stent stent strut D, C 0 Drug Diffusivity (cm 2 /s) Drug Loading (μg/cm 2 ) Current Optimized Current Optimized Paclitaxel x Sirolimus x ~ x 10 5

16 Optimization Example 1: Drug Diffusivity and Initial Loading Paclitaxel Stent Current Parameters Optimized Parameters

17 Optimization Example 2: Strut Shape ellipse major and minor axes and measure of roundness Work in Progress Paclitaxel Sirolimus

18 Conclusions and Future Directions Stents perturb arterial flow fields and these perturbations affect endothelial cell wound healing rates. The extent of flow perturbation depends on stent design. One-layer models of the arterial wall capture global drug distribution but fail to capture possible flow redistribution details. Optimization of drug release kinetics and DES drug loading suggests that currently used parameters may be far from optimal. Future directions: 3D, incorporation of blood flow pulsatility, and modeling thrombosis.

19 Acknowledgments