Modelling drug elution from stents: effects of reversible binding in the vascular wall and degradable polymeric matrix

An unsteady analysis of two-phase binding of drug in an asymmetric stenosed vessel

In this paper, we investigate endovascular delivery to get a step ahead of the pharmacological limitations it has due to the complexity of dealing with a patient-specific vessel through a mathematical model. We divide the domain of computation into four sub-domains: the lumen, the lumen-tissue interface, the upper tissue and the lower tissue which are extracted from an asymmetric atherosclerotic image derived by the intravascular ultrasound (IVUS) technique. The injected drug at the luminal inlet is transported with the streaming blood which is considered Newtonian. An irreversible uptake kinetics of the injected drug at the lumen-tissue interface from the luminal side to the tissue domains is assumed. Subsequently, the drug is dispersed within the tissue followed by its retention in the extracellular matrix (ECM) and by receptor-mediated binding. The Marker and Cell (MAC) method has been leveraged to get a quantitative insight into the model considered. The effect of the wall absorption parameter on the concentration of all drug forms (free as well as two-phase bound) has been thoroughly investigated, and some other important factors, such as the averaged concentration, the tissue content, the fractional effect, the concentration variance and the effectiveness of drug have been graphically analyzed to gain a clear understanding of endovascular delivery. The simulated results predict that with increasing values of the absorption parameter, the averaged concentrations of all drug forms do decrease. An early saturation of binding sites takes place for smaller values of the absorption parameter, and also rapid saturation of ECM binding sites occurs as compared to receptor binding sites. Results also predict the influence of surface roughness as well as asymmetry of the domain about the centerline on the distribution and retention of drug. A thorough sensitivity analysis has been carried out to determine the influence of some parameters involved.

Specific and nonspecific binding of drug eluted from a half-embedded stent in presence of atherosclerotic plaque

This study is dealt with the two-phase binding (specific and nonspecific) of drug eluted from a half- embedded drug-eluting stent in presence of atherosclerotic plaque. The specific binding due to the interaction of drug molecules with specific receptors and nonspecific binding caused by the trapping of drug in the extra-cellular matrix have been paid due attention. An idealised wall consisting of a plaque and a healthy tissue region has been considered. Moreover, a Dirichlet release condition is imposed on the strut surface. In this investigation, a two-dimensional model governing drug transport and its two-phase binding in cylindrical polar coordinate system has been solved numerically by a finite-difference method. Our simulation predicts that plaque behaves like a physical barrier in two types of the binding process and there is an inverse relationship between bound drug concentration and plaque thickness. Simulations show that a single peak profile of drug is noted when the struts are situated one-strut radius apart and as the inter-strut distance increases, the peak concentration falls and distinct peak profiles over each strut are visualised. The model also reveals that in the region downstream of a strut, the concentration of both bound drug forms in the plaque and healthy regions increases, and eventually, the saturation length of binding sites increases. Predicted results show for smaller Damköhler number, the rapid saturation of binding sites takes place and the stent having thinner strut may perform well in terms of effectiveness as well as efficacy in the stent-based delivery.

Modelling chemistry and biology after implantation of a drug-eluting stent. Part I: Drug transport

Drug-eluting stents have been used widely to prevent restenosis of arteries following percutaneous balloon angioplasty. Mathematical modelling plays an important role in optimising the design of these stents to maximise their efficiency. When designing a drug-eluting stent system, we expect to have a sufficient amount of drug being released into the artery wall for a sufficient period to prevent restenosis. In this paper, a simple model is considered to provide an elementary description of drug release into artery tissue from an implanted stent. From the model, we identified a parameter regime to optimise the system when preparing the polymer coating. The model provides some useful order of magnitude estimates for the key quantities of interest. From the model, we can identify the time scales over which the drug traverses the artery wall and empties from the polymer coating, as well as obtain approximate formulae for the total amount of drug in the artery tissue and the fraction of drug that has released from the polymer. The model was evaluated by comparing to in-vivo experimental data and good agreement was found.

