Harmonic Motion Imaging Research Articles

Informing subjects on the measurements performed induces changes in their running mechanics

A finite element (FE) model is employed to investigate the dynamic response of soft tissues under external excitations, particularly corresponding to the case of harmonic motion imaging. A solid 3D mixed 'u-p' element S8P0 is implemented to capture the near-incompressibility inherent in soft tissues. Two important aspects in structural modelling of these tissues are studied; these are the influence of viscous damping on the dynamic response and, following FE-modelling, a developed state-space formulation that valuates the efficiency of several order reduction methods. It is illustrated that the order of the mathematical model can be significantly reduced, while preserving the accuracy of the observed system dynamics. Thus, the reduced-order state-space representation of soft tissues for general dynamic analysis significantly reduces the computational cost and provides a unitary framework for the 'forward' simulation and 'inverse' estimation of soft tissues. Moreover, the results suggest that damping in soft-tissue is significant, effectively cancelling the contribution of all but the first few vibration modes.

In Vivo Feasibility of Real-Time Monitoring of Focused Ultrasound Surgery (FUS) Using Harmonic Motion Imaging (HMI)

In this study, the Harmonic Motion Imaging for Focused Ultrasound (HMIFU) technique is applied to monitor changes in mechanical properties of tissues during thermal therapy in a transgenic breast cancer mouse model in vivo. An HMIFU system, composed of a 4.5-MHz focused ultrasound (FUS) and a 3.3-MHz phased-array imaging transducer, was mechanically moved to image and ablate the entire tumor. The FUS transducer was driven by an amplitude-modulated (AM) signal at 15 Hz. The acoustic intensity ( I(spta)) was equal to 1050 W/cm(2) at the focus. A digital low-pass filter was used to filter out the spectrum of the FUS beam and its harmonics prior to displacement estimation. The resulting axial displacement was estimated using 1-D cross-correlation on the acquired RF signals. Results from two mice with eight lesions formed in each mouse (16 lesions total) showed that the average peak-to-peak displacement amplitude before and after lesion formation was respectively equal to 17.34 +/- 1.34 microm and 10.98 +/- 1.82 microm ( p << 0.001). Cell death was also confirmed by hematoxylin and eosin histology. HMI displacement can be used to monitor the relative tissue stiffness changes in real time during heating so that the treatment procedure can be performed in a time-efficient manner. The HMIFU system may, therefore, constitute a cost-efficient and reliable alternative for real-time monitoring of thermal ablation.

Quantitative viscoelastic parameters measured by harmonic motion imaging

Quantifying the mechanical properties of soft tissues remains a challenging objective in the field of elasticity imaging. In this work, we propose an ultrasound-based method for quantitatively estimating viscoelastic properties, using the amplitude-modulated harmonic motion imaging (HMI) technique. In HMI, an oscillating acoustic radiation force is generated inside the medium by using focused ultrasound and the resulting displacements are measured using an imaging transducer. The proposed approach is a two-step method that uses both the properties of the propagating shear wave and the phase shift between the applied stress and the measured strain in order to infer to the shear storage (G′) and shear loss modulus (G″), which refer to the underlying tissue elasticity and viscosity, respectively. The proposed method was first evaluated on numerical phantoms generated by finite-element simulations, where a very good agreement was found between the input and the measured values of G′ and G″. Experiments were then performed on three soft tissue-mimicking gel phantoms. HMI measurements were compared to rotational rheometry (dynamic mechanical analysis), and very good agreement was found at the only overlapping frequency (10 Hz) in the estimate of the shear storage modulus G′ (14% relative error, averaged p-value of 0.34), whereas poorer agreement was found in G″ (55% relative error, averaged p-value of 0.0007), most likely due to the significantly lower values of G″ of the gel phantoms, posing thus a greater challenge in the sensitivity of the method. Nevertheless, this work proposes an original model-independent ultrasound-based elasticity imaging method that allows for direct, quantitative estimation of tissue viscoelastic properties, together with a validation against mechanical testing.

Finite element dynamic analysis of soft tissues using state-space model

A finite element (FE) model is employed to investigate the dynamic response of soft tissues under external excitations, particularly corresponding to the case of harmonic motion imaging. A solid 3D mixed ‘u–p’ element S8P0 is implemented to capture the near-incompressibility inherent in soft tissues. Two important aspects in structural modelling of these tissues are studied; these are the influence of viscous damping on the dynamic response and, following FE-modelling, a developed state-space formulation that valuates the efficiency of several order reduction methods. It is illustrated that the order of the mathematical model can be significantly reduced, while preserving the accuracy of the observed system dynamics. Thus, the reduced-order state-space representation of soft tissues for general dynamic analysis significantly reduces the computational cost and provides a unitary framework for the ‘forward’ simulation and ‘inverse’ estimation of soft tissues. Moreover, the results suggest that damping in soft-tissue is significant, effectively cancelling the contribution of all but the first few vibration modes.

