Smoothed finite element methods in simulation of active contraction of myocardial tissue samples

In modelling and simulation of cardiac mechanics, tetrahedral meshes are often used due to the easy availability of efficient meshing algorithms. This is beneficial in particular when complex geometries such as cardiac structures are considered. The gold standard in simulating the cardiac cycle is to solve the mechanical balance equations with the finite element method (FEM). However, using linear shape functions in the FEM in combination with nearly-incompressible material models is known to produce overly stiff approximations, whereas higher order elements are computationally more expensive. To overcome these problems, smoothed finite element methods (S-FEMs) have been proposed by Liu and co-workers. So far, S-FEMs in 3D have been utilised only in simulations of passive mechanics. In the present work, different S-FEMs are for the first time used for simulation of an active cardiac contraction on three-dimensional myocardial tissue samples. Further, node-based S-FEM (NS-FEM), face-based S-FEM (FS-FEM) and selective FS/NS-FEM are for the first time implemented as user subroutine in the commercial software Abaqus. Our results confirm that all S-FEMs perform softer than linear FEM and volumetric locking is reduced. The FS/NS-FEM produces solutions with the relative error in maximum displacement and rotation being less than 5% with respect to the reference solution obtained by the quadratic FEM for all considered mesh sizes, although linear shape functions are used. We therefore conclude that in particular FS/NS-FEM is an efficient and accurate numerical method in the simulation of an active cardiac muscle contraction.

The value of the spatial QRS-T angle for assessing the severity of heart damage in patients with arterial hypertension

Aim      To study the relationship between clinical, echocardiographic, and laboratory indexes with increased QRS-T spatial angle (sQRS-T) in patients with arterial hypertension (AH).Material and methods  The study included 160 patients with AH, 61 (38 %) men and 99 (62 %) women aged 58 [49; 67] years. Patients with ischemic heart disease or His bundle blocks were not included. Echocardiography was used to determine the left ventricular end-diastolic dimension (LV EDD), left ventricular posterior wall thickness (LVPWT), interventricular septal thickness (IVST), relative wall thickness (RWT), left ventricular myocardial mass (LVMM), and LVMM index (LVMMI). Also, the following indexes were analyzed: office systolic and diastolic blood pressure (SBP, DBP), disease duration, body mass index, plasma levels of glucose, cholesterol, and creatinine, and glomerular filtration rate. The QRS-T spatial angle was calculated as an angle between the integral vectors QRS and T using a vectorcardiogram derived from a 12-lead digital electrocardiogram. Data are presented as median (25th percentile; 75th percentile].Results The QRS-T spatial angle for the group was 65 [43; 90]°. The QRS-T spatial angle increased with increases in the AH grade (grade 1 AH, 55 [37; 74]°; grade 2 AH, 60 [41; 82]°; grade 3 AH, 88 [62; 107]°; р<0.0001); the AH stage (stage 1, 50 [41; 77]°; stage 2, 68 [44; 93]°; stage 3, 78 [59; 110]°; р=0.0002), and the cardiovascular risk degree (low and moderate risk, 49 [37; 70]°, high risk, 62 [43; 88]° (р=0.005); very high risk, 88 [61; 117]° vs. high risk, 62 [43; 88]° (р=0.0002). The QRS-T spatial angle was greater with diabetes mellitus (78 [60; 117]°) than without it (63 [43; 89]°) (р=0.03). Weak but significant correlations were found between sQRS-T and body mass index (r=0.2; p<0.01), SBP (r=0.4; p<0.0001), DBP (r=0.2; p<0.01), LV EDD (r=0.2; p<0.01), LV PWT (r=0.3; p<0.001), IVST (r=0.3; p<0.001), LVMM (r=0.3; p<0.001), LVMMI (r=0.3; p<0.001), and blood glucose (r=0.2; p<0.01).Conclusion      In patients with AH, a large QRS-T spatial angle is related with significantly higher values of SBP and DBP, LV dimension, blood glucose, and body mass index.

[Factors Associated with the Increase in Spatial and Frontal QRS-T Angles in Patients with Inferior Myocardial Infarction]

