Optimization Algorithms for Multi-species Spherical Spin Glasses.

This paper develops approximate message passing algorithms to optimize multi-species spherical spin glasses. We first show how to efficiently achieve the algorithmic threshold energy identified in our companion work (Huang and Sellke in arXiv preprint, 2023. arXiv:2303.12172), thus confirming that the Lipschitz hardness result proved therein is tight. Next we give two generalized algorithms which produce multiple outputs and show all of them are approximate critical points. Namely, in an r-species model we construct 2r approximate critical points when the external field is stronger than a "topological trivialization" phase boundary, and exponentially many such points in the complementary regime. We also compute the local behavior of the Hamiltonian around each. These extensions are relevant for another companion work (Huang and Sellke in arXiv preprint, 2023. arXiv:2308.09677) on topological trivialization of the landscape.

An analytical, mathematical annuloplasty ring curvature model for planning of valve-in-ring transcatheter mitral valve replacement.

Objectives: An increasing number of high-risk patients with previous mitral valve annuloplasty require transcatheter mitral valve replacement due to recurrent regurgitation. Annulus dilation with a transcatheter balloon is often performed before valve-in-ring transcatheter mitral valve replacement, which is believed to reduce misalignment and paravalvular leakage, yet little evidence exists to support this practice. Our objective was to generate intuitive annuloplasty ring analyses for improved valve-in-ring transcatheter mitral valve replacement planning. Methods: We generated a mathematical model that calculates image-tracked differential ring curvature to build quantifications for improved planning for valve-in-ring procedures. Carpentier-Edwards Physio M24 and M30 (n = 2 each), Physio II M24 and M26 (n = 3 each), LivaNova AnnuloFlex M26 (n = 2), and Edwards Geoform M28 (n = 2) rings were tested with a 30-mm Toray Inoue balloon inflated to maximum rated pressures. Results: Curvature variance reduces with larger ring sizes, indicating that larger rings are initially more circular than smaller ones. Evaluated semi-rigid and rigid rings showed little to no difference between pre- and post-dilation states. Annuloflex rings (flexible band) showed a postdilation variance reduction of 32.83% (P < .001) followed by an increase after 10 minutes of relaxation that was still reduced by 19.62% relative to the initial state (P < .001). Conclusions: We discovered that balloon dilation does not significantly deform evaluated semi-rigid or rigid rings at maximum rated balloon pressures. This may mean that dilation for these conditions before valve-in-ring transcatheter mitral valve replacement is unnecessary. Our mathematical approach creates a foundation for extended classification of this practice, providing meaningful quantification of ring geometry.

A novel accelerated fatigue testing system for pulsatile applications of cardiac devices using widely translatable cam and linkage-based mechanisms.

Fatigue testing of mechanical components is important for designing safe implantable medical prosthetics, and accelerated systems can be used to increase the speed of evaluation. We developed a platform for accelerated testing of linear force applications of cardiac devices, called the Fatigue Acceleration System Tester (FAST). FAST operates using a core translation mechanism, converting motor-driven rotary motion to linear actuation. The advantages of using this mechanism include 40x rate increases with largely 3D-printed components, versatility based on modular design paradigms, and accessible manufacturability with 3D-printable forms, enabling access for small and large research laboratories alike. FAST has been crucial in informing our designs for continuing device development. Over two fatigue cycle courses of 52 and 110 days, the motor cycled at rotational frequencies up to 1500 rpm, 43 times faster than those experienced in a typical heart and equating to approximate life cycles of five and ten years, respectively. In designing FAST, our goal was to accessibly bring a strong mechanical basis to study the long-term effects of repeated loading, and we present a design that can be applied across many industries to not only evaluate fatigue performance, but also generate any cycling linear motion.

Biomimetic six-axis robots replicate human cardiac papillary muscle motion: pioneering the next generation of biomechanical heart simulator technology.

Papillary muscles serve as attachment points for chordae tendineae which anchor and position mitral valve leaflets for proper coaptation. As the ventricle contracts, the papillary muscles translate and rotate, impacting chordae and leaflet kinematics; this motion can be significantly affected in a diseased heart. In ex vivo heart simulation, an explanted valve is subjected to physiologic conditions and can be adapted to mimic a disease state, thus providing a valuable tool to quantitatively analyse biomechanics and optimize surgical valve repair. However, without the inclusion of papillary muscle motion, current simulators are limited in their ability to accurately replicate cardiac biomechanics. We developed and implemented image-guided papillary muscle (IPM) robots to mimic the precise motion of papillary muscles. The IPM robotic system was designed with six degrees of freedom to fully capture the native motion. Mathematical analysis was used to avoid singularity conditions, and a supercomputing cluster enabled the calculation of the system's reachable workspace. The IPM robots were implemented in our heart simulator with motion prescribed by high-resolution human computed tomography images, revealing that papillary muscle motion significantly impacts the chordae force profile. Our IPM robotic system represents a significant advancement for ex vivo simulation, enabling more reliable cardiac simulations and repair optimizations.