This study provides evidence to show that both BSI and Doppler techniques can make accurate estimations of low pressure drops in a controlled and reproducible aortic phantom. However, for stenotic conditions of clinical relevance in the setting of aortic stenosis, BSI underestimates while Doppler overestimates the pressure drop.
The assessment of the pressure drop by echocardiography in conventional clinical practice is subject to important methodological limitations that cannot be solved by current BSI technology. Significantly different pressure drop estimations, large percentage errors, bias values and wide limits of agreement exist for Doppler and BSI when compared with ground-truth pressure drop estimations. This is coupled with poor intra-technique reproducibility across two days of experiments. These findings illustrate that despite its theoretical advantages, further development of BSI or alternative novel and more comprehensive methods for pressure drop estimation are required to improve clinical practice.
Pressure drop estimation
A good agreement between pressure sensors, Doppler and BSI was found at low stenosis levels (10.5 ± 1.00 mmHg) but BSI significantly underestimated pressure drop at the next stenotic condition tested (13.3 ± 1.20 mmHg; Fig. 6). With the onset of pressure drop underestimations using BSI occurring at these low stenotic conditions, BSI in its current form is inappropriate for the classification of aortic stenosis severity, which begins at 20 mmHg [16]. BSI would likely be accurate in the estimations of trans-mitral valve pressure drop, where the upper classification limit is 10 mmHg [17]. That said, when comparing Doppler and BSI to ground-truth pressure drop estimations, the limits of agreement are wide for both methods (upper limit 14.6 mmHg, lower limit -6.74 mmHg for Doppler vs. upper limit 2.82 mmHg, lower limit -9.43 mmHg for BSI; Fig. 8). Over/underestimations of transvalvular pressure drop by these margins are clinically significant as they could lead to incorrect diagnoses and the misclassification of disease severity. The differences between the experimental conditions should only be attributed to the ability to capture the peak velocity events, since both methods used the simplified Bernoulli formulation to estimate pressure drop. Pressure sensors were used to demonstrate that comparing ground-truth pressure values, acquired using pressure sensors, to velocity-based estimations of pressure drop results in discrepancies.
At the higher pressure drops, with higher flow velocities, BSI significantly underestimates pressure drop (Fig. 6). A negative linear relationship is observed for absolute error (Fig. 7) and agreement (Fig. 8B). Absolute error at the highest flow rate was significantly different to that at the lowest flow rate (Fig. 7). Underestimation of pressure drop with BSI is therefore more pronounced at higher flow rates. These results are consistent with previous findings conducted in vitro/in silico, whereby BSI was shown to underestimate flow velocity [18,19,20,21]. The largest in vivo study to date was performed in 51 healthy paediatric controls, where underestimations of velocity values acquired using BSI were also observed. The same study also revealed that the difference tended to increase at higher velocities [8]. High velocity gradients and considerable out-of-plane flow generated across flow obstructions lead to speckle decorrelation [18, 22]. This explains the underestimation of pressure drop at the higher flow rates using BSI.
On the other hand, pressure drops estimated using Doppler were significantly higher than ground-truth pressure drop at the greatest level of stenosis tested (20.9 ± 1.92 mmHg). This is likely due to the error in estimation of momentum from a single velocity value: the characterisation of the pressure drop requires the full velocity profile [3, 5]. This finding has clinical significance as a pressure drop of 20 mmHg is the lower limit for the classification of moderate aortic stenosis [16]. Significant overestimation of pressure drops in this range could result in misclassification of aortic stenosis severity and the inappropriate treatment of patients. The bias of Doppler measurements across the experimental conditions was 3.92 mmHg (p < 0.05); with peak overestimations of up to 20 mmHg (Fig. 8A). These findings are consistent with those reported by Donati et al. (2017), where pressure drop values obtained using the Simplified Bernoulli formulation were shown to overestimate the true pressure drop by 54% [3].
The peak pressure drop values measured by the pressure sensors in the phantom are different to net pressure drops measured in clinical practice during cardiac catheterisation, which measure the pressure difference between the left ventricular outflow tract and the ascending aorta, downstream of the vena contracta [23]. The peak pressure drop measured by the pressure sensors in the phantom is at the location of the vena contracta, as is the case for the Doppler data. The effect of pressure recovery further downstream, which is the traditional understanding of the reason of pressure drop overestimation by Doppler, can therefore be excluded.