Dynamic simulation of viscoelastic soft tissues in harmonic motion imaging application

A finite element model was built to simulate the dynamic behavior of soft tissues subjected to sinusoidal excitation during harmonic motion imaging. In this study, soft tissues and tissue-like phantoms were modeled as isotropic, viscoelastic, and nearly incompressible media. A 3D incompressible mixed u– p element of eight nodes, S1P0, was developed to accurately calculate the stiffness matrix for soft tissues. The finite element equations of motion were solved using the Newmark method. The Voigt description for tissue viscosity was applied to estimate the relative viscous coefficient from the phase shift between the response and excitation in a harmonic case. After validating our model via ANSYS simulation and experiments, a MATLAB finite element program was then employed to explore the effect of excitation location, viscosity, and multiple frequencies on the dynamic displacement at the frequency of interest.

Simulations of lesion detection using a combined phased array LHMI-technique

Ultrasound based elasticity imaging techniques have been developed during the past decades. Some of these techniques are based on an internal radiation force stimulation in which a transient or dynamic radiation force is produced by using a single or dual-frequency sonication. In addition, sonication and data acquisition can be implemented using combined or separate transducers. In this simulation study of lesion detection using localized harmonic motion imaging (LHMI), we used a combined phased array designed for simultaneous thermal ablation and lesion detection. In the sonication mode, a focused single-frequency amplitude-modulated sonication is used to induce harmonic motion and in the tracking mode, some of the array elements are used for pulse-echo tracking of the induced displacements. The results showed that the size of the lesion affected the induced displacement around the sonication point. The displacement tracking simulations demonstrated that these changes in the displacement distributions can be detected using only a few of the array elements in the tracking mode but the exact size of the lesion can not be detected accurately. The simulations also showed that two lesions having the radius of 2.5 mm can be distinguished if distance between these lesions is at least 2.5 mm.

A mechanical model to compute elastic modulus of tissues for harmonic motion imaging

Numerous experimental and computational methods have been developed to estimate tissue elasticity. The existing testing techniques are generally classified into in vitro, invasive in vivo and non-invasive in vivo. For each experimental method, a computational scheme is accordingly proposed to calculate mechanical properties of soft biological tissues. Harmonic motion imaging (HMI) is a new technique that performs radio frequency (RF) signal tracking to estimate the localized oscillatory motion resulting from a radiation force produced by focused ultrasound. A mechanical model and computational scheme based on the superposition principle are developed in this paper to estimate the Young's modulus of a tissue mimicking phantom and bovine liver in vitro tissue from the harmonic displacement measured by HMI. The simulation results are verified by two groups of measurement data, and good agreement is shown in each comparison. Furthermore, an inverse function is observed to correlate the elastic modulus of uniform phantoms with amplitude of displacement measured in HMI. The computational scheme is also implemented to estimate 3D elastic modulus of bovine liver in vitro.

Experimental validation of the amplitude‐modulated harmonic motion imaging for tissues stiffness estimation

It has been previously shown that amplitude‐modulated harmonic motion imaging (AM‐HMI) has the capability of induce and image tissue displacement during the application of an oscillatory radiation force. Here, we aim at validating theoretical HMI findings with experimental results on similar phantoms. A finite‐element‐method (FEM) was first used to model a dynamic response of phantoms with inclusions at different stiffnesses and sizes. The FEM and experimental results were compared and used to describe the behavior of the locally displaced tissue. The radiation force was generated by a 4.68 MHz FUS transducer modulated at 50 Hz with acoustic pressure levels varied between 1.2 and 4 MPa. A 7.5 MHz pulse‐echo transducer was placed through the center of the FUS transducer and used to image the displaced tissue. A 1D‐cross‐correlation method on successive RF signals was used to estimate the axial‐displacement. The FEM and experimental results displayed good agreement in displacement patterns, i.e., the highes...

