### Purpose:

To investigate blood flow and transit time measurement, using the pseudo-random arterial modulation (PRAM).

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Technical Note# Pseudo-random arterial modulation (PRAM): A novel arterial spin labeling approach to measure flow and blood transit times

## Authors

### Mohammad-Reza Taei-Tehrani PhD,

Corresponding author- E-mail address: mr.tehrani@rutgers.edu

- Rutgers University Brain Imaging Center, Rutgers University, Newark, New Jersey, USA
- Department of Radiology and Biomedical Engineering, Columbia University, New York, New York, USA

- 143 Autumn Ridge Road, Bedminster, NJ 07921

### Matthias J.P. Van Osch PhD,

- Department of Radiology, Leiden University Medical Center, Leiden, the Netherlands

### Truman R. Brown PhD

- Department of Radiology and Biomedical Engineering, Columbia University, New York, New York, USA
- Department of Radiology, Medical University of South Carolina, Charleston, South Carolina, USA

- First published: Full publication history
- DOI: 10.1002/jmri.22844 View/save citation
- Cited by (CrossRef): 1 article Check for updates

To investigate blood flow and transit time measurement, using the pseudo-random arterial modulation (PRAM).

PRAM is based on a pseudo-random sequence of inversions and noninversions of the arterial blood at a labeling plane inferior to the imaging plane. To accomplish this, a pseudo-continuous tagging is used to create inversion or noninversion prepulses before a gradient echo sequence and tested on phantoms and human volunteers.

We have shown here that the PRAM technique can measure the velocity profile and the transit time accurately and efficiently both in a phantom and in vivo in a human brain.

PRAM does not require separate control and label acquisition as is common in arterial spin labeling (ASL) but rather measures the distribution of transit times to a voxel within one integrated scan. The PRAM method is a model-free approach in measuring transit time distributions, and therefore ultimately should provide more accurate perfusion measurements. J. Magn. Reson. Imaging 2012;35:223-228. © 2011 Wiley Periodicals, Inc.

CEREBRAL BLOOD FLOW (CBF) is one of the most important physiological variables involved in local brain metabolism. CBF together with local oxygen consumption provides the physiological basis for blood oxygen level dependent (BOLD) contrast, the most frequently used imaging technique for estimating changes in neural activation (1). In addition to its variations during normal brain function, CBF also changes during many of the pathological events that lead to acute or chronic brain dysfunction. Because changes in physiological variables typically have an earlier onset than structural biomarkers, reproducible and reliable measurement of CBF has considerable potential for both research and in clinical applications such as evaluation of stroke and brain tumors, as well as the diagnosis of dementia. For accurate quantification of CBF, knowledge of local transit times of arterial blood is of important, especially for patients with steno-occlusive diseases (2, 3).

Arterial spin labeling (ASL) has been increasingly used for measuring perfusion and transit times due to its noninvasiveness. As the name suggests, in ASL the magnetization of protons in arterial water are typically inverted (labeled) at a plane through a cerebral artery and later observed after they have flowed into the area being imaged. Because ASL uses water as an endogenous tracer, experiments can easily be repeated and requires no exogenous agents. Furthermore, with certain assumptions, CBF can be quantified using ASL, making it possible to compare measurements across individuals or within a subject at different time points, something that is difficult to do with other perfusion modalities. However, for accurate quantification, the transit times need to be known to ensure that all labeled spins have reached the microvasculature in the imaging plane, by either choosing an appropriate delay time before acquisition or correcting for this effect in postprocessing. Continuous ASL (CASL) reduces this uncertainty by introducing a postlabeling delay (PLD) between the end of the inverting pulse and the start of data acquisition (4). As long as this time is longer than the longest transit time the result is relatively independent of the transit times, although the difference in relaxation times between the intravascular and intracellular spaces can still cause errors in the quantification. This effect can be particularly prominent in the case of stroke and tumors, where substantial changes in transit times can occur. This suggests that an effective and reliable way to incorporate the measurement of transit times into an ASL measurement would be of considerable importance.

