From wave speed to cardiac stiffness

Diastolic heart failure is one of the principal causes of death in Western countries, and there is currently no treatment available; prevention, on the other hand, may be possible, provided an early enough diagnosis. The worsening of diastolic functionality is associated with increased values of cardiac stiffness, which could therefore provide a measurable quantification of the diastolic health of the heart. Ultrasound imaging technologies can be used to non-invasively record the propagation of small amplitude shear waves propagating in the cardiac muscle. In principle, since the propagation speed of a wave is proportional to the stiffness of the medium in which it travels, ultrasonic shear wave imaging could provide a measure of the stiffness of the heart. However, various features of the heart, such as shape and contractility, complicate the relation between wave speed and stiffness in unknown ways. This thesis aims at understanding how wave propagation is affected by the temporal behaviour and the varying thickness of the heartmuscle, and consequently howultrasonic images of the propagation should be analysed to correctly convertwave speed intomuscle stiffness.Human-Robot InteractionImPhys/Medical Imagin

Fundamental modeling of wave propagation in temporally relaxing media with applications to cardiac shear wave elastography

Shear wave elastography (SWE) might allow non-invasive assessment of cardiac stiffness by relating shear wave propagation speed to material properties. However, after aortic valve closure, when natural shear waves occur in the septal wall, the stiffness of the muscle decreases significantly, and the effects of such temporal variation of medium properties on shear wave propagation have not been investigated yet. The goal of this work is to fundamentally investigate these effects. To this aim, qualitative results were first obtained experimentally using a mechanical setup, and were then combined with quantitative results from finite difference simulations. The results show that the amplitude and period of the waves increase during propagation, proportional to the relaxation of the medium, and that reflected waves can originate from the temporal stiffness variation. These general results, applied to literature data on cardiac stiffness throughout the heart cycle, predict as a major effect a period increase of 20% in waves propagating during a healthy diastolic phase, whereas only a 10% increase would result from the impaired relaxation of an infarcted heart. Therefore, cardiac relaxation can affect the propagation of waves used for SWE measurements and might even provide direct information on the correct relaxation of a heart.ImPhys/Medical Imagin

Modelling Lamb waves in the septal wall of the heart

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, at the lower frequencies, propagation speed can decrease during propagation by ~20% due to the thickness reduction, producing a nonlinear space-time relation from which multiple speed values can be extracted. At higher frequencies, the main observation is a dependence of the dispersion behavior on the shape of the tapering (e.g., linear, concave, or convex). These results suggest that septal geometry is likely to play a role in deriving cardiac stiffness from propagation speed measurements.ImPhys/Acoustical Wavefield Imagin

Error analysis and reliability of zero-order Lamb mode inversion for waveguide characterization

In recent years, several fitting techniques have been presented to reconstruct the parameters of a plate from its Lamb wave dispersion curves. Published studies show that these techniques can yield high accuracy results and have the potential of reconstructing several parameters at once. The precision with which parameters can be reconstructed by inverting Lamb wave dispersion curves, however, remains an open question of fundamental importance to many applications. In this work, we introduce a method of analyzing dispersion curves that yields quantitative information on the precision with which the parameters can be extracted. In our method, rather than employing error minimization algorithms, we compare a target dispersion curve to a database of theoretical ones that covers a given parameter space. By calculating a measure of dissimilarity (error) for every point in the parameter space, we reconstruct the distribution of the error in that space, beside the location of its minimum. We then introduce dimensionless quantities that describe the distribution of this error, thus yielding information about the spread of similar curves in the parameter space. We demonstrate our approach by considering both idealized and realistic scenarios, analyzing the dispersion curves obtained numerically for a plate and experimentally for a pipe. Our results show that the precision with which each parameter is reconstructed depends on the mode used, as well as the frequency range in which it is considered.Human-Robot InteractionImPhys/Medical ImagingBUS/TNO STAF

Tapering of the interventricular septum can affect ultrasound shear wave elastography: An in vitro and in silico study

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.ImPhys/Medical Imagin

Measurement of Pipe and Fluid Properties with a Matrix Array-based Ultrasonic Clamp-on Flow Meter

Current ultrasonic clamp-on flow meters consist of a pair of single-element transducers that are carefully positioned before use. This positioning process consists of manually finding the distance between the transducer elements, along the pipe axis, for which maximum signal-to-noise ratio (SNR) is achieved. This distance depends on the sound speed, thickness, and diameter of the pipe and on the sound speed of the liquid. However, these parameters are either known with low accuracy or completely unknown during positioning, making it a manual and troublesome process. Furthermore, even when sensor positioning is done properly, uncertainty about the mentioned parameters, and therefore on the path of the acoustic beams, limits the final accuracy of flow measurements. In this research, we address these issues using an ultrasonic clamp-on flow meter consisting of two matrix arrays, which enables the measurement of pipe and liquid parameters by the flow meter itself. Automatic parameter extraction, combined with the beam-steering capabilities of transducer arrays, yields a sensor capable of compensating for pipe imperfections. Three parameter extraction procedures are presented. In contrast to similar literature, the procedures proposed here do not require that the medium be submerged nor do they require a priori information about it. First, axial Lamb waves are excited along the pipe wall and recorded with one of the arrays. A dispersion curve-fitting algorithm is used to extract bulk sound speeds and wall thickness of the pipe from the measured dispersion curves. Second, circumferential Lamb waves are excited, measured, and corrected for dispersion to extract the pipe diameter. Third, pulse-echo measurements provide the sound speed of the liquid. The effectiveness of the first two procedures has been evaluated using simulated and measured data of stainless steel and aluminum pipes, and the feasibility of the third procedure has been evaluated using simulated data.Accepted Author ManuscriptImPhys/Medical ImagingElectronic Instrumentatio