Modeling and analysis of drug-eluting stents with biodegradable PLGA coating: consequences on intravascular drug delivery

Increasing interests have been raised toward the potential applications of biodegradable poly(lactic-co-glycolic acid) (PLGA) coatings for drug-eluting stents in order to improve the drug delivery and reduce adverse outcomes in stented arteries in patients. This article presents a mathematical model to describe the integrated processes of drug release in a stent with PLGA coating and subsequent drug delivery, distribution, and drug pharmacokinetics in the arterial wall. The integrated model takes into account the PLGA degradation and erosion, anisotropic drug diffusion in the arterial wall, and reversible drug binding. The model simulations first compare the drug delivery from a biodegradable PLGA coating with that from a biodurable coating, including the drug release profiles in the coating, average arterial drug levels, and arterial drug distribution. Using the model for the PLGA stent coating, the simulations further investigate drug internalization, interstitial fluid flow in the arterial wall, and stent embedment for their impact on drug delivery. Simulation results show that these three factors, while imposing little change in the drug release profiles, can greatly change the average drug concentrations in the arterial wall. In particular, each of the factors leads to significant and yet distinguished alterations in the arterial drug distribution that can potentially influence the treatment outcomes. The detailed integrated model provides insights into the design and evaluation of biodegradable PLGA-coated drug-eluting stents for improved intravascular drug delivery.

Controlled release for local delivery of drugs: barriers and models

Controlled release systems are an effective means for local drug delivery. In local drug delivery, the major goal is to supply therapeutic levels of a drug agent at a physical site in the body for a prolonged period. A second goal is to reduce systemic toxicities, by avoiding the delivery of agents to non-target tissues remote from the site. Understanding the dynamics of drug transport in the vicinity of a local drug delivery device is helpful in achieving both of these goals. Here, we provide an overview of controlled release systems for local delivery and we review mathematical models of drug transport in tissue, which describe the local penetration of drugs into tissue and illustrate the factors - such as diffusion, convection, and elimination - that control drug dispersion and its ultimate fate. This review highlights the important role of controlled release science in development of reliable methods for local delivery, as well as the barriers to accomplishing effective delivery in the brain, blood vessels, mucosal epithelia, and the skin.

Numerical modelling of the physical factors that affect mass transport in the vasculature at early time periods

Coronary artery disease results in blockages or narrowing of the artery lumen. Drug eluting stents were developed to replace bare metal stents in an effort to combat re-blocking of the lumen. A key element in determining the therapeutic success of a drug eluting stent is an in-depth understanding of the physical factors that affect mass transport of the drug into the arterial wall, over early time periods. The numerical models developed within this study focus on assessing the influence of a host of physical factors that either facilitate or impede therapeutic drug delivery into the arterial wall from the unit cell of an idealised stent. This study demonstrates that model reduction strategies to 2D and 1D can still adequately represent a 3D curved arterial wall and strut polymer coating, respectively, using an idealistic stent geometry. It was shown that the level of strut compression can have a significant impact on therapeutic drug delivery in the arterial wall.

Modeling stented coronary arteries: where we are, where to go

In the last two decades, numerical models have become well-recognized and widely adopted tools to investigate stenting procedures. Due to limited computational resources and modeling capabilities, early numerical studies only involved simplified cases and idealized stented arteries. Nowadays, increased computational power allows for numerical models to meet clinical needs and include more complex cases such as the implantation of multiple stents in bifurcations or curved vessels. Interesting progresses have been made in the numerical modeling of stenting procedures both from a structural and a fluid dynamics points of view. Moreover, in the drug eluting stents era, new insights on drug elution capabilities are becoming essential in the stent development. Lastly, image-based methods able to reconstruct realistic geometries from medical images have been proposed in the recent literature aiming to better describe the peculiar anatomical features of coronary vessels and increase the accuracy of the numerical models. In this light, this review provides a comprehensive analysis of the current state-of-the-art in this research area, discussing the main methodological advances and remarkable results drawn from a number of significant studies.

