Computational Framework for Modeling In-Stent Restenosis1

The living biological tissue adapts to the changes in its biomechanical environment by growth and remodeling. For instance, the arterial thickening and stiffening are observed in hypertensive rats [1], and the neo-tissue grows toward the lumen of stented artery as a result of stent implantation [2]. To better understand the tissue response to the induced mechanical stimuli, many experiments using animal models were conducted. As important complement to experiment, the computational models were also developed to capture and predict the tissue response once they were validated by experimental results. The most popular models for artery growth and remodeling are mathematical models [3–5]. The arteries are usually modeled as hollow cylinders subjected to uniform pressure, and the evolution of geometrical parameters on one cross section, such as wall thickness, deformed inner radius, or opening angle, were usually obtained to describe the arterial growth and adaptation. Therefore, they are not competent in modeling the response of artery subjected to complex loading and boundary conditions, such as the restenosis formation after stent implantation. In this work, a computational framework for artery remodeling was developed by means of commercial finite element software, and it was illustrated by simulating the restenosis formation.The computational model for simulating the restenosis of stented artery is shown in Fig. 1. The artery is highlighted in red color, and the potential neo-tissue, highlighted in blue color, is attached to the inner wall of artery. A stent strut is also virtually simulated to induce mechanical stimuli for activating the remodeling. Both the artery and neo-tissue are meshed using volumetric elements. In this work, the stent strut is modeled as a circular ring with uniform thickness. It is represented as the void elements in the potential neo-tissue, i.e., the stent strut is buried in the neo-tissue when restenosis occurs. The interaction between artery and stent is simplified as the stent-induced high pressure acting on the stent-artery interface. Larger arterial stress induced by the high pressure will initiate the remodeling process.In the remodeling process, the volume and shape of the artery are changed continuously. In order to track the volume and shape of the artery, an one-dimension array, v(i), is used to record and determine the status of the element. v(i) = 1 indicates that the volume element exists in the current remodeling phase, while v(i) = 0 indicates the volume element disappears from the remodeling phase. The whole artery is divided into growth domain and nongrowth domain. In the remodeling process simulating restenosis formation, the nongrowth domain (the original artery) will maintain its volume and topology, while the elements in the growth domain (the potential neo-tissue) may remain or disappear depending on the stress of elements. In each remodeling phase, the growth domain includes only one layer of virtual material, i.e., only one layer of the neo-tissue is activated at the beginning of each phase. The homogenization method is used to find the optimized topology of the artery in the current growth domain, i.e., the elements with larger stress than the predefined stress threshold will be remained while others will disappear. The remodeling will continue by activating the next layer of virtual material, until the maximum stress of all elements is smaller than the stress threshold.One straight artery, which has inner diameter of 4 mm, wall thickness of 1 mm and length of 10 mm, is used to illustrate the remodeling process. The virtual material representing the potential neo-tissue, which has a thickness of 1 mm, is meshed into eight layers of elements. The stent strut, which is positioned at the center of artery, is modeled as the circular ring with uniform thickness of 0.25 mm. Linear elastic material property is assigned to artery and neo-tissue, i.e., Young's modulus is 900 kPa, and Poisson's ratio is 0.4. The axial and circumferential displacements of two ends of the artery are constrained, while the displacement along radial direction is allowed. The stent-induced high pressure acting on inner wall of artery is set as 26.6 kPa. The von Mises stress threshold is defined as [σ] = 3000 Pa. The remodeling process of the restenosis formation is shown in Fig. 2, where the neo-tissue growth toward the arterial lumen is observed. The comparison of the arterial stress distribution before and after remodeling is shown in Fig. 3. It can be observed that the larger arterial stress induced by stent-strut expansion is alleviated by the neo-tissue ingrowth due to its load-sharing capacity.The stent implantation results in significant changes in biomechanical environment of artery, which is believed to initiate the process of artery remodeling, i.e., the restenosis formation. Many mechanical measurements, such as strain, stress, strain energy density or strain rate, are identified as the mechanical stimuli for artery remodeling, though no agreement has been reached [6]. In this work, the arterial stress, which determines the activation of elements in neo-tissue, is used. The computational framework is illustrated by simulating the restenosis formation induced by one stent strut, indicating its capability to model the arterial remodeling under other conditions. Comparing to other computational models, the computational model in this work captures the volume change of artery and its structural change, rather than using dimensionless parameter to indicate where and how much the tissue grows [7,8].It is admitted that there are some limitations associated with this computational model for artery remodeling. First, the material property adaptation to changes in its biomechanical environment is not considered, and constant mechanical properties of artery and neo-tissue are used through the whole remodeling process. Second, the stent-artery interaction is not taken into account by simplifying the stent-induced loading as higher pressure acting on inner wall of artery. Usually the thickness of tissue growth at each remodeling phase is not constant, and varied tissue growth along remodeling time will be considered in our future work.In addition, the layer-specific artery model and the contribution of each component (collagen, elastin, smooth muscle cell, etc.,) to the arterial remodeling will be taken into account in future.The authors are grateful for funding from the National Science Foundation under Grant No. 0926880. They thank Dr. Liu for initiating this work.