Development of a fast high fidelity FSI workflow to simulate polymeric aortic valves: a RBF mesh morphing study

Abstract In 2018, The World Health Organization identified cardiovascular diseases as the major causes of death in the world and among them, aortic stenosis is one of the most common and serious. It consists in a narrowing of the aortic valve orifice obstructing the blood flow from the left ventricle to the aorta and may also affect the pressure in the left atrium. Comparing to several years ago, medical treatments, diagnostic equipment and engineering tools have come a long way succeeding into improving life quality and expectancy. In this context, numerical simulation offers the possibility to improve the treatment of aortic valve diseases, allowing to prevent the tendency that regurgitation (leaking), malocclusion, high shear stresses or other phenomena may occur and to optimize the design of prosthetic heart valves in a controlled and patient-specific way. It also provided an important role in the understanding of the interaction between the blood flow and the leaflets of a prosthetic valve, allowing to control if the valve is inclined to cause thrombogenic or haemolytic diseases. One of the main obstacles which has slowed down the spread of numerical simulation in clinical setting, especially in the prosthetic field, is the long time required to set a new patient-specific model and to evaluate the results in particular conditions of interest. This matter obviously involves even the prosthetic aortic valves, whose realization and testing procedures require a large amount of time. In this regard, the first aim of this thesis is to build a parametric model of the aortic valve which can be updated and adapted in few seconds according to the geometric dimensions of the patient, using the information derived from imaging analysis in the most direct and quick possible way. After that, fixing a set of construction dimensions such as external and internal diameter or height of the valve, to simulate the identification of a surgical candidate, this work aims to investigate the influence of a list of parameters, in this case not fixed, on the structural domain of the valve, measuring and discussing several output values like Geometric Orifice Area, Leaflet Coaptation Area, maximum equivalent von-Mises stress and maximum equivalent strain. Finally, a mesh morphing Fluid-Structure Interaction procedure based on Radial Basis Function to deform the fluid domain of the blood in proximity to the valve and to simulate the flow across it during the opening phase of the valve is conducted, presented and for the first time compared to remeshing solutions. In this latter case, what will be tried to demonstrate is the possibility to assess the most important haemodynamic parameters, like Wall Shear Stress (WSS) and Volumetric Flow Rate in a time drastically lower in comparison to the procedures until now developed, tearing down in this way one of the most complex problems of standard numerical simulation. Riassunto Nel 2018, La World Health Organization ha identificato le malattie cardiovascolari come la più frequente causa di morte nel mondo e tra queste, la stenosi aortica è una delle più pericolose e frequenti. Essa consiste nel restringimento dell’orifizio della valvola aortica che causa di conseguenza l’ostruzione del flusso sanguigno dal ventricolo sinistro all’aorta ed influisce persino sulla pressione dell’atrio sinistro. Rispetto a diversi anni fa, i trattamenti medici, la strumentazione diagnostica e i mezzi ingegneristici hanno svolto molti passi avanti, riuscendo ad apportare un forte miglioramento nella qualità e nell’aspettativa di vita. In questo contest, la simulazione numerica offre la possibilità di migliorare il trattamento delle disfunzioni cardiovascolari, permettendo di prevenire la possibilità che rigurgiti, errate occlusioni, elevati sforzi di taglio o altri fenomeni possano verificarsi e di ottimizzare il design delle valvole stesse secondo procedura adattata sul paziente. Può anche essere messo alla luce un ruolo molto importante nella comprensione dell’interazione tra il flusso sanguigno e i leaflets della valvola stessa, permettendo di controllare se la valvola è incline a trombogenicità ed emolisi. Uno dei principali ostacoli che ha rallentato molto la diffusione della simulazione nell’ambito clinico, specialmente nel campo protesico, è il lungo tempo richiesto per settare un nuovo modello paziente specifico e valutare i risultati in particolari situazioni di interesse. Questa problematica ovviamente riguarda anche le valvole cardiache, la cui realizzazione, così come tutte le procedure di testing, richiede un’elevatissima quantità di tempo. In questo contesto, il primo scopo di questa tesi è quello di costruire un modello parametrico di valvola aortica che può essere aggiornato e adattato in poco tempo, secondo le dimensioni geometriche del paziente, usando la semplice informazione derivante dall’imaging nel modo più diretto e veloce possibile. Successivamente, fissando un set di dimensioni di costruzione come diametro esterno, interno ed altezza per simulare l’individuazione di un candidato chirurgico, questo lavoro si pone l’obiettivo di indagare l’influenza di una lista di parametri, in questo caso non fissati, sul dominio strutturale della valvola, misurando e discutendo diversi valori tra cui Area Geometrica di Orifizio, Area di Contatto, massimo stress equivalente e massimo strain equivalente. Infine, un’analisi di interazione Fluido-Struttura è stata condotta mediante mesh morphing basato sull’impiego di Radial Basis Function per deformare il dominio fluido del sangue in prossimità della valvola e simulare il flusso sanguigno durante la fase di apertura. Tali risultati sono stati poi comparati con quelli ottenuti con una più nota procedura di remeshing. Il lavoro ha quindi come obiettivo finale quello di dimostrare la possibilità di ricavare i più importanti parametri emodinamici come WSS e portata cardiaca in un tempo decisamente minore rispetto alle procedure sviluppate fino a questo momento, abbattendo in questo modo uno dei più complessi problemi della classica simulazione numerica

