CYCLIC MOTION ENCODING FOR ENHANCED MR VISUALIZATION OF SLIP INTERFACES

Abstract

Purpose

To develop and test an MRI-based method for assessing the mechanical shear connectivity across tissue interfaces with phantom experiments and in vivo feasibility studies.

Materials and Methods

External vibrations were applied to phantoms and tissue and the differential motion on either side of interfaces within the media was mapped onto the phase of the MR images using cyclic motion encoding gradients. The phase variations within the voxels of functional slip interfaces reduced the net magnitude signal in those regions, thus enhancing their visualization. A simple two-compartment model was developed to relate this signal loss to the intravoxel phase variations. In vivo studies of the abdomen and forearm were performed to visualize slip interfaces in healthy volunteers.

Results

The phantom experiments demonstrated that the proposed technique can assess the functionality of shear slip interfaces and they provided experimental validation for the theoretical model developed. Studies of the abdomen showed that the slip interface between the small bowel and the peritoneal wall can be visualized. In the forearm, this technique was able to depict the slip interfaces between the functional compartments of the extrinsic forearm muscles.

Conclusion

Functional shear slip interfaces can be visualized sensitively using cyclic motion encoding of externally applied tissue vibrations.

INTRODUCTION

The presence of low-friction interfaces allowing for shearing motions between tissue surfaces is critical for the normal function of many structures in the body. Biological evolution has provided several solutions for this requirement. Apposed serosal surfaces in the pleura, pericardium, and peritoneum provide the slip interfaces needed for the normal function of the lungs, heart, and intra-abdominal organs, respectively (1). Bursal structures allow the shearing motions necessary for the function of tendons and parts of the musculoskeletal system (2). Areolar adipose tissue surrounding blood vessels, muscles, and the capsules of organs provide for smaller degrees of shear motion, allowing relative movement between structures during gross body motion and breathing (3,4).

The loss of functional shear interfaces, such as due to scarring or tumor invasion, can lead to serious consequences. For instance, the development of adhesions between the visceral and parietal peritoneum in the abdomen, typically due to scarring following surgery, can lead to functional impairment, intermittent bowel obstruction, and acute conditions with catastrophic ischemic consequences (5,6). Adhesions in peritendinous tissues can cause serious impairment in extremity and hand function (7). The loss of normal areolar tissue and replacement with fibrosis around the carotid arteries in the neck following radiotherapy subjects these structures to increased mechanical stress during normal body motion, which is thought to be instrumental in the accelerated development of atherosclerotic changes in these patients (8).

Conventional imaging techniques such as magnetic resonance imaging (MRI) and computed tomography (CT) can depict the gross morphology of tissues at structural shear interfaces and may demonstrate focal thickening or other changes that are likely to be associated with the loss of slip functionality, but they do not directly assess this property. The goal of this work was to develop and test an MRI-based method for sensitively assessing the mechanical shear connectivity across tissue interfaces. The approach is based on the phenomenon of motion-induced “shear lines” that are occasionally observed in conventional MRI studies. In some cardiac MR acquisitions, portions of the pericardial interface are depicted as sharp, low-intensity lines (9), as can be seen in Fig. 1a.

Figure 1. Signal loss due to intravoxel phase dispersion with MRI.

(a) A heart image showing a dark line between the moving heart and the stationary tissues due to the high phase variations within the interface voxel. (b) A sagittal image of the human carotid artery acquired with a cine phase-contrast MRI sequence. Signal loss at the heart and vessel walls can be seen, as indicated by the arrows

This signal loss has been attributed to intravoxel phase dispersion (IVPD) in volume elements that include both the rapidly moving cardiac surface and the stationary parietal surface (9). Similarly, shear lines due to IVPD are often observed at the boundary layer between flowing blood and vessel walls and the static surrounding tissue in MRI (10–12), as seen in Fig. 1b. In these examples, the large differential motion between the tissues on either side of the interface due to physiological motion causes a large phase shift across the interface, due to the intrinsic motion encoding of the pulse sequence.

