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Optimizing tissue contrast in magnetic resonance imaging
Magnetic Resonance Imaging. Vol. 2, pp. Printed in the USA. All rights reserved.
193-204, 1984 Copyright ©
0730-725X/84 $3.00+ .00 1984 Pergamon Press Ltd .
• Original Contribution OPTIMIZING TISSUE CONTRAST IN MAGNETIC RESONANCE IMAGING
R. E.
HENDRICK,
T. R.
NELSON, AND WILLIAM
R.
HENDEE
Department of Radiology, University of Colorado Health Sciences Center, Denver, Colorado 80262 Magnetic resonance imaging demands that tissue contrast and signal-to-noise advantages be sought in each component of the imaging system. One component of magnetic resonance imaging in which contrast and signal-to-noise ratios are easily manipulated is in the choice of pulse sequences and interpulse delay times. This article provides a general method for determining the best choices of interpulse delay times in pulse sequences and applies that method to saturation recovery, inversion recovery, and spin-echo sequences. Saturation recovery and inversion recovery sequences with rephasing pulses, and tissues with unequal hydrogen densities are considered. Optimization of pulse sequences is carried out for the two distinct cases of (a) a fixed number of sequence repetitions and (b) a fixed total imaging time. Analytic expressions are derived or approximate expressions are provided for the interpulse delay times that optimize contrast-to-noise ratios in each pulse sequence. The acceptable range of interpulse delay times to obtain reasonable contrast using each pulse sequence is discussed. Keywords: Magnetic resonance imaging, Tissue contrast, Signal-to-noise ratio, Interpulse delay times, Pulse sequence optimization.
INTRODUCTION Increased tissue contrast and improved signal-to-noise ratios are of paramount importance in magnetic resonance imaging. Each component of the magnetic resonance imaging system is designed to enhance contrast, improve signal-to-noise ratios, and reduct patient imaging time. One component of magnetic resonance imaging in which contrast and signal-to-noise improvements are possible without physically' altering the system is in the selection of pulse sequences and interpulse delay times, Considerable clinical and theoretical work has been done to address the question of the best choice of pulse sequences and interpulse delay times for particular imaging tasks. 1-1O,12,14-20 Early work by Taylor and Bore" focused on the effect of water content and T 1 values on signal-to-noise ratios; they concluded that a single imaging sequence will not always give the best tissue contrast. Edelstein et alY addressed the question of interpulse delay times giving the best signal difference-to-noise ratios in T1-weighted sequences for tissues with equal hydrogen spin densities. More recent work by Wehrli et al.,'? reported variations in hydro-
gen densities of up to 30% for in vivo white matter, gray matter, and cerebrospinal fluid (CSF), suggesting the importance of pulse sequence optimization for unequal spin densities. Other recent work has demonstrated the effect of pulse sequence and interpulse delay time selection on tissue contrast.Y:":" Most analyses have been carried out with one or both of the following simplifying assumptions: (a) tissues are assumed to have identical spin densities (although refs. 12 and 17 are exceptions to this assumption) and (b) saturation recovery and inversion recovery are assumed to be applied without signal rephasing between 90° read pulses and signal measurement (ref. 14 being an exception to this). While these sequences may be applied without rephasing pulses in nuclear magnetic resonance (NMR) spectroscopy, current magnetic resonance imaging systems require rephasing pulses and small delay times prior to signal detection. Delay times on the order of 10 ms are required to apply gradients and reduce receiver saturation before signal measurement can begin. Rather than allowing signal decay due to both spin-spin interactions and magnetic field inhomogeneities during this
RECEIVED 5/1/84; ACCEPTED 5/30/84. Acknowledgment-s-This work was supported in part by Public Health Service Grant Number 5T32CA09073-08, awarded by the National Cancer Institute, Department of Health and Human Services.
Address correspondence and reprint requests to Dr. R. E, Hendrick.
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Magnetic Resonance Imaging. Volume 2, Number 3, 1984
period, a rephasing pulse is applied to eliminate transverse relaxation due to field inhomogeneities. Then the spin-echo, the peak of which is reduced only by spinspin ( T 2 ) relaxation of the transverse magnetization, is measured. In this article, we present a general method of determining interpulse delay times that optimize contrast-to-noise ratios. This method is applied to three pulse sequences common to magnetic resonance imaging: saturation recovery or partial saturation (SR), inversion recovery (IR), and spin-scho (SE). The optimization of SR and IR sequences includes the case of rephasing pulses between 90° pulses and signal measurement. The case of tissues with equal and unequal spin densities is considered. Optimal interpulse delay times are determined in two clinically relevant cases: (a) imaging in which the total number of sequence repetitions is fixed and (b) imaging in which the total imaging time is fixed. A range of reasonable interpulse delay times is provided for the case of fixed total imaging time. The analysis of optimal interpulse delay times presented in this article makes several assumptions about the imaging system:
Table I. Equations for signal strength from saturation recovery, inversion recovery, and spin-echo sequences Saturation recovery (with a rephasing pulse) or spin-echo: Pulse sequence: 90°-TE/2-l800-TE/2-measurement-T-repeat TR ~ TE + T •I
I•
Signal strength:
S
~ kN(H)e-TEjT'(1 _
2e-(TR-TEj2)jT,
+ e- TRj T,)
Inversion recovery (with a rephasing pulse): Pulse sequence: 180°-TI-900-TE/2-l800-TE/2-measurement-T-repeat I. TR ~ TI + TE + T ---+ I Signal strength: S = kN(H)e -TEjT'll
_
2e- TilT,
+ 2e-(TR-TEj2)jT, _
e- TRj T,
I
are scarce, but to date no counter-example to this assumption is known.
where N(H;) and T li are the spin density and longitudinal relaxation time of tissue i. With tissues A and B labeled according to the equation above, it is assumed that the transverse relaxation times of the two tissues satisfy the condition T 2A < T 2B• This statement assumes that tissues with higher spin densities and lower T , values also have lower T 2 values. Accurate data on spin density, T 1 and T 2 values for in vivo tissues
The equations for signal strength from SR, IR, and SE sequences are summarized in Table I. The SR and IR sequence equations in Table 1 include the case of a 1800 rephasing pulse and an echo delay of duration TE between 90° read pulses and signal measurement. The case of no rephasing pulse or echo delay is described by setting TE to zero in the SR and IR sequence equations. With a rephasing pulse, the SR sequence depicted in Fig. 1 is identical in form to the SE sequence. The sequence has two independent delay times: TE is the time between 90° pulses and signal measurement and TR is the time for a full sequence repetition. Interpulse delay times are chosen differently in the two cases. Typically, SR sequences are applied to emphasize T 1 contrast by setting TE as short as possible and TR to the order of the T 1 values of tissues of interest. On the other hand, SE sequences are applied to emphasize T 2 contrast by setting TE near the T 2 values of tissues of interest and choosing TR values of longer duration than in SR. Evaluation of the best TE and TR values for both approaches is presented in later sections of this report. Inversion recovery with a rephasing pulse is depicted in Fig. 2, where TI is the time between the initial 180° pulse and the subsequent 90° pulse, TE is the time between the 90° pulse and signal measurement, and TR is the repetition time of the full sequence. (TR = TI + TE + T', T' being the time between signal measurement and repetition of the initial 180° pulse.) Typically, IR is a T1-weighted sequence that is
*While we have assumed fixed flip angles of 90° and 180°, in a more general analysis these angles might be included as free parameters to be optimized simultaneously with inter-
pulse delay times. This possibility is mentioned briefly in ref. 7, but a complete optimization analysis with flip angles as free parameters has yet to be carried out.
1. Pulse sequences consist of homogeneous 90° and 180° pulses with rectangular profiles, applied for a time that is short compared with all interpulse delay times.* 2. In combining multiple scans into a single image, signals add coherently, while noise adds incoherently. Equal noise levels are assumed for all tissues in a scan. 3. Planar reconstruction of single slices is assumed. The results derived for single slice acquisition apply to multislice acquisition with the caveat that short repetition times (TR) and long echo delay times (TE) may limit the number of slices acquired simultaneously. 4. We consider the contrast between two tissues, A and B, labeled such that
Optimizing contrastin MRI • R. E. HENDRICK ET AL.
RF
195
90·x' IBO·y'
~_TE_---.~
_
Mz Fig. I. Schematic plot of the radiofrequency (RF) pulse sequence for saturation recovery (applied with a rephasing pulse) or spin-echo. Plotted below the pulse sequence are typical longitudinal (M z) and transverse (My) magnetization components for this sequence. My' is the transverse magnetization measured in a reference frame rotating at the Larmor frequency relative to the laboratory. The vertical dashed lines and the letter M indicate the times at which the signal, My., is measured. For schematic purposes the durations of RF pulses have been exaggerated.
+
applied with TE at or near the minimum echo delay time of the system. The scales of TI and TR are determined by the T, values of the tissues of interest. The absolute value of the IR signal appears in Table 1 because most current magnetic resonance reconstruction algorithms present images representing the magnitudes of received signals. As pointed out elsewhere' J this leads to a loss of contrast for some interpulse delay settings in IR imaging. Optimal values of the three independent interpulse delay times in IR are determined in later sections of this article.
INVERSION RECOVERY WITH REPHASING PULSE
RF
Jf
====r=
T1
=:.F
TE
A
'ft
90[Ji~"
"1 I
I
TR
M
M
~
t I I I
1 I
I I I
I I I
:~Spin Echo
- - - _......~---M Fig. 2. Plot of the inversion recovery radiofrequency (RF) pulse sequence (with rephasing pulses), and typical longitudinal (M z) and transverse (My.) components of the magnetization in the rotating reference frame. The vertical dashed lines and the letter M indicate the times at which the signal, My., is measured. For schematic purposes, the durations of RF pulses have been exaggerated.
