Structure–mechanics relationships in mineralized tendons

In this paper, we review the hierarchical structure and the resulting elastic properties of mineralized tendons as obtained by various multiscale experimental and computational methods spanning from nano- to macroscale. The mechanical properties of mineralized collagen fibres are important to understand the mechanics of hard tissues constituted by complex arrangements of these fibres, like in human lamellar bone. The uniaxial mineralized collagen fibre array naturally occurring in avian tendons is a well studied model tissue for investigating various stages of tissue mineralization and the corresponding elastic properties. Some avian tendons mineralize with maturation, which results in a graded structure containing two zones of distinct morphology, circumferential and interstitial. These zones exhibit different amounts of mineral, collagen, pores and a different mineral distribution between collagen fibrillar and extrafibrillar space that lead to distinct elastic properties. Mineralized tendon cells have two phenotypes: elongated tenocytes placed between fibres in the circumferential zone and cuboidal cells with lower aspect ratios in the interstitial zone. Interestingly some regions of avian tendons seem to be predestined to mineralization, which is exhibited as specific collagen cross-linking patterns as well as distribution of minor tendon constituents (like proteoglycans) and loss of collagen crimp. Results of investigations in naturally mineralizing avian tendons may be useful in understanding the pathological mineralization occurring in some human tendons.

Pseudospectra in non-Hermitian quantum mechanics

We propose giving the mathematical concept of the pseudospectrum a central role in quantum mechanics with non-Hermitian operators. We relate pseudospectral properties to quasi-Hermiticity, similarity to self-adjoint operators, and basis properties of eigenfunctions. The abstract results are illustrated by unexpected wild properties of operators familiar from PT -symmetric quantum mechanics.

Solvation-Driven Charge Transfer and Localization in Metal Complexes

In any physicochemical process in liquids, the dynamical response of the solvent to the solutes out of equilibrium plays a crucial role in the rates and products: the solvent molecules react to the changes in volume and electron density of the solutes to minimize the free energy of the solution, thus modulating the activation barriers and stabilizing (or destabilizing) intermediate states. In charge transfer (CT) processes in polar solvents, the response of the solvent always assists the formation of charge separation states by stabilizing the energy of the localized charges. A deep understanding of the solvation mechanisms and time scales is therefore essential for a correct description of any photochemical process in dense phase and for designing molecular devices based on photosensitizers with CT excited states. In the last two decades, with the advent of ultrafast time-resolved spectroscopies, microscopic models describing the relevant case of polar solvation (where both the solvent and the solute molecules have a permanent electric dipole and the mutual interaction is mainly dipole−dipole) have dramatically progressed. Regardless of the details of each model, they all assume that the effect of the electrostatic fields of the solvent molecules on the internal electronic dynamics of the solute are perturbative and that the solvent−solute coupling is mainly an electrostatic interaction between the constant permanent dipoles of the solute and the solvent molecules. This well-established picture has proven to quantitatively rationalize spectroscopic effects of environmental and electric dynamics (time-resolved Stokes shifts, inhomogeneous broadening, etc.). However, recent computational and experimental studies, including ours, have shown that further improvement is required. Indeed, in the last years we investigated several molecular complexes exhibiting photoexcited CT states, and we found that the current description of the formation and stabilization of CT states in an important group of molecules such as transition metal complexes is inaccurate. In particular, we proved that the solvent molecules are not just spectators of intramolecular electron density redistribution but significantly modulate it. Our results solicit further development of quantum mechanics computational methods to treat the solute and (at least) the closest solvent molecules including the nonperturbative treatment of the effects of local electrostatics and direct solvent−solute interactions to describe the dynamical changes of the solute excited states during the solvent response.

