Download TREMR: Table-resonance elastography with MR

Magnetic Resonance in Medicine 62:815– 821 (2009)
TREMR: Table-Resonance Elastography with MR
Daniel Gallichan,1* Matthew D. Robson,2 Andreas Bartsch,3 and Karla L. Miller1
Magnetic resonance elastography (MRE) is a noninvasive
method of measuring tissue compliance. Current MRE methods
rely on custom-built hardware to elicit vibrations that are
tracked by MR imaging. Knowledge of the wave propagation
can be used to calculate the local shear stiffness of the tissue.
We sought to determine whether the vibrations of the patient
table that result from low-frequency switching of the imaging
gradients could be used as an alternative mechanical driving
mechanism for MRE. We designed a pulse sequence that includes a gradient lobe specifically for the excitation of mechanical resonance, allowing control of the time between the onset
of the vibrations and the velocity-encoding of the readout. Data
collected from a gelatin phantom with stiff cylindrical gelatin
inserts demonstrated that wave propagation can be imaged
with this method. Postprocessing to estimate the local spatial
frequency of the waves also allows estimation of the local shear
stiffness, where the stiff inserts are clearly identifiable. Data
collected on the brain of a normal healthy volunteer showed
clear rotational waves propagating from the skull inwards, also
allowing generation of shear stiffness maps. Magn Reson
Med 62:815– 821, 2009. © 2009 Wiley-Liss, Inc.
Key words: MRE; elastography; vibration; resonance
Magnetic resonance elastography (MRE) is a noninvasive
method of measuring tissue compliance (1–3). Typically, a
motion-sensitive MR readout measures the displacement
of the tissue in response to either a single external impulse
or at a range of phases in response to an oscillating external driver. Detailed knowledge of the motion of the tissue
in response to the applied force can be used to generate
maps of the tissue stiffness. There are many potential
clinical applications for MRE, as it offers the possibility to
“palpate” tissues well below the skin, or even within the
skull. In addition to the ability to detect abnormally stiff
tissue, MRE is also able to quantify stiffness—a measure
that has already been demonstrated to have clinical relevance when imaging pathology in the liver (4), as well as
potentially for breast imaging (5). However, the need for
specialized hardware is a constraint of MRE: a mechanical
driver is required to provide the external compressional
force. While recent liver experiments have been carried
out with clinically compatible devices that apply pneumatic vibrations delivered remotely via a flexible tube (6),
such a device would be unlikely to perform well in areas
1Centre for Functional Magnetic Resonance Imaging of the Brain, John Radcliffe Hospital, University of Oxford, Oxford, UK.
2University of Oxford Centre for Clinical Magnetic Resonance Research,
Oxford, UK.
3Department of Neuroradiology, University of Würzburg, Würzburg, Germany.
Grant sponsor: Vera and Volker Doppelfeld Foundation (to A.B.).
*Correspondence to: Daniel Gallichin, Medical Physics, Department of Diagnostic Radiology, University Hospital Freiburg, Hugstetter Str. 55, 79106
Freiburg, Germany. E-mail: [email protected]
Received 7 January 7 2009; revised 9 March 2009; accepted 26 March 2009.
DOI 10.1002/mrm.22046
Published online 7 July 2009 in Wiley InterScience (www.interscience.wiley.
com).
© 2009 Wiley-Liss, Inc.
such as the brain. MRE has been successfully performed in
the brain using elaborate hardware that couples an electromechanical driver (sited outside of the magnet) to a
bite-bar (7–9) or to a “head-rocker unit” (10). Bite-bars are
cumbersome to use clinically, and not all subjects tolerate
them (11). The head-rocker appears to be more clinically
feasible, but less intrusive hardware would be advantageous.
The large gradient lobes used in diffusion-weighted MRI
are known to induce vibrations that propagate to the patient table, which are noticeable to the subject during the
scan. A recent study used a laser vibrometer to quantify
these vibrations on a clinical 3T system during a standard
diffusion-tensor imaging protocol, finding a strong component at 20 –25 Hz with an amplitude of ⬇100 ␮m (12). As
these amplitudes are a similar magnitude to the displacements used for MRE experiments, we sought to determine
whether the vibrations resulting from low-frequency
switching of the gradient coils could be used as the mechanical driver for MRE, thus obviating the need for external driver hardware.
