Computational simulation methodologies for mechanobiological modelling: a cell-centred approach to neointima development in stents

Impact of Tissue Damage and Hemodynamics on Restenosis Following Percutaneous Transluminal Angioplasty: A Patient-Specific Multiscale Model

Multiscale agent-based modeling frameworks have recently emerged as promising mechanobiological models to capture the interplay between biomechanical forces, cellular behavior, and molecular pathways underlying restenosis following percutaneous transluminal angioplasty (PTA). However, their applications are mainly limited to idealized scenarios. Herein, a multiscale agent-based modeling framework for investigating restenosis following PTA in a patient-specific superficial femoral artery (SFA) is proposed. The framework replicates the 2-month arterial wall remodeling in response to the PTA-induced injury and altered hemodynamics, by combining three modules: (i) the PTA module, consisting in a finite element structural mechanics simulation of PTA, featuring anisotropic hyperelastic material models coupled with a damage formulation for fibrous soft tissue and the element deletion strategy, providing the arterial wall damage and post-intervention configuration, (ii) the hemodynamics module, quantifying the post-intervention hemodynamics through computational fluid dynamics simulations, and (iii) the tissue remodeling module, based on an agent-based model of cellular dynamics. Two scenarios were explored, considering balloon expansion diameters of 5.2 and 6.2 mm. The framework captured PTA-induced arterial tissue lacerations and the post-PTA arterial wall remodeling. This remodeling process involved rapid cellular migration to the PTA-damaged regions, exacerbated cell proliferation and extracellular matrix production, resulting in lumen area reduction up to 1-month follow-up. After this initial reduction, the growth stabilized, due to the resolution of the inflammatory state and changes in hemodynamics. The similarity of the obtained results to clinical observations in treated SFAs suggests the potential of the framework for capturing patient-specific mechanobiological events occurring after PTA intervention.

An intricate interplay between stent drug dose and release rate dictates arterial restenosis

Since the introduction of percutaneous coronary intervention (PCI) for the treatment of obstructive coronary artery disease (CAD), patient outcomes have progressively improved. Drug eluting stents (DES) that employ anti-proliferative drugs to limit excess tissue growth following stent deployment have proved revolutionary. However, restenosis and a need for repeat revascularisation still occurs after DES use. Over the last few years, computational models have emerged that detail restenosis following the deployment of a bare metal stent (BMS), focusing primarily on contributions from mechanics and fluid dynamics. However, none of the existing models adequately account for spatiotemporal delivery of drug and the influence of this on the cellular processes that drive restenosis. In an attempt to fill this void, a novel continuum restenosis model coupled with spatiotemporal drug delivery is presented. Our results indicate that the severity and time-course of restenosis is critically dependent on the drug delivery strategy. Specifically, we uncover an intricate interplay between initial drug loading, drug release rate and restenosis, indicating that it is not sufficient to simply ramp-up the drug dose or prolong the time course of drug release to improve stent efficacy. Our model also shows that the level of stent over-expansion and stent design features, such as inter-strut spacing and strut thickness, influence restenosis development, in agreement with trends observed in experimental and clinical studies. Moreover, other critical aspects of the model which dictate restenosis, including the drug binding site density are investigated, where comparisons are made between approaches which assume this to be either constant or proportional to the number of smooth muscle cells (SMCs). Taken together, our results highlight the necessity of incorporating these aspects of drug delivery in the pursuit of optimal DES design.

