Correction to: Scientific Reportshttps://doi.org/10.1038/s41598-023-44588-4, published online 17 October 2023 The original version of this Article contained errors. An error in the pulse repetition frequency (PRF) of the imaging sequence was discovered during subsequent analysis of the data. Acoustic verification of the original acquisition script confirmed the incorrect PRF. Although the relative comparisons in the study remain valid because the PRF error was the same across all conditions, the absolute wave speed values require correction with a factor 0.901 to ensure scientific accuracy. As the result, in Materials and methods section, under ‘Shear wave elastography’ subheading, “One SWE sequence consisted of 1.5 - 2 s recording time in which multiple individual SWE acquisitions were performed at intervals of 28 ms (34 SWE acquisitions per second), as illustrated in the first row of Fig. 2.” now reads: “One SWE sequence consisted of 1.7 - 2.2 s recording time in which multiple individual SWE acquisitions were performed at intervals of 32 ms (31 SWE acquisitions per second), as illustrated in the first row of Fig. 2.” “The resulting shear wave propagation was consecutively recorded at a minimal frame rate of 6.2 kHz using diverging wave imaging.” now reads: “The resulting shear wave propagation was consecutively recorded at a minimal frame rate of 5.6 kHz using diverging wave imaging.” As the result, Figure 2 and its legend were incorrect. The original Figure 2 and accompanying legend appear below. (Figure presented.) Shear wave elastography (SWE) sequence and postprocessing workflow. First row: schematic of a SWE imaging sequence, consisting of SWE acquisitions that were taken at 34 Hz during 1.5–2 s. Second row: schematic of an ECG signal. Third row: tissue velocity panels along the septum for different acquisitions at different time points, together with shear wave speed estimation. Fourth row: Shear wave speed data for three different SWE sequences at one intervention stage. The last panel demonstrates the procedure of obtaining diastolic and systolic shear wave propagation speed (SWS_dia and SWS_sys) via piecewise linear model fitting. Different colors of grey represent different heartbeats. Spread of estimated wave speed at one time point represents variability across 10 anatomical M-lines drawn by the 2 observers. Figure 2 legend, “Shear wave elastography (SWE) sequence and postprocessing workflow. First row: schematic of a SWE imaging sequence, consisting of SWE acquisitions that were taken at 34 Hz during 1.5–2 s. Second row: schematic of an ECG signal. Third row: tissue velocity panels along the septum for different acquisitions at different time points, together with shear wave speed estimation. Fourth row: Shear wave speed data for three different SWE sequences at one intervention stage. The last panel demonstrates the procedure of obtaining diastolic and systolic shear wave propagation speed (SWS_dia and SWS_sys) via piecewise linear model fitting. Different colors of grey represent different heartbeats. Spread of estimated wave speed at one time point represents variability across 10 anatomical M-lines drawn by the 2 observers.” now reads: “Shear wave elastography (SWE) sequence and postprocessing workflow. First row: schematic of a SWE imaging sequence, consisting of SWE acquisitions that were taken at 31 Hz during 1.7-2.2 s. Second row: schematic of an ECG signal. Third row: tissue velocity panels along the septum for different acquisitions at different time points, together with shear wave speed estimation. Fourth row: Shear wave speed data for three different SWE sequences at one intervention stage. The last panel demonstrates the procedure of obtaining diastolic and systolic shear wave propagation speed (SWSdia and SWSsys) via piecewise linear model fitting. Different colors of grey represent different heartbeats. Spread of estimated wave speed at one time point represents variability across 10 anatomical M-lines drawn by the 2 observers.” In the Results section, under the subheading ‘Diastolic wave speed’, “The diastolic wave speed for the different interventions is summarized in Fig. 5a, with a wave speed of 1.3 m/s in baseline. Significant changes in wave speed were only observed after ischemia injury (+ 57%), whereas other interventions did not significantly alter the wave speed (− 18% in preload decrease, + 5% in afterload increase, + 4% in preload increase and + 94% after reperfusion).” now reads: “The diastolic wave speed for the different interventions is summarized in Figure 5a, with a wave speed of 1.2 m/s in baseline. Significant changes in wave speed were only observed after ischemia injury (+57%), whereas other interventions did not significantly alter the wave speed (-17% in preload decrease, +5% in afterload increase, +4% in preload increase and +94% after reperfusion).” “A similar correlation is found between SWS and operational chamber stiffness dP/dV (R = 0.57; p < 0.01 in Fig. 6b). SWE measurements during and after I/R injury—as depicted in orange in Fig. 6—showed a strong significant correlation to EDP (R = 0.68; p < 0.01), operational chamber stiffness dP/dV (R = 0.73; p < 0.01) and stiffness constant β (R = 0.50; p = 0.03). Diastolic wave speed is more sensitive to changes in intrinsic stiffness than in loading, as reflected by the larger slope of the regression line (0.8 vs. 0.35 in Fig. 6b).” now reads: “A similar correlation is found between SWS and operational chamber stiffness dP/dV (R=0.54; p<0.01 in Figure 6b). SWE measurements during and after I/R injury – as depicted in orange in Figure 6 – showed a strong significant correlation to EDP (R=0.68; p<0.01), operational chamber stiffness dP/dV (R=0.73; p<0.01) and stiffness constant β (R=0.50; p=0.036). Diastolic wave speed is more sensitive to changes in