In this article we present preliminary data demonstrating clear vibrational wave propagation in both a gelatin
phantom and the in vivo brain where the waves were
elicited via gradient-induced table vibrations.
THEORY
The proposed pulse-sequence used for performing MRE is
shown in Fig. 1. A high-amplitude gradient lobe of 20 ms
duration is applied to excite the mechanical resonance in
the 20 –25 Hz range. There is then a variable delay, which
we refer to as ␦e, before a spin-echo sequence with velocity-encoding gradients. The velocity-encoding gradients
introduce a phase offset at each voxel that is directly
proportional to the local velocity in the direction of the
gradients. We refer to this method as table-resonance elastography with MR (TREMR). We have not explicitly determined that it is the patient table itself that exhibits the
strong resonance in this low-frequency range, but the patient table is the hardware responsible for transmitting the
vibrations to the subject.
For multislice acquisitions, each slice needs to be acquired following its own vibration-inducing gradient lobe.
It is also important that the TR per slice is increased from
the minimum available to allow time for the vibrations to
decay between successive measurements.
A variety of algorithms have been proposed to estimate
stiffness from MRE data. Some of these methods estimate
the local wave propagation speed (13) or spatial frequency
(14) which, by assuming an isotropic medium of uniform
density, can be used to used to estimate the local elastic
modulus. Other methods find approximate solutions to the
Navier equation, which describes the internal motion of an
elastic solid, usually making similar assumptions regard-
815
816
Gallichan et al.
RF
GRO
GV
enc
⌬e
90°
180°
EPI Readout
Vibration-inducing
gradient
FIG.
1. Proposed
pulse-sequence diagram for MRE. [Color
figure can be viewed in the online
issue, which is available at www.
interscience.wiley.com]
Velocity-encoding gradients
ing isotropy and uniform density in order to simplify the
procedure (7). It has also been demonstrated that using the
local wave propagation speed to calculate stiffness is
equivalent to solving the Navier equation under the assumptions of incompressibility, local homogeneity, and
negligible attenuation of the waves (7). Calculations based
on the equations of motion require making estimates of the
spatial derivatives of the displacement field within the
material. The TREMR method measures the velocity field
rather than the displacement field, and although timeintegration of the velocity field will yield the displacement
field, the data do not allow direct determination of the
appropriate integration constant. This is because the
TREMR approach is unable to measure the velocity field
until a short time after the system is displaced from equilibrium due to the time between the end of the vibrationinducing gradient and the time of the velocity measurement (which is approximately at the midpoint between the
two velocity-encoding gradients). To simplify the stiffness
estimation we chose to use a method that estimates the
local wave propagation speed, as this can be estimated
from the waves observed directly in the velocity field,
without needing to calculate the displacement field.
There are three distinct approaches to MRE proposed in
the literature. Displacement can be determined between
equilibrium and during the application of a single external
force, thereby allowing determination of the strain field
(1). Displacement may also be determined at various
phases of a harmonic external force (2). Alternatively, the
single transient wave following a single external force can
be measured (13). The data resulting from TREMR are
distinct from all three previous approaches as the driving
force, although close to a single frequency, is of varying
magnitude due to the response of the mechanical resonance to the gradient switching. We have therefore found
it beneficial to collect data that follow several periods of
the mechanical resonant frequency to aid stiffness calculation, as the response is not in a steady state.
To estimate the stiffness from TREMR data, it was first
smoothed in the temporal domain for each voxel by fitting
a cubic spline to the data from each voxel. We then applied
spatiotemporal directional filtering (using simple filters on
the velocity data Fourier transformed in space and time
(15)) to split the data into the components representing
waves propagating in the ⫹x, ⫺x, ⫹y, and ⫺y directions.
We restricted the calculations to 2D for simplicity. For
each timepoint we then estimated the local spatial frequency in the direction of the wave propagation. This was
achieved by finding the spatial derivative of the phase of
the analytic signal of each line of data in the direction of
the wave propagation. We then took the mean spatial
frequency across all timepoints, which we refer to as fsp.
This approach to estimating the spatial frequency is only
accurate for timepoints where there is a significant wave
passing through the voxel, so contributions to the overall
mean were only included where the filtered velocity component was greater than an arbitrary threshold corresponding to an empirically determined phase accrual of 0.08
radians. Using the timecourse of the filtered data we could
then estimate the frequency of the driving force, fmech. The
shear modulus, ␮, is then given by the equation ␮ ⫽
2
2 , where ␳ is the density of the material, which we
␳fmech
/fsp
assumed to be 1 g/cm3.
