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In recent years, our scientific interest in spaceflight has grown exponentially and resulted in a thriving area of research, with hundreds of astronauts spending months of their time in space. A recent shift toward pursuing territories farther afield, aiming at near-Earth asteroids, the Moon, and Mars combined with the anticipated availability of commercial flights to space in the near future, warrants continued understanding of the human physiological processes and response mechanisms when in this extreme environment. Acute skeletal loss, more severe than any bone loss seen on Earth, has significant implications for deep space exploration, and it remains elusive as to why there is such a magnitude of difference between bone loss on Earth and loss in microgravity. The removal of gravity eliminates a critical primary mechano-stimulus, and when combined with exposure to both galactic and solar cosmic radiation, healthy human tissue function can be negatively affected. An additional effect found in microgravity, and one with limited insight, involves changes in dynamic fluid flow. Fluids provide the most fundamental way to transport chemical and biochemical elements within our bodies and apply an essential mechano-stimulus to cells. Furthermore, the cell cytoplasm is not a simple liquid, and fluid transport phenomena together with viscoelastic deformation of the cytoskeleton play key roles in cell function. In microgravity, flow behavior changes drastically, and the impact on cells within the porous system of bone and the influence of an expanding level of adiposity are not well understood. This review explores the role of interstitial fluid motion and solute transport in porous bone under two different conditions: normogravity and microgravity.

A recurring motif in soft matter and biophysics is modeling the mechanics of interacting particles on fluid membranes. One of the main outstanding challenges in these applications is the need to model the strong coupling between the substrate deformation and the particles’ positions as the latter freely move on the former. This work presents a thin-shell finite element formulation based on subdivision surfaces to compute equilibrium configurations of a thin fluid shell with embedded particles. We use a variational Lagrangian framework to couple the mechanics of the particles and the substrate without having to resort to ad hoc constraints to anchor the particles to the surface. Unlike established methods for such systems, the particles are allowed to move between elements of the finite element mesh. This is achieved by parametrizing the particle locations on the reference configuration. Using the Helfrich–Canham energy as a model for fluid shells, we present the finite element method’s implementation and an efficient search algorithm required to locate particles on the reference mesh. Several analyses with varying numbers of particles are finally presented reproducing symmetries observed in the classic Thomson problem and showcasing the coupling between interacting particles and deformable membranes.

Cardiac diffusion tensor magnetic resonance imaging (cDTI) allows estimating the aggregate cardiomyocyte architecture in healthy subjects and its remodeling as a result of cardiac disease. In this study, cDTI was used to quantify microstructural changes occurring in swine (N = 7) six to ten weeks after myocardial infarction. Each heart was extracted and imaged ex vivo with \(1\,\mathrm {mm}\) isotropic spatial resolution. Microstructural changes were quantified in the border zone and infarct region by comparing diffusion tensor invariants – fractional anisotropy (FA), mode, and mean diffusivity (MD) – radial diffusivity, and diffusion tensor eigenvalues with the corresponding values in the remote myocardium. MD and radial diffusivity increased in the infarct and border regions with respect to the remote myocardium (\(p< 0.01\)). In contrast, FA and mode decreased in the infarct and border regions (\(p< 0.01\)). Diffusion tensor eigenvalues also increased in the infarct and border regions, with a larger increase in the secondary and tertiary eigenvalues.

Cardiac tagged MR images allow for deformation fields to be measured in the heart by tracking the motion of tag lines throughout the cardiac cycle. Machine learning (ML) algorithms enable accurate and robust tracking of tag lines. Herein, the use of a massive synthetic physics-driven training dataset with known ground truth was used to train an ML network to enable tracking any number of points at arbitrary positions rather than anchored to the tag lines themselves. The tag tracking and strain calculation methods were investigated in a computational deforming cardiac phantom with known (ground truth) strain values. This enabled both tag tracking and strain accuracy to be characterized for a range of image acquisition and tag tracking parameters. The methods were also tested on in vivo volunteer data. Median tracking error was< 0.26 mm in the computational phantom, and strain measurements were improved in vivo when using the arbitrary point tracking for a standard clinical protocol.

Purpose: Myofiber strain, Eff , is a mechanistically relevant metric of cardiac cell shortening and is expected to be spatially uniform in healthy populations, making it a prime candidate for the evaluation of local cardiomyocyte contractility. In this study, a new, efficient pipeline was proposed to combine microstructural cDTI and functional DENSE data in order to estimate Eff in vivo.Methods: Thirty healthy volunteers were scanned with three long-axis (LA) and three short-axis (SA) DENSE slices using 2D displacement encoding and one SA slice of cDTI. The total acquisition time was 11 minutes ± 3 minutes across volunteers. The pipeline first generates 3D SA displacements from all DENSE slices which are then combined with cDTI data to generate a cine of myofiber orientations and compute Eff . The precision of the post-processing pipeline was assessed using a computational phantom study. Transmural myofiber strain was compared to circumferential strain, Ecc , in healthy volunteers using a Wilcoxon sign rank test.Results: In vivo, computed Eff was found uniform transmurally compared to Ecc (-0.14[-0.15, -0.12] vs -0.18 [-0.20, -0.16], P < .001, -0.14 [-0.16, -0.12] vs -0.16 [-0.17, -0.13], P < .001 and -0.14 [-0.16, -0.12] vs Ecc_C = -0.14 [-0.15, -0.11], P = .002, Eff_C vs Ecc_C in the endo, mid, and epi layers, respectively).Conclusion: We demonstrate that it is possible to measure in vivo myofiber strain in a healthy human population in 10 minutes per subject. Myofiber strain was observed to be spatially uniform in healthy volunteers making it a potential biomarker for the evaluation of local cardiomyocyte contractility in assessing cardiovascular dysfunction.

