Magnetic Resonance in Medicine 66:1798–1808 (2011)
Results for Diffusion-Weighted Imaging With a Fourth-Channel Gradient Insert Rebecca E. Feldman,1* Timothy J Scholl,2,3 Jamu K. Alford,4 William B. Handler,4 Chad T. Harris,4 and Blaine A. Chronik3,4 Diffusion-weighted imaging suffers from motion artifacts and relatively low signal quality due to the long echo times required to permit the diffusion encoding. We investigated the inclusion of a noncylindrical fourth gradient coil, dedicated entirely to diffusion encoding, into the imaging system. Standard three-axis whole body gradients were used during image acquisition, but we designed and constructed an insert coil to perform diffusion encodings. We imaged three phantoms on a 3-T system with a range of diffusion coefficients. Using the insert gradient, we were able to encode b values of greater than 1300 s/mm2 with an echo time of just 83 ms. Images obtained using the insert gradient had higher signal to noise ratios than those obtained using the whole body gradient: at 500 s/mm2 there was a 18% improvement in signal to noise ratio, at 1000 s/mm2 there was a 39% improvement in signal to noise ratio, and at 1350 s/mm2 there was a 56% improvement in signal to noise ratio. Using the insert gradient, we were capable of doing diffusion encoding at high b values by using relatively short echo times. Magn Reson Med 66:1798– C 2011 Wiley Periodicals, Inc. 1808, 2011. V Key words: diffusion-weighted imaging, gradient coil design, 3 Tesla.
Diffusion-weighted imaging (DWI) produces data about the composition and structure of tissues that are unique from T1-, T2-, or proton density-weighted imaging, and it has been shown to be effective in the segmentation and classification of carotid atherosclerotic plaques (1) and the investigation of joint and cartilage structure (2). Unfortunately, because of the time required to encode diffusion weighting in the pulse sequence, DWI is susceptible to motion artifacts (3) and suffers from relatively low image signal to noise ratio (4,5). The magnetization that results from a diffusionweighted pulse sequence is (6) M / M0 e
TE=T bD 2e :
½1
1 Department of Biomedical Engineering, University of Alberta, Edmonton, Alberta, Canada. 2 Department of Medical Biophysics, University of Western Ontario, London, Ontario, Canada. 3 Imaging Research Laboratories, Robarts Research Institute, University of Western Ontario, London, Ontario, Canada. 4 Department of Physics and Astronomy, University of Western Ontario, London, Ontario, Canada. *Correspondence to: Rebecca E. Feldman, Ph.D., Department of Biomedical Engineering, University of Alberta, 1098 Research Transition Facility, Edmonton, Alberta T6G 2V2, Canada. E-mail:
[email protected] Received 10 August 2010; revised 16 February 2011; accepted 25 March 2011. DOI 10.1002/mrm.22971 Published online 20 May 2011 in Wiley Online Library (wileyonlinelibrary. com). C 2011 Wiley Periodicals, Inc. V
In Eq. 1, the magnetization (M) is proportional to a TE T2-relaxation weighting factor (M0 e =T2 ) as well as a difbD fusion-weighting factor (e ). D (mm2/s) is the diffusion coefficient of the tissue and b (s/mm2) is the b value. The b value is a function of the pulse sequence, and for a pulsed-gradient spin echo, it is given by (7,8): d b ¼ g2 G 2 d2 D : 3
½2
In Eq. 2, G is the applied gradient, d is the duration of the gradient pulse, and D is the separation between the gradient pulses. Eqs. 1 and 2 indicate that an increase in the strength of the applied gradient pulse would result in a decreased pulse duration (to maintain a consistent b value). A decrease in the pulse duration would permit a reduced echo time (TE) and thus the final image would be subjected to less T2 relaxation. A highly efficient gradient magnet, pulsed rapidly, has the potential to reduce the minimum TE required for diffusion pulse sequences, thus improving signal to noise ratio and reducing motion sensitivity. Some practical problems arise with increased gradient performance. Pulse sequences with high slew rates run the risk of inducing peripheral nerve stimulation (9). Some localized and noncylindrical gradients have been shown to have higher stimulation thresholds (10,11) and permit rapidly switched gradient fields to be operated with larger gradient magnitudes. The obvious challenge is that restricting the field of view results in artifacts (12). We hypothesize that an improved gradient system for DWI would have a strong, localized gradient over a small area for the diffusion weighting and a weaker, whole-body linear gradient for image acquisition. These requirements suggest the inclusion of a fourth gradient