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Aims Electromechanical coupling in patients receiving cardiac resynchronization therapy (CRT) is not fully understood. Our aim was to determine the best combination of electrical and mechanical substrates associated with effective CRT. Methods and results Sixty-two patients were prospectively enrolled from two centres. Patients underwent 12-lead electrocardiogram (ECG), cardiovascular magnetic resonance (CMR), echocardiography, and anatomo-electromechanical mapping (AEMM). Remodelling was measured as the end-systolic volume (ΔESV) decrease at 6 months. CRT was defined effective with ΔESV ≤ −15%. QRS duration (QRSd) was measured from ECG. Area strain was obtained from AEMM and used to derive systolic stretch index (SSI) and total left-ventricular mechanical time. Total left-ventricular activation time (TLVAT) and transeptal time (TST) were derived from AEMM and ECG. Scar was measured from CMR. Significant correlations were observed between ΔESV and TST [rho = 0.42; responder: 50 (20–58) vs. non-responder: 33 (8–44) ms], TLVAT [−0.68; 81 (73–97) vs. 112 (96–127) ms], scar [−0.27; 0.0 (0.0–1.2) vs. 8.7 (0.0–19.1)%], and SSI [0.41; 10.7 (7.1–16.8) vs. 4.2 (2.9–5.5)], but not QRSd [−0.13; 155 (140–176) vs. 167 (155–177) ms]. TLVAT and SSI were highly accurate in identifying CRT response [area under the curve (AUC) > 0.80], followed by scar (AUC > 0.70). Total left-ventricular activation time (odds ratio = 0.91), scar (0.94), and SSI (1.29) were independent factors associated with effective CRT. Subjects with SSI >7.9% and TLVAT Conclusion Electromechanical measurements are better associated with CRT response than conventional ECG variables. The absence of scar combined with high SSI and low TLVAT ensures effectiveness of CRT.

We examine the dual formulation of the frictionless Signorini problem for a deformable body in contact with a rigid obstacle. We discretize the problem by means of the finite element method. Since the dual formulation solves directly for the stress variable and is not affected by locking, it is very attractive for many engineering applications. However, it is hard to solve it efficiently, since many challenges arise. First, the stress belongs to the non-Sobolev space (Formula presented.). Second, the matrix block related to the stress is only semi-positive definite in the incompressible limit. Third, global equality constraints and box-constraints are enforced. In this paper, we propose a novel and optimal nonlinear multigrid method for the dual formulation of the Signorini problem, that works even in the incompressible limit. We opt for the combination of a truncation of the basis functions strategy and a nonlinear monolithic patch smoother with Robin conditions of parameter (Formula presented.). Numerical experiments show that multigrid performance is recovered if (Formula presented.) is chosen properly. We propose an algorithm to dynamically update the parameter (Formula presented.) during the multigrid process, in order to provide a near optimal value of (Formula presented.).

The dual formulation for linear elasticity, in contrast to the primal formulation, is not affected by locking, as it is based on the stresses as main unknowns. Thus it is quite attractive for nearly incompressible and incompressible materials. Discretization with mixed finite elements will lead to -- possibly large -- linear saddle point systems with a particular structure. Whereas efficient multigrid methods exist for solving problems in mixed plane elasticity, to the knowledge of the authors, no multigrid methods are readily available for the general dual formulation. Two are the main challenges in constructing a multigrid method for the dual formulation for linear elasticity. First, in the incompressible limit, the matrix block related to the stress is semi-positive definite. Second, the stress belongs to $\textbf{H}_{\text{div}}$ and standard smoothers, working for $\textbf{H}^1$ regular problems, cannot be applied. We present a novel patch-based smoother for the dual formulation for linear elasticity. We discuss different types of local boundary conditions for the patch subproblems. Based on our patch-smoother, we build a multigrid method for the solution of the resulting saddle point problem and investigate its efficiency and robustness. Numerical experiments show that Robin conditions best fit the multigrid framework, leading eventually to multigrid performance.