Computing a physiologically accurate electrocardiogram (ECG) is one of the key outcomes of cardiac electrophysiology (EP) simulations. Indeed, the simulated ECG serves as a validation, may be the target for optimization in inverse EP problems, and in general allows to link simulation results to clinical ECG data. Several approaches are available to compute the ECG corresponding to an EP simulation. Lead field approaches are commonly used to compute ECGs from cardiac EP simulations using the Monodomain or Eikonal models. A coupled passive conductor model is instead common when the full Bidomain model is adopted. An approach based on solving an auxiliary Poisson problem propagating the activation field from the heart surface to the torso surface is also possible, although not commonly described in the literature. In this work, through a series of numerical experiments, we investigate the limits of validity of the different approaches to compute the ECG from simulations based on the Monodomain and Bidomain models. Significant discrepancies are observed between the common lead field and direct ECG approaches in most realistic cases – e.g., when conduction anisotropy is included – while the ECG computed via solution of an auxiliary Poisson problem is similar to the direct ECG approach. We conclude that either the direct ECG or Poisson approach should be adopted to improve the accuracy of the computed ECG.

A CNN based method for cardiac MRI tag tracking was developed and validated. A synthetic data simulator was created to generate large amounts of training data using natural images, a Bloch equation simulation, a broad range of tissue properties, and programmed ground-truth motion. The method was validated using both an analytical deforming cardiac phantom and in vivo data with manually tracked reference motion paths. In the analytical phantom, error was investigated relative to SNR, and accurate results were seen for SNR > 10 (displacement error 0.3 mm). Excellent agreement was seen in vivo for tag locations (mean displacement difference = − 0.02 pixels, 95% CI [ − 0.73, 0.69]) and calculated cardiac circumferential strain (mean difference = 0.006, 95% CI [ − 0.012, 0.024]). Automated tag tracking with a CNN trained on synthetic data is both accurate and precise.

Purpose Cardiomyocyte organization and performance underlie cardiac function, but the in vivo mobility of these cells during contraction and filling remains difficult to probe. Herein, a novel trigger delay (TD) scout sequence was used to acquire high in-plane resolution (1.6 mm) Spin-Echo (SE) cardiac diffusion tensor imaging (cDTI) at three distinct cardiac phases. The objective was to characterize cardiomyocyte organization and mobility throughout the cardiac cycle in healthy volunteers. Materials and methods Nine healthy volunteers were imaged with cDTI at three distinct cardiac phases (early systole, late systole, and diastasis). The sequence used a free-breathing Spin-Echo (SE) cDTI protocol (b-values = 350s/mm2, twelve diffusion encoding directions, eight repetitions) to acquire high-resolution images (1.6x1.6x8mm3) at 3T in ~7 minutes/cardiac phase. Helix Angle (HA), Helix Angle Range (HAR), E2 angle (E2A), Transverse Angle (TA), Mean Diffusivity (MD), diffusion tensor eigenvalues (λ1-2-3), and Fractional Anisotropy (FA) in the left ventricle (LV) were characterized. Results Images from the patient-specific TD scout sequence demonstrated that SE cDTI acquisition was possible at early systole, late systole, and diastasis in 78%, 100% and 67% of the cases, respectively. At the mid-ventricular level, mobility (reported as median [IQR]) was observed in HAR between early systole and late systole (76.9 [72.6, 80.5]° vs 96.6 [85.9, 100.3]°, p Conclusion We demonstrate that it is possible to probe cardiomyocyte mobility using multi-phase and high resolution cDTI. In healthy volunteers, aggregate cardiomyocytes re-orient themselves more longitudinally during contraction, while cardiomyocyte sheetlets tilt radially during wall thickening. These observations provide new insights into the three-dimensional mobility of myocardial microstructure during systolic contraction.

Computational modeling of the heart requires accurately incorporating both gross anatomical detail and local microstructural information. Together, these provide the necessary data to build 3D meshes for simulation of cardiac mechanics and electrophysiology. Recent MRI advances make it possible to measure detailed heart motion in vivo, but in vivo microstructural imaging of the heart remains challenging. Consequently, the most detailed measurements of microstructural organization and microanatomical infarct details are obtained ex vivo. The objective of this work was to develop and evaluate a new method for restoring ex vivo ventricular geometry to match the in vivo configuration. This approach aids the integration of high-resolution ex vivo microstructural information with in vivo motion measurements. The method uses in vivo cine imaging to generate surface meshes, then creates a 3D printed left ventricular (LV) blood pool cast and a pericardial mold to restore the ex vivo cardiac geometry to a mid-diastasis reference configuration. The method was evaluated in healthy (N = 7) and infarcted (N = 3) swine. Dice similarity coefficients were calculated between in vivo and ex vivo images for the LV cavity (0.93 ± 0.01), right ventricle (RV) cavity (0.80 ± 0.05), and the myocardium (0.72 ± 0.04). The R(2) coefficient between in vivo and ex vivo LV and RV cavity volumes were 0.95 and 0.91, respectively. These results suggest that this method adequately restores ex vivo geometry to match in vivo geometry. This approach permits a more precise incorporation of high-resolution ex vivo anatomical and microstructural data into computational models that use in vivo data for simulation of cardiac mechanics and electrophysiology.