Aim      To identify clinical, echocardiographic, and angiographic factors related with an increase in the frontal QRS-T angle (fQRS-T) and the spatial QRS-T angle (sQRS-T) in patients with inferior myocardial infarction.Material and methods  The study included 128 patients aged (median [25th percentile; 75th percentile]) 59.5 [51.5; 67.0] years diagnosed with inferior wall acute myocardial infarction. fQRS-T was calculated as a module of difference between the QRS axis and the Т axis in the frontal plane. sQRS-T was calculated by a synthesized vectorcardiogram as a spatial angle between the QRS and Т integral vectors.Results The fQRS-T for the group was 54.0 [18; 80] and sQRS-T was 80.1 [53; 110]. The correlation coefficient for fQRS-T and sQRS-T values was 0.42 (p<0.001). Both fQRS-T >80° and sQRS-T >110° compared to their lower values were associated with a higher frequency of history of postinfarction cardiosclerosis (44% and 12 %, respectively; p<0.05), a lower left ventricular ejection fraction (51 [47; 60]% at fQRS-T >80° and 55 [50; 60]% at fQRS-T <80° (p<0,05); 49 [44; 57]% at sQRS-T >110° and 57 [51; 60] % at sQRS-T <110° (p<0.01); more frequent development of acute heart failure (16 and 2 %, respectively; p<0.05); and early postinfarction angina (13 and 2 %, respectively; p<0.05). The increased fQRS-T was associated with a higher incidence of damage to the circumflex artery (45 and 20 %, respectively; p<0.05). The increased sQRS-T was associated with a history of arterial hypertension (97 and 76 %, respectively; p<0.05), chronic heart failure (22 and 3 %, respectively; p<0.05), chronic kidney disease (19 and 4 %, respectively; p<0.05), and a larger myocardial lesion (mean number of damaged segments by echocardiography was 3.8 [2; 6] at sQRS-T >110° and 2.6 [1; 4] at sQRS-T <110°; p<0.01). sQRS-T was significantly greater in multivascular damage (87 [68; 121]° than in one- or two-vascular damage (72 [51; 100]°; p<0.05). sQRS-T values were significantly lower with spontaneous reperfusion (66 [29; 79] than without spontaneous reperfusion (77 [55; 115]°; p<0.05).Conclusion      In patients after inferior wall acute myocardial infarction, increases in fQRS-T and sQRS-T were associated with more severe damage of coronary vasculature, decreased left ventricular ejection fraction, and more severe course of disease.

Correlation between global longitudinal strain and QRS voltage on electrocardiogram in patients with left ventricular hypertrophy

PURPOSE

Left ventricular hypertrophy (LVH) is as an independent risk factor. Discrepancies were reported between LV mass (LVM) estimated by echocardiography and electrocardiography (ECG) findings. We hypothesized that QRS voltage criteria may reflect not only anatomical changes (LVM) but also changes in LV function and we tested the relationship between QRS voltage and echocardiographic parameters of LV function in patients (pts) with different types of LVH.

METHODS

We prospectively enrolled pts with LVH and preserved ejection fraction (LVEF >50%): 20 pts with isolated arterial hypertension, HTN, 20 pts with severe aortic stenosis, AS (indexed aortic valve area <0.6 cm(2)/m(2)), and 20 pts with symmetric hypertrophic cardiomyopathy, HCM. Standard 12-lead ECG (including Sokolow and Cornell voltage indices) and a comprehensive two-dimensional (2D) echocardiography were performed in all. Left ventricular mass was calculated according to Devereux formula. Global longitudinal strain (GLS) was assessed by speckle tracking echocardiography.

RESULTS

A significant correlation was found between both ECG indices and LVM assessed by echocardiography. Moreover, significant correlations were found between Sokolow-Lyon voltage and LVEF (r = 0.26; P = 0.03), GLS (r = 0.59; P < 0.001) and E/e' average (r = 0.43; P < 0.001). Cornell voltage index correlated significantly only with GLS. In multivariable analysis GLS emerged as the only independent correlate of both Sokolow-Lyon (ß = 0.6, P < 0.001) and Cornell voltage indices (ß = 0.45, P < 0.001).

CONCLUSION

These findings suggest that in pts with LVH, ECG should no longer be used only as a surrogate method for LVM estimation (structural changes only), but rather as an investigation complementary to imaging, incorporating information on overall LV remodeling (changes in structure and function).

Global and regional longitudinal strain assessed by two-dimensional speckle tracking echocardiography identifies early myocardial dysfunction and transmural extent of myocardial scar in patients with acute ST elevation myocardial infarction and relatively preserved LV function

AIMS

Global and regional longitudinal strain (GLS-RLS) assessed by two-dimensional speckle tracking echocardiography (2D-STE) are considered reliable indexes of left-ventricular (LV) function and myocardial viability in chronic ischaemic patients when compared with delayed-enhanced cardiac magnetic resonance (DE-CMR). In the present study, we tested whether GLS and RLS could also identify early myocardial dysfunction and transmural extent of myocardial scar in patients with acute ST elevation myocardial infarction (STEMI) and relatively preserved LV function.

METHODS AND RESULTS

Twenty STEMI patients with LVEF ≥40%, treated with PPCI within 6 h from symptoms onset, underwent DE-CMR and 2D-echocardiography for 2D-STE analysis 6 ± 2 days after STEMI. Wall motion score index (WMSI) and LV ejection fraction (LVEF) were calculated by both methods. Infarct size and transmural extent of necrosis were assessed by CMR. GLS and RLS were obtained by 2D-STE. Mean GLS of the study population was -14 ± 3.3, showing a significant correlation with both LVEF and WMSI, by CMR (r = -0.86, P = 0.001, and r = 0.80, P = 0.001, respectively) and time-to-PCI (r = 0.66, P = 0.038). A weaker correlation was found between GLS and LVEF and WMSI assessed by 2D-echo (r = -0.65, P = 0.001, and r = 0.53, P = 0.013, respectively). RLS was significantly lower in DE-segments when compared with normal myocardium (P < 0.0001). A cut-off value of RLS of -12.3% by receiver-operating characteristic (ROC) curves identified DE-segments (sensitivity 82%, specificity 78%), whereas a cut-off value of -11.5% identified transmural extent of DE (sensitivity 75%, specificity 78%).

CONCLUSION

Our findings indicate that RLS and GLS evaluation provides an accurate assessment of global myocardial function and of the presence of segments with transmural extent of necrosis, with several potential clinical implications.