coil dedicated to diffusion contrast. Previous work by Turner et al. (13–15) has shown the viability of a fourth axis when used in DWI. Their work produced a linear z-gradient in a cylindrical head insert that was used for diffusion and perfusion imaging. Provided that the profile of the gradient is known, the linearity requirements for the dedicated diffusion gradient can be relaxed, allowing the design of a much stronger, noncylindrical magnet. A powerful gradient for diffusion imaging, that is useful over a limited volume, could permit improved DWI focused on small structures which require only limited regions of interest situated within larger fields of view, such as atherosclerotic plaques in the neck or tissues in knee or wrist joints. Additionally, a noncylindrical gradient would permit the
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ciency was calculated to be 10 mT/(m A) at 5 cm from the surface of the coil. This was calculated to drop to 0.10 mT/(m A) at 10 cm from the surface of the coil. The solenoids were constructed using hollow copper wire wound around lexan bobbins of 1.0 cm outer radius. During construction, the wire was encapsulated in a thermally conductive epoxy. The two solenoids were aligned in parallel and then potted in place in the same epoxy. Electrical connections were attached to run the current counter-clockwise in the upper solenoid and clockwise in the lower solenoid; this produced a maximum magnetic field in the centre of the magnet as shown in Fig. 2(a,b). At 1 kHz, the inductance of the constructed coil, with full electrical connections, was measured to be 83 6 5 mH, and the resistance was measured to be 17 6 3 mV.
FIG. 1. Butterfly gradient coil. a: Two solenoids side by side, similar to a trans-cranial magnetic stimulation coil. b: Solenoids wound in thermal epoxy prior to final potting. c: Butterfly coil potted into a black casing and mounted on press-board base and paired with the 1-L phantom.
targeting of regions in the neck that are otherwise difficult to access with reduced-radius cylindrical insert designs (16). In this work, we described the design and construction of a gradient coil for this purpose and demonstrate the feasibility of our approach.
Equipment All experiments were carried out on a 3-T Siemens Tim Trio whole-body MR scanner (Siemens Health Systems Erlangen, Germany) with a 12-channel head matrix coil for reception. The diameter of the bore was 60 cm, and the full body field of view was up to 50 cm in diameter. The maximum gradient strength of the whole body gradients was 45 mT/m. The gradient coil was attached to a press-board base as pictured in Fig. 1c. The base was designed to weigh down the insert gradient during imaging and to position
MATERIALS AND METHODS The gradient was simulated using custom software written in Cþþ to ensure that the gradient efficiency and electrical properties of the design were suitable for construction. Next, the prototype was constructed, based on the simulation, and connected to power amplifiers and a laptop-based control system to integrate it with the MRI. Finally, the control system (17) was triggered from a preexisting pulse sequence to permit a DWI experiment using the insert gradient. Insert Gradient The insert gradient coil has two connected solenoids, similar in design to the configuration of trans-cranial magnetic stimulation coils (18,19). The solenoids were arranged side by side along the z-axis, as illustrated in Fig. 1. This configuration was referred to as a ‘‘butterfly’’ design, and it was selected as the prototype insert gradient because the design produces a sharp, focused peak in magnetic field strength above the centre of the insert magnet. The steep decline in field results in a highly efficient, although not linear, gradient region in the centre of the figure 8 or butterfly. The inner radius of each solenoid was 1 cm, and the outer radius was 3.7 cm. The dimensions of the butterfly magnet were 2.0 cm deep (accumulated layers of wire along the x-axis), 7.5 cm wide (the diameter of the solenoid in the y-axis), and 15.0 cm long (the two solenoids side by side along the z-axis). At the centre of the magnet, the gradient was expected to have an efficiency significantly higher than that of the whole body gradient. Based on the simulation, the effi-
FIG. 2. Butterfly coil magnetic profiles. a: A contour plot of the simulated magnetic field. The z-component of the magnetic field produced by 1 A on the y–z plane and (b) on the x–z plane. c: A contour plot of the magnitude of the gradient efficiency in the y–z plane and (d) x–z plane resulting from the magnetic field in (a) and (b).