The standard way to measure transit times in ASL is by acquiring sets of images with increasing labeling delays, and by observing when labeling spins reach the imaging slices. Typically 5 to 10 different scans with different labeling delays are used to reconstruct transit time (5). Other groups (6, 7) have investigated the use of Look-Locker technique with repeated small flip angle acquisition in PASL to reconstruct transit time map in a single acquisition. Different modulation techniques have been developed for perfusion measurement in ASL such as Hadmard modulation by Gunther et al (8), sinusoidal modulation by Mildner et al (9), or frequency modulation by Barbier et al (10). As shown in this study, using pseudo-random arterial modulation (PRAM), we are able to determine the transit time distribution in an integrated and efficient acquisition without the need for long continuous radiofrequency (RF) pulses. An additional advantage of the PRAM method is that it does not require separate control and label acquisition and therefore the effects of off-resonance saturation are spread equally throughout the pulse sequence.

The underlying concept in PRAM is that the signal in each voxel of the imaging plane is an integral over the labeling input function convolved with the temporal transfer function to that voxel. If the input arterial spins are exposed to a pseudo-random modulation then this pattern will subsequently move toward the imaging plane and the magnetization in the voxel can be expressed as:

or in discrete form

(1)

where *M(t)* is the magnetization signal at time *t* of a voxel, *F*(τ) is the fraction of spins in this voxel with transit time τ, and *P*(*t* − τ) is the pseudo-random modulation scheme at time *t* − τ. In the discrete equation *F*_{j} and *P _{i-j}* corresponding to

Inversion of arterial blood is performed using velocity driven adiabatic RF pulses (11) in a plane inferior to the imaging slice so that the inversion is achieved by the motion of spins along the gradient through the inversion plane. A pseudo-CASL pulse was used for the human subjects instead of a continuous CASL pulse, due to lower the specific absorption rate (SAR) and higher inversion efficiency (12) as well as the difficulty in operating the RF amplifier continuously.

An important property of the PRAM modulation sequences (also known as maximum length sequences) used in this study is the fact that their autocorrelation function is essentially a delta function, which allows us to easily evaluate the above integral. They are of length of 2^{n} − 1 and generated using linear shift registers of prime binary polynomials (13). In other words, for a PRS of length *N*, elements of *a*_{j} for *j* = 0, 1, … , *N*−1, autocorrelation function has the property of:

(2)

The −1 comes from the fact that number of elements in the sequence is odd and thus cannot be exactly cancelled out.

The full dataset in a PRAM experiment contains an image for each element of the PRS for every phase encode direction. Therefore in the *k*-space data, the order of acquisition is the frequency direction first, followed by the PRAM loop, and finally the phase direction. For analysis the data is re-ordered to frequency, phase direction and PRAM loop, and subsequently Fourier transformed in the frequency and phase directions. The results are *N* images, corresponding to the magnetization signal encoded with the PRAM phases for the total duration of *N***N*_{p}**TR*, where *TR* is the normal repetition time between acquisitions and *N*_{p} is the number of phase encode directions. The magnetization signal at time *t*_{i} is denoted by *M*(*t*_{i}), where *i* varies from 0 to *N*−1. We assign the initial time *t*_{0} to *TR/2*, because it is the middle of the interval due to the fact that adiabatic inversion pulses smoothly invert the magnetization of flow along the gradient and it takes at least TR/2 to partially invert them. Similarly *t*_{i} corresponds to:

(3)

For velocity estimation, we use *V*_{i} = *L*/*t*_{i}, where L is the labeling offset distance.

Because ASL inversions modulate the longitudinal magnetization, we need to use the real part of the magnetization rather than the more commonly imaged magnitude. To do this, we correct the images to be of constant phase (real) by performing pixel-wise phase correction by:

(4)

where is the mean phase map over the pram cycle.

