International Journal for Numerical Methods in Biomedical Engineering
○ Wiley
Preprints posted in the last 90 days, ranked by how well they match International Journal for Numerical Methods in Biomedical Engineering's content profile, based on 12 papers previously published here. The average preprint has a 0.01% match score for this journal, so anything above that is already an above-average fit.
Duca, F.; Tavarone, S.; Domanin, M.; Bissacco, D.; Trimarchi, S.; Vergara, C.; Migliavacca, F.
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Thoracic Endovascular Aortic Repair (TEVAR) is a minimally invasive procedure for the treatment of thoracic aortic pathologies, such as Thoracic Aortic Aneurysm (TAA). Computational simulations can provide valuable insights into TEVAR outcomes and complications prior to surgery, making them a useful tool in the procedural planning. In this work, Fluid-Structure Interaction (FSI) computational simulations are carried out in ten pre-TEVAR patient-specific TAA cases, for which post-TEVAR outcomes are known, to quantify the hemodynamic drag forces acting on the aortic wall. Based on these results, this study proposes a new risk factor R to predict the occurrence of type I and III endoleaks. The patient cohort is divided in a calibration set, used to associate specific R values with three different risk levels, and a validation set, to test the risk factor efficacy. Based on the risk factor values obtained for the calibration set, R[≤] 0.33 is associated with low risk of endoleak formation, 0.33 < R[≤] 0.67 with moderate risk, and R > 0.67 with high risk. Once it is applied to the validation set,the risk factor is able to predict the formation of a type Ia endoleak. The risk factor proposed in this work is capable of identifying all the endoleak cases analysed, as well as conditions known to increase the risk of TEVAR complications. This study represents a preliminary attempt to determine whether pre-TEVAR hemodynamics can effectively predict post-TEVAR complications and thereby aid clinicians in the pre-operative planning.
Kim, T.; Malipeddi, A. R.; Capecelatro, J.; Figueroa, A.
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Thin structures such as heart valves and aortic dissection flaps interact dynamically with blood flow in human vessels. Their flexibility and capacity for large deformations generate complex, highly transient hemodynamic patterns over the cardiac cycle. Accurately resolving these interactions remains challenging for conventional boundary-fitted fluid-structure interaction approaches. We present an immersed boundary method for simulating thin structures in incompressible flow on unstructured grids. The method couples a stabilized finite element fluid solver with a nonlinear, rotation-free shell formulation through a direct forcing immersed boundary approach. The framework supports both weak (explicit) and strong (implicit) time-coupling strategies, enabling stable simulations over a wide range of solid-to-fluid density ratios. Hydrodynamic forces acting on thin structures are computed from fluid solutions sampled on both sides of the structure, allowing accurate force reconstruction for zero-thickness shells. To our knowledge, this is the first immersed boundary formulation that couples an unstructured finite element fluid solver with a two-dimensional, rotation-free shell model to simulate interactions between thin structures and incompressible flow. Fluid-structure coupling is achieved using predefined finite element shape functions, which provide consistent projection between Eulerian and Lagrangian fields without additional interpolation procedures. The framework is validated using three-dimensional benchmark problems involving thin structures. Then, valve-like model is used to compare strong and weak coupling strategies. Finally, the method is applied to an idealized type-B aortic dissection model. The proposed approach is implemented within the open-source software CRIMSON, a finite element platform for cardiovascular simulation.
Kargarbahrkhazar, B.; Razian, S. A.; Jadidi, M.
