Improved quantification precision of human brain short echo-time ¹H MRS at high magnetic field: A simulation study

Abstract

Purpose

The gain in quantification precision that can be expected in human brain ¹H MRS at very high field remains a matter of debate. Here we investigate this issue using Monte-Carlo simulations.

Methods

Simulated human brain-like ¹H spectra were fitted repeatedly with different noise realizations using LCModel at B₀ ranging from 1.5T to 11.7T, assuming a linear increase in SNR with B₀ in the time domain, and assuming a linear increase in linewidth with B₀ based on experimental measurements. Average quantification precision (Cramér-Rao Lower Bound, CRLB) was then determined for each metabolite as a function of B₀.

Results

For singlets, CRLB improved (decreased) by a factor ~ $\sqrt{{\mathrm{B}}_0}$ as B₀ increased, as predicted by theory. For most J-coupled metabolites, CRLBs decreased by a factor ranging from $\sqrt{{\mathrm{B}}_0}$ to B₀ as B₀ increased, reflecting additional gains in quantification precision compared to singlets due to simplification of spectral pattern and reduced overlap.

Conclusion

Quantification precision of ¹H MRS in human brain continues to improve with B₀ up to 11.7T, even though peak SNR in the frequency domain levels off above 3T. In most cases, the gain in quantification precision is higher for J-coupled metabolites than for singlets.

INTRODUCTION

Proton magnetic resonance spectroscopy (¹H MRS) allows non-invasive measurement of the concentration of multiple metabolites in the brain in vivo. In principle, high magnetic fields are beneficial for ¹H MRS due to increased signal-to-noise ratio (SNR), increased spectral dispersion and simplification of J-coupled spectral patterns. However, these benefits are mitigated by other factors, such as increased RF power and B₀ shimming requirements. In addition, even with perfect B₀ shimming, the spectral linewidth gets broader at high fields due to shorter T₂ relaxation times and increased B₀ microsusceptibility effects (1,2). As a result, even with a very short echo-time (T_E) sequence (so that signal loss from T₂ relaxation is minimized), the actual gain in sensitivity and quantification precision of ¹H MRS in human brain at ultra high-field (7T and beyond) is still a matter of debate.

Multiple studies have documented experimental gains in SNR in human brain ¹H MRS with high fields. However the reported gains vary significantly from study to study. Peak SNR in the frequency domain (SNR_freq, defined as peak height divided by RMS noise) was shown to increase 23% to 46% at 3T relative to 1.5T (3–5) while another study reported no improvement (6). Another study found a ~80% increase in SNR_freq at 4T compared to 1.5T (7). Furthermore a 1:1 linear increase in SNR_freq of singlet resonances with B₀ was reported from 1.5T to 7T (8). More recently, a 1.7-fold increase in SNR_freq from 3T to 7T (9), and a 1.91-fold increase from 4T to 7T (10) were also reported. Therefore, there is significant variability in the actual sensitivity gains observed at high field. Such variability can be explained in part by the difficulty to match experimental conditions (design and construction of RF coils, B₁ spatial distribution, etc) between different systems at different B₀ field strengths.

Another possible approach to assess potential gains in quantification precision at high field is using simulations. Previous simulations in rodent brain suggested that SNR_freq is expected to flatten out as B₀ increases, with little increase (< 10%) in SNR_freq of singlet resonances (NAA, Cr) above 10T (11). However, further gains in quantification can reasonably be expected for J-coupled metabolites due to simplification of spectral patterns and reduced overlap at high field (11). Therefore, the improvement in quantification precision for every individual metabolite as B₀ increases remains an open question.

In this context, the goal of the present study was to determine the relationship between quantification precision (estimated by Cramér-Rao Lower Bounds or CRLBs) and B₀ for every brain metabolite present in in vivo ¹H MR spectra. To achieve this goal, we performed Monte-Carlo simulations together with LCModel and simulated ‘brain-like’ spectra at multiple B₀ field strengths.

