**6. Experimental validation of mass transport behaviour**

Historically, experimental validations have been necessary to prove researchers hypotheses across all paradigms of science. In order to validate a theory one must not only be mindful of their goal but also their ability to achieve it. For instance, trying to validate a computational DES model using excised arterial DES would be nice in theory but in practice may prove fruitless because it would be near impossible to obtain the site specific drug concentrations within the artery wall, necessary for the researcher to examine the nuances of stent design that they are interested in analysing. It is often useful to validate a single aspect of the model if possible. With regards to DES, a solitary WSMT model may be acceptable,as a vast body of knowledge pertaining to fluid flow problems already exists, unlike the as of yet mature understanding of WSMT and how the behaviour of the porous artery wall and other pertinent features influence the mass transport therein.

Figure 3 illustrates an example of a validation flowchart for a study of mass transport from DES. The first process in designing a validation experiment is to analyse the problem as a whole and see what you would like to prove. Then certain aspects of the problem that are relatively rudimentary can be neglected from the validation, providing they won't have a fundamental impact on the outcome of the test. The flowchart is divided up into two streams that are developed jointly in order to achieve a desired validation. The experimental mass transport validation is on the left and the development of the corresponding computational mass transport model is on the right. In both streams BSMT is not highlighted for inclusion in this example's validation procedure. This may be due to the readily available examples of validations of this nature in literature or its minimal impact on the outcome of the results. This study was designed to investigate instances of WSMT in relation to DES design and deployment.

How accurate do you want your computational model to be and what assumptions are going to be made? The flowchart (Figure 3) describing this example validation decided to neglect convection-diffusion mass transport in the artery wall and concentrate on validating a diffusion only model. The reason for such a decision could be threefold; 1) an artery requiring a DES would be highly calcified and therefore the plaque can act as a buffer to stop or considerably reduce the flow in the porous wall, 2) an analysis of the Peclet number (equation 8) demonstrates diffusion dominated transport for a give drug or 3) the inability to create and obtain tangible results from an applicable experimental model with both convection and diffusion. The next aspect of the computational model is the characterisation of the artery wall, i.e. should it be modelled as a porous medium. Although flow in the wall has been neglected the application of a porous wall still can have a bearing on the outcome of mass transport due to the characterisation of the effective diffusivity and its propensity to change under varying stenting conditions (equation 12).

In this example a computational model has been identified in which many of the aspects of the *in vivo* stenting conditions remain but more importantly contains the ability to develop and analyse a corresponding experimental validation. Validations of this nature are a powerful tool in a researchers arsenal because once the initial hypotheses has been validated the computational model can be changed to any geometry imaginable to create more realistic stenting scenarios, and when solving the problem using the same physics one can have full confidence in the results.

symmetry. Intuitively this condition states that the gradient across the boundary must be

Historically, experimental validations have been necessary to prove researchers hypotheses across all paradigms of science. In order to validate a theory one must not only be mindful of their goal but also their ability to achieve it. For instance, trying to validate a computational DES model using excised arterial DES would be nice in theory but in practice may prove fruitless because it would be near impossible to obtain the site specific drug concentrations within the artery wall, necessary for the researcher to examine the nuances of stent design that they are interested in analysing. It is often useful to validate a single aspect of the model if possible. With regards to DES, a solitary WSMT model may be acceptable,as a vast body of knowledge pertaining to fluid flow problems already exists, unlike the as of yet mature understanding of WSMT and how the behaviour of the porous artery wall and

Figure 3 illustrates an example of a validation flowchart for a study of mass transport from DES. The first process in designing a validation experiment is to analyse the problem as a whole and see what you would like to prove. Then certain aspects of the problem that are relatively rudimentary can be neglected from the validation, providing they won't have a fundamental impact on the outcome of the test. The flowchart is divided up into two streams that are developed jointly in order to achieve a desired validation. The experimental mass transport validation is on the left and the development of the corresponding computational mass transport model is on the right. In both streams BSMT is not highlighted for inclusion in this example's validation procedure. This may be due to the readily available examples of validations of this nature in literature or its minimal impact on the outcome of the results. This study was designed to investigate instances of WSMT in

