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Keywords:

  • arterial spin labeling;
  • cerebral perfusion;
  • vascular territory;
  • magnetic resonance imaging;
  • stroke;
  • cerebrovascular disease

Abstract

  1. Top of page
  2. Abstract
  3. THEORY
  4. MATERIALS AND METHODS
  5. DATA PROCESSING
  6. RESULTS
  7. DISCUSSION
  8. Acknowledgements
  9. REFERENCES

A new signal-to-noise ratio (SNR) efficient method is introduced for the mapping of vascular territories based on pseudocontinuous arterial spin labeling (ASL). A pseudocontinuous tagging pulse train is modified using additional transverse gradient pulses and phase cycling to place some arteries in a tag condition, while others passing through the same tagging plane are in a control condition. This is combined with a Hadamard or similar encoding scheme such that all vessels of interest are fully inverted or relaxed for nearly all of the encoding cycles, providing optimal SNR. The relative tagging efficiency for each vessel is measured directly from the ASL data and is used in the decoding process to improve the separation of vascular territories. High SNR maps of left carotid, right carotid, and basilar territories are generated in 6 min of scan time. Magn Reson Med, 2007. © 2007 Wiley-Liss, Inc.

In vascular territory imaging (VTI) (1–4), blood in individual or groups of feeding arteries are tagged using arterial spin labeling (ASL) methodology, and images are acquired that map the vascular distribution of those feeding arteries. Potential clinical applications for the mapping of vascular territories include the evaluation of vascular stenoses and the mapping of blood supplies to tumors. VTI is typically performed sequentially for two or more vascular territories to develop a complete map of the blood supply to the target tissue.

Recently, more time-efficient methods for mapping multiple vascular territories have been introduced, in which combinations of vessels are tagged in encoding schemes that allow for efficient generation of vascular territory maps (5–7). We demonstrate here an implementation of this vessel-encoded approach, based on pseudocontinuous tagging (8), that provides high signal-to-noise ratio (SNR) tagging as well as good vessel selectivity and flexibility in tagging geometry.

THEORY

  1. Top of page
  2. Abstract
  3. THEORY
  4. MATERIALS AND METHODS
  5. DATA PROCESSING
  6. RESULTS
  7. DISCUSSION
  8. Acknowledgements
  9. REFERENCES

Vessel Encoding

In conventional (non-vessel-encoded) ASL, the scan typically consists of two image types, both of which contain identical static tissue signal, but which differ in the sign of the inflowing arterial magnetization. This encoding process can be described mathematically by y = Ax, where x is the contribution to the signal from inflowing blood and static tissue components, A is the encoding matrix, and y is the resulting signal intensities. For this measurement:

  • equation image(1)

where V is the MR signal of inflowing blood and S is the MR signal of static tissue. The rows of A are the encoding steps necessary to generate y1 and y2, which are typically referred to as “tag” and “control” images. By inspection it is clear that the ASL signal V can be recovered by subtraction of y2y1. More formally, when A has a pseudoinverse A+, x can be reconstructed by inversion to yield x = A+y. Thus

  • equation image(2)

yielding the same result that V is proportional to y2y1.

To separately encode the contribution of more than one vessel to the MR signal, more than two encoding steps are necessary, in which the vessels of interest are encoded in different patterns. For the three-vessel encoding scheme of Gunther (7):

  • equation image(3)

where R, L, and B are the contributions of tagged blood signal from the right carotid, left carotid, and basilar arteries, respectively. In both of the above examples, the encoding matrix consists of columns from a Hadamard matrix (9), and the resultant encoding is SNR optimal in the sense that all inflowing blood is either fully inverted or fully relaxed for each tagging cycle, and there are equal numbers of tag and control conditions for each vessel. All encoding matrices that consist of columns from a Hadamard matrix will have these properties, even if they are not square, and decoding of this type of data amounts to simple subtraction of tag from control images for each vessel. In general, vessel geometry and tagging methodology may not allow for optimal encoding, but the expected SNR efficiency can be calculated from the decoding matrix A+. For unit signal and unit noise, the decoding process outlined above will produce unit signal, because it is a direct inversion of the encoding process, while the noise for each territory will be given by the square root of the sum of squared elements across a row of A+. For comparison, the SNR for simple averaging across N samples with unit signal and noise per sample is equation image. Taking a ratio of these SNR values as an index E of SNR efficiency, we have:

  • equation image(4)

where N is the number of samples (and therefore the number of columns in A+). For any Hadamard encoding scheme, E = 1.