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FIG. 3. Pulse sequences used for diffusion-weighted imaging. a: Diffusion weighting using the whole-body gradient system for (a0 ) slice selection, (b0 ) diffusion encoding, and (c0 ) image acquisition. b: Diffusion weighting using the whole body gradient for imaging, and the gradient insert for diffusion encoding prior to image acquisition. d0 : The shaded bars below the b value and echo time (TE) indicate the pulse sequence parameters used for wholebody gradient diffusion-weighted imaging. e0 : The shaded bars above the current indicate the magnitude of the maximum current applied to the gradient for diffusion-weighted imaging using the insert.
both the phantom and the insert gradient inside the radio frequency coil. The insert gradient was attached to Copley Amplifier Model 226 (Copley Controls, Canton, MA, USA). The maximum output was 6475 A. The gradient amplifier was attached to the custom gradient coil by way of a Siemens’ gradient filter located in the filter panel. The Copley amplifier was operated in constant-current mode. The amplifier sourced an output current which was held at 30 times the input voltage (1 volt input to the amplifier ¼ 30 A amplifier output). The Copley feedback circuit was tuned to compensate for the particular inductance and resistance of the load. Input waveforms to the amplifiers were generated by National Instruments data acquisition hardware (National Instruments NI Model 6629) and controlled via custom software written in LabView 2009 (National Instruments, Baltimore, MD) run on a Toshiba laptop. The insert gradient wave forms were synchronized by triggering off a TTL (transistor-transistor-logic) pulse in the, otherwise normal, whole-body gradient diffusion pulse sequence (20). Phantoms Three 1-L MRI phantoms were constructed to provide a range of apparent diffusion coefficients (ADCs). All phantoms contained Cu2SO4 to reduce the longitudinal relaxation time. The first phantom contained 5 g of Cu2SO4, 25% glycerol (by volume), and distilled water;
the second phantom contained 5 g of Cu2SO4 and distilled water; the third phantom contained 5 g of Cu2SO4 and 99% acetone. Pulse Sequence A twice-refocused diffusion-weighted echo-planar imaging pulse sequence was used to reduce the impact of eddy currents on the acquired images (20). The following pulse sequence parameters were used in a diffusion-weighted sequence (Nave ¼ 1) for all images: 2100 ms pulse repetition time, 128 128 acquisition matrix, bandwidth (BW) ¼ 2170 Hz/pixel, 256 mm field of view, 5 mm slice thickness, and nine axial slices were acquired with a slice separation of 2.5 mm. The phase encode direction was anterior to posterior (along the y-axis), and the readout direction was left to right (along the x-axis). Diffusion-weighted images were obtained for each of the phantoms using the whole body gradient only (both with and without the insert gradient magnet physically present) and with the insert gradient providing the diffusion encoding. The pulse sequences used for diffusion weighting are illustrated in Fig. 3. The magnitude of the trailing edge of the second lobe of the insert diffusion pulse was decreased by the smallest increment (0.05 A) to balance the lobes and maximize the received signal. When diffusion encoding was performed by the whole body gradients, two images were reconstructed from the sequence: a standard T2-weighted echo-planar imaging
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sequence with no intentional diffusion weighting and a diffusion-weighted T2 image. The sequence was run nine times for each phantom. Each diffusion-weighted image in a sequence, corresponding to a selection of nine b values, was matched with an identical T2-weighted image with the diffusion-encoding gradient held at 0 A (approximately b ¼ 0 s/mm2). Figure 3d0 details the TE/b value pairs acquired for each sample. When diffusion encoding was performed by the insert gradient, each phantom was imaged 10 times. Each diffusion-weighted pulse sequence had a TE of 83 ms. A bipolar pulse was applied with a ramp time of 1 ms, a flat top duration of 11 ms, and a pulse separation of 16 ms. Each phantom was initially imaged with a current amplitude of 0 A, applied during the diffusion encoding (corresponding to a T2-weighted image of b value ¼ 0 s/mm2). Subsequently, each phantom was imaged with a selection of nine additional bipolar current amplitudes, supplied to the insert and timed to provide diffusion encoding. Figure 3e0 details the set of current amplitudes for the pulse sequences applied to the phantoms. Analysis The value of the noise was calculated by finding the standard deviation in each slice for a region of 30 128 pixels across the top of the image. The region was selected to avoid the phantom for all cases and, although the gradient insert was not visible in any image, to avoid the region where the insert gradient would theoretically be situated. To provide a value for comparison, the ADC was precalculated for each of the phantoms using only the whole body gradients to apply a range of b values. The calculation was done using the DWI and the corresponding TE-matched b ¼0 s/mm2 image. Using the sequence’s b value, the ADC for each pixel could be determined with S ¼ So ebD :
