Arbitrary-Shape Dielectric Particles Interacting in the Linearized Poisson-Boltzmann Framework: An Analytical Treatment.

This work considers the interaction of two dielectric particles of arbitrary shape immersed into a solvent containing a dissociated salt and assuming that the linearized Poisson-Boltzmann equation holds. We establish a new general spherical re-expansion result which relies neither on the conventional condition that particle radii are small with respect to the characteristic separating distance between particles nor on any symmetry assumption. This is instrumental in calculating suitable expansion coefficients for the electrostatic potential inside and outside the objects and in constructing small-parameter asymptotic expansions for the potential, the total electrostatic energy, and forces in ascending order of Debye screening. This generalizes a recent result for the case of dielectric spheres to particles of arbitrary shape and builds for the first time a rigorous (exact at the Debye-Hückel level) analytical theory of electrostatic interactions of such particles at arbitrary distances. Numerical tests confirm that the proposed theory may also become especially useful in developing a new class of grid-free, fast, highly scalable solvers.

Charged dielectric spheres interacting in electrolytic solution: A linearized Poisson-Boltzmann equation model.

We present an analytical theory of electrostatic interactions of two spherical dielectric particles of arbitrary radii and dielectric constants, immersed into a polarizable ionic solvent (assuming that the linearized Poisson-Boltzmann framework holds) and bearing arbitrary charge distributions expanded in multipolar terms. The presented development entails a novel two-center re-expansion analytical theory that expands upon and improves the existing ones, bypassing the conventional expansions in modified Bessel functions. On this basis, we develop a specific matrix formalism that facilitates the construction of asymptotic expansions in ascending order of Debye screening terms of potential coefficients, which are then employed to find exact closed-form expressions for the total electrostatic energy. In particular, this work allows us to explicitly and precisely quantify the k-screened terms of the potential coefficients and mutual interaction energy. Specific cases of monopolar and dipolar distributions are described in particular detail. Comprehensive numerical examples and tests of series convergence and the relative balance of leading and higher-order terms of the mutual interaction energy are presented depending on the inter-particle distance and particles' radii. The results of this work find application in soft matter modeling and, in particular, in computational biophysics and colloid science, where the availability of increasingly larger experimental structures at the atomic-level resolution makes numerical treatment challenging and calls for more efficient expressions and an increased range of validity.

4D Flow MRI hemodynamic benchmarking of surgical bioprosthetic valves.

PURPOSE: We exploited 4-dimensional flow magnetic resonance imaging (4D Flow), combined with a standardized in vitro setting, to establish a comprehensive benchmark for the systematic hemodynamic comparison of surgical aortic bioprosthetic valves (BPVs). MATERIALS AND METHODS: 4D Flow analysis was performed on two small sizes of three commercialized pericardial BPVs (Trifecta™ GT, Carpentier-Edwards PERIMOUNT Magna and Crown PRT®). Each BPV was tested over a clinically pertinent range of continuous flow rates within an in vitro MRI-compatible system, equipped with pressure transducers. In-house 4D Flow post-processing of the post-valvular velocity field included the quantification of BPV effective orifice area (EOA), transvalvular pressure gradients (TPG), kinetic energy and viscous energy dissipation. RESULTS: The 4D Flow technique effectively captured the 3-dimensional flow pattern of each device. Trifecta exhibited the lowest range of velocity and kinetic energy, maximized EOA (p < 0.0001) and minimized TPGs (p ≤ 0.015) if compared with Magna and Crown, these reporting minor EOA difference s (p ≥ 0.042) and similar TPGs (p ≥ 0.25). 4D Flow TPGs estimations strongly correlated against ground-truth data from pressure transducers; viscous energy dissipation proved to be inversely proportional to the fluid jet penetration. CONCLUSION: The proposed 4D Flow analysis pinpointed consistent hemodynamic differences among BPVs, highlighting the not negligible effect of device size on the fluidynamic outcomes. The efficacy of non-invasive 4D Flow MRI protocol could shed light on how standardize the comparison among devices in relation to their actual hemodynamic performances and improve current criteria for their selection.

Experimental quantification of the fluid dynamics in blood-processing devices through 4D-flow imaging: A pilot study on a real oxygenator/heat-exchanger module.

The performance of blood-processing devices largely depends on the associated fluid dynamics, which hence represents a key aspect in their design and optimization. To this aim, two approaches are currently adopted: computational fluid-dynamics, which yields highly resolved three-dimensional data but relies on simplifying assumptions, and in vitro experiments, which typically involve the direct video-acquisition of the flow field and provide 2D data only. We propose a novel method that exploits space- and time-resolved magnetic resonance imaging (4D-flow) to quantify the complex 3D flow field in blood-processing devices and to overcome these limitations. We tested our method on a real device that integrates an oxygenator and a heat exchanger. A dedicated mock loop was implemented, and novel 4D-flow sequences with sub-millimetric spatial resolution and region-dependent velocity encodings were defined. Automated in house software was developed to quantify the complex 3D flow field within the different regions of the device: region-dependent flow rates, pressure drops, paths of the working fluid and wall shear stresses were computed. Our analysis highlighted the effects of fine geometrical features of the device on the local fluid-dynamics, which would be unlikely observed by current in vitro approaches. Also, the effects of non-idealities on the flow field distribution were captured, thanks to the absence of the simplifying assumptions that typically characterize numerical models. To the best of our knowledge, our approach is the first of its kind and could be extended to the analysis of a broad range of clinically relevant devices.