Changes in left ventricular (LV) aggregate cardiomyocyte orientation and deformation underlie cardiac function and dysfunction. As such, in vivo aggregate cardiomyocyte “myofiber” strain ( ${E}_{\text {ff}}$ ) has mechanistic significance, but currently there exists no established technique to measure in vivo ${E}_{\text {ff}}$ . The objective of this work is to describe and validate a pipeline to compute in vivo ${E}_{\text {ff}}$ from magnetic resonance imaging (MRI) data. Our pipeline integrates LV motion from multi-slice Displacement ENcoding with Stimulated Echoes (DENSE) MRI with in vivo LV microstructure from cardiac Diffusion Tensor Imaging (cDTI) data. The proposed pipeline is validated using an analytical deforming heart-like phantom. The phantom is used to evaluate 3D cardiac strains computed from a widely available, open-source DENSE Image Analysis Tool. Phantom evaluation showed that a DENSE MRI signal-to-noise ratio (SNR) ≥20 is required to compute ${E}_{\text {ff}}$ with near-zero median strain bias and within a strain tolerance of 0.06. Circumferential and longitudinal strains are also accurately measured under the same SNR requirements, however, radial strain exhibits a median epicardial bias of −0.10 even in noise-free DENSE data. The validated framework is applied to experimental DENSE MRI and cDTI data acquired in eight ( ${N}={8}$ ) healthy swine. The experimental study demonstrated that ${E}_{\text {ff}}$ has decreased transmural variability compared to radial and circumferential strains. The spatial uniformity and mechanistic significance of in vivo ${E}_{\text {ff}}$ make it a compelling candidate for characterization and early detection of cardiac dysfunction.

In this work we extend the Caspar-Klug construction to the archaeal viruses, which in recent years have captured the attention of many researchers for their ability to thrive in extreme environments. We assume that the shells of archaeal viruses are composed of hexamers and pentamers-as is true for icosahedral viruses-together with heptamers, necessary to introduce negative Gauss curvature. Following the original work of Caspar and Klug, we first construct models capable of reproducing the shape observed in electron microscopy images of archaeal viruses. Next, using the technique of kirigami, we present a systematic way to formulate archaeal virus templates from regular hexagonal lattices. Finally, we utilize the presented techniques to build finite element models of archaeal virus geometries and investigate their shapes as a function of material properties. In particular, using thin-shell elasticity theory, we describe a buckling transition as a function of a modified Föppl-von Kármán number γ^{★} and we show how changes in γ^{★} may initiate the tail formation in the Acidianus two-tailed archaeal virus.

Since heart contraction results from the electrically activated contraction of millions of cardiomyocytes, a measure of cardiomyocyte shortening mechanistically underlies cardiac contraction. In this work we aim to measure preferential aggregate cardiomyocyte (“myofiber”) strains based on Magnetic Resonance Imaging (MRI) data acquired to measure both voxel-wise displacements through systole and myofiber orientation. In order to reduce the effect of experimental noise on the computed myofiber strains, we recast the strains calculation as the solution of a boundary value problem (BVP). This approach does not require a calibrated material model, and consequently is independent of specific myocardial material properties. The solution to this auxiliary BVP is the displacement field corresponding to assigned values of myofiber strains. The actual myofiber strains are then determined by minimizing the difference between computed and measured displacements. The approach is validated using an analytical phantom, for which the ground-truth solution is known. The method is applied to compute myofiber strains using in vivo displacement and myofiber MRI data acquired in a mid-ventricular left ventricle section in N=8 swine subjects. The proposed method shows a more physiological distribution of myofiber strains compared to standard approaches that directly differentiate the displacement field.

We propose a hybrid discrete-continuum model to study the ground state of protein shells. The model allows for shape transformation of the shell and buckling transitions as well as the competition between states with different symmetries that characterize discrete particle models with radial pair potentials. Our main results are as follows. For large Föppl-von Kármán (FvK) numbers the shells have stable isometric ground states. As the FvK number is reduced, shells undergo a buckling transition resembling that of thin-shell elasticity theory. When the width of the pair potential is reduced below a critical value, then buckling coincides with the onset of structural instability triggered by over-stretched pair potentials. Chiral shells are found to be more prone to structural instability than achiral shells. It is argued that the well-width appropriate for protein shells lies below the structural instability threshold. This means that the self-assembly of protein shells with a well-defined, stable structure is possible only if the bending energy of the shell is sufficiently low so that the FvK number of the assembled shell is above the buckling threshold.

Many problems in softmatter and membrane biophysics, such as finding the equilibrium configurations of protein clusters on cell-membranes, the highly defect ridden structure of Gag polyproteins in immature HIV capsids, and the unusual fluid-like state of Archaeal viruses can be understood as systems of interacting particles (typically representing proteins or protein capsomers) on deformable surfaces. The coupled interactions between the particles and the underlying elastic medium to which they are constrained pose significant computational challenges. Existing methods often employ expensive constraints to anchor particles to the surface or artificially restrict the particles movement yielding spurious equilibrium states. In this work, a new method is presented where the particles positions are parameterized in the reference configuration. This pull-back operation allows the particles to move freely on the surface without the need of additional constraints. Furthermore, the mapping necessary to describe the particles positions in a discretized setting, e.g., in a finite element mesh, can be done on the reference undeformed configuration at a reduced computational cost. The proposed method is applied to particles moving on manifolds in one and two dimensions to study its convergence characteristics and error when compared to derived analytical and semi-analytical solutions. Finally, the newly developed method is applied to generalized Tammes problems of packing interacting point particles on a deformable shell.

Computational models of cardiac contraction can provide critical insight into cardiac function and dysfunction. A necessary step before employing these computational models is their validation. Here we propose a series of validation criteria based on left ventricular (LV) global (ejection fraction and twist) and local (strains in a cylindrical coordinate system, aggregate cardiomyocyte shortening, and low myocardial compressibility) MRI measures to characterize LV motion and deformation during contraction. These validation criteria are used to evaluate an LV finite element model built from subject-specific anatomy and aggregate cardiomyocyte orientations reconstructed from diffusion tensor MRI. We emphasize the key role of the simulation boundary conditions in approaching the physiologically correct motion and strains during contraction. We conclude by comparing the global and local validation criteria measures obtained using two different boundary conditions: the first constraining the LV base and the second taking into account the presence of the pericardium, which leads to greatly improved motion and deformation.

