Page 1

Optimizing Saturation-Recovery Measurements of the Longitudinal Relaxation Rate Under Time Constraints

J-J. Hsu1, G. H. Glover1, and G. Zaharchuk1

1Lucas Center for Imaging, Stanford University, Stanford, California, United States

Introduction. The oxygen level of brain tissue and cerebrospinal fluid (CSF) are related; thus CSF oximetry can allow insight into brain regional

oxygenation. All existing clinical methods of oximetry are highly invasive, requiring either microelectrode or optode insertion. The non-

invasiveness of MRI oximetry is hence desirable. It has been shown recently [1] that the oxygen concentration of CSF can be determined by MR

longitudinal relaxation rate R1 measurement. The saturation–recovery (SR) method is a common technique for tissue, which derives R1 by curve-

fitting the data points acquired with different recovery times. But CSF has long T1 (T1 = 1/R1); consequently, when the recovery times that are

optimal for imaging tissue (T1 ~ 1 s) are scaled for CSF (T1 ~ 4 s), the total scan time can be too long to be clinically feasible. Despite earlier efforts

[2] to optimize the SR method, very little is known about the feasibility and optimization for long-relaxation substances. To overcome the scan-time

obstacle of translating CSF oximetry to the clinic, Monte Carlo computer simulation was performed in this work to determine the recovery times that

generate optimal accuracy and precision of SR R1 measurements under strict constraint on constant total scan time. With the optimization, 3D, high

resolution, whole brain SR scans completed in a scan time of 10 min can generate R1 measurements of CSF in agreement with the best literature

results, as described below.

Methods. In the interest of clinical feasibility, the present work focuses on two-

and three-point SR methods with the sum of the recovery times (SRT) subject to a

constant. The SR equation is given by M(τ) = Meq [1−exp(−τR1)], where M(τ) and

Meq represent the magnetization at recovery time τ and at thermal equilibrium,

respectively. Time is expressed in unites of the true T1 and the value of R1 is in

units of 1/T1 unless a physical unit is attached. §Computer Simulation.—The

distribution of R1 values obtained by solving or curve-fitting the SR equation was

simulated by using a large number of computer-synthesized signals for various

SNR levels. A distribution was established for each vertex on a Cartesian grid of

recovery-time spacing 0.05T1. Then the ideal set of the recovery times was

determined as the one that minimizes the standard deviation (SD) of the

distribution. The signals were synthesized as the SR equation plus noise. The

noise was generated by a zero-mean, normally-distributed random number

generator of standard deviation defined by the given signal-to-noise ratio (SNR).

§SR MRI with XETA.—3D imaging by the SR method was implemented by

repetition of a fast spin-echo (FSE) train. Each repetition was delayed by the

desired amount of recovery time τ. The FSE train had a large number of

refocusing rf pulses (146 pulses) and very short pulse spacing (6.8 ms); therefore,

each pulse train is effectively a saturation (90°) pulse. The FSE train had an echo

time of ~500 ms, more than five times longer than the transverse relaxation time

T2 of brain tissue but much shorter than the T2 of CSF; thus the MR signals

recorded arise almost entirely from the CSF. This T2-weighting effect reduces the

partial-volume-effect error. 3D XETA [3], an advanced FSE pulse sequence, was

employed in this work; each 3D image contained 84 2-mm thick, 22×22 cm,

sagittal slices; each slice had resolution of 0.86×0.86×2.0 mm or 1.5×10−3 c.c.,

reconstructed from data that was 85% undersampled in the phase encoding

direction. XETA images of different τ were acquired as separate scans.

Results and Discussion. It was determined in preliminary scans at 1.5 T that

the SNR of interest is in the range of 50–240. The simulation was performed for

SRT of 1.5T1 to 3T1; these conditions can reduce the scan time considerably and

have adequate SNR for R1 measurement. Figure 1 shows sample results of the

simulation for the two-point method. In general, the minimal SD occurs at the

same or approximately the same set of the recovery times despite the SNR. For

the two-point method, the ideal recovery times are (0.4, 1.6)T1 and (0.55, 2.45)T1,

for SRT of 2T1 and 3T1, respectively. For the three-point method, the recovery

times are (0.25, 0.30, 1.45)T1 and (0.40, 0.40, 2.20)T1, for SRT of 2T1 and 3T1,

respectively; it is very interesting that two of the recovery times should be set the

same or approximately the same and shorter than the third one, which has not

been reported in earlier work using analytical formulae. The accuracy of setting

the recovery times to their exact values for optimal R1 precision is not critical if

the SNR is high. Under a common constraint of SRT, the two-point method is

more efficient than the three-point method because the improvement in accuracy and precision by the latter is only marginal (~0.5%). Figure 2

shows sample CSF R1 maps using our method. The total scan time was 9 min 55 s. The advantage of the optimization might not be easily

discernable in this figure. Nevertheless, by adding computer generated noise to the XETA images and recalculating R1, it is confirmed that the R1

results of the optimal recovery times are always more stable under noise influence. The R1 measurements are in agreement with earlier literature

results as shown in Table I, which demonstrates the clinical feasibility of applying two-point SR method for R1 mapping for CSF.

Acknowledgements. This work is supported by NIH RR09784 and the Richard Lucas Foundation. References: [1] G Zaharchuk et al., Acad Radiol

13, 1016 (2006). [2] See, for example, GH Weiss et al., J Magn Reson 37, 369 (1980); ED Becker et al., ibid. 37, 381 (1980); H Hanssum and H Rüterjans, ibid. 39, 65

(1980); SJ Doran et al., ibid. 100, 101 (1992); RJ Kurland, Magn Reson Med 2, 136 (1985). [3] GE Gold et al., Am J Roentgenol 188, 1287 (2007).

Figure 2 Sample slices of the 3D CSF R1 maps acquired at 1.5

T by the two-point SR method with the optimal recovery time

pair (0.4, 1.6)T1 (left) and a suboptimal pair (0.6, 1.4)T1 (right).

Table I Mean R1 values (and SDs; in s−1) of CSF at 1.5 T.

Lat. Ventricle Subarachnoid Space

Subj. I, Day 1 0.225 (0.016) 0.233 (0.038)

Subj. I, Day 3 0.223 (0.022) 0.244 (0.046)

Subj. II 0.213 (0.019) 0.220 (0.039)

Zaharchuk et al. [1] 0.226±0.004

SNR 190

SNR 240

SNR 110

SNR 140

SNR 50

SNR 80

0

0.05/T1

0.1/T1

0.15/T1

0.2/T1

0.25/T1

0.3/T1

0

0.5T1

RECOVERY TIME 1

1T1

1.5T1

SUM OF RECOVERY TIMES = 3.00T1

1/T1

1.01/T1

1.02/T1

0

0.5T1

RECOVERY TIME 1

1T1

1.5T1

SUM OF RECOVERY TIMES = 3.00T1

0

0.05/T1

0.1/T1

0.15/T1

0.2/T1

0.25/T1

0.3/T1

0

0.5T1

1T1

SUM OF RECOVERY TIMES = 2.00T1

1/T1

1.01/T1

1.02/T1

0

0.5T1

1T1

SUM OF RECOVERY TIMES = 2.00T1

Figure 1 The standard deviation (SD, left column) and the

mean (right) of the computer simulated distribution of R1 for

the two-point method. The SD and the mean represent

precision and bias, respectively. Recovery time 2 can be

derived by subtracting the sum by recovery time 1.

0.247±0.011

Proc. Intl. Soc. Mag. Reson. Med. 17 (2009)2637