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Vertebroplasty is a minimally invasive surgical procedure used to treat vertebral fractures, which conventionally involves injecting polymethylmethacrylate (PMMA) bone cement into the fractured vertebra. A common risk associated with vertebroplasty is cement leaking out of the vertebra during the injection, which may occur due to a lack of understanding of the bone cement's complex flow behavior. Therefore, experiments to quantify the cement's flow properties are necessary for understanding and proper handling of the bone cement. In this study, we aimed to characterize the behavior of the PMMA bone cement in its curing stages to obtain parameters that govern the flow behavior during the injection. We used rotational and oscillatory rheometry for our measurements, as well as a custom-made injector setup that replicated a typical vertebroplasty setting. Our results showed that the complex viscoelastic behavior of the bone cement is significantly affected by deformations and temperature. We found that the results from rotational tests, often used for characterizing the bone cement, are susceptible to measurement artifacts caused by wall slip and "ridge"-like formations in the test sample. We also found the Cox-Merz rule to be conditionally valid, which affects the use of oscillatory tests to obtain shear-thinning characteristics for the bone cement. Our findings identify important differences in the measured flow behavior of PMMA bone cement when assessed by different rheological methods, understanding which is crucial for its risk-free usage in downstream medical applications., Comment: 39 pages, 7 figures

This paper presents a novel neural network architecture for the purpose of pervasive visualisation of a 3D human upper limb musculoskeletal system model. Bringing simulation capabilities to resource-poor systems like mobile devices is of growing interest across many research fields, to widen applicability of methods and results. Until recently, this goal was thought to be out of reach for realistic continuum-mechanical simulations of musculoskeletal systems, due to prohibitive computational cost. Within this work we use a sparse grid surrogate to capture the surface deformation of the m.~biceps brachii in order to train a deep learning model, used for real-time visualisation of the same muscle. Both these surrogate models take 5 muscle activation levels as input and output Cartesian coordinate vectors for each mesh node on the muscle's surface. Thus, the neural network architecture features a significantly lower input than output dimension. 5 muscle activation levels were sufficient to achieve an average error of 0.97 +/- 0.16 mm, or 0.57 +/- 0.10 % for the 2809 mesh node positions of the biceps. The model achieved evaluation times of 9.88 ms per predicted deformation state on CPU only and 3.48 ms with GPU-support, leading to theoretical frame rates of 101 fps and 287 fps respectively. Deep learning surrogates thus provide a way to make continuum-mechanical simulations accessible for visual real-time applications., Comment: 10 pages, 4 figures, 5 tables, to be submitted to Medical Image Analysis

In recent decades, the main focus of computer modeling has been on supporting the design and development of engineering prototyes, but it is now ubiquitous in non-traditional areas such as medical rehabilitation. Conventional modeling approaches like the finite element~(FE) method are computationally costly when dealing with complex models, making them of limited use for purposes like real-time simulation or deployment on low-end hardware, if the model at hand cannot be simplified in a useful manner. Consequently, non-traditional approaches such as surrogate modeling using data-driven model order reduction are used to make complex high-fidelity models more widely available anyway. They often involve a dimensionality reduction step, in which the high-dimensional system state is transformed onto a low-dimensional subspace or manifold, and a regression approach to capture the reduced system behavior. While most publications focus on one dimensionality reduction, such as principal component analysis~(PCA) (linear) or autoencoder (nonlinear), we consider and compare PCA, kernel PCA, autoencoders, as well as variational autoencoders for the approximation of a structural dynamical system. In detail, we demonstrate the benefits of the surrogate modeling approach on a complex FE model of a human upper-arm. We consider both the models deformation and the internal stress as the two main quantities of interest in a FE context. By doing so we are able to create a computationally low cost surrogate model which captures the system behavior with high approximation quality and fast evaluations., Comment: 29 pages, 12 figures. Submitted to Archive of Applied Mechanics

