Computed tomography (CT) is currently the imaging modality of choice to assess the position of implantable devices such as endovascular stent grafts (1) or prostate brachytherapy seeds (2). Although CT allows relatively easy visualization of stents, their functional assessment (patency) by flow measurements is limited. Furthermore, CT is used to assess the dosimetry of prostate brachytherapy seeds post implant. However, due to the limited soft tissue contrast of CT, the prostate is often not adequately depicted, which can result in overestimation of its volume (3). Magnetic resonance imaging (MRI), which provides superior soft-tissue imaging and no known biologically harmful effects, is becoming an alternative modality to guide and assess interventional procedures. Combined X-ray radiography and MRI systems have been shown to provide an alternative method for combining the advantages of MRI with a more accurate device depiction from X-ray (4, 5). However, coregistration of MR and X-ray data is subject to error from movement and/or misregistration. Therefore, a more reliable MR-visualization of metallic devices is of interest.
In MRI, the visualization of metallic devices such as endovascular stent grafts or prostate brachytherapy seeds (6) is traditionally based on signal voids due to local susceptibility gradients. It has been shown that for better visualization of devices, it is attractive to convert the signal loss into positive contrast (7). For this, a variety of positive contrast techniques have been proposed (8, 9), but often require optimization based on the magnitude of the local field gradients and local off-resonance effects. These are either applied during image acquisition or in a postprocessing step afterward. In particular, susceptibility gradient mapping (SGM) allows the production of a positive contrast image from the acquired complex image data (10). For this, a short-term Fourier transform (STFT) is applied for each pixel computed over a small number of adjacent pixels (window), and the shift of the echo top is determined in the STFT domain. The calculated shift is proportional to the local susceptibility gradient assuming a constant gradient over the window length. As metallic devices result in high local susceptibility effects, the calculation of a susceptibility gradient map allows for positive visualization. However, recently introduced nitinol based stent grafts have a much localized susceptibility effect (11) making the visualization subject to confusion with other sources of hypointensity. Vonken et al. (12) have shown that the SGM technique can be used for positive contrast imaging of nitinol stents. However, SGM requires a relatively high spatial resolution (<1 mm) to determine the echo-shift with sufficient accuracy, which makes it difficult to apply in clinical practice. Recently, a method for susceptibility field mapping was proposed to correct field distortions in echo-planar imaging used for functional MRI (13). This technique is based on a k-space filter applied in a sequential fashion exploiting the effect on the amplitude for each pixel separately. In this way, the resulting parameter map of the susceptibility gradient can be considered to maintain the resolution of the original data (14).
In this work, we have modified the k-space filter technique allowing SGM using the original resolution (SUMO) for visualization of implantable devices. The technique was compared with SGM in simulation, and applied in phantoms for visualization of a nitinol aortic stent and brachytherapy seeds with a positive contrast. In particular, the influence of image resolution was investigated. The clinical feasibility of SUMO was analyzed using MR data of an aortic nitinol stent graft case and patients implanted with prostate brachytherapy seeds. Aspects of the work were approved by Guy's Research Ethics Committee (reference number 05/Q0704/17) and the Bexley and Greenwich Research Ethics Committee (reference number 08/H0809/49). Informed consent was obtained for the use of anonymized data for research purposes.
During the acquisition of a gradient echo based image, local field perturbations from metallic devices disturb the linear relationship between frequency and position imposed by the imaging gradients, Gi, applied for a duration τ. In addition to the well-known geometric distortion, this leads to a shift of the affected echo in k-space. In SGM, a STFT is performed over N pixels. The susceptibility gradient Gs can be calculated from the echo-shift by determining the position of the maximum in the STFT by (Eq. 5 in Ref.10):
It is noted that from the original description, for accurate location of the echo-shift the window size is increased (i.e., N = N + 1) if the maximum lies at the first or last component of the STFT (10). In using a larger window, the effect from Gs within a SGM parameter map becomes increasingly compensated by unaffected neighboring pixels (i.e., partial volume [PV] effects). Therefore, for localized susceptibility effects, a relatively high resolution is required to detect a significant gradient over the adjacent pixels used in the STFT.