We hypothesized that these shear lines can be intentionally created at other tissue interfaces of interest and can be used to characterize them. We propose that this can be accomplished by applying extrinsic motion to preferentially move tissue on one side of an interface while encoding this motion into the phase of MR images. The purpose of this work is to test this hypothesis and to evaluate its potential for the enhanced visualization of slip interfaces in simple phantom experiments and to perform initial in vivo feasibility studies on normal human volunteers.

THEORY

Intravoxel Phase Dispersion

Intravoxel phase dispersion is a phenomenon by which the magnitude signal of a volume element (voxel) reduces due to the presence of significant phase variations within that voxel. This is because the magnitude signal of a voxel is a vector sum of the magnetization of a large number of isochromats (spins) present within that voxel. This effect can occur due to phase variations through the thickness of an imaged slice as well as within the imaging plane. It has been considered as an artifact and has been corrected by some researchers (13) or has been exploited to create specialized contrasts by others (14).

The proposed interface visualization technique attempts to exploit this process by introducing sinusoidal shear motion into the body and mapping the motion of the tissues on either side of the interface into the phase of the MR images. At low-friction slip interfaces, a phase discontinuity would be expected at the interface voxels due to the difference in the amount of motion. With enough motion, this phase discontinuity can result in local regions of signal loss at the interface (referred to in this work as shear lines) in the magnitude images, thus making the functional slip interface discernable.

Motion Encoding

To encode the cyclic motion of the tissues on either side of the interface into the phase of the MR images, cyclic bipolar motion-encoding gradient pairs (MEG) are added to a normal MRI pulse sequence. The phase of the magnetization of a moving spin is given by the following equation (15)

$$\phi (t_1)=\gamma {\displaystyle {\int }_0^{t_1}\overrightarrow{G}(t)·\overrightarrow{r}(t)\mathit{\text{dt}}}$$ [1]

where φ(t₁) is the time-dependent phase of the transverse magnetization of a particular spin, G⃗_r(t) is the motion-sensitizing gradient, r⃗(t) is the position vector of the moving spin and γ is the gyromagnetic ratio. In this work, harmonic sinusoidal vibrations are applied and the phase of the magnetization of the spin moving sinusoidally is given by the equation

$$\varphi (\overrightarrow{r},\theta )=\frac{\gamma N_{g}T(\overrightarrow{G}·{\xi }_0)}{2}\text{cos}(\overrightarrow{k}·\overrightarrow{r}+\theta ),$$ [2]

where N_g is the number of MEG used to sensitize the motion, T is the period of a gradient pair, ξ⃗₀is the peak amplitude of motion, k⃗ is the wave number, and θ is an adjustable temporal phase offset between the motion-encoding gradient and the motion (16). This pulse sequence with the added MEG is actually described in an elasticity imaging technique called magnetic resonance elastography (MRE) to image externally induced shear waves propagating in tissues (16).

IVPD and the Two-Compartment Model

An MR image of an object is obtained by Fourier transforming a discretely sampled and truncated region of k-space corresponding to the spatial frequency domain representation of the object. The signal of a pixel in an MR image is given by a convolution of the true MR signal with a point spread function defined as a ratio of two sinc functions (Eq. 13.18 in (17)). However, for much of this work, a simpler two-compartment model where the pixel is considered to be rectangular and to have two subsections was developed to demonstrate and explain the magnitude signal reduction in an interface voxel due to the phase difference across that voxel. The model is shown schematically in Fig. 2a with the two compartments identified, one with spins from the moving object on one side of the interface and the other compartment with spins from the nonmoving object (or an object moving differently) on the other side of the interface. This model assumes that the isochromats within the voxel can only possess one of two phase values based on the compartment in which it is located. The compartment with the moving spins has αN_s isochromats, where N_s is the total number of spins in the voxel and α is the fraction of moving spins in the voxel. The other compartment has (1-α)N_s spins. The schematic depicts the situation with α is equal to 0.5, where the interface is exactly in the middle of the voxel. M₁ and M₂ are the magnitudes of the isochromats in the two compartments and, for this initial work, both of these values are assumed to be the same with unit value. θ₁ and θ₂ are the corresponding phases in the two compartments and the assumption is made that all the spins in each compartment have the same phase. The difference in these two phase values is dependent upon the type and amount of relative displacement occurring on either side of the interface and the motion sensitivity of the MR imaging sequence.

