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.

Of concern in the paper is a numerical study of endovascular drug delivery in a patient-specific atherosclerotic artery through a mathematical model in which the luminal flow is governed by an incompressible vis- cous Newtonian fluid, and the transport of luminal as well as tissue concentration is modeled as an unsteady convection-diffusion process. An image processing technique has been successfully adopted to detect the edges of the computational domain extracted from an asymmetric (about the centerline of the artery) patient-specific atherosclerotic artery. Considering each pixel as a control volume, the Marker and Cell (MAC) method has been leveraged to get a quantitative insight of the model considered by exploiting physiologically realistic initial, boundary as well as interface conditions. Simulated results reveal that the number as well as the length of separation zone does increase with increasing Re, and the near-wall velocity contour might be important for estimating the near-wall residence time for the pool of drug molecules available for tissue uptake. Results also show that the more the tissue porosity and interface roughness do not necessarily imply the more the effective- ness of delivery, even though they enhance the averaged concentration in the tissue domains, and also the area under concentration diminishes with increasing Peclet number. Thus, the tissue porosity, the Peclet number and various geometrical shapes (interface roughness) play a pivotal role in the dispersion and the effectiveness of drug delivery. GANITJ. Bangladesh Math. Soc.41.1 (2021) 62-77

To quantify the biology and physical understanding of endovascular drug delivery, a mathematical model that accounts for the two-phase binding of drug molecules in a diseased patient-specific artery has been developed. Using an image segmentation technique, the edges of the computational domain have been successfully extracted from an asymmetric intravascular ultrasound longitudinal image. The flow inside the porous tissue is described by the Brinkman model, and the luminal flow is Newtonian. At the lumen–tissue interface, an irreversible uptake kinetics for the injected drug from the luminal side into the tissue is taken into account. Furthermore, the drug's two-phase binding process, namely, the nonspecific binding caused by the drug's trapping in the extracellular medium (ECM-bound) and the specific binding caused by the interaction between drug molecules and receptors (REC-bound), has been considered. The Marker and Cell method has been leveraged to solve the governing equations numerically. Spatiotemporal variations of free drug, ECM-bound drug, and REC-bound drug are examined thoroughly for varying absorption parameter. Simulated results reveal that the interstitial flow amplifies drug distribution, retention, and delivery effectiveness, but flow separation downstream of the constriction reduces transmural flux. Concomitantly, the larger the absorption parameter, the higher the tissue content and effectiveness; nevertheless, significantly, larger absorption parameter values do not necessarily suggest improved delivery effectiveness. A thorough sensitivity analysis was carried out to predict the effects of some of the parameters involved.