Computational modeling of the heart requires accurately incorporating both gross anatomical detail and local microstructural information. Together, these provide the necessary data to build 3D meshes for simulation of cardiac mechanics and electrophysiology. Recent MRI advances make it possible to measure detailed heart motion in vivo, but in vivo microstructural imaging of the heart remains challenging. Consequently, the most detailed measurements of microstructural organization and microanatomical infarct details are obtained ex vivo. The objective of this work was to develop and evaluate a new method for restoring ex vivo ventricular geometry to match the in vivo configuration. This approach aids the integration of high-resolution ex vivo microstructural information with in vivo motion measurements. The method uses in vivo cine imaging to generate surface meshes, then creates a 3D printed left ventricular (LV) blood pool cast and a pericardial mold to restore the ex vivo cardiac geometry to a mid-diastasis reference configuration. The method was evaluated in healthy (N = 7) and infarcted (N = 3) swine. Dice similarity coefficients were calculated between in vivo and ex vivo images for the LV cavity (\(0.93\pm 0.01\)), right ventricle (RV) cavity (\(0.80\pm 0.05\)), and the myocardium (\(0.72\pm 0.04\)). The \(R^2\) coefficient between in vivo and ex vivo LV and RV cavity volumes were 0.95 and 0.91, respectively. These results suggest that this method adequately restores ex vivo geometry to match in vivo geometry. This approach permits a more precise incorporation of high-resolution ex vivo anatomical and microstructural data into computational models that use in vivo data for simulation of cardiac mechanics and electrophysiology.

Author(s): Li, Xinzhou; Perotti, Luigi E; Martinez, Jessica A; Duarte-Vogel, Sandra M; Ennis, Daniel B; Wu, Holden H | Abstract: PURPOSE:Real-time magnetic resonance imaging (MRI) is a promising alternative to X-ray fluoroscopy for guiding cardiovascular catheterization procedures. Major challenges, however, include the lack of guidewires that are compatible with the MRI environment, not susceptible to radiofrequency-induced heating, and reliably visualized. Preclinical evaluation of new guidewire designs has been conducted at 1.5T. Here we further evaluate the safety (device heating), device visualization, and procedural feasibility of 3T MRI-guided cardiovascular catheterization using a novel MRI-visible glass-fiber epoxy-based guidewire in phantoms and porcine models. METHODS:To evaluate device safety, guidewire tip heating (GTH) was measured in phantom experiments with different combinations of catheters and guidewires. In vivo cardiovascular catheterization procedures were performed in both healthy (N = 5) and infarcted (N = 5) porcine models under real-time 3T MRI guidance using a glass-fiber epoxy-based guidewire. The times for each procedural step were recorded separately. Guidewire visualization was assessed by measuring the dimensions of the guidewire-induced signal void and contrast-to-noise ratio (CNR) between the guidewire tip signal void and the blood signal in real-time gradient-echo MRI (specific absorption rate [SAR] = 0.04 W/kg). RESULTS:In the phantom experiments, GTH did not exceed 0.35°C when using the real-time gradient-echo sequence (SAR = 0.04 W/kg), demonstrating the safety of the glass-fiber epoxy-based guidewire at 3T. The catheter was successfully placed in the left ventricle (LV) under real-time MRI for all five healthy subjects and three out of five infarcted subjects. Signal void dimensions and CNR values showed consistent visualization of the glass-fiber epoxy-based guidewire in real-time MRI. The average time (minutes:seconds) for the catheterization procedure in all subjects was 4:32, although the procedure time varied depending on the subject's specific anatomy (standard deviation = 4:41). CONCLUSIONS:Real-time 3T MRI-guided cardiovascular catheterization using a new MRI-visible glass-fiber epoxy-based guidewire is feasible in terms of visualization and guidewire navigation, and safe in terms of radiofrequency-induced guidewire tip heating.

In vivo cardiac microstructure acquired using cardiac diffusion tensor imaging (cDTI) is a critical component of patient-specific models of cardiac electrophysiology and mechanics. In order to limit bulk motion artifacts and acquisition time, cDTI microstructural data is acquired at a single cardiac phase necessitating registration to the reference configuration on which the patient-specific computational models are based. Herein, we propose a method to register subject-specific microstructural data to an arbitrary cardiac phase using measured cardiac displacements. We validate our approach using a subject-specific computational phantom based on data from human subjects. Compared to a geometry-based non-rigid registration method, the displacement-based registration leads to improved accuracy (less than 1° versus 10° average median error in cardiomyocyte angular differences) and tighter confidence interval (3° versus 65° average upper limit of the 95% confidence interval).

In vivo cardiac microstructure acquired using cardiac diffusion tensor imaging (cDTI) is a critical component of patient-specific models of cardiac electrophysiology and mechanics. In order to limit bulk motion artifacts and acquisition time, cDTI microstructural data is acquired at a single cardiac phase necessitating registration to the reference configuration on which the patient-specific computational models are based. Herein, we propose a method to register subject-specific microstructural data to an arbitrary cardiac phase using measured cardiac displacements. We validate our approach using a subject-specific computational phantom based on data from human subjects. Compared to a geometry-based non-rigid registration method, the displacement-based registration leads to improved accuracy (less than 1° versus 10° average median error in cardiomyocyte angular differences) and tighter confidence interval (3° versus 65° average upper limit of the 95% confidence interval).

