Time-harmonic Elastography Research Articles

Direct error in constitutive equation formulation for inverse problems in time harmonic elastography

Shear wave imaging techniques allow the evaluation of rigidity and viscosity of tissues locally within a material. From an inverse problem perspective, the approach is quite attractive insofar as it provides a densely sampled displacement field in the interior of the object from which to invert for material properties. We consider several challenges related to elastic wave inverse problems arising in acoustic radiation force imaging. First, we validate an axisymmetric viscoelasticity model suitable for some applications of acoustic radiation force imaging. Second, we consider reconstructing lateral displacement components from measured axial displacement components. Finally, we present a new variational formulation, the direct error in constitutive equation formulation, for inverse problems in time harmonic viscoelastic wave propagation with full-field data. The formulation relies on minimizing the error in the constitutive equation with a momentum equation constraint. Numerical results on model problems show that the formulation is capable of handling discontinuous and noisy strain fields and also converging with mesh refinement for continuous and discontinuous material property distributions. Applications to MRE and ARFI measured wave data are considered.

Performance of a THED system for ruling in/ruling out Liver Cirrhosis as compared with Transient Elastography

Introduction While most ultrasound elastography methods employ transient stimulation methods, the new time harmonic elastography (THED) relies on time-harmonic vibrations in the same manner as magnetic resonance elastography. The aim of our study was to assess the performance of the THED system for ruling in/out liver cirrhosis (LC) considering transient elastography (TE) as the reference method, as well as and the correlation of THED values with TE. Material & Method We evaluated by THED a group of 70 patients. Each subject has been fasting for more than 6 hours before evaluation. 10 valid LS measurements were performed in the same day, both by THED and by TE. We used the TE cut-off values published by Tsochatzis (1): significant fibrosis (F ≥ 2)- 7.0kPa and for LC (F = 4)- 12kPa as reference values. Quality criteria recommended by the manufacturer: SR ≥ 60%, IQR Results From the 70 patients, 34 were women and 36 men. Mean age 55.2 ± 11.7, mean BMI 27.8 ± 6.2 kg/m2. Of the 70 patients, 15.8% (11/70) were F4, 25.7% (18/70) were F2-3, 58.5 % (41/70) were F0-1.We had 100% feasibility for all the patients that were previously evaluated by TE. The cut-off for ruling out LC by THED measurements on our study group was 2 m/s (11.9 kPa). AUROC = 0.83, 95%CI (0.73-0.91), P Conclusions In our study, the cut-of values to rule-out and rule-in LC by LS measurements with THED system were 11.9 kPa, respectively. There was a strong correlation between the LS values obtained by the two elastographic methods.

In vivo time-harmonic ultrasound elastography of the human brain detects acute cerebral stiffness changes induced by intracranial pressure variations

Cerebral stiffness (CS) reflects the biophysical environment in which neurons grow and function. While long-term CS changes can occur in the course of chronic neurological disorders and aging, little is known about acute variations of CS induced by intracranial pressure variations. Current gold standard methods for CS and intracranial pressure such as magnetic resonance elastography and direct pressure recordings are either expensive and slow or invasive. The study objective was to develop a real-time method for in vivo CS measurement and to demonstrate its sensitivity to physiological aging and intracranial pressure variations induced by the Valsalva maneuver in healthy volunteers. We used trans-temporal ultrasound time-harmonic elastography (THE) with external shear-wave stimulation by continuous and superimposed vibrations in the frequency range from 27 to 56 Hz. Multifrequency wave inversion generated maps of shear wave speed (SWS) as a surrogate maker of CS. On average, cerebral SWS was 1.56 ± 0.08 m/s with a tendency to reduce with age (R = −0.76, p < 0.0001) while Valsalva maneuver induced an immediate stiffening of the brain as reflected by a 10.8 ± 2.5% increase (p < 0.0001) in SWS. Our results suggest that CS is tightly linked to intracranial pressure and might be used in the future as non-invasive surrogate marker for intracranial pressure, which otherwise requires invasive measurements.