GENERAL APPROACH TO CONTRAST OPTIMIZATION The contrast-to-noise ratio is a single quantity that attempts to describe both tissue contrast and signalto-noise ratios. The contrast-to-noise ratio has been shown by Wehrli et al." to accurately reflect tissue differentiation in magnetic resonance images. Consider a planar image reconstructed from a single scan of Nlines of data, giving Nlines X Nlines pixels in the reconstructed planar image. The time for acquisition of a single line of data is TR, the sequence repetition time. The contrast between two tissues, A and B, is proportional to the signal difference, Stl: (1)
The proportionality constant between C and S tl is often taken to be the inverse of Smax = kN(HmaJ, the maximum pixel value attainable from either tissue in the image." The critical point in this analysis is that the proportionality constant between C and S tl does not vary with changes in interpulse delay times. Thus, the maximum contrast-to-noise ratio occurs at the same interpulse delay times as the maximum signal difference-to-noise ratio. Because of this, our notation adopts the simplifying convention that the proportionality constant is unity. Assuming equal noise levels, a, from each tissue in the image, the contrast-to-noise ratio (CjN) for tissues A and B from a single scan (typically Nlines of data) is
C/N 1 = SA - SB (N.hnes )1/2 •
(2)
U
If N ayg scans are combined to produce the final image, then since signals add coherently while noise adds
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Magnetic Resonance Imaging. Volume 2, Number 3,1984
incoherently, the contrast-to-noise ratio is (3)
where the total time for image acquisition is (4)
Two separate cases of contrast-to-noise optimization are considered: (a) imaging with a fixed number of averages and (b) imaging with fixed total time. The first case seeks the best interpulse delay times independent of the total time for image acquisition. The second case seeks the best interpulse delay times given that the shorter TR is made, the more averages may be used to construct the final image. Optimal interpulse delay times can differ considerably in the two cases. For case (a), Navg in Eq. 3 is fixed during the optimization of C jN. Therefore, finding the interpulse delay times maximizing CjN in Eq. 3 is equivalent to maximizing CjN j in Eq. 2. That is, optimizing interpulse delay times for Navg fixed is equivalent to maximizing CjN for a single sequence repetition. For case (b) r.; not Navp is fixed. The quantity to be maximized with respect to each interpulse delay time is then
introducing a TR -1/2 dependence in addition to the TR dependence of the signals from tissues A and B. The
TR - 1/2 term accounts for the greater number of averages that can contribute to the final image if the 'sequence repetition time is made shorter. The optimization of contrast-to-noise ratios with respect to each interpulse delay time (generically referred to as TD) makes use of the simple condition for maximizing a function with respect to several variables, namely, that the maximum of the contrastto-noise ratio occurs where either:
I
d(CjN) d(TD) TD~TD.p,
(1)
2(CjN)
or (2) TD
=
TD opt at an extremum (e.g., at TD opt
TR
~
apt
Spin-echo:
TR opt ->
00
Inversion recovery (with a rephasing pulse):
TRap, ->
00
[I
0).
OPTIMAL INTERPULSE DELAY TIMES WITH FIXED In this section, results of the optimization process with N avg fixed are presented for SR, IR, and SE sequences. For Navg fixed in these three sequences, exact analytic expressions have been derived for the interpulse delay times that optimize contrast-to-noise ratios. The results are summarized in Table 2 and discussed below for each pulse sequence.
«:
TE min T I A T IB T IB _ T I A
=
These two conditions may be distinguished by a direct comparison of calculated contrast-to-noise ratios at the local maxima and extrema to determine the overall maximum.
Saturation recovery (with a rephasing pulse): ~
I
'th d 2 <0 d(TD) TD~TD.P'
Wi
Table 2. Optimized interpulse delay times with N av8 fixed
TE op,
-0
(N(H A ) TIB) _ TE . T 2B - T 2A] moo T T 2B 2A
n N(H B ) T I A
Optimizing contrast in MRI • R. E. HENDRICK ET AL.
Saturation recovery or spin-echo sequences Both saturation recovery (with rephasing pulses) and spin-echo are described by the same sequence equation, given in Table 1. Since for clinically relevant imaging applications TE « TR, we may use the approximate expression for the difference signal between tissues A and B for a single sequence repetition:
S/1 = kN(H A) e- TE/TlA(1 _ e- TR/TIA) _ kN(H B ) e- TE/ T,B(1 _ e-TR/T'B).
197
as the SE maximum. It usually occurs at nonzero TE values that maximize the difference between spin-spin "relaxation rates of the two tissues. An analytic expression for TEoPl in SE for N avg fixed may be found by differentiation of CjN with respect to TE:
(9)
(6)
For N avg fixed, CjN = S/1Navgl/2, and it is simply S/1 that must be maximized with respect to each independent interpulse delay time to determine optimal delay times. For tissues satisfying assumption (4), the CjN ratio has two maxima that occur at distinctly different values of TE and TR. The first maximum is due to T1-dependent contrast and is referred to as the SR maximum, occurring at relatively short TR values. The SR maximum can be shown to occur at TE = 0 for tissues satisfying assumption (4), since CjN is positive at TE = 0 and decreases as TE increases from zero. The loss of T1-dependent contrast as TE increases is due to the T 2 decay of each signal amplitude. It can be minimized only by setting TE to be as short as possible. Based on the assumptions stated above, the optimal interpulse delay times in SR with N avg fixed may be found analytically and are
For N avg fixed the total time (TR) required for SE sequence repetition is not constrained and the contrastto-noise ratio is maximized as TR approaches infinity. For practical purposes, setting TR at 4 to 5 times the largest T 1 value is sufficient to ensure essentially complete recovery of the longitudinal magnetization before beginning the next sequence. Taking TR oPl to be infinity in Eq. (9) gives a simpler expression for TEoPl in the case of N avg fixed:
Inversion recovery sequences In inversion recovery with rephasing pulses, as in SR and SE sequences, the echo delay time TE is short compared to the sequence repetition time TR. The signal difference in IR may be approximated by the expression:
S/1 = kN(HA)e-TE/TlA 11 - 2e- Tl / T'A (7)
Setting TE to zero means doing away with the rephasing 1800 pulse and measuring the free induction decay signal immediately after the 90 0 read pulse. However, in magnetic resonance imaging this procedure usually is not possible. A nonzero TE value has a subtle effect on the TR value at which tissue contrast is maximized. For an imaging system with a nonzero minimum attainable TE value of TE rnin, the optimal TR value is
+ e-TR/T'A I
- kN(HB)e-TE/T,B 11 - 2e- Tl / T'B
(11)
As in SR and SE, optimizing the IR CjN ratio with Navg fixed is equivalent to maximizing S/1 with respect to each delay time. For tissues satisfying assumption (4), the maximum CjN ratio occurs in IR sequences at TE oPl ~ 0 and TR oPl approaching infinity. An analytic expression for the optimum TI value is found by differentiation of C jN with respect to TI:
(12) (8)
which is weakly dependent on TE rnin • There exists a second maximum of the contrastto-noise ratio due to T2-dependent contrast, referred to
In IR with rephasing pulses, as in SR, T1-dependent contrast is reduced as TE increases from zero, suggesting that TE should be made as small as possible to maximize T1-dependent tissue contrast.
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OPTIMAL INTERPULSE DELAY TIMES WITH Ttota I FIXED Fixing the total imaging time for acquisition of a planar image poses a more challenging problem for contrast-to-noise optimization. With fixed total time, an interplay exists between making TR short, which permits larger numbers of scans to be averaged into a single image, and making TR long, which permits more complete T 1 recovery before initiating the next sequence. The mathematical expression for the contrast-to-noise ratio for T tot fixed is given by Eq. 5, where the TR dependence occurs both in signal amplitudes, SA and SB, and in the TR -I/Z factor. Where possible, analytic expressions have been derived for the interpulse delay times that maximize tissue contrast. Where analytic expressions for optimal interpulse delay times are not possible, parametric expressions that approximate the optimal interpulse delay times are given. These parametric expressions are determined by numerically optimizing the contrast-to-noise ratio for a clinically relevant range of hydrogen spin density, T I, and T z values (0 < T IA ~ T]B ~ 1 s, 0 < T ZA < T ZB ~ 200 ms, 0.8 ~ N(H B) / N(H A ) ~ 1.2), and then performing a least-squares fit to that data set. The parametric expressions are not unique, but provide a reasonable guide to the choice of interpulse delay times maximizing tissue contrast. Both exact and approximate expressions for optimal interpulse delay times in SR, SE, and IR with t.; fixed
are summarized in Table 3 and discussed below. For each interpulse delay time, ranges that preserve approximately 80% of the maximum contrast-to-noise ratio are given in Table 4. Saturation recovery and spin-echo sequences In SR (with rephasing pulses) and SE sequences with fixed T tot , the contrast-to-noise ratio is well approximated by
C/N
=
[kN(HA)e-TE/TlA(1 _ e- TR/TIA)
_ kN(H B) e- TE/ T'B(1 _ e-TR/T'B)] (J
As in the case of fixed Navp for tissues satisfying assumption (4) the T]-dependent maximum occurs at TE = O. An expression for the TR value giving maximum tissue contrast cannot be found analytically, . but a good approximation is given by one-half the value of TR opt for the case of N avg fixed:
(14)
Table 3. Optimal interpulse delay times with T tot fixed Saturation recovery (with a rephasing pulse): TE opt
~
TR
~ ~2 TT
opt
TErn!"
1B
1A -
[I (N(H N(H
T 1B T 1A n
A) B
)
T 1B ) T 1A
_
TE . T ZB rnm
-
T ZA ]
T ZA T ZB
(approximate)
Spin-echo: (exact)
(approximate) Inversion recovery:
(13)
(Ttot/TR)I/Z
Optimizing contrast in MRI • R. E.
199
HENDRICK ET AL.
