OPTIMIZED VELOCITY-SELECTIVE ARTERIAL SPIN LABELLING MODULE

A velocity selective preparation method is disclosed, for velocity selective arterial spin labelling (VSASL), the VSASL method using non-selective radiofrequency pulses and magnetic field gradients to modulate the longitudinal magnetization of the spins as a function of their velocity, wherein said velocity selective preparation method comprises an n-segment B1 insensitive rotation that is resistant to eddy current artifacts.

DETAILED DESCRIPTION

Velocity Selective Preparations

In the present method arterial spins are tagged based on their velocity rather than their spatial location. The velocity spin preparations saturate spins above a pre-defined Vc. The spins are first tipped into the transverse plane without spatial selection. Bipolar gradients are then applied which result in a phase accrual of the spins that is proportional to their velocity. The spins are then flipped back to the longitudinal axis. The longitudinal magnetization of the spins at the end of a VS preparation is then given by

where α is the tagging efficiency of the preparation, m1is the first moment of the VS gradients and v is the velocity of the spins. Within a laminar vessel the total expected magnetization is given by

where VMAXis the maximum velocity of the vessel. Vcis then defined as the first zero crossing of the sin c function, where Vc=π/(γm1), above which the spins are considered to be saturated. It has previously been shown that for Vc<4 cm/s VSASL becomes insensitive to transit time in gray matter, therefore, in the present method Vc=2 cm/s is used. The cut off velocity can be in the range 0<|Vc|<=infinity.

To overcome the spatial variation in tagging efficiency of prior art methods, in the present invention, spins are in the transverse plane at the zero points of the RF amplitude function, so monopolar gradients for velocity selection are inserted between segments 1 and 2, and between segments 3 and 4, resulting in a spatially independent tagging efficiency.

In VSASL two acquisitions are made, a tag acquisition with m1=π/(γVc), and a control acquisition with m1=0. Eddy currents generated by the VS preparation in the tag acquisition are not present in the control. To include the bipolar gradient concept to the improved B0and B1insensitive BIR preparation, the present invention uses an eight-segment B1 insensitive (BIR-8) VS preparation.

A BIR pulse produces an adiabatic rotation over a designed off-resonance range. The RF amplitude function (A(t)) is given by

where ξ is a dimensionless constant and TSEGis the duration of one pulse segment. The corresponding phase is given by

where κ is a dimensionless constant and ωMAXis the maximum frequency sweep. It can be shown that a composite BIR pulse made up of four segments is the most robust pulse to B0and B1inhomogeneity due to the time symmetry of φ(t) about the mid point of A(t).

To allow for the addition of bipolar gradients, in the present method, the number of RF segments are eight. This maintains RF pulse symmetry about the mid point of A(t), and therefore preserves the B0insensitivity of the preparation. Of course, the number of RF segments may be more or less than eight. The present use of eight segments is an example only. The bipolar gradient lobes for velocity selection were then inserted between segments 3 and 4, segments 5 and 6, and between segments 7 and 8, where A(t)=0.FIG. 1Ashows the RF amplitude (top), the RF phase (middle) and the desired VS gradient waveform (bottom). The gradients shown in the tag condition for Vc=2 cm/s, Gmax=40 mT/m and gradient ramp time r=0.5 ms. In the control acquisition the gradients in the VS preparation are set to zero. The VS preparations were inserted into the pulse sequence (FIG. 1B), keeping Tsatand TI constant. The gradients are arranged with timing ratios 0:1:2:1 at the A(t)=0 points of the BIR-8. This timing scheme balances the linear phase accrual from off resonance as the odd and even delays have the same total time. Subject to these constraints, any gradient pattern could be used within the BIR-8 preparation.

For the present method, the BIR-8 preparation is designed so that the pulses are insensitive over ΔB0=±250 Hz with an adiabatic threshold of 15 μT by optimising ξ, κ and ωMAXthrough Bloch equation simulations. To limit the duration of the preparations, TSEG=2 ms, is set. However, it will be understood by the skilled person that other values may be used.

Bloch Equation Simulations

A Bloch equation simulation was used to evaluate the responses of the VS preparation to the presence of B1and B0inhomogeneity and eddy currents. The simulation considers rotations about the effective B field followed by relaxation with a time step of 5 μs. The simulation was implemented in MATLAB 2011a (The MathWorks Inc., Natick, Mass., USA). However, any other suitable software may be used.

