Speaker
Description
Hierarchical Model (HiMod) reduction is a mathematical technique developed to accurately model problems exhibiting an intrinsic dominant directionality (e.g., in pipe-like domains) at an affordable computational effort. HiMod reduction has been successfully employed in several applications, including hemodynamics [1] and acoustic wave propagation [2].
The approach relies on a separation-of-variables paradigm that allows the leading fiber to be treated independently from the transverse dynamics. The leading dynamics is discretized using spline-based basis functions, enabling the treatment of curvilinear centrelines and complex geometries, such as vascular domains [1]. The transverse dynamics are described through a modal basis expansion. The full-order model is thus reduced to a system of coupled 1D equations whose dimension depends on the number of modes [3].
Recent developments have established the inf-sup stability of the HiMod discretization and enabled the development of a MATLAB HiMod library for fluid dynamics applications. In this talk, HiMod reduction is employed to handle patient-specific vascular geometries reconstructed from medical images, including stenotic coronary arteries and abdominal aortic aneurysms. Comparisons with full-order solutions show that HiMod is a reliable tool for biomedical analyses, balancing computational efficiency and accuracy in evaluating clinically relevant hemodynamic quantities. Furthermore, a preliminary investigation about the integration of machine learning algorithms in HiMod reduction is carried out to further enhance the methodology performance, with the goal of enabling real-time simulations.
[1] Brandes Costa Barbosa, Y. A., Perotto, S. (2020). Hierarchically reduced models for the Stokes problem in patient-specific artery segments. Int. J. Comput. Fluid Dyn., 34(2), 160-171.
[2] Gentili, G. G., et al. (2022). Efficient modeling of multimode guided acoustic wave propagation in deformed pipelines by hierarchical model reduction. Appl. Numer. Math., 173, 329-344.
[3] Perotto, S., Ern, A., Veneziani, A. (2010). Hierarchical local model reduction for elliptic problems: a domain decomposition approach. Multiscale Model. Simul., 8(4), 1102-1127.