Electromechanical Reciprocity Research Articles

Temporal variability of electromechanical-window negativity in patients with inherited long-QT syndrome or drug-induced QT prolongation: relation to torsades de pointes

Abstract Background Electromechanical window (EMW) negativity is a novel parameter that identifies long-QT syndrome (LQTS) patients at increased arrhythmia risk. Whether the EMW remains stable or alters, especially close to arrhythmic events, is unknown. Purpose To study temporal variability of the EMW in controls and in patients with LQTS or drug-induced QT prolongation (di-QTprol), in relation to the timing of torsades de pointes (TdP) or ventricular fibrillation (VF). Methods In a retrospective cohort study with 5 participating centers, we assessed the EMW (ms) at 2 or 3 timepoints (if applicable, one of them close to TdP/VF) from cw-Doppler echocardiography in the apical long-axis view and concomitant ECG. EMW was calculated by subtracting the QT time from the aortic-valve closure time measured from QRS onset (surrogate of mechanical systole). Data are shown as mean±SD or median (25th to 75th percentile). Results Forty patients (75% female, 43±18 years old) were included: 8 controls, 27 LQTS (10 symptomatic: 9 TdP, 1 VF), and 5 di-QTprol (all TdP). LQTS genotypes were LQT1 (n=11), LQT2 (n=6), LQT3 (n=7), LQT7 (n=2), and genotype-negative (n=1). Overall, 67% of LQTS patients and 20% of di-QTprol were treated with β-blockers. Baseline QTc was 409±32 ms in controls, 444±32 ms in asymptomatic LQTS, 491±41 ms in symptomatic LQTS, and 498±49 ms in di-QTprol. Baseline EMW was 6±14 ms in controls, -12±29 ms in asymptomatic LQTS, -52±16 ms in symptomatic LQTS, and -5±69 ms in di-QTprol. Over years of follow-up, EMW remained stable in controls (8±10 ms; Fig. 1A) and the asymptomatic LQTS group (-17±20 ms; Fig. 1B). In LQTS patients with TdP/VF, EMW (baseline measured at -534 (-962 to -143) days before arrhythmia) had become profoundly more negative, -127±42 ms, (p=0.01 vs. baseline) at 1 (0 to 5) days after the arrhythmia and returned to basal values, -52±18 ms, (p=0.005) after 722 (155 to 3100) days (Fig. 1C). There was a significant correlation between time-to-event and EMW negativity (r=0.72, p<0.0001), indicating stronger EMW negativity when measured closer to TdP/VF. For the di-QTprol patients (n=2 amiodarone; n=2 escitalopram; n=1 sotalol) a trend towards more exaggerated EMW negativity was observed: from baseline (at -19 (-785 to -13) days before the event) to -125±33 ms (p=0.08 vs. baseline) at 1 (1 to 5) days after TdP (Fig. 1D). Again, significant correlation was found between time-to-event and EMW negativity (r=0.6, p=0.03). Conclusion Episodes of electrical instability in patients with LQTS or di-QTprol are associated with profound but reversible exaggeration of EMW negativity. If also present just prior to TdP/VF (as in experimental models of torsadogenic di-QTprol and anecdotal LQTS cases), imminent ventricular arrhythmias may be anticipated as electromechanical reciprocity may contribute to arrhythmogenesis.Figure 1Graphical Abstract

Mechano-electrical interactions and heterogeneities in wild-type and drug-induced long QT syndrome rabbits.