MATERIAL AND METHODS

Simulations were performed with two main assumptions: (a) the in vivo linewidth increases linearly with B₀ above 1.5T as measured experimentally (1) and (b) the SNR in the time domain (SNR_time) increases linearly with B₀ (12,13). ‘Brain-like’ ¹H NMR spectra were simulated in Matlab (14), assuming no J-evolution (pulse-acquire sequence analogous to an ultrashort T_E sequence). Nineteen metabolites were included with concentrations similar to those found in human occipital cortex: 0.5 mM alanine (Ala), 1 mM ascorbate (Asc), 2 mM aspartate (Asp), 4 mM creatine (Cr), 1 mM γ-aminobutyric acid (GABA), 1 mM glucose (Glc), 10 mM glutamate (Glu), 2.5 mM glutamine (Gln), 0.5 mM glycerophosphorylcholine (GPC), 1 mM glutathione (GSH), 0.5 mM lactate (Lac), 6 mM myo-inositol (Ins), 12 mM N-acetylaspartate (NAA), 1 mM N-acetylaspartylglutamate (NAAG), 4 mM phosphocreatine (PCr), 0.5 mM phosphorylcholine (PCho), 1.5 mM phosphorylethanolamine (PE), 0.25 mM scyllo-inositol (sIns) and 1.5 mM taurine (Tau). Macromolecules were also simulated and added to the spectrum (see Supplemental Methods for details).

Brain-like spectra were then generated at 6 different magnetic field strengths: 1.5, 3, 4, 7, 9.4 and 11.7T with a spectral linewidth of 2.1, 3.7, 4.9, 8.5, 11.2 and 14.0 Hz respectively. These values were obtained by measuring the linewidth of the tCr peak at 3.03 ppm at 4T, 7T and 9.4T, and subtracting the Cr-PCr chemical shift difference (0.0033 ppm or 0.14 Hz/T). Values at 1.5T, 3T and 11.7T were obtained by linear extrapolation of the fit from 4T to 9.4T. The slope was 1.31 Hz/T and 1.17 Hz/T before and after subtraction of the Cr-PCr chemical shift difference respectively. All metabolites were simulated with the same linewidth, neglecting small differences in linewidth due to different T₂ relaxation times. The resulting simulated spectra (Figure 1) were very similar in appearance to those obtained experimentally in the human brain (1,3,8–10,15).

Figure 1.

Examples of ‘brain-like’ simulated ¹H NMR spectra with low SNR (left) and high SNR (right) from 1.5T (top) to 11.7T (bottom) using the linewidth values and the concentrations of metabolites given in the text. Fore each condition (low SNR or high SNR), spectra are scaled so that the RMS noise is identical at each magnetic field.

For Monte-Carlo simulations, Gaussian noise was added to the simulated ¹H NMR spectra, with a noise level inversely proportional to B₀. The resulting spectra were fitted with LCModel version 6.1-4A (16). This procedure was repeated 50 times with 50 different random noise realizations (sufficient for proper convergence), yielding 50 CRLB values for each metabolite at each B₀. The quantification precision for each metabolite at a given B₀ was calculated as the average of these 50 CRLB values.

The SNR of the simulated spectra was chosen in order to obtain accurate estimates of the CRLBs at all magnetic fields. If SNR is too low, many low concentration metabolites cannot be reliably fitted. If SNR is too high, estimates of CRLBs for high concentration metabolites are very small (< 2%) and are not precise enough because of rounding in LCModel. Therefore, two simulations were performed. One simulation was performed with ‘low’ SNR (SNR of NAA peak measured in the frequency domain was 25±1 at 4T) to estimate CRLBs for Cr, PCr, Glu, NAA and Ins as well as the sums tCho = PCho+GPC, tCr = Cr+PCr and Glx = Glu+Gln. A second simulation was performed with ‘high’ SNR (SNR of NAA peak in the frequency domain was 100±4 at 4T) to determine CRLBs for all other metabolites.

