Conference Agenda

The treatment of cardiovascular diseases most often involves coronary stents. Even with drug-eluting stents, implantation can give rise to in-stent restenosis: endothelial denudation and overstretch injuries may result in uncontrolled tissue growth and formation of obstruction to the blood flow. Critical areas where such side effects occur highly depend on the shear stresses and drug distribution inside the artery. For this reason, the analysis of blood flow dynamics in stented arteries is of great interest. The current work is aimed at coupling hemodynamics and tissue growth to include the fluid-structure interaction of pharmacokinetics at the interface between artery and lumen.

Navier Stokes equations and Newtonian constitutive model are used to simulate blood in a stented artery. Wall shear stress (WSS) related quantities are analyzed as indicators of the possible areas of inflammation and thrombosis. Drug elution and deposition on the vessel wall is modeled by means of an advection-diffusion equation and tailored boundary conditions [1]. The convective field is obtained coupling the drug equation to a steady averaged blood flow over three heart beats. Since the healing process and drug elution span a time frame of weeks, a staggered approach is derived to simulate the drug release into the blood stream. Advection-diffusion-reaction equations form the basis of modeling the transport and interaction of species in the vessel wall. The corresponding equations for PDGF, TGF-ß, ECM and SMC can be found in [2]. The drug concentration field is coupled at the interface between the arterial wall and the lumen to account for downstream deposition of the drug. All governing equations for the wall species are coupled to a continuum mechanical description of volumetric growth.

In this work, we test our method on a simplified ring stent geometry with matching interface between the artery wall and the blood domain. We compare the effects of drug coupling and WSS on the endothelium and volumetric growth. All simulations are performed by means of finite element method using FEAP and the in-house code XNS.

[1] Hassler S, Ranno AM, Behr M. Finite-element formulation for advection–reaction equations with change of variable and discontinuity capturing. Computer Methods in Applied Mechanics and Engineering, 2020; 369: 113171.

[2] Manjunatha K, Behr M, Vogt F, Reese S. A multiphysics modeling approach for in-stent restenosis: Theoretical aspects and finite element implementation. Computers in Biology and Medicine, 2022; 150: 106166.

In-stent restenosis is one of the main adverse events after initially successful percutaneous coronary interventions (PCI) with stent implantation. Comprehensive statistical analyses of large clinical datasets identified several independent risk factors for restenosis occurrence, such as patient- or lesion-specific factors, which include small vessel size or the extended length of the stented section. However, it is widely accepted that the local mechanical state within the vessel wall strongly affects vascular growth mechanisms. Nevertheless, these biomechanical factors are currently not integrated into the predictive assessment of lesions at risk. For instance, high intramural stresses and overstretch of healthy vascular tissue during PCI may disturb the natural homeostasis and thus promote excessive tissue growth. Additionally, insufficient stent expansion and incomplete stent apposition reduce the long-term success rate of the procedure. We propose an individualized biomechanical model to study the influence of specific plaque characteristics on the mechanical state of the artery wall during loading conditions experienced in PCI and the final stent placement. In this work, we employ patient-specific artery models based on coronary computed tomography angiography data combined with resolved models of the stent delivery system for physics-informed PCI simulations. We define the system as a computational structural mechanics problem with large deformations and a nonlinear, viscoelastic material formulation for the artery considering the plaque constituents in a heterogeneous manner. The stent structure is resolved and is discretized with reduced-dimensional 1D Cosserat continua with an elastoplastic material formulation. An idealized inflatable balloon model governs the stent expansion. The interaction between balloon catheter and artery is modeled with computational contact mechanics using mortar methods; for the stents, we utilize a beam-to-solid contact approach. All simulations are performed with our in-house multiphysics high-performance code BACI, which uses finite element methods for all problem types considered here. We assess the local stresses and strains within the vessel wall during and after the stent implantation and collate cases with different lesion characteristics. We evaluate the contact between stent struts and endothelium for lesions at risk of incomplete stent apposition. Additionally, we compare the results of our resolved approach to a simplified model, where we model the stent as a pure cylinder with similar mechanical characteristics. In the future, insights from such modeling may inform the clinical assessment of lesions considered for stent implantation.