How accurate do you want your computational model to be and what assumptions are going to be made? The flowchart (Figure 3) describing this example validation decided to neglect convection-diffusion mass transport in the artery wall and concentrate on validating a diffusion only model. The reason for such a decision could be threefold; 1) an artery requiring a DES would be highly calcified and therefore the plaque can act as a buffer to stop or considerably reduce the flow in the porous wall, 2) an analysis of the Peclet number (equation 8) demonstrates diffusion dominated transport for a give drug or 3) the inability to create and obtain tangible results from an applicable experimental model with both convection and diffusion. The next aspect of the computational model is the characterisation of the artery wall, i.e. should it be modelled as a porous medium. Although flow in the wall has been neglected the application of a porous wall still can have a bearing on the outcome of mass transport due to the characterisation of the effective diffusivity and its propensity to

In this example a computational model has been identified in which many of the aspects of the *in vivo* stenting conditions remain but more importantly contains the ability to develop and analyse a corresponding experimental validation. Validations of this nature are a powerful tool in a researchers arsenal because once the initial hypotheses has been validated the computational model can be changed to any geometry imaginable to create more realistic stenting scenarios, and when solving the problem using the same physics one can

zero, therefore it is impermeable to mass transport.

**6. Experimental validation of mass transport behaviour** 

other pertinent features influence the mass transport therein.

relation to DES design and deployment.

have full confidence in the results.

change under varying stenting conditions (equation 12).

Fig. 3. Flowchart demonstrating the process of identifying an appropriate route for the experimental validation of DES mass transport.

### **6.1 Historical experimental mass transport validations**

Experimental techniques to simulate mass transport in the vasculature have been an integral part in the development of DES. Various techniques can be applied depending on the required outcome from the analysis. For example if lumen transport is to be analysed a common approach would be to introduce a dye to a flowing system. Concentrations are then measured at certain time points and locations by withdrawing fluid samples so that the optical dye intensity can be determined.

Markou et al. (1998) employed this approach when analysing the local transport of antirestenotic agents from a novel drug delivery device. The device consisted of a porous membrane that lined the artery wall and was the location where drugs would be infused into the artery. Their experimental approach consisted of a simulated artery section with a 1cm slit around its circumference. Dye was then infused from this slit in a radial direction into the lumen at uniform speed. It was found that the radial diffusion of the species was minimal in comparison to the axial convection therefore the majority of species remain in close proximity to the wall. This experiment was validated with the commercially available finite volume solver Fluent (Lebanon, NH). The computational models predicted an increase in dye concentration at the wall with an increase in the infusion rate. The same effect was witnessed experimentally and there was good agreement between the results. This study indicates the dominance of convective transport over diffusive transport in the arteries lumen.

Lutostansky et al. (2003) adopted a similar technique when conducting an experimental analysis of mass transport in the recirculation region downstream of a sudden expansion. Dye concentrations were determined at four equidistant locations after the sudden expansion. Experimental concentrations were taken over the course of one hour and showed very good correlation with predicted results from two numerical codes, the finite volume code Fluent (Lebanon, NH) and a finite element code FTSP (developed by Graz University of Technology). Although these experiments provided a validation of their numerical approach, they are limited in that they cannot be used to analyse mass transport within a porous wall.

In 2001, Hwang et al. found that stent based delivery, from a Palmaz-Schatz Crown stent (Cordis), resulted in large variations in concentration gradients. Drug concentrations were found to vary from zero to several times the mean over a few micrometres. The aforementioned stents were spray coated with a fluorescein sodium/ethylene vinyl acetate copolymer and deployed in excised bovine carotid arteries. The arteries were positioned in an *ex vivo* perfusion apparatus and immersed in a perivascular bath where coronary flow was simulated. After 3 hours the arteries were removed and cut into slices. The fluorescein concentration was then measured with a spectrofluorometer. Although the experiment was not used to validate a computational model, the effects witnessed experimentally were compared to variations in simulated drug physicochemical properties. They concluded that the proximity of the device does not necessarily ensure adequate targeting because transport forces can cause local concentrations to deviate from the mean concentration.

In a later paper Hwang et al. (2005) evaluated the paclitaxel uptake in stented abdominal aortas of adult male Sprague-Dawley rats in the presence and absence of controlled mural thrombus. The in vivo clot dimensions were determined and used as boundary conditions and input parameters for the computational model. The computational analysis predicted an arterial drug ratio of 0.56 which correlates with the 50% decrease in arterial uptake ascertained from the animal experiments. Hwang et al. (2005) discovered that by varying clot size and location, large variations in arterial uptake were witnessed.