T₁ effects were neglected because T₁ relaxation times show only modest increases with B₀ (1). For example, assuming a T_R of 5s and an increase in the T₁ of tCr-CH₃ from 1.39s at 1.5T to 1.75s at 9.4T (1) would result in a negligible 3% loss in SNR at 9.4T compared to 1.5T due to T₁ saturation.

RESULTS

SNR_freq becomes nearly constant as the B₀ field increases

In our simulated ¹H NMR spectra, both the linewidth (in Hz) and the SNR in the time domain were assumed to increase linearly with B₀. With those two assumptions, SNR_freq of singlets, defined as peak height relative to RMS noise, was found to level off and showed only modest increase above 3–4T (Figure 2). This is explained by the fact that the increase in SNR_time is offset by the increase in linewidth. Quantitatively, SNR_freq is proportional to SNR_time/Δν_Hz, where Δν_Hz is the spectral linewidth in Hz. With our assumptions: SNR_time=C·B₀ and Δν_Hz=D·B₀ + E where C, D and E are constants. It follows that SNR_freq is proportional to C·B₀/(D·B₀+E). When B₀ increases, then D·B₀>>E and SNR_freq becomes nearly constant. For example using experimental values for the tCr linewidth at 3.03 ppm, the linewidth of tCr in the human brain (including the small chemical shift difference between Cr and PCr) can be expressed as Δν_Hz = 1.31B₀ + 0.27 (1) or in ppm, Δν_ppm = Δν_Hz/γB₀ = 0.031 + 0.006/B₀. For B₀>3T, the second term becomes negligible (< 5%) resulting in a constant linewidth (in ppm) of ~0.031 ppm as well as constant SNR_freq. The above formula is valid for tCr, and the constants would be slightly different for other singlets, but NAA shows a similar behavior, with a plateau in SNR_freq above 3–4T (Figure 2).

Figure 2.

SNR_freq as a function of B₀ measured as NAA peak intensity relative to RMS noise using both the low and high SNR conditions. Error bars represent SD.

Quantification precision continues to increase with B₀ at very high field

In spite of the fact that SNR_freq become nearly constant at very high field, simulations show that the quantification precision (estimated by CRLBs) continues to increase substantially for all metabolites as B₀ increases. Figure 3 shows examples of this improvement for tCr, Glu, Gln and GABA.

Figure 3.

Mean CRLBs for selected metabolites (tCr, Glu, Gln and GABA) obtained from Monte-Carlo simulations. The data are plotted in logarithmic scale. Solid lines represent the best fits. Error bars represent SD of 50 CRLB values obtained from Monte-Carlo simulations. Note that values for tCr and Glu were obtained with the “low SNR” condition and values for Gln and GABA with the “high SNR” condition.

To quantify the improvement of CRLBs as a function of B₀, these plots were fitted with a function in the form CRLB ∝ B₀^α or, in logarithm coordinates, with a linear function log(CRLB) = α·log(B₀)+C, with α and C as free parameters. Results show a close linear relationship between log(CRLB) and log(B₀) for all metabolites (R² ranging from 0.96 to 1 for all metabolites, except R²=0.88 for glucose and R²=0.93 for sIns). The fitted slope ranged from α=−0.42 (for glucose) to α=−1.05 (for glutamine) (Table 1). A slope value of −1.0 corresponds to CRLB ∝ 1/B₀, whereas −0.5 corresponds to $\mathrm{C}\mathrm{R}\mathrm{L}\mathrm{B}\propto 1/\sqrt{{\mathrm{B}}_0}$.

Table 1.

Slope (α) and R² correlation coefficient obtained after fitting the CRLBs as a function of B₀ using a power regression function i.e. σ·B₀^α (equivalent to a linear fit in logarithmic coordinates).