Alternatively, the shift in k-space can also be determined by applying a truncation filter in k-space (13), in which successive k-space coefficients are set to zero and the resulting signal amplitude is evaluated at each pixel in the image obtained by inverse Fourier transform. However, the truncation of k-space data results in Gibbs ringing artifacts that influence the signal amplitudes in the corresponding image. To avoid these ringing artifacts, we propose a filter, F(k,sk), that completely nulls a single k-space line at position sk using a Lorentzian shape:
The value for Δk was empirically chosen to ensure gradual recovery of the filter shape F(k,sk) to unity either side of sk and to minimize Gibbs effects. Figure 1 shows the effect of such a filter for two regions with susceptibility gradients against a homogeneous background. The filter is applied in a sliding window fashion by shifting its centre sk over k-space separately in all three different directions (i.e., kx, ky, and kz). For each application of the filter, the k-space value at position sk will be completely set to zero, and the corresponding image M(x) of the filtered k-space is calculated by an inverse Fourier transform, i.e.,
This allows a plot of the signal amplitude for each pixel and for all possible filter positions sk. The k-space shift, ks, is then determined for each pixel by locating the signal minimum along this sk axis (Fig. 1e):
Evaluating ks for each pixel and in each of the three orthogonal directions in k-space allows parameter maps of the echo-shift to be constructed, which can be used to provide an indication of the Gs vector. A threshold can be used for selective visualization to suppress areas of low ks values.
MATERIALS AND METHODS
A simulation was composed in MATLAB® (2007b, The MathWorks, MA) using a numerical phantom with 64 × 64 matrix size. In particular, the numerical phantom contained multiple rectangular regions with one-tenth in signal intensity and varying in size from 1 × 1 to 4 × 4 pixels with a given shift in ky. SUMO and SGM were both applied to the numerical phantom and used to compare their ability to accurately visualize the echo-shift in these areas. Positive contrast images were formed by displaying the resulting map of |ks| values, which could be overlaid onto the original negative contrast image without registration. By calculating ks, it was possible to obtain a signal response curve based on the echo-shift at each pixel. This was used to analyze PV effects based on the reported symmetry of the signal with respect to echo-shift under dephasing conditions (15). PV effects were apparent, when the intravoxel contribution to the overall signal varied in strength. On reversal of the external dephasing, the phases of intravoxel spins were inverted exactly and a symmetric nonzero response existed in the echo-shift. An asymmetric response and a single ks value were expected from a difference in susceptibility.
MR images of a GORE TAG® (Gore Medical, AZ) thoracic stent graft were obtained on a clinical 3.0 T MR system (Achieva, Philips Healthcare, Best, The Netherlands) using a six-element cardiac coil. The stent is made up of an expanded polytetrafluoroethylene tube supported by a self-expanding nitinol wire-frame. The device was placed horizontally in its deployed state (length = 170 mm, diameter = 37 mm) in a Duran® dish with 5% gelatin (Sigma-Aldrich Company, Gillingham, UK). Experiments were designed to investigate the influence of stent orientation and spatial resolution on susceptibility gradients:
iDatasets were obtained with the main axis of the stent orientated at 0, 30, 60, and 90° relative to the main magnetic field, B0. Three-dimensional (3D) MR data were acquired using a gradient echo sequence with: acquisition resolution approximately 1 × 1 × 2 mm3; field of view (FOV) = 250 × 360 × 60 mm3; flip angle (FA) = 20°; and echo time (TE)/pulse repetition time (TR) = 3.1/6.5 msec.
iiAt 0°, relative to B0, MR data were acquired with a spatial resolution of 1, 2, and 3 mm isotropic (FOV = 240 × 240 × 60 mm3; FA = 25°; and TE/TR = 2.3/15 msec).