Tagging Method

The required modulation of tag and control states can be accomplished using either pulsed or continuous ASL methodology, but we focus here on a modification of the pseudocontinuous ASL (PCASL) tagging method (8) that allows for efficient modulation of tag and control states across vessels within a single tagging plane. In PCASL, a train of closely spaced RF pulses, in conjunction with a synchronously pulsed gradient field, effects a flow driven adiabatic inversion as blood flows through the tagging plane. Requirements for both the mean gradient and the mean RF amplitude to satisfy adiabatic conditions are similar to those of continuous ASL, and the mechanism of tagging is identical. The major theoretical advantage of PCASL is that because the RF is applied in the presence of a larger gradient than in continuous ASL, the RF irradiation is farther off resonance in the target tissue, and magnetization transfer effects are greatly reduced (8). A fortuitous feature of PCASL for the present work is that there are time gaps in between the RF pulses during which additional transverse gradient pulses can be applied to modulate the relative phase of spins in different vessels within the tagging plane.

Three modifications of the original PCASL method are used here to allow for differential encoding of vessels within the inversion plane: 1) the use of a single labeling gradient waveform in the direction of flow with nonzero mean for both tag and control conditions; 2) the application of additional gradients perpendicular to the labeling gradient to generate phase shifts between the vessels of interest; and 3) the use of RF phase modulation across pulses to place the vessels of interest in tag and control conditions according to the encoding schedule.

The tagging geometry and pulse train are shown in Fig. 1 for four cycles: 1) all vessels inverted; 2) no vessels inverted; 3) only vessel A inverted; and 4) only vessel B inverted. In the original implementation of PCASL, the labeling gradient (Gz) has nonzero mean for the tag condition, and zero mean for the control condition (8). While it is sensible to use a gradient with zero mean for the control condition, this is not necessary in order to obtain a transparent control pulse (see RF pulse simulations below). For all four cycles the same tagging gradient in the direction of flow is used. For cycles 3 and 4, an additional gradient pulse (Gxy) is applied between RF pulses in the direction of the vector from one vessel to the other within the tagging plane. This pulse is applied with alternating sign and an area of π/γb, where b is the separation between vessels, producing a phase shift of π between the two vessels. If the phases of the RF pulses are adjusted so that all pulses are coherent with spins at the location of one vessel, then spins in that vessel experience adiabatic inversion, while spins in the other vessel experience pulses with alternating sign, resulting in a transparent pulse. The phase modulation across the RF pulse train for the four cycles is summarized as:

  • equation image(5)

where i is the pulse number, Ḡz is the mean value of Gz, t is the RF pulse spacing, z is the offset of the labeling plane from isocenter, “mod” is the integer modulus function, and a and b are the vessel location and separation as shown in Fig. 1. ϕz is the phase needed to keep the pulses coherent with spins under the influence of Gz, while ϕxyA and ϕxyB are the additional phases needed to keep the pulses in phase with spins in vessels A and B, respectively, in the presence of Gxy. This encoding method generates alternating lines of tag and control conditions within the tagging plane.

thumbnail image

Figure 1. Top: Diagram of tagging geometry for two vessels, separated by distance b. Within the tagging plane, Gxy is applied along the line from one vessel to the other, and vessel A is a distance a from the projection of the isocenter onto this line. Middle and bottom: RF and gradient waveforms for a small segment of the tagging pulse-train.

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MATERIALS AND METHODS

  1. Top of page
  2. Abstract
  3. THEORY
  4. MATERIALS AND METHODS
  5. DATA PROCESSING
  6. RESULTS
  7. DISCUSSION
  8. Acknowledgements
  9. REFERENCES

Tagging Pulse Train Simulations

The effect of the mean gradient phase alternation, flow velocity, and resonance offset were calculated by Bloch equation simulation for the following pulse-train parameters: Hanning-shaped RF pulses of 600 μs duration and 0.04 Gauss (G) amplitude (4 μT); gradient amplitude of 0.6 G/cm during RF pulses, with refocusing lobes applied at a slew rate of 15 G/cm/ms and a maximum magnitude of 4 G/cm. The flip angle at the center of the pulse profile was 20°, and the width over which the flip angle exceeded 2° was 2.0 cm. For the simulations, T2 was assumed to be 200 ms, and T1 relaxation was neglected in order to simplify the calculation of the tagging efficiency.

