Waveguide effects and implications for cardiac magnetic resonance elastography: A finite element study

Magnetic resonance elastography (MRE) is increasingly being applied to thin or small structures in which wave propagation is dominated by waveguide effects, which can substantially bias stiffness results with common processing approaches. The purpose of this work was to investigate the importance of such biases and artifacts on MRE inversion results in: (i) various idealized 2D and 3D geometries with one or more dimensions that are small relative to the shear wavelength; and (ii) a realistic cardiac geometry. Finite element models were created using simple 2D geometries as well as a simplified and a realistic 3D cardiac geometry, and simulated displacements acquired by MRE from harmonic excitations from 60 to 220 Hz across a range of frequencies. The displacement wave fields were inverted with direct inversion of the Helmholtz equation with and without the application of bandpass filtering and/or the curl operator to the displacement field. In all geometries considered, and at all frequencies considered, strong biases and artifacts were present in inversion results when the curl operator was not applied. Bandpass filtering without the curl was not sufficient to yield accurate recovery. In the 3D geometries, strong biases and artifacts were present in 2D inversions even when the curl was applied, while only 3D inversions with application of the curl yielded accurate recovery of the complex shear modulus. These results establish that taking the curl of the wave field and performing a full 3D inversion are both necessary steps for accurate estimation of the shear modulus both in simple thin-walled or small structures and in a realistic cardiac geometry when using simple inversions that neglect the hydrostatic pressure term. In practice, sufficient wave amplitude, signal-to-noise ratio, and resolution will be required to achieve accurate results.

Vibration safety limits for magnetic resonance elastography

Magnetic resonance elastography (MRE) has been demonstrated to have potential as a clinical tool for assessing the stiffness of tissue in vivo. An essential step in MRE is the generation of acoustic mechanical waves within a tissue via a coupled mechanical driver. Motivated by an increasing volume of human imaging trials using MRE, the objectives of this study were to audit the vibration amplitude of exposure for our IRB-approved human MRE studies, to compare these values to a conservative regulatory standard for vibrational exposure and to evaluate the applicability and implications of this standard for MRE. MRE displacement data were examined from 29 MRE exams, including the liver, brain, kidney, breast and skeletal muscle. Vibrational acceleration limits from a European Union directive limiting occupational exposure to whole-body and extremity vibrations (EU 2002/44/EC) were adjusted for time and frequency of exposure, converted to maximum displacement values and compared to the measured in vivo displacements. The results indicate that the vibrational amplitudes used in MRE studies are below the EU whole-body vibration limit, and the EU guidelines represent a useful standard that could be readily accepted by Institutional Review Boards to define standards for vibrational exposures for MRE studies in humans.

Shear waves induced by moving needle in MR elastography

Magnetic resonance elastography (MRE) is a phase contrast-based method for observing shear wave propagation in a material to determine its stiffness. The objective of this study was to determine whether shear waves suitable for MRE could be induced using a moving acupuncture needle. Tissue-simulating bovine gel phantom and a 0.4 mm diameter acupuncture needle were used in the experiment. The results showed that observable shear waves could be induced in the gel phantom by cyclic needle motion. The observed wavelength varied with excitation frequency, as expected. Generating shear waves using moving needles may be a useful tool to study the basic mechanism of acupuncture with MRE. Further study will be conducted to observe the wave motion in inhomogeneous media and acupuncture-induced effects in in-vivo studies.

Vascular wall elasticity measurement by magnetic resonance imaging

The goal of this current study was to determine whether an MRI-based elastography (MRE) method can visualize and assess propagating mechanical waves within fluid-filled vessels and to investigate the feasibility of measuring the elastic properties of vessel walls and quantitatively assessing stenotic lesions by using MRE. The ability to measure the Young's modulus-wall thickness product was tested using a thin-walled latex vessel model. Also tested in vessel models was the ability to quantitate the degree of stenosis by measuring transmitted and reflected mechanical waves. This method was then applied to ex vivo porcine models and in vivo human arteries to further test its feasibility. The results provide preliminary evidence that MRE can be used to quantitatively assess the stiffness of blood vessels, and provide a non-morphologic method to measure stenosis. With further development, it is possible that the method can be implemented in vivo.