Figure 2. Two-compartment model: Theory.

(a) A schematic representation of the two-compartment model for an interface voxel. The net normalized voxel magnitude signal is shown as a function of (b) phase difference for increasing values of the spin fraction from 0.1 to 0.5 (top to bottom) in steps of 0.1, and (c) spin fraction for increasing values of the phase difference from 0.1π to π (top to bottom) in steps of π/10.

The net magnitude signal of this voxel, R, is the vector sum of all the spins in the two compartments and is given by

$$\frac{R^2}{{N_s}^2}=1-4\alpha (1-\alpha ){\text{sin}}^2\left(\frac{\mathrm{\Delta }\theta }{2}\right),$$ [3]

where Δθ is the phase difference across the voxel, calculated as (θ₁ – θ₂). With this model, the total number of spins present in the voxel is only a scaling factor for the absolute magnitude value, and the relative magnitude signal loss is only dependent upon the phase difference between the moving and nonmoving compartments and the fraction of the spins present in each compartment. If Δθ is zero, then R²/N_s² = 1, implying that there is no signal reduction in the voxel. The magnitude signal is lowest when the phase difference is π for any particular value of α and it goes to zero when α is 0.5. The equation reduces to $\frac{R^2}{{N_s}^2}={\text{cos}}^2\left(\frac{\mathrm{\Delta }\theta }{2}\right)$ when the interface is exactly in the middle of the voxel (α = 0.5). Figure 2b shows the behavior of the normalized theoretical magnitude signal with respect to phase difference for different values of α. The five curves, from top to bottom, depict the magnitude values for α values ranging from 0.1 to 0.5 in steps of 0.1, respectively. In Fig. 2c, the normalized magnitude signal is drawn as a function of the fraction of the spins α, and the ten curves correspond to values of Δθ ranging from 0.1π to π in steps of π/10. The magnitude signal has the lowest relative value when α is 0.5 and the symmetry in the behavior of the magnitude with respect to α = 0.5 is evident from this graph.

MATERIALS AND METHODS

Phantom Experiments

A series of phantom experiments were designed to demonstrate the feasibility of detecting functional interfaces and to validate the two-compartment model for shear-line imaging. Sagittal images were acquired in a 1.5-T whole-body scanner (GE Signa, Milwaukee, WI, USA) with a single-channel, quadrature, transmit/receive head coil.

Two cylindrical Wirosil silicone (Bego, Lincoln, RI, USA) phantoms of 8-cm radius were made and were placed one above the other as seen in the schematic representation of the experimental setup shown in Fig. 3a. The bottom block was 5 cm in height and was fixed to the base. The top block was 2-cm tall and was moved in a shear-like motion with respect to the bottom block with the help of an electromechanical driver as indicated in the schematic. A drive shaft extending from the electromechanical driver was inserted into the top block. When an alternating current is passed through the voice coil of the driver, the magnetic moment created tries to align with the main magnetic field B₀ moving the drive shaft and the top block in one direction (the superior-inferior (SI) direction in this case). When the alternating current reverses, the magnetic moment also reverses and moves the block in the opposite direction. A very thin layer of mineral oil was added between the two blocks to increase the slipperiness of the interface. For the phantom experiments, the top block was moved with respect to the bottom block at a frequency of 50 Hz for a maximum excursion distance of 100 µm.

Figure 3. Experimental setup.

(a) A schematic of the electromechanical driver and the two-part phantom used for the phantom experiments. (b) A schematic of the pressure-activated driver system used for the in vivo human studies.