Table 4. 80% range of interpulse delay times with T tot fixed Saturation recovery: 0.3 rn., < TR < 2.5TR opt Spin-echo: 0.52 [N(HA)j N(H B ) ]
rs., < TE <
1.75 [N(HA)j N(H B ) ] TE opt
0.5TR opt < TR < 2.25TR op, Inversion recovery: 0.53TI opt < TI < 1.73TIopt TI + TE < TR < 2.5TR opt Over the clinically relevant range of T 1, T z, and spin density values stated above, use of this approximation for TRopt gives a CjN ratio within 1% of its maximum value found by numerical maximization of Eq. 13. Setting TR within the range 0.3 TRopt < TR < 2.5 TRopt preserves at least 80% of the maximum contrastto-noise ratio attainable at that value of TE min• For tissues satisfying assumption (4), a second maximum of CjN exists at larger TR values and (usually) nonzero TE values due to Tz-dependent contrast. The TE value at which maximum contrast-to-noise occurs can be found analytically in terms ofTRoPl' and is given by
TEoPl and
rx.; as:
0.52 [N(HA)j N(H B) ] TEopt < TE < 1.75 [N(HA)j N(H B)]
rn.,
0.5TRopt < TR < 2.25TRopt.
Inversion recovery The contrast-to-noise ratio in IR with T tot fixed may be approximated by the equation: CjN
=
[kN(H A) e- TE/T" 11 _ 2e- TI / TIA+ e-TR/TIA - kN(H B) e-TE/T,B
.Jl -
2e- TI / T'B
+ e-TR/T,B!J
I
(17)
(TtotjTR)l/Z
(15)
No analytic expression can be derived for TRop!> but a reasonable parametric expression is
As in the case of N a vg fixed, with tissue parameters satisfying assumption (4) CjN for IR has a maximum at TE = 0 and drops off as TE increases. The TI value at which contrast-to-noise is a maximum may be found analytically in terms of TE min and is identical to its value in IR for N a vg fixed:
(18)
Together, Egs. 15 and 16 give a contrast-to-noise ratio within a few percent of its maximum value found by numerical maximization over the range of spin density, Tl> and T, values stated above. A guideline for an acceptable range of SE delay times is provided in Table 4. The range is determined by establishing the TI values that degrade CjN by no more than 20% with TR fixed at TRopt, and by establishing the TR values that degrade CjN by no more than 20% with TI fixed at TloPI' That range is given approximately in terms of
Because of the additional TR dependence of CjN in the case of T t ol fixed, the contrast-to-noise ratio peaks at finite TR values. No analytic solution for TR oPl is possible, but a reasonable approximation for TRopt is found to be
(19)
Magnetic Resonance Imaging. Volume 2, Number 3,1984
200
Note the reversal of the spin density factors in the argument of the logarithm between Eqs. 18 and 19. Use of this approximation for TR apt along with the exact expression for TI apt in Eq. 18 gives contrastto-noise ratios within a few percent of maximum values found by numerical optimization for the clinically relevant range of tissue characteristics. Because TE cannot be set to zero in most imaging systems, the expressions for TI apt and TRapt are given in terms of TE min , the smallest TE setting available on the imaging system. The range ofTI and TR values that gives CjN to within 80% of its maximum is 0.53TI opt < TI < 1.73TI opt
~
6SA _--------~,.
»"
/
/
"
//
»: ..--
/
...........
. . . »«:
..--'
"
S8 _ . -
~.
"
............
",/
I
",/
/
l.Y' / o
TI + TE < TR < 2.5TR opt '
3A
SIGNAL STRENGTH
TR (sec)
.25
.50
.75
1.00
3B
EXAMPLES OF TISSUE DIFFERENTIATION To illustrate the optimization of tissue contrastto-noise ratios in SR, IR, and SE sequences we consider the example of white matter-gray matter contrast in images acquired at 0.5 T. Wehrli et al." recently measured the following values for tissue parameters at this field strength by a least-squares fit to signals from four inversion recovery sequences (to determine T 1) and four spin-echo sequences (to determine T 2 ) : White matter Gray matter (corpus callosum) (cerebrum)
T1 T2 Hydrogen spin density (normalized to CSF ~ 1.00)
0.375 s 0.070 s
0.550 s 0.080 s
0.72
0.84
To illustrate the effect of spin densities on optimal interpulse delay times in the SR, SE, and IR examples that follow, we consider cases of equal hydrogen spin densities as well as the unequal spin densities listed above. Saturation recovery (with echo delay) or spin-echo sequences The optimization of contrast-to-noise in SR with N avg fixed is illustrated by considering the relative signal strengths from white matter and gray matter at TE = O. Figure 3 shows the dependence of SA (white matter), SB (gray matter), and Sil (the signal difference) on TR. Figure 3A shows the case of equal spin densities and Fig. 3B the case of unequal spin densities listed above. While SA and SB have maxima as TR approaches infinity in each case, Sil' which is proportional to the CjN ratio for N avg fixed, peaks at a finite value of TR. The CjN maximum in SR is given exactly by the expression for TR opt in Eq. 8 for both
SIGNAL STRENGTH
TR (sec)
o
.25
.50
.75...........
... ...
1.00 ..... .....
... ...
Fig. 3. Plot of SA' SB, and 6S A versus TR in saturation recovery with TE ~ O. A ~ white matter; B ~ gray matter; Ll = the difference between signals. In this example, T 1A ~ 0.375 s, T I B ~ 0.550 s at 0.5 T. A: Plot for equal hydrogen spin densities. B: Plot for a white matter hydrogen density of 0.72 and a gray matter density of 0.84. Arrows indicate the optimum delay times predicted by Eq. 7 for these two cases: (a) at TR apt = 0.45 s and (b) at TRapt ~ 0.27 s.
equal and unequal spin densities and for both zero and nonzero TE min values. The dependence of the white matter-gray matter CjN ratio on both TE and TR in saturation recovery and spin-echo with N avg fixed is illustrated as a contour plot in Fig. 4, where equal spin densities for the two tissues are assumed. The TI-dependent SR maximum occurs at TE apt = 0 and at the TR opt given exactly by Eq. 7, a TR value slightly smaller than the T 1 value of either tissue. The CjN ratio drops precipitously as TE increases from zero. The Trdependent SE maximum occurs at nonzero TE values given exactly by Eq. 10 with TR opt approaching infinity. The corresponding example of CjN maximization with Tlot fixed is illustrated in Fig. 5, again for SR or SE sequences assuming equal spin densities for white
Optimizing contrast in MRI • R. E.
201
HENDRICK ET AL.
5A
TEems) 10% 180
20'%
150
30%
120
90
60 30
o
1.0
2.0
3.0
4.0
Fig. 4. Contour plot of white matter-gray matter contrastto-noise ratio as a function of TE and TR in saturation recovery (with rephasing pulses) and spin-echo for N avg fixed, assuming equal hydrogen spin densities for the two tissues.
and gray matter. The primary differences between Figs. 4 and 5 are that (a) for T IOI fixed (Fig. 5) the SR maximum occurs at a TR oPI value that is roughly one-half the TR oPI value for the case of N avg fixed (Fig. 4), and (b) the SE maximum occurs at the same TEoPI but at a finite TR opl in the case of T i ol fixed. Figure 5A shows the region of the T]-dependent SR maximum; Fig. 58 spans wider TE and TR ranges to include the SE maximum. Note that the SE maximum is only 12% of the SR maximum in this example, primarily because the T 2 values of the two tissues are similar while T] values differ considerably. Small changes in spin densities have a major effect on the interpulse delay times that maximize contrastto-noise ratios, as illustrated by comparison of Figs. 5 and 6. Figure 6 shows white matter-gray matter contrast-to-noise ratios with the unequal spin densities measured by Wehrli et al." rather than equal spin densities. A major shift occurs in both the location and strength of the SE maximum. The SE maximum now occurs at TEoPI = 0 and is 76% of the SR maximum in this case, due primarily to spin density induced contrast rather than T 2 induced contrast. The parametric expressions of TE oPI and TR oPI in Eqs. 15 and 16 predict the SE maximum to be at TEoPI ~ .001 sand TR oPI = 1.98 s, which gives a C/N value well within 1% of the numerically determined maximum at TE = 0 and TR ~ 2.20 s. Inversion recovery sequences The optimization of IR interpulse delay times is illustrated for the case of T IOI fixed and unequal spin densities in Fig. 7, which plots C/N contours against TE and TI, with TR fixed at TRopl = 1.65 s. The TI
58
TEems)
180
150
\ \ \ \ \
\ \ \
120
90
\ \
\ \
\
60
\0%
\
\
30
,, , "-... .......
1.0
2.0
3.0
4.0
Fig. 5. Contour plot of white matter-gray matter contrastto-noise ratio versus TE and TR in SR and SE for T l ot fixed, assuming equal hydrogen spin densities for the two tissues. A: The T]-dependent SR maximum only is shown. B: A wider TE and TR range is shown to include the Tz-dependent SE maximum.
value at which C/N peaks varies weakly with TE, and is given exactly by Eq. 18. As in SR, with tissues satisfying assumption (4) the C/N ratio peaks at TE = o and falls as TE increases. However, the falloff of C/N with TE is less severe in IR than in SR. For example, in an imaging system which has TE min = 30 ms, C/N in IR is reduced by only 30% at properly chosen TI and TR values, while C/N in SR is reduced by more than 50% for the best choice of TR values. This general behavior may explain why early clinical studies on systems with moderate TE min values favored IR over SR as a source of T] contrast, while early theoretical studies that ignored TE effects in SR and IR claimed that SR should give superior T] contrast. Figure 7 also shows the region of contrast reduction
202
Magnetic Resonance Imaging. Volume 2, Number 3, 1984 TE (ms) 40
180 35 150
30
120
25 20
90
15 60
10 30
5 lJl1J>ll..lo..U~L)..~--.------r~--,.--~-~TR (sec) 3.0 1.0 2.0 4.0 5.0
Fig. 6. Contour plot of the white matter-gray matter contrast-to-noise ratio as a function ofTE and TR in SR and SE for T,o, fixed, using the unequal hydrogen spin densities measured by Wehrli et al. 17 for the two tissues. The SE maximum is moved to TE ~ 0 due to spin density differences.
0.2
e,--"-r-'-~----''-r--'---f--'-r----'--,-l..,. TI
04
0.6
0.8
1.0
(s ee)
Fig. 7. Contour plot of the white matter-gray matter contrast-to-noise ratio as a function of TE and TI in inversion recovery for T ,o! fixed, using the unequal hydrogen densities of the two tissues measured by Wehrli et al."
