Copyright © 2011 by ASME 1

INTRODUCTION Drug-eluting stents (DESs) perform their antiproliferative effects through the use of localized drug delivery. The delivery may be computationally modeled to determine efficacy of the DES-tissue system and utilizes coupled convective and diffusive transport. Since the movement of solutes through the wall is via the coupled effects of convective and diffusive transport, the relative influence of these factors provides insight into the governing forces of localized DES drug delivery [1]. Material properties have shown spatial variations based on the location of the tissue [2]. Using an axisymmetric stented pulsatile model in ABAQUS with custom-written Fortran routines allows for the analysis of porohyperelastic mass transport [3]. We have taken values of permeability and mechanical behavior based on location, and have determined how location modifies species concentrations temporally and through the arterial wall.

MATERIALS AND METHODS The overall transport model is governed via the generalized potentials (concentration, pore pressure). This results in the Eulerian Darcy and Fick laws [3]:

€

vifr = −kij

ff ∂p f

∂x j ,

€

jicr = −dij

cc ∂c∂x j

+ bijcf cv j

fr

(1), (2) Where vifr is the relative fluid velocity, kijff is the permeability,

€

∂p f /∂x j is the pressure gradient, jicr is the diffusive flux, dijcc is the

diffusivity,

€

∂p f /∂x j is the concentration gradient, and bijcf is the

coupling coefficient describing the relative influences of the convective to diffusive forces (Note

€

Pe = vifrLbij

cf /dijcc , L is the

characteristic length). Since the model is based off of these governing equations, the testing for properties is based on these laws. Porcine hearts were obtained from the local Meat Sciences Laboratory. Vessels were marked with a cyanoacrylate/ceramic marker mix to determine prestrains in the circumferential and axial directions. The vessels were cleaned of any fat and connective tissue then split into segments 10mm in length. The original locations of the segments were noted to know what distance from the ostia the segment was originally located (e.g., proximal, middle, distal regions). Since the focus of this study was the effects of permeability on species concentration in a stented vessel in a pulsatile model a single value was taken for dijcc and bijcf with kijff and mechanical properties changing based on location (proximal, middle, and distal). Each transport constant was determined by placing the tissue in a testing fixture, securing the sample to the measured prestrains, and applying a concentration, pressure, or pressure+concentration gradient (Figure 1). For diffusivity a 1mg/ml solution of FITC in DIH2O was applied to the intimal side of the sample then multiphoton microscopy scans

Proceedings of the ASME 2011 Summer Bioengineering Conference SBC2011

June 22-25, Nemacolin Woodlands Resort, Famington, Pennsylvania, USA

SBC2011-53998

ALTERATIONS IN CONCENTRATIONS IN PULSATILE AXISYMMETRIC STENTED ARTERIAL MODELS FROM LOCATION-DEPENDENT VARIATIONS IN PERMEABILITY

AND MECHANICAL PROPERTIES

Joseph T Keyes (1), Bruce R Simon (1,2), Jonathan P Vande Geest (1,2,3,4)

(1) Graduate Interdisciplinary Program in Biomedical

Engineering

(2) Department of Aerospace and Mechanical Engineering

(3) BIO5 Institute for Biocollaborative Research

(4) Department of Biomedical Engineering

The University of Arizona Tucson, AZ

Figure 1: Setup for mass transport testing. (A)=sample in the fixture, (B)=capillary, (C)=bubble, (D)=pressure transducer, (E)=pump, (F)=saline filled silicone, (G)=saline/FITC filled silicone, (H)=microscope objective