A Multiscale Approach for Predicting Certain Effects of Hand-Transmitted Vibration on Finger Arteries

Prolonged exposure to strong hand-arm vibrations can lead to vascular disorders such as Vibration White Finger (VWF). We modeled the onset of this peripheral vascular disease in two steps. The first consists in assessing the reduction in shearing forces exerted by the blood on the walls of the arteries (Wall Shear Stress—WSS) during exposure to vibrations. An acute but repeated reduction in WSS can lead to arterial stenosis characteristic of VWF. The second step is devoted to using a numerical mechano-biological model to predict this stenosis as a function of WSS. WSS is reduced by a factor of 3 during exposure to vibration of 40 m·s−2. This reduction is independent of the frequency of excitation between 31 Hz and 400 Hz. WSS decreases logarithmically when the amplitude of the vibration increases. The mechano-biological model simulated arterial stenosis of 30% for an employee exposed for 4 h a day for 10 years. This model also highlighted the chronic accumulation of matrix metalloproteinase 2. By considering daily exposure and the vibratory level, we can calculate the degree of stenosis, thus that of the disease for chronic exposure to vibrations.

A predictive multiscale model of in-stent restenosis in femoral arteries: linking haemodynamics and gene expression with an agent-based model of cellular dynamics

In-stent restenosis (ISR) is a maladaptive inflammatory-driven response of femoral arteries to percutaneous transluminal angioplasty and stent deployment, leading to lumen re-narrowing as consequence of excessive cellular proliferative and synthetic activities. A thorough understanding of the underlying mechanobiological factors contributing to ISR is still lacking. Computational multiscale models integrating both continuous- and agent-based approaches have been identified as promising tools to capture key aspects of the complex network of events encompassing molecular, cellular and tissue response to the intervention. In this regard, this work presents a multiscale framework integrating the effects of local haemodynamics and monocyte gene expression data on cellular dynamics to simulate ISR mechanobiological processes in a patient-specific model of stented superficial femoral artery. The framework is based on the coupling of computational fluid dynamics simulations (haemodynamics module) with an agent-based model (ABM) of cellular activities (tissue remodelling module). Sensitivity analysis and surrogate modelling combined with genetic algorithm optimization were adopted to explore the model behaviour and calibrate the ABM parameters. The proposed framework successfully described the patient lumen area reduction from baseline to one-month follow-up, demonstrating the potential capabilities of this approach in predicting the short-term arterial response to the endovascular procedure.

Multiscale Modeling of Vascular Remodeling Induced by Wall Shear Stress

Objective

Hemodynamics-induced low wall shear stress (WSS) is one of the critical reasons leading to vascular remodeling. However, the coupling effects of WSS and cellular kinetics have not been clearly modeled. The aim of this study was to establish a multiscale modeling approach to reveal the vascular remodeling behavior under the interaction between the macroscale of WSS loading and the microscale of cell evolution.

Methods

Computational fluid dynamics (CFD) method and agent-based model (ABM), which have significantly different characteristics in temporal and spatial scales, were adopted to establish the multiscale model. The CFD method is for the second/organ scale, and the ABM is for the month/cell scale. The CFD method was used to simulate blood flow in a vessel and obtain the WSS in a vessel cross-section. The simulations of the smooth muscle cell (SMC) proliferation/apoptosis and extracellular matrix (ECM) generation/degradation in a vessel cross-section were performed by using ABM. During the simulation of the vascular remodeling procedure, the damage index of the SMC and ECM was defined as deviation from the obtained WSS. The damage index decreased gradually to mimic the recovery of WSS-induced vessel damage.

Results

(1) The significant wall thickening region was consistent with the low WSS region. (2) There was no evident change of wall thickness in the normal WSS region. (3) When the damage index approached to 0, the amount and distribution of SMCs and ECM achieved a stable state, and the vessel reached vascular homeostasis.

Conclusion

The established multiscale model can be used to simulate the vascular remodeling behavior over time under various WSS conditions.

