continuous radial data acquisition for dynamic mri

Continuous Radial Data Acquisition for Dynamic MRI Volker Rasche, Ruud W. de Boer, Dietrich Holz, Roland Proksa

Since image acquisition times in MRI have been reduced con- siderably over recent years, several new important application areas of MRI have appeared. In addition to pure static anatomic information, the evolution of a dynamic process may be visualized by a sequence of temporal snapshots of the process acquired within a short time period. This makes applications like interactive or interventional MRI as well as the acquisition of additional functional information feasible. For high temporal resolution, all these applications require a quasi real-time image acquisition during the time the interaction or dynamic process evolves. We present an approach to real- time imaging using a continuous radial acquisition scheme. The intrinsic advantages of radial or projection reconstruction (PR) techniques are used to minimize motion-related image distortions. Modifications of the acquisition scheme as well as dedicated reconstruction techniques are used to further reduce the temporal blurring due to the finite acquisition time of one entire data set in our approach. So far we have used this technique for the visualization of active joint motion. Key words: projection reconstruction; real-time imaging; fluoroscopy; fast radial imaging.

INTRODUCTION

Magnetic resonance imaging (MRI) has become a major tool for diagnostic imaging since its introduction in the early 1980s. So far, it has mainly been used to provide morphological information of static objects. However, functional information with a high temporal and spatial resolution is additionally needed in certain applications.

By using additional functional information, e.g., in orthopedics, the specificity of examinations concerning idiopathic pain syndromes of, e.g., patellofemoral joint, wrist, shoulder, and C-spine (neck) can be increased. Imaging “moving joints” will have an impact on diagno- sis and can be helpful in planning and evaluation of arthroscopic surgery. In the evaluation of patients with joint pain, the majority of patients visit the orthopedic surgeon with arthralgia (joint pain) related to specific movements or activities during forceful loading of the joint. Consequently, it is often imperative to not only define anatomic abnormalities (using a set of static images) but also evaluate the complex functional changes that may occur during the range of active motion of the joint (1). The recent development and implementation of

MRM W754-761 (1995) From Philips GmbH Forschungslaboratorien, D-22335 Hamburg, Germany (V.R., D.H., R.P.); and Philips Medical Systems, Best, The Netherlands (R.W.d.B.). Address correspondence to: Volker Rasche, Ph.D., Philips GmbH For- schungslaboratorien, Forschungsabteilung Technische Systeme Hamburg. RontgenstraOe 24-26, D-22315 Hamburg. Received November 17, 1994; revised June 16, 1995; accepted June 19, 1995. 0740-31 94/95 $3.00 Copyright 0 1995 by Williams & Wilkins All rights of reproduction in any form reserved.

kinematic MRI (2-4) to these specific disorders provide the clinician with an augmented data base of anatomical and functional information. Based on the present scien- tific literature it is to be expected that this improvement in MR technology will result in refined conceptual inter- pretations of a multitude of musculoskeletal conditions. A very important consideration is the necessity to study normal physiological motion with active muscular con- tractions: functional joint imaging. Recent studies (3, 4) on patellar tracking abnormalities clearly indicated the need for loaded and true dynamic scanning techniques.

Such functional studies require methods that are able to visualize dynamic processes. First approaches to provide fluoroscopic data sets were investigated in the late 1980s (5, 6) using steady-state gradient echo sequences (TFE) (7). Although an acceptable image quality and temporal resolution could be achieved, these approaches suffered from the discontinuities when the scan passed the origin in k-space (8, 9). Recently, a modified approach using a statistical order of phase encoding has been presented (10). Other approaches that cover only the low spatial frequency parts of k-space (11,12) or use different trajectories in k-space (13) have been introduced, but in many cases spatial or temporal resolution is still insufficient. Even ultra-fast imaging methods like EPI (14), GRASE (15), or spiral (16) can usually not provide an entire data set from one excitation. Therefore, a segmentation of the k-space is necessary, and image quality often suffers from phase errors due to the motion of the object (17).