Determination and analysis of guided wave propagation using magnetic resonance elastography

We present a novel extension of standard magnetic resonance elastography (MRE) measurement and analysis methods, which is applicable in cases where the medium is characterized by waveguides or fiber bundles (i.e., muscle) leading to constrained propagation of elastic waves. As a demonstration of this new method, MRI is utilized to identify the pathways of the individual fibers of a stalk of celery, and 3D MRE is then performed throughout the volume containing the celery fibers for a measurement of the displacements. A Helmholtz decomposition is performed permitting a separation of the displacements into longitudinal and transverse components, and an application of a hybrid Radon transform permits a spectral decomposition of wave propagation along the fibers. Dot product projections between these elastic displacements measured in the global coordinate system and three Frenet vectors representing the tangent and two corresponding orthogonal vectors along any particular fiber orientation yield the displacement contributions to wave propagation along the fiber as if it were a waveguide. A sliding window spatial Fourier transform is then performed along the length of each fiber to obtain dispersion images that portray space-wavenumber profiles. Therefore, this method can permit localized tracking and characterization of wave types, velocities, and coupling along arbitrarily oriented fibers.

Magnetic resonance elastography of skeletal muscle

While the contractile properties of skeletal muscle have been studied extensively, relatively little is known about the elastic properties of muscle in vivo. Magnetic resonance elastography (MRE) is a phase contrast-based method for observing shear waves propagating in a material to determine its stiffness. In this work, MRE is applied to skeletal muscle under load to quantify the change in stiffness with loading. A mathematical model of muscle is developed that predicts a linear relationship between shear stiffness and muscle load. The MRE technique was applied to bovine muscle specimens (N = 10) and human biceps brachii in vivo (N = 5). Muscle stiffness increased linearly for both passive tension (14.5 +/- 1.77 kPa/kg) and active tension, in which the increase in stiffness was dependent upon muscle size, as predicted by the model. A means of noninvasively assessing the viscoelastic pro-perties of skeletal muscle in vivo may provide a useful method for studying muscle biomechanics in health and disease.

Determination of appropriate RF blocking impedance for MRI surface coils and arrays

Surface and phased array receiving coils in MRI typically require that RF excitation be accomplished using the body coil. This process requires that the receiving coils contain blocking circuitry to increase the overall circuit impedance during RF excitation and withstand the electromotive force induced by the applied electromagnetic field. The aim of this study was to determine the optimal impedance range required during RF excitation based on an assessment of image quality. The experimental results are fit by an exponential model and establish criteria that can be applied for general receiver coil design.

Three-dimensional contrast-enhanced MR angiography with real-time fluoroscopic triggering: design specifications and technical reliability in 330 patient studies

Technical reliability was determined for triggering three-dimensional (3D) contrast material-enhanced magnetic resonance (MR) angiography with MR fluoroscopy. Technical requirements for high reliability were also identified. Reliability was evaluated in 330 consecutive patient studies of the neck, thorax, abdomen, and pelvis. Contrast material arrival was detected fluoroscopically in 325 of the 330 studies (98.5%), and the 3D sequence was successfully triggered in 321 of 330 studies (97.3%). Fluoroscopic triggering of centrically encoded 3D MR angiographic acquisitions is a highly reliable means of obtaining 3D MR angiograms with high spatial resolution.

Comparison of four motion correction techniques in SPECT imaging of the heart: a cardiac phantom study

The aim of this study was to evaluate the accuracy of four different motion correction techniques in SPECT imaging of the heart.

METHODS

We evaluated three automated techniques: the cross-correlation (CC) method, diverging squares (DS) method and two-dimensional fit method and one manual shift technique (MS) using a cardiac phantom. The phantom was filled with organ concentrations of 99mTc closely matching those seen in patient studies. The phantom was placed on a small sliding platform connected to a computer-controlled stepping motor. Linear, random, sinusoidal and bounce motions of magnitude up to 2 cm in the axial direction were simulated. Both single- and dual-detector 90 degrees acquisitions were acquired using a dual 90 degrees detector system. Data were acquired over 180 degrees with 30 or 15 frames/detector (single-/dual-head) at 30 sec/frame in a 64x64 matrix.