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IntroductionArteries, like other soft tissues, exhibit viscoelastic mechanical behavior, meaning their response to stress and strain is time dependent. This implies that the way arteries deform depends not only on the amount of force applied but also on the rate at which the force is applied. This study investigates the effects of different loading rates on the mechanical behavior of human femoropopliteal arteries (FPAs) to understand their rate-dependent characteristics. MethodsHuman FPA specimens were collected from 14 donors, including 7 males and 7 females, aged 45-55 years. A 10x10 mm segment was isolated, mounted onto a biaxial testing device, and subjected to varying loading rates (10 to 50 mN/s). Mechanical responses were recorded, and stress-stretch curves were analyzed. Statistical analyses, including mixed-design ANOVA, assessed the impact of sex and loading rates on tissue stiffness. ResultsResults indicated significant loading-rate dependency, particularly in the circumferential direction. Stretch values decreased with increasing loading rates, more prominently in the circumferential than in the longitudinal direction (p-value<0.01). Statistical analyses revealed no significant interaction between sex and loading rate, though male arteries exhibited slightly higher compliance than female arteries. DiscussionThe findings demonstrate that the mechanical response of FPAs is highly dependent on the loading rate, with more pronounced effects observed in the circumferential direction. At higher loading rates, the human FPAs demonstrated a stiffer response in the circumferential direction. DedicationWe dedicate this work to the memory of our late student, Ali Zolfaghari Sichani, who passed away tragically during his doctoral studies. Ali performed the majority of the experiments and the initial analysis reported in this paper. His passion, dedication, and hard work were the foundation of this research, and he is deeply missed.
Chen, Y.
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Clavicle fractures often exhibit markedly different clinical outcomes: some patients recover acceptable function despite shortening or displacement, whereas others with apparently similar deformity develop persistent pain, functional loss, or poor healing. To explain this distinction, we propose a minimal nonlinear mechanical model for prognostic analysis of clavicle fractures. The model describes the interaction between fracture-related shortening and compensatory shoulder-girdle posture through a reduced equilibrium equation incorporating stiffness, geometric nonlinearity, and shortening-posture coupling. Within this framework, we analyze equilibrium branches, local stability, and the emergence of critical thresholds. We show that post-fracture destabilization can be interpreted as a fold bifurcation, while more complex parameter dependence gives rise to cusp-type structures and multistability. These bifurcation mechanisms provide a mathematical explanation for sudden deterioration after injury or treatment, as well as for strong inter-individual variability. We further introduce an optimization principle based on a utility functional to guide treatment planning. The analysis predicts that the optimal safe correction should lie strictly below the bifurcation threshold, thereby generating a natural safety margin. Although the model is simplified and has not yet been calibrated against patient data, it nevertheless provides a theoretical framework for understanding why fracture prognosis may deteriorate abruptly near critical mechanical conditions and offers a dynamical-systems interpretation of empirical treatment thresholds used in clinical practice.
Pico-Cabiro, S.; Zingaro, A.; Puche-Garcia, V.; Lialios, D.; Vazquez, M.; Echebarria-Dominguez, B.; Izquierdo, M.; Carreras-Costa, F.; Saiz, J.; Casoni, E.
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Atrial electromechanics plays a key role in cardiac function by regulating ventricular filling and global hemodynamics, yet remains challenging to model consistently across scales. In this work, a multiscale atrial digital twin for simulations of normal and pathological atrial function is presented, formulated as an electromechanical framework for biatrial simulations that couples three-dimensional atrial electrophysiology and mechanics with a closed-loop zero-dimensional circulatory model. The framework is calibrated on a patient-specific biatrial anatomy to reproduce physiological regional activation times, atrial volumes, ejection fractions, and pressure-volume loop characteristics. The simulations capture all atrial functional phases throughout the cardiac cycle, including realistic figure-eight pressure-volume loops, an aspect hard to achieve in computational studies. A systematic sensitivity analysis quantifies the influence of active contraction, passive stiffness, boundary conditions, and circulatory parameters on atrial function. Finally, application to a pathological scenario through induced persistent atrial fibrillation demonstrates how electrophysiological remodelling propagates across scales, leading to loss of effective atrial contraction, altered atrioventricular flow patterns, and a clinically relevant reduction in cardiac output. Overall, this multiphysics and multiscale framework provides a robust platform to investigate how atrial electrical alterations drive mechanical and hemodynamic alterations in both healthy and pathological conditions.
Daehlin, T. E.; Ross, S. A.; De Groote, F.; Wakeling, J. M.