In one patient with aortic dissection, SUMO was used to highlight the position of the GORE TAG® endovascular stent graft. Gadolinium based blood-pool agent (Vasovist™, Bayer Schering Pharma AG, Berlin, Germany) was used for intravascular enhancement. A 3D gradient echo sequence with inversion recovery and the following parameters were used: acquisition resolution = 1.5 × 1.5 × 3.0 mm3; FOV = 251 × 400 × 156 mm3; FA = 20°; and TE/TR = 2.7/5.6 msec. The positive contrast image produced by SUMO was fused with the 3D gradient echo data using OsiriX Imaging Software (16). Positive contrast was produced using the original dataset, and, therefore, no image registration step was required.
Prostate Seed Imaging
MR images were obtained on a 1.5-T system (Achieva, Philips Healthcare) using a quadrature receive head-coil and a 3D gradient echo acquisition with resolution = 1.4 × 1.4 × 1.6 mm3; FOV = 355 × 250 × 112 mm3; FA = 8°; number of averages = 2; and TE/TR = 4.6/7.5. The prostate seeds (EchoSeed™, Oncura, Chalfont St. Giles, UK) had a titanium (χTi = 182 × 10−6) (17) capsule (4.5 mm in length and 0.8 mm in diameter), and contained a silver rod impregnated with iodine-125. Nonradioactive seeds were obtained for phantom experiments. To explore selective visualization in comparison with the surrounding material, Perspex rods (χPerspex = −5.95 × 10−6) (18) with the same dimensions as the prostate seeds were used as examples of small areas with low proton density while ensuring a similar susceptibility as water. The effect of grouping and quantification was investigated on clusters of one to five prostate seeds.
MR datasets were acquired in the combined X-ray radiography and MRI facility, which comprises of a 1.5-T MR system (Achieva, Philips Heathcare) and a fluoroscopy unit (BV Pulsera, Philips Healthcare) with a common table (Angio Diagnost 5 Sycratilit). Five patients with permanent interstitial implanted brachytherapy seeds were imaged using a four-element body array coil and the same scan parameters as the phantom study. Calibration and tracking of the moving table using an optical tracking system allowed registration of MR and X-ray images (5).
For suppression of low echo-shift values, a threshold of five times the standard deviation in |ks|, i.e., 5σks was used. To obtain a background value, the standard deviation σks was measured within a homogenous region and away from any source of susceptibility. The threshold of 5σks was used for selective visualization and produced distinct volumes of nonzero values relating to a cluster of seeds. For quantification, the k-space shift over this region was integrated, and compared with the number of seeds in each cluster.
The simulation in Fig. 2 illustrates the loss of resolution due to the averaging effect in SGM. The magnitude image (Fig. 2a) shows a negative contrast in the numerical phantoms at areas with simulated susceptibility gradients. The positive contrast image from application of SUMO to the simulated data accurately depicts all of the areas that correspond to a simulated susceptibility gradient (Fig. 2b). However, the positive image formed by SGM fails to resolve all the shifted regions. In particular, for those areas with small dimensions, calculation of |ks| by SGM resulted in little hyperintensities because of PVs, i.e., the values were diminished by neighboring pixels of negligible shift included in the window (Fig. 2c). Such PV effects can be distinguished using SUMO: the signal intensity is extracted from a single pixel based on the value in k-space to which the filter's centre was applied, sk. A plot of the resultant intensity profile shows a defined asymmetric minimum that is used to calculate ks (Fig. 2d). However, for a pixel that shows two minima located around ks = 0 (Fig. 2e), the symmetry in their position relates to almost equal and opposite values for ks, and, therefore, any positive contrast may be attributed in part to PV effects.
Figure 3 shows the results of stent phantom experiments. Positive visualization of the stent-graft using SUMO was achieved at different acquisition resolutions of 1, 2, and 3 mm isotropic (Fig. 3a,d,g). For comparison, positive images were also formed from SGM applied to the same data (Fig. 3b,e,h). Profiles of the maximum |ks| values from SUMO and SGM within a region-of-interest around the centre of the left stent edge were calculated along the length of the stent. Peaks representing the nitinol frame were resolved by both methods at 1 mm isotropic resolution (Fig. 3c). The effect from use of neighboring pixels was again observed for the 2 mm isotropic acquisition but, relative to the |ks| values in between, the peaks from SGM (dashed line) are smaller than those from SUMO (Fig. 3f). At 3 mm isotropic resolution, the profile from SUMO is still able to depict separate peaks from the positive contrast because of the stent's framework (Fig. 3i).