RESULTS

The simulated single-detector system, CC method, failed to accurately correct for any of the simulated motions. The DS technique overestimated the magnitude of phantom motion, particularly for images acquired between 45 degrees left anterior oblique and 45 degrees left posterior oblique. The two-dimensional and MS techniques accurately corrected for motion. The simulated dual 90 degrees detector system, CC method, only partially tracked random or bounce cardiac motion and failed to detect sinusoidal motion. The DS technique overestimated motion in the latter half of the study. Both the two-dimensional and MS techniques provided superior tracking, although no technique was able to accurately track the rapid changes in cardiac location simulated in the random motion study. Average absolute differences between true and calculated position of the heart on single- and dual 90 degrees -detectors were 1.7 mm and 1.5 mm for the two-dimensional and MS techniques, respectively. The corresponding values for the DS and CC techniques were 5.7 and 8.9 mm, respectively.

CONCLUSION

Of the four techniques evaluated, manual correction by an experienced technologist proved to be the most accurate, although results were not significantly different from those observed with the two-dimensional method. Both techniques accurately determined cardiac location and permitted artifact-free reconstruction of the simulated cardiac studies.

Real-time reconstruction and high-speed processing in functional MR imaging

Access to fully processed activation maps in near real time during a functional MR examination enables run-to-run assessment of results. This is particularly useful in clinical studies, since the results of the functional MR examination can be ascertained before the patient leaves the MR suite, permitting interactive tailoring of the functional MR study. We describe how a real-time MR system can be customized to complete the following tasks in less than 3 minutes: obtain an 81-second acquisition of a multisection functional MR imaging time series using single-shot echo-planar imaging, perform image reconstruction, extract functional MR activation maps using cross-correlation and thresholding, and superimpose activation maps on previously acquired T1-weighted anatomic images.

Fluoroscopically triggered contrast-enhanced three-dimensional MR angiography with elliptical centric view order: application to the renal arteries

PURPOSE

To determine the reliability of obtaining arterial-phase, contrast-material-enhanced three-dimensional (3D) magnetic resonance (MR) angiograms of the renal arteries by using a technique that combines two-dimensional real-time MR fluoroscopy and a 3D MR angiographic acquisition with elliptical centric view order.

MATERIALS AND METHODS

Twenty-five consecutive patients suspected of having renal artery disease were evaluated with the fluoroscopically triggered technique by using a mean dose of 0.18 mmol/kg gadoteridol. Left renal vein suppression, inferior vena cava suppression, motion artifact, and image quality for depiction of the renal arteries were each evaluated on a five-point scale (1 = best). The findings were compared with those of another 25 consecutive patients who underwent conventional gadolinium-enhanced 3D MR angiography.

RESULTS

The fluoroscopically triggered technique produced 4.6 times less left renal vein enhancement than did the conventional method (P < .01). With the fluoroscopically triggered technique, visualization of the renal arteries was adequate for diagnosis in 24 patients (96%) and the overall result (score of 1-3 for all criteria) was of good quality in 22 patients (88%).

CONCLUSION

With this fluoroscopically triggered MR angiographic technique, high-quality, arterial phase, relatively motion immune angiograms can be routinely obtained.

3D MR angiography of pulmonary arteries using real-time navigator gating and magnetization preparation

An ECG-triggered magnetization-prepared segmented 3D fast gradient echo sequence was developed to perform pulmonary arterial MR angiography. A selective inversion recovery pulse was used in the magnetization preparation to suppress venous vasculature. A real-time gating technique based on navigator echoes was implemented to reduce respiration effects. Pencil-beam navigator echoes were acquired immediately before and after the readout train and processed in real-time to dynamically measure the diaphragm position, which was used to control data acquisition with an accept-or-reject-reacquire logic. In a study of 10 volunteers, a gated 3D acquisition with 28 slices required on average approximately 4 min of acquisition time, and six to seven segmental arteries related to the interlobar trunk of the pulmonary artery were depicted. The use of SIR pulse reduced venous signal by 99%. The gated acquisitions were superior to the ungated acquisitions (n = 10, P < 0.005). The real-time navigator gating technique is effective for reduction of respiration effects and thereby makes high resolution 3D MRA of the pulmonary arteries feasible.