Metrics of regional myocardial function can detect the onset of cardiovascular disease, evaluate the response to therapy, and provide mechanistic insight into cardiac dysfunction. Knowledge of local myocardial microstructure is necessary to distinguish between isotropic and anisotropic contributions of local deformation and to quantify myofiber kinematics, a microstructurally anchored measure of cardiac function. Using a computational model we combine in vivo cardiac displacement and diffusion tensor data to evaluate pointwise the deformation gradient tensor and isotropic and anisotropic deformation invariants. In discussing the imaging methods and the model construction, we identify potential improvements to increase measurement accuracy. We conclude by demonstrating the applicability of our method to compute myofiber strain in five healthy volunteers.

We develop a mixed finite-element approximation scheme for Kirchhoff plate theory based on the reformulation of Kirchhoff plate theory of Ortiz and Morris [1]. In this reformulation the moment-equilibrium problem for the rotations is in direct analogy to the problem of incompressible two-dimensional elasticity. This analogy in turn opens the way for the application of diamond approximation schemes (Hauret et al. [2]) to Kirchhoff plate theory. We show that a special class of meshes derived from an arbitrary triangulation of the domain, the diamond meshes, results in the automatic satisfaction of the corresponding inf − sup condition for Kirchhoff plate theory. The attendant optimal convergence properties of the diamond approximation scheme are demonstrated by means of the several standard benchmark tests. We also provide a reinterpretation of the diamond approximation scheme for Kirchhoff plate theory within the framework of discrete mechanics. In this interpretation, the discrete moment-equilibrium problem is formally identical to the classical continuous problem, and the two differ only in the choice of differential structures. It also follows that the satisfaction of the inf − sup condition is a property of the cohomology of a certain discrete transverse differential complex. This close connection between the classical inf − sup condition and cohomology evinces the important role that the topology of the discretization plays in determining convergence in mixed problems.

Metrics of regional myocardial function can detect the onset of cardiovascular disease, evaluate the response to therapy, and provide mechanistic insight into cardiac dysfunction. Knowledge of local myocardial microstructure is necessary to distinguish between isotropic and anisotropic contributions of local deformation and to quantify myofiber kinematics, a microstructurally anchored measure of cardiac function. Using a computational model we combine in vivo cardiac displacement and diffusion tensor data to evaluate pointwise the deformation gradient tensor and isotropic and anisotropic deformation invariants. In discussing the imaging methods and the model construction, we identify potential improvements to increase measurement accuracy. We conclude by demonstrating the applicability of our method to compute myofiber strain in five healthy volunteers.

We propose a physical model for the capsids of tailed archaeal viruses as viscoelastic membranes under tension. The fluidity is generated by thermal motion of scarlike structures that are an intrinsic feature of the ground state of large particle arrays covering surfaces with nonzero Gauss curvature. The tension is generated by a combination of the osmotic pressure of the enclosed genome and an extension force generated by filamentous structure formation that drives the formation of the tails. In continuum theory, the capsid has the shape of a surface of constant mean curvature: an unduloid. Particle arrays covering unduloids are shown to exhibit pronounced subdiffusive and diffusive single-particle transport at temperatures that are well below the melting temperature of defect-free particle arrays on a surface with zero Gauss curvature.

Heart failure is a leading cause of death, yet its underlying electrophysiological (EP) mechanisms are not well understood. In this study, we use a multiscale approach to analyze a model of heart failure and connect its results to features of the electrocardiogram (ECG). The heart failure model is derived by modifying a previously validated electrophysiology model for a healthy rabbit heart. Specifically, in accordance with the heart failure literature, we modified the cell EP by changing both membrane currents and calcium handling. At the tissue level, we modeled the increased gap junction lateralization and lower conduction velocity due to downregulation of Connexin 43. At the biventricular level, we reduced the apex-to-base and transmural gradients of action potential duration (APD). The failing cell model was first validated by reproducing the longer action potential, slower and lower calcium transient, and earlier alternans characteristic of heart failure EP. Subsequently, we compared the electrical wave propagation in one dimensional cables of healthy and failing cells. The validated cell model was then used to simulate the EP of heart failure in an anatomically accurate biventricular rabbit model. As pacing cycle length decreases, both the normal and failing heart develop T-wave alternans, but only the failing heart shows QRS alternans (although moderate) at rapid pacing. Moreover, T-wave alternans is significantly more pronounced in the failing heart. At rapid pacing, APD maps show areas of conduction block in the failing heart. Finally, accelerated pacing initiated wave reentry and breakup in the failing heart. Further, the onset of VF was not observed with an upregulation of SERCA, a potential drug therapy, using the same protocol. The changes introduced at the cell and tissue level have increased the failing heart’s susceptibility to dynamic instabilities and arrhythmias under rapid pacing. However, the observed increase in arrhythmogenic potential is not due to a steepening of the restitution curve (not present in our model), but rather to a novel blocking mechanism., Author Summary Ventricular fibrillation (VF) is one of the leading causes of sudden death. During VF, the electrical wave of activation in the heart breaks up chaotically. Consequently, the heart is unable to contract synchronously and pump blood to the rest of the body. In our work we formulate and validate a model of heart failure (HF) that allows us to evaluate the arrhythmogenic potential of individual and combined electrophysiological changes. In diagnostic cardiology, the electrocardiogram (ECG) is one of the most commonly used tools for detecting abnormalities in the heart electrophysiology. One of our goals is to use our numerical model to link changes at the cellular and tissue level in a failing heart to a numerically computed ECG. This allows us to characterize the precursor to and the risk of VF. In order to understand the mechanisms underlying VF in HF, we design a test that simulates a HF patient performing physical exercise. We show that under fast heart rates with changes in pacing, HF patients are more prone to VF due to a new conduction blocking mechanism. In the long term, our mathematical model is suitable for investigating the effect of drug therapies in HF.

