arXiv subjects

David Nordsletten

Publications and source records attributed to David Nordsletten.

13 recordsLinked to original sources

arXiv2026

Quantifying the Spatiotemporal Dynamics of Engineered Cardiac Microbundles

Brightfield time-lapse imaging is widely used in cardiac tissue engineering, yet the absence of standardized, interpretable analytical frameworks limits reproducibility and cross-platform comparison. We present an open, scalable computational pipeline for quantifying spatiotemporal contractile dynamics in microscopy videos of human induced pluripotent stem cell-derived cardiac microbundles. Building on our open-source tools "MicroBundleCompute" and "MicroBundlePillarTrack," we define a suite of 16 interpretable structural, functional, and spatiotemporal metrics that capture tissue deformation, synchrony, and heterogeneity. The framework integrates full-field displacement tracking, strain reconstruction, spatial registration, dimensionality reduction, and topology-based vector-field analysis within a unified workflow. Applied to a dataset of 670 cardiac microbundles spanning 20 experimental conditions, the pipeline reveals continuous variation in contractile phenotypes rather than discrete condition-specific clustering, with intra-condition variability often exceeding inter-condition differences. Redundancy analysis identifies a reduced core set of 10 metrics that retain most informational content while minimizing multicollinearity. Analysis of denoised displacement fields shows that contraction is dominated by a global isotropic mode, with localized saddle-type deformation patterns present in approximately half of the samples. All software and workflows are released openly to enable reproducible, scalable analysis of dynamic tissue mechanics.

q-bio.QM↗

arXiv2025

Deep learning for temporal super-resolution 4D Flow MRI

4D Flow Magnetic Resonance Imaging (4D Flow MRI) is a non-invasive technique for volumetric, time-resolved blood flow quantification. However, apparent trade-offs between acquisition time, image noise, and resolution limit clinical applicability. In particular, in regions of highly transient flow, coarse temporal resolution can hinder accurate capture of physiologically relevant flow variations. To overcome these issues, post-processing techniques using deep learning have shown promising results to enhance resolution post-scan using so-called super-resolution networks. However, while super-resolution has been focusing on spatial upsampling, temporal super-resolution remains largely unexplored. The aim of this study was therefore to implement and evaluate a residual network for temporal super-resolution 4D Flow MRI. To achieve this, an existing spatial network (4DFlowNet) was re-designed for temporal upsampling, adapting input dimensions, and optimizing internal layer structures. Training and testing were performed using synthetic 4D Flow MRI data originating from patient-specific in-silico models, as well as using in-vivo datasets. Overall, excellent performance was achieved with input velocities effectively denoised and temporally upsampled, with a mean absolute error (MAE) of 1.0 cm/s in an unseen in-silico setting, outperforming deterministic alternatives (linear interpolation MAE = 2.3 cm/s, sinc interpolation MAE = 2.6 cm/s). Further, the network synthesized high-resolution temporal information from unseen low-resolution in-vivo data, with strong correlation observed at peak flow frames. As such, our results highlight the potential of utilizing data-driven neural networks for temporal super-resolution 4D Flow MRI, enabling high-frame-rate flow quantification without extending acquisition times beyond clinically acceptable limits.

cs.LG↗

arXiv2024

Effective Block Preconditioners for Fluid Dynamics Coupled to Reduced Models of a Non-Local Nature

Modeling cardiovascular blood flow is central to many applications in biomedical engineering. To accommodate the complexity of the cardiovascular system, in terms of boundary conditions and surrounding vascular tissue, computational fluid dynamics (CFD) often are coupled to reduced circuit and/or solid mechanics models. These allow for realistic simulations of hemodynamics in the heart or the aorta, but come at additional computational cost and complexity. In this contribution, we design a novel block preconditioner for the solution of the stabilized Navier-Stokes equations coupled to reduced-order models of a non-local nature. These models encompass lumped-parameter systems that impose flux-dependent boundary tractions, and Galerkin reduced-order models that can be used to account for outlying mechanical structures. Here we propose a 3x3 preconditioner derived from the block factorization and approximation to the Schur complement(s). The solver performance is demonstrated for a series of examples with increasing complexity, culminating in a reduced FSI simulation in a patient-specific contracting left heart model. For all test cases, we show that our proposed approach is superior to other frequently presented 2x2 schemes that merge stiffness contributions from reduced models into the fluid Jacobian or consolidate some variables for the purpose of efficiency - with an up to six times shorter overall computing time and/or only half as many linear iterations.