US Time-Harmonic Elastography: Detection of Liver Fibrosis in Adolescents with Extreme Obesity with Nonalcoholic Fatty Liver Disease.

Purpose To measure in vivo liver stiffness by using US time-harmonic elastography in a cohort of pediatric patients who were overweight to extremely obese with nonalcoholic fatty liver disease (NAFLD) and to evaluate the diagnostic value of time-harmonic elastography for differentiating stages of fibrosis associated with progressive disease. Materials and Methods In this prospective study, 67 consecutive adolescents (age range, 10-17 years; mean body mass index, 34.7 kg/m2; range, 21.4-50.4 kg/m2) with biopsy-proven NAFLD were enrolled. Liver stiffness was measured by using time-harmonic elastography based on externally induced continuous vibrations of 30 Hz to 60 Hz frequency and real-time B-mode-guided wave profile analysis covering tissue depths of up to 14 cm. The diagnostic accuracy of time-harmonic elastography in staging liver fibrosis was assessed with area under the receiver operating characteristic curve (AUC) analysis. Liver stiffness cutoffs for the differentiation of fibrosis stages were identified based on the highest Youden index. Results Time-harmonic elastography was feasible in all patients (0% failure rate), including 70% (n = 47) of individuals with extreme obesity (body mass index above the 99.5th percentile). AUC analysis for the detection of any fibrosis (≥ stage F1), moderate fibrosis (≥ stage F2), and advanced fibrosis (≥ stage F3) was 0.88 (95% confidence interval [CI]: 0.80, 0.96), 0.99 (95% CI: 0.98, 1.00), and 0.88 (95% CI: 0.80, 0.96), respectively. The best liver stiffness cutoffs were 1.52 m/sec for at least stage F1, 1.62 m/sec for at least stage F2, and 1.64 m/sec for at least stage F3. Conclusion US time-harmonic elastography allows accurate detection of moderate fibrosis even in pediatric patients with extreme obesity. Larger clinical trials are warranted to confirm the accuracy of US time-harmonic elastography.

Full-Field-of-View Time-Harmonic Elastography of the Native Kidney

The purpose of this study was to analyze full-field-of-view maps of renal shear wave speed (SWS) measured by time-harmonic elastography (THE) in healthy volunteers in terms of reproducibility, regional variation and physiologic effects. The kidneys of 37 healthy volunteers were investigated by multifrequency THE. The complete renal parenchyma, as well as cortex and medulla, was analyzed. A subgroup was investigated to test reproducibility (n = 3). Significant differences between SWS in cortex, medulla and full parenchyma were observed (2.10 ± 0.17, 1.35 ± 0.11 and 1.71 ± 0.16 m/s, all p values < 0.001) with mean intra-volunteer standard deviations of repeated measurements of 0.04 m/s (1.6%), 0.06 m/s (4.0%) and 0.08 m/s (4.5%), respectively. No effects of kidney anatomy, age, body mass index, blood pressure and heart rate on SWS were observed. THE allows generation of full-field-of-view SWS maps of native kidneys with high reproducibility.

Time-Harmonic Ultrasound elastography of the Descending Abdominal Aorta: Initial Results

