A simple and efficient adaptive time stepping technique for low-order operator splitting schemes applied to cardiac electrophysiology.

We present a simple, yet efficient adaptive time stepping scheme for cardiac electrophysiology (EP) simulations based on standard operator splitting techniques. The general idea is to exploit the relation between the splitting error and the reaction's magnitude-found in a previous one-dimensional analytical study by Spiteri and Ziaratgahi-to construct the new time step controller for three-dimensional problems. Accordingly, we propose to control the time step length of the operator splitting scheme as a function of the reaction magnitude, in addition to the common approach of adapting the reaction time step. This conforms with observations in numerical experiments supporting the need for a significantly smaller time step length during depolarization than during repolarization. The proposed scheme is compared with classical proportional-integral-differential controllers using state-of-the-art error estimators, which are also presented in details as they have not been previously applied in the context of cardiac EP with operator splitting techniques. Benchmarks show that choosing the time step as a sigmoidal function of the reaction magnitude is highly efficient and full cardiac cycles can be computed with precision even in a realistic biventricular setup. The proposed scheme outperforms common adaptive time stepping techniques, while depending on fewer tuning parameters.

Changes in interstitial fluid flow, mass transport and the bone cell response in microgravity and normogravity.

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 Lagrangian Thin-Shell Finite Element Method for Interacting Particles on Fluid Membranes.

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 Biomarkers of Chronic Infarction Based on In Vivo Data.

In vivo cardiac diffusion tensor imaging (cDTI) data were acquired in swine subjects six to ten weeks post-myocardial infarction (MI) to identify microstructural-based biomarkers of MI. Diffusion tensor invariants, diffusion tensor eigenvalues, and radial diffusivity (RD) are evaluated in the infarct, border, and remote myocardium, and compared with extracellular volume fraction (ECV) and native T1 values. Additionally, to aid the interpretation of the experimental results, the diffusion of water molecules was numerically simulated as a function of ECV. Finally, findings based on in vivo measures were confirmed using higher-resolution and higher signal-to-noise data acquired ex vivo in the same subjects. Mean diffusivity, diffusion tensor eigenvalues, and RD increased in the infarct and border regions compared to remote myocardium, while fractional anisotropy decreased. Secondary (e2) and tertiary (e3) eigenvalues increased more significantly than the primary eigenvalue in the infarct and border regions. These findings were confirmed by the diffusion simulations. Although ECV presented the largest increase in infarct and border regions, e2, e3, and RD increased the most among non-contrast-based biomarkers. RD is of special interest as it summarizes the changes occurring in the radial direction and may be more robust than e2 or e3 alone.

Arbitrary Point Tracking with Machine Learning to Measure Cardiac Strains in Tagged MRI.

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 <0.26mm in the computational phantom, and strain measurements were improved in vivo when using the arbitrary point tracking for a standard clinical protocol.

Diffusion biomarkers in chronic myocardial infarction.

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 1mm 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.

Using synthetic data generation to train a cardiac motion tag tracking neural network.

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.

Myofiber strain in healthy humans using DENSE and cDTI.

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.

Estimating cardiomyofiber strain in vivo by solving a computational model.

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.

Probing cardiomyocyte mobility with multi-phase cardiac diffusion tensor MRI.

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<0.001). E2A also changed significantly between early systole, late systole, and diastasis (27.7 [20.8, 35.1]° vs 45.2 [42.1, 49]° vs 20.7 [16.6, 26.4]°, p<0.001). 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.

Real-time 3T MRI-guided cardiovascular catheterization in a porcine model using a glass-fiber epoxy-based guidewire.

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.

Estimating Aggregate Cardiomyocyte Strain Using In Vivo Diffusion and Displacement Encoded MRI.

Changes in left ventricular (LV) aggregate cardiomyocyte orientation and deformation underlie cardiac function and dysfunction. As such, in vivo aggregate cardiomyocyte "myofiber" strain ( [Formula: see text]) has mechanistic significance, but currently there exists no established technique to measure in vivo [Formula: see text]. The objective of this work is to describe and validate a pipeline to compute in vivo [Formula: see text] 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 [Formula: see text] 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 [Formula: see text] has decreased transmural variability compared to radial and circumferential strains. The spatial uniformity and mechanistic significance of in vivo [Formula: see text] make it a compelling candidate for characterization and early detection of cardiac dysfunction.

High-Resolution Ex Vivo Microstructural MRI After Restoring Ventricular Geometry via 3D Printing.

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.

Model of Left Ventricular Contraction: Validation Criteria and Boundary Conditions.

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.

Kirigami and the Caspar-Klug construction for viral shells with negative Gauss curvature.

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.

TIME RESOLVED DISPLACEMENT-BASED REGISTRATION OF IN VIVO CDTI CARDIOMYOCYTE ORIENTATIONS.

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).

Ground state instabilities of protein shells are eliminated by buckling.

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.

Method for the unique identification of hyperelastic material properties using full-field measures. Application to the passive myocardium material response.

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.

Microstructurally Anchored Cardiac Kinematics by Combining In Vivo DENSE MRI and cDTI.

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.

Electrophysiology of Heart Failure Using a Rabbit Model: From the Failing Myocyte to Ventricular Fibrillation.

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.