Multiscale Computational Modeling of Vascular Adaptation: A Systems Biology Approach Using Agent-Based Models

The widespread incidence of cardiovascular diseases and associated mortality and morbidity, along with the advent of powerful computational resources, have fostered an extensive research in computational modeling of vascular pathophysiology field and promoted in-silico models as a support for biomedical research. Given the multiscale nature of biological systems, the integration of phenomena at different spatial and temporal scales has emerged to be essential in capturing mechanobiological mechanisms underlying vascular adaptation processes. In this regard, agent-based models have demonstrated to successfully embed the systems biology principles and capture the emergent behavior of cellular systems under different pathophysiological conditions. Furthermore, through their modular structure, agent-based models are suitable to be integrated with continuum-based models within a multiscale framework that can link the molecular pathways to the cell and tissue levels. This can allow improving existing therapies and/or developing new therapeutic strategies. The present review examines the multiscale computational frameworks of vascular adaptation with an emphasis on the integration of agent-based approaches with continuum models to describe vascular pathophysiology in a systems biology perspective. The state-of-the-art highlights the current gaps and limitations in the field, thus shedding light on new areas to be explored that may become the future research focus. The inclusion of molecular intracellular pathways (e.g., genomics or proteomics) within the multiscale agent-based modeling frameworks will certainly provide a great contribution to the promising personalized medicine. Efforts will be also needed to address the challenges encountered for the verification, uncertainty quantification, calibration and validation of these multiscale frameworks.

Do we really understand how drug eluted from stents modulates arterial healing?

The advent of drug-eluting stents (DES) has revolutionised the treatment of coronary artery disease. These devices, coated with anti-proliferative drugs, are deployed into stenosed or occluded vessels, compressing the plaque to restore natural blood flow, whilst simultaneously combating the evolution of restenotic tissue. Since the development of the first stent, extensive research has investigated how further advancements in stent technology can improve patient outcome. Mathematical and computational modelling has featured heavily, with models focussing on structural mechanics, computational fluid dynamics, drug elution kinetics and subsequent binding within the arterial wall; often considered separately. Smooth Muscle Cell (SMC) proliferation and neointimal growth are key features of the healing process following stent deployment. However, models which depict the action of drug on these processes are lacking. In this article, we start by reviewing current models of cell growth, which predominantly emanate from cancer research, and available published data on SMC proliferation, before presenting a series of mathematical models of varying complexity to detail the action of drug on SMC growth in vitro. Our results highlight that, at least for Sodium Salicylate and Paclitaxel, the current state-of-the-art nonlinear saturable binding model is incapable of capturing the proliferative response of SMCs across a range of drug doses and exposure times. Our findings potentially have important implications on the interpretation of current computational models and their future use to optimise and control drug release from DES and drug-coated balloons.

Computational modelling of magnesium stent mechanical performance in a remodelling artery: Effects of multiple remodelling stimuli

Significant research has been conducted in the area of coronary stents/scaffolds made from resorbable metallic and polymeric biomaterials. These next-generation bioabsorbable stents have the potential to completely revolutionise the treatment of coronary artery disease. The primary advantage of resorbable devices over permanent stents is their temporary presence which, from a theoretical point of view, means only a healed coronary artery will be left behind following degradation of the stent potentially eliminating long-term clinical problems associated with permanent stents. The healing of the artery following coronary stent/scaffold implantation is crucial for the long-term safety of these devices. Computational modelling can be used to evaluate the performance of complex stent devices in silico and assist in the design and development and understanding of the next-generation resorbable stents. What is lacking in computational modelling literature is the representation of the active response of the arterial tissue in the weeks and months following stent implantation, ie, neointimal remodelling, in particular for the case of biodegradable stents. In this paper, a computational modelling framework is developed, which accounts for two major physiological stimuli responsible for neointimal remodelling and combined with a magnesium corrosion model that is capable of simulating localised pitting (realistic) stent corrosion. The framework is used to simulate different neointimal growth patterns and to explore the effects the neointimal remodelling has on the mechanical performance (scaffolding support) of the bioabsorbable magnesium stent.