CONCLUSIONS The primary goal of this work is to present a general method for maximizing contrast-to-noise ratios in magnetic resonance imaging arid to apply that method to some of the more common pulse sequences. Our work includes certain realistic conditions, such as unequal spin densities and rephasing pulses in SR and IR imaging sequences. Optimal interpulse delay times have been found for SR, IR, and SE sequences in the two distinct cases of N avg fixed and TIOI fixed. In all cases with N avg fixed (summarized in Table 2) and in some cases with TIOI fixed (summarized in Table 3), exact analytic expressions have been found for the optimal interpulse delay times in terms of spin density, T lo and T 2 values for the tissues of interest. In cases in which analytic solutions are not possible, parametric expressions that provide a good approximation of opti-
mal interpulse delay times have been found by leastsquares fitting of numerically optimized pulse sequences over the clinically relevant range of spin density, T j , and T 2 values. Equally important, a range of reasonable values for each interpulse delay time is presented .in Table 4, based on the arbitrarily chosen criterion of preserving at least 80% of maximum tissue contrast. One observation that can be drawn from Table 4 is that the selection of most interpulse delay times is forgiving. In some cases, delay times can be off by as much as a factor of two and still give greater than 80% of maximum contrast. However, the echo delay time TE, the time between 90° pulses and signal measurement, can seriously affect Tj-dependent tissue contrast in SR and IR sequences applied with rephasing pulses. Even TE values on the order of 15-30 ms result in significant T 2 signal decay, reducing Tj-induced tissue contrast. That TEmin cannot be set arbitrarily small in most existing imaging systems has at least two effects on tissue contrast in magnetic resonance images. The first is that contrast in SR and IR sequences is severely reduced by moderate machine-imposed TE min values, while contrast in SE sequences usually is not affected. The best T 2 tissue contrast usually occurs at TE values similar to the T 2 values of the tissues being imaged, which generally are larger than TE min • The Tj-dependent contrast in SR and IR sequences, on the
tAn example of a T1-weighted sequence with positive definite signals is the IR-SR sequence of ref. 7 with inter-
pulse delay times chosen appropriately (TA notation).
due to loss of information about the sign of the IR signal. For the case of equal spin densities this region of contrast loss occurs for TI values that are shorter than TIoPI.Jj However, as in Fig. 7, unequal spin densities may move this region of contrast loss near the TI values that optimize tissue contrast. This poses a potential liability for IR imaging that can be overcome either by switching to other Tj-weighted sequences'[ or by preserving sign information in each pixel or voxel of the reconstructed image.
~
T B in their
Optimizing contrast in MRI. R. E. HENDRICKETAL.
other hand, is seriously degraded by any nonzero TEmin value. This may be the reason that clinical studies on imaging systems with TE min on the order of 30 ms have turned to SE sequences as a primary source of tissue contrast. Such imaging systems throwaway considerable T, contrast at the outset, so Tz-weighted sequences such as spin-echo are the only alternative for reasonable tissue contrast. This, in turn, has a deleterious effect on the total time required to acquire an image with reasonable contrast. SE sequences with maximized contrast generally require much longer TR values (by a factor of 3 to 10) than SR sequences with good contrast. If TE min could be shortened so that the imaging system was made more sensitive to T[-dependent contrast, total patient imaging times might be shortened considerably. Second, with rephasing pulses and nonzero TE min values, IR sequences suffer less contrast loss from T,
203
decay than do SR sequences. This may explain why early clinical studies preferred IR to SR as a source of T,-dependent tissue contrast, while early theoretical analyses (which ignored the effects of nonzero TE min values in SR and IR) indicated that SR should provide better contrast. This point will be explored more fully in a subsequent article" which considers the effects of nonzero TE min and unequal spin densities on the choice of the best imaging sequences for a particular imaging task. Finally, it is worth noting that short TR values do not necessarily limit the rnultislice capabilities of imaging systems. The number of simultaneously acquired slices is not simply proportional to TR, but to TRITE. Thus, if TE is shortened to a reasonably small TEmin value, while TR is shortened to a value which maximizes T 1 contrast, large numbers of simultaneously acquired slices are still possible.
REFERENCES 1. Bydder, G.M.; Doyle, F.H.; Young, I.R.; Hall, A.S. NMR: initial clinical results. Witcofski, R.L.; Karstaedt, N.; Partain, C.L., eds. NMR imaging, proceedings ofan international symposium on nuclear magnetic resonance imaging. Winston-Salem, NC: BowmanGray School of Medicine; 1982:107-113. 2. Bydder, G.M.; Steiner, R.E.; Young, I.R.; Hall, A.S.; Thomas, D.J.; Marshall, J.; Pallis, c.x., Legg, N.J. Clinical NMR imaging of the brain: 140 cases. Am. J. Roentgenol. 138:215-236; 1982. 3. Crookes, L.E.; Hoenninger, J.; Arakawa, M.; Watts, J.; McCarten, B.; Sheldon, P.; Kaufman, L.; Mills, C.M.; Davis, P.; Margulis, A.R. High resolution magnetic resonance imaging. Radiology 150:163-171; 1984. 4. Crooks, L.E.; Mills, C.M.; Davis, P.L.; Brant-Zawadzki, M.; Hoenninger, J.; Arakawa, M.; Watts, J.; Kaufman, L. Visualization of cerebral and vascular abnormalities by NMR imaging: the effects of imaging parameters on contrast. Radiology 144:843-852; 1982. 5. Davis, P.L.; Kaufman, L.; Crooks, L.E. Potential diagnostic specificity of NMR. Witcofski, R.L.; Karstaedt, N.; Partain, C.L., eds. N M R imaging, proceedings ofan international symposium on nuclear magnetic resonance imaging. Winston-Salem, NC: Bowman-Gray School of Medicine; 1982:101-105. 6. Davis, P.L.; Kaufman, L.; Crooks, L.E.; Margulis, A.R. NMR characteristics of normal and abnormal rat tissues. Kaufman, L.; Crooks, L.E.; Margulis, A.R., eds. Nuclear magnetic resonance imaging in medicine. New York: Igaku-Shoin; 1981:71-100. 7. Edelstein, W.A.; Bottomley, P.A.; Hart, H.R.; Smith, L.S. Signal, noise, and contrast in nuclear magnetic resonance (NMR) imaging. J. Comput. Assist. Tomogr. 7:391-401; 1983. 8. Edelstein, W.A.; Bottomley, P.A.; Hart, H.R.; Leue, W.M.; Schenck, J.F.; Redington, R.W. NMR imaging at 5.1 MHz: work in progress. Witcofski, R.L., Karstaedt, N.; Partain, e.L., eds. NMR imaging, proceedings ofan international symposium on nuclear magnetic
resonance imaging. Winston-Salem, NC: BowmanGray School of Medicine; 1982:139-145. 9. Gore, J.e. The meaning and significance of relaxation in NMR. Witcofski, R.L., Karstaedt, N.; Partain, C.L., eds. NMR imaging, proceedings of an international symposium on nuclear magnetic resonance imaging. Winston-Salem, NC: Bowman-Gray School of Medicine; 1982:15-23. 10. Gore, J.C.; Doyle, F.H.; Penncock, J.M. Relaxation rate enhancement observed in vivo by NMR imaging. Partain, e.L.; James, A.E.; Rollo, F.D.; Price, R.R., eds. Nuclear magnetic resonance (NMR) imaging. Philadelphia: W.B. Saunders; 1983:94-106 11. Hendrick, R.E.; Nelson, T.R. Phase detection and contrast loss in magnetic resonance imaging. Magn. Reson. Imaging (in press). 12. Hendrick, R.E.; Nelson, T.R.; Hendee, W.R. Choosing pulse sequences and interpulse delay times in NMR imaging. Jaklovsky, J., ed. NMR imaging:future potential. Reading, MA: Addison-Wesley: 1984: (in press). 13. Nelson, T.R.; 'Hendrick, R.E.; Hendee, W.R. Selection of pulse sequences producing maximum tissue contrast. Magn. Reson. Imaging (in press). 14. Berman, W.H.; Hilal, S.K.; Simon, H.E.; Maudsley, A.A. Contrast manipulation in NMR imaging. Magn. Reson. Imaging 2:23-32; 1984. 15. Straughan, K.; Spencer, D.H.; Bydder, G.M. NMR clinical results: Hammersmith. Partain, e.L.; James, A.E.; Rollo, F.D.; Price, R.R., eds. Nuclear magnetic resonance (NMR) imaging. Philadelphia: W.B. Saunders; 1983:145-206. 16. Taylor, D.G.; Bore, C.F. A-review of the magnetic resonance response of biological tissue and its applicability to the diagnosis of cancer by NMR radiology. CT 5:122~133; 1981. 17. Wehrli, F.W.; MacFall, J.R.; Glover, G.H.; Grigsby, N. The dependence of nuclear magnetic resonance (NMR) image contrast on intrinsic and pulse sequence timing parameters. Magn. Reson. Imaging 2:3-16; 1984.
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18. Wehrli, F.W.; MacFall, J.R.; Newton, T.H. Parameters determining the appearance of NMR images. Newton, T.H.; Potts, D.G., eds. Modern neuroradiology, vol. 2: Advanced imaging techniques. San Anselmo, CA: Clavadel Press; 1983:81-117. 19. Young, I.R.; Bailes, D.R.; Collins, A.G.; Gilderdale, D.J. Image options in NMR. Witcofski, R.L.; Karstaedt, N.; Partain, C.L., eds. NMR imaging, proceed-
ings ofan international symposium on nuclear magnetic resonance. Winston-Salem, NC: Bowman-Gray School of Medicine; 1982:93-100. 20. Young, E.R.; Bailes, D.R.; Collins, A.G.; Gilderdale, D.J. Image choice in NMR. Partain, C.L; James, A.E.; Rollo, F.D.; Price, R.R., eds. Nuclear magnetic resonance (NMR) imaging. Philadelphia, W.B. Saunders; 1983:183-191.