Phantom Experiment
A phantom was constructed with two cylindrical inclusions of high gelatin concentration set within a body of
gelatin mixed at a low concentration. To ensure strong
mechanical coupling between the table and the phantom
the coil, head restraints were placed tightly against the
phantom container. The vibration-inducing gradient (amplitude 35 mT/m) was always applied along the left–right
axis, as we have found this to produce the largest amplitude vibrations of the patient table. A 64 ⫻ 64 echo-planarimaging (EPI) readout at 3 mm isotropic resolution followed the velocity-encoding gradients, which consisted of
two 8.5 ms gradient lobes at 36 mT/m with 26.2 ms between their centers. This corresponds to a venc (the velocity
required to induce a phase offset of ␲) of 1.5 mm/s. The TE
was 57 ms and the minimum achievable TR per slice was
75 ms. All imaging was performed on a Siemens (Erlangen,
Germany) 3T TIM Trio system, using a single-channel T/R
head coil to ensure reliable phase information. The minimum TR per slice was set to 600 ms and ␦e was varied from
0 to 300 ms in increments of 2 ms, with the TR per slice
increasing by the same amount. The phantom was positioned with the long axis of the cylindrical inserts in the
anterior/posterior direction for a human subject, meaning
that imaging slices perpendicular to this axis were selected
by choosing a “coronal” orientation. The readout direction
was set to be the left–right direction. Five slices were
acquired with velocity-encoding along the readout direction and then repeated with velocity-encoding along the
phase-encoding direction. This led to a total acquisition
time of ⬇19 min. Raw data were reconstructed offline
using MatLab (MathWorks, Natick, MA). The resulting
phase images were unwrapped in 2D using PRELUDE software (16). Any remaining phase discontinuities in the
time-dimension were then easily removed using 1D unwrapping. The final shear stiffness map was calculated by
averaging the values calculated from all four Fourier-filtered versions of both velocity-encoding directions.
TREMR
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FIG. 2. Example of measured
phase offsets in gelatin phantom
with ␦e ⫽ 100 ms with velocity
encoding in (a) readout direction
and (b) phase-encoding direction
(readout direction runs left–right
in these images). c: Mean magnitude image. d: Calculated shear
stiffness map in units of kPa. e:
Example unfiltered timecourses
of a single voxel with velocity-encoding in the phase-encoding
(PE) and readout (RO) directions.
[Color figure can be viewed in the
online issue, which is available at
www.interscience.wiley.com]
In Vivo Experiment
A healthy 25-year-old male subject was scanned with 40
slices (64 ⫻ 64 matrix, 3 mm isotropic resolution) covering
the entire brain. Foam padding was placed between the
coil and the headphones to reduce subject movement and
to ensure good mechanical coupling between the table and
the subject’s head. Preliminary experiments found the vibrations to decay faster in the brain than in the gelatin
phantom, so a minimum TR per slice of 150 ms was used
(double the minimum possible). ␦e was increased from 0 to
80 ms in increments of 2 ms, although due to the need for
a fat-saturation pulse the actual time between the vibration-inducing gradient and the excitation pulse was
12.2 ms for ␦e ⫽ 0 ms. Velocity-encoding was performed
separately along each of the three principal axes of the
system. This resulted in a total acquisition time of
⬇16 min. A brain mask was generated using the Brain
Extraction Tool (BET) software (17). Following 2D phase
unwrapping the median phase for each masked slice was
subtracted from the values for each slice. This was found
to be necessary to achieve smooth timecourses for each
voxel as the 1D unwrapping used for the phantom data
proved unreliable. The subtraction of the median should
not affect the validity of the stiffness estimation, as this
should correspond (approximately) to using velocity measurements in the frame-of-reference of the head rather than
the scanner.
The mean magnitude image across all volumes was
coregistered to a T1-weighted structural scan at 1 mm
isotropic resolution using FLIRT software (18) with 12
degrees of freedom and trilinear interpolation. This then
allowed the same transformation to be applied to the calculated stiffness map to better compare the stiffness values
with the underlying anatomy.
RESULTS
Phantom Experiment
Figure 2a,b shows examples of the wave patterns observed
in the gelatin phantom for ␦e ⫽ 100 ms with velocity
encoding in the readout and phase-encoding directions.