intrinsic stiffness than in loading, as reflected by the larger slope of the regression line (0.73 vs. 0.29 in Figure 6b).” As the result, Figures 4, 5, 6 and 8 were incorrect. The original Figures 4, 5, 6 and 8 and accompanying legends appear below. (Figure presented.) (Figure presented.) (Figure presented.) (Figure presented.) Variability of shear wave speed (SWS) estimation. (a) Example of low variability and good fit. (b) Example of high variability and moderate fit. (c) Averaged relative wave speed deviation from fit for all pigs is depicted for each condition and diastole/systole. Diastolic and systolic wave speeds for the different interventions: baseline (BL), preload decrease (PD), afterload increase (AI), preload increase (PI), myocardial ischemia (MI) and reperfusion (RP). *p < 0.05 for t-test with Bonferroni correction. Correlations of diastolic and systolic wave speed, with (a) end-diastolic pressure (EDP), (b) operational stiffness (dP/dV), (c) stiffness constant β, (d) end-systolic pressure (ESP) and (e) preload-recruitable stroke work (PRSW) during loading (blue) and stiffness interventions (orange). Correlation between diastolic wave speed and operational chamber stiffness (dP/dV) and between wave speed ratio and preload-recruitable stroke work (PRSW) for all interventions. Additionally, Table 2 was incorrect. The original Table 2 and accompanying legends appear below. (Table presented.) Linear regression results between diastolic wave speed (SWS_dia) and end-diastolic pressure (EDP) on one hand and systolic wave speed (SWS_sys) and end-systolic pressure (ESP) on the other hand during loading interventions, with goodness of fit R². Pig # SWS_dia vs. EDP SWS_sys vs. ESP Slope (m/s/mmHg) Intercept (m/s) R² Slope (m/s/mmHg) Intercept (m/s) R² 1 0.011 1.1 0.92 0.019 1.6 0.93 2 0.026 1.3 0.92 0.017 1.7 0.99 3 0.016 1.1 0.93 0.024 1.4 0.95 4 0.021 1.1 0.53 0.026 1.7 0.997 5 0.018 1.3 0.60 0.012 2.8 0.85 6 0.014 1.3 0.81 0.024 1.6 0.91 7 0.014 1.2 0.70 0.019 2.2 0.94 Mean 0.017 ± 0.005 1.2 ± 0.1 0.77 ± 0.17 0.020 ± 0.005 1.9 ± 0.5 0.94 ± 0.05 Under the subheading ‘Systolic wave speed’, “Figure 5b shows the resulting systolic wave speed for all interventions, with a wave speed of 3.9 m/s at baseline. The individual correlations with ESP are given in Table 2, and show in general a slightly higher goodness-of-fit (R²) than for the diastolic measurements, probably due to the limited sensitivity of the manual wave speed estimator to detect differences in speed (ΔSWS_dia = 0.37 m/s vs. ΔSWS_sys = 1.27 m/s).” now reads: “Figure 5b shows the resulting systolic wave speed for all interventions, with a wave speed of 3.5 m/s at baseline. The individual correlations with ESP are given in Table 2, and show in general a slightly higher goodness-of-fit (R²) than for the diastolic measurements, probably due to the limited sensitivity of the manual wave speed estimator to detect differences in speed (ΔSWS_dia = 0.33 m/s vs. ΔSWS_sys = 1.14 m/s).” In the Discussion section, under the subheading ‘Myocardial operational stiffness’, “Our study confirms this earlier research: the change in the stiffness constant β of the EDPVR increased after the ischemia period (0.073 vs. 0.045 1/ml; p = 0.06) and increased even further after the reperfusion period (0.087 vs. 0.045 1/ml; p < 0.05), which was reflected in the change of diastolic wave speed after ischemia injury (2.0 vs. 1.3 m/s; p < 0.05) and reperfusion injury (2.5 m/s). The difference in the slopes of the fitted linear regression curves in Fig. 6b (0.80 vs. 0.35) suggests that diastolic speed is more sensitive to changes in intrinsic characteristics than changes in loading.” now reads: “Our study confirms this earlier research: the change in the stiffness constant β of the EDPVR increased after the ischemia period (0.073 vs. 0.045 1/ml; p = 0.06) and increased even further after the reperfusion period (0.087 vs. 0.045 1/ml; p < 0.05), which was reflected in the change of diastolic wave speed after ischemia injury (1.8 vs. 1.2 m/s; p < 0.05) and reperfusion injury (2.3 m/s). The difference in the slopes of the fitted linear regression curves in Figure 6b (0.73 vs. 0.29) suggests that diastolic speed is more sensitive to changes in intrinsic characteristics than changes in loading.” Under the subheading ‘Contractility’, “However, systolic wave speed increased significantly after ischemia injury (4.9 vs. 3.9 m/s; p = 0.01 in Fig. 6c), which does not correspond with the observed decline in contractility in terms of pressure–volume measures after the I/R injury (see Table 1).” now reads: “However, systolic wave speed increased significantly after ischemia injury (4.4 vs. 3.5 m/s; p=0.01 in Figure 5b), which does not correspond with the observed decline in contractility in terms of pressure-volume measures after the I/R injury (see Table 1).” Further, in the original version of this Article Jürgen Duchenne was incorrectly affiliated with Affiliation 4. Their correct affiliation is Affiliation 5: 5. Cardiology, KU Leuven, Leuven, Belgium Finally, the Funding section was incomplete, “This work was supported by the Research Foundation Flanders (FWO, Brussels, Belgium) under Grant 1211620N to Annette Caenen and, Grants G092318N and 1832922N to Jens-Uwe Voigt. This work is also part of the TTW–Dutch Heart Foundation partnership program ‘Earlier recognition of cardiovascular diseases’ with project number 14740.” now reads: "This work was supported by the Research Foundation Flanders (FWO, Brussels, Belgium) under Grant 1211620N to Annette Caenen and, Grants G092318N and 1832922N to Jens-Uwe Voigt and Grant 12ZZN22N to Jürgen Duchenne. This work is also part of the TTW–Dutch Heart Foundation partnership program ‘Earlier recognition of cardiovascular diseases’ with project number 14740." The original Article has been corrected.

