Pierre Nauleau

An inverse approach to determining spatially varying arterial compliance using ultrasound imaging

The mechanical properties of arteries are implicated in a wide variety of cardiovascular diseases, many of which are expected to involve a strong spatial variation in properties that can be depicted by diagnostic imaging. A pulse wave inverse problem (PWIP) is presented, which can produce spatially resolved estimates of vessel compliance from ultrasound measurements of the vessel wall displacements. The 1D equations governing pulse wave propagation in a flexible tube are parameterized by the spatially varying properties, discrete cosine transform components of the inlet pressure boundary conditions, viscous loss constant and a resistance outlet boundary condition. Gradient descent optimization is used to fit displacements from the model to the measured data by updating the model parameters. Inversion of simulated data showed that the PWIP can accurately recover the correct compliance distribution and inlet pressure under realistic conditions, even under high simulated measurement noise conditions. Silicone phantoms with known compliance contrast were imaged with a clinical ultrasound system. The PWIP produced spatially and quantitatively accurate maps of the phantom compliance compared to independent static property estimates, and the known locations of stiff inclusions (which were as small as 7 mm). The PWIP is necessary for these phantom experiments as the spatiotemporal resolution, measurement noise and compliance contrast does not allow accurate tracking of the pulse wave velocity using traditional approaches (e.g. 50% upstroke markers). Results from simulations indicate reflections generated from material interfaces may negatively affect wave velocity estimates, whereas these reflections are accounted for in the PWIP and do not cause problems.

3D myocardial elastography in vivo

Strain evaluation is of major interest in clinical cardiology as it can quantify the cardiac function. Myocardial elastography, a radio-frequency (RF)-based cross-correlation method, has been developed to evaluate the local strain distribution in the heart in vivo. However, inhomogeneities such as RF ablation lesions or infarction require a three-dimensional approach to be measured accurately. In addition, acquisitions at high volume rate are essential to evaluate the cardiac strain in three dimensions. Conventional focused transmit schemes using 2D matrix arrays, trade off sufficient volume rate for beam density or sector size to image rapid moving structure such as the heart, which lowers accuracy and precision in the strain estimation. In this study, we developed 3D myocardial elastography at high volume rates using diverging wave transmits to evaluate the local axial strain distribution in three dimensions in three open-chest canines before and after radio-frequency ablation. Acquisitions were performed with a 2.5 MHz 2D matrix array fully programmable used to emit 2000 diverging waves at 2000 volumes/s. Incremental displacements and strains enabled the visualization of rapid events during the QRS complex along with the different phases of the cardiac cycle in entire volumes. Cumulative displacement and strain volumes depict high contrast between non-ablated and ablated myocardium at the lesion location, mapping the tissue coagulation. 3D myocardial strain elastography could thus become an important technique to measure the regional strain distribution in three dimensions in humans.

Technical Note: A 3‐D rendering algorithm for electromechanical wave imaging of a beating heart

Purpose Arrhythmias can be treated by ablating the heart tissue in the regions of abnormal contraction. The current clinical standard provides electroanatomic 3‐D maps to visualize the electrical activation and locate the arrhythmogenic sources. However, the procedure is time‐consuming and invasive. Electromechanical wave imaging is an ultrasound‐based noninvasive technique that can provide 2‐D maps of the electromechanical activation of the heart. In order to fully visualize the complex 3‐D pattern of activation, several 2‐D views are acquired and processed separately. They are then manually registered with a 3‐D rendering software to generate a pseudo‐3‐D map. However, this last step is operator‐dependent and time‐consuming. Methods This paper presents a method to generate a full 3‐D map of the electromechanical activation using multiple 2‐D images. Two canine models were considered to illustrate the method: one in normal sinus rhythm and one paced from the lateral region of the heart. Four standard echographic views of each canine heart were acquired. Electromechanical wave imaging was applied to generate four 2‐D activation maps of the left ventricle. The radial positions and activation timings of the walls were automatically extracted from those maps. In each slice, from apex to base, these values were interpolated around the circumference to generate a full 3‐D map. Results In both cases, a 3‐D activation map and a cine‐loop of the propagation of the electromechanical wave were automatically generated. The 3‐D map showing the electromechanical activation timings overlaid on realistic anatomy assists with the visualization of the sources of earlier activation (which are potential arrhythmogenic sources). The earliest sources of activation corresponded to the expected ones: septum for the normal rhythm and lateral for the pacing case. Conclusions The proposed technique provides, automatically, a 3‐D electromechanical activation map with a realistic anatomy. This represents a step towards a noninvasive tool to efficiently localize arrhythmias in 3‐D.

