127 research outputs found
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
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
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
Imaging and biophysical modelling of thrombogenic mechanisms in atrial fibrillation and stroke
Atrial fibrillation (AF) underlies almost one third of all ischaemic strokes, with the left atrial appendage (LAA) identified as the primary thromboembolic source. Current stroke risk stratification approaches, such as the CHA2DS2-VASc score, rely mostly on clinical comorbidities, rather than thrombogenic mechanisms such as blood stasis, hypercoagulability and endothelial dysfunction—known as Virchow’s triad. While detection of AF-related thrombi is possible using established cardiac imaging techniques, such as transoesophageal echocardiography, there is a growing need to reliably assess AF-patient thrombogenicity prior to thrombus formation. Over the past decade, cardiac imaging and image-based biophysical modelling have emerged as powerful tools for reproducing the mechanisms of thrombogenesis. Clinical imaging modalities such as cardiac computed tomography, magnetic resonance and echocardiographic techniques can measure blood flow velocities and identify LA fibrosis (an indicator of endothelial dysfunction), but imaging remains limited in its ability to assess blood coagulation dynamics. In-silico cardiac modelling tools—such as computational fluid dynamics for blood flow, reaction-diffusion-convection equations to mimic the coagulation cascade, and surrogate flow metrics associated with endothelial damage—have grown in prevalence and advanced mechanistic understanding of thrombogenesis. However, neither technique alone can fully elucidate thrombogenicity in AF. In future, combining cardiac imaging with in-silico modelling and integrating machine learning approaches for rapid results directly from imaging data will require development under a rigorous framework of verification and clinical validation, but may pave the way towards enhanced personalised stroke risk stratification in the growing population of AF patients. This Review will focus on the significant progress in these fields
Magnetic resonance elastography in nonlinear viscoelastic materials under load.
Characterisation of soft tissue mechanical properties is a topic of increasing interest in translational and clinical research. Magnetic resonance elastography (MRE) has been used in this context to assess the mechanical properties of tissues in vivo noninvasively. Typically, these analyses rely on linear viscoelastic wave equations to assess material properties from measured wave dynamics. However, deformations that occur in some tissues (e.g. liver during respiration, heart during the cardiac cycle, or external compression during a breast exam) can yield loading bias, complicating the interpretation of tissue stiffness from MRE measurements. In this paper, it is shown how combined knowledge of a material's rheology and loading state can be used to eliminate loading bias and enable interpretation of intrinsic (unloaded) stiffness properties. Equations are derived utilising perturbation theory and Cauchy's equations of motion to demonstrate the impact of loading state on periodic steady-state wave behaviour in nonlinear viscoelastic materials. These equations demonstrate how loading bias yields apparent material stiffening, softening and anisotropy. MRE sensitivity to deformation is demonstrated in an experimental phantom, showing a loading bias of up to twofold. From an unbiased stiffness of [Formula: see text] Pa in unloaded state, the biased stiffness increases to 9767.5Â [Formula: see text]1949.9Â Pa under a load of [Formula: see text]Â 34% uniaxial compression. Integrating knowledge of phantom loading and rheology into a novel MRE reconstruction, it is shown that it is possible to characterise intrinsic material characteristics, eliminating the loading bias from MRE data. The framework introduced and demonstrated in phantoms illustrates a pathway that can be translated and applied to MRE in complex deforming tissues. This would contribute to a better assessment of material properties in soft tissues employing elastography
In Silico Modeling of Shear-Stress-Induced Nitric Oxide Production in Endothelial Cells through Systems Biology
Nitric oxide (NO) produced by vascular endothelial cells is a potent vasodilator and an antiinflammatory mediator. Regulating production of endothelial-derived NO is a complex undertaking, involving multiple signaling and genetic pathways that are activated by diverse humoral and biomechanical stimuli. To gain a thorough understanding of the rich diversity of responses observed experimentally, it is necessary to account for an ensemble of these pathways acting simultaneously. In this article, we have assembled four quantitative molecular pathways previously proposed for shear-stress-induced NO production. In these pathways, endothelial NO synthase is activated 1), via calcium release, 2), via phosphorylation reactions, and 3), via enhanced protein expression. To these activation pathways, we have added a fourth, a pathway describing actual NO production from endothelial NO synthase and its various protein partners. These pathways were combined and simulated using CytoSolve, a computational environment for combining independent pathway calculations. The integrated model is able to describe the experimentally observed change in NO production with time after the application of fluid shear stress. This model can also be used to predict the specific effects on the system after interventional pharmacological or genetic changes. Importantly, this model reflects the up-to-date understanding of the NO system, providing a platform upon which information can be aggregated in an additive way.National Institutes of Health (U.S.) (Grant R01HL090856)Singapore-MIT Alliance Computational and Systems Biology Progra
MicroBundleCompute: Automated segmentation, tracking, and analysis of subdomain deformation in cardiac microbundles
Advancing human induced pluripotent stem cell derived cardiomyocyte
(hiPSC-CM) technology will lead to significant progress ranging from disease
modeling, to drug discovery, to regenerative tissue engineering. Yet, alongside
these potential opportunities comes a critical challenge: attaining mature
hiPSC-CM tissues. At present, there are multiple techniques to promote maturity
of hiPSC-CMs including physical platforms and cell culture protocols. However,
when it comes to making quantitative comparisons of functional behavior, there
are limited options for reliably and reproducibly computing functional metrics
that are suitable for direct cross-system comparison. In addition, the current
standard functional metrics obtained from time-lapse images of cardiac
microbundle contraction reported in the field (i.e., post forces, average
tissue stress) do not take full advantage of the available information present
in these data (i.e., full-field tissue displacements and strains). Thus, we
present "MicroBundleCompute," a computational framework for automatic
quantification of morphology-based mechanical metrics from movies of cardiac
microbundles. Briefly, this computational framework offers tools for automatic
tissue segmentation, tracking, and analysis of brightfield and phase contrast
movies of beating cardiac microbundles. It is straightforward to implement,
requires little to no parameter tuning, and runs quickly on a personal
computer. In this paper, we describe the methods underlying this computational
framework, show the results of our extensive validation studies, and
demonstrate the utility of exploring heterogeneous tissue deformations and
strains as functional metrics. With this manuscript, we disseminate
"MicroBundleCompute" as an open-source computational tool with the aim of
making automated quantitative analysis of beating cardiac microbundles more
accessible to the community.Comment: 16 main pages, 7 main figures, Supplementary Information included as
appendice
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