Computational Methods in Cardiovascular Mechanics

Abstract

Introduction: The Role and the Development of Computational MethodsThe introduction of computational models in cardiovascular sciences has been progressively bringing new and unique tools for the investigation of the physiopathology. Together with the dramatic improvement of imaging and measuring devices on one side, and of computational architectures on the other one, mathematical and numerical models have provided a new -clearly noninvasiveapproach for understanding not only basic mechanisms but also patient-specific conditions, and for supporting the design and the development of new therapeutic options. The terminology in silico is, nowadays, commonly accepted for indicating this new source of knowledge added to traditional in vitro and in vivo investigations. The advantages of in silico methodologies are basically the low cost in terms of infrastructures and facilities, the reduced invasiveness and, in general, the intrinsic predictive capabilities based on the use of mathematical models. The disadvantages are generally identified in the distance between the real cases and their virtual counterpart required by the conceptual modeling that can be detrimental for the reliability of numerical simulations. In this respect, the terrific development of new devices and algorithms for image and data retrieval and processing allowed the migration from (over)simplified idealized descriptions to high-fidelity patient-specific models, in a critical -still ongoingprocess of merging measures and conceptualizations. Meanwhile, the progressive improvement of computational resources provides the infrastructures to perform numerical simulations of complex dynamics in reasonable timelines. All such processes required, in background, the crucial development of novel specific modeling techniques and solvers in the field of computational mechanics, in an exciting process involving mathematics, engineering, computer science, and biomedical knowledge that is now having an impact not only on research but also on clinical practice. As a matter of fact, mathematical and computational modeling has been recognized more than a research tool, a service to be integrated in products for the clinical market, as the example of the company HeartFlow [Taylor et al., 2013] demonstrates.

Reduced order methods for parametric optimal flow control in coronary bypass grafts, towards patient-specific data assimilation

“…In this work, we have utilized proper orthogonal decomposition (POD) (Ballarin et al, 2015, Hesthaven et al, 2015, Kunisch and Volkwein, 2008, Müller, 2008 to construct reduced order spaces, however a greedy algorithm (Hesthaven et al, 2015 using residual-based error estimators can be alternatively employed. Both techniques have been well-applied to optimal flow control problems (Bader et al, 2016, Dedè, 2012, Kärcher et al, 2018, Negri et al, 2013, Strazzullo et al, 2018 and patient-specific computational cardiovascular modelling (Auricchio et al, 2018, Tezzele et al, 2018. We summarize the algebraic details, following Rozza et al (Hesthaven et al, 2015, Quarteroni and and Ballarin et al (Ballarin et al, 2015), below.…”

Smart Biomaterials in Biomedical Applications: Current Advances and Possible Future Directions

“…Reproduced with permission. [ 146 ] Copyright 2010, Tech Science Press. (iv) Transcatheter aortic valve prostheses currently used in clinical practice: the Medtronic CoreValve (Medtronic, Inc., MN, USA) (left) and the Edwards SAPIEN XT (Edwards Life Sciences, Inc., CA, USA) (right).…”

“…(iii) Simulation of self-expanding NiTi stent expansion process. Reproduced with permission [146]. Copyright 2010, Tech Science Press.…”