Live-cell imaging allows the study of apoptosis at cellular level, highlighting morphological hallmarks such as nuclear shrinkage, membrane blebbing, and cell disruption. Identifying the exact location and timing of this process is essential to foster the understanding of its spatial-temporal regulation. However, the analysis of live-cell imaging datasets is complex, whereas computational tools tailored to this task are yet scarce. Therefore, we developed ADeS, an Apoptosis Detection System based on deep learning and activity recognition. ADeS uses morpho-dynamic hallmarks to detect the exact location and timing of apoptotic events in different cell types, reaching an accuracy above 97% in the classification of our validation datasets acquiredin vitroandin vivo. Moreover, ADeS is the first successful implementation of a deep learning network for the automatic detection of apoptotic cells in full microscopy movies in an end-to-end fashion, outperforming human in the same task. As a case study, we employed ADeS for the analysis of cell survivalin vitro, and for tissue damage assessmentin vivo, showing its potential application for toxicity assays, treatments evaluation and measuring of tissue dynamics.

Multigrid methods for two-body contact problems are mostly based on special mortar discretizations, nonlinear Gauss-Seidel solvers, and solution-adapted coarse grid spaces. Their high computational efficiency comes at the cost of a complex implementation and a nonsymmetric master-slave discretization of the nonpenetration condition. Here we investigate an alternative symmetric and overconstrained segment-to-segment contact formulation that allows for a simple implementation based on standard multigrid and a symmetric treatment of contact boundaries, but leads to nonunique multipliers. For the solution of the arising quadratic programs, we propose augmented Lagrangian multigrid with overlapping block Gauss-Seidel smoothers. Approximation and convergence properties are studied numerically at standard test problems.

We present a new multilevel minimization framework for the training of deep residual networks (ResNets), which has the potential to significantly reduce training time and effort. Our framework is based on the dynamical system’s viewpoint, which formulates a ResNet as the discretization of an initial value problem. The training process is then formulated as a time-dependent optimal control problem, which we discretize using different time-discretization parameters, eventually generating multilevel-hierarchy of auxiliary networks with different resolutions. The training of the original ResNet is then enhanced by training the auxiliary networks with reduced resolutions. By design, our framework is conveniently independent of the choice of the training strategy chosen on each level of the multilevel hierarchy. By means of numerical examples, we analyze the convergence behavior of the proposed method and demonstrate its robustness. For our examples we employ a multilevel gradient-based methods. Comparisons with standard single level methods show a speedup of more than factor three while achieving the same validation accuracy.

Aims Non-invasive imaging of electrical activation requires high-density body surface potential mapping. The nine electrodes of the 12-lead electrocardiogram (ECG) are insufficient for a reliable reconstruction with standard inverse methods. Patient-specific modelling may offer an alternative route to physiologically constraint the reconstruction. The aim of the study was to assess the feasibility of reconstructing the fully 3D electrical activation map of the ventricles from the 12-lead ECG and cardiovascular magnetic resonance (CMR). Methods and results Ventricular activation was estimated by iteratively optimizing the parameters (conduction velocity and sites of earliest activation) of a patient-specific model to fit the simulated to the recorded ECG. Chest and cardiac anatomy of 11 patients (QRS duration 126–180 ms, documented scar in two) were segmented from CMR images. Scar presence was assessed by magnetic resonance (MR) contrast enhancement. Activation sequences were modelled with a physiologically based propagation model and ECGs with lead field theory. Validation was performed by comparing reconstructed activation maps with those acquired by invasive electroanatomical mapping of coronary sinus/veins (CS) and right ventricular (RV) and left ventricular (LV) endocardium. The QRS complex was correctly reproduced by the model (Pearson’s correlation r = 0.923). Reconstructions accurately located the earliest and latest activated LV regions (median barycentre distance 8.2 mm, IQR 8.8 mm). Correlation of simulated with recorded activation time was very good at LV endocardium (r = 0.83) and good at CS (r = 0.68) and RV endocardium (r = 0.58). Conclusion Non-invasive assessment of biventricular 3D activation using the 12-lead ECG and MR imaging is feasible. Potential applications include patient-specific modelling and pre-/per-procedural evaluation of ventricular activation.