193-204, 1984 Copyright ©
0730-725X/84 $3.00+ .00 1984 Pergamon Press Ltd .
• Original Contribution OPTIMIZING TISSUE CONTRAST IN MAGNETIC RESONANCE IMAGING
R. E.
HENDRICK,
T. R.
NELSON, AND WILLIAM
R.
HENDEE
Department of Radiology, University of Colorado Health Sciences Center, Denver, Colorado 80262 Magnetic resonance imaging demands that tissue contrast and signal-to-noise advantages be sought in each component of the imaging system. One component of magnetic resonance imaging in which contrast and signal-to-noise ratios are easily manipulated is in the choice of pulse sequences and interpulse delay times. This article provides a general method for determining the best choices of interpulse delay times in pulse sequences and applies that method to saturation recovery, inversion recovery, and spin-echo sequences. Saturation recovery and inversion recovery sequences with rephasing pulses, and tissues with unequal hydrogen densities are considered. Optimization of pulse sequences is carried out for the two distinct cases of (a) a fixed number of sequence repetitions and (b) a fixed total imaging time. Analytic expressions are derived or approximate expressions are provided for the interpulse delay times that optimize contrast-to-noise ratios in each pulse sequence. The acceptable range of interpulse delay times to obtain reasonable contrast using each pulse sequence is discussed. Keywords: Magnetic resonance imaging, Tissue contrast, Signal-to-noise ratio, Interpulse delay times, Pulse sequence optimization.
INTRODUCTION Increased tissue contrast and improved signal-to-noise ratios are of paramount importance in magnetic resonance imaging. Each component of the magnetic resonance imaging system is designed to enhance contrast, improve signal-to-noise ratios, and reduct patient imaging time. One component of magnetic resonance imaging in which contrast and signal-to-noise improvements are possible without physically' altering the system is in the selection of pulse sequences and interpulse delay times, Considerable clinical and theoretical work has been done to address the question of the best choice of pulse sequences and interpulse delay times for particular imaging tasks. 1-1O,12,14-20 Early work by Taylor and Bore" focused on the effect of water content and T 1 values on signal-to-noise ratios; they concluded that a single imaging sequence will not always give the best tissue contrast. Edelstein et alY addressed the question of interpulse delay times giving the best signal difference-to-noise ratios in T1-weighted sequences for tissues with equal hydrogen spin densities. More recent work by Wehrli et al.,'? reported variations in hydro-
gen densities of up to 30% for in vivo white matter, gray matter, and cerebrospinal fluid (CSF), suggesting the importance of pulse sequence optimization for unequal spin densities. Other recent work has demonstrated the effect of pulse sequence and interpulse delay time selection on tissue contrast.Y:":" Most analyses have been carried out with one or both of the following simplifying assumptions: (a) tissues are assumed to have identical spin densities (although refs. 12 and 17 are exceptions to this assumption) and (b) saturation recovery and inversion recovery are assumed to be applied without signal rephasing between 90° read pulses and signal measurement (ref. 14 being an exception to this). While these sequences may be applied without rephasing pulses in nuclear magnetic resonance (NMR) spectroscopy, current magnetic resonance imaging systems require rephasing pulses and small delay times prior to signal detection. Delay times on the order of 10 ms are required to apply gradients and reduce receiver saturation before signal measurement can begin. Rather than allowing signal decay due to both spin-spin interactions and magnetic field inhomogeneities during this
RECEIVED 5/1/84; ACCEPTED 5/30/84. Acknowledgment-s-This work was supported in part by Public Health Service Grant Number 5T32CA09073-08, awarded by the National Cancer Institute, Department of Health and Human Services.
Address correspondence and reprint requests to Dr. R. E, Hendrick.
193
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Magnetic Resonance Imaging. Volume 2, Number 3, 1984
period, a rephasing pulse is applied to eliminate transverse relaxation due to field inhomogeneities. Then the spin-echo, the peak of which is reduced only by spinspin ( T 2 ) relaxation of the transverse magnetization, is measured. In this article, we present a general method of determining interpulse delay times that optimize contrast-to-noise ratios. This method is applied to three pulse sequences common to magnetic resonance imaging: saturation recovery or partial saturation (SR), inversion recovery (IR), and spin-scho (SE). The optimization of SR and IR sequences includes the case of rephasing pulses between 90° pulses and signal measurement. The case of tissues with equal and unequal spin densities is considered. Optimal interpulse delay times are determined in two clinically relevant cases: (a) imaging in which the total number of sequence repetitions is fixed and (b) imaging in which the total imaging time is fixed. A range of reasonable interpulse delay times is provided for the case of fixed total imaging time. The analysis of optimal interpulse delay times presented in this article makes several assumptions about the imaging system:
Table I. Equations for signal strength from saturation recovery, inversion recovery, and spin-echo sequences Saturation recovery (with a rephasing pulse) or spin-echo: Pulse sequence: 90°-TE/2-l800-TE/2-measurement-T-repeat TR ~ TE + T •I
I•
Signal strength:
S
~ kN(H)e-TEjT'(1 _
2e-(TR-TEj2)jT,
+ e- TRj T,)
Inversion recovery (with a rephasing pulse): Pulse sequence: 180°-TI-900-TE/2-l800-TE/2-measurement-T-repeat I. TR ~ TI + TE + T ---+ I Signal strength: S = kN(H)e -TEjT'll
_
2e- TilT,
+ 2e-(TR-TEj2)jT, _
e- TRj T,
I
are scarce, but to date no counter-example to this assumption is known.
where N(H;) and T li are the spin density and longitudinal relaxation time of tissue i. With tissues A and B labeled according to the equation above, it is assumed that the transverse relaxation times of the two tissues satisfy the condition T 2A < T 2B• This statement assumes that tissues with higher spin densities and lower T , values also have lower T 2 values. Accurate data on spin density, T 1 and T 2 values for in vivo tissues
The equations for signal strength from SR, IR, and SE sequences are summarized in Table I. The SR and IR sequence equations in Table 1 include the case of a 1800 rephasing pulse and an echo delay of duration TE between 90° read pulses and signal measurement. The case of no rephasing pulse or echo delay is described by setting TE to zero in the SR and IR sequence equations. With a rephasing pulse, the SR sequence depicted in Fig. 1 is identical in form to the SE sequence. The sequence has two independent delay times: TE is the time between 90° pulses and signal measurement and TR is the time for a full sequence repetition. Interpulse delay times are chosen differently in the two cases. Typically, SR sequences are applied to emphasize T 1 contrast by setting TE as short as possible and TR to the order of the T 1 values of tissues of interest. On the other hand, SE sequences are applied to emphasize T 2 contrast by setting TE near the T 2 values of tissues of interest and choosing TR values of longer duration than in SR. Evaluation of the best TE and TR values for both approaches is presented in later sections of this report. Inversion recovery with a rephasing pulse is depicted in Fig. 2, where TI is the time between the initial 180° pulse and the subsequent 90° pulse, TE is the time between the 90° pulse and signal measurement, and TR is the repetition time of the full sequence. (TR = TI + TE + T', T' being the time between signal measurement and repetition of the initial 180° pulse.) Typically, IR is a T1-weighted sequence that is
*While we have assumed fixed flip angles of 90° and 180°, in a more general analysis these angles might be included as free parameters to be optimized simultaneously with inter-
pulse delay times. This possibility is mentioned briefly in ref. 7, but a complete optimization analysis with flip angles as free parameters has yet to be carried out.
1. Pulse sequences consist of homogeneous 90° and 180° pulses with rectangular profiles, applied for a time that is short compared with all interpulse delay times.* 2. In combining multiple scans into a single image, signals add coherently, while noise adds incoherently. Equal noise levels are assumed for all tissues in a scan. 3. Planar reconstruction of single slices is assumed. The results derived for single slice acquisition apply to multislice acquisition with the caveat that short repetition times (TR) and long echo delay times (TE) may limit the number of slices acquired simultaneously. 4. We consider the contrast between two tissues, A and B, labeled such that
Optimizing contrastin MRI • R. E. HENDRICK ET AL.
RF
195
90·x' IBO·y'
~_TE_---.~
_
Mz Fig. I. Schematic plot of the radiofrequency (RF) pulse sequence for saturation recovery (applied with a rephasing pulse) or spin-echo. Plotted below the pulse sequence are typical longitudinal (M z) and transverse (My) magnetization components for this sequence. My' is the transverse magnetization measured in a reference frame rotating at the Larmor frequency relative to the laboratory. The vertical dashed lines and the letter M indicate the times at which the signal, My., is measured. For schematic purposes the durations of RF pulses have been exaggerated.
+
applied with TE at or near the minimum echo delay time of the system. The scales of TI and TR are determined by the T, values of the tissues of interest. The absolute value of the IR signal appears in Table 1 because most current magnetic resonance reconstruction algorithms present images representing the magnitudes of received signals. As pointed out elsewhere' J this leads to a loss of contrast for some interpulse delay settings in IR imaging. Optimal values of the three independent interpulse delay times in IR are determined in later sections of this article.
INVERSION RECOVERY WITH REPHASING PULSE
RF
Jf
====r=
T1
=:.F
TE
A
'ft
90[Ji~"
"1 I
I
TR
M
M
~
t I I I
1 I
I I I
I I I
:~Spin Echo
- - - _......~---M Fig. 2. Plot of the inversion recovery radiofrequency (RF) pulse sequence (with rephasing pulses), and typical longitudinal (M z) and transverse (My.) components of the magnetization in the rotating reference frame. The vertical dashed lines and the letter M indicate the times at which the signal, My., is measured. For schematic purposes, the durations of RF pulses have been exaggerated.