To determine the adiabatic threshold and off-resonance sensitivity of each preparation, the response of arterial spins were simulated. Simulations were performed over a range of ΔB0(±500 Hz), B1(0.5-25 μT) and v (−4-4 cm/s). A maximum gradient strength of 40 mT/m with a rise time of 0.5 ms was assumed. The predicted tagging efficiency for the preparation was also determined by simulation. As adiabatic pulses are used the relaxation decay of the bolus during the VS preparations is a mix of T1and T2effects. For the preparation of the present invention, the response of arterial spins with B1=20 μT, v=0 and 2 cm/s were assumed, assuming arterial T1=1664 ms (19) and T2=150 ms (20). The tagging efficiency, a, for the preparation is then given by

at the end of the preparation.

The effect of the preparation on static spins in the presence of eddy currents was also modelled. The eddy current effects are modeled as linearly independent components with eddy current amplitudes Anand time constants τn. The additional gradient due to eddy currents (g(t)) is given by

where {circle around (x)} represents convolution with the desired gradient waveform, G(t), and H(t) is the unit step function. Then the static spins were simulated at different positions from gradient isocenter (±25 cm) with τn=10−4−1 s and An=0.001−1%. Only the presence of a single time constant τnwas considered and relaxation effects were ignored.

In Vivo Measurements

VSASL measurements with the preparation were performed in five healthy volunteers using a 3 Tesla Siemens Verio scanner (Siemens Healthcare, Erlangen, Germany) to assess the influence of eddy currents. The VSASL pulse sequence (FIG. 1B) begins with a global pre-saturation (22) to remove any spin history effects as the tag is being generated within the imaging volume. After time TSAT=3.2 s the VS preparation is applied with Vc=2 cm/s. The tagging gradients were applied on the x axis, although other axes could be used. A spin echo, Echo Planar Imaging (EPI) readout is then applied after inflow time TI. During the readout portion of the sequence flow-crushing Stejskal-Tanner gradients with m1=π/(γVc) are applied for both tag and control acquisitions, on the same axis as the tagging gradient. This dephases spins above Vcso that only signal from spins that have exchanged into tissue during time TI, and thus have decelerated to a velocity below Vc, are acquired.

Other acquisition parameters were TR=5.1 s, TE=32 ms, TI=0.7 s, acquisition time per slice=61.92 ms, 18 slices, 256 mm FOV, 64×64 matrix, slice thickness=5 mm. The volunteers were moved so that the center of the imaging slice group was at the magnet isocenter. The VS preparations were played out on a whole body transmission coil at maximum amplitude (23 μT) and a 32-channel head receive coil was used. A separate body coil receive image was acquired for coil sensitivity correction and M0CSFcalibration. A double inversion recovery acquisition with inversion times designed to null white matter and CSF was used as a gray matter mask with adiabatic inversions 4150 ms and 550 ms before an identical SE-EPI readout.

Modulation of Eddy Currents In Vivo

The eddy current spectrum will be different for each scanner. As Anand τnare generally not known, the eddy current amplitudes are varied by varying GMAX. At the end of a gradient ramp (t=r), the unwanted additional gradient due to eddy currents is given by

where GMAXis the maximum amplitude of the desired trapezoidal gradient. Therefore, the eddy current gradient amplitude can be linearly modulated by applying the VS preparation with different GMAX, keeping rise time r constant. For the preparation, five GMAXvalues (10-40 mT/m) with r=0.5 ms were applied. Sixteen tag-control pairs were acquired for the preparation and GMAXcombination. The acquisition order was randomized. Total scan time was 50 minutes.

Data Analysis

Data were corrected for motion and registered to the M0scan using FLIRT. Images were subtracted pairwise and then averaged to form the ΔM image. Perfusion was quantified on a voxelwise basis by non-linear fitting to a modified general kinetic model:

where M0BLOODis the magnetization of a fully relaxed voxel of blood as determined from calculation via the M0CSFscan; α is the tagging efficiency of the VS preparation; ƒ is perfusion and qp(f), takes into account the different relaxation times of the bolus and the tissue. The quantification assumes that the bolus arrival time is zero and that the bolus length is equal to TI. Since reducing GMAXwill increase the tagging gradient duration, a for each VS preparation and GMAXwas simulated.