To encode the motion into the phase of the MR images, two 20-ms cyclic bipolar motion-encoding gradient waveforms were placed one on each side of the 180° RF pulse of a conventional spin echo pulse sequence. The MEGs used in this experiment were sensitive to motion in the SI direction, the horizontal direction in Fig. 3a. The amplitude of the MEGs could be adjusted from 0 to 40 mT/m to encode an increasing amount of phase into the transverse magnetization of the moving phantom. Other relevant imaging parameters were FOV = 12 cm, acquisition matrix = 128², frequency-encoding direction = SI, TR/TE = 300/48 ms and slice thickness = 10 mm. The acquisition was repeated twice with the motion-encoding gradient polarities inverted, and the final complex image to be examined was calculated with a magnitude equal to the mean of the magnitude images of the two encoding directions and with a phase equal to the difference of the phases of these two datasets. As in (16), with appropriate manipulation of the timing of the MEG and the motion, 4 of these images (also called phase offset images or wave images) evenly spaced over one period of the motion were acquired and the effects of the mechanical motion on the magnitude signal through the wave period were analyzed.

To compare the experimentally observed data to the theoretical predictions, the values for the phases of the moving and nonmoving compartments (θ₁ and θ₂, respectively) within an interface voxel were assumed to be the same as those of the adjacent voxels, and thus the phase difference across the interface was calculated as the difference in the phase between the voxels on either side of the interface voxel. To fix the value of α for each image for subsequent processing, the complex wave image data were sub-pixel shifted in the image domain by tenths of a pixel (using the Fourier shift theorem) by applying phase ramps (linear phase variations across k-space) in the spatial frequency domain to produce the required spatial shifts in the image domain. From these sub-pixel shifted images, the image that resulted in the lowest magnitude signal was assumed to correspond to an α value of 0.5. To compare the reduction of magnitude signal at the interface with the theoretically predicted values, data were acquired for a fixed phase offset exhibiting a shear line with the MEG amplitude adjusted to different amplitude values evenly spaced from 0 to 40 mT/m.

To demonstrate that the simple two-compartment model is a valid approximation of the signal in the pixels of these images, an additional numerical simulation was performed where a synthetically created image resembling the phantom, with sharp phase discontinuities equivalent to those observed in the experiments, was convolved with a theoretical point spread function (PSF) calculated according to the equation

$$\mathit{\text{psf}}=N_k\mathrm{\Delta }k\frac{\text{sinc}(\pi N_k\mathrm{\Delta }\mathit{\text{kx}})}{\text{sinc}(\pi \mathrm{\Delta }\mathit{\text{kx}})}{e}^{-i\pi \mathrm{\Delta }\mathit{\text{kx}}}$$ [4]

where N_k is the number of k-space sampling points and Δk is the k-space resolution (refer to Eq. 13.18 in (17)) . The data obtained from this numerical simulation was then compared to the two compartment model data and the experimentally observed data.

In Vivo Feasibility Experiments: Abdomen

The in vivo feasibility of this technique was investigated by performing an experiment to detect the slip interface present between the small bowel and the abdominal peritoneal wall, where the loss of the slip interface due to the formation of adhesions after abdominal surgeries is a significant clinical problem. To create relative motion between these two tissues, a pressure-activated driver was placed on the abdomen of a human volunteer after obtaining verbal consent and in compliance with the institutional review board. Axial images of the subject were obtained with the subject positioned in the prone position. Longitudinal motion at 90 Hz was applied to the abdomen in the anterior-posterior direction and the motion occurring in the SI direction was encoded in the wave images. Additional imaging parameters included 32-cm FOV, 256×64 acquisition matrix, 33.3-ms TR, 19.2-ms TE, 30° flip angle, 16-kHz receiver bandwidth, 5-mm slice thickness, right-left frequency-encoding direction, 1 11.1-ms MEG, and 4 time offsets acquired within a single breath-hold using parallel imaging with an 8-channel torso-array surface coil. Figure 3b shows the schematic of the pressure-activated driver, which has an active driver component (located outside of the scan room) that creates cyclic pressure waves, a passive driver component coupled to the tissue of interest, and a long flexible tube that connects these two components. To differentiate the signal loss created at this interface due to intravoxel phase incoherence from the inherent MR signal contrast in the images, a pseudo-magnitude filter analysis (14) was performed by creating complex images with unit magnitude and with phase equal to the phase of the complex images. Signal loss was then produced by low-pass filtering these complex images using a 9-point Hamming window low-pass filter with a normalized frequency cutoff of 0.5. The boundary between the small bowel and the abdominal peritoneal wall was then inspected for the presence of a shear line.