Spin systems	Metabolites	Slope, α	R2
Mostly singlet	NAA†	−0.67	0.94
	Creatine†	−0.62	0.96
	Phosphocreatine†	−0.57	0.96
	Scyllo-inositol	−0.56	0.93
	Total choline†	−0.51	1.00
	Total creatine†	−0.61	0.98
J-coupled	Alanine	−0.75	0.98
	Ascorbate	−0.67	0.98
	Aspartate	−0.44	0.96
	Glucose	−0.42	0.88
	GABA	−0.97	1.00
	Glutamate†	−0.95	0.99
	Glutamine	−1.05	0.99
	Glutathione	−0.87	0.97
	Glycerophosphorylcholine	−0.92	0.99
	Lactate	−0.72	0.98
	Myo-Inositol†	−0.52	0.96
	NAAG	−0.70	1.00
	Phosphethanolamine	−0.87	0.99
	Phosphocholine	−0.80	1.00
	Taurine	−0.78	1.00
	Glutamate + glutamine†	−0.86	0.99

^†The † sign indicates values obtained using the “low SNR” condition. The SD for the slope was < 0.1 for all metabolites.

These findings are supported by theory. Indeed, theoretical calculations of CRLB for a singlet predict that, if SNR_time and Δν_Hz both increase linearly with B₀ (i.e constant SNR_freq) then the CRLB of the estimated concentration decreases as $1/\sqrt{{\mathrm{B}}_0}$ (17). Our simulation results show that, for metabolites appearing primarily as singlets in the ¹H NMR spectrum, the slope α was close to −0.5 (−0.61 for tCr, −0.51 for tCho and −0.56 for sIns), which is in good agreement with theoretical predictions.

For other metabolites that appear as multiplets with complex J-coupled spectral patterns, such theoretical calculations are generally not possible. However, the increase in quantification precision was higher than for singlets in most cases, with the slope α generally comprised between −0.5 and −1. Metabolites that showed the highest increase in quantification precision with B₀ were glutamine (α=−1.05), glutamate (α=−0.95) and GABA (α=−0.97). This reflects the simplification of spectral pattern and reduced overlap of these metabolites at high field, whereas they overlap strongly at lower field (Figure 1), Similarly, reduced overlap between the J-coupled resonances of GPC and PCho at high field contributed to higher α values for these two metabolites (α=−0.92 for GPC and α=−0.80 for PCho). However, we found exceptions to this trend: for Glc (α=−0.42), Asp (α=−0.44), or Ins (α=−0.52), the decrease in CRLBs with B₀ was more modest. Therefore, the actual improvement in quantification precision with B₀ is strongly dependent on the spectral pattern of each metabolite.

The number of metabolites that can be quantified reliably increases with B₀

The improvement in quantification precision with B₀ resulted in a steady increase in the number of metabolites that could be quantified reliably, using CRLB < 25% as a threshold (Table 2). With the ‘low SNR’ simulation condition, which is typical of in vivo MRS in human brain, five metabolites could be quantified reliably with CRLB < 25% (tCr, tCho, NAA, Glx and Ins) at 1.5T, six metabolites (Cr, PCr, tCho, NAA, Glx and Ins) at 3T and up to sixteen metabolites at 11.7T (Table 2). The remaining three metabolites (Asc, Glc and sIns) had CRLBs around 30% at 11.7T. Although this is only valid for those particular SNR conditions, it illustrates how gains in quantification precision translate into increased neurochemical information content.

Table 2.

List of metabolites that can be quantified reliably with CRLB < 25% at different B₀ using the ‘low SNR’ simulation condition. While this result is valid only for this particular SNR condition, it illustrates how gains in quantification precision translate into a higher number of metabolites that can be quantified reliably.