Mean perfusion, f(GMAX), was calculated for each preparation and GMAXwithin the gray matter mask derived from the subject's double inversion recovery scan. The effect of eddy currents on apparent perfusion should only depend on the scanner used, the relaxation times of static tissue and the TI, but not the underlying perfusion of an individual subject. Therefore, Δƒ=ƒ(GMAX)−ƒ(GMAX) whereƒ(GMAX) is the individual subject's perfusion, were correlated averaged over all GMAX(reported in Table 1).

Simulations

For the BIR VS preparation it was found that ξ=15, tan(κ)=60 and ωMAX=39.8 kHz produced an adiabatic rotation over ΔB0=±250 Hz. The adiabatic threshold was found as B1=14 μT.FIG. 2A(top) shows the resulting longitudinal magnetization of moving spins after the application of the BIR-8 VS preparation with Vc=2 cm/s and GMAX=40 mT/m. For on-resonant spins the tagging efficiency was found as αDRHS=0.92, αBIR-4=0.93, αBIR-8=0.89. The simulations demonstrate that the desired co-sinusoidal modulation of magnetization as a function of velocity is produced for the preparation.

FIG. 2B(bottom) shows the predicted response of static spins to the VS preparation with GMAX=40 mT/m and An=0.25%. At isocenter static spins are returned to +MZ, as expected for a VS preparation. Simulations show the BIR-8 preparation of the present invention has very little sensitivity to eddy currents compared with DRHS and BIR-4 preparations.

In Vivo Measurements

Mean gray matter perfusion values averaged over all GMAXfor the BIR-8 preparation are reported in Table 1, (below) corrected for differences in the theoretical efficiency for the preparation, and for regional receive coil sensitivity differences. The mean perfusion over all subjects for the BIR-8 preparation was 53.9±2.6 ml/100 g/min.

Representative perfusion maps are displayed inFIG. 3for GMAX=10 and 40 mT/m. The perfusion maps based on the BIR-8 preparation display reduced eddy current artifacts in the subtraction image compared with the DRHS and BIR-8 preparations.

FIG. 4shows the variation of apparent perfusion versus GMAXfor the preparation. Perfusion measured by the BIR-8 method correlates to P=0.011. The slope of Δf/GMAXwas 0.21 (ml/100 g/min)/(mT/m) for the BIR-8 preparation. This compares favorably to the DRHS and BIR-4 preparations that show a greater dependence of perfusion with GMAXvalue.

It has been shown that the BIR-8 VS preparation of the present invention is less sensitive to eddy-current effects, whilst preserving a good insensitivity to B0and B1inhomogeneities. The data show that the standard VS preparations may overestimate perfusion due to static spin contamination in the ΔM image, caused by eddy currents, but also shows that the BIR-8 preparation performs extremely well.

For the BIR-8 VS preparation the average gray matter perfusion estimates that were calculated over all GMAXvalues fall within expected normal physiological ranges. For GMAX=10 mT/m, the apparent perfusion as measured by the present invention was 51.4±3 ml/100 g/min.

The τncompensated by the preparation will depend on the time between the gradient lobes and the gradient rise time. Although changing GMAXfrom 10 mT/m to 40 mT/m will change the time between the gradient lobes, simulations suggests that this would not significantly alter the τndistribution. In the present method, all the gradient durations within an individual VS preparation were equal for simplicity. The duration of the gradient lobes could be adjusted to null a particular τn, similar to the approach used for designing diffusion gradient, subject to the timing constraints of the BIR-8 pulse.

In the present case, the tagging gradients were applied on the x axis, since any changes in perfusion as a function of z slice position could be attributed to a slice timing error, which would cause an erroneous TI for each slice. The Vcof 2 cm/s means that the method may be sensitive to vessels on the order of arterioles in the cortical surface, so the direction of the encoding should not matter.

Although the BIR-8 preparation is RF intensive, SAR did not present a problem at 3 T with the protocol used. It was found that a TR of 2 s is possible, but will reduce the SNR due to a shorter TSAT. To maximize SNR efficiency the TR and TI were chosen by maximizing ΔM/√TR (equation 8) for the central slice, with an expected perfusion of 60 ml/100 g/min. Equation 8 assumes that the bolus was in the field of view of the RF coil as the saturation pulse was played out, which may not be the case with the long TR used.