Electromechanical reciprocity - comprising electro-mechanical (EMC) and mechano-electric coupling (MEC) - provides cardiac adaptation to changing physiological demands. Understanding electromechanical reciprocity and its impact on function and heterogeneity in pathological conditions - such as (drug-induced) acquired long QT syndrome (aLQTS) - might lead to novel insights in arrhythmogenesis. Our aim is to investigate how electrical changes impact on mechanical function (EMC) and vice versa (MEC) under physiological conditions and in aLQTS. To measure regional differences in EMC and MEC in vivo, we used tissue phase mapping cardiac MRI and a 24-lead ECG vest in healthy (control) and IKr-blocker E-4031-induced aLQTS rabbit hearts. MEC was studied in vivo by acutely increasing cardiac preload, and ex vivo by using voltage optical mapping (OM) in beating hearts at different preloads. In aLQTS, electrical repolarization (heart rate corrected RT-interval, RTn370) was prolonged compared to control (P<0.0001) with increased spatial and temporal RT heterogeneity (P<0.01). Changing electrical function (in aLQTS) resulted in significantly reduced diastolic mechanical function and prolonged contraction duration (EMC), causing increased apico-basal mechanical heterogeneity. Increased preload acutely prolonged RTn370 in both control and aLQTS hearts (MEC). This effect was more pronounced in aLQTS (P<0.0001). Additionally, regional RT-dispersion increased in aLQTS. Motion-correction allowed us to determine APD-prolongation in beating aLQTS hearts, but limited motion correction accuracy upon preload-changes prevented a clear analysis of MEC ex vivo. Mechano-induced RT-prolongation and increased heterogeneity were more pronounced in aLQTS than in healthy hearts. Acute MEC effects may play an additional role in LQT-related arrhythmogenesis, warranting further mechanistic investigations. KEY POINTS: Electromechanical reciprocity comprising excitation-contraction coupling (EMC) and mechano-electric feedback loops (MEC) is essential for physiological cardiac function. Alterations in electrical and/or mechanical heterogeneity are known to have potentially pro-arrhythmic effects. In this study, we aimed to investigate how electrical changes impact on the mechanical function (EMC) and vice versa (MEC) both under physiological conditions (control) and in acquired long QT syndrome (aLQTS). We show that changing the electrical function (in aLQTS) results in significantly altered mechanical heterogeneity via EMC and, vice versa, that increasing the preload acutely prolongs repolarization duration and increases electrical heterogeneity, particularly in aLQTS as compared to control. Our results substantiate the hypothesis that LQTS is an ‛electro-mechanical', rather than a 'purely electrical', disease and suggest that acute MEC effects may play an additional role in LQT-related arrhythmogenesis.

Electromechanical Reciprocity Applied to the Sensing Properties of Guided Elastic Wave Transducers

Guided elastic wave (GEW) transducers for structural health monitoring (SHM) can act as transmitters (senders) and receivers (sensors). Their performance in both cases depends on the structure to which they are coupled. Therefore, they must be characterized as system transducer- structure. The characterization of the transducer-structure as transmitter using a Scanning Laser Doppler Vibrometer (SLDV) is straightforward, whereas its characterization as receiver is non-trivial. We propose to exploit electromechanical reciprocity, which is an identity between the transfer functions of electrical-to-mechanical and mechanical-to-electrical conversions. For this purpose, the well-known electromechanical reciprocity theorem was adapted to the following situation: The two reciprocal states are "electrical excitation and detection of the surface velocity at point P" and "mechanical excitation at P and measurement of the electrical quantities". According to the derived formulas, the quantities on the mechanical and electrical sides must be chosen appropriately to ensure reciprocity as well as that the corresponding transfer functions are equal. We demonstrate the reciprocity with experimental data for correctly chosen transfer functions and show the deviation in reciprocity for a different choice. Furthermore, we propose further applications of electromechanical reciprocity.

Electromechanical reciprocity and arrhythmogenesis in long-QT syndrome and beyond

An abundance of literature describes physiological and pathological determinants of cardiac performance, building on the principles of excitation-contraction coupling. However, the mutual influencing of excitation-contraction and mechano-electrical feedback in the beating heart, here designated 'electromechanical reciprocity', remains poorly recognized clinically, despite the awareness that external and cardiac-internal mechanical stimuli can trigger electrical responses and arrhythmia. This review focuses on electromechanical reciprocity in the long-QT syndrome (LQTS), historically considered a purely electrical disease, but now appreciated as paradigmatic for the understanding of mechano-electrical contributions to arrhythmogenesis in this and other cardiac conditions. Electromechanical dispersion in LQTS is characterized by heterogeneously prolonged ventricular repolarization, besides altered contraction duration and relaxation. Mechanical alterations may deviate from what would be expected from global and regional repolarization abnormalities. Pathological repolarization prolongation outlasts mechanical systole in patients with LQTS, yielding a negative electromechanical window (EMW), which is most pronounced in symptomatic patients. The electromechanical window is a superior and independent arrhythmia-risk predictor compared with the heart rate-corrected QT. A negative EMW implies that the ventricle is deformed-by volume loading during the rapid filling phase-when repolarization is still ongoing. This creates a 'sensitized' electromechanical substrate, in which inadvertent electrical or mechanical stimuli such as local after-depolarizations, after-contractions, or dyssynchrony can trigger abnormal impulses. Increased sympathetic-nerve activity and pause-dependent potentiation further exaggerate electromechanical heterogeneities, promoting arrhythmogenesis. Unraveling electromechanical reciprocity advances the understanding of arrhythmia formation in various conditions. Real-time image integration of cardiac electrophysiology and mechanics offers new opportunities to address challenges in arrhythmia management.