Stiffening of central large vessels is considered a key pathophysiologic factor within the cardiovascular system. Current diagnostic parameters such as pulse wave velocity (PWV) indirectly measure aortic stiffness, a hallmark of coronary diseases. The aim of the present study was to perform elastography of the proximal abdominal aorta based on externally induced time-harmonic shear waves. Experiments were performed in 30 healthy volunteers (25 young, 5 old, >50 y) and 5 patients with longstanding hypertension (PWV >10 m/s). B-Mode-guided sonographic time-harmonic elastography was used for measurement of externally induced shear waves at 30-Hz vibration frequency. Thirty-hertz shear wave amplitudes (SWAs) within the abdominal aorta were measured and displayed in real time and processed offline for differences in SWA between systole and diastole (ΔSWA). Data were analyzed using the Kruskal–Wallis test and receiver operating characteristic curve analysis. The change in SWA over the cardiac cycle was reduced significantly in all patients as assessed with ΔSWA (volunteers: mean = 10 ± 5 μm, patients: mean = 4 ± 1 μm; p < 0.001). The best separation of healthy volunteers from patients was obtained with a ΔSWA threshold of 4.7 μm, resulting in a sensitivity of 0.9 and a specificity of 1.0, with an overall area under the curve of 0.96. Time harmonic elastography of the abdominal aorta is feasible and shows promise for the exploitation of time-varying shear wave amplitudes as a diagnostic marker for aortic wall stiffening. Patients with elevated PWVs suggesting increased aortic wall stiffness were best identified by ΔSWA—a parameter that could be related to the ability of the vessel walls to distend on passages of the pulse wave.

Physiologic Reduction of Hepatic Venous Blood Flow by the Valsalva Maneuver Decreases Liver Stiffness.

Liver stiffness increases after intake of food or water, suggesting that hepatic venous blood flow affects the results of elastographic measurements. This study investigated the correlation between in vivo liver stiffness and hepatic blood flow using the Valsalva maneuver for reducing intrahepatic venous blood flow. Intrahepatic changes in venous blood flow were assessed by sonography based on the pulsed wave Doppler velocity, vessel diameter assessment, and blood flow volume measurements in the portal vein and right hepatic vein. Time-harmonic elastography at 7 harmonic driving frequencies (30-60 Hz) was used to measure liver stiffness in the right liver lobe of 15 healthy volunteers. The right hepatic vein diameter, flow volume, and peak pulsed wave velocity decreased during the Valsalva maneuver from mean ± SD values of 8.64 ± 1.85 to 6.55 ± 1.84 mm (P = .002), 0.53 ± 0.23 to 0.37 ± 0.26 L/min (P = .037), and 22.14 ± 4.87 to 17.38 ± 5.41 cm/s (P = .01), respectively. This maneuver decreased liver stiffness in all volunteers by a mean of approximately 13% from 1.71 ± 0.22 to 1.48 ± 0.22 m/s (P = .00006). Our results demonstrate that liver stiffness is sensitive to altered venous blood flow, which is of clinical importance when using elastography for evaluation of portal hypertension. Furthermore, our results indicate that accurate measurement of liver stiffness requires standardized breathing conditions to rule out effects of changes in hepatic blood flow on elastographic findings.

Time-Harmonic Elastography of the Liver is Sensitive to Intrahepatic Pressure Gradient and Liver Decompression after Transjugular Intrahepatic Portosystemic Shunt (TIPS) Implantation

We investigated the correlation between hepatic venous pressure gradient (HVPG) and liver shear wave speed (SWS) measured by multi-frequency time-harmonic ultrasound elastography (THE) before and after transjugular intrahepatic portosystemic shunt (TIPS) implantation. Ten patients with ascites, cirrhotic liver disease and portal hypertension were prospectively examined with invasive HVPG measurement and THE before and after TIPS implantation. HVPG and SWS decreased after TIPS placement from 20.4 ± 2.2 mmHg to 9.8 ± 4.1 mmHg (mean ± standard deviation) and from 3.87 ± 0.54 m/s to 3.27 ± 0.44 m/s. Mean reduction HVPG was −10.6 ± 3.7 mmHg, p < 0.001; mean reduction SWS was −0.60 ± 0.29 m/s, p < 0.001. A linear correlation was observed between HVPG and SWS (R = 0.59, p = 0.0061). THE-measured SWS is a first potential direct ultrasound marker for liver decompression following TIPS in ascites-associated cirrhotic liver disease and therefore might be suitable to non-invasively detect portal hypertension.

