Multiscale homogenisation of diffusion in enzymatically-calcified hydrogels

Hydrogels are a promising class of material in biomedical and industrial applications, where both the mechanical and diffusion properties play an important role. The wide range of polymers that can be used and the different production methods allows these properties to be specifically tuned to a high degree for their application. Producing tough hydrogels with high stiffness has been a long-standing challenge that has recently been addressed by mineralisation methods. Those methods modify the hydrogel into one with a supporting mineral microstructure that is highly heterogeneous. This work investigates methods to determine the macroscopic diffusion behaviour of heterogeneous gels by a homogenisation method implemented in a finite element framework. This is applied to two recently developed materials by calcifying poly-dimethyl-acrylamide (PDMA) and polyacrylamide hydrogels (PAAm). The former has porous, spherical inclusions obstructing diffusion, while the latter has spherical pores enabling it. For both gels the unobstructed volume can be used as the primary parameter to tune the diffusivity. In PDMA the porosity of the obstructions is shown by multiscale analysis to give a strong, non-linear dependence of the diffusivity on the solute molecule radius. The framework is extended to other materials and comparisons are made to experimental works from the literature.

Review paper: The importance of consideration of collagen cross-links in computational models of collagen-based tissues

Collagen as the main protein in Extra Cellular Matrix (ECM) is the main load-bearing component of fibrous tissues. Nanostructure and architecture of collagen fibrils play an important role in mechanical behavior of these tissues. Extensive experimental and theoretical studies have so far been performed to capture these properties, but none of the current models realistically represent the complexity of network mechanics because still less is known about the collagen's inner structure and its effect on the mechanical properties of tissues. The goal of this review article is to emphasize the significance of cross-links in computational modeling of different collagen-based tissues, and to reveal the need for continuum models to consider cross-links properties to better reflect the mechanical behavior observed in experiments. In addition, this study outlines the limitations of current investigations and provides potential suggestions for the future work.

Changes in health perception of COVID-19 among patients with aortic diseases: a longitudinal study between the first and second wave of the COVID-19 pandemic

Background

The rapidly spread of the novel coronavirus disease (COVID-19) worldwide has become the most challenging global health pandemic since the 1918 flu. In Germany, more than 2.5 million cases are confirmed so far, with more than 70,000 deaths. An increased fatality rate was seen among patients with preexisting comorbid conditions, especially with cardiovascular diseases, representing this group at particular risk.

Purpose

Risk perceptions of public health crises like the COVID-19 pandemic can affect people's mental health, reveal gaps in support, and influences the adherence to regulatory requirements. The aim of this study was to evaluate changes in health perception among patients with aortic diseases during the first and second wave of the COVID-19 pandemic in Germany.

Methods

Patients (n=262) diagnosed with aortic disease participated in telephone interviews during the first (w1, April 6–April 29, 2020) and second wave (w2, January 11–January 29, 2021) of the pandemic in Germany. The perception of COVID-19 as a threat was examined using relevant items of the Brief Illness Perception (BIP) questionnaire to address four dimensions (consequences, control, personal control, and understanding). Relevant data focusing on different aortic diseases and cardiovascular risk factors were taken from patient records.

Results

Aortic diseases included mainly aortic aneurysm of the ascending (n=164, 62.6%) and the descending aorta (n=37, 14.1%). Patients with acute or chronic aortic dissection made up a third (n=41, 15.6%, and n=48, 18.3%, respectively). At baseline (w1), none of the participants had neither been quarantined nor were taken ill with COVID-19. At the second survey (w2), 24 participants (n=252, 9.5%) had already been quarantined and five (n=252, 2%) were diagnosed with COVID-19. The BIP score increased 9.18 (SD=7.132) to 14.58 (SD = 6.956) between w1 and w2 (p<.001). At the level of dimensions, that meant a significant difference between w1 and w2 regarding “consequences” (M=−2.821, SD=3.049, 95% CI [−3.200, −2.443], t(251)=−14.691, p<.001, d=0.92), “control” (M=0.908, SD=2.492, 95% CI [0.589, 1.218], t(249)=5.760, p<.001, d=0.36), and “concern” (M=−1.669, SD=3.349, 95% CI [−2.086, −1.253], t(250)=−7.898, p<0.001, d=0.50). Only “understanding” showed no significant difference (M=−0.032, SD=1.520, 95% CI [−0.220, 0.157], t(251)=−0.332, p=0.740).

Conclusion

Although patients with aortic diseases are highly at risk of having worse outcomes from COVID-19, their overall perception of COVID-19 as a threat was low in the beginning, but rising during the second wave. The main reasons were the increased effects on personal life and elevated concerns about the COVID-19 pandemic, but concerns did not include the educational aspect of COVID-19. Tailored risk communication strengthens the mental health of people in a public health crisis and ensures the success of governmental guidelines and policies.