½3
S was the diffusion-weighted (b > 0 s/mm2) image, So was the ‘‘original’’ image (b ¼ 0 s/mm2), b was the sequence’s non-zero b value, and the ADC for the phantom was represented by D in Eq. 3. From the pixel-by-pixel determination of the ADC for the image, the ADC for the phantom was calculated as the result of the mean of 2025 pixels (the same 15 15 pixels area for all nine slices) taken from a region situated in the centre of each phantom. The standard deviation was calculated from the same region. To assess the effect of the presence of the conducting insert gradient on the system, the determination of the ADC for each phantom, using the whole body gradients, was repeated in the presence of the insert gradient. To compare our simulation of the gradient system with actual system performance, the calculated gradient efficiency (based on the original gradient design) was contrasted with the calculation of apparent gradient efficiency (based on image data taken using the insert gradient). The magnitude of the gradient produced by the system was simulated assuming that the centre of the
phantom was 60 mm to the right (positive x-axis) of the surface of the gradient and 1 mm below (negative y-axis) the centre of the insert gradient. This corresponded to the observed positioning of the phantom/insert system. To use the image data to calculate the ADC, it was necessary to know the applied gradient strength. Because the insert gradient was highly nonlinear the value of the gradient varied spatially across the image. The insert gradient was constructed according to a design whose gradient profile was well known. We compared measurements of the shape and magnitude of the actual gradient profile and the gradient profile obtained from simulation of the design to ensure that the gradient coil was operating as expected. To calculate the magnitude of the apparent gradient, the apparent b value of the system was calculated using Eq. 3. S was the signal obtained after diffusion encoding was performed with the insert gradient; So was the signal obtained using TE ¼ 83 ms, I ¼ 0 A, and the D used was the ADC for the phantom material that was calculated from the image data obtained with the whole body gradient in the absence of the insert at a b value of 250 s/mm2, TE ¼ 83 ms. Using the timing of the current pulsed through the insert gradient and Eq. 2, the apparent gradient for each point in the image was calculated. The apparent gradient efficiency was calculated for each position in the data using the maximum current applied for the pulse sequence and G ¼ hI:
½4
In Eq. 4, G was the apparent gradient, h was the apparent efficiency of the gradient coil, and I was the maximum current applied in the pulse. The apparent gradient efficiency calculated was compared to the simulated gradient efficiency. For each pulse sequence, a map of applied b values was calculated using Eq. 2, the pulse sequence timing, the calculation of the gradient efficiency map (from the signal loss in the water phantom I ¼ 28 A), and the magnitude of the applied current. The insert gradient was used to determine the ADC in each phantom based on So (the image data obtained with TE ¼ 83 ms, and I ¼ 0 A), S (the image data obtained when the insert gradient was pulsed as illustrated in Fig. 2), and the map of apparent gradient efficiency. Because each image obtained using the insert gradient for diffusion encoding contained the diffusion weighting for a range of b values, the calculated ADC data were aggregated from multiple images to create an analysis of the ADC versus b value. To perform the calculation of ADCs, the image was sampled in a 15 15 voxel area in the centre of the phantom, for all nine slices and all nine current amplitudes. The calculated ADCs were binned according to the calculated b value at that point (bin width ¼ 50 s/mm2). Then the mean and standard deviation of the ADC was calculated. RESULTS The inset of Fig. 4 shows a typical axial slice through the centre of the phantom. The line through the image
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FIG. 4. Magnitude of signal for the white line through the phantom (inset image) obtained by the whole body gradients in the absence of the insert gradient. The graph represents the magnitude of the signal across each of the acetone, water, and glycerol phantoms for b ¼ 0 s/mm2 and b ¼ 250 s/mm2. Incomplete overlap of the phantom profiles was due to slight position differences within the field of view during imaging.