The feasibility of local harmonic motion imaging for the guidance and control of focused ultrasound surgery

A local harmonic motion (LHM) can be generated within the tissues by the periodic induction of radiation force using a focused ultrasound (FUS) transducer. Tissue motion can then be tracked by collecting RF signals during the excitation using a separate transducer. Finally, displacement estimates can be obtained by cross-correlating the collected RF signals. The characteristics of the induced LHM depend on the local elastic properties of the tissues making it an attractive tool for imaging and therapy control applications. LHM measurements have been obtained in vivo on rabbit muscle and it was observed that the amplitude of the motion was significantly reduced after coagulation. LHM was successfully used to spatially detect the presence of the coagulation lesions within the tissues as a drop in LHM amplitude. It was also possible to detect the location of an implanted VX2 tumor when a spatial scan was performed as the LHM amplitude was lower inside the tumor because of an increased stiffness. Measurements of LHM during tissue heating using FUS reflected the changes in stiffness and revealed the apparition of coagulation showing the potential of these measurements as an alternative control for the FUS exposure. [Work supported by NIH GrantR33 CA102884 and CRC.]

In vivo feasibility of local harmonic motion imaging and its use for thermal surgery control

A local harmonic motion can be generated within the tissues by the periodic induction of radiation force using a focused ultrasound (FUS) transducer. Tissue motion can then be tracked by collecting rf signals during the excitation using a separate transducer. Finally, displacement estimates can be obtained by cross‐correlating the collected rf signals. The characteristics of the induced LHM depend on the local elastic properties of the tissues making it an attractive tool for imaging and therapy control applications. LHM measurements have been obtained in vivo on rabbit muscle and it was observed that the amplitude of the motion was significantly reduced after coagulation. LHM was successfully used to spatially detect the presence of the coagulation lesions within the tissues as a drop in LHM amplitude. It was also possible to detect the location of an implanted VX2 tumor when a spatial scan was performed as the LHM amplitude was lower inside the tumor because of an increased stiffness. Measurements of LHM during tissue heating using FUS reflected the changes in stiffness and revealed the apparition of coagulation showing the potential of these measurements as an alternative control for the FUS exposure. [Work supported by NIH Grant R33 CA102884 and the Canadian Research Chair Program.]

Harmonic motion imaging for focused ultrasound (HMIFU): a fully integrated technique for sonication and monitoring of thermal ablation in tissues

FUS (focused ultrasound), or HIFU (high-intensity-focused ultrasound) therapy, a minimally or non-invasive procedure that uses ultrasound to generate thermal necrosis, has been proven successful in several clinical applications. This paper discusses a method for monitoring thermal treatment at different sonication durations (10 s, 20 s and 30 s) using the amplitude-modulated (AM) harmonic motion imaging for focused ultrasound (HMIFU) technique in bovine liver samples in vitro. The feasibility of HMI for characterizing mechanical tissue properties has previously been demonstrated. Here, a confocal transducer, combining a 4.68 MHz therapy (FUS) and a 7.5 MHz diagnostic (pulse-echo) transducer, was used. The therapy transducer was driven by a low-frequency AM continuous signal at 25 Hz, producing a stable harmonic radiation force oscillating at the modulation frequency. A pulser/receiver was used to drive the pulse-echo transducer at a pulse repetition frequency (PRF) of 5.4 kHz. Radio-frequency (RF) signals were acquired using a standard pulse-echo technique. The temperature near the ablation region was simultaneously monitored. Both RF signals and temperature measurements were obtained before, during and after sonication. The resulting axial tissue displacement was estimated using one-dimensional cross correlation. When temperature at the focal zone was above 48 °C during heating, the coagulation necrosis occurred and tissue damage was irreversible. The HMI displacement profiles in relation to the temperature and sonication durations were analyzed. At the beginning of heating, the temperature at the focus increased sharply, while the tissue stiffness decreased resulting in higher HMI displacements. This was confirmed by an increase of 0.8 µm °C−1(r = 0.93, p < .005). After sustained heating, the tissue became irreversibly stiffer, followed by an associated decrease in the HMI displacement (−0.79 µm °C−1, r = −0.92, p < 0.001). Repeated experiments showed a reproducible pattern of the HMI displacement changes with a temperature at a slope equal to 0.8 ± 0.11 and − 0.79 ± 0.14 µm °C−1, prior to and after lesion formation in seven bovine liver samples, respectively. This technique was thus capable of following the protein-denatured lesion formation based on the variation of the HMI displacements. This method could, therefore, be applied for real-time monitoring of temperature-related stiffness changes of tissues during FUS, HIFU or other thermal therapies.