Projection reconstruction (PR)-based techniques have favorable intrinsic properties with respect to the de- mands of dynamic MRI. First, motion-induced artifacts have a different appearance and result predominantly in radial streaks with only low intensity near the source of motion (18) and a slight image blurring (19). Second, no displacement artifacts are present (20). Third, the coverage of the k-space center in each radial line avoids contrast discontinuities (21) and preserves the continuity of the process. Fourth, by applying a magnitude reconstruction a reduced sensitivity to statistical phase errors may be achieved (22), although the amplitude of motion-induced artifacts increases (18). Beside the intrinsic advantages of PR, a major drawback has to be mentioned. Because of the symmetry of the acquisition, all off-resonances cause a degradation of the point-spread-function (PSF) (23). To avoid severe blurring in the final image, the pixel bandwidth has to be chosen appropriate to the off-resonances present.

In this paper, we demonstrate the feasibility of applying PR to dynamic MRI. Different acquisition schemes as well as different reconstruction techniques are compared and a coarse estimation of the possible temporal resolution is given.

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Continuous Radial Data Acquisition for Dynamic MRI 755

METHOD

To follow the dynamic process, the data are continuously acquired during their evolution. Due to the finite acquisition time, the signal S(k) does not only depend on its position in k-space but also on the point in time t it is acquired. Assuming that the temporal evolution of the object may be neglected during the acquisition of a single radial line, the two-dimensional version of this technique can be depicted in a two-dimensional graph. Fig- ure 1 shows the principle of this approach. Each point of the straight line marks the acquisition of one radial line with orientation e at time t .

To provide short image acquisition times, a radial steady state gradient echo sequence (21, 24), as shown in Fig. 2, is used. Compared with the standard radial gradient echo sequence, an additional gradient pair (Gx3, Gy3) is applied. Their amplitude is modulated according to the readout direction to provide constant phase accumulation between subsequent excitation pulses. The sequence still uses a symmetric echo to encode a certain radial line. To further decrease the repetition time and hence the image acquisition time of this sequence, an asymmetric echo can be acquired by reducing the prephasing gradients (Gxl , GJ.

The final image quality and temporal resolution of this approach may be increased by some modifications de- scribed in the sections below.

Modified Acquisition Scheme

Let N be the number of radial lines used for a complete data set, Oacq be the covered angular segment and 68 = O,,,/N be the angular increment between neighboring projections required to provide full angular resolution. In a standard radial acquisition, the different orientations are covered subsequently in angular direction with an angular increment 60 as depicted in Fig. 3a. With n being the number of the corresponding excitations and 0 5 n < N , the relation between the orientation 0 of the radial line acquired and n is given by, e.g.:

FIG. 1. The orientation 8 of a certain radial line in k-space versus t h e acquisition time t in radial continuous MRI. Each point on the straight line represents the acquisition of a certain radial line in k-space with orientation 8. The acquisition of a complete data set covers an angular range of 27~ with an angular resolution of 66 and is performed periodically with the acquisition time Tats.

t

FIG. 2. Radial steady-state sequence: in addition to the dephasing gradients (G,,, Gy,) and readout gradients (Gx2, G,J, rephasing gradients (Gx3, Gy3) are applied that are modulated according to the orientation of the corresponding projection to provide constant phase accumulation between subsequent LY pulses.

An MR image can be seen as a superposition of several point-like objects O(?) = 6(? - ?o)I(?) with I(?) being the intensity of the object at location i. and 6 the delta function. Assuming a dynamic behavior of the object, O(?) may additionally show a temporal dependence and hence becomes O(?, t). A change of the object results in a change of the intensity of a certain point in time to. For simplification, only one change during the acquisition of one complete data set is considered. Hence, O(?, t ) is given by:

O(?, t) = 6(? - Fo,)H(t - tJAI(?), [21

with H being the unit step function and A@) the change in intensity at location ?. Let the acquisition window T,,. be as:

[to - n,TR, to + ( N - n,)TR], [31

with TR being the repetition time. Choosing Tacq as in Eq. [3] guarantees that, depending on n,, only a limited number of radial lines, and hence only a certain angular segment, holds information about the object. Figure 4a depicts O(f , t ) reconstructed from a data set in which only 6.25% of the projections hold information of the object. To visualize the resulting artifacts, intensities ex- ceeding 50% are set to maximum. Figure 4a clearly shows that the loss of information about the object over a wide angular range causes a strong degradation of the object imaged.

