A partition of unity approach to fluid mechanics and fluid-structure interaction

For problems involving large deformations of thin structures, simulating fluid-structure interaction (FSI) remains challenging largely due to the need to balance computational feasibility, efficiency, and solution accuracy. Overlapping domain techniques have been introduced as a way to combine the fluid-solid mesh conformity, seen in moving-mesh methods, without the need for mesh smoothing or re-meshing, which is a core characteristic of fixed mesh approaches. In this work, we introduce a novel overlapping domain method based on a partition of unity approach. Unified function spaces are defined as a weighted sum of fields given on two overlapping meshes. The method is shown to achieve optimal convergence rates and to be stable for steady-state Stokes, Navier-Stokes, and ALE Navier-Stokes problems. Finally, we present results for FSI in the case of a 2D mock aortic valve simulation. These initial results point to the potential applicability of the method to a wide range of FSI applications, enabling boundary layer refinement and large deformations without the need for re-meshing or user-defined stabilization.Comment: 34 pages, 15 figur

Multilevel convergence analysis of multigrid-reduction-in-time

This paper presents a multilevel convergence framework for multigrid-reduction-in-time (MGRIT) as a generalization of previous two-grid estimates. The framework provides a priori upper bounds on the convergence of MGRIT V- and F-cycles, with different relaxation schemes, by deriving the respective residual and error propagation operators. The residual and error operators are functions of the time stepping operator, analyzed directly and bounded in norm, both numerically and analytically. We present various upper bounds of different computational cost and varying sharpness. These upper bounds are complemented by proposing analytic formulae for the approximate convergence factor of V-cycle algorithms that take the number of fine grid time points, the temporal coarsening factors, and the eigenvalues of the time stepping operator as parameters. The paper concludes with supporting numerical investigations of parabolic (anisotropic diffusion) and hyperbolic (wave equation) model problems. We assess the sharpness of the bounds and the quality of the approximate convergence factors. Observations from these numerical investigations demonstrate the value of the proposed multilevel convergence framework for estimating MGRIT convergence a priori and for the design of a convergent algorithm. We further highlight that observations in the literature are captured by the theory, including that two-level Parareal and multilevel MGRIT with F-relaxation do not yield scalable algorithms and the benefit of a stronger relaxation scheme. An important observation is that with increasing numbers of levels MGRIT convergence deteriorates for the hyperbolic model problem, while constant convergence factors can be achieved for the diffusion equation. The theory also indicates that L-stable Runge-Kutta schemes are more amendable to multilevel parallel-in-time integration with MGRIT than A-stable Runge-Kutta schemes.Comment: 26 pages; 17 pages Supplementary Material

A method for intramedullary fixation offractures and segmental grafts in the rat tibia

A new technique for intramedullary nailing ot the tibia in rats is described. The results of fracture and segmental graft fixations with the nail are presented. The modular nail consists of three parts that are threaded into and past each other, givingit a conical outer diameter which fits the tibial inedullary canal. The biomechanieal properties of this nail are similar to those ofintact tibias of 230 g male rats. which makes it suitable for experiments with rats weighing more than 200 g

Weight gain and the risk of total hip replacement a population-based prospective cohort study of 265,725 individuals

SummaryObjectiveTo study the association between change in the body mass index (BMI) at different ages and the risk of a later total hip replacement (THR) due to primary osteoarthritis (OA).DesignA total of 265,725 individuals who had two repeated measurements of weight and height were included from national health screenings. These individuals were followed prospectively. The data were matched with the Norwegian Arthroplasty Register and 4,442 of these individuals were identified as having received a THR for primary OA. Cox proportional hazard regression was used to calculate sex-specific relative risks for having a THR according to age at screening and BMI change.ResultsMen and women aged 20 years or younger at the first screening in the quartile with the greatest BMI change per year had more than twice the risk of later having a THR compared with those in the quartile with the smallest BMI change per year. For men older than 30 years at the first screening, there was no relationship between BMI gain, or weight gain, and later risk of THR. For older women, BMI gain was associated with risk of THR, but to a lesser degree than in younger women.ConclusionThere was a clear relationship between change in BMI and the risk of later THR in young men and women, whereas the association was absent in older men and weaker in older women. It is important to focus on weight control to prevent future OA, and the preventive strategy should be focused on the young population

Patterns of Nonrandom Mating Within and Across 11 Major Psychiatric Disorders

Psychiatric disorders are heritable, polygenic traits, which often share risk alleles and for which nonrandom mating has been suggested. However, despite the potential etiological implications, the scale of nonrandom mating within and across major psychiatric conditions remains unclear

Risk factors for knee replacement due to primary osteoarthritis, a population based, prospective cohort study of 315,495 individuals

Background: Osteoarthritis (OA) of the knee is a common and disabling condition. We wanted to investigate the modifiable risk factors Body Mass Index (BMI) and physical activity, using knee replacement (KR) as a marker for severely symptomatic disease, focusing on the interaction between these risk factors. Methods: 315,495 participants (mean age 43.0 years) from national health screenings were followed prospectively with respect to KR identified by linkage to the Norwegian Arthroplasty Register. Data were analysed by Cox proportional hazard regression. Results: During 12 years of follow up 1,323 individuals received KR for primary OA. There was a dose–response relationship between BMI and heavy labour, and later KR. Comparing the highest versus the lowest quarter of BMI, the relative risk was 6.2 (95% CI: 4.2-9.0) in men and 11.1 (95% CI: 7.8-15.6) in women. Men reporting intensive physical activity at work had a relative risk of 2.4 (95% CI: 1.8-3.2) versus men reporting sedentary activity at work, the corresponding figure in women being 2.3 (95% CI: 1.7-3.2). The effect of BMI and physical activity at work was additive. The heaviest men with the most strenuous work had a RR of 11.7 (95% CI: 5.9-23.1) compared to the ones with the lowest BMI and most sedentary work. For women the corresponding RR was 15.8 (95% CI: 8.2-30.3). There was no association between physical activity during leisure and KR. Conclusion: We found that a high BMI and intensive physical activity at work both contribute strongly to the risk of having a KR. As the two risk factors seem to act independently, people with strenuous physical work with a high BMI are at particularly high risk for severely disabling OA of the knee, and should be targeted with effective preventive measures.publishedVersio

A Data-Driven Computational Model for Engineered Cardiac Microtissues

Engineered heart tissues (EHTs) present a potential solution to some of the current challenges in the treatment of heart disease; however, the development of mature, adult-like cardiac tissues remains elusive. Mechanical stimuli have been observed to improve whole-tissue function and cardiomyocyte (CM) maturation, although our ability to fully utilize these mechanisms is hampered, in part, by our incomplete understanding of the mechanobiology of EHTs. In this work, we leverage the experimental data produced by a mechanically tunable experimental setup to generate tissue-specific computational models of EHTs. Using imaging and functional data, our modeling pipeline generates models with tissue-specific ECM and myofibril structure, allowing us to estimate CM active stress. We use this experimental and modeling pipeline to study different mechanical environments, where we contrast the force output of the tissue with the computed active stress of CMs. We show that the significant differences in measured experimental forces can largely be explained by the levels of myofibril formation achieved by the CMs in the distinct mechanical environments, with active stress showing more muted variations across conditions. The presented model also enables us to dissect the relative contributions of myofibrils and extracellular matrix to tissue force output, a task difficult to address experimentally. These results highlight the importance of tissue-specific modeling to augment EHT experiments, providing deeper insights into the mechanobiology driving EHT function.Comment: 19 pages, 7 figure