Aims The aim of this study was to determine the relationship between electrical and mechanical activation in heart failure (HF) patients and whether electromechanical coupling is affected by scar. Methods and results Seventy HF patients referred for cardiac resynchronization therapy or biological therapy underwent endocardial anatomo-electromechanical mapping (AEMM) and delayed-enhancement magnetic resonance (CMR) scans. Area strain and activation times were derived from AEMM data, allowing to correlate mechanical and electrical activation in time and space with unprecedented accuracy. Special attention was paid to the effect of presence of CMR-evidenced scar. Patients were divided into a scar (n = 43) and a non-scar group (n–27). Correlation between time of electrical and mechanical activation was stronger in the non-scar compared to the scar group [R = 0.84 (0.72–0.89) vs. 0.74 (0.52–0.88), respectively; P = 0.01]. The overlap between latest electrical and mechanical activation areas was larger in the absence than in presence of scar [72% (54–81) vs. 56% (36–73), respectively; P = 0.02], with smaller distance between the centroids of the two regions [10.7 (4.9–17.4) vs. 20.3 (6.9–29.4) % of left ventricular radius, P = 0.02]. Conclusion Scar decreases the association between electrical and mechanical activation, even when scar is remote from late activated regions.

Relating the attenuation and velocity dispersion of seismic waves to fluid pressure diffusion (FDP) by means of numerical simulations is essential for constraining the mechanical and hydraulic properties of heterogeneous porous rocks. This, in turn, is of significant importance for a wide range of prominent applications throughout the Earth, environmental, and engineering sciences, such as, for example, geothermal energy production, hydrocarbon exploration, nuclear waste disposal, and CO2 storage. In order to assess the effects of wave-induced FDP in heterogeneous porous rocks, we simulate time-harmonic oscillatory tests based on a finite element (FE) discretization of Biot’s equations in the time-frequency domain for representative elementary volumes (REVs) of the considered rock masses. The major challenge for these types of simulations is the creation of adequate computational meshes, which resolve the numerous and complex interfaces between the heterogeneities and the embedding background. To this end, we have developed a novel method based on adaptive mesh refinement (AMR), which allows for the fully automatic creation of meshes for strongly heterogenous media. The key concept of the proposed method is to start from an initially uniform coarse mesh and then to gradually refine elements which have non-empty overlaps with the embedded heterogeneities. This results in a hierarchy of non-uniform meshes with a large number of elements close to the interfaces, which do, however, not need to be explicitly resolved. This dramatically simplifies and accelerates the laborious and time-consuming process of meshing strongly heterogeneous poroelastic media, thus enabling the efficient simulation of REVs containing heterogeneities of quasi-arbitrary complexity. After a detailed description of the methodological foundations, we proceed to demonstrate that the FE discretization with low-order FE has a unique solution and hence does not present spurious modes. We assess the practical effectiveness and accuracy of the proposed method by means of four case studies of increasing complexity.

Cell migration is a pivotal biological process, whose dysregulation is found in many diseases including inflammation and cancer. Advances in microscopy technologies allow now to study cell migration in vitro, within microenvironments that resemble in vivo conditions. However, when cells are observed within large 3D migration chambers at low magnification and for extended periods of time, data analysis becomes difficult. Indeed, cell detection and tracking are hampered due to the large pixel size, the possible low signal-to-noise ratio and distortions in the cell shape due to changes in the z-axis position. Although fluorescent staining can be used to facilitate cell detection, it may alter cell behavior and suffer from fluorescence loss over time (photobleaching).Here we describe the application of an image analysis pipeline based on deep learning to convert the transmitted light signal from unlabeled lymphoma cells to pseudofluorescence. Such pipeline confers a significant improvement in tracking accuracy while not suffering from photobleaching. This is reflected in the possibility of tracking cells for three-fold longer periods of time.

Two-photon intravital microscopy (2P-IVM) has become a widely used technique to study cell-to-cell interactions in living organisms. Four-dimensional imaging data obtained via 2P-IVM are classically analyzed by performing automated cell tracking, a procedure that computes the trajectories followed by each cell. However, technical artifacts, such as brightness shifts, the presence of autofluorescent objects, and channel crosstalking, affect the specificity of imaging channels for the cells of interest, thus hampering cell detection. Recently, machine learning has been applied to overcome a variety of obstacles in biomedical imaging. However, existing methods are not tailored for the specific problems of intravital imaging of immune cells. Moreover, results are highly dependent on the quality of the annotations provided by the user. In this study, we developed CANCOL, a tool that facilitates the application of machine learning for automated tracking of immune cells in 2P-IVM. CANCOL guides the user during the annotation of specific objects that are problematic for cell tracking when not properly annotated. Then, it computes a virtual colocalization channel that is specific for the cells of interest. We validated the use of CANCOL on challenging 2P-IVM videos from murine organs, obtaining a significant improvement in the accuracy of automated tracking while reducing the time required for manual track curation.