Shear wave elastography (SWE) has the potential to determine cardiac tissue stiffness from non-invasive shear wave speed measurements, important, e.g., for predicting heart failure. Previous studies showed that waves traveling in the interventricular septum (IVS) may display Lamb-like dispersive behaviour, introducing a thickness-frequency dependency in the wave speed. However, the IVS tapers across its length, which complicates wave speed estimation by introducing an additional variable to account for. The goal of this work is to assess the impact of tapering thickness on SWE. The investigation is performed by combining in vitro experiments with acoustic radiation force (ARF) and 2D finite element simulations, to isolate the effect of the tapering curve on ARF-induced and natural waves in the heart. The experiments show a 11% deceleration during propagation from the thick to the thin end of an IVS-mimicking tapered phantom plate. The numerical analysis shows that neglecting the thickness variation in the wavenumber-frequency domain can introduce errors of more than 30% in the estimation of the shear modulus, and that the exact tapering curve, rather than the overall thickness reduction, determines the dispersive behaviour of the wave. These results suggest that septal geometry should be accounted for when deriving cardiac stiffness with SWE.

Natural and active shear wave elastography (SWE) are potential ultrasound-based techniques to non-invasively assess myocardial stiffness, which could improve current diagnosis of heart failure. This study aims to bridge the knowledge gap between both techniques and discuss their respective impacts on cardiac stiffness evaluation. We recorded the mechanical waves occurring after aortic and mitral valve closure (AVC, MVC) and those induced by acoustic radiation force throughout the cardiac cycle in four pigs after sternotomy. Natural SWE showed a higher feasibility than active SWE, which is an advantage for clinical application. Median propagation speeds of 2.5–4.0 m/s and 1.6–4.0 m/s were obtained after AVC and MVC, whereas ARF-based median speeds of 0.9–1.2 m/s and 2.1–3.8 m/s were reported for diastole and systole, respectively. The different wave characteristics in both methods, such as the frequency content, complicate the direct comparison of waves. Nevertheless, a good match was found in propagation speeds between natural and active SWE at the moment of valve closure, and the natural waves showed higher propagation speeds than in diastole. Furthermore, the results demonstrated that the natural waves occur in between diastole and systole identified with active SWE, and thus represent a myocardial stiffness in between relaxation and contraction.

Different shear wave elastography methods have been proposed to measure cardiac material properties. This study compared shear waves naturally generated by aortic and mitral valve closure to those externally induced with an acoustic radiation force throughout the cardiac cycle. The shear wave timing and propagation speeds were measured in four pigs with open-chest recordings. Despite spatial and temporal differences in excitation source, the propagation speeds of the natural shear waves were found to be in the same range as the propagation speeds of the active shear waves. The results also suggested a large inter-beat variability for the natural shear waves.

Shear Wave Elastography (SWE) has been proposed to investigate cardiac health by non-invasively monitoring tissue stiffness. Previous work has shown that the plate-like geometry of the Interventricular Septum (IVS) may result in a dispersion similar to Lamb waves, complicating the link between shear wave speed and cardiac stiffness. However, the IVS is not a simple plate, e.g., its thickness tapers across its length. We have used 2-D Finite Element simulations to investigate the effects of tapering on Lamb waves. The model consists of an elastic slab immersed in water, with a thickness decreasing smoothly in space from 9 to 3 mm. Pulses with low (0-80 Hz) and high (0-700 Hz) frequency contents were used to excite natural and acoustic radiation force induced waves. The results show that natural waves can decelerate by up to 20% during propagation, leading to ambiguities in speed estimation. Moreover, neglecting tapering when fitting their dispersion curves can introduce errors in shear modulus estimation by up to 30%. In contrast, fits performed on waves with high frequency content yielded shear modulus estimations with < 5%. These results suggest that septal geometry can affect cardiac stiffness estimation performed by SWE, especially when natural waves are employed.