Array-Based Guided Wave Source Location Using Dispersion Compensation

Abstract An important advantage of guided waves is their ability to propagate large distances and yield more information about flaws than bulk waves. Unfortunately, the multi-modal, dispersive nature of guided waves makes them difficult to use for locating flaws. In this work, we present a method and experimental data for removing the deleterious effects of multi-mode dispersion allowing for source localization at frequencies comparable to those of bulk waves. Time domain signals are obtained using a novel 64-element phased array and processed to extract wave number and frequency spectra. By an application of Auld’s electro-mechanical reciprocity relation, mode contributions are extracted approximately using a variational method. Once mode contributions have been obtained, the dispersion for each mode is removed via back-propagation techniques. Excepting the presence of a small artifact at high frequency-thicknesses, experimental data successfully demonstrate the robustness and viability of this approach to guided wave source location.

A Receiver Model for Ultrasonic Ray Tracing in an Inhomogeneous Anisotropic Weld

In this paper, a receiver model for ultrasonic ray tracing simulation is described. This is a complementary part of an existing simulation model and is the next step towards a numerical solution to the inverse problem and thus a NDT methodology for characterization of the dendrite orientation in a weld. The establishment of the receiver model is based on the electromechanical reciprocity principle. A concise retrospect of the weld model and the 2D model is made. The reciprocity principle is applied in an original way to handle the model problem including the back wall. Experimental qualitative validations for both P and SV waves on a specific weld are also made for C-scans included in this paper. Two different cases are studied. The first is a direct incidence of an ultrasonic ray towards the weld, and the second is a reflection from the back surface in the base material followed by an incidence to the weld. Even though mode-converted rays are excluded in the simulations, both the P and SV probe-models show the same behavior as the experimental results. The qualitative validation though reveals that it even if a thorough time-gating of received information would enable exclusion of mode-conversion in the model, inaccuracy of experimental results is affecting the evaluation of the weld model.

2D SH modelling of ultrasonic testing for cracks near a non-planar surface

A model of 2D SH ultrasonic nondestructive testing for interior strip-like cracks near a non-planar back surface in a thick-walled elastic solid is presented. The model employs a Green's function to reformulate the 2D antiplane wave scattering problem as two coupled boundary integral equations (BIE): a displacement BIE for the back surface displacement and a hypersingular traction BIE for the crack opening displacement (COD). The integral equations are solved by performing a boundary element discretization of the back surface and expanding the COD in a series of Chebyshev functions which incorporate the correct behaviour at the crack edges. The transmitting ultrasonic probe is modelled by prescribing the traction underneath it, enabling the consequent calculation of the incident field. An electromechanical reciprocity relation is used to model the action of the receiving probe. A few numerical examples which illustrate the influence of the non-planar back surface are given.

Equivalence of Gaussian and piston ultrasonic transducer voltages.

A plane-wave decomposition of collimated beams and electromechanical reciprocity relations are used to demonstrate fundamental differences and unusual similarities about transducer fields and transducer voltages at ultrasonic frequencies under various conditions. It is shown that the voltage induced by a transmitting acoustic piston transducer (constant particle velocity over the transducer surface) radiating into an ideal fluid medium on a second identical piston transducer, operating as a receiver, is nearly identical to the voltage observed when the two transducers have instead a Gaussian radial surface velocity distribution. The strong similarity in induced voltage begins when the two devices are separated by only several acoustic wavelengths, still well within the nearfield of both transducers, and the similarity increases with separation. Cases of transducer velocity distributions different from piston, such as Lorentzian or triangular, yield results nearly identical to the piston case. Transducers of differing size are also treated. It is further shown that an "equivalent transducer" can be derived for any combination of radiators, whose field is identical to the voltage measured using the pair. Moreover, with this concept the calculation of voltage in two-probe experiments is as simple as well-known approximations to the Rayleigh integral for a single transducer. These results have substantial consequences for calculations, either analytical or numerical, that predict the voltage measured in two-transducer experiments.