Modelling intravascular delivery from drug-eluting stents with biodurable coating: investigation of anisotropic vascular drug diffusivity and arterial drug distribution

In-stent restenosis occurs in coronary arteries after implantation of drug-eluting stents with non-uniform restenosis thickness distribution in the artery cross section. Knowledge of the spatio-temporal drug uptake in the arterial wall is useful for investigating restenosis growth but may often be very expensive/difficult to acquire experimentally. In this study, local delivery of a hydrophobic drug from a drug-eluting stent implanted in a coronary artery is mathematically modelled to investigate the drug release and spatio-temporal drug distribution in the arterial wall. The model integrates drug diffusion in the coating and drug diffusion with reversible binding in the arterial wall. The model is solved by the finite volume method for both high and low drug loadings relative to its solubility in the stent coating with varied isotropic-anisotropic vascular drug diffusivities. Drug release profiles in the coating are observed to depend not only on the coating drug diffusivity but also on the properties of the surrounding arterial wall. Time dependencies of the spatially averaged free- and bound-drug levels in the arterial wall on the coating and vascular drug diffusivities are discussed. Anisotropic vascular drug diffusivities result in slightly different average drug levels in the arterial wall but with very different spatial distributions. Higher circumferential vascular diffusivity results in more uniform drug loading in the upper layers and is potentially beneficial in reducing in-stent restenosis. An analytical expression is derived which can be used to determine regions in the arterial with higher free-drug concentration than bound-drug concentration.

Modeling drug-carrier interaction in the drug release from nanocarriers

Numerous nanocarriers of various compositions and geometries have been developed for the delivery and release of therapeutic and imaging agents. Due to the high specific surface areas of nanocarriers, different mechanisms such as ion pairing and hydrophobic interaction need to be explored for achieving sustained release. Recently, we developed a three-parameter model that considers reversible drug-carrier interaction and first-order drug release from liposomes. A closed-form analytical solution was obtained. Here, we further explore the ability of the model to capture the release of bioactive molecules such as drugs and growth factors from various nanocarriers. A parameter study demonstrates that the model is capable of resembling major categories of drug release kinetics. We further fit the model to 60 sets of experimental data from various drug release systems, including nanoparticles, hollow particles, fibers, and hollow fibers. Additionally, bootstrapping is used to evaluate the accuracy of parameter determination and validate the model in selected cases. The simplicity and universality of the model and the clear physical meanings of each model parameter render the model useful for the design and development of new drug delivery systems.

Evaluation of the effect of stent strut profile on shear stress distribution using statistical moments

BACKGROUND

In-stent restenosis rates have been closely linked to the wall shear stress distribution within a stented arterial segment, which in turn is a function of stent design. Unfortunately, evaluation of hemodynamic performance can only be evaluated with long term clinical trials. In this work we introduce a set of metrics, based on statistical moments, that can be used to evaluate the hemodynamic performance of a stent in a standardized way. They are presented in the context of a 2D flow study, which analyzes the impact of different strut profiles on the wall shear stress distribution for stented coronary arteries.

RESULTS

It was shown that the proposed metrics have the ability to evaluate hemodynamic performance quantitatively and compare it to a common standard. In the context of the simulations presented here, they show that stent's strut profile significantly affect the shear stress distribution along the arterial wall. They also demonstrates that more streamlined profiles exhibit better hemodynamic performance than the standard square and circular profiles. The proposed metrics can be used to compare results from different research groups, and provide an improved method of quantifying hemodynamic performance in comparison to traditional techniques.

CONCLUSION

The strut shape found in the latest generations of stents are commonly dictated by manufacturing limitations. This research shows, however, that strut design can play a fundamental role in the improvement of the hemodynamic performance of stents. Present results show that up to 96% of the area between struts is exposed to wall shear stress levels above the critical value for the onset of restenosis when a tear-drop strut profile is used, while the analogous value for a square profile is 19.4%. The conclusions drawn from the non-dimensional metrics introduced in this work show good agreement with an ordinary analysis of the wall shear stress distribution based on the overall area exposed to critically low wall shear stress levels. The proposed metrics are able to predict, as expected, that more streamlined profiles perform better hemodynamically. These metrics integrate the entire morphology of the shear stress distribution and as a result are more robust than the traditional approach, which only compares the relative value of the local wall shear stress with a critical value of 0.5 Pa. In the future, these metrics could be employed to compare, in a standardized way, the hemodynamic performance of different stent designs.