Two-Dimensional Time-Harmonic Elastography of the Human Liver and Spleen

Measurement of shear wave speed of the liver and spleen by elastography is an established diagnostic procedure for the detection of hepatic fibrosis, portal hypertension and esophageal varices. However, current elastography systems are limited by the size and penetration depth of elastographic windows. In this study, 2D time-harmonic elastography is proposed for generating full field-of-view shear wave speed maps in great depth. Two-dimensional time-harmonic elastography uses external harmonic stimulation at multiple frequencies to create compound shear wave speed maps. The method is tested in a phantom with soft and stiff inclusions and used for elastography of the liver and spleen in 13 asymptomatic volunteers. Each volunteer was scanned twice to determine the sensitivity of the method to physiologic variations: first, after 2 h of fasting, and a second time, 15 min after drinking 1 L of water. The wave speed maps of the phantom clearly identified the soft and stiff inclusions, yielding values that were consistent with those from magnetic resonance elastography. In vivo wave speed values were 1.49 ± 0.11 m/s for the liver and 2.03 ± 0.15 m/s for the spleen in a lower-frequency band centered at 40 Hz and 3.15 ± 0.30 m/s for the spleen in a higher-frequency band centered at 120 Hz. After water intake, wave speed values increased by 6% in the liver (p = 0.002) and decreased in the spleen by 4% (p = 0.021, low-frequency band) and 6% (p = 0.0002, high-frequency band), suggesting the high sensitivity of the method to altered blood flow and perfusion pressure. Two-dimensional time-harmonic elastography of the liver and spleen is a promising method for measuring tissue stiffness at different states of blood flow and perfusion in a large tissue window and at great penetration depth.

Time Harmonic Elastography Reveals Sensitivity of Liver Stiffness to Water Ingestion

The aim of the study was to test the sensitivity of liver stiffness (LS) measured by time harmonic elastography in large tissue windows to water uptake and post-prandial effects. Each subject gave written informed consent to participate in this institutional review board-approved prospective study. LS was measured by time harmonic elastography in 10 healthy volunteers pre- and post-prandially, as well as before, directly after and 2 h after drinking water. The LS–time function during water intake was measured in 14 scans over 3 h in five volunteers. LS increased by 10% (p = 0.0015) post-prandially and by 11% (p = 0.0024) after pure water ingestion, and decreased to normal values after 2 h. LS was lower after overnight fasting than after 2-h fasting (3%, p = 0.04). Over the time course, LS increased to post-water peak values 15 min after drinking 0.25 L water and remained unaffected by further ingestion of water. In conclusion, our study indicates that LS measured by time harmonic elastography represents an effective-medium property sensitive to physiologic changes in vascular load of the liver.

Multifrequency Time-Harmonic Elastography for the Measurement of Liver Viscoelasticity in Large Tissue Windows

Elastography of the liver for the non-invasive diagnosis of hepatic fibrosis is an established method. However, investigations of obese patients or patients with ascites are often limited by small and superficial elastographic windows. Therefore, multifrequency time-harmonic elastography (THE) based on time-resolved A-line ultrasound has recently been developed for measuring liver viscoelasticity in wide soft tissue windows and at greater depths. In this study, THE was integrated into a clinical B-mode scanner connected to a dedicated actuator bed driven by superimposed vibrations of 30- to 60-Hz frequencies. The resulting shear waves in the liver were captured along multiple profiles 7 to 14 cm in width and automatically processed for reconstruction of mean efficient shear wave speed and shear wave dispersion slope. This new modality was tested in healthy volunteers and 22 patients with clinically proven cirrhosis. Patients could be separated from controls by higher shear wave speeds (3.11 ± 0.64 m/s, 2.14–4.81 m/s, vs. 1.74 ± 0.10 m/s, 1.60–1.91 m/s) without significant degradation of data by high body mass index or ascites. Furthermore, the wave speed dispersion slope was significantly (p = 0.0025) lower in controls (5.2 ± 1.8 m/s/kHz) than in patients (39.1 ± 32.2 m/s/kHz). In conclusion, THE is useful for the diagnosis of cirrhosis in large tissue windows.