corresponds to the position of the line of data used to produce the graph in Fig. 4. The magnitude of the noise varied only slightly from slice to slice. For water, at b ¼ 150 s/mm2, the noise for phantoms imaged without the presence of the insert was 12 6 4, 12 6 4, and 13 6 4 for the first, fifth, and ninth slices, respectively. With the presence of the insert, the noise for the first, fifth, and ninth samples was 13 6 4, 13 6 5, and 14 6 4. The average noise for the acetone, water, and glycerol phantoms imaged without the presence of the insert was 12 6 4, 12 6 4, and 12 6 3. When imaged with the presence of the insert, the noise was 13 6 4, 13 6 4, and 12 6 3 for each of the acetone, water, and glycerol phantoms.
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The average noise, as a fraction of the maximum signal intensity for images, taken in the absence of the insert gradient was 5.9 6 1.9% (acetone), 4.7 6 1.5% (water), and 26 6 8.5% (25% glycerol) at TE ¼ 83 ms. In the presence of the insert, the average noise floor, as a fraction of the maximum signal intensity for images was 7.2 6 2.7% (acetone), 6.2 6 2.5% (water), and 33 6 12% (25% glycerol) at TE ¼ 83 ms. The diffusion coefficient, calculated using the image data from the whole-body gradient alone (b value of 250 s/mm2, TE ¼ 83 ms) was 1.138 6 0.004 103 mm2/s for the 25% glycerol phantom, 2.262 6 0.001 103 mm2/s for the water phantom, and 4.90 6 0.01 103 mm2/s for the acetone phantom. The magnitude of the signal across the phantom is illustrated with an example in Fig. 4. Both acetone and water provided relatively high signal; however, the signal from the glycerol phantom was relatively low. In all cases, the magnitude of signal dropped with the increased TE required to obtain larger b values. This progression is illustrated in Fig. 5a. Figure 5(b–d) illustrates the calculated ADC across each phantom for images obtained with the whole body gradient. In each case, as the b value increases, the variance in the ADC calculation increases and the magnitude of the calculated diffusion coefficient changes. This variation in ADC values is illustrated in Fig. 6b for data obtained with and without the presence of insert. Figure 6a shows that the presence of the insert does cause some image distortion in the received signal. Figure 6c is an overlay of the image of the phantom obtained both with and without the insert. Regions of
FIG. 5. Calculation of apparent diffusion coefficient. a: Magnitude of the image signal for range of TEs. b: Point-by-point calculation of apparent diffusion coefficient through the glycerol phantom, (c) water phantom, and (d) acetone phantom. Error in the calculation increases as the strength of the component signals decreases relative to the noise.
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FIG. 6. Image data (a) acquired using the whole body gradient (TE ¼ 83 ms) without (left) and with (right) the presence of insert in the bore of the magnet. The top row shows a slice through the phantom with no diffusion weighting. The middle row shows a slice through the phantom when diffusion weighting was applied to a b value of 250. The bottom row represents the apparent diffusion calculated from the data in the first two images. The square box represents the location of the data averaged, for each slice in the phantom to create the line plots. b: The change in apparent diffusion coefficient with applied b value. The top plot shows the change in ADC for b values ranging from 250 to 4000 in glycerol calculated from data acquired by the whole-body gradient both in the presence of the insert gradient and in its absence. The middle row represents the same calculation for the water phantom, and the bottom row represents this calculation for the acetone phantom. c: An overlay of the water image obtained using the whole body gradients in the presence and absence of the insert gradient. Regions of overlap are shown in white, regions of insert-only signal are shown in light grey, regions of noinsert-only signal are shown in dark gray.