Funding Acknowledgement

Type of funding sources: None. Course of COVID-19 pandemic in Germany

Numerical analysis of the impact of cytoskeletal actin filament density alterations onto the diffusive vesicle-mediated cell transport

The interior of a eukaryotic cell is a highly complex composite material which consists of water, structural scaffoldings, organelles, and various biomolecular solutes. All these components serve as obstacles that impede the motion of vesicles. Hence, it is hypothesized that any alteration of the cytoskeletal network may directly impact or even disrupt the vesicle transport. A disruption of the vesicle-mediated cell transport is thought to contribute to several severe diseases and disorders, such as diabetes, Parkinson’s and Alzheimer’s disease, emphasizing the clinical relevance. To address the outlined objective, a multiscale finite element model of the diffusive vesicle transport is proposed on the basis of the concept of homogenization, owed to the complexity of the cytoskeletal network. In order to study the microscopic effects of specific nanoscopic actin filament network alterations onto the vesicle transport, a parametrized three-dimensional geometrical model of the actin filament network was generated on the basis of experimentally observed filament densities and network geometries in an adenocarcinomic human alveolar basal epithelial cell. Numerical analyzes of the obtained effective diffusion properties within two-dimensional sampling domains of the whole cell model revealed that the computed homogenized diffusion coefficients can be predicted statistically accurate by a simple two-parameter power law as soon as the inaccessible area fraction, due to the obstacle geometries and the finite size of the vesicles, is known. This relationship, in turn, leads to a massive reduction in computation time and allows to study the impact of a variety of different cytoskeletal alterations onto the vesicle transport. Hence, the numerical simulations predicted a 35% increase in transport time due to a uniformly distributed four-fold increase of the total filament amount. On the other hand, a hypothetically reduced expression of filament cross-linking proteins led to sparser filament networks and, thus, a speed up of the vesicle transport.

Many vital processes in our eukaryotic cells and organs require an astonishingly precise routing of intermediate products to various intra- and extracellular destinations using vesicles as transporters. This can be illustrated by numerous examples, such as the production and destruction of proteins, the export of neurotransmitters or insulin to the extracellular domain, etc. However, the inside of a cell is tightly packed with numerous structural scaffoldings (filaments), which serve as obstacles and impede the vesicle motion. It is thought that any disturbances of the vesicle-mediated cell transport contribute to numerous degenerative diseases and disorders, which highlights the clinical relevance for investigating this intracellular transport mechanism by developing computational models and performing experimental studies. In this study, we numerically quantified how different specific alterations of the filament density inside a human lung cell—due to changed mechanical loadings or genetic disorders of proteins being responsible for filament branching—affect the diffusion of vesicles inside the intracellular fluid. Therefore, based on the concept of homogenization, a computationally efficient numerical method was developed and utilized to simulate the diffusion of vesicles inside the whole cell, considering the detailed structural information of the filament network.

Multiscale FEM simulations of cross-linked actin network embedded in cytosol with the focus on the filament orientation

The present contribution focuses on the application of the multiscale finite element method to the modeling of actin networks that are embedded in the cytosol. These cell components are of particular importance with regard to the cell response to external stimuli. The homogenization strategy chosen uses the Hill-Mandel macrohomogeneity condition for bridging 2 scales: the macroscopic scale that is related to the cell level and the microscopic scale related to the representative volume element. For the modeling of filaments, the Holzapfel-Ogden β-model is applied. It provides a relationship between the tensile force and the caused stretches, serves as the basis for the derivation of the stress and elasticity tensors, and enables a novel finite element implementation. The elements with the neo-Hookean constitutive law are applied for the simulation of the cytosol. The results presented corroborate the main advantage of the concept, namely, its flexibility with regard to the choice of the representative volume element as well as of macroscopic tests. The focus is particularly placed on the study of the filament orientation and of its influence on the effective behavior.

A mechanical model for dissolution–precipitation creep based on the minimum principle of the dissipation potential

In contrast to previous approaches that consider dissolution–precipitation creep as a multi-stage process and only simulate its governing subprocess, the present model treats this phenomenon as a single continuous process. The applied strategy uses the minimum principle of the dissipation potential according to which a Lagrangian consisting of elastic power and dissipation is minimized. Here, the elastic part has a standard form while the assumption for dissipation stipulates the driving forces to be proportional to two kinds of velocities: the material-transport velocity and the boundary-motion velocity. A Lagrange term is included to impose mass conservation. Two ways of solution are proposed. The strong form of the problem is solved analytically for a simple case. The weak form of the problem is used for a finite-element implementation and for simulating more complex cases.

Investigation of the influence of reflection on the attenuation of cancellous bone

The model proposed in this paper is based on the fact that the reflection might have a significant contribution to the attenuation of the acoustic waves propagating through the cancellous bone. The numerical implementation of the mentioned effect is realized by the development of a new representative volume element that includes an infinitesimally thin 'transient' layer on the contact surface of the bone and the marrow. This layer serves to model the amplitude transformation of the incident wave by the transition through media with different acoustic impedances and to take into account the energy loss due to the reflection. The proposed representative volume element together with the multiscale finite element is used to simulate the wave propagation and to evaluate the attenuation coefficient for samples with different effective densities in the dependence of the applied excitation frequency. The obtained numerical values show a very good agreement with the experimental results. Moreover, the model enables the determination of the upper and the lower bound for the attenuation coefficient.