Focused ultrasound surgery monitoring using local harmonic motion imaging

The present study established the feasibility of a real-time monitoring technique for focused ultrasound (FUS) lesion formation using localized harmonic motion imaging. This oscillatory motion was generated within tissues by periodically induced radiation force using a FUS transducer (oscillatory motion frequencies between 50 and 300 Hz). The harmonic motion was estimated using cross correlation of rf ultrasonic signals acquired at different instances during the motion by using a separate US diagnostic transducer excited by a pulser/receiver. The technique was evaluated on rabbit muscle under in vitro and in vivo conditions. Fourteen FUS lesions were induced in vivo inside an MR scanner to obtain simultaneous ultrasound harmonic motion tracking and MR thermometry. The calculated maximum amplitude of the induced harmonic motion before and after the lesion formation was significantly different for all the tested motion frequencies. During the FUS exposure a drop in the maximum amplitude value was observed and could be associated to a lesion formation. After the lesion formation, the harmonic motion was measured across the exposure region, and the lesion was detected as a reduction in the maximum motion amplitude value at the coagulated region. [Work supported by NIH Grant R21/R33 CA102884-01.]

Single-Element Focused Ultrasound Transducer Method for Harmonic Motion Imaging

The harmonic motion imaging (HMI) technique for simultaneous monitoring and generation of ultrasound therapy using two separate focused ultrasound transducer elements was previously demonstrated. In this study, a new HMI technique is described that images tissue displacement induced by a harmonic radiation force using a single focused-ultrasound element. A wave propagation simulation model first indicated that, unlike in the two-beam configuration, the amplitude-modulated beam produced a stable focal zone for the applied harmonic radiation force. The AM beam thus offered the unique advantage of sustaining the application of the spatially-invariant radiation force. Experiments were performed on gelatin phantoms and ex vivo tissues. The radiation force was generated by a 4.68 MHz focused ultrasound (FUS) transducer using a 50 Hz amplitude-modulated wave. A 7.5 MHz pulse-echo transducer was used to acquire rf echoes during the application of the harmonic radiation force. Consecutive rf echoes were acquired with a pulse repetition frequency (PRF) of 6.5 kHz and 1D cross-correlation was performed to estimate the resulting axial tissue displacement. The HMI technique was shown capable of estimating stiffness-dependent displacement amplitudes. Finally, taking advantage of the real-time capability of the HMI technique, temperature-dependent measurements enabled monitoring ofHIFU sonication in ex vivo tissues. The new HMI method may thus enable a highly-localized force and stiffness-dependent measurements as well as real-time and low-cost HIFU monitoring.

An amplitude-modulated harmonic motion imaging method for mapping tissue ablation

Previously, a single-element focused transducer method inducing amplitude-modulated (AM) radiation force deep within the tissue was introduced. This technique offers real-time capability for monitoring the change in the tissue mechanical properties during focused ultrasound (FUS) therapy. In this paper, we extend the application of this technique for 2D mapping of the FUS lesion. The harmonic radiation force was generated by a 4.68-MHz focused transducer modulated at 50–100 Hz. Radio frequency (rf) data were acquired at 7.5 MHz with a PRF of 6.5 kHz, and displacements were estimated using a 1D cross-correlation algorithm on successive rf signals. A bandpass analog filter with fc1=5 MHz and fc2=8 MHz was employed to remove the spectrum of the focused beam. The real-time monitoring method was adjusted to induce 2-s sonication time using a continuous wave, followed by 100-ms AM signal to image tissue displacements. The experiments were performed on ex vivo porcine liver. The tissue was raster-scanned before and after lesion formation. Results indicated that displacement amplitudes decreased after lesion formation due to the associated elasticity change, and thus 1-cm-diameter lesions were accurately mapped. Future investigations of this technique will include temperature and coagulation mapping in vivo.

Investigation of Optimal Method for Inducing Harmonic Motion in Tissue Using a Linear Ultrasound Phased Array — A Simulation Study

Many noninvasive ultrasound techniques have been developed to explore mechanical properties of soft tissues. One of these methods, Localized Harmonic Motion Imaging (LHMI), has been proposed to be used for ultrasound surgery monitoring. In LHMI, dynamic ultrasound radiation-force stimulation induces displacements in a target that can be measured using pulse-echo imaging and used to estimate the elastic properties of the target. In this initial, simulation study, the use of a one-dimensional phased array is explored for the induction of the tissue motion. The study compares three different dual-frequency and amplitude-modulated single-frequency methods for the inducing tissue motion. Simulations were computed in a homogeneous soft-tissue volume. The Rayleigh integral was used in the simulations of the ultrasound fields and the tissue displacements were computed using a finite-element method (FEM). The simulations showed that amplitude-modulated sonication using a single frequency produced the largest vibration amplitude of the target tissue. These simulations demonstrate that the properties of the tissue motion are highly dependent on the sonication method and that it is important to consider the full three-dimensional distribution of the ultrasound field for controlling the induction of tissue motion.