overlap are white. The light and dark gray regions at the edge of the phantom indicate that there is some distortion in the image due to the presence of the insert gradient. However, the image distortion is consistent for both the T2-weighted and the diffusionweighted images. The ADC calculated, both in the presence and absence of the insert gradient, is plotted in Fig. 6b. In all cases, a change in ADC with b value can be noted. Figure 7a illustrates the signal magnitude when the insert gradient is used for diffusion encoding. The first panel represents the signal with no current applied to the insert. The second panel illustrates that there is signal loss due to diffusion when the insert gradient is applied, and the third panel illustrates a pixel-by-pixel calculation of the apparent gradient, assuming that the
ADC for the phantom was 2.262 6 0.001 103 mm2/s. Figure 7c plots out the apparent gradient strength versus the applied current for two positions (boxed regions in Fig. 7a in all three phantoms). For both water and acetone, the apparent gradient strength appeared to level out at current amplitude of 64 A in the first position and 112 A in the second position. The apparent gradient strength measured in the glycerol phantom appeared to level out at a current amplitude of 45 A in the first position and 79 A in the second position. This corresponded to image data where the magnitude of the diffusionencoded signal approached the noise floor. The gradient strength (calculated using the applied current and the apparent gradient efficiency at that position) producing noise-level signal amplitude was similar for both positions examined in Fig. 7a.
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FIG. 7. Image data (a) a slice through the water phantom. The phantom was imaged with a TE of 83 ms when 0 A (left) and 28 A (middle) were pulsed through the insert gradient. Using an ADC for water of 2.2 103, the magnetic gradient for each point in the image was calculated (right). The solid blue line through the image indicates the source of the line plots. b: Intensity of signal for a line of data through the 25% glycerol phantom (top), water phantom (middle), and acetone phantom (bottom) for no current running through the insert gradient, and a selection of three pulsed current amplitudes. c: Gradient strength from two positions, indicated by the boxes in the right panel of (a), calculated as a function of the current pulsed through the gradient system.
Figure 8a illustrates the simulated gradient efficiency for the insert gradient and the apparent gradient efficiency calculated using image data from the water phantom when a current of 28 A was driven through the insert gradient. Data from the water phantom (I ¼ 28 A) was selected to illustrate the gradient profile because it represented the data from which largest range of gradient efficiencies could be calculated. Although acetone data was collected at a lower minimum current threshold (18 A), the high diffusion coefficient of acetone resulted in a larger region of total signal loss close to the insert and although glycerol has a lower diffusion coefficient, the lower signal from the phantom again resulted in a larger area of total signal loss. Figure 9 illustrates the result of using the gradient efficiency to calculate the ADC for a water phantom (I ¼ 45 A). The ADC value appears to decrease closer to the insert (corresponding to regions of higher b value) and increase farther from the insert (corresponding to regions of lower b value). The calculation of the ADC in regions of adequate signal (from both the T2-weighted image and the diffusion-weighted image) and b > 300 s/mm2
resulted in a value that was reasonably constant and consistent with what was expected for each phantom. In Fig. 10a, the ADC was calculated and binned according to magnitude of the b value producing that ADC. This was compared to the initial graph of the ADC versus b value (calculated using the whole body gradient). When using the insert gradient, b values were obtained using a constant TE and pulses of uniform duration. However, the whole body gradient required steadily increasing pulse durations and TEs to reach the desired diffusion encoding. DISCUSSION Pulse Sequence Calibration Every transition of the gradient, from on to off or off to on, causes some residual eddy currents (and associated magnetic field) in the system’s conductors. An on/off transition produces an eddy current that is equal, but opposite, to an off/on transition. The shorter the delay between paired transitions, the more complete the cancellation. The twice-refocused-spin-echo diffusion
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FIG. 8. a: Intensity of signal for a line of data through the water phantom [I ¼ 0 A and I ¼ 28 A]. b: Comparison of the simulated gradient efficiency and the gradient efficiency calculated from the data using ADC ¼ 2.2 103. c: Calculation of the gradient map based on the image data acquired of the water phantom using the whole body insert and diffusion encoding performed by the insert gradient. The white box in (c) represents the region of the gradient map shown in the contour map in (d). The corresponding region in the simulation is shown in (e). The black box in (d) and (e) represent the region of the phantom used in subsequent calculations of ADC.
