Daniel E. Hurtado

Verification of cardiac mechanics software: benchmark problems and solutions for testing active and passive material behaviour

Models of cardiac mechanics are increasingly used to investigate cardiac physiology. These models are characterized by a high level of complexity, including the particular anisotropic material properties of biological tissue and the actively contracting material. A large number of independent simulation codes have been developed, but a consistent way of verifying the accuracy and replicability of simulations is lacking. To aid in the verification of current and future cardiac mechanics solvers, this study provides three benchmark problems for cardiac mechanics. These benchmark problems test the ability to accurately simulate pressure-type forces that depend on the deformed objects geometry, anisotropic and spatially varying material properties similar to those seen in the left ventricle and active contractile forces. The benchmark was solved by 11 different groups to generate consensus solutions, with typical differences in higher-resolution solutions at approximately 0.5%, and consistent results between linear, quadratic and cubic finite elements as well as different approaches to simulating incompressible materials. Online tools and solutions are made available to allow these tests to be effectively used in verification of future cardiac mechanics software.

Computational modelling of electrocardiograms: repolarisation and T-wave polarity in the human heart.

For more than a century, electrophysiologists, cardiologists and engineers have studied the electrical activity of the human heart to better understand rhythm disorders and possible treatment options. Although the depolarisation sequence of the heart is relatively well characterised, the repolarisation sequence remains a subject of great controversy. Here, we study regional and temporal variations in both depolarisation and repolarisation using a finite element approach. We discretise the governing equations in time using an unconditionally stable implicit Euler backward scheme and in space using a consistently linearised Newton–Raphson-based finite element solver. Through systematic parameter-sensitivity studies, we establish a direct relation between a normal positive T-wave and the non-uniform distribution of the controlling parameter, which we have termed refractoriness. To establish a healthy baseline model, we calibrate the refractoriness using clinically measured action potential durations at different locations in the human heart. We demonstrate the potential of our model by comparing the computationally predicted and clinically measured depolarisation and repolarisation profiles across the left ventricle. The proposed framework allows us to explore how local action potential durations on the microscopic scale translate into global repolarisation sequences on the macroscopic scale. We anticipate that our calibrated human heart model can be widely used to explore cardiac excitation in health and disease. For example, our model can serve to identify optimal pacing sites in patients with heart failure and to localise optimal ablation sites in patients with cardiac fibrillation.

Generating Purkinje networks in the human heart

The Purkinje network is an integral part of the excitation system in the human heart. Yet, to date, there is no in vivo imaging technique to accurately reconstruct its geometry and structure. Computational modeling of the Purkinje network is increasingly recognized as an alternative strategy to visualize, simulate, and understand the role of the Purkinje system. However, most computational models either have to be generated manually, or fail to smoothly cover the irregular surfaces inside the left and right ventricles. Here we present a new algorithm to reliably create robust Purkinje networks within the human heart. We made the source code of this algorithm freely available online. Using Monte Carlo simulations, we demonstrate that the fractal tree algorithm with our new projection method generates denser and more compact Purkinje networks than previous approaches on irregular surfaces. Under similar conditions, our algorithm generates a network with 1219±61 branches, three times more than a conventional algorithm with 419±107 branches. With a coverage of 11±3mm, the surface density of our new Purkije network is twice as dense as the conventional network with 22±7mm. To demonstrate the importance of a dense Purkinje network in cardiac electrophysiology, we simulated three cases of excitation: with our new Purkinje network, with left-sided Purkinje network, and without Purkinje network. Simulations with our new Purkinje network predicted more realistic activation sequences and activation times than simulations without. Six-lead electrocardiograms of the three case studies agreed with the clinical electrocardiograms under physiological conditions, under pathological conditions of right bundle branch block, and under pathological conditions of trifascicular block. Taken together, our results underpin the importance of the Purkinje network in realistic human heart simulations. Human heart modeling has the potential to support the design of personalized strategies for single- or bi-ventricular pacing, radiofrequency ablation, and cardiac defibrillation with the common goal to restore a normal heart rhythm.