Cardiac magnetic resonance fluoroscopy

A technique is described for high speed interactive imaging of the heart with either white or black blood contrast. Thirty-two views of a segmented, magnetization-prepared gradient echo sequence are acquired during diastole. Using three-quarter partial Fourier sampling, data for a complete 128 x 128 image are acquired in three cardiac cycles. High speed reconstruction provides an image update of each cardiac cycle 159 ms after measurement. An independent graphical user interface facilitates interactive control of section localization and contrast by permitting pulse sequence parameter modification during scanning. The efficiency and image quality of the cardiac MR fluoroscopy technique were evaluated in 11 subjects. Compared with the conventional graphic prescription method, the cardiac fluoroscopy technique provides an approximate eightfold reduction in the time required to obtain subject-specific double oblique sections. Image quality for these scout acquisitions performed during free breathing was sufficient to identify small cardiac structures.

Real-time adaptive motion correction in functional MRI

Functional magnetic resonance imaging (fMRI) of the brain is often degraded by bulk head motion. Algorithms that address this by retrospective re-registration of images in an fMRI time series are all fundamentally limited by any motion that occurs through-plane. Here, a technique is described that can account for such motion by prospective correction in real time. A navigator echo is used before every image acquisition to detect superior/inferior displacements of the head. The displacement information is then used to adjust the plane of excitation of the ensuing single-shot echo-planar fMRI axial image. These correction updates can be completed in 100 mm with motion sensitivity at least as small as 0.5 mm. The efficacy of this method is documented in phantom and human studies.

Magnetic resonance imaging of transverse acoustic strain waves

We describe a phase contrast based MRI technique with high sensitivity to cyclic displacement that is capable of quantitatively imaging acoustic strain waves in tissue-like materials. A formalism for considering gradient waveforms as basis functions to measure arbitrary cyclic motion waveforms is introduced. Experiments with tissue-like agarose gel phantoms show that it is possible to measure small cyclic displacements at a submicron level by an appropriate choice of the applied gradient basis function and to use this capability to observe the spatial and temporal pattern of displacements caused by acoustic strain waves. The propagation characteristics of strain waves are determined by the mechanical properties of the media. It is therefore possible to use this technique to noninvasively estimate material properties such as elastic modulus.

Multiple breathhold 3D time-of-flight MR angiography of the renal arteries

A technique is described for angiographic imaging of the renal arteries with acquisition performed over several periods of suspended respiration. The 3D Fourier transform (FT) gradient-echo angiographic sequence uses magnetization preparation and appropriately chosen delay times for background nulling and time-of-flight enhancement of the vasculature. The sequence was applied to 10 volunteers, each of whom was imaged in three ways: (i) over a series of breathholds in which feedback was provided to enable reproducible breathholding; (ii) over a series of breathholds with no feedback; and (iii) over continuous respiration. Results were evaluated by measuring the transverse extent of the well-delineated renal vasculature and by noting the distal extent of the vasculature branching (main, segmental, and interlobar branches). The transverse extent of renal vasculature visible with breathhold feedback, breathholding, and free breathing was 6.1 +/- 0.9 cm, 5.0 +/- 1.8 cm, and 4.0 +/- 1.4 cm, respectively (mean +/- SD). Breathhold feedback enabled visualization of segmental renal arteries bilaterally in all 10 volunteers.

Navigator-echo-based real-time respiratory gating and triggering for reduction of respiration effects in three-dimensional coronary MR angiography

PURPOSE

To test the hypothesis that respiration effects in three-dimensional (3D) coronary magnetic resonance (MR) imaging can be reduced with navigator-echo-based gating or triggering according to the superior-inferior position of the diaphragm.

MATERIALS AND METHODS

Real-time respiratory gating and respiratory triggering (breath hold with feedback) were implemented with navigator echoes in a magnetization-prepared, segmented, 3D coronary imaging sequence. The two techniques were first tested with a motion phantom. An imaging protocol that compared real-time respiratory-gated acquisition, real-time respiratory-triggered acquisition, and continuous acquisition was then evaluated in six healthy subjects.