In Vivo Feasibility Experiments: Forearm

The technique was further investigated in an application which avoids the situation in which the inherent MR signal contrast can confound the shear-line-based signal contrast. The technique was used to detect the interfaces between the functional compartments of the multitendoned forearm muscles: the flexor digitorum profundus and the flexor digitorum superficialis. These muscles do not possess anatomically distinct compartments separated by fascicular boundaries specific for each finger (18), but highly individuated and independent finger movements are possible due to selective activation of functional compartments within each muscle (19). For these experiments, the pressure-activated driver shown in Fig. 3b was modified to use a smaller passive driver so that individual fingers could be vibrated independently of the other fingers. Each finger was vibrated at 60 Hz and an axial, cross-sectional imaging slice of the forearm was acquired while the volunteer was in the prone position with his arm above his head, palm down. Other relevant imaging parameters included 12-cm FOV, 256×64 acquisition matrix, 66.6-ms TR, 29.1-ms TE, 30° flip angle, 16-kHz receiver bandwidth, 5-mm slice thickness, right-left frequency encoding direction, one 16.7-ms MEG, and 4 time offsets acquired with a 10-cm inner diameter birdcage MRI coil (Mayo Clinic Health Solutions, Rochester, MN, USA). The motion occurring in the through-plane direction was encoded into the wave images and the MR magnitude images obtained from these experiments were examined for evidence of shear lines occurring between regions of the muscle corresponding to the vibrated finger.

In addition to examining the magnitude images obtained directly from the shear-line imaging technique and indirectly from the pseudo-magnitude filter analysis, 2D phase-difference values were calculated by root-sum-of-squares of the 1D phase-difference values in the × and y directions. Relative magnitude signal estimates were calculated from these values using Eq. 3 assuming that the interface was in the middle of the voxel (α = 0.5). These estimates represent predictions of the maximum observable magnitude loss of an interface voxel for general obliquely oriented interfaces where the phase differences of the surrounding voxels are entirely due to the slip interface motion.

RESULTS

Phantom Results

Figure 4 shows the results obtained from one of the phantom experiments. Figure 4a shows the MR magnitude image of the two-part phantom without the thin oil layer between the two parts. The motion-encoding gradient was set at 32 mT/m. Even though the driver was active and was vibrating the upper part of the phantom, since there was no functional slip interface, both parts of the phantom moved together and thus the interface between the two parts could not be visualized. Figure 4b shows the magnitude image of the phantom with the same amount of motion and motion-encoding gradient amplitude but with the added thin oil layer. The oil layer increases the differential motion between the two parts and the presence and location of the interface is visible due to the presence of the low-signal shear line indicated by the arrow. Figure 4c shows the magnitude image of the phantom with the same amount of motion, but with the motion-encoding gradient amplitude set at 0 mT/m. The interface could not be detected in this image.

Figure 4. Phantom shear line demonstration.

Normalized magnitude images of the two-part phantom are shown (a) without and (b) with a thin oil layer between the two parts. Equal amounts of motion were applied and the motion-encoding gradient value was set at 32 mT/m. A prominent “shear line” of reduced signal intensity in (b) indicates the presence of a functional slip interface. (c) A magnitude image of the phantom with the same amount of motion but with the motion-encoding gradient amplitude set to 0 mT/m.

The phase image of the phantom for the experiment without the thin oil layer is shown in Fig. 5a indicating no sharp phase discontinuity, and thus contiguous motion, at the interface. In contrast, in the phase image for the experiment with the oil layer, shown in Fig. 5b, the sharp phase discontinuity at the interface is clearly evident. Figures 5c and 5d show the phase-difference (Δθ) images for the two cases. It is clear that the amplitude reduction in the magnitude signal for a voxel occurs only where there is a large phase difference across the voxel.

Figure 5. Phantom shear line demonstration.