Magnetic Field (T)	1.5		3		4		7		9.4		11.7
Number of metabolites	5		6		8		12		14		16
	Metabolite	CRLB (%)	Metabolite	CRLB (%)	Metabolite	CRLB (%)	Metabolite	CRLB (%)	Metabolite	CRLB (%)	Metabolite	CRLB (%)
	NAA	8	NAA	4	NAA	3	NAA	2	NAA	2	NAA	2
	tCho	18	tCho	12	tCho	11	tCho	8	tCho	7	tCho†	6
	Ins	10	Ins	6	Ins	6	Ins	4	Ins	4	Ins	3
	Glx	13	Glx	7	Glx†	5	Glx†	3	Glx†	3	Glx†	2
	tCr	7	tCr†	4	tCr†	4	tCr†	3	tCr†	2	tCr†	2
			Cr	13	Cr	12	Cr	9	Cr	7	Cr	7
			PCr	13	PCr	12	PCr	10	PCr	8	PCr	7
					Glu	5	Glu	3	Glu	2	Glu	2
					Gln	18	Gln	10	Gln	8	Gln	6
					GSH	24	GSH	16	GSH	13	GSH	12
							NAAG	17	NAAG	14	NAAG	12
							PE	19	PE	15	PE	13
							GPC	23	GPC	21	GPC	18
							Tau	24	Tau	17	Tau	14
									GABA	18	GABA	15
									Asp	22	Asp	19
											Lac	22
											PCho	23
											Ala	24

^†Note that metabolites representing the sum of two other metabolites were not counted when their individual components could be quantified separately For instance, both Glu and Gln were reliably quantified at 4T such that Glx was not counted. Those metabolites are marked with a † sign.

DISCUSSION

Comparison between human brain and rat brain

In human brain, we show here that both peak SNR in the frequency domain (SNR_freq) and the linewidth expressed in ppm (Δν_ppm) are expected to become nearly constant above 3T. A similar prediction has been made in the rat brain, where the increase in linewidth (in ppm) was shown to become nearly constant at high field (11,18). According to de Graaf and colleagues (11), the linewidth of tCr in rat brain becomes nearly constant above 9.4T and converges to ~0.018 ppm (compared with ~0.031 ppm in human brain). Interestingly, the B₀ threshold above which Δν_ppm and SNR_freq level off is higher in rat brain (9.4T) than in human brain (3T). This is due to the longer T₂ relaxation times of metabolites and smaller microscopic B₀ inhomogeneity in rat brain compared to the human brain, resulting in smaller metabolites linewidth in the rat brain.

Relevance of assumptions used in simulations

Assumption on SNR

Simulations in the present study assumed a linear 1:1 increase in SNR_time with B₀, based on the expected theoretical gain in intrinsic SNR (13). However, the actual gain in SNR_time with B₀ is strongly dependent on experimental factors such as the performance of RF coils used or the spatial distribution of B₁ field. Even if experimental conditions (RF chain, RF coil geometry, etc) are kept nearly identical, the distribution of the B₁ field inevitably changes with B₀, especially at high field. As such, any increase in SNR_time with B₀ measured experimentally in human brain is valid only for a specific coil geometry and voxel location, even if all other experimental conditions are perfectly matched.

For example, a previous study reported a ~2-fold increase in SNR_freq at 7T versus 4T (10), in apparent contradiction with the results of the present simulation study, which predicts very little improvement in SNR_freq from 4T to 7T. However, a 2-fold increase in SNR_freq, together with the reported increase in tCr linewidth from 5.9Hz at 4T to 9.8Hz at 7T, would correspond to a 3.3-fold increase in SNR_time for tCr. This experimentally measured factor was much higher than the factor of 1.75 (i.e. 7/4) assumed in our simulations based on theoretical predictions (12,13). One possible explanation for the higher than expected gain in SNR_time measured experimentally is that different RF coils were used at 4T and 7T, with slightly different geometry and design, which could favor the 7T coil. Alternatively, even when using very similar surface coils at 4T and 7T, a larger portion of the available SNR may be concentrated close to the coil as B₀ increases. Indeed, when comparing images at 4T and 7T in (10), SNR clearly drops more quickly at 7T than at 4T when going away from the coil.