Harmonic motion imaging

A method of determining a property of a desired region in an object includes transmitting first and second energy beams from first and second sources into the object such that the beams intersect at the desired region to induce vibration of the desired region, transmitting energy from a third source into the desired region, receiving signals from the desired region due to the energy from the third source, and analyzing at least one of amplitude, phase and frequency of the vibration of the desired region indicated by the received signals to determine the property of the desired region.

Estimating localized oscillatory tissue motion for assessment of the underlying mechanical modulus

The technique of harmonic motion imaging (HMI) uses the localized stimulus of the oscillatory ultrasonic radiation force as produced by two overlapping beams of distinct frequencies, and estimates the resulting harmonic displacement in the tissue in order to assess its underlying mechanical properties. In this paper, we studied the relationship between measured displacement and stiffness in gels and tissues in vitro. Two focused ultrasound transducers with a 100 mm focal length were used at frequencies of 3.7500 MHz and either 3.7502 (or 3.7508 MHz), respectively, in order to produce an oscillatory motion at 200 Hz in the gel or tissue. A 1.1 MHz diagnostic transducer (Imasonics, Inc.) was also focused at 100 mm and acquired 5 ms RF signals (pulse repetition frequency (PRF)=3.5 kHz) at 100 MHz sampling frequency during radiation force application. First, three 50 × 50 mm 2 acrylamide gels were prepared at concentrations of 4%, 8% and 16%. The resulting displacement was estimated using crosscorrelation techniques between successively acquired RF signals with a 2 mm window and 80% window overlap at 1260 W/cm 2. A normal 1-D indentation instrument (TeMPeST) applied oscillatory loads at 0.1–200 Hz with a 5 mm-diameter flat indenter. Then, 12 displacement measurements in 6 porcine muscle specimens (two measurements/case, as above) were made in vitro, before and after ablation which was performed for 10 s at 1260 W/cm 2. In all gel cases, the harmonic displacement was found to linearly increase with intensity and exponentially decrease with gel concentration. The TeMPeST measurements showed that the elastic moduli for the 4%, 8% and 16% gels equaled 3.93 ± 0.06, 17.1 ± 0.2 and 75 ± 2 kPa, respectively, demonstrating that the HMI displacement estimate depends directly on the gel stiffness. Finally, in the tissues samples, the mean displacement amplitude showed a twofold decrease between non-ablated and ablated tissue, demonstrating a correspondence between the HMI response and an increase in stiffness measured with the TeMPeST instrument.

Localized harmonic motion imaging: theory, simulations and experiments

Several techniques have been developed in an effort to estimate mechanical properties of tissues. These techniques typically estimate static or harmonic motion resulting from an externally or internally applied mechanical stimulus. In this paper, we discuss the advantages of utilizing a new technique that performs radiofrequency (RF) signal tracking to estimate the localized oscillatory motion resulting from the harmonic radiation force produced by two focused ultrasound (US) transducer elements with overlapping beams oscillating at distinct frequencies. Finite-element and Monte-Carlo simulations were performed to characterize the range of oscillatory displacements produced by a harmonic radiation force. In the experimental verification, three transducers were used: two single-element focused transducers and one lead zirconate-titanate (PZT) composite 16-element probe. Four agar gels were utilized to determine the effect of stiffness on the motion amplitude. Estimates of the displacement relative to the initial position ( i.e., at the onset of the application of the radiation force) were obtained during the application of the radiation force that oscillated at frequencies ranging between 200 Hz and 800 Hz. In the simulations, the estimated oscillatory displacement spanned from −800 to 600 μm and the frequencies of excitation could easily be estimated from the temporal variation of the displacement. In addition, a frequency upshift (on the order of tens of Hz) was estimated with stiffness increase. Furthermore, an exponential decrease of the displacement amplitude with stiffness was observed at all frequencies investigated. An M-mode version to depict both the spatial and temporal variations of the locally induced displacement was used. In experiments with gels of different stiffness, the resulting amplitude of the harmonic displacement estimated oscillated at the same frequencies and ranged from −300 to 250 μm. An exponential decrease of the displacement amplitude with the gel stiffness was also observed. In tissue experiments, the results showed that the method is feasible in tissues and that focused US surgery (FUS) ablation can be detected. These preliminary results demonstrate the feasibility of imaging localized harmonic motion as induced by an oscillatory US radiation force. Due to the highly localized and harmonic nature of the estimated response, this technique may be proven to be highly suitable for simple and accurate estimation of the elastic modulus variation in tissues due to disease. (E-mail: elisak@bwh.harvard.edu)

Harmonic motion imaging: a new technique for the estimation of mechanical properties in tissues

Harmonic motion imaging: a new technique for the estimation of mechanical properties in tissues