A further improvement of the BIR-8 method is the symBIR-8 method described in detail below. Here it is shown that the errors due to eddy currents can be further reduced by inserting gradient lobes at all four |B1|=0 points of the BIR-8 preparation with polarities −1:+1:+1:−1 (FIG. 5A). This symmetric preparation, symBIR-8 was implemented on the system and compared to the BIR-4 and BIR-8 preparations.

Methods

The first gradient moment of symBIR-8 preparation is given by:

where F is the flat top time and R is the gradient rise time. The RF pulse used 2 ms BIR segments as previously. The response of static spins to symBIR-8 pulse was simulated with time constants 10−4s to 1 s with An=0.25%.

The BIR-4, BIR-8 and symBIR-8 preparations were then evaluated in a phantom. To eliminate the effects of diffusion, an 18 cm spherical silicone oil phantom was used. The phantom was placed at the center of the 32 channel head receive coil and positioned near the magnet isocenter. MR safe sandbags were used to immobilize the phantom. The preparations were applied immediately prior to a spin echo EPI readout without crushers. The TE was 37 ms, FOV=20 cm, 64×64 matrix and slice thickness was 8 mm. These are examples of the parameters only and other parameters may be used. Data were normalized for receive coil sensitivity using the scanner “pre-scan normalize” option. Each preparation (BIR-4, BIR-8 and symBIR-8) was applied with Vcut=2 cm/s, with GMAX=10, 20 and 40 mT/m. This was repeated for each tagging direction (X, Y, Z), readout direction (sagittal, transverse and coronal). This resulted in 81 acquisitions in total, with a TR of 3 s and 16 tag and control pairs. The value for M0was determined from a scan without a velocity selective preparation with TR=30 s.

Results

FIG. 5Ais a symBIR-8 pulse diagram for Vcut=2 cm/s at GMAX=40 mT/m. The simulations show that the symBIR-8 (FIG. 5C) does further reduce eddy current effects compared to the BIR-8 (shown inFIG. 5B).

The mean ΔM subtraction images for all three preparations, tagging directions, readout directions and gradient strengths are all depicted inFIG. 6. The BIR-4 (left column) has the greatest amount of artifacts compared to the BIR-8 (middle) and symBIR-8 (right). When labeling on the X axis the greatest variation is in the Y direction for the BIR-4, which matches the previous in vivo data, above. Similarly, when labeling on the Y-axis the variation is along X for the BIR-4. This is not the case for BIR-8 or symBIR-8, where the spatial variation of the artifacts is along the direction of the applied gradient. All artifacts are reduced as GMAXis reduced. Artifactual signal at isocenter is apparent for all preparations. The artifacts are reduced when using symBIR-8 compared to BIR-8, especially on the X and Z labeling axes.

The data inFIG. 6were quantified by taking the average root mean square error in a mask containing the phantom, plotted inFIG. 7, where the top line in each figure is the quantified subtraction error for BIR-4, the middle line is for BIR-8 and the lowest error line is for symBIR-8. Velocity gradients are applied in X (a-c), Y (d-f) and Z (g-i) directions. Data are from masks of the images inFIG. 6. The root mean squared error is calculated for each tag control pair, data are the mean of this±SD over the 16 tag control pairs.

This phantom experiment confirms that the symBIR-8 preparation does have reduced artifacts compared to the BIR-8, particularly on the X and Y axes. As these artifacts have a special distribution and reduce with GMAX, they are attributed to eddy currents. The artifacts are unlikely to be from diffusion as the diffusion coefficient of the silicone oil is of the order of 1 to 2 orders of magnitude lower than water and the artifacts are spatially inhomogeneous.

There was not a significant difference between symBIR-8 at 20 mT/m to 10 mT/m, so to minimize T2decay during the preparation, 20 mT/m was used on the scanner.

Eddy currents during the VS preparation cause unwanted tagging of static tissue and hence an overestimation of perfusion in VSASL. The BIR-8 preparation of the present invention is a highly robust VS preparation to both eddy currents and B1with excellent efficiency compared to prior art VS preparations. Its use improves the quality and reliability of VSASL measurements. The symBIR-8 preparation yields even better eddy current results.