Imaging Parameters

Imaging was performed on a General Electric (Waukesha, WI, USA) 3T scanner using a commercial eight-channel head RF coil array and the body coil for RF transmission. Four normal volunteers, two male and two female, ages 25–45 years, were scanned with prior informed consent under an Internal Review Board (IRB) approved protocol. The FOV was 24 cm × 8 mm with a 2-mm gap between slices, and a single-shot two-dimensional (2D) spiral readout was used. Tagging parameters were as described in the simulations above, with a total length of 1574 ms for the tagging pulse train, composed of 1640 RF pulses with a spacing of 960 μs. Two nonselective adiabatic inversion pulses were applied 950 ms and 300 ms prior to image acquisition for background suppression. The postlabeling delay was 1000 ms and TR was 3000 ms. A total of 20 images were acquired for each cycle of the encoding scheme, resulting in a scan time of 4 min for two-vessel encoding, and 6 or 8 min for three-vessel encoding. Mean and RMS B1 were 0.014 G and 0.020 G, respectively, during the tagging pulse-train and the average whole body specific absorption rate (SAR) reported by the integrated RF power monitor in the scanner was 1.7–1.8 W/kg. This is roughly consistent with the calculations of Wang et al. (10), which showed a head SAR of 1 W/kg for a labeling B1 of 0.023 G at 50% duty cycle, prior to the addition of imaging or background suppression pulses.

DATA PROCESSING

  1. Top of page
  2. Abstract
  3. THEORY
  4. MATERIALS AND METHODS
  5. DATA PROCESSING
  6. RESULTS
  7. DISCUSSION
  8. Acknowledgements
  9. REFERENCES

Vascular territory maps were generated by pseudoinversion of the encoding matrix as described above. Ideally, each vessel of interest was fully inverted or fully relaxed during each tagging period. In practice, because of vessel geometries and velocity distributions, this is not always possible. In order to correct for this, the tagging efficiencies of the vessel-encoded scans relative to nonselective scans were measured and included in the encoding matrix. From the nonselective scans cycles of the encoding process (all vessels relaxed or all vessels inverted), a conventional ASL image was calculated by simple subtraction. A signal intensity threshold was set at half of the intensity at the 99th percentile in this image, and voxels above this threshold were used as a rough gray matter mask. Within this mask, the ratio of signal intensities for vessel-encoded scans divided by nonselective scans was calculated on a voxel-wise basis and displayed as histograms. Local peaks in these histograms were fitted to Gaussian functions by least squares fitting and provided estimates of the tagging efficiency of each tagged vessel, relative to the tagging efficiency of the non-vessel-encoded scan. These relative tagging efficiencies are referred to as β, and were used directly in the construction of the encoding matrices. No spatial smoothing or masking of signal outside the brain was applied, and images are displayed according to radiological convention (left of image is right of subject).

RESULTS

  1. Top of page
  2. Abstract
  3. THEORY
  4. MATERIALS AND METHODS
  5. DATA PROCESSING
  6. RESULTS
  7. DISCUSSION
  8. Acknowledgements
  9. REFERENCES

Bloch equation simulations of several features of the vessel encoding pulse train of Fig. 1 are shown in Fig. 2. Figure 2a shows the calculated Mz of spins that have flowed through the tagging plane as a function of Ḡz, averaging across velocities from 5–40 cm/s. With a phase alternation of π between RF pulses, the perturbation of flowing spins is minimal for Ḡz from 0–0.1 G/cm, producing an efficient control condition across this range of mean gradients. In the absence of phase modulation (the tag condition), efficient flow driven inversion occurs from approximately 0.04–0.12 G/cm, and the tagging efficiency α = (Mz,controlMz,tag)/2 has a broad peak centered at approximately Ḡz = 0.08 G/cm. This value of Ḡz was used throughout this study. The calculated response of Mz as a function of the RF phase alternation is shown in Fig. 2b for a range of flow velocities. A vessel in the tag condition experiences zero phase alternation, while one in the control condition experiences an alternation of π radians from pulse to pulse. Vessels in other locations experience intermediate levels of phase alternation according to their position along Gxy. From these curves one can calculate the expected tagging efficiency as a function of vessel position and velocity. The sensitivity of this tagging scheme to resonance offset is shown in Fig. 2c, and demonstrates a marked drop in tagging efficiency above 100 Hz off-resonance.

thumbnail image

Figure 2. a: Calculated Mz of blood after flowing through the tagging plane as a function of the mean tagging gradient Ḡz. In the control condition with RF alternation, the pulse train is transparent for Ḡz ≤ 0.1 G/cm. The tagging efficiency α shows a broad peak around Ḡz = 0.08 G/cm. b: Calculated Mz as a function of velocity and phase alternation. In the tag condition, spins experience no phase modulation, and undergo adiabatic inversion. In the control condition, a phase shift of π radians per pulse is applied to make the pulse train transparent. At locations between the two vessels of interest, intermediate values of Mz are obtained. c: Calculated tagging efficiency vs. resonance offset. Above 100 Hz resonance offset, a marked reduction of tagging efficiency is expected.