In vivo time-harmonic multifrequency elastography of the human liver

Elastography is capable of noninvasively detecting hepatic fibrosis by imposing mechanical stress and measuring the viscoelastic response in the liver. Magnetic resonance elastography (MRE) relies on time-harmonic vibrations, while most dynamic ultrasound elastography methods employ transient stimulation methods. This study attempts to benefit from the advantages of time-harmonic tissue stimulation, i.e. relative insensitivity to obesity and ascites and mechanical approachability of the entire liver, and the advantages of ultrasound, i.e. time efficiency, low costs, and wide availability, by introducing in vivo time-harmonic elastography (THE) of the human liver using ultrasound and a broad range of harmonic stimulation frequencies. THE employs continuous harmonic shear vibrations at 7 frequencies from 30 to 60 Hz in a single examination and determines the elasticity and the viscosity of the liver from the dispersion of the shear wave speed within the applied frequency range. The feasibility of the method is demonstrated in the livers of eight healthy volunteers and a patient with cirrhosis. Multifrequency MRE at the same drive frequencies was used as elastographic reference method. Similar values of shear modulus and shear viscosity according the Kelvin–Voigt model were obtained by MRE and THE, indicating that the new method is suitable for in vivo quantification of the shear viscoelastic properties of the liver, however, in real-time and at a fraction of the costs of MRE. In conclusion, THE may provide a useful tool for fast assessment of the viscoelastic properties of the liver at low costs and without limitations in obesity, ascites or hemochromatosis.

Isovolumetric Elasticity Alteration in the Human Heart Detected by In Vivo Time-Harmonic Elastography

Time harmonic elastography (THE) has recently been introduced for measurement of the periodic alteration in myocardial shear modulus based on externally induced low-frequency acoustic vibrations produced by a loudspeaker. In this study, we propose further developments of cardiac THE toward a clinical modality including integration of the vibration source into the patient bed and automated parameter extraction from harmonic shear wave amplitudes, wall motion profiles and synchronized electrocardiographic records. This method has enabled us to evaluate the delay between wall motion and wave amplitude alteration for the measurement of isovolumetric times of elasticity alteration during contraction (τ(C)) and relaxation (τ(R)) in a group of 32 healthy volunteers. On average, the wave amplitudes changed between systole and diastole by a factor of 1.7 ± 0.3, with a τ(C) of 137 ± 61 ms and a τ(R) of 68 ± 73 ms, which agrees with results obtained with the more time-consuming and expensive cardiac magnetic resonance elastography. Furthermore, because of the high sampling rate, elasto-morphometric parameters such as transition times and the area of wave amplitude-cardiac motion cycles can be processed in an automated way for the future clinical detection of myocardial relaxation abnormalities.

In Vivo Time Harmonic Elastography of the Human Heart

Time harmonic elastography is introduced as a modality for assessing myocardial elasticity changes during the cardiac cycle. It is based on external stimulation and real-time analysis of 30-Hz harmonic shear waves in axial direction of a parasternal line of sight through the lateral heart wall. In 20 healthy volunteers, the externally induced waves showed smaller amplitudes during systole (76.0 ± 30.8 μm) and higher amplitudes during diastole (126.7 ± 52.1 μm). This periodic wave amplitude alteration preceded ventricular contraction and dilation by about 100 ms. The amplitude ratio of 1.75 ± 0.49 indicates a relative change in myocardial shear elasticity on the order of 14 ± 11. These results well agree with observations made by cardiac magnetic resonance elastography for a similar displacement component and region of the heart. The proposed method provides reproducible elastodynamic information on the heart in real-time and may help in diagnosing myocardial relaxation abnormalities in the future.