3D Quantification of Wall Shear Stress and Oscillatory Shear Index Using a Finite-Element Method in 3D CINE PC-MRI Data of the Thoracic Aorta

Several 2D methods have been proposed to estimate WSS and OSI from PC-MRI, neglecting the longitudinal velocity gradients that typically arise in cardiovascular flow, particularly on vessel geometries whose cross section and centerline orientation strongly vary in the axial direction. Thus, the contribution of longitudinal velocity gradients remains understudied. In this work, we propose a 3D finite-element method for the quantification of WSS and OSI from 3D-CINE PC-MRI that accounts for both in-plane and longitudinal velocity gradients. We demonstrate the convergence and robustness of the method on cylindrical geometries using a synthetic phantom based on the Poiseuille flow equation. We also show that, in the presence of noise, the method is both stable and accurate. Using computational fluid dynamics simulations, we show that the proposed 3D method results in more accurate WSS estimates than those obtained from a 2D analysis not considering out-of-plane velocity gradients. Further, we conclude that for irregular geometries the accurate prediction of WSS requires the consideration of longitudinal gradients in the velocity field. Additionally, we compute 3D maps of WSS and OSI for 3D-CINE PC-MRI data sets from an aortic phantom and sixteen healthy volunteers and two patients. The OSI values show a greater dispersion than WSS, which is strongly dependent on the PC-MRI resolution. We envision that the proposed 3D method will improve the estimation of WSS and OSI from 3D-CINE PC-MRI images, allowing for more accurate estimates in vessels with pathologies that induce high longitudinal velocity gradients, such as coarctations and aneurisms.

The renal compartment: a hydraulic view

BackgroundThe hydraulic behavior of the renal compartment is poorly understood. In particular, the role of the renal capsule on the intrarenal pressure has not been thoroughly addressed to date. We hypothesized that pressure and volume in the renal compartment are not linearly related, similar to other body compartments.MethodsThe pressure-volume curve of the renal compartment was obtained by injecting fluid into the renal pelvis and recording the rise in intrarenal pressure in six anesthetized and mechanically ventilated piglets, using a catheter Camino 4B® inserted into the renal parenchyma.ResultsIn healthy kidneys, pressure has a highly nonlinear dependence on the injected volume, as revealed by an exponential fit to the data (R2 = 0.92). On the contrary, a linear relation between pressure and volume is observed in decapsulated kidneys. We propose a biomechanical model for the renal capsule that is able to explain the nonlinear pressure-volume dependence for moderate volume increases.ConclusionsWe have presented experimental evidence and a theoretical model that supports the existence of a renal compartment. The mechanical role of the renal capsule investigated in this work may have important implications in elucidating the role of decompressive capsulotomy in reducing the intrarenal pressure in acutely injured kidneys.

Quantification of wall shear stress using a finite-element method in multidimensional phase-contrast MR data of the thoracic aorta

We present a computational method for calculating the distribution of wall shear stress (WSS) in the aorta based on a velocity field obtained from two-dimensional (2D) phase-contrast magnetic resonance imaging (PC-MRI) data and a finite-element method. The WSS vector was obtained from a global least-squares stress-projection method. The method was benchmarked against the Womersley model, and the robustness was assessed by changing resolution, noise, and positioning of the vessel wall. To showcase the applicability of the method, we report the axial, circumferential and magnitude of the WSS using in-vivo data from five volunteers. Our results showed that WSS values obtained with our method were in good agreement with those obtained from the Womersley model. The results for the WSS contour means showed a systematic but decreasing bias when the pixel size was reduced. The proposed method proved to be robust to changes in noise level, and an incorrect position of the vessel wall showed large errors when the pixel size was decreased. In volunteers, the results obtained were in good agreement with those found in the literature. In summary, we have proposed a novel image-based computational method for the estimation of WSS on vessel sections with arbitrary cross-section geometry that is robust in the presence of noise and boundary misplacements.