To provide information over all spatial orientations more frequently, the acquisition of the complete data set { S ( l ) ) can be split up into subsequent acquisitions of Nd angular undersampled data sets IS(@], as shown in Fig. 3b. Now, the dependence of 0 on n is given by:

e = (%mod N ) se + In'(&) 68, [41

756 Rasche et al.

0

0 I I

a

b

-10 x u x I:, -15

a

0

k, 0 I I

b

FIG. 3. Trajectory through k-space using a standard acquisition order (a) (i indicates the ith acquisition), and using the segmented approach (b) (i, indicates theith acquisition in thejth undersampled data set). Whereas in the standard technique the orientations of temporal succeeding projections are increased by 68, in the segmented approach the orientations of temporal succeeding projections differ by NdS8 (bold) providing a faster coverage of all spatial orientations with reduced angular resolution of NdS8. During the acquisition of the ith undersampled data set (dotted) an offset of iS8 is added to each orientation yielding a data set with full angular resolution after the acquisition of Nd angular undersampled data sets.

where mod denotes the modulus operator and Into gives the integer part of its argument. {S(k) ] is given by the union of all undersampled data sets (S(k))i as:

FIG. 4. Changes of the object during the acquisition of an entire data set are only covered over a certain angular segment. The loss of information over a wide angular range causes strong degradation of t h e point spread function (PSF) (a). Using a segmented acquisition (N,, = 16), the artifacts can be reduced to the well known streaking artifacts due to angular undersampling (b).

The final image of more complicated objects may be considered as a superposition of the images of several objects like O(F, t ) . Hence, streaking artifacts from many sources may add in the final image and the improvement in image quality may not be as obvious as in the example above.

Reconstruction

Due to the dynamic behavior of the object, no entire data set is available for any point to in time. We have investigated three different approaches to approximate a complete data set for to. Interpolative Reconstruction. Due to the periodic nature of the continuous scan an interpolation may be used to provide the data of a certain radial line with orientation 8 at time to. Whereas Meyer et al. (11) used a temporal filtering to provide the corresponding data set, we applied an interpolation between temporal succeeding projections. Hence, missing elements of the final data set may be estimated according to:

PdtLl) = CfiPdti) i = 0, . . * 9 N,,,,I, [61 I

with fi being arbitrary weighting factors with Zi f i = 1,

jection with orientation 8 at time to. We used a linear interpolation between the temporal preceding and succeeding radial line with same orientation. Hence, the resulting projection is given by:

I Ntota, the number of scans performed and p8(to) the pro- {~(k)} = U {S(Z)}i. [51

Figure 4b shows O(F, t) again reconstructed from only 6.25% of the required data but using Nd = 16. Now, according to the degree of subsampling, streaking arti-

[71 facts in some distance from the position of O(F, t ) arise (25), but significantly less degradation of O(F, t ) occurs.

- t o to - tl t z - tl P"(t") = -pe(tJ + -P&J

t z - tl

Continuous Radial Data Acquisition for Dynamic MRI 75 7

with t, = max(tilti <= to] and t, = min(tilti >= to] . The principle of this technique is depicted in Fig. 5, where the shaded area marks the amount of data that influences the final image. Moving Center. The disadvantage of the interpolative approach is that the final image is composed of data acquired over a time period of AT,,, = ZT,,,. To reduce AT,,, to Tacq, only the data of one complete acquisition were used. As introduced first by Riederer et al. (5), no modifications of the measured data were done before the reconstruction. The center of the data set was defined by the correlation of to with the corresponding acquisition time of the central orientation in the final data set. In Fig. 6 the principle of this approach is shown. Now, data of only AT,,, = Tacs influence the final image (see shaded area in Fig. 6 ) , but no further weighting of the data according to their temporal distance to to is done. Weighted Moving Center. In the Moving Center technique, two principle problems arise. First, all data are equally weighted in the final image. Second, a disconti- nuity arises between the radial line with orientation oo and with orientation 360° which is acquired Tacq later. Two properties of the radial acquisition may be used to further improve the reconstruction.

1. The energy E(p,) of a projection does not depend on its orientation 8:

FOV

E(PJ = pe(s) ds = const. [81 1; This implies that any projection contributes equally to the final image. 2. Let p e be the projection with polar orientation 8.

The comparison of p e and p e * shows that they only differ in the readout direction of the line inte- grals. In the case of a static object, both projections hold the same information. Further comparisons of p e with p e i,, so show that the information of these projections do not differ significantly because of the continuous nature of the imaged object.

FIG. 5. Using a linear interpolation to provide a complete data set for a certain point in time to implies a temporal blurring over a time interval of AT,,, = 2Ta,, (shaded area).