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AO_SCPLOWBSTRACTC_SCPLOWMuscle fibre type distribution influences both the metabolic and contractile properties of individual muscles. However, as humans tend to self-optimize their gait pattern to minimize cost of transport, these changes in muscle properties may influence gait biomechanics in manners that are difficult to isolate in in vivo experiments. The purpose of this study was to predict the influence of muscle fibre type distribution on the metabolic cost and biomechanics of simulated walking and running. We implemented a muscle model that could predict recruitment of slow and fast twitch muscle fibres in a framework for predictive musculoskeletal simulation. Subsequently, we employed the framework to investigate how metabolic cost of transport, stride length, stride frequency, and mechanical work performed by slow and fast twich muscle fibres were influenced by fibre type distribution across locomotion speeds from 1.0 to 4.5 m {middle dot} s-1. Our results predict that cost of transport increases as slow twitch area fraction decreases, while stride length and frequency was minimally affected by fibre type distribution at speeds resulting in walking. In contrast, fibre type distribution interacts with locomotion speed at speeds resulting in running. Specifically, we predict the existence of a threshold speed below which cost of transport decreases with an increasing proportion of slow twitch fibres, while cost of transport increases with increasing proportions of slow twitch fibres above it. The shift in fibre type distribution was accompanied by an increase in stride frequency and decrease in stride length. These shifts in spatiotemporal characteristics appear to allow the muscles to operate at speeds close to those that achieve peak mechanical efficiency. Taken together, the results of this study predict that muscle fibre type distribution may influence both the energetics and biomechanics of gait, and that this influence is dependent upon the locomotion speed.
Ingalkar, P.; Kakaletsis, S.; Rausch, M.; Kuhl, E.; Martonova, D.
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The mechanical behavior of right ventricular (RV) myocardium is governed by its anisotropic microstructure, yet constitutive models that account for fiber dispersion and enable reliable parameter identification remain limited. In this study, we propose a physics-embedded constitutive neural network framework for automated discovery of strain energy functions and microstructural parameters from experimental data. The model is formulated within an incompressible, orthotropic hyperelastic setting using invariant-based representations. Fiber, sheet, and normal directions are incorporated through a rotated structural basis, and dispersion effects are modeled using a generalized structure tensor approach. The framework is trained on multi-axial mechanical data from ovine RV myocardium, including uniaxial tension-compression and simple shear tests. We investigate two training scenarios: (i) full datasets containing both tensile and compressive regimes and (ii) datasets restricted to tensile loading. In both cases, the model accurately reproduces the measured stress-strain responses and identifies sparse, interpretable constitutive models which involve isotropic, anisotropic, and coupling invariants. However, the identifiability of microstructural parameters strongly depends on the available loading conditions. While tensile-only data yield higher predictive accuracy, they result in non-unique or biased estimates of fiber dispersion. In contrast, inclusion of compressive data enables consistent identification of dispersion parameters by separating fiber and matrix contributions. These results highlight the importance of multi-axial loading data for robust parameter identification and demonstrate the capability of constitutive neural network-based approaches for data-driven modeling of anisotropic soft tissues.
Kim, T.; Baker, T.; Burris, N.; Figueroa, A.
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Aortic stiffness is both heterogenous and anisotropic. Current non-invasive methods to estimate aortic stiffness are limited to characterizing the aortic tissue as isotropic due to the lack the techniques required to extract multi-axial strain from 3D dynamic images. Vascular deformation mapping (VDM) is a nonrigid image registration technique which has thus far been applied to map aortic growth using longitudinal imaging. In this study, we propose to use VDM to assess 3D aortic deformation by mapping diastolic and systolic images. During image registration process, penalty parameters are employed to fine-tune image alignment and penalize non-physiological deformations. These penalty parameters must be calibrated to ensure that VDM successfully reproduces multi-axial aortic motion patterns in health and disease. In this paper, we developed a calibration pipeline for these parameters using synthetic data. A rotation-free shell model was used to generate physics-based synthetic data on aortic motion incorporating patient-specific geometries, root motion, and blood pressure from a cohort of 14 subjects (healthy, Marfans syndrome and thoracic aortic aneurysm). An error metric was defined to quantify the quality of the VDM results. Furthermore, a k-means clustering technique was used to categorize the subjects into three clusters based on ascending aortic motion. Optimal penalty parameters were identified for each of the three clusters. The results indicated that patient clusters with smaller aortic root motion required larger rigidity penalty values. The calibrated parameters successively reduced errors in 3D displacement and multi-axial stretch compared to un-optimized VDM predictions, enhancing the accuracy of capturing aortic deformation from dynamic images. Among the different aortic regions, the ascending thoracic aorta exhibits the largest error reduction.