GENERAL APPROACH TO CONTRAST OPTIMIZATION The contrast-to-noise ratio is a single quantity that attempts to describe both tissue contrast and signalto-noise ratios. The contrast-to-noise ratio has been shown by Wehrli et al." to accurately reflect tissue differentiation in magnetic resonance images. Consider a planar image reconstructed from a single scan of Nlines of data, giving Nlines X Nlines pixels in the reconstructed planar image. The time for acquisition of a single line of data is TR, the sequence repetition time. The contrast between two tissues, A and B, is proportional to the signal difference, Stl: (1)
The proportionality constant between C and S tl is often taken to be the inverse of Smax = kN(HmaJ, the maximum pixel value attainable from either tissue in the image." The critical point in this analysis is that the proportionality constant between C and S tl does not vary with changes in interpulse delay times. Thus, the maximum contrast-to-noise ratio occurs at the same interpulse delay times as the maximum signal difference-to-noise ratio. Because of this, our notation adopts the simplifying convention that the proportionality constant is unity. Assuming equal noise levels, a, from each tissue in the image, the contrast-to-noise ratio (CjN) for tissues A and B from a single scan (typically Nlines of data) is
C/N 1 = SA - SB (N.hnes )1/2 •
(2)
U
If N ayg scans are combined to produce the final image, then since signals add coherently while noise adds
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Magnetic Resonance Imaging. Volume 2, Number 3,1984
incoherently, the contrast-to-noise ratio is (3)
where the total time for image acquisition is (4)
Two separate cases of contrast-to-noise optimization are considered: (a) imaging with a fixed number of averages and (b) imaging with fixed total time. The first case seeks the best interpulse delay times independent of the total time for image acquisition. The second case seeks the best interpulse delay times given that the shorter TR is made, the more averages may be used to construct the final image. Optimal interpulse delay times can differ considerably in the two cases. For case (a), Navg in Eq. 3 is fixed during the optimization of C jN. Therefore, finding the interpulse delay times maximizing CjN in Eq. 3 is equivalent to maximizing CjN j in Eq. 2. That is, optimizing interpulse delay times for Navg fixed is equivalent to maximizing CjN for a single sequence repetition. For case (b) r.; not Navp is fixed. The quantity to be maximized with respect to each interpulse delay time is then
introducing a TR -1/2 dependence in addition to the TR dependence of the signals from tissues A and B. The
TR - 1/2 term accounts for the greater number of averages that can contribute to the final image if the 'sequence repetition time is made shorter. The optimization of contrast-to-noise ratios with respect to each interpulse delay time (generically referred to as TD) makes use of the simple condition for maximizing a function with respect to several variables, namely, that the maximum of the contrastto-noise ratio occurs where either:
I
d(CjN) d(TD) TD~TD.p,
(1)
2(CjN)
or (2) TD
=
TD opt at an extremum (e.g., at TD opt
TR
~
apt
Spin-echo:
TR opt ->
00
Inversion recovery (with a rephasing pulse):
TRap, ->
00
[I
0).
OPTIMAL INTERPULSE DELAY TIMES WITH FIXED In this section, results of the optimization process with N avg fixed are presented for SR, IR, and SE sequences. For Navg fixed in these three sequences, exact analytic expressions have been derived for the interpulse delay times that optimize contrast-to-noise ratios. The results are summarized in Table 2 and discussed below for each pulse sequence.
«:
TE min T I A T IB T IB _ T I A
=
These two conditions may be distinguished by a direct comparison of calculated contrast-to-noise ratios at the local maxima and extrema to determine the overall maximum.
Saturation recovery (with a rephasing pulse): ~
I
'th d 2 <0 d(TD) TD~TD.P'
Wi
Table 2. Optimized interpulse delay times with N av8 fixed
TE op,
-0
(N(H A ) TIB) _ TE . T 2B - T 2A] moo T T 2B 2A
n N(H B ) T I A
Optimizing contrast in MRI • R. E. HENDRICK ET AL.
Saturation recovery or spin-echo sequences Both saturation recovery (with rephasing pulses) and spin-echo are described by the same sequence equation, given in Table 1. Since for clinically relevant imaging applications TE « TR, we may use the approximate expression for the difference signal between tissues A and B for a single sequence repetition:
S/1 = kN(H A) e- TE/TlA(1 _ e- TR/TIA) _ kN(H B ) e- TE/ T,B(1 _ e-TR/T'B).
197
as the SE maximum. It usually occurs at nonzero TE values that maximize the difference between spin-spin "relaxation rates of the two tissues. An analytic expression for TEoPl in SE for N avg fixed may be found by differentiation of CjN with respect to TE:
(9)
(6)
For N avg fixed, CjN = S/1Navgl/2, and it is simply S/1 that must be maximized with respect to each independent interpulse delay time to determine optimal delay times. For tissues satisfying assumption (4), the CjN ratio has two maxima that occur at distinctly different values of TE and TR. The first maximum is due to T1-dependent contrast and is referred to as the SR maximum, occurring at relatively short TR values. The SR maximum can be shown to occur at TE = 0 for tissues satisfying assumption (4), since CjN is positive at TE = 0 and decreases as TE increases from zero. The loss of T1-dependent contrast as TE increases is due to the T 2 decay of each signal amplitude. It can be minimized only by setting TE to be as short as possible. Based on the assumptions stated above, the optimal interpulse delay times in SR with N avg fixed may be found analytically and are
For N avg fixed the total time (TR) required for SE sequence repetition is not constrained and the contrastto-noise ratio is maximized as TR approaches infinity. For practical purposes, setting TR at 4 to 5 times the largest T 1 value is sufficient to ensure essentially complete recovery of the longitudinal magnetization before beginning the next sequence. Taking TR oPl to be infinity in Eq. (9) gives a simpler expression for TEoPl in the case of N avg fixed:
Inversion recovery sequences In inversion recovery with rephasing pulses, as in SR and SE sequences, the echo delay time TE is short compared to the sequence repetition time TR. The signal difference in IR may be approximated by the expression:
S/1 = kN(HA)e-TE/TlA 11 - 2e- Tl / T'A (7)
Setting TE to zero means doing away with the rephasing 1800 pulse and measuring the free induction decay signal immediately after the 90 0 read pulse. However, in magnetic resonance imaging this procedure usually is not possible. A nonzero TE value has a subtle effect on the TR value at which tissue contrast is maximized. For an imaging system with a nonzero minimum attainable TE value of TE rnin, the optimal TR value is
+ e-TR/T'A I
- kN(HB)e-TE/T,B 11 - 2e- Tl / T'B
(11)
As in SR and SE, optimizing the IR CjN ratio with Navg fixed is equivalent to maximizing S/1 with respect to each delay time. For tissues satisfying assumption (4), the maximum CjN ratio occurs in IR sequences at TE oPl ~ 0 and TR oPl approaching infinity. An analytic expression for the optimum TI value is found by differentiation of C jN with respect to TI:
(12) (8)
which is weakly dependent on TE rnin • There exists a second maximum of the contrastto-noise ratio due to T2-dependent contrast, referred to
In IR with rephasing pulses, as in SR, T1-dependent contrast is reduced as TE increases from zero, suggesting that TE should be made as small as possible to maximize T1-dependent tissue contrast.
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Magnetic Resonance Imaging. Volume 2, Number 3,1984
OPTIMAL INTERPULSE DELAY TIMES WITH Ttota I FIXED Fixing the total imaging time for acquisition of a planar image poses a more challenging problem for contrast-to-noise optimization. With fixed total time, an interplay exists between making TR short, which permits larger numbers of scans to be averaged into a single image, and making TR long, which permits more complete T 1 recovery before initiating the next sequence. The mathematical expression for the contrast-to-noise ratio for T tot fixed is given by Eq. 5, where the TR dependence occurs both in signal amplitudes, SA and SB, and in the TR -I/Z factor. Where possible, analytic expressions have been derived for the interpulse delay times that maximize tissue contrast. Where analytic expressions for optimal interpulse delay times are not possible, parametric expressions that approximate the optimal interpulse delay times are given. These parametric expressions are determined by numerically optimizing the contrast-to-noise ratio for a clinically relevant range of hydrogen spin density, T I, and T z values (0 < T IA ~ T]B ~ 1 s, 0 < T ZA < T ZB ~ 200 ms, 0.8 ~ N(H B) / N(H A ) ~ 1.2), and then performing a least-squares fit to that data set. The parametric expressions are not unique, but provide a reasonable guide to the choice of interpulse delay times maximizing tissue contrast. Both exact and approximate expressions for optimal interpulse delay times in SR, SE, and IR with t.; fixed
are summarized in Table 3 and discussed below. For each interpulse delay time, ranges that preserve approximately 80% of the maximum contrast-to-noise ratio are given in Table 4. Saturation recovery and spin-echo sequences In SR (with rephasing pulses) and SE sequences with fixed T tot , the contrast-to-noise ratio is well approximated by
C/N
=
[kN(HA)e-TE/TlA(1 _ e- TR/TIA)
_ kN(H B) e- TE/ T'B(1 _ e-TR/T'B)] (J
As in the case of fixed Navp for tissues satisfying assumption (4) the T]-dependent maximum occurs at TE = O. An expression for the TR value giving maximum tissue contrast cannot be found analytically, . but a good approximation is given by one-half the value of TR opt for the case of N avg fixed:
(14)
Table 3. Optimal interpulse delay times with T tot fixed Saturation recovery (with a rephasing pulse): TE opt
~
TR
~ ~2 TT
opt
TErn!"
1B
1A -
[I (N(H N(H
T 1B T 1A n
A) B
)
T 1B ) T 1A
_
TE . T ZB rnm
-
T ZA ]
T ZA T ZB
(approximate)
Spin-echo: (exact)
(approximate) Inversion recovery:
(13)
(Ttot/TR)I/Z
Optimizing contrast in MRI • R. E.
199
HENDRICK ET AL.
