A Two-Species Finite Volume Scalar Model for Modeling the Diffusion of Poly(lactic-co-glycolic acid) into a Coronary Arterial Wall from a Single Half-Embedded Drug Eluting Stent Strut
Abstract
:1. Introduction
- A theoretical methodology for computational modeling of the diffusion of PLGA into a coronary arterial wall from a single half-embedded drug eluting stent strut.
- A computational drug diffusion model that considers the pharmaco-kinetic reactions in the arterial wall as equilibrium reversible binding reaction source terms for the free and bound-drug.
- Validation of the reported computational model via simulation-based results from a finite difference model developed from methods reported in previous works.
- A computational drug diffusion model that provides an understanding of the relationship between drug physicochemical properties and the local transport environment which is crucial to the success of new stent designs.
- The model reported in this work is the second reported model in literature that successfully uses an ANSYS FLUENT user-defined scalar (UDS) model to model the diffusion of the free and bound drug in the arterial wall with reversible binding source terms. Additionally, this is the first reported model to use a UDS model to incorporate the polymer layer in the computational domain.
2. Material and Methods
2.1. Model Development
2.2. Boundary Conditions and Meshing
2.3. Plasma Flow
2.4. Drug Transport in the PLGA Coating and Arterial Domains
- Drug Binding:
- Free Drug in the PLGA Coating Domain:
- Free Drug in the Arterial Domain:
- Bound Drug in the Arterial Domain:
- Drug Transport Boundary Conditions:
- User Defined Scalar and Numerical Modelling
2.5. Non-Dimensional Pre-Analyses
2.6. Grid Independence Analysis, Modelling Parameters, and Validation and Verification
3. Results
3.1. Interstitial Flow into the Arterial Wall
3.2. Free and Bound Drug Concentration Profiles with Erosion and Interstitial Flow
3.3. Free and Bound Drug Concentration Profiles with Erosion and Convection
3.4. Average Weighted Concentration Results for Varying Tortuosity
4. Conclusions
Author Contributions
Funding
Data Availability Statement
Conflicts of Interest
Abbreviations
Cf | Free drug |
Cb | Bound drug |
Cp | Perivascular drug concentration |
Cw | Wall drug concentration |
C0 | Initial drug concentration |
D | Outer diameter of the artery |
DC | Coefficient of the coating diffusion |
Da | Dimensionless DamKöhler number in the tissue |
Dfree | Coefficient of free diffusivity |
Deff | Coefficient of effective diffusivity |
DT | True diffusivity of the free drug |
Jwp | PLGA flux parameter |
Lx | Arterial domain length |
Ly | Arterial domain wall thickness |
Lsx | Stent length |
Lsy | Stent thickness |
ka | Tissue binding capacity |
kd | Dissociation rate constant |
PeC | Dimensionless Peclet number in the coating |
PeT | Dimensionless Peclet number in the tissue |
Rd | Equilibrium dissociation constant |
Rwp | Mass transfer resistance |
S0 | Available binding sites |
T | Time |
Vy | Transmural filtration velocity |
x | x-coordinate |
y | y-coordinate |
δ | Strut dimension |
ε | Porosity of the arterial wall |
ε1 and ε2 | Dimensionless scaling parameters |
τ | Tortuosity of the arterial wall |
τ1, τ2, and τ2 | Characteristic time scales |
PLGA | Poly(lactic-co-glycolic acid) |
UDS | User defined scalar |
Appendix A
- Free-drug in the PLGA Coating Domain:
- Free-drug in the Arterial Domain:
- Bound-drug in the Arterial Domain:
- Scaled free-drug concentration time derivative:
- Scaled bound-drug concentration time derivative:
- Scaled free-drug concentration first-order x-direction derivative:
- Scaled free-drug concentration first-order y-direction derivative:
- Scaled free-drug concentration second-order x-direction derivative:
- Scaled free-drug concentration second-order y-direction derivative:
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Element Number | Average Weighted Concentration | Average Velocity |
---|---|---|
74,212 | 1.121327 | 13.72 × 10−6 |
82,458 | 1.057641 | 12.68 × 10−6 |
91,621 | 1.034241 | 10.23 × 10−6 |
101,802 | 0.983541 | 9.83 × 10−6 |
113,114 | 0.977732 | 9.77 × 10−6 |
372,125 | 0.977654 | 9.76 × 10−6 |
Description | Parameter | Value |
---|---|---|
Outer diameter of the artery, mm | D | 3 |
Artery wall thickness, µm | Ly | 200 |
Strut dimension, m | δ | 0.00014 |
Transmural filtration velocity, m/s | Vy | 4 × 10−8 |
Porosity of the arterial wall | ε | 0.787 |
Tortuosity of the arterial wall | τ | 1.333 |
Coating drug diffusivity, m2/s | Dc | 1.0 × 10−12 |
Coefficient of free diffusivity, m2/s | Dfree | 3.65 × 10−12 |
Coefficient of effective diffusivity, m2/s | Deff | 2.15 × 10−12 |
True diffusivity of the free drug, m2/s | DT | 24 × 10−12 |
Initial drug concentration in the coating, mol/m3 | C0 | 0.01 |
Tissue binding capacity, mol/m3 | ka | 10 |
Dissociation rate constant | kd | 0.01 |
Equilibrium dissociation constant, mol/m3 | Rd | 0.001 |
Dimensionless Peclet number in the coating | PeC | 100 |
Dimensionless Peclet number in the tissue | PeT | 2 |
Dimensionless DamKöhler number in the tissue | Da | 40 |
Dimensionless scaling parameter 1 | ε1 | 0.001 |
Dimensionless scaling parameter 2 | ε2 | 100 |
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Hewlin, R.L., Jr.; Edwards, M.; Kizito, J.P. A Two-Species Finite Volume Scalar Model for Modeling the Diffusion of Poly(lactic-co-glycolic acid) into a Coronary Arterial Wall from a Single Half-Embedded Drug Eluting Stent Strut. Biophysica 2023, 3, 385-408. https://doi.org/10.3390/biophysica3020026
Hewlin RL Jr., Edwards M, Kizito JP. A Two-Species Finite Volume Scalar Model for Modeling the Diffusion of Poly(lactic-co-glycolic acid) into a Coronary Arterial Wall from a Single Half-Embedded Drug Eluting Stent Strut. Biophysica. 2023; 3(2):385-408. https://doi.org/10.3390/biophysica3020026
Chicago/Turabian StyleHewlin, Rodward L., Jr., Maegan Edwards, and John P. Kizito. 2023. "A Two-Species Finite Volume Scalar Model for Modeling the Diffusion of Poly(lactic-co-glycolic acid) into a Coronary Arterial Wall from a Single Half-Embedded Drug Eluting Stent Strut" Biophysica 3, no. 2: 385-408. https://doi.org/10.3390/biophysica3020026
APA StyleHewlin, R. L., Jr., Edwards, M., & Kizito, J. P. (2023). A Two-Species Finite Volume Scalar Model for Modeling the Diffusion of Poly(lactic-co-glycolic acid) into a Coronary Arterial Wall from a Single Half-Embedded Drug Eluting Stent Strut. Biophysica, 3(2), 385-408. https://doi.org/10.3390/biophysica3020026