Figure 3j–n illustrates the positive contrast generated for different stent orientations with respect to B0, which is important for in vivo stent graft visualization in a curved vessel. Application of SUMO to MR datasets acquired with the stent graft orientated at 30° intervals to B0 going from parallel to perpendicular showed a consistent positive contrast relating to the stent (Fig. 3k–n). The hyperintensity in the SUMO image correlates with the signal distortions in the negative contrast image for all orientations along B0. In all planes, the entire cross section of the stent is visible and its length and diameter can be measured using the positive contrast. The diameter at the narrowest point in all the positive contrast images measures 38 ± 1 mm, which represents a deviation of only 3% from the true stent diameter.
SUMO was also used to visualize a stent graft in vivo from MR data acquired post stent graft implantation for a case of aortic dissection using a resolution of 1.5 × 1.5 × 3.0 mm3. Figure 4 shows the positive contrast from SUMO being used to display the stent in red. Parameter maps for all directions were calculated by SUMO in less than 3 min per slice on a computer with 2.4 GHz CPU. The anatomical information from the gradient echo images was used to create a mask for the automatically calculated k-space shift maps. For this, the area of interest was roughly segmented by manually selecting regions around the aorta in each slice of the negative contrast images. Figure 4a shows a maximum intensity projection of the segmented positive contrast in 3D. Fusion of the positive contrast with the original MR data was used to indicate the stent graft's placement. Proximal apposition of the stent graft to the wall can be seen with good resolution in the positive contrast images (Fig. 4b).
Figure 5 illustrates visualization of the prostate seeds in the phantom and in vivo. The seeds were visualized with positive contrast because of the susceptibility difference between the titanium outer casing and its surroundings. In contrast to this, no positive contrast was generated in the vicinity of Perspex seeds (circles in Fig. 5a,b) because of negligible susceptibility gradient. For quantification, the integrated |ks| values over each distinct volume from the positive image were compared with the number of seeds and a linear relationship was found (Fig. 5c).
The result from one clinical dataset is shown in Fig. 5d–g. The soft tissue contrast in the gradient echo image was used to define the prostate volume and ensure encapsulation of the seeds (Fig. 5d). The positive contrast image was based on mapping |ks| with a threshold to exclude values relating to negligible susceptibility gradients, i.e., |ks| < 5σks (Fig. 5e). Significant positive contrast is also visible at the border of the rectum because of the air-to-tissue interface. Fusion of the image from SUMO in red with the gradient echo image shows a colocalization of positive contrast with dephased voxels. However, all hypointensities were not matched with a visible susceptibility gradient by SUMO. In particular, a region of low intensity within the prostate (arrow in Fig. 5f) that might have been mistaken for a group of seeds displayed no positive contrast. The presence of prostate seeds detected by SUMO was validated by registration of X-ray and MR data as described in Ref.5.
Furthermore, regions of interest were defined, and the value of |ks| was integrated in these. Information from the registered X-ray data was used to determine a true count of the number of seeds within each cluster. A plot of the integral of |ks| over each cluster against the number of seeds within each cluster showed a linear relationship with R2 = 0.94 on linear regression (Fig. 5g).
A technique for mapping susceptibility gradients in MR data, based on measurement of the echo-shift in k-space, has been presented and is referred to as SUMO. The theory of this technique is similar to SGM, which is also based on estimating the k-space shift, ks. However in SGM, the resolution of the resulting susceptibility map (k-space shift map) is reduced by the use of a STFT. In contrast to this, SUMO can calculate a susceptibility map at the original resolution of the image. This was shown in simulations and phantom experiments. However, in combination with this effect, the noise in background areas relating to negligible susceptibility gradient are greater in SUMO than for SGM, due to the averaging in SGM over the window used for STFT (Figs. 2b,c, and 3c,f,i). PV effects are distinguished by analyzing the symmetry of the signal response after application of the filter (Fig. 2d,e).
