Understanding how anti–proliferative drug modulates arterial healing following stent deployment

The treatment of coronary artery disease (CAD) was revolutionized following the advent of drug–eluting stents (DES). Since their adoption, patient outcome has significantly improved over earlier systems devoid of drug, where notable indices such as in–stent restenosis (ISR) and repeat revascularisations were reduced. However, such indices remain stubbornly high despite this technological innovation, with patients often returning after one–year for a follow–up procedure. In an attempt to better understand the physical mechanisms that give rise to ISR, many computational models have emerged in recent years. Chapter 1 discusses these in more depth, where the literature is neatly separable into three distinct categories: (i) structural mechanics and computational fluid dynamics, (ii) drug transport models and (iii) mechano–biological models of restenosis. Although the first category is important, it is limitations in (ii) and (iii) that are more pressing. Firstly, drug transport models assume static arteries, where the effect of drug on cell function is ignored, and the artery does not change in response to the growing population of cells. As such, Chapter 2 explores this simplification in depth through a variety of different models describing the effectiveness of drug. Results allude to possible issues with current state–of–the–art drug transport models, such that when coupled to cell function, they are unable to capture the dose–dependent effect of drug on cell growth in vitro. In an attempt to better understand these issues, Chapter 3 explores the efficacy of these drugs when their cell cycle specificity is accounted for, discussing the possible implications of this, particularly in vivo. Moreover, mechano–biological models of restenosis often neglect the delivery of drug, with the devices considered emulating earlier bare metal stents (BMS). Those which do account for the anti–proliferative nature of drug do so through inadequate means, where key findings from (ii) are ignored. Thus, building on the efforts of Chapter 2, Chapters 4–6 explore the spatiot-meporal effect of drug on restenosis, emulating drug delivery in vivo. Key conclusions from Chapter 5 reveals an intricate interplay between stent drug dose and release rate; simultaneously illustrating the impact of stent design on performance. The model is then built upon in Chapter 6, with the implications of delayed arterial healing analysed, a recurring issues associated with DES. The model is the first of its kind to explore the explicit role of anti–proliferative drug on multiple cell types (endothelial and smooth muscle cells), further highlighting the need for optimal drug release strategies to ensure the drug is both efficacious and safe

Parameter search to find ranges of activation and inhibition of wound healing rate in a mathematical model with introduced photobiomodulation

When light stimulation is used for wound healing therapy, a biphasic dose-response curve is observed, where cells are activated below and inhibited above a treatment dose threshold. Light treatment-dose responses are not yet incorporated into mathematical models of wound healing—yet these relationships would support optimization of wound healing treatment protocols. This work adapts an existing wound healing mathematical model by exploring parameter values and introducing exogenous photobiomodulation treatment inputs for future applications in model-based experimental research. A wound healing mathematical model, created by Sherratt and Murray in 1990, includes proliferation, migration, and activating and inhibitory chemical terms. This model was implemented and discretized by Forward Euler (FE) in time and the Central Difference Method (CDM) in space in 1D. Travelling wave solutions of cell density and chemical concentration were obtained and used to plot wound closure in time and to estimate the wound healing rate. A parameter search was conducted to identify ranges where model simulations resulted in activation, inhibition, saturation, or numeric instability of wound healing. Published results of photobiomodulation treatment-control studies reporting a percentage change in proliferation were used to scale proliferation terms, thus serving as a proxy for light stimulation. Results showed the inhibition model was more sensitive to parameter variation than the activation model. Changes in the cell migration parameter are most sensitive overall. Most model parameters were bounded by saturation or numeric instabilities, while otherwise demonstrating activating and/or inhibitory effects on the rate of wound healing. Light stimulation simulations were consistent with expectations that increasing the proliferation term increased wound healing rate. To support photobiomodulation model-based experimental wound healing research, the model parameter search identified threshold values categorizing activation or inhibition of wound healing rate and this work also adapted a model proliferation term consistent with photobiomodulation biological effects

Investigating the effect of drug release on in-stent restenosis: A hybrid continuum – agent-based modelling approach