The absolute error of measurements made using Doppler increased with flow rate and a significant difference in absolute error was observed between the highest and lowest flow rates (Fig. 7). A linear increase in the difference between the estimated pressure drop of Doppler vs. ground-truth with increasing level of stenosis can also be observed in the respective Bland-Alman agreement plot in Fig. 8A. These findings support the observation that the overestimation of pressure drop by Doppler echocardiography is more pronounced at higher flow rates. The simplified Bernoulli formulation is accurate for uniform spatial velocity profiles (i.e. at the cross-section), observed at low flow velocities [3]. As flow rate increases, the spatial flow profiles, driven by viscous effects, become sharper and more paraboloidal in shape (Fig. 10A), deviating from the flatter spatial flow profiles, driven by inertial effects, observed at low flow rates (Fig. 10B). Donati et al. (2017) report that the variable deviations from the flat velocity profile cause an uncontrolled source of overestimation of pressure drop when applying the simplified Bernoulli equation (Supplemental material C-D of Donati et al. 2017) [3]. Our results report that the high velocity regimes, driven by viscous effects, gradually introduce a larger overestimation. This explains why Doppler is less accurate under these higher flow regimes (Fig. 7). Further variability would be expected if different valve models and geometries were studied, or indeed if using in vivo data. These conditions would likely increase the degree of mismatch between true and estimated pressure drops further.
As a final minor remark, no significant difference was observed between the mean pressure drops achieved under constant and pulsatile conditions, allowing them to be grouped within each pump flow rate (Fig. 6; n = 4).
Intra-technique reproducibility
The intra-technique reproducibility analysis demonstrates a small, but statistically significant, bias of the ground-truth pressure readings (Bias = 0.46 mmHg (p < 0.05), upper limit 1.23 mmHg, lower limit -0.31 mmHg; Fig. 9A). Albeit small, this significant bias should be considered when interpreting the agreement between Doppler and BSI vs. pressure sensors. Variability is greater in the pulsatile estimations despite the fact each pressure drop is calculated as the mean over 6 cycles. BSI is less variable than Doppler (Bias = 1.61 (p > 0.05), upper limit 6.73 mmHg, lower limit -3.51 vs Bias = 5.19 mmHg (p < 0.05), upper limit 16.3 mmHg, lower limit -5.89, respectively; Fig. 9B-C). However, the reproducibility of BSI may be positively influenced by its inability to track high pressures, resulting in false clustering of measurements (Fig. 9C). The reproducibility of Doppler measurements is influenced by large disagreement at the greatest pulsatile flow rate (Fig. 9B). Disagreement also exists in the ground-truth measurements under this condition (Fig. 9A), which may account for intrinsic variability of the experimental conditions and not the measurement devices, and should be considered when interpreting the reproducibility of Doppler pressure drop measurements at higher flow rates.
Limitations
These experiments were performed using a single model of a healthy aortic valve. The ultrasound probe was placed directly against the phantom to make the BSI and Doppler acquisitions with low penetration depth. These two factors represent a best-case scenario for the acquisition data for pressure drop estimation. In human subjects, acquisitions would be at an increased penetration depth, thus reducing the imaging frame rate, with an increased level of attenuation. In addition, experiments in human valves would exhibit more physiological and/or pathological variation. The results, therefore, would likely be different if data were obtained in vivo.
Although qualitative evidence (Fig. 5 and Additional File 1) and quantitative evidence (Fig. 6) demonstrate plausible haemodynamic behaviour, it is important to consider that similarity between the mechanical properties of the silicone valve and those of a human valve is not demonstrated beyond the reasonable confidence reported previously [12, 13].
In these experiments, the velocity profile and resultant pressure drop were controlled by modifying the pump flow rate. Changing the valve type or orifice area would be the ideal workbench for this experiment as it changes the velocity profile under the same flow conditions. However, this was not performed in order to avoid damaging the valves during the changeover procedure, and to maximise the reproducibility of the pressure drops created by a fixed valve. Additional experiments with different pulsatile conditions, using different frequencies and duty cycles, would allow for a better understanding of transient effects during the upstroke/downstroke of the acceleration of the jet, and thus secondary effects of the impact of the temporal resolution of data. The lack of these results is a limitation of the study.
In this work, pressure drop estimations were made using a single peak velocity value acquired by BSI. The reported limitations of current BSI technology preclude the use of pressure estimations made using the full velocity profile at this stage as underestimation will exist across the region of interest where higher flow velocities are found. Future technological advances and resultant improvements in temporal resolution may improve the ability of BSI to track higher flow velocities and therefore estimate greater pressure drops more accurately, allowing for two advantages, to correctly account for the physics of advection by capturing the full velocity profile [3], and to overcome the angle-dependence and aliasing limitations of Doppler echocardiography.
Given the small sample size, the results of this pilot study should be considered as preliminary. Future in vivo studies are required before BSI can be used in the clinical setting.