A. Reali

ISOGEOMETRIC COLLOCATION METHODS

We initiate the study of collocation methods for NURBS-based isogeometric analysis. The idea is to connect the superior accuracy and smoothness of NURBS basis functions with the low computational cost of collocation. We develop a one-dimensional theoretical analysis, and perform numerical tests in one, two and three dimensions. The numerical results obtained confirm theoretical results and illustrate the potential of the methodology.

GeoPDEs: A research tool for Isogeometric Analysis of PDEs

GeoPDEs (http://geopdes.sourceforge.net) is a suite of free software tools for applications on Isogeometric Analysis (IGA). Its main focus is on providing a common framework for the implementation of the many IGA methods for the discretization of partial differential equations currently studied, mainly based on B-Splines and Non-Uniform Rational B-Splines (NURBS), while being flexible enough to allow users to implement new and more general methods with a relatively small effort. This paper presents the philosophy at the basis of the design of GeoPDEs and its relation to a quite comprehensive, abstract definition of IGA.

AN ISOGEOMETRIC ANALYSIS APPROACH FOR THE STUDY OF STRUCTURAL VIBRATIONS

The concept of Isogeometric Analysis recently introduced by Hughes et al. [2005] is herein applied to the study of structural vibrations. In this framework, the favourable behaviour of the method is verified and compared with some classical finite element results. Numerical experiments are shown for structural one-, two- and three-dimensional problems in order to test the performance of this promising technique in the field of the analysis of natural frequencies and modes.

Accurate, efficient, and (iso)geometrically flexible collocation methods for phase-field models

We propose new collocation methods for phase-field models. Our algorithms are based on isogeometric analysis, a new technology that makes use of functions from computational geometry, such as, for example, Non-Uniform Rational B-Splines (NURBS). NURBS exhibit excellent approximability and controllable global smoothness, and can represent exactly most geometries encapsulated in Computer Aided Design (CAD) models. These attributes permitted us to derive accurate, efficient, and geometrically flexible collocation methods for phase-field models. The performance of our method is demonstrated by several numerical examples of phase separation modeled by the Cahn-Hilliard equation. We feel that our method successfully combines the geometrical flexibility of finite elements with the accuracy and simplicity of pseudo-spectral collocation methods, and is a viable alternative to classical collocation methods.

Simulation of transcatheter aortic valve implantation through patient-specific finite element analysis: Two clinical cases

Transcatheter aortic valve implantation (TAVI) is a minimally invasive procedure introduced to treat aortic valve stenosis in elder patients. Its clinical outcomes are strictly related to patient selection, operator skills, and dedicated pre-procedural planning based on accurate medical imaging analysis. The goal of this work is to define a finite element framework to realistically reproduce TAVI and evaluate the impact of aortic root anatomy on procedure outcomes starting from two real patient datasets. Patient-specific aortic root models including native leaflets, calcific plaques extracted from medical images, and an accurate stent geometry based on micro-tomography reconstruction are key aspects included in the present study. Through the proposed simulation strategy we observe that, in both patients, stent apposition significantly induces anatomical configuration changes, while it leads to different stress distributions on the aortic wall. Moreover, for one patient, a possible risk of paravalvular leakage has been found while an asymmetric coaptation occurs in both investigated cases. Post-operative clinical data, that have been analyzed to prove reliability of the performed simulations, show a good agreement with analysis results. The proposed work thus represents a further step towards the use of realistic computer-based simulations of TAVI procedures, aiming at improving the efficacy of the operation technique and supporting device optimization.

Simulation of transcatheter aortic valve implantation: a patient-specific finite element approach.

Until recently, heart valve failure has been treated adopting open-heart surgical techniques and cardiopulmonary bypass. However, over the last decade, minimally invasive procedures have been developed to avoid high risks associated with conventional open-chest valve replacement techniques. Such a recent and innovative procedure represents an optimal field for conducting investigations through virtual computer-based simulations: in fact, nowadays, computational engineering is widely used to unravel many problems in the biomedical field of cardiovascular mechanics and specifically, minimally invasive procedures. In this study, we investigate a balloon-expandable valve and we propose a novel simulation strategy to reproduce its implantation using computational tools. Focusing on the Edwards SAPIEN valve in particular, we simulate both stent crimping and deployment through balloon inflation. The developed procedure enabled us to obtain the entire prosthetic device virtually implanted in a patient-specific aortic root created by processing medical images; hence, it allows evaluation of postoperative prosthesis performance depending on different factors (e.g. device size and prosthesis placement site). Notably, prosthesis positioning in two different cases (distal and proximal) has been examined in terms of coaptation area, average stress on valve leaflets as well as impact on the aortic root wall. The coaptation area is significantly affected by the positioning strategy ( − 24%, moving from the proximal to distal) as well as the stress distribution on both the leaflets (+13.5%, from proximal to distal) and the aortic wall ( − 22%, from proximal to distal). No remarkable variations of the stress state on the stent struts have been obtained in the two investigated cases.