Feasibility and validation of 4D Pulse wave Imaging (PWI) in vitro: 3D automated estimation of regional Pulse Wave Velocity vector

Pulse wave Imaging (PWI) is a noninvasive technique for tracking the propagation of the pulse waves along the arterial wall. Estimation of regional Pulse Wave Velocity (PWV) using 2D long-axis views of arterial vessels assumes propagation parallel to the imaging plane. 3D ultrasound imaging would aid in objectively estimating the PWV vector. The aims of this study were to introduce a novel method for PWV estimation along the direction of the wave propagation, and validate it in phantoms. Silicone vessel phantoms consisting of stiff and soft segments along the longitudinal axis were constructed and embedded into a very soft silicone background. A 2D array with a center frequency of 2.5 MHz was used to image each section using plane wave transmissions. Static and dynamic mechanical testing was used for PWV validation. The propagation was successfully visualized in 3D. PWVs were estimated in both the stiff (3.42 ± 0.23 m/s) and soft (2.41 ± 0.07 m/s) sections of the phantoms. Good agreement was found between the estimated PWVs and the corresponding static testing values (stiff. 3.41 m/s, soft. 2.48 m/s). Additionally, PWI-derived vessel compliance values were validated with dynamic testing. Thus, 4D PWI was successfully implemented and validated in silicone phantoms with plane waves at high volume rates.

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

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.

3D rendering of electromechanical wave imaging for the characterization and optimization of biventricular pacing conditions in heart failure patients undergoing Cardiac Resynchronization Therapy

Assessing the response of heart failure (HF) patients to Cardiac Resynchronization Therapy (CRT) currently relies on the ECG and left ventricular (LV) ejection fraction. Electromechanical Wave Imaging (EWI) is a high frame-rate (2000 Hz) ultrasound-based technique capable of non-invasively mapping the electromechanical activation in all four cardiac chambers in vivo. In this study, we aim to show the capability of EWI in identifying different pacing conditions in patients with CRT and to characterize the resulting activation pattern directly following biventricular (BiV) device placement.

Multi-2D reconstruction of electromechanical activation maps of a beating heart

Arrhythmias can be treated by ablating the heart tissue in the regions of abnormal conduction, e.g. activating too early or with a different speed. The key of the treatment then lies in the location of these areas. In current clinical practice, 3-D electroanatomic maps can be created during the procedure by probing the heart with a specific catheter. However, it is a time-consuming and invasive procedure. Electromechanical wave imaging (EWI) is an ultrasound-based technique that can provide 2-D maps of the electromechanical activation of the heart. Yet, the activation follows a complex 3-D pattern. We thus propose an automated method to generate pseudo 3-D activation maps using several 2-D maps. These maps are subsequently analyzed qualitatively to locate the source of arrhythmia or quantitatively to evaluate the conduction speed in the myocardial tissue.

In vivo repeatability of the pulse wave inverse problem in human carotid arteries

Accurate arterial stiffness measurement would improve diagnosis and monitoring for many diseases. Atherosclerotic plaques and aneurysms are expected to involve focal changes in vessel wall properties; therefore, a method to image the stiffness variation would be a valuable clinical tool. The pulse wave inverse problem (PWIP) fits unknown parameters from a computational model of arterial pulse wave propagation to ultrasound-based measurements of vessel wall displacements by minimizing the difference between the model and measured displacements. The PWIP has been validated in phantoms, and this study presents the first in vivo demonstration. The common carotid arteries of five healthy volunteers were imaged five times in a single session with repositioning of the probe and subject between each scan. The 1D finite difference computational model used in the PWIP spanned from the start of the transducer to the carotid bifurcation, where a resistance outlet boundary condition was applied to approximately model the downstream reflection of the pulse wave. Unknown parameters that were estimated by the PWIP included a 10-segment linear piecewise compliance distribution and 16 discrete cosine transformation coefficients for each of the inlet boundary conditions. Input data was selected to include pulse waves resulting from the primary pulse and dicrotic notch. The recovered compliance maps indicate that the compliance increases close to the bifurcation, and the variability of the average pulse wave velocity estimated through the PWIP is on the order of 11%, which is similar to that of the conventional processing technique which tracks the wavefront arrival time (13%).