Copyright © 2011 by ASME 2

done to obtain fluorescein, collagen, and elastin signal through the depth over time. The diffusivity can be determined via equation 2. For permeability several pressure gradients (70, 90 110, 130 mmHg) were applied across the vessel wall (intima to adventitia). The fluid flow across vessel wall can be determined by placing a bubble in a capillary inline with the pressure head between it and the vessel. The movement of the bubble indicates the permeation velocity and the permeability can be backfit using equation 1 [4]. bijcf (equation 2) can be determined from the same method as used with permeability but the pressure head is filled with a FITC-H2O solution. The bubble velocity and the concentration are tracked. Mechanical properties were obtained by performing planar biaxial tensile testing via a previously demonstrated device [5]. The samples were taken biaxially to tension at 130mmHg via the Law of LaPlace, and 2nd Piola-Kirchoff stress and Green’s strain recorded. The biomechanical response of the axial and circumferential directions were averaged together and 2nd order polynomial effective strain energy constants determined. The computational model (sequence in Figure 2) is an axisymmetric model with two struts, and driven from dimensions of a 3-dimensional stented arterial model (2mm inner radius vessel, 0.4mm thickness, 15mm stent, and 0.25mm thickness). Axismmetry was used in addition to axial one-half symmetry boundary conditions. The model had 2748 elements and used 4-node quadrilateral elements.

Figure 2: Schematic for porohyperelatic mass transport

analysis RESULTS kijff (n=3) increased by 264.4±59.4% from the proximal to middle region and 172.1±31.1% from the middle to distal region. dijcc was taken to be 2E-11 m2/s and bijcf was determined to be 0.31. The mesh and example of a result can be seen in Figure 3. The nodal concentrations were exported for nodes along the yellow dotted line for the three finite element models. Percent concentration change on a node-by-node basis was calculated then 3D surface plots made showing how concentrations change along the length of the yellow line over time (Figure 4). Variations are expressed in percent

difference. Concentrations toward the lumen were higher in the proximal region compared to the middle region by 9.8%. Moving toward the adventitia the middle region displayed higher concentrations by 13.8%. Comparing the middle and distal regions showed respectively minor variations in concentration toward the adventitia with the distal region showing lower concentrations in this region by 5.7%. In comparing the proximal to distal regions the differences were more pronounced. Toward the outer region of the medial layer concentrations varied by as much as 88% at small times and 24.3% at longer times with the distal region showing significantly higher concentrations.

DISCUSSION We have shown how concentrations vary based on spatial variations to mechanical properties and permeability. Concentrations showed the most amount of variation near-term, however, variations still existed on a longer time-scale. Given these changes, variations in patient success in long-term restenosis could potentially be partially attributed to changes in the local transport properties, thus preventing proper delivery of drugs in the proper time-course. ACKNOWLEDGEMENTS The authors would like to thank Urs Utzinger, PhD for his assistance in interpreting microscopy data. Funding for this work was provided by the NIH Cardiovascular Biomedical Engineering Training Grant (T32 HL007955), NSF Career Award to JPVG (0644570) and an AHA Grant-in-Aid to JPVG (10GRNT4580045). REFERENCES

1. Hwang, et al., Physiological transport forces govern drug distribution for stent-based delivery. Circulation 2001.

2. Fung, YC, Biomechanical Mechanical Properties of Living Tissues. Springer, 1993.

3. Vande Geest, et al., Coupled Porohyperelastic Mass Transport (PHEXPT) Finite Element Models for Soft Tissues Using ABAQUS, JBME 2011.

4. Simon, et al. Identification and determination of material properties for porohyperelastic analysis of large arteries. JBME 1998.

5. Keyes, et al., Design and demonstration of a microbiaxial optomechanical device for multi-scale characterization of soft biological tissues with 2-photon microscope. Mic&Mic 2011.

Figure 3: (A) Axisymmetric mesh of vessel wall with two stent struts, (B) PHE vifr result, (C) Concentration profile after PHEXPT subroutine. Yellow dotted line nodal concentrations were exported for post-processing.

Figure 4: Percent difference between the (A) prox. and dist. regions, (B) mid. and dist., (C) prox. and mid.. Surfaces are smoothed with Delaunay triangulation in Matlab