Quantitative measurement of the material properties (e.g., stiffness) of biological tissues is poised to become a powerful diagnostic tool. There are currently several methods in the literature to estimating material stiffness and we extend this work by formulating a framework that leads to uniquely identified material properties. We design an approach to work with full field displacement data — i.e., we assume the displacement field due to the applied forces is known both on the boundaries and also within the interior of the body of interest — and seek stiffness parameters that lead to balanced internal and external forces in a model. For in vivo applications, the displacement data can be acquired clinically using magnetic resonance imaging while the forces may be computed from pressure measurements, e.g., through catheterization. We outline a set of conditions under which the least-square force error objective function is convex, yielding uniquely identified material properties. An important component of our framework is a new numerical strategy to formulate polyconvex material energy laws that are linear in the material properties and provide one optimal description of the available experimental data. An outcome of our approach is the analysis of the reliability of the identified material properties, even for material laws that do not admit unique property identification. Lastly, we evaluate our approach using passive myocardium experimental data at the material point and show its application to identifying myocardial stiffness with an in silico experiment modeling the passive filling of the left ventricle.

Local Maximum-Entropy (LME) approximation schemes are meshfree approximation schemes that satisfy consistency conditions of order 1, i.e., they approximate affine functions exactly. In addition, LME approximation schemes converge in the Sobolev space \({W}^{1,p}\), i.e., they are C 0-continuous in the conventional terminology of finite-element interpolation. Here we present a generalization of the Local Max-Ent approximation schemes that are consistent to arbitrary order, i.e., interpolate polynomials of arbitrary degree exactly, and which converge in \({W}^{k,p}\), i.e., they are C k -continuous to arbitrary order k. We refer to these approximation schemes as High Order Local Maximum-Entropy Approximation Schemes (HOLMES). We prove uniform error bounds for the HOLMES approximates and their derivatives up to order k. Moreover, we show that the HOLMES of order k is dense in the Sobolev Space \({W}^{k,p}\), for any \(1 \leq p < \infty \). The good performance of HOLMES relative to other meshfree schemes in selected test cases is also critically appraised.

We present a model to understand quantitatively the role of symmetry breaking in assembly of macromolecular aggregates in general, and the protein shells of viruses in particular. A simple dodecahedral lattice model with a quadrupolar order parameter allows us to demonstrate how symmetry breaking may reduce the probability of assembly errors and, consequently, enhance assembly efficiency. We show that the ground state is characterized by large-scale cooperative zero-energy modes. In analogy with other models, this suggests a general physical principle: the tendency of biological molecules to generate symmetric structures competes with the tendency to break symmetry in order to achieve specific functional goals.

Many viral capsids undergo a series of significant structural changes following assembly, a process known as maturation. The driving mechanisms for maturation usually are chemical reactions taking place inside the proteins that constitute the capsid (“subunits”) that produce structural changes of the subunits. The resulting alterations of the subunits may be directly visible from the capsid structures, as observed by electron microscopy, in the form of a shear shape change and/or a rotation of groups of subunits. The existing thin shell elasticity theory for viral shells does not take account of the internal structure of the subunits and hence cannot describe displacement patterns of the capsid during maturation. Recently, it was proposed for the case of a particular virus (HK97) that thin shell elasticity theory could in fact be generalized to include transformations of the constituent proteins by including such a transformations as a change of the stress-free reference state for the deformation free energy. In this study, we adopt that approach and illustrate its validity in more generality by describing shape changes occurring during maturation across different T-numbers in terms of subunit shearing. Using phase diagrams, we determine the shear directions of the subunits that are most effective to produce capsid shape changes, such as transitions from spherical to facetted capsid shape. We further propose an equivalent stretching mechanism offering a unifying view under which capsid symmetry can be analyzed. We conclude by showing that hexamer shearing not only drives the shape change of the viral capsid during maturation but also is capable of lowering the capsid elastic energy in particular for chiral capsids (e.g., T = 7 ) and give rise to pre-shear patterns. These additional mechanisms may provide a driving force and an organizational principle for virus assembly.

Quantitative measurement of the material properties (eg, stiffness) of biological tissues is poised to become a powerful diagnostic tool. There are currently several methods in the literature to estimating material stiffness, and we extend this work by formulating a framework that leads to uniquely identified material properties. We design an approach to work with full-field displacement data-ie, we assume the displacement field due to the applied forces is known both on the boundaries and also within the interior of the body of interest-and seek stiffness parameters that lead to balanced internal and external forces in a model. For in vivo applications, the displacement data can be acquired clinically using magnetic resonance imaging while the forces may be computed from pressure measurements, eg, through catheterization. We outline a set of conditions under which the least-square force error objective function is convex, yielding uniquely identified material properties. An important component of our framework is a new numerical strategy to formulate polyconvex material energy laws that are linear in the material properties and provide one optimal description of the available experimental data. An outcome of our approach is the analysis of the reliability of the identified material properties, even for material laws that do not admit unique property identification. Lastly, we evaluate our approach using passive myocardium experimental data at the material point and show its application to identifying myocardial stiffness with an in silico experiment modeling the passive filling of the left ventricle.

