Assessment of wall stresses and mechanical heart power in the left ventricle: Finite element modeling versus Laplace analysis

The geometric evolution of aortic dissections: Predicting surgical success using fluctuations in integrated Gaussian curvature

Clinical imaging modalities are a mainstay of modern disease management, but the full utilization of imaging-based data remains elusive. Aortic disease is defined by anatomic scalars quantifying aortic size, even though aortic disease progression initiates complex shape changes. We present an imaging-based geometric descriptor, inspired by fundamental ideas from topology and soft-matter physics that captures dynamic shape evolution. The aorta is reduced to a two-dimensional mathematical surface in space whose geometry is fully characterized by the local principal curvatures. Disease causes deviation from the smooth bent cylindrical shape of normal aortas, leading to a family of highly heterogeneous surfaces of varying shapes and sizes. To deconvolute changes in shape from size, the shape is characterized using integrated Gaussian curvature or total curvature. The fluctuation in total curvature (δK) across aortic surfaces captures heterogeneous morphologic evolution by characterizing local shape changes. We discover that aortic morphology evolves with a power-law defined behavior with rapidly increasing δK forming the hallmark of aortic disease. Divergent δK is seen for highly diseased aortas indicative of impending topologic catastrophe or aortic rupture. We also show that aortic size (surface area or enclosed aortic volume) scales as a generalized cylinder for all shapes. Classification accuracy for predicting aortic disease state (normal, diseased with successful surgery, and diseased with failed surgical outcomes) is 92.8±1.7%. The analysis of δK can be applied on any three-dimensional geometric structure and thus may be extended to other clinical problems of characterizing disease through captured anatomic changes.

Comparison of two ellipsoidal models for the estimation of left ventricular end-systolic stress in patients with significant coronary artery disease

Background

The shape of the left ventricle (LV) is an important index to explore cardiac pathophysiology. A comparison was provided to estimate circumferential, longitudinal, and radial wall stress in LV based on the thick-walled ellipsoidal models of Mirsky and Ghista-Sandler for discriminating significant coronary artery disease (CAD) patients from no CAD patients.

Materials and Methods

According to the angiography findings, 82 patients with CAD were divided into two groups: 25 patients without significant CAD and 57 patients with significant CAD of single vessel and multivessel. An ellipsoidal LV geometry was used to calculate end-systolic passive stress as the mechanical behavior of LV. Echocardiographic views-based measurements of LV diameters used to estimate the end-systolic wall stress.

Results

Circumferential wall stress between the control group and significant CAD groups was significantly elevated for the Ghista model (P = 0.008); also, radial and longitudinal stress of the multi-vessel CAD group was significantly higher than the control group (P = 0.01 and P = 0.005, respectively). All stress parameters of the multi-vessel CAD group were statistically significant compared to the control group for the Mirsky model. Receiver operating characteristics curve analysis was shown the circumferential stress of multi-vessel CAD with an area under the curve (AUC) of 0.736 for the Ghista model and an AUC of 0.742 for the Mirsky model.

Conclusion

These results indicated that Ghista and Mirsky model estimates of circumferential passive stress were the potential biomechanical markers to predict patients with multi-vessel CAD. It could be a noninvasive and helpful tool to quantify the contractility of LV.

Atlas-Based Evaluation of Hemodynamic in Ascending Thoracic Aortic Aneurysms

Atlas-based analyses of patients with cardiovascular diseases have recently been explored to understand the mechanistic link between shape and pathophysiology. The construction of probabilistic atlases is based on statistical shape modeling (SSM) to assess key anatomic features for a given patient population. Such an approach is relevant to study the complex nature of the ascending thoracic aortic aneurysm (ATAA) as characterized by different patterns of aortic shapes and valve phenotypes. This study was carried out to develop an SSM of the dilated aorta with both bicuspid aortic valve (BAV) and tricuspid aortic valve (TAV), and then assess the computational hemodynamic of virtual models obtained by the deformation of the mean template for specific shape boundaries (i.e., ±1.5 standard deviation, σ). Simulations demonstrated remarkable changes in the velocity streamlines, blood pressure, and fluid shear stress with the principal shape modes such as the aortic size (Mode 1), vessel tortuosity (Mode 2), and aortic valve morphologies (Mode 3). The atlas-based disease assessment can represent a powerful tool to reveal important insights on ATAA-derived hemodynamic, especially for aneurysms which are considered to have borderline anatomies, and thus challenging decision-making. The utilization of SSMs for creating probabilistic patient cohorts can facilitate the understanding of the heterogenous nature of the dilated ascending aorta.

