Cross-correlation analysis of pulse wave propagation in arteries: in vitro validation and in vivo feasibility

Abstract

The stiffness of the arteries is known to be an indicator of the progression of various cardiovascular diseases. Clinically, the pulse wave velocity (PWV) is used as a surrogate for arterial stiffness. Pulse wave imaging (PWI) is a non-invasive, ultrasound-based imaging technique capable of mapping the motion of the vessel walls, allowing the local assessment of arterial properties. Conventionally, a distinctive feature of the displacement wave (e.g. the 50% upstroke) is tracked across the map to estimate the PWV. However, the presence of reflections, such as those generated at the carotid bifurcation, can bias the PWV estimation. In this paper, we propose a two-step cross-correlation based method to characterize arteries using the information available in the PWI spatio-temporal map. First, the area under the cross-correlation curve is proposed as an index for locating the regions of different properties. Second, a local peak of the cross-correlation function is tracked to obtain a less biased estimate of the PWV. Three series of experiments were conducted in phantoms to evaluate the capabilities of the proposed method compared with the conventional method. In the ideal case of a homogeneous phantom, the two methods performed similarly and correctly estimated the PWV. In the presence of reflections, the proposed method provided a more accurate estimate than conventional processing: e.g. for the soft phantom, biases of -0.27 and -0.71 m · s^-1 were observed. In a third series of experiments, the correlation-based method was able to locate two regions of different properties with an error smaller than 1 mm. It also provided more accurate PWV estimates than conventional processing (biases: -0.12 versus -0.26 m · s^-1). Finally, the in vivo feasibility of the proposed method was demonstrated in eleven healthy subjects. The results indicate that the correlation-based method might be less precise in vivo but more accurate than the conventional method.

Figure 1

Example illustrating the four packets observed in the cross-correlation function (bottom row) of two signals: s_A(t) (top row) and s_B(t) (middle row) containing a forward-propagating wave (bold line, labelled FA and FB) and a reflected wave (dotted line, labelled RA and RB).

Figure 2

Three experimental configurations investigated on a phantom with two parts of different scatterer concentration and stiffnesses: a) ideal conditions: an homogeneous part (either soft or stiff) was imaged with little influence from the reflection at the outlet fitting (light blue arrow) by emitting a wave (dark blue arrow) on the side close to the probe, b) an homogeneous part (either soft or stiff) was imaged with strong influence from the reflection, c) the transition between the soft and the stiff parts was imaged with emission on each side successively.

Figure 3

Each map represents the correlation functions between a reference line and all the other lines of a spatio-temporal map, coded in color. On each map, the peak located at the highest abscissa (shown to be less affected by reflections) is tracked across the field of view. A linear fitting yields a PWV estimate for each correlation map (2.50 m · s⁻¹ for the first map). These different PWV are averaged to obtain the PWV estimate (2.50 ± 0.07 m · s⁻¹) for this experiment.

Figure 4

Examples of spatio-temporal maps obtained for each configuration: for homogeneous soft phantom a) under ideal conditions, b) in the presence of a strong reflection, and, c) for a bi-phasic phantom, the softer part being on the top of the map. The indicated PWV have been estimated by conventional processing (linear fitting in red of the 50% upstroke markers in black). The true PWV values are PWV_soft = 2.41 m · s⁻¹ and PWV_stiff = 3.52 m · s⁻¹.

Figure 5

Examples of evolution of the AUC index for each experimental configuration. For the homogeneous phantom experiments, the index remains constant across the field of view. For the heterogeneous phantom, two phases can be identified and the location of the transition between the soft and the stiff parts can thus be estimated.

Figure 6

Evolution of the AUC index for three acquisitions of the transition between the soft and the stiff parts, the probe having been moved by 6.35 mm between acquisitions. Using the AUC index, the transition is estimated to have moved respectively by 5.40 and 6.00 mm between acquisitions.

Figure 7

Differences between the PWV estimated by conventional processing with the gold standard, static testing method (a) and the PWV estimated by correlation-based processing with the same gold standard (b). Light lines and circles are related to the soft part, bold lines and crosses to the stiff part. Each of the circles (or crosses) represents one of the five experiments performed on the homogeneous phantom in ideal conditions (configuration a). The solid line indicates the bias while the dashed lines represent the limits of agreement.

Figure 8

Differences between the PWV estimated by conventional processing with the gold standard, static testing method (a) and the PWV estimated by correlation-based processing with the same gold standard (b). Light lines and circles are related to the soft part, bold lines and crosses to the stiff part. Each of the circles (or crosses) represents one of the five experiments performed on the homogeneous phantom in presence of a strong reflection (configuration b). The solid line indicates the bias while the dashed lines represent the limits of agreement.

Figure 9

Differences between the PWV estimated by conventional processing with the gold standard, static testing method (a) and the PWV estimated by correlation-based processing with the same gold standard (b). The dark squares (resp. light crosses) depict the estimates obtained from the 10 experiments on the soft to stiff transition (resp. the stiff to soft transition) of an heterogeneous phantom (configuration c).

Figure 10

Examples of spatio-temporal maps showing the propagation of the displacement pulse wave in three different locations along the common carotid of a healthy subject. In each case, a forward wave and a reflected wave can be observed. Depending on the location of the measurement site, relatively to the carotid bifurcation, these two waves interfere more (close to the bifurcation) or less (far from the bifurcation). The inserts depict the waveform observed by the last element over a full cardiac cycle.

Figure 11

For each of the five healthy subjects, the evolution of the area under the curve of cross-correlation between a reference signal (first line of the spatio-temporal map) and the other lines indicates that the scanned part of the carotids consists of a single homogeneous region.

Figure 12

PWV estimates obtained with conventional processing (blue thin lines) and the correlation-based processing (red thick lines) in series of five acquisitions in five human carotids in vivo. Estimates are slightly but not significantly different between the methods, except for subject #3 (p = 0.05).