Ultrasonic scattering by a side-drilled hole

The scattering of elastic waves by a side-drilled hole (sdh) i.e. a circular cylindrical cavity, is considered. The scattering of plane or cylindrical waves by an sdh is an old subject; here the T matrix solution is adopted. The elastic waves are excited by an ultrasonic probe and a model of such a probe is thus used. The waves from the probes are expressed as a Fourier transform, i.e. as a superposition of plane waves. These plane waves are then transformed to the cylindrical system centred at the sdh. To obtain the signal in a receiving ultrasonic probe an electromechanical reciprocity relation is used. The signal response is obtained as a double wavenumber integral and an azimuthal summation. In the far field the integrals can be calculated approximately by the stationary phase approximation. Some numerical examples are given, in particular concentrating on when this approximation is valid.

Scattering of elastic waves by a rectangular crack in an anisotropic half-space

The scattering of elastic waves by a rectangular crack in a half-space of arbitrary anisotropy is considered. The application in mind is ultrasonic testing of thick-walled anisotropic components where the crack is close to a planar back surface. The orientation of the crack and the back surface may be arbitrary relative to the anisotropy. The scattering problem is formulated as a hypersingular integral equation for the crack-opening-displacement (COD) by means of the half-space Green’s tensor. The integral equation is solved by expanding the COD in a double series of Chebyshev functions with the correct behavior along the crack’s edges. Insertion into the integral equation and projection onto the same set of functions result in a linear system of equations for the expansion coefficients appearing in the representation of the COD. The transmitting transducer is modeled by the traction beneath it on the scanning surface and the incident field may then be calculated. An electromechanical reciprocity relation is used to model the receiving transducer. Numerical examples are included which show the influence of the anisotropy and especially the presence of a nearby planar back surface.

Ultrasonic 2D SH Crack Detection in a Layered Anisotropic Plate

The 2-D scattering problem of an internal crack in a layered anisotropic plate is considered in this paper. In the model, two ultrasonic SH probes are attached on the upper surface of the plate and the incoming displacement field is generated by one of the probes and the other probe is acting as a receiver. The transmitting and the receiving probe may be the same. The problem is solved by deriving the Green function for the layered plate and then using the integral representation for the total field to obtain an integral equation for the crack opening displacement. The integral equation is solved by expanding the crack opening displacement (COD) in Chebyshev functions. A crucial part of the method is the expansion of the Green function in a free space part, expressed in the crack coordinate system, and a reflection part, expressed in the plate coordinate system. The electrical signal response is calculated by an electromechanical reciprocity relation. Numerical examples are given for a transversally isotropic graphite-epoxy plate, where the symmetry axes are mutually perpendicular in the layers. The results are presented as A-scans, i.e. the electrical response as a function of time.

Modelling of ultrasonic crack detection in anisotropic materials

A 3D elastodynamic model for ultrasonic wave propagation and crack detection in anisotropic materials has been developed. By means of Fourier methods a solution is given for the probe sound field propagating in a half-space or a layered structure. Quasi P-, SV- and SH-mode fields are generated at arbitrary angles. The field interacts with a strip-like crack which is embedded in a half-space or surface breaking in a thick plate with inclined back surface. The probe signal response is calculated via Auld's electromechanical reciprocity relation. Numerical examples of A- and B-scans are presented for transversely isotropic solids.

Measurement models for ultrasonic nondestructive evaluation

The article reviews ways to use the electromechanical reciprocity relation to construct theoretical models of measurement processes in ultrasonic nondestructive evaluation. This relationship is important because it connects the change in the voltages measured at the electrical terminal of the transducer to the perturbation in the mechanical wavefield caused by the change in the propagation environment. It does so by mixing an unperturbed reference wavefield with one containing the perturbed wavefield. Two problems of progressive difficulty are explored. We begin by investigating the imaging of a one-dimensional sinusoidal fluid-solid interface using a cylindrically focused beam and continue by developing a model of the imaging of the mechanical properties of a two-dimensional, thin solid film using a confocal arrangement of point-focused transducers. This last problem uses an approximation to the thin solid film, which reduces its mechanical response to one similar to that of a membrane. Integral relations are given that can be used to form integral equations or to generate asymptotic approximations to the particle displacements and stresses in the film.