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Vessel-encoded images from one subject are shown in Fig. 3. Rows A, B, and C show the results of three different two-vessel encoding schemes, with the encoding locations shown in the right panel. Also shown are histograms of the measured tagging efficiencies for each encoding scheme. In row A, the left and right carotid arteries are encoded and separable with high efficiency, but the posterior circulation cannot be clearly separated from the anterior circulation. In this subject, the right vertebral artery is dominant, and the posterior territory appears in the histogram as a peak with β ≈ −0.5 (see green arrows). In row B, the anterior and posterior circulations are separated using anterior/posterior encoding, while in row C, the same separation is accomplished using left/right encoding, but with lower measured β for all vessels. Row D shows a three vessel separation based on the data from rows A and B. With perfect tagging efficiency the encoding and decoding matrices and SNR efficiency for this separation are:

  • equation image(6)

where the columns of A correspond to the right carotid, basilar, left carotid, and static tissue components, respectively, and the rows represent six encoding cycles. Note that the theoretical SNR efficiency is not one because two of the six encoding cycles generate zero signal from the basilar artery. Using the values of β measured from the histograms shown in Fig. 3, these become:

  • equation image(7)
thumbnail image

Figure 3. Left: Perfusion territory maps. In each map the calculated ASL signal from each territory is shown as the intensity of the red, blue, or green (RGB) channel of the RGB color scale. Center: Histograms of measured tagging efficiency in vessel-encoded scans relative to nonencoded ASL scans. Histogram data is shown in blue, and Gaussian fits to the peaks in the histograms are shown in red. The center of the Gaussian fits are used as estimated tagging efficiencies for each vessel, and used to generate the encoding matrix. Right: Tagging geometries used to obtain images in rows A, B, and C. Red and blue lines represent the locations that are placed in contrast. In row A, left and right carotids are contrasted. Note that the right vertebral artery in this subject is prominent, leading to an incorrect grouping of the posterior territory with the right carotid territory (see green arrows). In row B, carotid and vertebral arteries are cleanly contrasted, and in row C, the same contrast is obtained using the left/right separation of these vessels, and taking advantage of the periodic nature of the tag/control bands in the tagging plane. Row D shows a three-vessel separation using the data from rows A and B (see Results). Scan times were 4 min each for rows A–C, and 6 min for row D.

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Across four subjects, the average value of β was 0.94 ± 0.07 in the carotid arteries, and across three subjects it was 0.69 ± 0.14 in the vertebral arteries.

Figure 4 shows examples of three-vessel encoding from two additional subjects. In the top row, the encoding method was identical to that used for Fig. 3, row D, but in this subject, the basilar circulation supplied only the left posterior cerebral territory, which was consistent with MR angiographic findings. In addition, the right anterior cerebral territory appears to be supplied by mixed left and right carotid blood, suggesting active flow in the anterior communicating artery. In the lower row, an eight-cycle Hadamard scheme was used to encode the vessels in the neck, as shown on the right panel. Each of the vessel encodings A, B, and C contrast two vessels with the third. While the theoretical values of E for this encoding are [1, 1, 1, 1], the measured β ranged from 0.54 to 0.91, and the SNR efficiency was E = [0.88, 0.80, 0.89, 1].

thumbnail image

Figure 4. Three-vessel maps from two additional subjects. Top: Three-vessel separation using the same encoding geometry as Fig. 3 (row D). In this subject, the basilar artery does not communicate with the right PCA, and the right ACA has mixed contributions from left and right carotid arteries. Scan time: 6 min. Bottom: Three-vessel encoding using a Hadamard encoding scheme with the tagging geometry shown on the right, which places each vessel in an inverted or relaxed state for every encoding cycle. Scan time: 8 min.