Patient-specific aortic endografting simulation: From diagnosis to prediction

Traditional surgical repair of ascending aortic pseudoaneurysm is complex, technically challenging, and associated with significant mortality. Although new minimally invasive procedures are rapidly arising thanks to the innovations in catheter-based technologies, the endovascular repair of the ascending aorta is still limited because of the related anatomical challenges. In this context, the integration of the clinical considerations with dedicated bioengineering analysis, combining the vascular features and the prosthesis design, might be helpful to plan the procedure and predict its outcome. Moving from such considerations, in the present study we describe the use of a custom-made stent-graft to perform a fully endovascular repair of an asymptomatic ascending aortic pseudoaneurysm in a patient, who was a poor candidate for open surgery. We also discuss the possible contribution of a dedicated medical images analysis and patient-specific simulation as support to procedure planning. In particular, we have compared the simulation prediction based on pre-operative images with post-operative outcomes. The agreement between the computer-based analysis and reality encourages the use of the proposed approach for a careful planning of the treatment strategy and for an appropriate patient selection, aimed at achieving successful outcomes for endovascular treatment of ascending aortic pseudoaneurysms as well as other aortic diseases.

SMA Numerical Modeling Versus Experimental Results: Parameter Identification and Model Prediction Capabilities

In this work, we briefly review the one-dimensional version of a well-known phenomenological shape memory alloy (SMA) constitutive model able to represent the main macroscopic SMA macroscopic behaviors (i.e., superelasticity and shape-memory effect). We then show how to identify the needed parameters from experimental results and, in particular, from strain-temperature tests. We finally use the obtained material parameters to test the prediction properties of the model, comparing numerical results with some experiments (different from those used for the identification), and we discuss model capabilities and further required enhancements.

Aortic hemodynamics after thoracic endovascular aortic repair, with particular attention to the bird-beak configuration.

Purpose: To quantitatively evaluate the impact of thoracic endovascular aortic repair (TEVAR) on aortic hemodynamics, focusing on the implications of a bird-beak configuration. Methods: Pre- and postoperative CTA images from a patient treated with TEVAR for post-dissecting thoracic aortic aneurysm were used to evaluate the anatomical changes induced by the stent-graft and to generate the computational network essential for computational fluid dynamics (CFD) analysis. These analyses focused on the bird-beak configuration, flow distribution into the supra-aortic branches, and narrowing of the distal descending thoracic aorta. Three different CFD analyses (A: preoperative lumen, B: postoperative lumen, and C: postoperative lumen computed without stenosis) were compared at 3 time points during the cardiac cycle (maximum acceleration of blood flow, systolic peak, and maximum deceleration of blood flow). Results: Postoperatively, disturbance of flow was reduced at the bird-beak location due to boundary conditions and change of geometry after TEVAR. Stent-graft protrusion with partial coverage of the origin of the left subclavian artery produced a disturbance of flow in this vessel. Strong velocity increase and flow disturbance were found at the aortic narrowing in the descending thoracic aorta when comparing B and C, while no effect was seen on aortic arch hemodynamics. Conclusion: CFD may help physicians to understand aortic hemodynamic changes after TEVAR, including the change in aortic arch geometry, the effects of a bird-beak configuration, the supra-aortic flow distribution, and the aortic true lumen dynamics. This study is the first step in establishing a computational framework that, when completed with patient-specific data, will allow us to study thoracic aortic pathologies and their endovascular management.

Prediction of patient-specific post-operative outcomes of TAVI procedure: The impact of the positioning strategy on valve performance

Prosthesis positioning in transcatheter aortic valve implantation procedures represents a crucial aspect for procedure success as demonstrated by many recent studies on this topic. Possible complications, device performance, and, consequently, also long-term durability are highly affected by the adopted prosthesis placement strategy. In the present work, we develop a computational finite element model able to predict device-specific and patient-specific replacement procedure outcomes, which may help medical operators to plan and choose the optimal implantation strategy. We focus in particular on the effects of prosthesis implantation depth and release angle. We start from a real clinical case undergoing Corevalve self-expanding device implantation. Our study confirms the crucial role of positioning in determining valve anchoring, replacement failure due to intra or para-valvular regurgitation, and post-operative device deformation.