Transmural Distribution of Coronary Perfusion and Myocardial Work Density Due to Alterations in Ventricular Loading, Geometry and Contractility

Myocardial supply changes to accommodate the variation of myocardial demand across the heart wall to maintain normal cardiac function. A computational framework that couples the systemic circulation of a left ventricular (LV) finite element model and coronary perfusion in a closed loop is developed to investigate the transmural distribution of the myocardial demand (work density) and supply (perfusion) ratio. Calibrated and validated against measurements of LV mechanics and coronary perfusion, the model is applied to investigate changes in the transmural distribution of passive coronary perfusion, myocardial work density, and their ratio in response to changes in LV contractility, preload, afterload, wall thickness, and cavity volume. The model predicts the following: (1) Total passive coronary flow varies from a minimum value at the endocardium to a maximum value at the epicardium transmurally that is consistent with the transmural distribution of IMP; (2) Total passive coronary flow at different transmural locations is increased with an increase in either contractility, afterload, or preload of the LV, whereas is reduced with an increase in wall thickness or cavity volume; (3) Myocardial work density at different transmural locations is increased transmurally with an increase in either contractility, afterload, preload or cavity volume of the LV, but is reduced with an increase in wall thickness; (4) Myocardial work density-perfusion mismatch ratio at different transmural locations is increased with an increase in contractility, preload, wall thickness or cavity volume of the LV, and the ratio is higher at the endocardium than the epicardium. These results suggest that an increase in either contractility, preload, wall thickness, or cavity volume of the LV can increase the vulnerability of the subendocardial region to ischemia.

Non-invasive Global and Regional Myocardial Work Predicts High-Risk Stable Coronary Artery Disease Patients With Normal Segmental Wall Motion and Left Ventricular Function

Background: Previous studies suggested that myocardial work (MW) may identify abnormalities in the left ventricular (LV) function and establish a more sensitive index for LV dysfunction at the early stage. This study aimed to explore the value of global and regional MW parameters in predicting high-risk stable coronary artery disease (SCAD) patients with normal wall motion and preserved LV function. Patients and Methods: A total of 131 patients, who were clinically diagnosed as SCAD with normal wall motion and LV function, were finally included in this study. Global MW parameters, including global work index (GWI), global constructive work (GCW), global waste work (GWW), and global work efficiency (GWE) were measured with non-invasive LV pressure-strain loops constructed from speckle-tracking echocardiography. Regional myocardial work index (RWI) and work efficiency (RWE) were also calculated according to the perfusion territory of each major coronary artery. All patients underwent coronary angiography and were divided into the high-risk SCAD group, the non-high-risk SCAD group, and the No SCAD group according to the range and degrees of coronary arteries stenosis. Results: The global longitudinal strain (GLS), GWI and GCW were statistically different (P < 0.001) among the three groups. In the high-risk SCAD group, GLS, GWI, and GCW were significantly lower than the other two groups (P < 0.05). Receiver operating characteristic analysis demonstrated GWI and GCW could predict high-risk SCAD at a cutoff value of 1,808 mm Hg% (sensitivity, 52.6%; specificity, 87.8%; predictive positive value, 76.3%; predictive negative value, 69.9%) and 2,308 mm Hg% (sensitivity, 80.7%; specificity, 64.9%; predictive positive value, 63.3%; predictive negative value, 80.0%), respectively. Multivariate analyses showed that carotid plaque, decreased GWI, and GCW was independently related to high-risk SCAD. The cutoff values of RWI_LAD, RWI_LCX, and RWI_RCA were 2,156, 1,929, and 1,983 mm Hg% in predicting high-risk SCAD, respectively (P < 0.001). When we combined RWI in two or three perfusion regions, the diagnostic performance of SCAD was improved (P < 0.001). Conclusions: Both global and regional MW parameters have great potential in non-invasively predicting high-risk SCAD patients with normal wall motion and preserved LV function, contributing to the early identification of high-risk patients who may benefit from revascularization therapy.