Local mechanical response of cells to the controlled rotation of magnetic nanorods

The mechanical response of the cytoplasm was investigated by the intracellular implantation of magnetic nanorods and exposure to low-frequency rotatory magnetic fields. Nanorods (Pt-Ni, ∼200 nm diameter) fabricated by electrodeposition in templates of porous alumina with lengths of approximately 2 and 5 µm were inserted into NIH/3T3 fibroblasts and manipulated with a rotational magnetic field. Nanorod rotation was observed only for torques greater than 3.0 × 10(-16) Nm, suggesting a Bingham-type behavior of the cytoplasm. Higher torques produced considerable deformation of the intracellular material. The cell nucleus and cell membrane were significantly deformed by nanorods actuated by 4.5 × 10(-15) Nm torques. Our results demonstrate that nanorods under magnetic fields are an effective tool to mechanically probe the intracellular environment. We envision that our findings may contribute to the noninvasive and direct mechanical characterization of the cytoplasm.

The importance of mechano-electrical feedback and inertia in cardiac electromechanics

In the past years, a number cardiac electromechanics models have been developed to better understand the excitation-contraction behavior of the heart. However, there is no agreement on whether inertial forces play a role in this system. In this study, we assess the influence of mass in electromechanical simulations, using a fully coupled finite element model. We include the effect of mechano-electrical feedback via stretch activated currents. We compare five different models: electrophysiology, electromechanics, electromechanics with mechano-electrical feedback, electromechanics with mass, and electromechanics with mass and mechano-electrical feedback. We simulate normal conduction to study conduction velocity and spiral waves to study fibrillation. During normal conduction, mass in conjunction with mechano-electrical feedback increased the conduction velocity by 8.12% in comparison to the plain electrophysiology case. During the generation of a spiral wave, mass and mechano-electrical feedback generated secondary wavefronts, which were not present in any other model. These secondary wavefronts were initiated in tensile stretch regions that induced electrical currents. We expect that this study will help the research community to better understand the importance of mechanoelectrical feedback and inertia in cardiac electromechanics.

Improving the Accuracy of Registration-Based Biomechanical Analysis: A Finite Element Approach to Lung Regional Strain Quantification

Tissue deformation plays an important role in lung physiology, as lung parenchyma largely deforms during spontaneous ventilation. However, excessive regional deformation may lead to lung injury, as observed in patients undergoing mechanical ventilation. Thus, the accurate estimation of regional strain has recently received great attention in the intensive care community. In this work, we assess the accuracy of regional strain maps computed from direct differentiation of B-Spline (BS) interpolations, a popular technique employed in non-rigid registration of lung computed tomography (CT) images. We show that, while BS-based registration methods give excellent results for the deformation transformation, the strain field directly computed from BS derivatives results in predictions that largely oscillate, thus introducing important errors that can even revert the sign of strain. To alleviate such spurious behavior, we present a novel finite-element (FE) method for the regional strain analysis of lung CT images. The method follows from a variational strain recovery formulation, and delivers a continuous approximation to the strain field in arbitrary domains. From analytical benchmarks, we show that the FE method results in errors that are a fraction of those found for the BS method, both in an average and pointwise sense. The application of the proposed FE method to human lung CT images results in 3D strain maps are heterogeneous and smooth, showing high consistency with specific ventilation maps reported in the literature. We envision that the proposed FE method will considerably improve the accuracy of image-based biomechanical analysis, making it reliable enough for routine medical applications.

Pressure gradient prediction in aortic coarctation using a computational-fluid-dynamics model: Validation against invasive pressure catheterization at rest and pharmacological stress

Background Aortic Coarctation (AoCo) accounts for 5-8% of the children with CHD. Even after successful early repair, life expectancy is still markedly reduced (80% at 50 years after surgery) compared to normal population due to long term complications (hypertension). Usually, invasive diagnostic catheter investigations are required to evaluate the pressure gradient across the aorta at rest, or unmask such a gradient by use of isoprenaline stress to mimic physical exercise. The application of imagebased computational fluid dynamics (CFD) in patients with AoCo appears promising as an alternative noninvasive diagnostic tool, as it may allow the avoidance of cardiac catheterization to determine pressure gradients. The motivation of this research is to know if a MRI based CFD model can accurately predict the pressure