Wave-motion is observable throughout the imaging slice.
Figure 2c shows the magnitude image, where the stiff
inserts are barely discernible. By examining the timecourse of individual voxels (an example is shown in Fig.
2e), the frequency of the vibrations, fmech, was found to be
23 Hz. The stiff inserts are clearly identifiable in the calculated stiffness image (Fig. 2d). Average calculated shear
stiffness values are 2.6 kPa for the background, with 11.2
kPa and 8.6 kPa for the left and right inclusions, respectively.
The peak measured phase offset was ⬇10 rad, corresponding to a peak velocity of ⬇5 mm/s. By integration of
the velocity over time, this corresponds to a maximum
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Gallichan et al.
LR
AP
SI
FIG. 3. Examples of the unwrapped median-subtracted phase images at ␦e ⫽ 34 ms (close to peak absolute velocity). Axial, sagittal, and
coronal slices are shown for velocity encoding in the left/right (LR), anterior/posterior (AP), and superior/inferior (SI) directions.
peak–peak displacement of ⬇100 ␮m. The vibration frequency and maximum displacement are in good agreement with previous measurements of table vibrations from
low-frequency gradient switching (12) (even though the
MR system is different).
In Vivo Experiment
Figure 3 shows the unwrapped median-subtracted phase
images for ␦e ⫽ 34 ms (chosen as it is close to the peak
absolute velocity). Peak values were ⬇7.5 mm/s for left/
right (LR) encoding, ⬇5 mm/s for anterior/posterior (AP)
encoding, and ⬇2.5 mm/s for superior/inferior (SI) encoding. As with the phantom, the maximum peak-to-peak
displacements were ⬇100 ␮m. The LR and AP encodings
demonstrate wavefronts that appear to move in synchrony
with each other, whereas the SI waves appear to move
independently. The peak velocity in the SI direction was
found to be later than for the LR and AP directions (at
⬇75 ms rather than ⬇34 ms).
The synchrony of the LR and AP encodings is made
clearer when they are combined to create a 2D velocity
vector, as is represented for a single slice over time in Fig.
4. Observation of the vector field over time allows rotational waves to be observed propagating from the skull
inwards, with the wave of strongest amplitude beginning
at ␦e ⬇20 ms. As only ⬇2 cycles of the driving frequency
were measured (␦e up to 80 ms) the frequency itself was
difficult to estimate directly from the data. For stiffness
calculations it was therefore assumed that the frequency
was the same as for the phantom at 23 Hz.
The calculated shear stiffness map is shown after coregistration to a T1-weighted structural scan in Fig. 5. The
shear stiffness map is blurred due to the upsampling in the
registration (3 mm isotropic resolution of elastography
data upsampled to match 1 mm isotropic structural data).
By examining regions less affected by partial-voluming it
is clear that gray matter has a lower stiffness (⬇5–10 kPa)
than white matter (⬇15–30 kPa).
TREMR
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δe = 0 ms
δe = 10 ms
δe = 20 ms
δe = 30 ms
δe = 40 ms
δe = 50 ms
δe = 60 ms
δe = 70 ms
FIG. 4. Arrows representing the direction and magnitude of the in-plane velocity vectors (from LR and AP velocity sensitizations only) of
a single axial slice as ␦e is increased from 0 to 70 ms. Size of arrows encodes magnitude of velocity, color of arrow encodes direction.
FIG. 5. a: Reference T1-weighted
structural image. b: Calculated
shear stiffness map coregistered
to structural image. c: Calculated
shear stiffness map with transparency to allow comparison with
structural features.
820
DISCUSSION
We have demonstrated that vibrations of the patient table
induced by low-frequency gradient switching are sufficient to generate vibrational waves that can be tracked
with the proposed TREMR pulse sequence. In a gelatin
phantom with stiff cylindrical inserts, the inserts could be
clearly identified in the calculated shear stiffness map.
When applied in vivo to a normal healthy brain, clear
rotational waves propagating inwards from the skull can
be observed and tracked with this method. These data can
also be used to generate shear stiffness maps, indicating
greater shear stiffness for white matter than gray matter.