Mathematical modelling of the restenosis process after stent implantation

The stenting procedure has evolved to become a highly successful technique for the clinical treatment of advanced atherosclerotic lesions in arteries. However, the development of in-stent restenosis remains a key problem. In this work, a novel two-dimensional continuum mathematical model is proposed to describe the complex restenosis process following the insertion of a stent into a coronary artery. The biological species considered to play a key role in restenosis development are growth factors, matrix metalloproteinases, extracellular matrix, smooth muscle cells and endothelial cells. Diffusion-reaction equations are used for modelling the mass balance between species in the arterial wall. Experimental data from the literature have been used in order to estimate model parameters. Moreover, a sensitivity analysis has been performed to study the impact of varying the parameters of the model on the evolution of the biological species. The results demonstrate that this computational model qualitatively captures the key characteristics of the lesion growth and the healing process within an artery subjected to non-physiological mechanical forces. Our results suggest that the arterial wall response is driven by the damage area, smooth muscle cell proliferation and the collagen turnover among other factors.

A versatile hybrid agent-based, particle and partial differential equations method to analyze vascular adaptation

Peripheral arterial occlusive disease is a chronic pathology affecting at least 8–12 million people in the USA, typically treated with a vein graft bypass or through the deployment of a stent in order to restore the physiological circulation. Failure of peripheral endovascular interventions occurs at the intersection of vascular biology, biomechanics, and clinical decision making. It is our hypothesis that the majority of endovascular treatment approaches share the same driving mechanisms and that a deep understanding of the adaptation process is pivotal in order to improve the current outcome of the procedure. The postsurgical adaptation of vein graft bypasses offers the perfect example of how the balance between intimal hyperplasia and wall remodeling determines the failure or the success of the intervention. Accordingly, this work presents a versatile computational model able to capture the feedback loop that describes the interaction between events at cellular/tissue level and mechano-environmental conditions. The work here presented is a generalization and an improvement of a previous work by our group of investigators, where an agent-based model uses a cellular automata principle on a fixed hexagonal grid to reproduce the leading events of the graft’s restenosis. The new hybrid model here presented allows a more realistic simulation both of the biological laws that drive the cellular behavior and of the active role of the membranes that separate the various layers of the vein. The novel feature is to use an immersed boundary implementation of a highly viscous flow to represent SMC motility and matrix reorganization in response to graft adaptation. Our implementation is modular, and this makes us able to choose the right compromise between closeness to the physiological reality and complexity of the model. The focus of this paper is to offer a new modular implementation that combines the best features of an agent-based model, continuum mechanics, and particle-tracking methods to cope with the multiscale nature of the adaptation phenomena. This hybrid method allows us to quickly test various hypotheses with a particular attention to cellular motility, a process that we demonstrated should be driven by mechanical homeostasis in order to maintain the right balance between cells and extracellular matrix in order to reproduce a distribution similar to histological experimental data from vein grafts.

A chemo-mechano-biological formulation for the effects of biochemical alterations on arterial mechanics: the role of molecular transport and multiscale tissue remodelling

This paper presents a chemo-mechano-biological framework for arterial physiopathology. The model accounts for the fine remodelling in the multiscale hierarchical arrangement of tissue constituents and for the diffusion of molecular species involved in cell-cell signalling pathways. Effects in terms of alterations in arterial compliance are obtained. A simple instructive example is introduced. Although oversimplified with respect to realistic case studies, the proposed application mimics the biochemical activity of matrix metalloproteinases, transforming growth factors beta and interleukins on tissue remodelling. Effects of macrophage infiltration, of intimal thickening and of a healing phase are investigated, highlighting the corresponding influence on arterial compliance. The obtained results show that the present approach is able to capture changes in arterial mechanics as a consequence of the alterations in tissue biochemical environment and cellular activity, as well as to incorporate the protective role of both autoimmune responses and pharmacological treatments.

Mechanobiological model of arterial growth and remodeling

A coupled agent-based model (ABM) and finite element analysis (FEA) computational framework is developed to study the interplay of bio-chemo-mechanical factors in blood vessels and their role in maintaining homeostasis. The agent-based model implements the power of REPAST Simphony libraries and adapts its environment for biological simulations. Coupling a continuum-level model (FEA) to a cellular-level model (ABM) has enabled this computational framework to capture the response of blood vessels to increased or decreased levels of growth factors, proteases and other signaling molecules (on the micro scale) as well as altered blood pressure. Performance of the model is assessed by simulating porcine left anterior descending artery under normotensive conditions and transient increases in blood pressure and by analyzing sensitivity of the model to variations in the rule parameters of the ABM. These simulations proved that the model is stable under normotensive conditions and can recover from transient increases in blood pressure. Sensitivity studies revealed that the model is most sensitive to variations in the concentration of growth factors that affect cellular proliferation and regulate extracellular matrix composition (mainly collagen).