Haese, C. E.; LaRue, T. G.; Guajardo, D.; Harkness, C.; Hiesinger, W.; Fuhg, J. N.; Timek, T. A.; Rausch, M. K.
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BackgroundTricuspid transcatheter edge-to-edge repair (TEER) can induce an acute annuloplasty effect. While this has a therapeutic benefit, the mechanisms driving the reduction in annular size remain unclear. ObjectivesWe quantify the annular force induced by TEER in vitro in whole porcine heart preparations. We explore the impact of clipping different leaflet pairs on the TEER-induced annular forces. MethodsWe performed 49 interventions in 13 porcine hearts using a MitraClip XT. The clip was implanted between either the anterior-septal (AS), anterior-posterior (AP), or posterior-septal (SP) leaflet pairs. We also considered two-clip interventions between the combination of the AS-AP, AS-PS, or AP-PS leaflet pairs. For each intervention, we measured the right ventricular pressure, transvalvular flow rate, and force at eight locations around the annulus. ResultsTEER induced significant inward-pulling forces on the annulus. The maximum force was induced following an AS-PS two-clip intervention. A single AS clip induced the largest force among the one-clip interventions. Furthermore, the AP and AS-AP interventions induced the smallest annular forces. ConclusionsThe magnitude of the TEER-induced force depends on the intervention and number of clips implanted.
Mackenzie, J. A.; Hill, N. A.
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Background and ObjectivesLung cancer is one of the most frequently diagnosed cancers worldwide. While non-surgical treatment options have increased in number and efficacy, lung resection for primary cancers is still a mainstay of treatment. Lung resection has been shown to impair right ventricular function, although the mechanism for the impairment remains unclear. Wave intensity is increasingly used as a metric for increased post-operative afterload. Here, we develop a computational framework to assess the impact of simulated lung resection on wave intensity to establish that post-operative changes in wave intensity are attributable to the change in pulmonary artery morphometry. MethodsWe analyse a 48 pulmonary arterial surfaces segmented from CT images in patients with no evidence of lung disease to obtain 1D representations of the pulmonary vasculature. For each pulmonary vasculature we sequentially remove vessel branches to mimic post-operative morphometric changes to the arterial network. Using an established 1D computational flow model, we simulate pulsate blood flow in 44 pre-operative cases and 1596 post-operative cases. We compute wave intensity in the main, right, and left pulmonary arteries for all simulations. ResultsWe compare the change in computed wave intensities pre-versus post-operatively to the results of an experimental clinical study comparing pre- and post-operative wave intensity in a 27 patient cohort. We see good agreement between the changes in the parameters of wave intensity between this study and those reported in the clinical study. Further, we capture flow distribution the changes pre-versus post-operatively which indicates that the computational model behaves as expected. ConclusionsIn this preliminary study on a computational framework to capture changes in pulmonary arterial haemodynamics following lung resection, we have shown that our model and analysis pipeline is capable of capturing post-operative changes to wave intensity and flow redistribution between the pulmonary arteries following lung resection. These results motivate further research to develop and validate a patient specific model which is an area of active research for us.
Dvoriashyna, M.; Zwanenburg, J. J. M.; Goriely, A.