FIG. 6. The time interval ATrw can be decreased by the use of the Moving Center technique. Data of only one Tacq (shaded area) contribute to the final image but the data are not weighted according to their temporal distance to t,.

To modify the influence of a certain projection with orientation el, its value may be multiplied with a factor c,. To avoid image artifacts the corresponding projection with orientation 8, = 8, + 7~ has to be multiplied with a factor c, = 1 - c, to keep the contribution of all orientations constant. More general, the multiplication of the projections with a weighting function w(t(e)) with

w(t(e)) + w(t(e + T) ) = const. V e E [-T, TI [91

should have no influence on the final image. This is only valid in the static case. Nevertheless, assuming moderate changes during the acquisition, the properties of PR may be used to further improve the image quality.

Considering the continuous data acquisition, an appropriate weighting function can be applied to (1) avoid the noncontinuous passage from orientation e = Oo to e = 360° and (2) to weight the data according to their temporal distance to to. A reasonable function complying with the above requirements is given by

W(t(@))

Tacq At < t(0) < ~ - At 2

I' ' At

-- :-;+At

1 acq

2 ~ + At < t(0) < Tacs - At

Tacq - At 5 t(0) 5 Tacq

with At being the temporal length of the ramp as shown in Fig. 7.

758 Rasche et al.

FIG. 7. The additional weighting in the Weighted Moving Center reconstruction provides a short AT,,, (shaded area) in combination with a weighting of the data according to their temporal distance to to. To provide equal contribution of all spatial orientations W(t(0)) + W(t(0 + T)) must be constant.

A similar weighting function can be applied in the case of a segmented data acquisition, because, as in the non- segmented case, the orientations of a projection acquired at t , and the projection acquired at t, = t, + T,,,/2 differ approximately about At)= ?iIr and hence fulfill the requirements for the correction scheme.

RESULTS AND APPLICATIONS

So far, we have applied the continuous radial data acquisition to functional joint imaging. All images were acquired on a Philips Gyroscan T5 whole-body scanner with modified backend, equipped with a fast reconstruction unit for filtered backprojection. The acquisition pa- rameters were: echo time TE = 3.15 ms, repetition time TR = 8.5 ms, pixel bandwidth = 360 Hz, the voxel size was chosen as 1.2 x 1.2 X 7 mm” using a field of view as FOV = 300 mm and the acquisition time for an entire data set was Tacq = 1.35 s using 160 projections. All images were acquired with slight undersampling in angular direction to reduce T,,..

The comparison of the different acquisition and reconstruction schemes was done using a data set acquired during active flexion of the knee. To compare the different acquisition techniques. the motion of the knee was controlled externally to approximately guarantee a constant motion and position in both movies. In Fig. 8 the resulting image qualities using Nd = 1 (Figs. 8a and 8c) and N,, = 4 (Figs. 8b and 8d) undersampled data sets are

FIG. 8. The comparison of a non- segmented (a) with a fourfold-segmented acquisition (c) shows an improved temporal definition of the snapshot, but extreme level and window setting shows a simulta- neous increase of streaking artifacts (b, d).


compared. Both images were reconstructed without additional interpolation or weighting. As predicted the improvement in image quality is not as obvious as in the image of the point-like object. Nevertheless, in the marked region of Figs. 8a and 812, a slight increase of image sharpness results by the use of four undersampled data sets. On the other hand, due to the increasing incon- sistencies between neighboring projections, the intensity of the arising streaking artifacts increases as shown on Figs. 8b and 8d. The experiments show that a good compromise between image sharpness and arising streaking artifacts can be found using up to Nd = 8 angular undersampled data sets. We got the best results using Nd = 4.

A more effective way to improve the temporal definition of the reconstructed slice can be obtained by the use of the different reconstruction schemes. Figure 9 summa- rizes the final image quality of the different approaches. In the interpolative reconstruction (Fig. ga), a kind of temporal blurring can be clearly observed (see marks) and due to the interpolation, the final image looks rather smooth. The use of the Moving Center technique (Fig. gb) reduces the temporal blurring, but a slight unsharpness can still be observed in the marked region. A significant reduction of the temporal blurring can be achieved by the application of an additional weighting (Fig. gc).

a b

C

FIG. 9. The comparison of the different reconstruction techniques shows that t h e use of the Weighted Moving Center approach (c) improves the image sharpness compared with the lnterpolative (a) and Moving Center (b) techniques.