Objective: Studying motor units (MUs) is essential for understanding motor control, the detection of neuromuscular disorders and the control of human-machine interfaces. Individual motor unit firings are currently identified in vivo by decomposing electromyographic (EMG) signals. Due to our body's properties and anatomy, individual motor units can only be separated to a limited extent with surface EMG. Unlike electrical signals, magnetic fields do not interact with human tissues. This physical property and the emerging technology of quantum sensors make magnetomyography (MMG) a highly promising methodology. However, the full potential of MMG to study neuromuscular physiology has not yet been explored. Approach: In this work, we perform in silico trials that combine a biophysical model of EMG and MMG with state-of-the-art algorithms for the decomposition of motor units. This allows the prediction of an upper-bound for the motor unit decomposition accuracy. Main results: It is shown that non-invasive high-density MMG data is superior over comparable high-density surface EMG data for the robust identification of the discharge patterns of individual motor units. Decomposing MMG instead of EMG increased the number of identifiable motor units by 76%. Notably, MMG exhibits a less pronounced bias to detect superficial motor units. Significance: The presented simulations provide insights into methods to study the neuromuscular system non-invasively and in vivo that would not be easily feasible by other means. Hence, this study provides guidance for the development of novel biomedical technologies.

The outcome of vertebroplasty is hard to predict due to its dependence on complex factors like bone cement and marrow rheologies. Cement leakage could occur if the procedure is done incorrectly, potentially causing adverse complications. A reliable simulation could predict the patient-specific outcome preoperatively and avoid the risk of cement leakage. Therefore, the aim of this work was to introduce a computationally feasible and experimentally validated model for simulating vertebroplasty. The developed model is a multiphase continuum-mechanical macro-scale model based on the Theory of Porous Media. The related governing equations were discretized using a combined Finite Element - Finite Volume approach by the so-called Box discretization. Three different rheological upscaling methods were used to compare and determine the most suitable approach for this application. For validation, a benchmark experiment was set up and simulated using the model. The influence of bone marrow and parameters like permeability, porosity, etc., was investigated to study the effect of varying conditions on vertebroplasty. The presented model could realistically simulate the injection of bone cement in porous materials when used with the correct rheological upscaling models, of which the semi-analytical averaging of the viscosity gave the best results. The marrow viscosity is identified as the crucial reference to categorize bone cements as high- or low- viscosity in the context of vertebroplasty. It is confirmed that a cement with higher viscosity than the marrow ensures stable development of the injection and a proper cement interdigitation inside the vertebra., Comment: Published in the journal 'Biomechanics and Modeling in Mechanobiology' on 12th May, 2023. Link: https://link.springer.com/article/10.1007/s10237-023-01715-4

While electromyography (EMG) and magnetomyography (MMG) are both methods to measure the electrical activity of skeletal muscles, no systematic comparison between both signals exists. Within this work, we propose a systemic in silico model for EMG and MMG and test the hypothesis that MMG surpasses EMG in terms of spatial selectivity. The results show that MMG provides a slightly better spatial selectivity than EMG when recorded directly on the muscle surface. However, there is a remarkable difference in spatial selectivity for non-invasive surface measurements. The spatial selectivity of the MMG components aligned with the muscle fibres and normal to the body surface outperforms the spatial selectivity of surface EMG. Particularly, for the MMG's normal-to-the-surface component the influence of subcutaneous fat is minimal. Further, for the first time, we analyse the contribution of different structural components, i.e., muscle fibres from different motor units and the extracellular space, to the measurable biomagnetic field. Notably, the simulations show that the normal-to-the-surface MMG component, the contribution from volume currents in the extracellular space and in surrounding inactive tissues is negligible. Further, our model predicts a surprisingly high contribution of the passive muscle fibres to the observable magnetic field., Comment: Preprint, Submitted to Biomechanics and Modeling in Mechanobiology

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., Comment: 29 pages; 7 pages Supplementary Materials

We present efficient reduced basis (RB) methods for the simulation of the coupled problem consisting of a rigid robot hand interacting with soft tissue material which is modeled by the linear elasticity equation and discretized with the Finite Element Method. We look at two different scenarios: (i) the forward simulation and (ii) a feedback control formulation of the model. In both cases, large-scale systems of equations appear, which need to be solved in real-time. This is essential in practice for the implementation in a real robot. For the feedback-scenario, in the context of the linear quadratic regulator, we encounter a high-dimensional Algebraic Riccati Equation (ARE). To overcome the real-time constraint by significantly reducing the computational complexity, we use several structure-preserving and non-structure-preserving reduction methods. These include proper orthogonal decomposition-based reduced basis techniques. For the ARE, instead of solving a full dimensional problem we compute a low-rank-factor and hence a low-dimensional ARE is solved. Numerical examples for both cases are provided. These illustrate the approximation quality of the reduced solution and speedup factors of the different reduction approaches.