In 2007, Balakrishnan et al. deployed a Cypher sirolimus eluting stents in porcine arteries. At the desired time points of 1, 8, 14, 30, 60 and 90 days after implantation the stents were harvested and analysed. In each case the stents were carefully removed from the artery and the remaining drug within the polymer was determined. When subtracted from the amount of drug prior to implantation the release fraction can be calculated. At each time point this fractional drug release was compared to numerical predictions using Fluent (Lebanon, NH). A good correlation validated the Fickian diffusion analysis applied with the numerical solver to approximate the drug transport from the coating. However, validating drug release from the polymer coating does not elucidate subsequent drug uptake within the porous artery wall.

In 2010, O'Connell and Walsh developed an analogous model of artery wall mass transport, examining the hypothesis of how compression of a porous media alters mass transport within. Due to the difficulty in measuring site specific concentrations within the artery wall they developed a scaled up experiment. It consisted of a bed of pH paper that was saturated in a neutral pH solution in order to fill the pore space of the material, similar to that of the artery walls interstitial fluid. The wall is then compressed, in increments up to a maximum of 23.75% of its initial thickness, and then the species of interest, an acid of pH 2.0, is introduced to the system and the resulting colour change was used as a marker for concentration. This enabled the site specific measurement of concentration at different depths throughout the porous wall. These experimental results were then validated computationally using the finite element solver COMSOL Multiphysics. The authors concluded that compression of a porous artery wall contributes significantly to the modulation of arterial WSMT and should be considered in future DES computational studies.

concentrations were determined at four equidistant locations after the sudden expansion. Experimental concentrations were taken over the course of one hour and showed very good correlation with predicted results from two numerical codes, the finite volume code Fluent (Lebanon, NH) and a finite element code FTSP (developed by Graz University of Technology). Although these experiments provided a validation of their numerical approach, they are

In 2001, Hwang et al. found that stent based delivery, from a Palmaz-Schatz Crown stent (Cordis), resulted in large variations in concentration gradients. Drug concentrations were found to vary from zero to several times the mean over a few micrometres. The aforementioned stents were spray coated with a fluorescein sodium/ethylene vinyl acetate copolymer and deployed in excised bovine carotid arteries. The arteries were positioned in an *ex vivo* perfusion apparatus and immersed in a perivascular bath where coronary flow was simulated. After 3 hours the arteries were removed and cut into slices. The fluorescein concentration was then measured with a spectrofluorometer. Although the experiment was not used to validate a computational model, the effects witnessed experimentally were compared to variations in simulated drug physicochemical properties. They concluded that the proximity of the device does not necessarily ensure adequate targeting because transport

In a later paper Hwang et al. (2005) evaluated the paclitaxel uptake in stented abdominal aortas of adult male Sprague-Dawley rats in the presence and absence of controlled mural thrombus. The in vivo clot dimensions were determined and used as boundary conditions and input parameters for the computational model. The computational analysis predicted an arterial drug ratio of 0.56 which correlates with the 50% decrease in arterial uptake ascertained from the animal experiments. Hwang et al. (2005) discovered that by varying

In 2007, Balakrishnan et al. deployed a Cypher sirolimus eluting stents in porcine arteries. At the desired time points of 1, 8, 14, 30, 60 and 90 days after implantation the stents were harvested and analysed. In each case the stents were carefully removed from the artery and the remaining drug within the polymer was determined. When subtracted from the amount of drug prior to implantation the release fraction can be calculated. At each time point this fractional drug release was compared to numerical predictions using Fluent (Lebanon, NH). A good correlation validated the Fickian diffusion analysis applied with the numerical solver to approximate the drug transport from the coating. However, validating drug release from the polymer coating does not elucidate subsequent drug uptake within the porous artery wall. In 2010, O'Connell and Walsh developed an analogous model of artery wall mass transport, examining the hypothesis of how compression of a porous media alters mass transport within. Due to the difficulty in measuring site specific concentrations within the artery wall they developed a scaled up experiment. It consisted of a bed of pH paper that was saturated in a neutral pH solution in order to fill the pore space of the material, similar to that of the artery walls interstitial fluid. The wall is then compressed, in increments up to a maximum of 23.75% of its initial thickness, and then the species of interest, an acid of pH 2.0, is introduced to the system and the resulting colour change was used as a marker for concentration. This enabled the site specific measurement of concentration at different depths throughout the porous wall. These experimental results were then validated computationally using the finite element solver COMSOL Multiphysics. The authors concluded that compression of a porous artery wall contributes significantly to the modulation of arterial WSMT and should be considered in

limited in that they cannot be used to analyse mass transport within a porous wall.

forces can cause local concentrations to deviate from the mean concentration.

clot size and location, large variations in arterial uptake were witnessed.

future DES computational studies.