The SUMO technique has been successfully applied as a postprocessing technique for selective visualization of both a stent graft and brachytherapy prostate seeds. The GORE TAG® stent graft used in this study was previously shown by Eggebrecht et al. (11) to be suitable for MRI. Visualization of the edge of the stent was also used to compare SUMO with SGM. Plots of maximal |ks| values show that the nitinol framework could be visualized with positive contrast for acquisitions up to 3 mm isotropic, whereas the peaks from SGM at this resolution are negligible. The effect of averaging from SGM is also evident in the background |ks| values from between peaks, which is lower than for SUMO.
Application of SUMO to MR datasets acquired with the stent graft in different orientations to B0 showed a consistent positive contrast relating to the stent (Fig. 3k–n). The nitinol wire frame is depicted more clearly, when parallel to B0, and the extent of hyperintensity increased for larger angles up to the perpendicular orientation due to a greater perturbation of the field as the angle made by the main axis of the stent with B0 increased (19). Measurements of the hyperintensities allude to the actual dimensions of the stent graft. As other nitinol based stent grafts studied in vitro have been well visualized without complete loss of the surrounding signal (11, 20), these results suggest SUMO might be applied for positive contrast images of other stents in vivo. The positive contrast produced by SUMO is such that it can be fused with the original 3D gradient echo images without registration (Fig. 4b–d).
The SUMO postprocessing technique has also been applied for detection and quantification of prostate brachytherapy seeds. Phantom experiments showed strong correlation of hyperintensity at the location of the seeds. Integration of |ks| over a volume formed by threshold of the positive contrast showed a linear relationship with the number of seeds. Although nonzero values were found in volumes containing zero prostate seeds, they were relatively small and may have been contributed to further by imperfections in the phantom (i.e., tiny air bubbles).
Similar procedures were used in analysis of the data in vivo acquired from a prostate cancer patient who underwent brachytherapy. As with visualization of the stent in vivo, anatomical information from the original negative contrast was fused with the positive contrast image without registration. Furthermore, a linear relationship was observed from linear regression of the plot of integrated |ks| values with the number of seeds. Thus with further development, analysis of the echo-shift in k-space compared with the number of prostate seeds may aid dosimetry solely by MRI.
The applications of SUMO described above involved gradient echo Cartesian acquisitions, but the technique can be extended to other gradient echo based acquisition schemes (e.g., radial or spiral), provided a complete set of complex k-space data exist. As the susceptibility gradient mapping technique is based on the influence of local field gradients on the obtained signal phase, this technique cannot be applied to images obtained by spin-echo based techniques, which refocus the local field inhomogeneities. Furthermore, the technique should not be applied to SSFP imaging data, as its signal consists of a superposition of the primary echo and of several RF pulse-refocused states. Similar to SGM, SUMO is relatively time-consuming in terms of computational complexity, which increases with matrix size, because of substantial use of Fourier transforms. As in other positive contrast techniques, SUMO cannot differentiate positive contrast generated by the devices from other unrelated sources of susceptibility (e.g., air-to-tissue interfaces). This ambiguity may be reduced by taking the direction, size, and shape of the susceptibility gradient generated from the devices into account (7).
A susceptibility gradient mapping technique, called SUMO has been developed using a k-space filter for calculation of the echo-shift. The SUMO technique showed an ability to resolve smaller local susceptibility gradients in simulations and those acquired with a lower resolution in experiments, whereas the parameter map from SGM failed to depict them all. SUMO has been applied to MRI data from a nitinol stent graft in vivo and allowed positive visualization of the device. The positive contrast based on a quantifiable echo-shift achieved with SUMO may be used for broader application including visualization of other implants; interventional devices (catheters), and tracking of labelled cells.