We describe a sequence of methods to produce a partial differential equation model of the electrical activation of the ventricles. In our framework, we incorporate the anatomy and cardiac microstructure obtained from magnetic resonance imaging and diffusion tensor imaging of a New Zealand White rabbit, the Purkinje structure and the Purkinje-muscle junctions, and an electrophysiologically accurate model of the ventricular myocytes and tissue, which includes transmural and apex-to-base gradients of action potential characteristics. We solve the electrophysiology governing equations using the finite element method and compute both a 6-lead precordial electrocardiogram (ECG) and the activation wavefronts over time. We are particularly concerned with the validation of the various methods used in our model and, in this regard, propose a series of validation criteria that we consider essential. These include producing a physiologically accurate ECG, a correct ventricular activation sequence, and the inducibility of ventricular fibrillation. Among other components, we conclude that a Purkinje geometry with a high density of Purkinje muscle junctions covering the right and left ventricular endocardial surfaces as well as transmural and apex-to-base gradients in action potential characteristics are necessary to produce ECGs and time activation plots that agree with physiological observations., Shankarjee Krishnamoorthi et. al

Viral capsids undergo significant mechanical deformations during their assembly, maturation, and infective life-span. In order to characterize the mechanics of viral capsids, their response to applied external forces is analyzed in several experimental studies using, for instance, Atomic Force Microscope (AFM) indentation experiments. In recent years, a broader approach to study the mechanics of viral capsids has leveraged the theoretical tools proper of continuum mechanics. Even though the theory of continuum elasticity is most commonly used to study deformable bodies at larger macroscopic length scales, it has been shown that this very rich theoretical field can still offer useful insights into the mechanics of viral structures at the nanometer scale. Here we show the construction of viral capsid continuum mechanics models starting from different forms of experimental data. We will discuss the kinematics assumptions, the issue of the reference configuration, the material constitutive laws, and the numerical discretization necessary to construct a complete Finite Element capsid mechanical model. Some examples in the second part of the chapter will show the predictive capabilities of the constructed models and underline useful practical aspects related to efficiency and accuracy. We conclude each example by collecting several key findings discovered by simulating AFM indentation experiments using the constructed numerical models.

Viral capsids undergo significant mechanical deformations during their assembly, maturation, and infective life-span. In order to characterize the mechanics of viral capsids, their response to applied external forces is analyzed in several experimental studies using, for instance, Atomic Force Microscope (AFM) indentation experiments. In recent years, a broader approach to study the mechanics of viral capsids has leveraged the theoretical tools proper of continuum mechanics. Even though the theory of continuum elasticity is most commonly used to study deformable bodies at larger macroscopic length scales, it has been shown that this very rich theoretical field can still offer useful insights into the mechanics of viral structures at the nanometer scale. Here we show the construction of viral capsid continuum mechanics models starting from different forms of experimental data. We will discuss the kinematics assumptions, the issue of the reference configuration, the material constitutive laws, and the numerical discretization necessary to construct a complete Finite Element capsid mechanical model. Some examples in the second part of the chapter will show the predictive capabilities of the constructed models and underline useful practical aspects related to efficiency and accuracy. We conclude each example by collecting several key findings discovered by simulating AFM indentation experiments using the constructed numerical models.

This paper, a follow-up to previous research, examines how a complex and coupled constitutive model for the alkali-aggregate reaction (AAR) in concrete can be used for the long-term (until reaction exhaustion) prediction of an AAR-affected concrete structure. The procedure presented in this paper accounts for thermal and load time fluctuations. Through a series of parametric studies, sensitivity analyses also are performed, and basic modeling questions are addressed. The viability of the methodology was illustrated through the analysis of two dams and a reinforced concrete structure.

The electrocardiogram (ECG) is one of the most significant outputs of a computational model of cardiac electrophysiology because it relates the numerical results to clinical data and is a universal tool for diagnosing heart diseases. One key features of the ECG is the T-wave, which is caused by longitudinal and transmural heterogeneity of the action potential duration (APD). Thus, in order to model a correct wave of repolarization, different cell properties resulting in different APDs must be assigned across the ventricular wall and longitudinally from apex to base. To achieve this requirement, a regional parametrization of the heart is necessary. We propose a robust approach to obtain the transmural and longitudinal segmentation in a general heart geometry without relying on ad hoc procedures. Our approach is based on auxiliary harmonic lifting analyses, already used in the literature to generate myocardial fiber orientations. Specifically, the solution of a sequence of Laplace boundary value problems allows parametrically controlled segmentation of both heart ventricles. The flexibility and simplicity of the proposed method is demonstrated through several representative examples, varying the locations and extents of the epicardial, midwall, and endocardial layers. Effects of the control parameters on the T-wave morphology are illustrated via computed ECGs.

The authors present a new model for alkali-aggregate reaction (AAR) expansion, which is the leading cause of dam concrete deterioration and currently has no economically feasible method to stop the reaction. The paper first presents a literature survey of AAR, next presents the proposed model, and finally addresses the issue of potential applications. By utilizing chemistry, physics, and the mechanics of concrete, the premises of the model are the assumption of the volumetric expansion of the gel and the redistribution on the basis of weights related to the stress tensor. A dam analysis data preparation for an application of a two-dimensional analysis of an arch gravity dam is presented.

Large scale three-dimensional numerical simulations of hypervelocity impact of Aluminum alloy 6061-T6 plates by Nylon 6/6 cylindrical projectile have been performed using the Optimal Transportation Meshfree (OTM) method of Li et al. [7] along with the seizing contact and variational material point failure algorithm [17, 18]. The dynamic response of the Al6061-T6 plate including phase transition in the high strain rate, high pressure and high temperature regime expected in our numerical analysis is described by the use of a variational thermomechanical coupling constitutive model with SESAME equation of state, rate-dependent J2 plasticity with power law hardening and thermal softening and temperature dependent Newtonian viscosity. A polytropic type of equation of state fit to in-house ReaxFF calculations is employed to model the Nylon 6/6 projectile under extreme conditions. The evaluation of the performance of the numerical model takes the form of a conventional validation analysis. In support of the analysis, we have conducted experiments over a range of plate thicknesses of [0.5, 3.0] mm, a range of impact velocities of [5.0, 7.0]km/s and a range of obliquities of [0, 70]° at Caltech's Small Particle Hypervelocity Range (SPHIR) Facility. Large scale three-dimensional OTM simulations of hypervelocity impact are performed on departmental class systems using a dynamic load balancing MPI/PThreads parallel implementation of the OTM method. We find excellent full field agreement between measured and computed perforation areas, debris cloud and temperature field.