The shear stiffness values obtained here are similar in
magnitude to those reported by a recent study using MRE
(19). However, the nature of the implemented algorithm
for calculation of the shear stiffness does not lend itself
easily to providing estimates of the accuracy of the estimated stiffness values. This means that care should be
taken in interpretation of the stiffness maps as they are
currently presented as a “proof-of-concept” rather than
attempting to make accurate measurements of the tissue
properties. The elastic properties can also vary with the
frequency of the applied vibrations, so this also needs to be
considered when comparing quantitative values. Qualitatively, however, the resulting quality of the stiffness maps
is similar to those obtained using existing MRE methods
that rely on additional specialist hardware (8 –10,19). It is
particularly noticeable in this dataset that a very stiff region is found close to the splenium of the corpus callosum.
Further investigation is required to determine to what
extent this is caused by a genuine variation in tissue stiffness or by an artifact arising from the postprocessing of the
data. It is interesting to note that a stiffer region was also
observed in this brain location in a previous MRE study
(9).
The main drawback of the proposed technique is that
the frequency of the vibrations is predetermined by the
mechanical resonance of the existing scanner hardware.
This removes the possibility to choose the driving frequency that provides the best stiffness estimates, as may
become possible for standard MRE methods as more data
become available. In particular it may be desirable to use a
higher driving frequency than the 23 Hz used here as this
will result in shorter wavelengths within the brain, which
are expected to lead to more reliable and higher-resolution
stiffness estimates. However, the fact that TREMR requires
no additional hardware remains a considerable advantage,
which may outweigh the limitations in many circumstances— especially given the complexity of current MRE driver
designs.
It should be noted that we have referred in this article to
the velocity measurements as though they are instantaneous samples, when in fact the phase offset will be proportional to the mean velocity during the velocity-encoding gradients. This means that the measurement will lose
sensitivity to oscillatory motion as the frequency of the
motion increases beyond the Nyquist limit associated with
the velocity-encoding gradient lobes. In the case of our
experiment the Nyquist frequency from the gradient timing was ⬇38 Hz, so the measurements close to the vibrational resonance at ⬇23 Hz should remain reliable.
Gallichan et al.
A further development that could be envisaged, related
to TREMR, is the design of new MRE hardware that has its
resonant frequency deliberately excited by gradient
switching rather than the conventional approach of using
a signal generator. This could act as a compromise between the ease of implementation of TREMR and the flexibility to choose the driving frequency of conventional
MRE approaches.
The estimation of the shear stiffness values from the
TREMR data may be improved by further investigation, as
the current implementation uses only a very simple approach to estimate the local spatial frequency of the vibrations. It may even be beneficial to develop algorithms
specifically for TREMR, as the data are not representing a
repeating harmonic wave (as in harmonic MRE) or following a single wave over time (as in transient MRE). Tailored
stiffness estimation algorithms may therefore result in
higher resolution and more reliable estimated stiffness
values than the method presented here.
The postprocessing may also be improved by knowledge
of the exact form of the mechanical driving function. We
have assumed that the driving function is a single frequency—measured to be 23 Hz from the TREMR phantom data.
We did not directly measure the movement of the patient
table, however, as we did not have easy access to appropriate hardware (such as a laser vibrometer or a magnetsafe accelerometer) to make such measurements. It is possible that a more complete careful characterization of the
driving function could improve the solution to the equations of motion of the sample, improving the stiffness
estimation. Additionally, knowledge of the relationship
between the gradient-switching and the motion of the table
could lead to more sophisticated design of the vibrationinducing gradient waveform to result in a more useful
table motion.
While we have chosen in this study to image the brain,
the same approach could also be used to image vibrations
in other parts of the body, provided sufficient mechanical
coupling can be established between the patient table and
the area of interest.
It is not clear to what extent TREMR would function on
scanner hardware different from the system used in our
study, as the mechanical resonances are likely to vary
greatly between scanner models and manufacturers. However, the close similarity between the waves that we observed in the TREMR data and those measured on a different 3T system from a different manufacturer (12) (both
20 –25 Hz, decaying over a few hundred milliseconds)
suggest that the method may not be restricted to the Siemens TIM Trio system used here.
CONCLUSION
TREMR represents a novel approach to acquiring MRE
data that requires no specialist hardware. Further work is
necessary to determine if clinically relevant data may be
acquired with this method.
ACKNOWLEDGMENT
The authors thank Dr. Lowri Cochlin for invaluable assistance in phantom construction.
TREMR
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