Wave images of the phantom are shown (a) without and (b) with the oil layer. The corresponding phase difference images (estimates of Δθ in the ‘y’ direction) are shown in (c) and (d). A sharp phase difference at the interface is visible in (d)

Figure 6 shows the results of the comparison of the experimentally observed magnitude signal values (labeled “Exp”, red) with the theoretical magnitude signal values calculated from the two-compartment model (“TCM”, blue) and the sinc PSF based calculation (“PSF”, green). A small scaling factor was introduced to the phase-difference values of the experimental data by assuming that the lowest magnitude signal observed corresponds to a phase difference of π to correct for the minor intra- and intervoxel phase variations that are unaccounted for in the model. Fig 6a shows these three datasets plotted as a function of the observed phase difference for an alpha value of 0.5. With α at 0.5, the magnitude signal values obtained from both the two-compartment model and the PSF based calculation were equal and hence only two curves are visible in this image. It can be seen that the theoretical values agree with the experimental values well.

Figure 6. Experimental validation of the theoretical model.

Comparisons are shown of the theoretical two-compartment model (“TCM”), the point spread function convolution analysis (“PSF”) and the experimentally observed magnitude signal values (“Exp”) with respect to (a) the phase difference with spin fraction α = 0.5 and (c) the spin fraction when the phase difference is π. In (a) both the TCM and PSF values are equal, thus only one curve is visible. The experimental magnitude signal variations equivalent to the results in Figs. 2b and 2c are also shown as a function of (b) the phase difference for increasing values of the spin fraction from 0.1 to 0.5 (top to bottom) in steps of 0.1, and (d) the fraction of spins for increasing values of the phase difference from 0.1π to π (top to bottom) in steps of π/10.

Figure 6b shows how the experimental magnitude signal values decrease with respect to the phase difference for values of α from 0.1 to 0.5 (from top to bottom). The corresponding curve for an α value of 0.6 is almost equivalent to the curve with an α value of 0.4, and similarly the curve pairs for α values of (0.7, 0.3), (0.8, 0.2) and (0.9, 0.1) are almost equivalent. Hence the curves for the higher values of α are not included in Fig. 6b to maintain its legibility. The fact that the signal change was mostly symmetric about α = 0.5 is evident in Figs. 6c and 6d where the magnitude signal values are plotted against α. Figure 6c shows the two-compartment model data, the sinc PSF based simulation data and the experimental data plotted with respect to α for a phase-difference value of π. It can be noted that even though the two-compartment model data values differ from the simulated data values when α is not equal to 0.5, the general trend and agreement are similar. Figure 6d shows the behavior of the experimental magnitude signal values as a function of α for increasing values of the phase difference from 0.1π to π (from top to bottom). The profiles in Figs. 6b and 6d agree well with the theoretical two-compartment model curves shown in Figs. 2b and 2c, respectively.

In Vivo Results

Figure 7 shows the data obtained from the volunteer study performed to demonstrate the creation of a shear line between the peritoneal wall and the small bowel when the movement of the small bowel is not restricted. The conventional magnitude image of an axial slice of the abdomen is shown in Fig. 7a, where the interface between the peritoneal wall and the small bowel is indicated by the arrow and portions of the intestinal system have been masked out via a mask defined by thresholding the magnitude data to remove noise from the images. The interface between the peritoneal wall and the small bowel already has reduced signal similar to a shear line due to inherent MR signal variations between the two tissues. Figure 7b shows the wave image of one of the phase offsets of the shear-line acquisition with the externally applied motion. The phase discontinuities present at the interface are clearly evident. These phase variations contribute some additional signal loss to the interfaces in Fig. 7a. Figures 7c and 7d show the images obtained from the pseudo-magnitude filter analysis. Figure 7c shows the magnitude image obtained by low-pass filtering the unit-magnitude complex data from an acquisition with no externally applied motion. No discernable signal changes are seen at the various tissue interfaces. In comparison, the magnitude of the low-pass-filtered, unit-magnitude complex data from the acquisition with motion present (the phase data are shown in Fig. 7b) is shown in Fig. 7d. The magnitude image in this case shows localized signal losses at the regions with sharp phase discontinuities. From this image, it could also be noted that the interfaces between the transversus abdominus muscle and the two oblique muscles could be visualized (arrow).

Figure 7. In vivo results: Abdomen.