Table 4. 80% range of interpulse delay times with T tot fixed Saturation recovery: 0.3 rn., < TR < 2.5TR opt Spin-echo: 0.52 [N(HA)j N(H B ) ]
rs., < TE <
1.75 [N(HA)j N(H B ) ] TE opt
0.5TR opt < TR < 2.25TR op, Inversion recovery: 0.53TI opt < TI < 1.73TIopt TI + TE < TR < 2.5TR opt Over the clinically relevant range of T 1, T z, and spin density values stated above, use of this approximation for TRopt gives a CjN ratio within 1% of its maximum value found by numerical maximization of Eq. 13. Setting TR within the range 0.3 TRopt < TR < 2.5 TRopt preserves at least 80% of the maximum contrastto-noise ratio attainable at that value of TE min• For tissues satisfying assumption (4), a second maximum of CjN exists at larger TR values and (usually) nonzero TE values due to Tz-dependent contrast. The TE value at which maximum contrast-to-noise occurs can be found analytically in terms ofTRoPl' and is given by
TEoPl and
rx.; as:
0.52 [N(HA)j N(H B) ] TEopt < TE < 1.75 [N(HA)j N(H B)]
rn.,
0.5TRopt < TR < 2.25TRopt.
Inversion recovery The contrast-to-noise ratio in IR with T tot fixed may be approximated by the equation: CjN
=
[kN(H A) e- TE/T" 11 _ 2e- TI / TIA+ e-TR/TIA - kN(H B) e-TE/T,B
.Jl -
2e- TI / T'B
+ e-TR/T,B!J
I
(17)
(TtotjTR)l/Z
(15)
No analytic expression can be derived for TRop!> but a reasonable parametric expression is
As in the case of N a vg fixed, with tissue parameters satisfying assumption (4) CjN for IR has a maximum at TE = 0 and drops off as TE increases. The TI value at which contrast-to-noise is a maximum may be found analytically in terms of TE min and is identical to its value in IR for N a vg fixed:
(18)
Together, Egs. 15 and 16 give a contrast-to-noise ratio within a few percent of its maximum value found by numerical maximization over the range of spin density, Tl> and T, values stated above. A guideline for an acceptable range of SE delay times is provided in Table 4. The range is determined by establishing the TI values that degrade CjN by no more than 20% with TR fixed at TRopt, and by establishing the TR values that degrade CjN by no more than 20% with TI fixed at TloPI' That range is given approximately in terms of
Because of the additional TR dependence of CjN in the case of T t ol fixed, the contrast-to-noise ratio peaks at finite TR values. No analytic solution for TR oPl is possible, but a reasonable approximation for TRopt is found to be
(19)
Magnetic Resonance Imaging. Volume 2, Number 3,1984
200
Note the reversal of the spin density factors in the argument of the logarithm between Eqs. 18 and 19. Use of this approximation for TR apt along with the exact expression for TI apt in Eq. 18 gives contrastto-noise ratios within a few percent of maximum values found by numerical optimization for the clinically relevant range of tissue characteristics. Because TE cannot be set to zero in most imaging systems, the expressions for TI apt and TRapt are given in terms of TE min , the smallest TE setting available on the imaging system. The range ofTI and TR values that gives CjN to within 80% of its maximum is 0.53TI opt < TI < 1.73TI opt
~
6SA _--------~,.
»"
/
/
"
//
»: ..--
/
...........
. . . »«:
..--'
"
S8 _ . -
~.
"
............
",/
I
",/
/
l.Y' / o
TI + TE < TR < 2.5TR opt '
3A
SIGNAL STRENGTH
TR (sec)
.25
.50
.75
1.00
3B
EXAMPLES OF TISSUE DIFFERENTIATION To illustrate the optimization of tissue contrastto-noise ratios in SR, IR, and SE sequences we consider the example of white matter-gray matter contrast in images acquired at 0.5 T. Wehrli et al." recently measured the following values for tissue parameters at this field strength by a least-squares fit to signals from four inversion recovery sequences (to determine T 1) and four spin-echo sequences (to determine T 2 ) : White matter Gray matter (corpus callosum) (cerebrum)
T1 T2 Hydrogen spin density (normalized to CSF ~ 1.00)
0.375 s 0.070 s
0.550 s 0.080 s
0.72
0.84
To illustrate the effect of spin densities on optimal interpulse delay times in the SR, SE, and IR examples that follow, we consider cases of equal hydrogen spin densities as well as the unequal spin densities listed above. Saturation recovery (with echo delay) or spin-echo sequences The optimization of contrast-to-noise in SR with N avg fixed is illustrated by considering the relative signal strengths from white matter and gray matter at TE = O. Figure 3 shows the dependence of SA (white matter), SB (gray matter), and Sil (the signal difference) on TR. Figure 3A shows the case of equal spin densities and Fig. 3B the case of unequal spin densities listed above. While SA and SB have maxima as TR approaches infinity in each case, Sil' which is proportional to the CjN ratio for N avg fixed, peaks at a finite value of TR. The CjN maximum in SR is given exactly by the expression for TR opt in Eq. 8 for both
SIGNAL STRENGTH
TR (sec)
o
.25
.50
.75...........
... ...
1.00 ..... .....
... ...
Fig. 3. Plot of SA' SB, and 6S A versus TR in saturation recovery with TE ~ O. A ~ white matter; B ~ gray matter; Ll = the difference between signals. In this example, T 1A ~ 0.375 s, T I B ~ 0.550 s at 0.5 T. A: Plot for equal hydrogen spin densities. B: Plot for a white matter hydrogen density of 0.72 and a gray matter density of 0.84. Arrows indicate the optimum delay times predicted by Eq. 7 for these two cases: (a) at TR apt = 0.45 s and (b) at TRapt ~ 0.27 s.
equal and unequal spin densities and for both zero and nonzero TE min values. The dependence of the white matter-gray matter CjN ratio on both TE and TR in saturation recovery and spin-echo with N avg fixed is illustrated as a contour plot in Fig. 4, where equal spin densities for the two tissues are assumed. The TI-dependent SR maximum occurs at TE apt = 0 and at the TR opt given exactly by Eq. 7, a TR value slightly smaller than the T 1 value of either tissue. The CjN ratio drops precipitously as TE increases from zero. The Trdependent SE maximum occurs at nonzero TE values given exactly by Eq. 10 with TR opt approaching infinity. The corresponding example of CjN maximization with Tlot fixed is illustrated in Fig. 5, again for SR or SE sequences assuming equal spin densities for white
Optimizing contrast in MRI • R. E.
201
HENDRICK ET AL.
5A
TEems) 10% 180
20'%
150
30%
120
90
60 30
o
1.0
2.0
3.0
4.0
Fig. 4. Contour plot of white matter-gray matter contrastto-noise ratio as a function of TE and TR in saturation recovery (with rephasing pulses) and spin-echo for N avg fixed, assuming equal hydrogen spin densities for the two tissues.
and gray matter. The primary differences between Figs. 4 and 5 are that (a) for T IOI fixed (Fig. 5) the SR maximum occurs at a TR oPI value that is roughly one-half the TR oPI value for the case of N avg fixed (Fig. 4), and (b) the SE maximum occurs at the same TEoPI but at a finite TR opl in the case of T i ol fixed. Figure 5A shows the region of the T]-dependent SR maximum; Fig. 58 spans wider TE and TR ranges to include the SE maximum. Note that the SE maximum is only 12% of the SR maximum in this example, primarily because the T 2 values of the two tissues are similar while T] values differ considerably. Small changes in spin densities have a major effect on the interpulse delay times that maximize contrastto-noise ratios, as illustrated by comparison of Figs. 5 and 6. Figure 6 shows white matter-gray matter contrast-to-noise ratios with the unequal spin densities measured by Wehrli et al." rather than equal spin densities. A major shift occurs in both the location and strength of the SE maximum. The SE maximum now occurs at TEoPI = 0 and is 76% of the SR maximum in this case, due primarily to spin density induced contrast rather than T 2 induced contrast. The parametric expressions of TE oPI and TR oPI in Eqs. 15 and 16 predict the SE maximum to be at TEoPI ~ .001 sand TR oPI = 1.98 s, which gives a C/N value well within 1% of the numerically determined maximum at TE = 0 and TR ~ 2.20 s. Inversion recovery sequences The optimization of IR interpulse delay times is illustrated for the case of T IOI fixed and unequal spin densities in Fig. 7, which plots C/N contours against TE and TI, with TR fixed at TRopl = 1.65 s. The TI
58
TEems)
180
150
\ \ \ \ \
\ \ \
120
90
\ \
\ \
\
60
\0%
\
\
30
,, , "-... .......
1.0
2.0
3.0
4.0
Fig. 5. Contour plot of white matter-gray matter contrastto-noise ratio versus TE and TR in SR and SE for T l ot fixed, assuming equal hydrogen spin densities for the two tissues. A: The T]-dependent SR maximum only is shown. B: A wider TE and TR range is shown to include the Tz-dependent SE maximum.
value at which C/N peaks varies weakly with TE, and is given exactly by Eq. 18. As in SR, with tissues satisfying assumption (4) the C/N ratio peaks at TE = o and falls as TE increases. However, the falloff of C/N with TE is less severe in IR than in SR. For example, in an imaging system which has TE min = 30 ms, C/N in IR is reduced by only 30% at properly chosen TI and TR values, while C/N in SR is reduced by more than 50% for the best choice of TR values. This general behavior may explain why early clinical studies on systems with moderate TE min values favored IR over SR as a source of T] contrast, while early theoretical studies that ignored TE effects in SR and IR claimed that SR should give superior T] contrast. Figure 7 also shows the region of contrast reduction
202
Magnetic Resonance Imaging. Volume 2, Number 3, 1984 TE (ms) 40
180 35 150
30
120
25 20
90
15 60
10 30
5 lJl1J>ll..lo..U~L)..~--.------r~--,.--~-~TR (sec) 3.0 1.0 2.0 4.0 5.0
Fig. 6. Contour plot of the white matter-gray matter contrast-to-noise ratio as a function ofTE and TR in SR and SE for T,o, fixed, using the unequal hydrogen spin densities measured by Wehrli et al. 17 for the two tissues. The SE maximum is moved to TE ~ 0 due to spin density differences.
0.2
e,--"-r-'-~----''-r--'---f--'-r----'--,-l..,. TI
04
0.6
0.8
1.0
(s ee)
Fig. 7. Contour plot of the white matter-gray matter contrast-to-noise ratio as a function of TE and TI in inversion recovery for T ,o! fixed, using the unequal hydrogen densities of the two tissues measured by Wehrli et al."