The role of inducible nitric oxide synthase for interstitial remodeling of alveolar septa in surfactant protein D-deficient mice

Surfactant protein D (SP-D) modulates the lung's immune system. Its absence leads to NOS2-independent alveolar lipoproteinosis and NOS2-dependent chronic inflammation, which is critical for early emphysematous remodeling. With aging, SP-D knockout mice develop an additional interstitial fibrotic component. We hypothesize that this age-related interstitial septal wall remodeling is mediated by NOS2. Using invasive pulmonary function testing such as the forced oscillation technique and quasistatic pressure-volume perturbation and design-based stereology, we compared 29-wk-old SP-D knockout (Sftpd(-/-)) mice, SP-D/NOS2 double-knockout (DiNOS) mice, and wild-type mice (WT). Structural changes, including alveolar epithelial surface area, distribution of septal wall thickness, and volumes of septal wall components (alveolar epithelium, interstitial tissue, and endothelium) were quantified. Twenty-nine-week-old Sftpd(-/-) mice had preserved lung mechanics at the organ level, whereas elastance was increased in DiNOS. Airspace enlargement and loss of surface area of alveolar epithelium coexist with increased septal wall thickness in Sftpd(-/-) mice. These changes were reduced in DiNOS, and compared with Sftpd(-/-) mice a decrease in volumes of interstitial tissue and alveolar epithelium was found. To understand the effects of lung pathology on measured lung mechanics, structural data were used to inform a computational model, simulating lung mechanics as a function of airspace derecruitment, septal wall destruction (loss of surface area), and septal wall thickening. In conclusion, NOS2 mediates remodeling of septal walls, resulting in deposition of interstitial tissue in Sftpd(-/-). Forward modeling linking structure and lung mechanics describes the complex mechanical properties by parenchymatous destruction (emphysema), interstitial remodeling (septal wall thickening), and altered recruitability of acinar airspaces.

Computational Comparison of Continuous and Discontinuous Galerkin Time-Stepping Methods for Nonlinear Initial Value Problems

This article centers on the computational performance of the continuous and discontinuous Galerkin time stepping schemes for general first-order initial value problems in R n , with continuous nonlinearities. We briefly review a recent existence result for discrete solutions from [6], and provide a numerical comparison of the two time discretization methods.

Outcomes of Active Surveillance for Ductal Carcinoma in Situ: A Computational Risk Analysis.

BACKGROUND Ductal carcinoma in situ (DCIS) is a noninvasive breast lesion with uncertain risk for invasive progression. Usual care (UC) for DCIS consists of treatment upon diagnosis, thus potentially overtreating patients with low propensity for progression. One strategy to reduce overtreatment is active surveillance (AS), whereby DCIS is treated only upon detection of invasive disease. Our goal was to perform a quantitative evaluation of outcomes following an AS strategy for DCIS. METHODS Age-stratified, 10-year disease-specific cumulative mortality (DSCM) for AS was calculated using a computational risk projection model based upon published estimates for natural history parameters, and Surveillance, Epidemiology, and End Results data for outcomes. AS projections were compared with the DSCM for patients who received UC. To quantify the propagation of parameter uncertainty, a 95% projection range (PR) was computed, and sensitivity analyses were performed. RESULTS Under the assumption that AS cannot outperform UC, the projected median differences in 10-year DSCM between AS and UC when diagnosed at ages 40, 55, and 70 years were 2.6% (PR = 1.4%-5.1%), 1.5% (PR = 0.5%-3.5%), and 0.6% (PR = 0.0%-2.4), respectively. Corresponding median numbers of patients needed to treat to avert one breast cancer death were 38.3 (PR = 19.7-69.9), 67.3 (PR = 28.7-211.4), and 157.2 (PR = 41.1-3872.8), respectively. Sensitivity analyses showed that the parameter with greatest impact on DSCM was the probability of understaging invasive cancer at diagnosis. CONCLUSION AS could be a viable management strategy for carefully selected DCIS patients, particularly among older age groups and those with substantial competing mortality risks. The effectiveness of AS could be markedly improved by reducing the rate of understaging.