While the assumption of a linear increase of SNR_time with B₀ may not hold true in all particular cases, our simulations give useful insight into the gains in quantification precision that can be expected at high field for every metabolite. Simulations make it possible to have a consistent SNR hypothesis across all B₀ values, and therefore identify general trends not easily identified from experimental data due to the difficulty to match experimental conditions at multiple B₀.

In addition, since CRLBs are inversely proportional to SNR_time for a given B₀ (17), results can easily be extrapolated using a different assumption for SNR_time = f(B₀). For example, if SNR_time varied as B₀^1.2 instead of B₀, all α coefficients in Table 1 would be simply multiplied by 1.2.

Assumption on very short T_E

Our simulations are valid for very short T_E sequences for which the loss of signal from T₂ relaxation during T_E can be neglected. At high field, however, such losses from T₂ relaxation may become significant. For similar experimental conditions, the minimum T_E tends to increase at high field due to increased power requirements, and T₂ relaxation times become shorter. This is particularly true for MRS sequences on clinical scanners, which are generally not optimized to minimize T_E.

State-of-the-art research sites, in contrast, recognizing that minimizing T_E is critical to harness gains in quantification precision at high-field, have used MRS methodology that keeps relatively short T_E even at 7T and 9.4T (1,9,15). However, even in those studies, loss of signal due to T₂ relaxation may not be completely negligible at high field.

Our results can be extended to take into account the additional loss of signal fromT₂ relaxation by taking advantage of the fact that all CRLB values obtained in our simulations are inversely proportional to SNR at each B₀ (17). Therefore, corrected CRLBs can be derived from our initial, uncorrected CRLB values as CRLB_corr=CLRB_uncorr*SNR_uncorr/SNR_corr with CRLB_uncorr proportional to B₀^α and α coefficients given in Table 1. If SNR_uncorr/SNR_corr is expressed empirically as B₀^β, then CRLB_corr is proportional to B₀^α+β and coefficients α in Table 1 simply need to be corrected by adding the term β.

Values of T_E(min) and even T₂ relaxation times depend on the specific sequence used. Therefore, we estimated the signal loss using approximate values of T_E(min) and T₂ relaxation times at each B₀ for the two MRS sequences currently being used in our center: STEAM and semi-LASER (19).

For STEAM, coefficients α in Table 1 need to be corrected by adding a term β=0.06 (average of 0.05 for NAA and 0.07 for tCr) (See Supplemental Data for an example). For semi-LASER, coefficients α in Table 1 need to be corrected by a term β=0.2 (average of 0.18 for NAA and 0.21 for tCr).

Assumption on optimal shimming and spectral quality

The ¹H NMR spectra used in the current study were simulated assuming perfect B₀ shimming in the human occipital lobe in vivo. Shimming imperfections (i.e. B₀ inhomogeneities that cannot be compensated for by 2^nd order shim coils) increase linearly with B₀, and these imperfections may be significant in areas of the brain other than the occipital lobe and/or in large voxels. Therefore the present study provides the maximum achievable improvement of quantification precision at high field for perfectly shimmed voxels.

It was also assumed that there was no baseline distortion and no lipid contamination due to imperfect outer volume suppression. Achieving such optimal conditions is not always possible experimentally, since spectral quality is strongly dependent on the pulse sequence and B₀ shimming algorithm used, the brain region under investigation, and any movement from the subject.

CRLB as estimator of quantification precision

Finally, it should be kept in mind that CRLBs represent only a lower bound of the experimental error. Nonetheless, CRLBs are generally good estimators of the quantification precision of a given metabolite when spectral noise is the main contributor to experimental error, as is the case when SNR for this metabolite is relatively low. At higher SNR, intra-subject experimental error typically becomes dominated by other experimental factors such as movement.

CONCLUSION

In conclusion, the quantification precision of metabolites is expected to continue to improve in the human brain with field strength up to 11.7T, even though SNR_freq does not increase substantially above 3T. The improvement in quantification precision is dependent on the spectral pattern of each metabolite. In general, greater improvement in quantification precision is obtained for J-coupled metabolites than for singlets as B₀ increases.