sequence, used by the whole body gradients during diffusion encoding, minimized the residual eddy current by using four short diffusion pulses and a slightly asymmetric waveform to control eddy currents during the highly sensitive echo-planar imaging readout phase. When the insert gradient was used for diffusion encoding, the trailing edge of each diffusion gradient pulse was refined to produce slightly asymmetric pulses, minimize the eddy currents, and maximize the signal. Although the amplitude of the diffusion pulses were refined to minimize eddy currents as far as possible, perfect cancellation was not possible due to limitations in the discretisation of the NI card used to control the power amplifier. Distortion Due To insert The presence of the insert gradient did result in some distortion in the image data collected from the whole body gradient, as can be seen in Fig. 6. The presence of the insert resulted in a warping of the image. The stretching of the image indicates that there is a local increase in the gradient strength near the insert, above those expected by the system during reconstruction. Previous work using localized gradients have also located the gradient set within the radio frequency system with
FIG. 9. a: The signal amplitude for a line through each phantom. b: Apparent diffusion coefficients calculated using the signal amplitude data and the simulation of the gradient.
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FIG. 10. a: A plot of the calculated apparent diffusion coefficient versus the applied b value. The data from the whole body gradient represents an average of the ADC calculated on a pixel-bypixel basis for the centre of the phantom. Data from the insert represents an average of the apparent ADC for a bin size of 50 s/mm2 aggregated from the entire dataset. b: A plot of the minimum time required to achieve a b value using this pulse sequence. The solid line represents the b value obtained 5 cm from the surface of the insert. The dashed line represents the b value obtained using the whole-body gradients, and the dotted line represents the decay from maximum transverse magnetization as the echo time lengthens.
good results (21), and it seems possible to do so here as well, although a unwarping algorithm may be required to register images acquired in the presence of the insert with images acquired using other sequences. Although the ADC values are slightly different for low b values, similar ADCs are calculated with and without the presence of insert for larger b values, which is reasonable considering the range of b values targeted by this technique.
ent operation inside the MRI. If the signal loss in the diffusion-encoded image were larger than that expected, it would translate into a larger apparent gradient strength. Although the simulated and measured field values are similar over the area of the phantom, the slight differences between the two curves indicate that the measurement of the ADC should be used as the basis for the ADC over the values found in the idealized simulation. Change in Apparent Diffusion Coefficient With b Value
Simulation Versus Calculation Figure 8 illustrates that the simulated magnitude of magnetic gradient did not precisely match the calculated profile of the applied gradient. This is most likely due to nonidealities in the construction of the gradient coil and limitations with the step size of the waveform generation software. Ideally, the matched diffusion pulses would produce perfectly balanced dephasing and rephasing. However, the residual eddy currents that result from the switched gradients may have induced some nonsymmetrical dephasing into the sample. The shape of the second diffusion pulse of the gradient waveform was adjusted to maximize received signal and compensate for the gradient experienced due to the unexpected currents in the magnet, but the waveform generator driving the insert gradient had a maximum time resolution of 4 ms and a maximum waveform output resolution of 1 mV (which translated into a current resolution of 0.05 A). While slight, these finite step sizes would have resulted in imperfect matching of the two lobes during insert gradi-
The diffusion coefficient for the phantoms appeared to change with increasing b values. This effect was shown in the ADCs calculated from image data obtained by using the whole-body gradient and was less apparent when using the insert gradient to do the diffusion encoding. The ADC shift was particularly obvious in the sharp rise in ADC of glycerol as the b-value increased towards 1000 s/mm2. The diffusion coefficient of various concentrations of glycerol–water mixtures have been determined by non-MRI-based experiments (22,23). While the 25 vol % (29 wt %) glycerol/water mixture phantoms have been used previously in investigations of various DWI pulse sequences (24), such solutions have demonstrated a range of ADCs from 0.62 103 mm2/s to 1.26 103 mm2/s (25). Previous investigations have also shown a variability in measured ADC that is in some way dependant on the b-value and pulse timing (26,27). Cotts et al. (27) discussed how differences in susceptibility of the components of the mixed solution may cause signal loss that would lead to errors in the calculation of