Background and objective: In-stent restenosis (ISR) following percutaneous coronary intervention with drug-eluting stent (DES) implantation remains an unresolved issue, with ISR rates up to 10%. The use of antiproliferative drugs on DESs has significantly reduced ISR. However, a complete knowledge of the mechanobiological processes underlying ISR is still lacking. Multiscale agent-based modelling frameworks, integrating continuum- and agent-based approaches, have recently emerged as promising tools to decipher the mechanobiological events driving ISR at different spatiotemporal scales. However, the integration of sophisticated drug models with an agent-based model (ABM) of ISR has been under-investigated. The aim of the present study was to develop a novel multiscale agent-based modelling framework of ISR following DES implantation. Methods: The framework consisted of two bi-directionally coupled modules, namely (i) a drug transport module, simulating drug transport through a continuum-based approach, and (ii) a tissue remodelling module, simulating cellular dynamics through an ABM. Receptor saturation (RS), defined as the fraction of target receptors saturated with drug, is used to mediate cellular activities in the ABM, since RS is widely regarded as a measure of drug efficacy. Three studies were performed to investigate different scenarios in terms of drug mass (DM), drug release profiles (RP), coupling schemes and idealized vs. patient-specific artery geometries. Results: The studies demonstrated the versatility of the framework and enabled exploration of the sensitivity to different settings, coupling modalities and geometries. As expected, changes in the DM, RP and coupling schemes illustrated a variation in RS over time, in turn affecting the ABM response. For example, combined small DM – fast RP led to similar ISR degrees as high DM – moderate RP (lumen area reduction of ∼13/17% vs. ∼30% without drug). The use of a patient-specific geometry with non-equally distributed struts resulted in a heterogeneous RS map, but did not remarkably impact the ABM response. Conclusion: The application to a patient-specific geometry highlights the potential of the framework to address complex realistic scenarios and lays the foundations for future research, including calibration and validation on patient datasets and the investigation of the effects of different plaque composition on the arterial response to DES

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

Mathematical Modelling of the Effect of Drug on Smooth Muscle Cell Proliferation

No abstract available

Investigating the effect of drug release on in-stent restenosis: a hybrid continuum – agent-based modelling approach

No abstract available

Mathematical Modelling of the Effect of Drug on Smooth Muscle Cell Proliferation

No abstract available

Calibration of patient-specific boundary conditions for coupled CFD models of the aorta derived from 4D flow-MRI

Patient-specific computational fluid dynamics (CFD) models permit analysis of complex intra-aortic hemodynamics in patients with aortic dissection (AD), where vessel morphology and disease severity are highly individualized. The simulated blood flow regime within these models is sensitive to the prescribed boundary conditions (BCs), so accurate BC selection is fundamental to achieve clinically relevant results. This study presents a novel reduced-order computational framework for the iterative flow-based calibration of 3-Element Windkessel Model (3EWM) parameters to generate patient-specific BCs. These parameters were calibrated using time-resolved flow information derived from retrospective four-dimensional flow magnetic resonance imaging (4D Flow-MRI). For a healthy and dissected case, blood flow was then investigated numerically in a fully coupled zero dimensional-three dimensional (0D-3D) numerical framework, where the vessel geometries were reconstructed from medical images. Calibration of the 3EWM parameters was automated and required ~3.5 minutes per branch. With prescription of the calibrated BCs, the computed near-wall hemodynamics (time-averaged wall shear stress, oscillatory shear index) and perfusion distribution were consistent with clinical measurements and previous literature, yielding physiologically relevant results. BC calibration was particularly important in the AD case, where the complex flow regime was captured only after BC calibration. This calibration methodology can therefore be applied in clinical cases where branch flow rates are known, for example via 4D Flow-MRI or ultrasound, to generate patient-specific BCs for CFD models. It is then possible to elucidate, on a case-by-case basis, the highly individualized hemodynamics which occur due to geometric variations in aortic pathology high spatiotemporal resolution through CFD