Neuroblastoma (NB) is the most frequent solid cancer of early childhood. It is a type of cancer that is highly representative of the cancer disease itself, since NB is strongly heterogeneous with very diverse clinical courses that may vary from an indolent disease causing little or no harm and exhibiting spontaneous regression, to an aggressive disease with fatal progression. For these reasons, NB is considered a paradigm of cancer disease and an excellent context of application for the validation of novel developments which have the ambition to be of potential application in a large variety of solid cancers.

NB tumours consist of two main cell populations, neuroblasts and Schwann cells, and the current neuroblastoma classification is based on histological criteria, e. g. the quantity of Schwannian stroma. Neuroblasts and Schwann cells are primary interest herein for contribute directly to the mechanical properties of the tissue through the proliferation and death processes. Extracellular matrix also have a principal role in the cell-microenvironmental cross-talk therefore the tumour can promote to a better stage or keep growing.

We here present a phenomenological model which takes into account as detail as possible to better mimic the real tumour behaviour. Our hypothesis proposes that tumour evolution can be attributed to three distinct processes: growth, shrinkage, and remodelling. The biomechanical model is based on the mass and cellular balance equations coupled with elasticity. The multispecies model simulates the effect of the cellular processes that occur during tumour growth and shrinkage, namely proliferation and death.

The biomechanical finite element model of NB tumour growth starts from imaging data derived mainly from MRI sequences. This data comprises the geometry, the initial cellularity distribution and the tumour vasculature evaluation. At the end of the simulation, the results obtained are validated with a second set of imaging data obtained after treatment.

The study simulates three-month chemotherapy using real patient cases, and presents two distinct outcomes: in one of them, the tumour volume was reduced 20% and in the other one, the volume decreased 90%. One of the patients was classified as low-risk, following the International Neuroblastoma Risk Group (INRG) system, whereas the other was classified as intermediate-risk. Differences appeared in the histology analysis, which reveal one tumour with a higher concentration of tumoural cells, and in the radiomic data obtained after image analysis. The model effectively reproduces these varying outcomes following the application of chemotherapy, facilitating the identification of cases in which the treatment may be effective.

Biomechanical models typically contain numerous parameters. Global sensitivity analysis helps identify the most influential and the non-influential parameters, as well as interactions between the parameters.

We show how to apply variance-based global sensitivity analysis to complex biomechanical models. As the method necessitates numerous model evaluations, we utilize Gaussian process metamodels [1] to lessen the computational burden. The approach is illustrated for models of active biomechanical systems by applying it to nanoparticle-mediated drug delivery in a multiphase tumour-growth model [2] and the formation of aneurysms in a model of aortic growth and remodelling [3].

We discover that a small number of full model evaluations suffices to effectively differentiate influential from non-influential parameters, while further evaluations enable the estimation of higher-order interactions. From a biomechanical modeling standpoint, we observe that often a few influential parameters predominantly govern the model output variance. Simultaneously, substantial parameter interactions can exist, emphasizing the necessity for global methods.

Gaussian process-based global sensitivity analysis proves feasible and beneficial for intricate, computationally demanding biomechanical models. Specifically, it can serve as a foundational building block for parameter identification.

[1] Le Gratiet L, Cannamela C, Iooss B. A Bayesian Approach for Global Sensitivity Analysis of (Multifidelity) Computer Codes. J Uncertain Quantif. 2, 336–363. DOI: 10.1137/130926869 (2014).

[2] Wirthl B, Brandstaeter S, Nitzler J, Schrefler BA, Wall WA. Global sensitivity analysis based on Gaussian-process metamodelling for complex biomechanical problems. Int J Numer Meth Biomed Engng. e3675. DOI: 10.1002/cnm.3675 (2023).

[3] Brandstaeter S, Fuchs SL, Biehler J, Aydin RC, Wall WA, Cyron CJ. Global Sensitivity Analysis of a Homogenized Constrained Mixture Model of Arterial Growth and Remodeling. J Elast. 145, 191–221 DOI: 10.1007/s10659-021-09833-9 (2021).