We experimentally and numerically investigate the response of fluid-filled filament-wound composite tubes subjected to axial shock wave loading in water. Our study focuses on the fluid–structure interaction occurring when the shock wave in the fluid propagates parallel to the axis of the tube, creating pressure waves in the fluid coupled to flexural waves in the shell. The in-house-developed computational scheme couples an Eulerian fluid solver with a Lagrangian shell solver, which includes a new and simple material model to capture the response of fiber composites in finite kinematics. In the experiments and simulations we examine tubes with fiber winding angles equal to 45° and 60°, and we measure the precursor and primary wave speeds, hoop and longitudinal strains, and pressure. The experimental and computational results are in agreement, showing the validity of the computational scheme in complex fluid–structure interaction problems involving fiber composite materials subjected to shock waves. The analyses of the measured quantities show the strong coupling of axial and hoop deformations and the significant effect of fiber winding angle on the composite tube response, which differs substantially from that of a metal tube in the same configuration.

International audience; Electrocardiographic Imaging (ECGI) is a non-invasive procedure that allows to reconstruct the electrical activity of the heart from body surface potential map (BSPM). In this paper, we present a volume model to solve the electrocardiography inverse problem capable to take into account structural informations obtained by imaging techniques. The direct problem maps a volume current in the cardiac muscle (ventricles) to the body surface electrical measures. The model is based on coupling bidomain heart model with torso conduction. The corresponding inverse problem is solved with the Tikhonov regularization. Simulated database are used for the evaluation of this method and we compared them to standard method of fundamental solutions (MFS). The sensitivity to noise is also assessed. The correlation coefficients (CC) and the relative error (RE) of activation times were computed. Results show that the CC (respectively RE) median is respectively 0.75 for the volume model and 0.4 for the MFS (respectively 0.31 vs 0.35) on the epicardium. On the endocardium, the CC and the RE median are 0.65 and 0.33 for the volume method. In conclusion, the volume method performs better than the method of fundamental solutions (MFS) for any noise level, and reconstruct in addition endocardial information.

International audience; Despite advances in many of the techniques used in Electrocardiographic Imaging (ECGI), uncertainty remains insufficiently quantified for many aspects of the pipeline. The effect of geometric uncertainty, particularly due to segmentation variability, may be the least explored to date. We use statistical shape modeling and uncertainty quantification (UQ) to compute the effect of segmentation variability on ECGI solutions. The shape model was made with Shapeworks from nine segmentations of the same patient and incorporated into an ECGI pipeline. We computed uncertainty of the pericardial potentials and local activation times (LATs) using polynomial chaos expansion (PCE) implemented in UncertainSCI. Uncertainty in pericardial potentials from segmentation variation mirrored areas of high variability in the shape model, near the base of the heart and the right ventricular outflow tract, and that ECGI was less sensitive to uncertainty in the posterior region of the heart. Subsequently LAT calculations could vary dramatically due to segmentation variability, with a standard deviation as high as 126ms, yet mainly in regions with low conduction velocity. Our shape modeling and UQ pipeline presented possible uncertainty in ECGI due to segmentation variability and can be used by researchers to reduce said uncertainty or mitigate its effects. The demonstrated use of statistical shape modeling and UQ can also be extended to other types of modeling pipelines.

International audience; We generalized and improved our clinical technique of twodimensional intraventricular vector flow mapping (2D-iVFM) for a full-volume three-component analysis of the intraventricular blood flow (3D-iVFM). While 2D-iVFM uses three-chamber color Doppler images, 3D-iVFM is based on the clinical mode of triplane color Doppler echocardiography. As in the previous twodimensional version, 3D-iVFM relies on mass conservation and free-slip endocardial boundary conditions. For sake of robustness, the optimization problem was written as a constrained least-squares problem. We tested and validated 3D-iVFM in silico through a patient-specific heart-flow CFD (computational fluid dynamics) model, as well as in vivo in one healthy volunteer. The intraventricular vortex that forms during left ventricular filling was deciphered. After further validation, 3D-iVFM could offer clinically compatible 3-D echocardiographic insights into left intraventricular hemodynamics.

Aortic stenosis (AS) is the most common acquired heart valve disease in the developed world. Traditional methods of grading AS have relied on the measurement of aortic valve area and transvalvular pressure gradient. Recent research has highlighted the existence of AS variants that do not meet classic criteria for severe AS such as low-flow, low-gradient AS. With the development of sophisticated multi-scale computational models, investigation into the left ventricular (LV) biomechanics of AS offers new insights into the pathophysiology that may guide treatment decisions surrounding AS. Building upon our prior study entailing LV-aortic coupling where AS conditions were applied to the idealized geometry of the Living Heart Human Model, we now describe the first patient-specific adaptation of the model to a case of low flow, low gradient AS. EKG-gated cardiac computed tomography images were segmented to provide surfaces to which the generic Living Heart model was adapted. The model was coupled to a lumped-parameter circulatory system; it was then calibrated to patient clinical data from echocardiography/cardiac catheterization with strong correlation (simulation versus clinical measurement): ascending aorta systolic pressure: 109mmHg vs 116mmHg, ascending aorta diastolic pressure 50mmHg vs 45mmHg, LV systolic pressure: 118mmHg vs 128mmHg, peak transvalvular gradient: 9mmHg vs 12mmHg, LV ejection fraction: 23% vs 25%. This work illustrates how the Living Heart Human Model geometry can be efficiently adapted to patient-specific parameters, enabling future biomechanics investigations into the LV dysfunction of AS.