(a) A conventional magnitude image of the abdomen with no applied motion is shown. The interface between the peritoneal wall and the small bowel with some inherent signal loss is indicated by the arrow. (b) A phase image is shown from an acquisition with the applied motion showing phase discontinuities occurring at the interface. The magnitude images obtained by low-pass filtering the unit-magnitude complex data from an acquisition (c) with no externally applied motion and (d) with applied motion. Slip interfaces can be observed as localized signal losses in (d) and the arrow indicates the shear lines created between the oblique muscles of the abdomen.

The results obtained from the human volunteer forearm experiments designed to visualize the slip interfaces between the functional compartments of the multitendoned muscles are shown in Fig. 8. Figure 8a shows an anatomical diagram of the deep-layer musculature of the forearm from Gray’s Anatomy (20) with the approximate location of the imaged slice indicated. The conventional MR magnitude image of the cross section of the forearm without any externally applied vibrations is shown in Fig. 8b. In this imaging plane, both the flexor and extensor regions (indicated by the letters F and E, respectively) could be visualized separated by the two forearm bones, the radius and the ulna. Figure 8c shows the magnitude image obtained when the index finger alone was vibrated. Comparing this to Fig. 8b, shear lines can be identified at the interfaces of both the flexor and extensor functional muscle compartments and are indicated by the arrows. Figure 8d shows the phase image that corresponds to the magnitude image with the slip interface shear lines, and the phase discontinuities due to the localized displacement induced in the muscle are clearly evident. The vibrational phase opposition of the flexor and extensor functional compartments for this finger can also be seen.

Figure 8. In vivo results: Forearm.

(a) Anatomical diagram of the deep-layer musculature of the forearm from Gray’s Anatomy with the approximate location of the imaging slice for MRE indicated. Magnitude images of the axial forearm slice are shown in (b) with no motion encoding and in (c) with motion encoding. The flexor and extensor regions are marked as “F” and “E” in (b). The shear lines present at the interface of the index finger functional compartment within the flexor and extensor digitorum muscles are indicated by the arrows in (c). (d) The corresponding phase image for the data shown in (c). Sharp phase discontinuities are easily visible between compartments.

Figure 9 shows the calculated 2D phase-difference images and the relative magnitude signal estimates obtained for the wave data for the in vivo experiments. Fig. 9a shows the phase-difference data obtained for the abdomen experiment, and the slip interfaces are visible as regions of large phase difference in this image. The relative magnitude signal estimates obtained from these data using Eq. 1 are shown in Fig. 9c. The slip interfaces can be easily detected as regions of lower signal values and this image is similar to the pseudo-magnitude filtered image shown in Fig. 7d. Similarly, the data obtained from the forearm experiments are shown in Figs. 9b and 9d and the functional slip interfaces surrounding the index finger muscle compartments can be readily detected from these images.

Figure 9. Phase difference and relative magnitude signal estimate images.

(a) 2D phase difference image and (c) relative magnitude signal estimate for the abdomen wave data, both vividly depicting the slip interfaces. The relative signal estimate image looks similar to the pseudo magnitude filtered data shown in Fig. 7d. Similarly, (b) 2D phase difference image and (d) relative magnitude signal estimate for the forearm wave data showing the slip interfaces clearly.

DISCUSSION

The results obtained from these experiments demonstrate that the presence of functional slip interfaces can be detected as magnitude signal losses due to intravoxel phase dispersion by producing differential motion between the tissues on either side of an interface and encoding this motion into the phase of MR images. There have been previous MRE-based studies that can depict tissue interfaces by inducing planar shear waves, encoding the propagation of these waves into the phase of the MR images with a pulse sequence similar to the one used in this study, and deriving the contrast by analyzing the scattering of these waves from these phase images (21, 22). In our work, the presence of functional slip interfaces becomes discernible directly in the magnitude image itself and the contrast is derived simply from the differential shear motion between the tissues on either side of an interface. This technique can also indicate the presence of slip interfaces in pseudo-magnitude images designed to remove the effects of intrinsic MR signal variations unrelated to the functional characteristics of the interfaces, and in phase-difference images which directly indicate the local relative motion of the tissue near the interfaces.