Computational Modeling of the Mechanical Performance of a Magnesium Stent Undergoing Uniform and Pitting Corrosion in a Remodeling Artery

Coronary stents made from degradable biomaterials such as magnesium alloy are an emerging technology in the treatment of coronary artery disease. Biodegradable stents provide mechanical support to the artery during the initial scaffolding period after which the artery will have remodeled. The subsequent resorption of the stent biomaterial by the body has potential to reduce the risk associated with long-term placement of these devices, such as in-stent restenosis, late stent thrombosis, and fatigue fracture. Computational modeling such as finite-element analysis has proven to be an extremely useful tool in the continued design and development of these medical devices. What is lacking in computational modeling literature is the representation of the active response of the arterial tissue in the weeks and months following stent implantation, i.e., neointimal remodeling. The phenomenon of neointimal remodeling is particularly interesting and significant in the case of biodegradable stents, when both stent degradation and neointimal remodeling can occur simultaneously, presenting the possibility of a mechanical interaction and transfer of load between the degrading stent and the remodeling artery. In this paper, a computational modeling framework is developed that combines magnesium alloy degradation and neointimal remodeling, which is capable of simulating both uniform (best case) and localized pitting (realistic) stent corrosion in a remodeling artery. The framework is used to evaluate the effects of the neointima on the mechanics of the stent, when the stent is undergoing uniform or pitting corrosion, and to assess the effects of the neointimal formation rate relative to the overall stent degradation rate (for both uniform and pitting conditions).

Patient-Specific, Multi-Scale Modeling of Neointimal Hyperplasia in Vein Grafts

Neointimal hyperplasia is amongst the major causes of failure of bypass grafts. The disease progression varies from patient to patient due to a range of different factors. In this paper, a mathematical model will be used to understand neointimal hyperplasia in individual patients, combining information from biological experiments and patient-specific data to analyze some aspects of the disease, particularly with regard to mechanical stimuli due to shear stresses on the vessel wall. By combining a biochemical model of cell growth and a patient-specific computational fluid dynamics analysis of blood flow in the lumen, remodeling of the blood vessel is studied by means of a novel computational framework. The framework was used to analyze two vein graft bypasses from one patient: a femoro-popliteal and a femoro-distal bypass. The remodeling of the vessel wall and analysis of the flow for each case was then compared to clinical data and discussed as a potential tool for a better understanding of the disease. Simulation results from this first computational approach showed an overall agreement on the locations of hyperplasia in these patients and demonstrated the potential of using new integrative modeling tools to understand disease progression.

A dynamical system that describes vein graft adaptation and failure

Adaptation of vein bypass grafts to the mechanical stresses imposed by the arterial circulation is thought to be the primary determinant for lesion development, yet an understanding of how the various forces dictate local wall remodeling is lacking. We develop a dynamical system that summarizes the complex interplay between the mechanical environment and cell/matrix kinetics, ultimately dictating changes in the vein graft architecture. Based on a systematic mapping of the parameter space, three general remodeling response patterns are observed: (1) shear stabilized intimal thickening, (2) tension induced wall thinning and lumen expansion, and (3) tension stabilized wall thickening. Notable is our observation that the integration of multiple feedback mechanisms leads to a variety of non-linear responses that would be unanticipated by an analysis of each system component independently. This dynamic analysis supports the clinical observation that the majority of vein grafts proceed along an adaptive trajectory, where grafts dilate and mildly thicken in response to the increased tension and shear, but a small portion of the grafts demonstrate a maladaptive phenotype, where progressive inward remodeling and accentuated wall thickening lead to graft failure.