Effect of turbulence and viscosity models on wall shear stress derived biomarkers for aorta simulations

International audienceAscending aorta simulations provide insight into patient-specific hemodynamic conditions. Numerous studies have assessed fluid biomarkers which show a potential to aid clinicians in the diagnosis process. Unfortunately, there exists a large disparity in the computational methodology used to model turbulence and viscosity. Recognizing this disparity, some authors focused on analysing the influence of either the turbulence or viscosity models on the biomarkers in order to quantify the importance of these model choices. However, no analysis has yet been done on their combined effect. In order to fully understand and quantify the effect of the computational methodology, an assessment of the combined effect of turbulence and viscosity model choice was performed. Our results show that (1) non-Newtonian viscosity has greater impact (2.9-5.0%) on wall shear stress than Large Eddy Simulation turbulence modelling (0.1-1.4%), (2) the contribution of non-Newtonian viscosity is amplified when combined with a subgrid-scale turbulence model, (3) wall shear stress is underestimated when considering Newtonian viscosity by 2.9-5.0% and (4) cycle-to-cycle variability can impact the results as much as the numerical model if insufficient cycles are performed. These results demonstrate that, when assessing the effect of computational methodologies, the resultant combined effect of the different modelling assumptions differs from the aggregated effect of the isolated modifications. Accurate aortic flow modelling requires non-Newtonian viscosity and Large Eddy Simulation turbulence modelling

Advanced radial basis functions mesh morphing for high fidelity fluid-structure interaction with known movement of the walls: simulation of an aortic valve

High fidelity Fluid-Structure Interaction (FSI) can be tackled by means of non-linear Finite Element Models (FEM) suitable to capture large deflections of structural parts interacting with fluids and by means of detailed Computational Fluid Dynamics (CFD). High fidelity is gained thanks to the spatial resolution of the computational grids and a key enabler to have a proper exchange of information between the structural solver and the fluid one is the management of the interfaces. A class of applications consists in problems where the complex movement of the walls is known in advance or can be computed by FEM and has to be transferred to the CFD solver. The aforementioned approach, known also as one-way FSI, requires effective methods for the time marching adaption of the computation grid of the CFD model. A versatile and well established approach consists in a continuum update of the mesh that is regenerated so to fit the evolution of the moving walls. In this study, an innovative method based on Radial Basis Functions (RBF) mesh morphing is proposed, allowing to keep the same mesh topology suitable for a continuum update of the shape. A set of key configurations are exactly guaranteed whilst time interpolation is adopted between frames. The new framework is detailed and then demonstrated, adopting as a reference the established approach based on remeshing, for the study of a Polymeric-Prosthetic Heart Valve (P-PHV)

High fidelity fluid-structure interaction by radial basis functions mesh adaption of moving walls: A workflow applied to an aortic valve

Fluid-Structure Interaction (FSI) can be investigated by means of non-linear Finite Element Models (FEM), suitable to capture large deflections of structural parts interacting with fluids, and Computational Fluid Dynamics (CFD). High fidelity simulations are obtained using the fine spatial resolution of both the structural and fluid computational grids. A key enabler to have a proper exchange of information between the structural solver and the fluid one is the management of the interface at wetted surfaces where the grids are usually non matching. A class of applications, known also as one-way FSI problems, involves a complex movement of the walls that is known in advance as measured or as computed by FEM, and that has to be imposed at the boundaries during a transient CFD solution. Effective methods for the time marching adaption of the whole computational grid of the CFD model according to the evolving shape of its boundaries are required. A very well established approach consists of a continuum update of the mesh that is regenerated by adding and removing cells to fit the evolution of the moving walls. In this paper, starting from the work originally presented in Meshfree Methods in Computational Sciences, ICCS 2020 [1], an innovative method based on Radial Basis Functions (RBF) mesh morphing is proposed, allowing the retention of the same mesh topology suitable for a continuum update of the shape. The proposed method is exact at a set of given key configurations and relies on shape blending time interpolation between key frames. The study of the complex motion of a Polymeric-Prosthetic Heart Valve (P-PHV) is presented using the new framework and considering as a reference the established approach based on remeshing

Calibration of the Mechanical Boundary Conditions for a Patient-Specific Thoracic Aorta Model Including the Heart Motion Effect

