Optimizing saturation–recovery measurements of the longitudinal relaxation rate under time constraints

Abstract

The saturation-recovery method using two and three recovery times is studied for conditions in which the sum of recovery times is 1.5T 1 to 3T 1 , where T 1 is the longitudinal relaxation time. These conditions can reduce scan time considerably for long T 1 species and make longitudinal relaxation rate R 1 (R 1 = 1/T 1 ) mapping for body fluids clinically feasible. Monte Carlo computer simulation is carried out to determine the ideal set of recovery times under various constraints of the sum of recovery times. The ideal set is found to be approximately invariant to the signal-to-noise ratio. For the three-point method, two of the recovery times should be set the same or approximately the same and should be shorter than the third one. Only marginal improvements in accuracy and precision can be achieved by the three-point method over the two-point method under a common constraint of the sum of recovery times. Three-dimensional, high resolution, whole-brain saturation-recovery scans on volunteers with a fast-spin-echo technique ( As demonstrated in a series of recent studies (1-4), mapping the magnetization longitudinal relaxation rate R 1 of body fluids by MRI holds great potential to be a method of determining the oxygenation (oximetry) of the fluids in vivo. The fluids of interest, e.g., urine, vitreous humor, cerebrospinal fluid (CSF), have long relaxation time constants T 1 (T 1 = 1/R 1 ) in comparison with tissues; thus when the imaging time parameters that are optimal for relaxation measurement of tissue (T 1 ∼ 1 s) are scaled for the body fluids (T 1 ∼ 4 s), the total scan time can be too long to be clinically feasible. All existing clinical methods of oximetry are highly invasive, requiring either microelectrode or optode insertion, and can obtain only point sample measurements. MRI oximetry is hence desirable for its noninvasiveness and volume coverage. However, the long scan time is a major obstacle in translating MRI oximetry of body fluids to the clinic, especially when the time allocated to R 1 mapping is only a portion of a radiological examination. Earlier efforts (5-9) to optimize MRI parameters were focused on the stability of measurement precision against noise influence or on optimizing for efficiency in terms of precision per unit of time. When the total scan time is further subject to a constraint, optimization of imaging time parameters remains to be studied. The saturation-recovery (SR) method (10) is a common technique for R 1 measurement, in which the longitudinal magnetization is set to zero and then measured after a delay time τ . The delay time τ is referred to as the recovery time. The value of R 1 is determined by curve-fitting separate measurements with different recovery times. SR does not need to wait for full magnetization recovery before the next repetition, a time-saving feature compared with the inversion-recovery method (11), and it has the signal-tonoise ratio (SNR) advantage of using large radio-frequency pulse flip angle (90• ) for signal acquisition in comparison with puls...

Formulas for Determining the Recovery Times for Optimal Two-Point Saturation–Recovery Measurement of the MR Longitudinal Relaxation Rate

“…This formula also independently reproduces the findings for the three cases considered in Ref. [8], in which the present Monte Carlo method was validated with the R 1 measurement of brain CSF of human subjects. That is, the optimal τ 1 for the SRT of 2T 1 , 3T 1 , and 6T 1 was found to be 0.4T 1 , 0.55T 1 , and 0.8T 1 , respectively, whereas Eq.…”

“…where M (τ) and M eq represent the magnetization at recovery time τ and at the thermal equilibrium, respectively. Given two data points, M (τ 1 ) and M (τ 2 ), the SR equation can be solved to obtain R 1 [8]. In this work, T 1 represents the true longitudinal relaxation time of the specimen and is used as the unit of time; R obs 1 is the longitudinal relaxation rate derived from data and is expressed in units of 1/T 1 .…”

“…(1), plus a computer-generated random number and the imaginary part was only a separately-generated random number. The SNR ρ is defined as [8]…”

“…Because the signal amplitude M varies as a function of the recovery time τ as described by Eq. (1), the definition of SNR uses M eq instead of M to characterize the SNR of the imaging environment rather than in the individual images [8].…”

“…[1][2][3][4][5][6][7], to these optimization questions would be very involved because of the increased mathematical complexity when the total imaging time is further subject to a constraint. Alternatively, a Monte Carlo computational study [8] was performed to answer these questions and the results were demonstrated with human subjects successfully. The Monte Carlo study was performed for a few settings of the total imaging time meant for experimental validation of the methodology.…”