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Cerebrospinal fluid (CSF) is a Newtonian fluid that bathes the brain and spinal cord and oscillates in response to the physiological periodic changes in brain volume, of which the cardiac cycle is a major driver. Understanding this motion is essential for clarifying its contribution to solute transport, waste clearance, and drug delivery. In this work, we study oscillatory and steady streaming flow in the cranial subarachnoid space using a lubrication-based theoretical framework. The model represents the cranial CSF compartment as a thin fluid layer bounded internally by the brain surface and externally by the dura, driven by time-dependent brain surface displacements. We first derive simplified governing equations for flow over an arbitrary smooth sphere-like brain surface and obtain analytical solutions for an idealised spherical geometry with uniform displacements. We then incorporate realistic displacement fields reconstructed from MRI measurements in healthy subjects and solve the reduced equations numerically. The results show that oscillatory forcing produces a steady streaming component that may enhance solute transport compared with diffusion alone. This work provides a mechanistic description of the flow generated by physiological brain motion and highlights the potential presence of steady streaming in cranial subarachnoid fluid dynamics.
Bonart, H.; Srinivasula, P.; Nuber, U. A.; Hardt, S.
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The development of large-scale, three-dimensional human tissues is crucial for various applications in therapeutic tissue engineering, disease modeling, and drug testing. However, due to the diffusion limit of oxygen, the lack of functional vascular networks is a significant limitation in maintaining these engineered tissues in the laboratory. To address this challenge, we present a systematic, model-based design process for artificial supply networks that can ensure a sufficient supply of oxygen and nutrients to engineered human tissue. Our approach combines mathematical models of fluid dynamics, cell metabolism, and network properties to identify key parameters influencing the supply performance. We demonstrate the applicability and possibilities of this design process by simulating different network structures, including cuboid and rhombic do-decahedral honeycombs, under various conditions. Our results show that the structure of the artificial supply network, oxygen concentration, and solute flow within the network strongly influence cellular metabolic activity and viability. We also examine the effects of non-uniform cell density, channel blockage, and long channel length on the oxygen distribution inside the cell-containing tissue compartment. Our findings highlight the importance of considering these factors in the design of artificial supply networks for large-scale engineered human tissues. This study provides a promising approach for quickly exploring the vast design space of possible network structures under different conditions for desired cell and tissue states, ultimately contributing to the development of more efficient and effective tissue engineering strategies.
Jaeger, K. H.; Tveito, A.
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The Poisson-Nernst-Planck (PNP) system is an accurate model of electrodiffusion of ionic species. It is commonly used in situations where nanoscale resolution is required, for instance close to ion channels in the membranes of biological cells. The inherent stiffness of the equations has made them challenging to solve and has limited the applicability of the system. In particular, the time step required for stable solutions has typically needed to be very short (nanoseconds), which makes simulations on the time scale of an action potential (milliseconds) difficult. Recently, it has been observed that avoiding operator splitting and instead solving the concentration equations and the electrostatic equation in a coupled manner relaxes the time-step limitation considerably. However, no theoretical explanation of this observation has been provided. Here, we aim to explain why the coupled scheme allows much larger time steps. We illustrate the mechanism by considering special cases that define necessary, but not sufficient, conditions for stability. We also show that these conditions remain relevant for the fully coupled PNP model in 3D.
Kuznetsov, A. V.
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Alzheimers disease (AD) is characterized by the accumulation of amyloid-{beta} (A{beta}), yet the specific link between plaque burden and cognitive decline remains a subject of intense investigation. This paper presents a mathematical model that simulates the coupled dynamics of A{beta} monomers, soluble oligomers, and fibrillar species in the brain tissue. By modifying existing moment equations to include a dedicated conservation equation for A{beta} monomers, the model explores how various microscopic processes, such as primary nucleation, surface-catalyzed secondary nucleation, fibril elongation, and fragmentation, contribute to macroscopic disease progression. Central to this study is the concept of "accumulated neurotoxicity" as a surrogate marker of biological age, defined as the time-integrated concentration of soluble A{beta} oligomers. Unlike plaque burden, accumulated neurotoxicity cannot be reversed, and the harm it causes depends critically on the sequence of events that produced it. Numerical results demonstrate that while plaque burden and neurotoxicity both increase over time, their relationship is non-linear and highly sensitive to the efficiency of protein degradation machinery. Specifically, impaired degradation leads to a rapid advancement of biological age relative to calendar age. The model further identifies oligomer dissociation and fibril fragmentation as potential protective mechanisms that can counterintuitively reduce neurotoxic burden by diverting monomers away from the soluble oligomer pool. These findings provide a quantitative framework for understanding why individuals with similar plaque burdens may experience vastly different cognitive outcomes, underscoring the importance of targeting soluble oligomers early in therapeutic interventions.