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the diffusion coefficient. This hypothesis would explain why a large change in ADC occurred at lower b values in the glycerol/water solution, but not in either the pure water or acetone phantoms. The consistent timing of the diffusion weighting applied using the insert gradient mitigated the effect of increasing b values and provided a more consistent calculation of the ADC. ADC Determination: Insert Versus Whole Body Although the ADCs obtained with the whole body did not precisely match those calculated using the insert, the ADCs were similar for low b values and the diffusion coefficients calculated using data weighted with the insert gradient demonstrated less of a variation as they progressed toward higher b values. This may have been for two reasons. While our measurements of the ADC of water resulted in the calculation of a value (D ¼2.262 6 0.001 103 mm2/s) close the value of those reported in literature (D ¼ 2.2 103 mm2/s) (28), the measurement of the ADC in the liquid phantom may have been confounded due to the presence of vibration in the liquid during image acquisition. Although distortions in the ADC would still occur, the consistent timing employed when using the insert gradient would prevent changes in the measured ADC due to liquid motion during diffusion encoding. Secondly, as a result of the shorter TE, more of the original signal was available for the calculation of ADCs when the diffusion weighting was performed using the insert gradient, resulting in the signal strength for the DWI being farther from the noise floor and yielding a more precise value for the diffusion coefficient. Figure 10b highlights that, given the overhead required for a diffusion-weighted echo-planar imaging sequence, there is not a particularly large TE advantage in using the insert gradient when lower b values are desired. Additionally, the difference between the ADCs calculated using the insert gradient and the whole body gradient (Fig. 10a) at low b values suggests that this approach would be best suited for situations where large b values are desired (and the TE benefits of using the inert gradient are maximized). Signal Loss The application of any diffusion-encoding gradient reduces the signal magnitude from the sample. This was expected and the signal loss is illustrated in Fig. 4. Based on the initial signal magnitude (TE ¼ 83 ms; b ¼ 0 s/mm2), a b value of 1000 s/mm2 might produce a diffusion-weighted water phantom signal with a magnitude that is 1.91 times the noise floor. However, due to the increase in TE that accompany the larger b values, for data obtained using only the whole body gradient, the actual magnitude of the diffusion-encoded signal at b ¼ 1000 s/mm2 was only 1.31 times the noise floor. However, when using the insert gradient to do the diffusion encoding at a position where b ¼ 1000 s/mm2 with the glycerol phantom (I ¼ 65 A; TE ¼ 83 ms; 5 cm from the surface), the signal was 1.81 times the noise floor. Similarly, acetone, which had a signal of 2.07 times the noise floor at b ¼ 500 (TE ¼ 88 ms; whole body), had a signal
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of 2.43 times the noise floor when that diffusion encoding was done using the insert gradient (I ¼ 45A; TE ¼ 83 ms; b ¼ 500 s/mm2; 5 cm from the surface). Finally, in an extreme case, water had a signal of 1.2 times the noise floor at b ¼ 1350 s/mm2 (TE ¼ 103 ms; whole body), but using the insert gradient (I ¼ 79 A; TE ¼ 83 ms; b ¼ 1350 s/mm2; 5 cm from the surface) the signal was 1.88 times the noise floor. The reduced TE possible with the insert gradients translates into a stronger received signal after diffusion encoding. To closely match the diffusion pulse sequences performed with the insert gradient to the timing of the pulse sequences performed with the only the whole body gradients, the full capabilities of the insert gradient were not used. The amplifier’s hardware was capable of supplying current at greater amplitude than the maximum pulse sequences used in this experiment. Thus, if the insert is pulsed more strongly for shorter duration, further reduction in TE is possible. CONCLUSIONS Highly localized, small, nonlinear gradients are possible to construct for a limited field of view. Provided that the region of interest is situated in the region of high efficiency for the insert gradient, it is possible to perform rapid, highly differentiated DWI using a fourth gradient for diffusion encoding, and larger, general gradients for image acquisition.
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