physics.flu-dyn↗

arXiv2024

MicroBundlePillarTrack: A Python package for automated segmentation, tracking, and analysis of pillar deflection in cardiac microbundles

Movies of human induced pluripotent stem cell (hiPSC)-derived engineered cardiac tissue (microbundles) contain abundant information about structural and functional maturity. However, extracting these data in a reproducible and high-throughput manner remains a major challenge. Furthermore, it is not straightforward to make direct quantitative comparisons across the multiple in vitro experimental platforms employed to fabricate these tissues. Here, we present "MicroBundlePillarTrack," an open-source optical flow-based package developed in Python to track the deflection of pillars in cardiac microbundles grown on experimental platforms with two different pillar designs ("Type 1" and "Type 2" design). Our software is able to automatically segment the pillars, track their displacements, and output time-dependent metrics for contractility analysis, including beating amplitude and rate, contractile force, and tissue stress. Because this software is fully automated, it will allow for both faster and more reproducible analyses of larger datasets and it will enable more reliable cross-platform comparisons as compared to existing approaches that require manual steps and are tailored to a specific experimental platform. To complement this open-source software, we share a dataset of 1,540 brightfield example movies on which we have tested our software. Through sharing this data and software, our goal is to directly enable quantitative comparisons across labs, and facilitate future collective progress via the biomedical engineering open-source data and software ecosystem.

q-bio.QM↗

arXiv2024

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.

q-bio.QM↗

arXiv2023

Generalized super-resolution 4D Flow MRI $\unicode{x2013}$ using ensemble learning to extend across the cardiovascular system

4D Flow Magnetic Resonance Imaging (4D Flow MRI) is a non-invasive measurement technique capable of quantifying blood flow across the cardiovascular system. While practical use is limited by spatial resolution and image noise, incorporation of trained super-resolution (SR) networks has potential to enhance image quality post-scan. However, these efforts have predominantly been restricted to narrowly defined cardiovascular domains, with limited exploration of how SR performance extends across the cardiovascular system; a task aggravated by contrasting hemodynamic conditions apparent across the cardiovasculature. The aim of our study was to explore the generalizability of SR 4D Flow MRI using a combination of heterogeneous training sets and dedicated ensemble learning. With synthetic training data generated across three disparate domains (cardiac, aortic, cerebrovascular), varying convolutional base and ensemble learners were evaluated as a function of domain and architecture, quantifying performance on both in-silico and acquired in-vivo data from the same three domains. Results show that both bagging and stacking ensembling enhance SR performance across domains, accurately predicting high-resolution velocities from low-resolution input data in-silico. Likewise, optimized networks successfully recover native resolution velocities from downsampled in-vivo data, as well as show qualitative potential in generating denoised SR-images from clinical level input data. In conclusion, our work presents a viable approach for generalized SR 4D Flow MRI, with ensemble learning extending utility across various clinical areas of interest.

eess.IV↗

arXiv2023

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.

q-bio.TO↗

arXiv2021

Time-periodic steady-state solution of fluid-structure interaction and cardiac flow problems through multigrid-reduction-in-time

In this paper, a time-periodic MGRIT algorithm is proposed as a means to reduce the time-to-solution of numerical algorithms by exploiting the time periodicity inherent to many applications in science and engineering. The time-periodic MGRIT algorithm is applied to a variety of linear and nonlinear single- and multiphysics problems that are periodic-in-time. It is demonstrated that the proposed parallel-in-time algorithm can obtain the same time-periodic steady-state solution as sequential time-stepping. It is shown that the required number of MGRIT iterations can be estimated a priori and that the new MGRIT variant can significantly and consistently reduce the time-to-solution compared to sequential time-stepping, irrespective of the number of dimensions, linear or nonlinear PDE models, single-physics or coupled problems and the employed computing resources. The numerical experiments demonstrate that the time-periodic MGRIT algorithm enables a greater level of parallelism yielding faster turnaround, and thus, facilitating more complex and more realistic problems to be solved.