Novel Methodology for Measuring Regional Myocardial Efficiency

Our approach differs from the usual global measure of cardiac efficiency by using PET/MRI to measure efficiency of small pieces of cardiac tissue whose limiting size is equal to the spatial resolution of the PET scanner. We initiated a dynamic cardiac PET study immediately prior to the injection of 15.1 mCi of ¹¹C-acetate acquiring data for 25 minutes while simultaneously acquiring MRI cine data. 1) A 3D finite element (FE) biomechanical model of the imaged heart was constructed by utilizing nonrigid deformable image registration to alter the Dassault Systèmes FE Living Heart Model (LHM) to fit the geometry in the cardiac MRI cine data. The patient specific FE cardiac model with estimates of stress, strain, and work was transformed into PET/MRI format. 2) A 1-tissue compartment model was used to calculate wash-in (K₁) and the linear portion of the decay in the PET ¹¹C-acetate time activity curve (TAC) was used to calculate the wash-out k₂(mono) rate constant. K₁ was used to calculate blood flow and k₂(mono) was used to calculate myocardial volume oxygen consumption ( MVO₂ ). 3) Estimates of stress and strain were used to calculate Myocardial Equivalent Minute Work ( MEMW ) and Cardiac Efficiency = MEMW/MVO₂ was then calculated for 17 tissue segments of the left ventricle. The global MBF was 0.96 ± 0.15 ml/min/gm and MVO₂ ranged from 8 to 17 ml/100gm/min. Six central slices of the MRI cine data provided a range of MEMW of 0.1 to 0.4 joules/gm/min and a range of Cardiac Efficiency of 6 to 18%.

A publicly available virtual cohort of four-chamber heart meshes for cardiac electro-mechanics simulations

Computational models of the heart are increasingly being used in the development of devices, patient diagnosis and therapy guidance. While software techniques have been developed for simulating single hearts, there remain significant challenges in simulating cohorts of virtual hearts from multiple patients. To facilitate the development of new simulation and model analysis techniques by groups without direct access to medical data, image analysis techniques and meshing tools, we have created the first publicly available virtual cohort of twenty-four four-chamber hearts. Our cohort was built from heart failure patients, age 67±14 years. We segmented four-chamber heart geometries from end-diastolic (ED) CT images and generated linear tetrahedral meshes with an average edge length of 1.1±0.2mm. Ventricular fibres were added in the ventricles with a rule-based method with an orientation of -60° and 80° at the epicardium and endocardium, respectively. We additionally refined the meshes to an average edge length of 0.39±0.10mm to show that all given meshes can be resampled to achieve an arbitrary desired resolution. We ran simulations for ventricular electrical activation and free mechanical contraction on all 1.1mm-resolution meshes to ensure that our meshes are suitable for electro-mechanical simulations. Simulations for electrical activation resulted in a total activation time of 149±16ms. Free mechanical contractions gave an average left ventricular (LV) and right ventricular (RV) ejection fraction (EF) of 35±1% and 30±2%, respectively, and a LV and RV stroke volume (SV) of 95±28mL and 65±11mL, respectively. By making the cohort publicly available, we hope to facilitate large cohort computational studies and to promote the development of cardiac computational electro-mechanics for clinical applications.

Personalization of electro-mechanical models of the pressure-overloaded left ventricle: fitting of Windkessel-type afterload models

Computer models of left ventricular (LV) electro-mechanics (EM) show promise as a tool for assessing the impact of increased afterload upon LV performance. However, the identification of unique afterload model parameters and the personalization of EM LV models remains challenging due to significant clinical input uncertainties. Here, we personalized a virtual cohort of N = 17 EM LV models under pressure overload conditions. A global-local optimizer was developed to uniquely identify parameters of a three-element Windkessel (Wk3) afterload model. The sensitivity of Wk3 parameters to input uncertainty and of the EM LV model to Wk3 parameter uncertainty was analysed. The optimizer uniquely identified Wk3 parameters, and outputs of the personalized EM LV models showed close agreement with clinical data in all cases. Sensitivity analysis revealed a strong dependence of Wk3 parameters on input uncertainty. However, this had limited impact on outputs of EM LV models. A unique identification of Wk3 parameters from clinical data appears feasible, but it is sensitive to input uncertainty, thus depending on accurate invasive measurements. By contrast, the EM LV model outputs were less sensitive, with errors of less than 8.14% for input data errors of 10%, which is within the bounds of clinical data uncertainty. This article is part of the theme issue 'Uncertainty quantification in cardiac and cardiovascular modelling and simulation'.