Nitrogen vacancy (NV) centers in diamond have developed into a powerful solid-state platform for compact quantum sensors. However, high sensitivity measurements usually come with additional constraints on the pumping intensity of the laser and the pulse control applied. Here, we demonstrate high sensitivity NV ensemble based magnetic field measurements with low-intensity optical excitation. DC magnetometry methods like, e.g., continuous-wave optically detected magnetic resonance and continuously excited Ramsey measurements combined with lock-in detection, are compared to get an optimization. Gradiometry is also investigated as a step towards unshielded measurements of unknown gradients. The magnetometer demonstrates a minimum detectable field of 0.3-0.7 pT in a 73 s measurement by further applying a flux guide with a sensing dimension of 2 mm, corresponding to a magnetic field sensitivity of 2.6-6 pT/Hz^0.5. Combined with our previous efforts on the diamond AC magnetometry, the diamond magnetometer is promising to perform wide bandwidth magnetometry with picotesla sensitivity and a cubic-millimeter sensing volume under ambient conditions., Comment: 20 pages, 12 figures

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., Comment: 30 pages; 6 pages Supplementary Materials

Throughout the process of aging, deterioration of bone macro- and micro-architecture, as well as material decomposition result in a loss of strength and therefore in an increased likelihood of fractures. To date, precise contributions of age-related changes in bone (re)modeling and (de)mineralization dynamics and its effect on the loss of functional integrity are not completely understood. Here, we present an image-based deep learning approach to quantitatively describe the dynamic effects of short-term aging and adaptive response to treatment in proximal mouse tibia and fibula. Our approach allowed us to perform an end-to-end age prediction based on $\mu$CT images to determine the dynamic biological process of tissue maturation during a two week period, therefore permitting a short-term bone aging prediction with $95\%$ accuracy. In a second application, our radiomics analysis reveals that two weeks of in vivo mechanical loading are associated with an underlying rejuvenating effect of 5 days. Additionally, by quantitatively analyzing the learning process, we could, for the first time, identify the localization of the age-relevant encoded information and demonstrate $89\%$ load-induced similarity of these locations in the loaded tibia with younger bones. These data suggest that our method enables identifying a general prognostic phenotype of a certain bone age as well as a temporal and localized loading-treatment effect on this apparent bone age. Future translational applications of this method may provide an improved decision-support method for osteoporosis treatment at low cost.

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 Materials

Realistic simulations of detailed, biophysics-based, multi-scale models require very high resolution and, thus, large-scale compute facilities. Existing simulation environments, especially for biomedical applications, are designed to allow for a high flexibility and generality in model development. Flexibility and model development, however, are often a limiting factor for large-scale simulations. Therefore, new models are typically tested and run on small-scale compute facilities. By using a detailed biophysics-based, chemo-electromechanical skeletal muscle model and the international open-source software library OpenCMISS as an example, we present an approach to upgrade an existing muscle simulation framework from a moderately parallel version towards a massively parallel one that scales both in terms of problem size and in terms of the number of parallel processes. For this purpose, we investigate different modeling, algorithmic and implementational aspects. We present improvements addressing both numerical and parallel scalability. In addition, our approach includes a novel visualization environment, which is based on the MegaMol environment capable of handling large amounts of simulated data. It offers a platform for fast visualization prototyping, distributed rendering, and advanced visualization techniques. We present results of a variety of scaling studies at the Tier-1 supercomputer HazelHen at the High Performance Computing Center Stuttgart (HLRS). We improve the overall runtime by a factor of up to 2.6 and achieved good scalability on up to 768 cores, where the previous implementation used only 4 cores.