Complexity bounds on supermesh construction for quasi-uniform meshes

Projecting fields between different meshes commonly arises in computational physics. This operation requires a supermesh construction and its computational cost is proportional to the number of cells of the supermesh $n$. Given any two quasi-uniform meshes of $n_A$ and $n_B$ cells respectively, we show under standard assumptions that n is proportional to $n_A + n_B$. This result substantially improves on the best currently available upper bound on $n$ and is fundamental for the analysis of algorithms that use supermeshes

Multiscale Multimodal Characterization and Simulation of Structural Alterations in Failed Bioprosthetic Heart Valves.

Calcific degeneration is the most frequent type of heart valve failure, with rising incidence due to the ageing population. The gold standard treatment to date is valve replacement. Unfortunately, calcification oftentimes re-occurs in bioprosthetic substitutes, with the governing processes remaining poorly understood. Here, we present a multiscale, multimodal analysis of disturbances and extensive mineralisation of the collagen network in failed bioprosthetic bovine pericardium valve explants with full histoanatomical context. In addition to highly abundant mineralized collagen fibres and fibrils, calcified micron-sized particles previously discovered in native valves were also prevalent on the aortic as well as the ventricular surface of bioprosthetic valves. The two mineral types (fibres and particles) were detectable even in early-stage mineralisation, prior to any macroscopic calcification. Based on multiscale multimodal characterisation and high-fidelity simulations, we demonstrate that mineral occurrence coincides with regions exposed to high haemodynamic and biomechanical indicators. These insights obtained by multiscale analysis of failed bioprosthetic valves may serve as groundwork for the evidence-based development of more durable alternatives. STATEMENT OF SIGNIFICANCE: Bioprosthetic valve calcification is a well-known clinically significant phenomenon, leading to valve failure. The nanoanalytical characterisation of bioprosthetic valves gives insights into the highly abundant, extensive calcification and disorganization of the collagen network and the presence of calcium phosphate particles previously reported in native cardiovascular tissues. While the collagen matrix mineralisation can be primarily attributed to a combination of chemical and mechanical alterations, the calcified particles are likely of host cellular origin. This work presents a straightforward route to mineral identification and characterization at high resolution and sensitivity, and with full histoanatomical context, hence providing design cues for improved bioprosthetic valve alternatives