The effects of stenting on shear stress: relevance to endothelial injury and repair

Stent deployment following balloon angioplasty is used routinely to treat coronary artery disease. These interventions cause damage and loss of endothelial cells (EC), and thus promote in-stent thrombosis and restenosis. Injured arteries are repaired (intrinsically) by locally derived EC and by circulating endothelial progenitor cells which migrate and proliferate to re-populate denuded regions. However, re-endothelialization is not always complete and often dysfunctional. Moreover, the molecular and biomechanical mechanisms that control EC repair and function in stented segments are poorly understood. Here, we propose that stents modify endothelial repair processes, in part, by altering fluid shear stress, a mechanical force that influences EC migration and proliferation. A more detailed understanding of the biomechanical processes that control endothelial healing would provide a platform for the development of novel therapeutic approaches to minimize damage and promote vascular repair in stented arteries.

In Silico Prediction of the Mechanobiological Response of Arterial Tissue: Application to Angioplasty and Stenting

One way to restore physiological blood flow to occluded arteries involves the deformation of plaque using an intravascular balloon and preventing elastic recoil using a stent. Angioplasty and stent implantation cause unphysiological loading of the arterial tissue, which may lead to tissue in-growth and reblockage; termed “restenosis.” In this paper, a computational methodology for predicting the time-course of restenosis is presented. Stress-induced damage, computed using a remaining life approach, stimulates inflammation (production of matrix degrading factors and growth stimuli). This, in turn, induces a change in smooth muscle cell phenotype from contractile (as exists in the quiescent tissue) to synthetic (as exists in the growing tissue). In this paper, smooth muscle cell activity (migration, proliferation, and differentiation) is simulated in a lattice using a stochastic approach to model individual cell activity. The inflammation equations are examined under simplified loading cases. The mechanobiological parameters of the model were estimated by calibrating the model response to the results of a balloon angioplasty study in humans. The simulation method was then used to simulate restenosis in a two dimensional model of a stented artery. Cell activity predictions were similar to those observed during neointimal hyperplasia, culminating in the growth of restenosis. Similar to experiment, the amount of neointima produced increased with the degree of expansion of the stent, and this relationship was found to be highly dependant on the prescribed inflammatory response. It was found that the duration of inflammation affected the amount of restenosis produced, and that this effect was most pronounced with large stent expansions. In conclusion, the paper shows that the arterial tissue response to mechanical stimulation can be predicted using a stochastic cell modeling approach, and that the simulation captures features of restenosis development observed with real stents. The modeling approach is proposed for application in three dimensional models of cardiovascular stenting procedures.

The consequences of the mechanical environment of peripheral arteries for nitinol stenting

The use of stents in peripheral arteries has not been as successful as in coronary arteries, with high rates of restenosis and stent fracture common. Normal joint flexion induces a range of forces on the arteries, which has an unknown effect on the outcomes of stenting. The objective of this study is to determine how physiological levels of vessel bending and compression following stent implantation will influence the magnitude of stent stresses and hence the risks of fatigue fracture. A further objective is to compare how this mechanical environment will influence arterial stresses following implantation of either stainless steel or nitinol stents. To this end, models of both nitinol and stainless steel stents deployed in peripheral arteries were created, with appropriate loading conditions applied. At high levels of bending and compression, the strain amplitude threshold value for fatigue failure is exceeded for nitinol stents. Bending was predicted to induce high stresses in the artery following stenting, with higher arterial stresses predicted following implantation of a stainless steel stent compared to a nitinol stent. Both bending and compression may contribute to stent fracture by increasing the strain amplitude within the stent, with the dominant factor dependant on location within the arterial tree. For the specific stent types investigated in this study, the model predictions suggest that compression is the dominant mechanical factor in terms of stent fatigue in the femoral arteries, whereas bending is the most significant factor in the popliteal artery. To increase fatigue life and reduce arterial injury, location specific stent designs are required for peripheral arteries.