Li, C.; Zhou, Z.
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Finite element (FE) head models are valuable tools for investigating brain injury mechanics, with their reliability critically dependent on accurate material modelling. White matter (WM) is often considered mechanically anisotropic due to its aligned axonal fiber architecture and is commonly represented using fiber-reinforced hyperelastic formulations such as the Gasser-Ogden-Holzapfel (GOH) model. A fundamental assumption of the GOH model is that fibers contribute only in tension and not in compression, requiring the use of tension-compression switches. However, inconsistencies were noted in the formulation of tension-compression switches with the influence on computational biomechanics unknown. To address this knowledge gap, three commonly used switching schemes - differing in both the switching parameter and the treatment of compressed fibers - were theoretically elaborated and numerical implementation within the GOH framework to simulate the mechanical anisotropy of WM in impact simulations. Results from the case-based and group-level analyses demonstrated that both the switching parameter and the treatment of compressed fibers affected WM deformation. Significant cross-scheme strain differences were noted in the first principal strain at the element level and fiber strain at the fiber level. These findings highlighted the mechanical role of tension-compression switch in the GOH-based brain modelling and advocated the adoption of fiber stretch itself as the switching parameter to discriminate the tensile and compressive fibers. The current study provides important guidance for the anisotropic constitutive models in brain tissue and calls for direct verification of the tension-compression switch hypothesis in axonal fibers.
Neumann, O. F.; Kravikass, M.; John, N.; Ramachandran, R. G.; Steinmann, P.; Zaburdaev, V.; Wehner, D.; Budday, S.
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Functional spinal cord repair in zebrafish is governed by regeneration-favorable biochemical and mechanical cues within the lesion microenvironment. Alterations in extracellular matrix composition and stiffness are closely associated with axon regeneration. However, experimentally dissecting the interplay between mechanical signals and axonal regrowth in vivo remains technically challenging. Here, we present an agent-based modeling framework to simulate stiffness-mediated axonal growth trajectories across the lesion. We use this model to explore potential mechanisms underlying the characteristic growth patterns observed during zebrafish spinal cord regeneration. Computational predictions were qualitatively compared with confocal imaging data obtained from larval zebrafish. These phenomenological comparisons revealed a close agreement between simulated and experimentally observed axon growth, indicating that experimentally observed patterns could be governed by transient changes in the stiffness profile of the spinal cord and lesion microenvironment. Hence, our computational framework provides an in silico platform for investigating the role of mechanical cues in axon regeneration in the injured spinal cord.
Giovanis, D. G.; Zhang, K.; Tso, J.; Maggioni, M.; Kevrekidis, I. G.; Trayanova, N.
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Uncertainty quantification (UQ) in computational heart models is essential for reliable cardiac digital twins (DTs) in personalized medicine, yet remains challenging. Traditional Monte Carlo and stochastic Galerkin methods often become impractical in the high-dimensional, nonlinear state variable and parameter spaces of cardiac electrophysiology and mechanics. This article introduces a framework for learning a joint probability density over cardiac observables and model parameters, enabling the characterization of statistical dependencies across a large number of variables in patient-specific cardiac DTs. By sampling from this density and conditioning on available data, useful predictive distributions can be constructed, allowing uncertainty to be propagated through the model and quantified in terms of variability. Conditional regression can then be performed directly on this learned density, enabling systematic exploration of interdependencies among observables for both predictive inference and model design. The statistical methodology adopts a geometry-aware generative learning framework, recently introduced by the authors, that decouples the learning of data geometry from sampling. First it identifies a low-dimensional latent representation that captures the intrinsic structure of the data and its multiscale geometric features. A stochastic differential equation is then formulated directly in the low-dimensional latent space to generate samples efficiently; these are subsequently mapped back to the high-dimensional space of cardiac states and parameters through a smooth lifting operator. We demonstrate the approach on a ventricular arrhythmia prediction benchmark, where the learned joint probability density enables the construction of predictive distributions over key parameters (e.g., conductivities, fibrosis patterns) through sampling and conditioning. This enables uncertainty to be propagated and quantified through sampling and conditioning on the learned joint density, with substantially fewer model evaluations than conventional UQ methods.