The simple two-compartment theoretical model developed to explain this signal reduction predicts that the signal has a sin² dependence on the phase difference across the interface. If sinusoidal motion of a particular frequency is introduced, then the magnitude signal variations over time occur at twice this frequency due to the temporal behavior of the phase difference and because sin² (Δθ) is an even function. This behavior has been experimentally validated with data obtained with many phase offsets (data not shown). For instance, in the experiments shown in this work, which were performed with four phase offsets acquired within a single period of the motion, images from two of the offsets possessed shear lines (when the phase due to motion was significantly different from the static tissue phase) and the other two offsets did not (when the motion-induced phase was similar to the static tissue phase). Furthermore, the theoretical model suggests that the number of spins within a voxel (N_s) only acts as a scaling factor for the absolute magnitude signal and hence the spatial resolution of the image should not affect the relative signal loss at the interface voxels (for a fixed α and Δθ). The independence of the relative magnitude signal and the resolution scale was validated by reconstructing low-resolution images from previously acquired high-resolution data by truncating the data in k-space.

The two-compartment model also predicts that the magnitude signal should increase after the phase difference exceeds π. However, the experimental observations do not show this signal increase. The two-compartment model is a very simple approximation of the true characteristics of a voxel and this inconsistency is likely due to factors such as Gibbs ringing caused by the finite k-space acquisition, off-center echo sampling due to gradient imperfections, minor unaccounted-for phase variations observed within the top and bottom blocks, and/or interview variations (23) of α and Δθ Additional investigations need to be performed to isolate all of these effects and to develop a more robust model. However, for the purpose of predicting the magnitude signal reduction observed in these experiments based on the phase discontinuities at interfaces, the two-compartment model correlated well with the experimental data.

The images shown in Fig. 9, where the presence of the slip interfaces can be easily detected, indicate that the calculation of the phase difference and the relative magnitude signal estimates using Eq. 3 may be complementary approaches for the visualization of slip interfaces. This approach to maximize the contrast of the slip interface due to the assumed α value of 0.5 is advantageous since it avoids intrinsic MR imaging contrast, but it may necessitate additional processing of the phase data. Also, this approach utilizes information from the neighboring voxels assuming that the phase differences across the neighboring voxels are entirely due to the slip interface in the central voxel, while the magnitude images directly obtained from the shear-line imaging experiments depicting the slip interfaces as regions of lower magnitude signal values, as shown in Fig. 4b and Fig. 8c, are due to phase variations within the interface voxel itself.

With the human abdomen and forearm volunteer studies, it was demonstrated that it is feasible to detect interfaces between tissues sensitively with this technique. Previous MRI cardiac studies have indicated that the focal absence of pericardial signal voids due to transpericardial tumor invasion or adhesions could be used to reliably diagnose the pericardial involvement in cases like hepatocellular carcinoma (9). Similarly, with the proposed shear-line imaging technique, abdominal adhesions (5,24–27) and local extracapsular invasion of prostate tumors (28) could also be detected using the focal absence of shear lines. Since pulse sequences with cyclic motion encoding can encode motion on the order of 100’s of nanometers (16), the proposed technique could be potentially very sensitive to any cyclic motion which is introduced into the tissue. The technique can also be used for the localization of the boundaries of functional compartments of the multitendoned forearm muscles (29). However, more work needs to be done to assess the clinical value of such information.

In conclusion, this work demonstrates that functional slip interfaces can be sensitively visualized by applying acoustic vibrations to tissue and encoding the resultant motions into the phase of MR images with cyclic motion-encoding gradients. This results in intravoxel phase incoherence and localized magnitude signal loss at interfaces with minimal friction or coupling across the interface. A simple theoretical model to predict the magnitude signal loss based on the phase variance across the voxel was developed and was validated with phantom experiments. Results also showed that it is feasible to apply this technique in vivo with the demonstration of low-signal shear lines at the peritoneal bowel interfaces and at functional compartment interfaces of the forearm musculature. The knowledge of functional connectedness obtained from this technique could be beneficial for applications such as the diagnosis of abdominal adhesions and in prostate cancer staging based on localized extracapsular invasions.