RESULTS

Real-time respiratory-gated and respiratory-triggered acquisition were superior to continuous acquisition with two signals averaged (P = .025). The performance of the gated acquisition was about the same as that of the triggered acquisition (P = .05).

CONCLUSION

Navigator-echo-based, real-time respiratory-gating and respiratory-triggering techniques are practical methods for effective reduction of respiration effects in coronary MR imaging.

Orbital navigator echoes for motion measurements in magnetic resonance imaging

A single "orbital" navigator echo, that has a circular k-space trajectory, is used to simultaneously measure in-plane rotational and multi-axis translational global motion. Rotation is determined from the shift in the magnitude profile of the echo with respect to a reference echo. Displacements are calculated from the phase difference between the current echo and a reference echo. Phantom studies show that this technique can accurately measure rotation and translations. Preliminary results from adaptive motion correction studies on phantom and human subjects indicate that the orbital navigator echo is an effective method for motion measurement in MRI.

Magnetic resonance elastography by direct visualization of propagating acoustic strain waves

A nuclear magnetic resonance imaging (MRI) method is presented for quantitatively mapping the physical response of a material to harmonic mechanical excitation. The resulting images allow calculation of regional mechanical properties. Measurements of shear modulus obtained with the MRI technique in gel materials correlate with independent measurements of static shear modulus. The results indicate that displacement patterns corresponding to cyclic displacements smaller than 200 nanometers can be measured. The findings suggest the feasibility of a medical imaging technique for delineating elasticity and other mechanical properties of tissue.

Error in MR volumetric flow measurements due to ordered phase encoding in the presence of flow varying with respiration

Respiratory ordered phase encoding is often employed in MRI studies to reduce image artifacts due to breathing motion. The purpose of this work was to evaluate error caused by the use of respiratory ordering of phase encoding in MR cine phase-contrast (CPC) volumetric flow measurements when the flow rate is sensitive to respiration. It was hypothesized that this effect is due to the systematic biasing of a respiratory-induced phase modulation function in k-space. A theoretical model for the effects of respiration was developed and then tested in flow phantom studies and in normal volunteer studies. In phantom experiments, the use of respiratory ordering induced an error of as much as 13% in CPC volumetric flow measurements. In preliminary volunteer studies, error was as high as 26% in superior vena cava flow measurements versus less than 1% error in the ascending aorta. It is concluded that a potential for error exists in CPC volumetric flow measurements obtained with the use of respiratory ordering schemes. Volunteer studies with larger numbers are warranted. Clinical applications in which this effect may be important include flow measurements in vessels subject to variations in flow due to respiration, such as the venae cavae, pulmonary vasculature, and portal vein.

3D coronary MR angiography in multiple breath-holds using a respiratory feedback monitor

To reduce respiratory blur and ghosts in 3D coronary imaging, a data acquisition scheme using consistent multiple breath-holds was implemented. A navigator echo was acquired and processed in real time to dynamically measure diaphragm position. This information was provided as a visual prompt to the patient to maintain consistency in breath-hold levels such that the variation range of diastolic heart position was less than 2 mm. Preliminary results indicate that this multiple breath-hold acquisition scheme, compared with acquisition under respiration, can significantly reduce blur and ghost artifacts in 3D coronary imaging.

Interactive selection of optimal section orientations using real-time MRI

In applications where precise image section positioning is vital, the interactive section rotation and offset capabilities of interactive MRI should be valuable. However, due to the independent nature of these two adjustments, the desired structure may often not be visible in the image after a rotation. Valuable time is wasted during relocation. An algorithm is presented that automatically alters the section offset after a rotation to provide continuous viewing of a marked structure, greatly improving section orientation efficiency. The technique is illustrated in the determination of double oblique angulation for through-plane imaging of the portal vein. This algorithm is expected to prove useful in applications of interactive MRI requiring precise positioning.