Profiling a surface using its echoes

The electromechanical reciprocity relation is used to construct a theoretical model of the imaging of a sinusoidal fluid–solid interface using a cylindrically focused acoustic beam. The electromechanical reciprocity relation is used to connect the change in the voltage measured at the electrical terminal of the transducer to the perturbation in the mechanical wave field caused by a change in the profile of the interface. It does so by mixing an unperturbed reference wave field with one containing the perturbed wave field. We use a regular boundary perturbation expansion to obtain an approximate boundary condition that fits directly into the reciprocity relation. This perturbation assumes both the amplitude and the slope of the profile are small. We limit our discussion to imaging a sinusoidal interface with the understanding that resolution of this profile is central to understanding that of more general profiles. We find that depending on the choice of parameter values the measured profile is not simply a replication of the original sinusoidal profile. Time permitting, we briefly indicate preliminary work on a related model of the imaging of the mechanical properties of a thin solid film using a confocal arrangement of point-focused transducers. [Work supported by NSF.]

Ultrasonic beam reflection from lossy layered cylindrical shells

Nonspecular reflection from a two-layer curved elastic structure consisting of rubber bonded to the outer surface of a steel shell has been studied experimentally and theoretically. The reciever voltage, in a two-transducer experiment, is measured as a function of azimuthal scan angle. The bond rigidity between the rubber and steel is accounted for by a spring model. This model is incorporated into an asymptotic evaluation of the spectral reflection integrals, accounting for the receiver characteristics by electromechanical reciprocity. Decreasing bond rigidity acts to weaken the leaky wave excited in the underlying steel shell and provides a method to assess bond integrity, while the damping loss of the rubber is found to be only a scale factor. A disbond completely suppresses the leaky wave. In comparisons between experimental data and predictions, good agreement is generally seen, also at incident angles different from phase-matched Lamb mode coupling.

A time-domain boundary element model for ultrasonic pulse echo

A time-domain boundary element method and an electro-mechanical reciprocity relation are applied to model the ultrasonic pulse echo in a solid. Three different coupling boundary integral equations have been obtained respectively for the scatterer represented by void, liquid and solid. An exact model is presented for the ultrasonic transmission, scattering and reception.

Three-Dimensional Ultrasonic Crack Detection in Anisotropic Materials

The scattering of probe-generated ultrasonic fields incident upon a strip-like crack in an anisotropic half-space is discussed. In the situation considered, two possibly coinciding probes are attached to the surface of the half-space. One is transmitting waves incident upon the crack and the other one is receiving the scattered waves. An electric signal response is calculated via an electromechanical reciprocity relation. For a crack far away from the probes and the surface, an approximate expression is calculated. Several numerical examples are presented for an isotropic and a transversely isotropic solid. The results are presented as A-, B-, and C-scans.

Three-Dimensional Ultrasonic Crack Detection in Anisotropic Materials

The scattering of probe-generated ultrasonic fields incident upon a strip-like crack in an anisotropic half-space is discussed. In the situation considered, two possibly coinciding probes are attached to the surface of the half-space. One is transmitting waves incident upon the crack and the other one is receiving the scattered waves. An electric signal response is calculated via an electromechanical reciprocity relation. For a crack far away from the probes and the surface, an approximate expression is calculated. Several numerical examples are presented for an isotropic and a transversely isotropic solid. The results are presented as A-, B-, and C-scans.

Research on the dynamic test method for force-balance accelerometers (FBAs) with electric stimulation

Abstract At present, an electromagnetic vibration exciter is the equipment commonly used for the dynamic testing of force-balance accelerometers (FBAs), which is a mechanical stimulation method. This paper researches a method with electric stimulation, which is based on the electromechanical reciprocity of current-output type FBAS (IFBAs). The equivalence between the electrical and mechanical stimulation methods and the test errors are analysed. Experimental results obtained from the two stimulation methods are compared. The test method for IFBAs with electrical stimulation is feasible and may be used instead of the commonly used electromagnetic vibration exciter under certain conditions. Equipment for this test method is inexpensive and can be utilized in on-line application environments.

Interpretation of Auld's electromechanical reciprocity relation via a one-dimensional example

The electromechanical reciprocity relation is interpreted through application to a model problem, the reflection and transmission of ultrasound at a thin layer. The results for this simple problem illustrate how the reciprocity formalism allows the effects of transducer efficiency and phase, ultrasonic propagation to and from the flaw, and ultrasonic interaction with the flaw to be systematically included in a description of the total measurement response. The importance of such descriptions in the separation of the measurement system and flaw contributions to laboratory observations is discussed, and a number of examples where this approach has been applied to more complex measurement geometries are cited by reference.