To measure flow and transit time distribution from *M*^{′}(*t*_{i}), we assume the signal at time *t*_{i} is the summation of all signals from spins with different velocities arriving at the imaging slice at time *t*_{i}. By including the *T*_{1} relaxation during the transit time, the magnetization can be written as:

(5)

where *F*(*t*_{j}) is the fraction of the spins that takes *t*_{j} to travel from the labeling plane to the image plane. The PRAM modulation sequence *P _{i-j}* is known, and can be represented as:

(6)

Therefore, *F*(*t*_{j}) can be calculated for each transit time by inverting *P* and solving for *F*_{i}

(7)

This can be denoted in the matrix format by

(8)

The PRAM method was validated using a cylindrical flow phantom which resulted in a parabolic flow profile. As the labeled spins move from the inversion plane to the imaging plane, the first labeled spins should appear at the center of the pipe, because the center exhibits the highest velocity with the subsequent labeled spins appearing as rings of increasing diameter. The radial velocity distribution is quadratic in the radius; suggesting that the square of the radius of the visible ring should vary inversely with the transit time. This relationship was validated for PRAM by keeping the flow constant and varying the labeling offsets as well as keeping the labeling offset constant and varying the flow.

The PRAM pulse sequence was developed and the data were acquired on a Philips Achieva 3 Tesla (T) MRI scanner (Philips Healthcare, Best, Netherlands). The flow pump (Cole-Parmer, Vernon Hills, IL) was set to 4.35 mL/s and the phantom had a 2.54-cm internal diameter. The images were acquired with 90° flip angle, matrix size of 64 × 64, 5-mm slice thickness, single slice acquisition, and field of view (FOV) of 64 mm, PRAM number of 15, and TR of 500 ms. The CASL pulses were used for inversion and cosine modulated CASL for noninversion in the phantom study. By measuring the transit time from the middle of PRAM pulse, we expected the maximum velocity in the flow phantom of 4.35 mL/s and labeling offset of 3 cm (*V*_{max} = 1.72 cm/s) to appear at 1747 ms.

Subsequently, the PRAM method was tested in five human subjects, all males between the age of 25 and 38 years. The protocol was approved by the institutional review board and written informed consents were obtained. The inversion plane was located 10 cm inferior of the center of the imaging slice and data were acquired with 15 PRAM number. The pseudo-CASL inversion module, used in the human study, consisted of a train of 18° Hanning RF pulses with the duration of 0.5 ms followed by 0.5-ms pause in combination with unbalanced slice selection gradients. The pseudo-CASL noninversion module is the same as inversion module but with the RF polarity alternating. The repetition time was the summation of inversion module duration plus 15-ms acquisition time. The images were acquired with 90° flip angle, matrix size of 64 × 64, 5-mm slice thickness, single slice acquisition, 192-mm FOV and *TR* of 175 and 335 ms corresponding to a total scan time of 2:48 and 5:21(min:s), respectively. The transit time maps were created by plotting the corresponding time of the maximum signal in the PRAM cycle in every pixel.

PRAM reconstructed images for the flow phantom for the first 8 transit times for four different labeling offsets of 2 cm, 3 cm, 4 cm, and 5 cm are shown in Figure 2a–d. Comparable results were also obtained by keeping the labeling offset constant and varying the flow (data not shown). The relationship between the squared radius of the visible rings in the flow phantom and the inverse of the transit times is plotted in Figure 3 for the PRAM data with 2 cm, 3 cm, 4 cm, and 5 cm labeling offset together with the theoretically expected relationship. As can be seen the agreement is excellent, particularly considering that there are no adjustable parameters in the calculation.