A monitoring, feedback, and triggering system for reproducible breath-hold MR imaging

A technique is described that provides improved reproducibility of breath-holding for MR image acquisition by monitoring the superior-inferior (S/I) position of the diaphragm. The method incorporates detection of the level of inspiration using an MR signal, rapid display to the patient of diaphragm position to enable breath-hold adjustment, and triggering of image data acquisition once appropriate position is attained. The response time of the system is short, approximately 10 ms. Studies in six volunteers using this method demonstrate a considerable decrease in the S/I range of diaphragm position over 10 consecutive periods of suspended respiration. The mean range is 1.3 mm with the system, while it is 8.3 mm without using it. It is expected that this method will be of assistance in many abdominal and cardiothoracic studies that use breath-hold techniques.

Analysis of systematic and random error in MR volumetric flow measurements

The spatial aspects of error in 2D MR cine phase-velocity mapping are considered in order to define acquisition strategies which will minimize error in measuring volumetric flow. Error was separated into two categories: systematic and random. Potential sources of systematic error examined were intravoxel phase dispersion (IVPD), partial volume effects, misalignment of flow axis and flow-encoding gradients, and improper choice of vessel voxels for flux calculations. Random error was addressed using analysis of propagation of variance. Analytical expressions for sources of error were derived; and computer models were used to test the analytical models. Flow phantom studies examining error in MR volumetric flow measurements were performed and compared with error predicted by the analytical models. Expected error in several clinical situations of interest was then derived to find appropriate acquisition strategies. Spatial resolution, signal to noise ratio, velocity sensitivity and the ratio of the modulus of moving isochromats to that of static isochromats were found to be the most important parameters in controlling error and were found to cause competing effects with respect to systematic and random error.

Analysis of MR phase-contrast measurements of pulsatile velocity waveforms

Errors in the measurement of the mean velocity of pulsatile velocity waveforms with ungated phase-contrast techniques were studied theoretically and experimentally. Waveforms consisting of a constant and two sinusoidal components were analyzed. Variations in magnitude and phase of the vascular magnetic resonance (MR) signal resulted in errors, the severity of which increased when either factor increased. Magnitude variations always resulted in overestimation. The general shape of the waveform greatly influenced the error, with certain waveforms producing greater inherent error than others. Experimental measurements were performed, validating the predicted sensitivity of these errors to changes in imaging parameters, including TR and flow-encoding sensitivity. Errors generally became more severe with increased flow-encoding sensitivity. The theoretical and experimental results suggest that accurate mean velocity measurements in many vessels of the body--with acquisition times of less than 15 seconds--should be attainable with ungated imaging techniques and with careful selection of relevant imaging parameters.

Real-time interactive color flow MR imaging

Real-time interactive color flow magnetic resonance (MR) imaging is a combination of real-time MR imaging and color encoding of velocity-induced phase angle. Flow-compensated (FC) and flow-encoded (FE) images are acquired continuously by using gradient echoes and a 12-msec repetition time. Each image is reconstructed within 200 msec of acquisition, and the FC magnitude image is displayed in gray-scale format. The phase difference between the reconstructed FC and FE images, a difference proportional to velocity along the flow-encoding direction, is encoded in color and superimposed on the gray-scale FC image. Magnitude and phase information are thus presented simultaneously. The viewer may interactively adjust many acquisition parameters during data acquisition. Experimental results of phantom and in vivo human studies validate the method. Characteristics of the color flow MR imaging technique are compared with those of duplex color ultrasound.

Ultrasound transmission measurements through the os calcis

A method of measuring ultrasonic propagation in the os calcis was devised for assessing bone properties in humans. Speed-of-sound (SOS) and broadband ultrasound attenuation (BUA) were measured using broadband acoustic pulses transmitted and received by a pair of focused transducers. The transducers are mounted coaxially in a water tank with the subject's heel in between. Reproducibility of results in an adult male was 10% for the BUA and 1.2% for the SOS. Both SOS and BUA changed when the transmission path through the os calcis was varied. For a population of normal male subjects, SOS and BUA were correlated with densitometry results on the os calcis, but less well correlated to area density at remote sites.

Real-time MR fluoroscopic data acquisition and image reconstruction

We describe an experimental system for performing high-speed reconstruction of MR image data acquired with a GRASS sequence. System characteristics are an image acquisition time of 627 ms, continuous image reconstruction at a rate of 6 images/s, and an image reconstruction time of 120 ms. The results is a system for performing MR imaging in real time.