The impact of wall thickness and curvature on wall stress in patient-specific electromechanical models of the left atrium

The left atrium (LA) has a complex anatomy with heterogeneous wall thickness and curvature. The anatomy plays an important role in determining local wall stress; however, the relative contribution of wall thickness and curvature in determining wall stress in the LA is unknown. We have developed electromechanical finite element (FE) models of the LA using patient-specific anatomical FE meshes with rule-based myofiber directions. The models of the LA were passively inflated to 10mmHg followed by simulation of the contraction phase of the atrial cardiac cycle. The FE models predicted maximum LA volumes of 156.5 mL, 99.3 mL and 83.4 mL and ejection fractions of 36.9%, 32.0% and 25.2%. The median wall thickness in the 3 cases was calculated as [Formula: see text] mm, [Formula: see text] mm, and [Formula: see text] mm. The median curvature was determined as [Formula: see text] [Formula: see text], [Formula: see text], and [Formula: see text]. Following passive inflation, the correlation of wall stress with the inverse of wall thickness and curvature was 0.55-0.62 and 0.20-0.25, respectively. At peak contraction, the correlation of wall stress with the inverse of wall thickness and curvature was 0.38-0.44 and 0.16-0.34, respectively. In the LA, the 1st principal Cauchy stress is more dependent on wall thickness than curvature during passive inflation and both correlations decrease during active contraction. This emphasizes the importance of including the heterogeneous wall thickness in electromechanical FE simulations of the LA. Overall, simulation results and sensitivity analyses show that in complex atrial anatomy it is unlikely that a simple anatomical-based law can be used to estimate local wall stress, demonstrating the importance of FE analyses.

Fluid Structure Interaction on Paravalvular Leakage of Transcatheter Aortic Valve Implantation Related to Aortic Stenosis: A Patient-Specific Case

This study investigated the impact of paravalvular leakage (PVL) in relation to the different valve openings of the transcatheter aortic valve implantation (TAVI) valve using the fluid structure interaction (FSI) approach. Limited studies were found on the subject of FSI with regards to TAVI-PVL condition, which involves both fluid and structural responses in coupling interaction. Hence, further FSI simulation with the two-way coupling method is implemented to investigate the effects of hemodynamics blood flow along the patient-specific aorta model subjected to the interrelationship between PVL and the different valve openings using the established FSI software ANSYS 16.1. A 3D patient-specific aorta model is constructed using MIMICS software. The TAVI valve identical to Edward SAPIEN XT 26 (Edwards Lifesciences, Irvine, California), at different Geometrical Orifice Areas (GOAs), is implanted into the patient's aortic annulus. The leaflet opening of the TAVI valve is drawn according to severity of GOA opening represented in terms of 100%, 80%, 60%, and 40% opening, respectively. The result proved that the smallest percentage of GOA opening produced the highest possibility of PVL, increased the recirculatory flow proximally to the inner wall of the ascending aorta, and produced lower backflow velocity streamlines through the side area of PVL region. Overall, 40% GOA produced 89.17% increment of maximum velocity magnitude, 19.97% of pressure drop, 65.70% of maximum WSS magnitude, and a decrement of 33.62% total displacement magnitude with respect to the 100% GOA.

Automating image-based mesh generation and manipulation tasks in cardiac modeling workflows using Meshtool

Advanced cardiac modeling studies rely on the ability to generate and functionalize personalized in silico models from tomographic multi-label image stacks. Eventually, this is used for building virtual cohorts that capture the variability in size, shape, and morphology of individual hearts. Typical modeling workflows involve a multitude of interactive mesh manipulation steps, rendering model generation expensive. Meshtool is software specifically designed for automating all complex mesh manipulation tasks emerging in such workflows by implementing algorithms for tasks describable as operations on label fields and/or geometric features. We illustrate how Meshtool increases efficiency and reduces costs by offering an automatable, high performance mesh manipulation toolbox.