Kuba, S.; Simpson, M. J.; Buenzli, P. R.
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Biological tissues grow at rates that depend on the geometry of the supporting tissue substrate. In this study, we present a novel discrete mathematical model for simulating biological tissue growth in a range of geometries. The discrete model is deterministic and tracks the evolution of the tissue interface by representing it as a chain of individual cells that interact mechanically and simultaneously generate new tissue material. To describe the collective behaviour of cells, we derive a continuum limit description of the discrete model leading to a reaction-diffusion partial differential equation governing the evolution of cell density along the evolving interface. In the continuum limit, the mechanical properties of discrete cells are directly linked to their collective diffusivity, and spatial constraints introduce curvature dependence that is not explicitly incorporated in the discrete model. Numerical simulations of both the discrete and continuum models reproduce the smoothing behaviour observed experimentally with minimal discrepancies between the models. The discrete model offers further individual-level details, including cell trajectory data, for any restoring force law and initial geometry. Where applicable, we discuss how the discrete model and its continuum description can be used to interpret existing experimental observations.
Sukekawa, T.; Ei, S.-I.
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Mass-conserved reaction-diffusion systems are used as mathematical models for various phenomena such as cell polarity. Numerical simulations of this system present transient dynamics in which multiple stripe patterns converge to spatially monotonic patterns. Previous studies indicated that the transient dynamics are driven by a mass conservation law and by variations in the amount of substance contained in each pattern, which we refer to as "pattern flux". However, it is challenging to mathematically investigate these pattern dynamics. In this study, we introduce a reaction-diffusion compartment model to investigate the pattern dynamics in view of the conservation law and the pattern flux. This model is defined on multiple intervals (compartments), and diffusive couplings are imposed on each boundary of the compartments. Corresponding to the transient dynamics in the original system, we consider the dynamics around stripe patterns in the compartment model. We derive ordinary differential equations describing the pattern dynamics of the compartment model and analyze the existence and stability of equilibria for the reduced ODE with respect to the boundary parameters. For a specific parameter setting, we obtained results consistent with previous studies. Moreover, we present that the stripe patterns in the compartment model are potentially stabilized by changing the parameter, which is not observed in the original system. We expect that the methodology developed in this paper is extendable to various directions, such as membrane-induced pattern control.
Hopenfeld, B.
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A multiple channel QRS detector is described. The detector partitions raw signal segments into peak domains, extracts parameters associated with the peak domains, and scores peaks based on these parameters. A multi-layer perceptron (MLP) with 11 inputs generates provisional peak scores, which are refined through application of rules involving 20-30 parameters. An optimal sequence of supra threshold peaks is determined. Separately, combinatorial optimization determines an optimal structured heart rhythm sequence. Adjudication between the general supra threshold sequence and the structured sequence depends on noise level, peak quality, and rhythm structure quality. For multiple channel fusion, peak scores are determined as a noise weighted function of channel peak scores. The MLP was trained on approximately 70% of channel 1 of the MIT-BIH Arrhythmia Database. The supplementary rules were heuristically chosen over all channel 1 records. Sensitivity (SE) and positive predictive value (PPV) of the detector applied to channel 2 were a function of the noise threshold used to discard segments. At a noise level that would exclude 2.2% of channel 1 data, the SE and PPV were 99.67% and 99.75% respectively. Importantly, even in high noise, the detector was able to track large scale features of heart rhythm. Fused channel 1 and channel 2 SE and PPV were 99.96% and 99.98% respectively. The present algorithm points the way toward maximal extraction of heart rhythm information from noisy signals, and the potential to reduce false alarms generated by automated rhythm analysis software.