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Figure 5 shows an example of vessel encoding above the Circle of Willis. In this example, three vascular territories, left middle cerebral artery (MCA), anterior cerebral artery (ACA), and right MCA, are mapped using left/right encoding, analogous to scans A and C in Fig. 3. While the ACA and some branches of the MCA along the insula are tagged with high efficiency, there are other branches of the MCAs that are not well tagged, hence the incomplete representation of the anterior portion of the MCA territories. For left MCA, ACA, and right MCA, E = [0.85, 0.82, 0.85].

thumbnail image

Figure 5. Three-vessel separation above the Circle of Willis. The encoding scheme is equivalent to that of rows A and C of Fig. 3. In the tagging plane shown on the right, the ACA is well confined to the midline, and the corresponding territory is represented in the ASL maps as bright green. The territories supplies by the insular branches of the MCAs are well tagged and are bright red and blue, but other smaller branches of the MCAs are not well tagged, leaving the ACA/MCA border unclear. Scan time: 6 min.

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DISCUSSION

  1. Top of page
  2. Abstract
  3. THEORY
  4. MATERIALS AND METHODS
  5. DATA PROCESSING
  6. RESULTS
  7. DISCUSSION
  8. Acknowledgements
  9. REFERENCES

The vessel-encoded ASL method described here provides simultaneous perfusion images of two or more vascular territories, with SNR that is close to that of conventional ASL images with the same total scan time. The data processing methods demonstrated here allow for the direct estimation and correction of the relative tagging efficiencies β associated with the vessel encoding process. Two advantages of this method when compared to pulsed methods (6, 7) are the higher SNR of the pseudocontinuous tagging method, and the spatial specificity that is gained from encoding of vessels within a single tagging plane. Discrimination between two vessels depends only on separation of the vessels as they pass through the tagging plane, rather than on the identification of 3D slabs that contain sufficiently long segments of one vessel or the other for pulsed tagging. In addition, the temporal width of the tag bolus is naturally identical for all tagged vessels, simplifying quantitation of perfusion. As in conventional continuous (11) or pseudocontinuous (8) ASL, the tagging process does not need to perturb spins either proximal or distal to the tagging plane, allowing for arterial spins proximal to the tagging plane to remain relaxed for the next tagging cycle, and for the tag to be placed close to the imaging region when this is desirable. In the current implementation, only vessels that are located along parallel lines within the tagging plane can be tagged with full efficiency. This generally does not pose a problem for encoding of three vessels, but four or more vessels will not in general fall along two parallel lines. In these cases, less efficient encoding must be accepted, or new tagging pulses developed to allow for curved tagging lines.

Because the tagging pulses perturb spins over a range of approximately 2 cm, a tagging plane with arterial segments that are relatively straight over this distance should be used. The minimum distance between the tagging plane and the most proximal imaging location is limited by the slice profile of the tagging pulses, and by magnetization transfer effects to approximately 2 cm.

Quantitation of perfusion using the present method is essentially the same as that for nonselective PCASL. The relative tagging efficiencies β of the vessel encoded scans are measured and included in the decoding process, resulting in decoded images that are on the same absolute scale as non-vessel-encoded PCASL images. The additional terms in the signal equations for PCASL, such as those that account for the basic tagging efficiency α, the tag duration, and relaxation are scaling terms that can be treated separately from the encoding/decoding process.

The identification of optimal tagging/encoding parameters and geometries, as well as efficient methods for prescribing these geometries, are important for the ongoing development of this method. The initial goal of providing efficient separation of the three main inputs to the Circle of Willis has been demonstrated here using two different encoding schemes (Figs. 3 and 4), which in our initial experience produce nearly identical results in healthy subjects, but differences may appear as we study their efficiency across subjects and patient populations. In general, the optimization of this method is likely to rest primarily upon the interaction between the tagging parameters, the vascular geometry and the velocity distributions. For example, slower flow velocities above the Circle of Willis may call for PCASL parameters that are better tuned for those velocities. Tagging in areas of greater vessel tortuosity may be improved using pulses with narrower slice profile, to reduce the amount of in-plane flow as blood traverses the tagging plane. Studies of these effects are currently underway.

Acknowledgements

  1. Top of page
  2. Abstract
  3. THEORY
  4. MATERIALS AND METHODS
  5. DATA PROCESSING
  6. RESULTS
  7. DISCUSSION
  8. Acknowledgements
  9. REFERENCES

I thank Eric Han, Ro Marolia, and Bryan Mock from GE Healthcare for hardware support, and Wen-Chau Wu and Julie Bykowski for help with data collection.

REFERENCES

  1. Top of page
  2. Abstract
  3. THEORY
  4. MATERIALS AND METHODS
  5. DATA PROCESSING
  6. RESULTS
  7. DISCUSSION
  8. Acknowledgements
  9. REFERENCES