Surrogates for myocardial power and power efficiency in patients with aortic valve disease

We aimed to assess surrogate markers for left ventricular (LV) myocardial power and efficiency in patients with isolated aortic stenosis (AS) and combined stenosis/regurgitation (AS/AR). In AS (n = 59), AS/AR (n = 21) and controls (n = 14), surrogates for LV myocardial power and circulatory/external myocardial efficiency were obtained from cardiac MRI. Median surrogate LV myocardial power was increased in AS, 7.7 W/m² (interquartile range 6.0–10.2; p = 0.010) and AS/AR, 10.8 W/m² (8.9–13.4; p < 0.001) when compared to controls, 5.4 W/m² (4.2–6.5), and was lower in AS than AS/AR (p < 0.001). Surrogate circulatory efficiency was decreased in AS, 8.6% (6.8–11.1; p < 0.001) and AS/AR, 5.4% (4.1–6.2; p < 0.001) when compared to controls, 11.8% (9.8–16.9). Surrogate external myocardial efficiency was higher in AS, 15.2% (11.9–18.6) than in AS/AR, 12.2% (10.1–14.2; p = 0.031) and was significantly lower compared to controls, 12.2% (10.7–18.1) in patients with reduced ejection fraction (EF), 9.8% (8.1–11.7; p = 0.025). In 16% of all cases, left ventricular mass/volume indices and EF were within normal ranges, wheras surrogate LV myocardial power was elevated and patients were symptomatic. Although influenced by pressure/volume load, the myocardium is additionally affected by remodelling processes. Surrogates for circulatory efficiency and LV myocardial power gradually reflect alterations in patients with AS and AS/AR, even when surrogate external myocardial efficiency, EF, mass and volume indices still remain compensated.

A magnetics-based approach for fine-tuning afterload in engineered heart tissues

Afterload plays important roles during heart development and disease progression, however, studying these effects in a laboratory setting is challenging. Current techniques lack the ability to precisely and reversibly alter afterload over time. Here, we describe a magnetics-based approach for achieving this control and present results from experiments in which this device was employed to sequentially increase afterload applied to rat engineered heart tissues (rEHTs) over a 7-day period. The contractile properties of rEHTs grown on control posts marginally increased over the observation period. The average post deflection, fractional shortening, and twitch velocities measured for afterload-affected tissues initially followed this same trend, but fell below control tissue values at high magnitudes of afterload. However, the average force, force production rate, and force relaxation rate for these rEHTs were consistently up to 3-fold higher than in control tissues. Transcript levels of hypertrophic or fibrotic markers and cell size remained unaffected by afterload, suggesting that the increased force output was not accompanied by pathological remodeling. Accordingly, the increased force output was fully reversed to control levels during a stepwise decrease in afterload over 4 hours. Afterload application did not affect systolic or diastolic tissue lengths, indicating that the afterload system was likely not a source of changes in preload strain. In summary, the afterload system developed herein is capable of fine-tuning EHT afterload while simultaneously allowing optical force measurements. Using this system, we found that small daily alterations in afterload can enhance the contractile properties of rEHTs, while larger increases can have temporary undesirable effects. Overall, these findings demonstrate the significant role that afterload plays in cardiac force regulation. Future studies with this system may allow for novel insights into the mechanisms that underlie afterload-induced adaptations in cardiac force development.

Non-invasive myocardial performance mapping using 3D echocardiographic stress-strain loops

Regional contribution to left ventricular (LV) ejection is of much clinical importance but its assessment is notably challenging. While deformation imaging is often used, this does not take into account loading conditions. Recently, a method for intraventricular pressure estimation was proposed, thus allowing for loading conditions to be taken into account in a non-invasive way. In this work, a method for 3D automatic myocardial performance mapping in echocardiography is proposed by performing 3D myocardial segmentation and tracking, thus giving access to local geometry and strain. This is then used to assess local LV stress-strain relationships which can be seen as a measure of local myocardial work. The proposed method was validated against ¹⁸F-fluorodeoxyglucose positron emission tomography, the reference method to clinically assess local metabolism. Averaged over all patients, the mean correlation between FDG-PET and the proposed method was [Formula: see text]. In conclusion, stress-strain loops were, for the first time, estimated from 3D echocardiography and correlated to the clinical gold standard for local metabolism, showing the future potential of real-time 3D echocardiography (RT3DE) for the assessment of local metabolic activity of the heart.