cs.CE↗

arXiv2021

A Viscoelastic Model for Human Myocardium

Understanding the biomechanics of the heart in health and disease plays an important role in the diagnosis and treatment of heart failure. The use of computational biomechanical models for therapy assessment is paving the way for personalized treatment, and relies on accurate constitutive equations mapping strain to stress. Current state-of-the art constitutive equations account for the nonlinear anisotropic stress-strain response of cardiac muscle using hyperelasticity theory. While providing a solid foundation for understanding the biomechanics of heart tissue, most current laws neglect viscoelastic phenomena observed experimentally. Utilizing experimental data from human myocardium and knowledge of the hierarchical structure of heart muscle, we present a fractional nonlinear anisotropic viscoelastic constitutive model. The model is shown to replicate biaxial stretch, triaxial cyclic shear and triaxial stress relaxation experiments (mean error ~7.65%), showing improvements compared to its hyperelastic (mean error ~25%) counterparts. Model sensitivity, fidelity and parameter uniqueness are demonstrated. The model is also compared to rate-dependent biaxial stretch as well as different modes of biaxial stretch, illustrating extensibility of the model to a range of loading phenomena.

physics.bio-ph↗

arXiv2020

Estimation of Cardiac Valve Annuli Motion with Deep Learning

Valve annuli motion and morphology, measured from non-invasive imaging, can be used to gain a better understanding of healthy and pathological heart function. Measurements such as long-axis strain as well as peak strain rates provide markers of systolic function. Likewise, early and late-diastolic filling velocities are used as indicators of diastolic function. Quantifying global strains, however, requires a fast and precise method of tracking long-axis motion throughout the cardiac cycle. Valve landmarks such as the insertion of leaflets into the myocardial wall provide features that can be tracked to measure global long-axis motion. Feature tracking methods require initialisation, which can be time-consuming in studies with large cohorts. Therefore, this study developed and trained a neural network to identify ten features from unlabeled long-axis MR images: six mitral valve points from three long-axis views, two aortic valve points and two tricuspid valve points. This study used manual annotations of valve landmarks in standard 2-, 3- and 4-chamber long-axis images collected in clinical scans to train the network. The accuracy in the identification of these ten features, in pixel distance, was compared with the accuracy of two commonly used feature tracking methods as well as the inter-observer variability of manual annotations. Clinical measures, such as valve landmark strain and motion between end-diastole and end-systole, are also presented to illustrate the utility and robustness of the method.

eess.IV↗

arXiv2020

A Class of Analytic Solutions for Verification and Convergence Analysis of Linear and Nonlinear Fluid-Structure Interaction Algorithms

Fluid-structure interaction (FSI) problems are pervasive in the computational engineering community. The need to address challenging FSI problems has led to the development of a broad range of numerical methods addressing a variety of application-specific demands. While a range of numerical and experimental benchmarks are present in the literature, few solutions are available that enable both verification and spatiotemporal convergence analysis. In this paper, we introduce a class of analytic solutions to FSI problems involving shear in channels and pipes. Comprised of 16 separate analytic solutions, our approach is permuted to enable progressive verification and analysis of FSI methods and implementations, in two and three dimensions, for static and transient scenarios as well as for linear and hyperelastic solid materials. Results are shown for a range of analytic models exhibiting progressively complex behavior. The utility of these solutions for analysis of convergence behavior is further demonstrated using a previously published monolithic FSI technique. The resulting class of analytic solutions addresses a core challenge in the development of novel FSI algorithms and implementations, providing a progressive testbed for verification and detailed convergence analysis.

math.NA↗

arXiv2019

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.

math.NA↗

arXiv2019

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.

cs.CE↗