Taking the above results into consideration, a coarse estimation of the temporal resolution can be given by:

In Eq. I l l ] , we assume that a change of the object must at least be covered over an angular segment OaCq of 180'. Therefore, the factor I is proportional to Oacq. In fact it should be one in the case of Oacq = 180' and two if Oacq = 360'. The factor E depends on the ramp width w,. = AtIT,,, used in the weighted reconstruction. The influence of the acquisition time Tacq and the number of subsampled data sets Nd is obvious. To provide a more homogeneous motion in movie mode, it is reasonable to reconstruct temporal snapshots at an even shorter temporal interval as predicted by At,,,.

Figure 10 shows several temporal snapshots of a dynamic study of active flexion of the knee. Figures 1Oa- lod show a transversal slice through the knee joint. Dur- ing the knee motion, eight complete data sets were acquired within 10.8 s . The sagittal slices (Figs. 10e-10h) were reconstructed using five entire data sets, acquired within 6.8 s . All images were obtained using a fourfold segmentation. During the reconstruction a ramp width w,. of 10% was used.

Because the knee was not fixed during the active flexion, rotation and translation OCCUT in-plane as well as through-plane. Nevertheless, the resulting image series show no severe artifacts due to this multidimensional and complete free motion. The only effect of motion is a slight image unsharpness that occurs in certain regions. However, the motion of the joint can be clearly followed (both patellar and cruciate ligaments are well visualized in the image). Due to the frequently acquired information of the k-space center, no severe intensity modulation can be observed in the final reconstructed data set.

CONCLUSION

In conclusion, the combination of fast radial acquisition schemes with continuous imaging provides the opportu- nity to follow dynamic processes with reasonable temporal and spatial resolution with only low artifact level. The artifacts caused by the dynamic behavior of the object are limited to streaking artifacts the intensity of which was in our experiments in the order of noise as can be seen in Figs. 8b and 8d. Of course, the amplitude of the streaking artifacts depends on several items such as, e.g., the type and speed of the motion and the SNR of the images. Nevertheless, having an appropriate relation between the speed of the motion and the acquisition time, the predominant effect may be limited to a slight temporal blurring. The intrinsic passing of the k-space center during the acquisition of each radial line in PR avoids severe intensity modulations in the final movies. The use of segmented acquisitions as well as the application of dedicated reconstruction techniques further reduce the temporal blurring. Thereby, a compromise between improved temporal definition and rising streaking artifacts can be found using a two- or fourfold segmentation in

760 Rasche et al.

FIG. 10. Temporal snapshots of the moving knee joint during active flexion. Although in-plane motion as well as through-plane motion occurs, the final image quality in the transversal study (a-d) and the sagittal study (e-h) is hardly dis- turbed. The motion of the joint can be clearly visualized within acquisition times of only some seconds for a complete dynamic study. All images were acquired using a fourfold segmentation and reconstructed by the use of the Weighted Moving Center technique.


combination with the Weighted Moving Center reconstruction technique.

The temporal resolution of this approach is still limited by the rather long acquisition time of one complete data set. Therefore, future investigations will focus on a further reduction of the acquisition time. Two techniques will be predominantly investigated. First, by the use of extremely asymmetric echoes, the repetition time can be reduced to less than 5 ms resulting in about half of the acquisition time used today. Second, the acquisition of several radial lines after one excitation yields a radial kind of EPI (rEPI) sequence. Due to the sensitivity of radial acquisition schemes to off-resonances, only few gradient echoes can be used. Nevertheless, the combination of rEPI and steady-state techniques can further decrease the overall acquisition time. Furthermore, the comparison of radial and spiral continuous data acquisition for dynamic MRI is an important topic for future investigations.

It is to be expected that functional evaluation of joints compared with the standard morphological images provides additional information of a painful joint for the orthopedic surgeon. To study these problems it is necessary to evaluate the joint during its normal physiological range of motion with all the muscles that are involved in the movement active. From an MR point of view, image sequences that are fast enough to follow the motion of interest without too much blur are needed. Kinematic studies are no replacement of the high-resolution standard morphological imaging techniques that are now cur- rently used, but should be considered as a new genera- tion of imaging techniques to study other aspects of a mal-functioning joint.

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continuous radial data acquisition for dynamic mri

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