Objective: We propose a procedure for calibrating 4 parameters governing the mechanical boundary conditions (BCs) of a thoracic aorta (TA) model derived from one patient with ascending aortic aneurysm. The BCs reproduce the visco-elastic structural support provided by the soft tissue and the spine and allow for the inclusion of the heart motion effect. Methods: We first segment the TA from magnetic resonance imaging (MRI) angiography and derive the heart motion by tracking the aortic annulus from cine-MRI. A rigid-wall fluid-dynamic simulation is performed to derive the time-varying wall pressure field. We build the finite element model considering patient-specific material properties and imposing the derived pressure field and the motion at the annulus boundary. The calibration, which involves the zero-pressure state computation, is based on purely structural simulations. After obtaining the vessel boundaries from the cine-MRI sequences, an iterative procedure is performed to minimize the distance between them and the corresponding boundaries derived from the deformed structural model. A strongly-coupled fluid-structure interaction (FSI) analysis is finally performed with the tuned parameters and compared to the purely structural simulation. Results and Conclusion: The calibration with structural simulations allows to reduce maximum and mean distances between image-derived and simulation-derived boundaries from 8.64 mm to 6.37 mm and from 2.24 mm to 1.83 mm, respectively. The maximum root mean square error between the deformed structural and FSI surface meshes is 0.19 mm. This procedure may prove crucial for increasing the model fidelity in replicating the real aortic root kinematics

Assessment of shape-based features ability to predict the ascending aortic aneurysm growth

International audienceThe current guidelines for the ascending aortic aneurysm (AsAA) treatment recommend surgery mainly according to the maximum diameter assessment. This criterion has already proven to be often inefficient in identifying patients at high risk of aneurysm growth and rupture. In this study, we propose a method to compute a set of local shape features that, in addition to the maximum diameter D, are intended to improve the classification performances for the ascending aortic aneurysm growth risk assessment. Apart from D, these are the ratio DCR between D and the length of the ascending aorta centerline, the ratio EILR between the length of the external and the internal lines and the tortuosity T. 50 patients with two 3D acquisitions at least 6 months apart were segmented and the growth rate (GR) with the shape features related to the first exam computed. The correlation between them has been investigated. After, the dataset was divided into two classes according to the growth rate value. We used six different classifiers with input data exclusively from the first exam to predict the class to which each patient belonged. A first classification was performed using only D and a second with all the shape features together. The performances have been evaluated by computing accuracy, sensitivity, specificity, area under the receiver operating characteristic curve (AUROC) and positive (negative) likelihood ratio LHR+ (LHR-). A positive correlation was observed between growth rate and DCR (r = 0.511, p = 1.3e-4) and between GR and EILR (r = 0.472, p = 2.7e-4). Overall, the classifiers based on the four metrics outperformed the same ones based only on D. Among the diameter-based classifiers, k-nearest neighbours (KNN) reported the best accuracy (86%), sensitivity (55.6%), AUROC (0.74), LHR+ (7.62) and LHR- (0.48). Concerning the classifiers based on the four shape features, we obtained the best accuracy (94%), sensitivity (66.7%), specificity (100%), AUROC (0.94), LHR+ (+∞) and LHR- (0.33) with support vector machine (SVM). This demonstrates how automatic shape features detection combined with risk classification criteria could be crucial in planning the follow-up of patients with ascending aortic aneurysm and in predicting the possible dangerous progression of the disease

Computer-aided shape features extraction and regression models for predicting the ascending aortic aneurysm growth rate

International audienceObjective: ascending aortic aneurysm growth prediction is still challenging in clinics. In this study, we evaluate and compare the ability of local and global shape features to predict the ascending aortic aneurysm growth. Material and methods: 70 patients with aneurysm, for which two 3D acquisitions were available, are included. Following segmentation, three local shape features are computed: (1) the ratio between maximum diameter and length of the ascending aorta centerline, (2) the ratio between the length of external and internal lines on the ascending aorta and (3) the tortuosity of the ascending tract. By exploiting longitudinal data, the aneurysm growth rate is derived. Using radial basis function mesh morphing, iso-topological surface meshes are created. Statistical shape analysis is performed through unsupervised principal component analysis (PCA) and supervised partial least squares (PLS). Two types of global shape features are identified: three PCA-derived and three PLS-based shape modes. Three regression models are set for growth prediction: two based on gaussian support vector machine using local and PCA-derived global shape features; the third is a PLS linear regression model based on the related global shape features. The prediction results are assessed and the aortic shapes most prone to growth are identified. Results: the prediction root mean square error from leave-one-out cross-validation is: 0.112 mm/month, 0.083 mm/month and 0.066 mm/month for local, PCA-based and PLS-derived shape features, respectively. Aneurysms close to the root with a large initial diameter report faster growth. Conclusion: global shape features might provide an important contribution for predicting the aneurysm growth