The PRAM reconstructed images for a human subject with *TR* of 175 ms and 335 ms are shown in Figures 4a and 4b, respectively. The estimated velocities observed in Figure 4a vary from 7.6 cm/s to 22.9 cm/s from Eq. [3], corresponding to arrival times between 438 ms (3rd image) and 1313 ms (8th image). This is also comparable with the results in Figure 4b, where the signal appears from 2nd to 5th images due to longer TA, corresponding to velocities between 6.6 cm/s and 19.9 cm/s. The results from other subjects were also comparable with the results shown for this subject. In Figure 5a, the Arterial Input Function (AIF) of a ROI (red box in the figure) for the same subject of Figure 4a and 4b is shown. The ROI signal plotted clearly shows that the labeled spins start reaching the imaging plane around 500 ms; the maximum numbers of spins reach the imaging plane around 850 ms, and beyond 1.4 second no inflow of labeled spins occurs in the ROI. The transit time map, which represents the corresponding time to the maximum signal during the PRAM cycle in every pixel, is shown in Figure 5b.

This study demonstrates that PRAM can measure flow distributions and transit times accurately. It has been tested on phantoms with results in agreement with Poiseuille flow calculations and achieved an accuracy of 99.5%. An earlier application of PRAM on human subjects was also able to measure average velocities in arteries and veins in the extremities (14). Applied to human brain, it provided satisfactory results, especially for gray matter regions. Results for white matter were less satisfactory. This is in part due to the fact that white matter has lower blood volume, and prolonged arrival time, causing reduced SNR and larger T_{1} signal decays.

To measure transit times, PRAM uses 90° flip angle pulse to clear the imaging slice from the tissue labeled spins. Therefore, the flow would entirely consist of the arterial input to the imaged slice. However, PRAM can also measure the parenchyma flow using flip angles of lower than 90°. With lower flip angles, the perfusion signal will be able to accumulate in the imaging slice, allowing perfusion measurements. However, the total signal is still likely to be dominated by the arterial signal at earlier arrival times but at later times the perfusion signal should dominate. Furthermore, the arterial signal can be addressed by using bipolar gradient pairs to crush the signal from fast-flowing spins (15).

Because of the nature of the PRS generation the most natural lengths are 2^{n}−1, i.e., 7, 15, 31, etc (13). The product of the TR in the experiment and the PRS length sets the sampling interval which needs to be at least as long as the spread in transit times for the tissue of interest. Otherwise the fastest arriving spins will be confused with the slower arriving spins from the previous PRAM cycle. To acquire the full transit time distribution, the whole PRAM cycle, the product of TR and PRAM number, should be 2 to 3 s. This will insure sufficient number of acquisitions has been acquired during the transit time to be able to reconstruct the flow transition. The PRAM method does not require separate control and label acquisitions, but rather all pseudo-random inversions are integrated into one acquisition. This eliminates the direct subtraction of label and control that is common in ASL analysis. On the other hand, the PRAM method is still sensitive to subject motion due to the fact that the acquisition of each transit time is distributed throughout the total acquisition time. Motion creates subtle blurriness on PRAM which is not completely correctable, although postacquisition processing of the original images, as is commonly done in BOLD analysis, can reduce these artifacts.

Quantification of the flow measurement directly depends on the inversion pulse performance. The Pseudo-CASL pulse has shown greater inversion efficiency and lower SAR effect compared with other adiabatic pulses (12). However, as we decrease *TR*, fewer labeled blood reach the imaging slice, causing reduction in inversion efficiency. This limits the PRAM acquisition to a minimum *TR* of approximately 100 ms. For this TR, we would need to use a PRAM sequence of 31 or 63 lengths to satisfy the time constraint mentioned above. The *TR* range used in PRAM for human brain varies between 100 ms and 400 ms; almost one-tenth of *TR* used in regular CASL or PASL. This allows PRAM technique to acquire the whole transit time distribution within one integrated acquisition.

In conclusion, we have demonstrated that PRAM can measure the transit time both in a phantom and in vivo in a human brain. Although only one imaging slice was acquired to simplify the pulse programming and processing of the transit times, the extension of PRAM to multi-slice acquisition is in the development which will provide three-dimensional views of transit times at the expense of longer acquisition times. The PRAM method is a model-free approach in measuring transit time distributions, and therefore it can be more widely used on different organs.

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