CONCLUSIONS The primary goal of this work is to present a general method for maximizing contrast-to-noise ratios in magnetic resonance imaging arid to apply that method to some of the more common pulse sequences. Our work includes certain realistic conditions, such as unequal spin densities and rephasing pulses in SR and IR imaging sequences. Optimal interpulse delay times have been found for SR, IR, and SE sequences in the two distinct cases of N avg fixed and TIOI fixed. In all cases with N avg fixed (summarized in Table 2) and in some cases with TIOI fixed (summarized in Table 3), exact analytic expressions have been found for the optimal interpulse delay times in terms of spin density, T lo and T 2 values for the tissues of interest. In cases in which analytic solutions are not possible, parametric expressions that provide a good approximation of opti-
mal interpulse delay times have been found by leastsquares fitting of numerically optimized pulse sequences over the clinically relevant range of spin density, T j , and T 2 values. Equally important, a range of reasonable values for each interpulse delay time is presented .in Table 4, based on the arbitrarily chosen criterion of preserving at least 80% of maximum tissue contrast. One observation that can be drawn from Table 4 is that the selection of most interpulse delay times is forgiving. In some cases, delay times can be off by as much as a factor of two and still give greater than 80% of maximum contrast. However, the echo delay time TE, the time between 90° pulses and signal measurement, can seriously affect Tj-dependent tissue contrast in SR and IR sequences applied with rephasing pulses. Even TE values on the order of 15-30 ms result in significant T 2 signal decay, reducing Tj-induced tissue contrast. That TEmin cannot be set arbitrarily small in most existing imaging systems has at least two effects on tissue contrast in magnetic resonance images. The first is that contrast in SR and IR sequences is severely reduced by moderate machine-imposed TE min values, while contrast in SE sequences usually is not affected. The best T 2 tissue contrast usually occurs at TE values similar to the T 2 values of the tissues being imaged, which generally are larger than TE min • The Tj-dependent contrast in SR and IR sequences, on the
tAn example of a T1-weighted sequence with positive definite signals is the IR-SR sequence of ref. 7 with inter-
pulse delay times chosen appropriately (TA notation).
due to loss of information about the sign of the IR signal. For the case of equal spin densities this region of contrast loss occurs for TI values that are shorter than TIoPI.Jj However, as in Fig. 7, unequal spin densities may move this region of contrast loss near the TI values that optimize tissue contrast. This poses a potential liability for IR imaging that can be overcome either by switching to other Tj-weighted sequences'[ or by preserving sign information in each pixel or voxel of the reconstructed image.
~
T B in their
Optimizing contrast in MRI. R. E. HENDRICKETAL.
other hand, is seriously degraded by any nonzero TEmin value. This may be the reason that clinical studies on imaging systems with TE min on the order of 30 ms have turned to SE sequences as a primary source of tissue contrast. Such imaging systems throwaway considerable T, contrast at the outset, so Tz-weighted sequences such as spin-echo are the only alternative for reasonable tissue contrast. This, in turn, has a deleterious effect on the total time required to acquire an image with reasonable contrast. SE sequences with maximized contrast generally require much longer TR values (by a factor of 3 to 10) than SR sequences with good contrast. If TE min could be shortened so that the imaging system was made more sensitive to T[-dependent contrast, total patient imaging times might be shortened considerably. Second, with rephasing pulses and nonzero TE min values, IR sequences suffer less contrast loss from T,
203
decay than do SR sequences. This may explain why early clinical studies preferred IR to SR as a source of T,-dependent tissue contrast, while early theoretical analyses (which ignored the effects of nonzero TE min values in SR and IR) indicated that SR should provide better contrast. This point will be explored more fully in a subsequent article" which considers the effects of nonzero TE min and unequal spin densities on the choice of the best imaging sequences for a particular imaging task. Finally, it is worth noting that short TR values do not necessarily limit the rnultislice capabilities of imaging systems. The number of simultaneously acquired slices is not simply proportional to TR, but to TRITE. Thus, if TE is shortened to a reasonably small TEmin value, while TR is shortened to a value which maximizes T 1 contrast, large numbers of simultaneously acquired slices are still possible.
REFERENCES 1. Bydder, G.M.; Doyle, F.H.; Young, I.R.; Hall, A.S. NMR: initial clinical results. Witcofski, R.L.; Karstaedt, N.; Partain, C.L., eds. NMR imaging, proceedings ofan international symposium on nuclear magnetic resonance imaging. Winston-Salem, NC: BowmanGray School of Medicine; 1982:107-113. 2. Bydder, G.M.; Steiner, R.E.; Young, I.R.; Hall, A.S.; Thomas, D.J.; Marshall, J.; Pallis, c.x., Legg, N.J. Clinical NMR imaging of the brain: 140 cases. Am. J. Roentgenol. 138:215-236; 1982. 3. Crookes, L.E.; Hoenninger, J.; Arakawa, M.; Watts, J.; McCarten, B.; Sheldon, P.; Kaufman, L.; Mills, C.M.; Davis, P.; Margulis, A.R. High resolution magnetic resonance imaging. Radiology 150:163-171; 1984. 4. Crooks, L.E.; Mills, C.M.; Davis, P.L.; Brant-Zawadzki, M.; Hoenninger, J.; Arakawa, M.; Watts, J.; Kaufman, L. Visualization of cerebral and vascular abnormalities by NMR imaging: the effects of imaging parameters on contrast. Radiology 144:843-852; 1982. 5. Davis, P.L.; Kaufman, L.; Crooks, L.E. Potential diagnostic specificity of NMR. Witcofski, R.L.; Karstaedt, N.; Partain, C.L., eds. N M R imaging, proceedings ofan international symposium on nuclear magnetic resonance imaging. Winston-Salem, NC: Bowman-Gray School of Medicine; 1982:101-105. 6. Davis, P.L.; Kaufman, L.; Crooks, L.E.; Margulis, A.R. NMR characteristics of normal and abnormal rat tissues. Kaufman, L.; Crooks, L.E.; Margulis, A.R., eds. Nuclear magnetic resonance imaging in medicine. New York: Igaku-Shoin; 1981:71-100. 7. Edelstein, W.A.; Bottomley, P.A.; Hart, H.R.; Smith, L.S. Signal, noise, and contrast in nuclear magnetic resonance (NMR) imaging. J. Comput. Assist. Tomogr. 7:391-401; 1983. 8. Edelstein, W.A.; Bottomley, P.A.; Hart, H.R.; Leue, W.M.; Schenck, J.F.; Redington, R.W. NMR imaging at 5.1 MHz: work in progress. Witcofski, R.L., Karstaedt, N.; Partain, e.L., eds. NMR imaging, proceedings ofan international symposium on nuclear magnetic
resonance imaging. Winston-Salem, NC: BowmanGray School of Medicine; 1982:139-145. 9. Gore, J.e. The meaning and significance of relaxation in NMR. Witcofski, R.L., Karstaedt, N.; Partain, C.L., eds. NMR imaging, proceedings of an international symposium on nuclear magnetic resonance imaging. Winston-Salem, NC: Bowman-Gray School of Medicine; 1982:15-23. 10. Gore, J.C.; Doyle, F.H.; Penncock, J.M. Relaxation rate enhancement observed in vivo by NMR imaging. Partain, e.L.; James, A.E.; Rollo, F.D.; Price, R.R., eds. Nuclear magnetic resonance (NMR) imaging. Philadelphia: W.B. Saunders; 1983:94-106 11. Hendrick, R.E.; Nelson, T.R. Phase detection and contrast loss in magnetic resonance imaging. Magn. Reson. Imaging (in press). 12. Hendrick, R.E.; Nelson, T.R.; Hendee, W.R. Choosing pulse sequences and interpulse delay times in NMR imaging. Jaklovsky, J., ed. NMR imaging:future potential. Reading, MA: Addison-Wesley: 1984: (in press). 13. Nelson, T.R.; 'Hendrick, R.E.; Hendee, W.R. Selection of pulse sequences producing maximum tissue contrast. Magn. Reson. Imaging (in press). 14. Berman, W.H.; Hilal, S.K.; Simon, H.E.; Maudsley, A.A. Contrast manipulation in NMR imaging. Magn. Reson. Imaging 2:23-32; 1984. 15. Straughan, K.; Spencer, D.H.; Bydder, G.M. NMR clinical results: Hammersmith. Partain, e.L.; James, A.E.; Rollo, F.D.; Price, R.R., eds. Nuclear magnetic resonance (NMR) imaging. Philadelphia: W.B. Saunders; 1983:145-206. 16. Taylor, D.G.; Bore, C.F. A-review of the magnetic resonance response of biological tissue and its applicability to the diagnosis of cancer by NMR radiology. CT 5:122~133; 1981. 17. Wehrli, F.W.; MacFall, J.R.; Glover, G.H.; Grigsby, N. The dependence of nuclear magnetic resonance (NMR) image contrast on intrinsic and pulse sequence timing parameters. Magn. Reson. Imaging 2:3-16; 1984.
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18. Wehrli, F.W.; MacFall, J.R.; Newton, T.H. Parameters determining the appearance of NMR images. Newton, T.H.; Potts, D.G., eds. Modern neuroradiology, vol. 2: Advanced imaging techniques. San Anselmo, CA: Clavadel Press; 1983:81-117. 19. Young, I.R.; Bailes, D.R.; Collins, A.G.; Gilderdale, D.J. Image options in NMR. Witcofski, R.L.; Karstaedt, N.; Partain, C.L., eds. NMR imaging, proceed-
ings ofan international symposium on nuclear magnetic resonance. Winston-Salem, NC: Bowman-Gray School of Medicine; 1982:93-100. 20. Young, E.R.; Bailes, D.R.; Collins, A.G.; Gilderdale, D.J. Image choice in NMR. Partain, C.L; James, A.E.; Rollo, F.D.; Price, R.R., eds. Nuclear magnetic resonance (NMR) imaging. Philadelphia, W.B. Saunders; 1983:183-191.