Field Dependence Study of In Vivo Brain ³¹P MRS up to 16.4 Tesla

Abstract

In vivo ³¹P MRS provides a unique tool for studying bioenergetics of living organs. Although its utility has been limited by the relatively low ³¹P NMR sensitivity, increasing magnetic field strength (B₀) could significantly improve the quality and reliability of the ³¹P MR spectra for biomedical research. To quantitatively understand the field dependence of in vivo ³¹P MRS for brain applications, ³¹P NMR sensitivity of phosphocreatine (PCr) in rat brains was measured and compared at 9.4 T and 16.4 T. Additionally, the linewidths and T₁ relaxation times of PCr and adenosine triphosphate (ATP) resonances obtained from human and animal brains over a wide B₀ range from 4 T, 7 T, 9.4 T to 16.4 T were examined and their field dependences were quantified. The results indicate an approximate 1.74 fold ³¹P signal-to-noise ratio (SNR) gain for PCr at 16.4 T compared to 9.4 T. An approximate power 1.4 dependence of ³¹P SNR on B₀ was concluded. Substantial improvements in spectral resolution and significantly shortened T₁ values of brain PCr and ATP were observed at high/ultrahigh fields, contributing to an additional sensitivity gain and spectral improvement. In summary, the overall findings from this study suggest that in vivo ³¹P MRS should greatly benefit from high/ultrahigh fields for noninvasive assessment of altered bioenergetics and metabolic processes associated with brain function and neurological diseases.

INTRODUCTION

In vivo ³¹P magnetic resonance spectroscopy (MRS) enables direct measurement and quantification of high-energy phosphate (HEP) compounds such as adenosine triphosphate (ATP) and phosphocreatine (PCr), as well as inorganic phosphate (Pi) and other metabolites in the brain (1–3). These phosphorus metabolites are tightly coupled to the cerebral bioenergetics and their changes detected by in vivo ³¹P MRS have been linked to numerous diseases, including brain ischemia (4), seizure, epilepsy (5,6), Alzheimer disease (7,8) and schizophrenia (9). When combined with magnetization transfer techniques, it is also possible to noninvasively measure the rates of ATP synthesis through the chemical exchange reactions involving creatine kinase and ATPase in the brain (10–17). Therefore, in vivo ³¹P MRS provides a unique tool for directly investigating the synthesis, transfer, and utilization of high-energy phosphate compounds, which should significantly advance the understanding of bioenergetics associated with brain functions and disorders. In addition, other important and physiologically relevant information such as intracellular pH, free magnesium concentration, intermediates of phospholipid metabolism, and NAD⁺/NADH redox states could also be obtained from brain ³¹P spectra (2,18,19). However, in vivo ³¹P MRS applications in biomedical research have faced a number of challenges including low concentration of phosphorus metabolites of interest, limited NMR sensitivity due to relatively low ³¹P gyromagnetic ratio compared to that of ¹H, and limited spectral and spatial resolutions.

Previous studies have demonstrated that in vivo ³¹P MRS can benefit from higher magnetic field strength (B₀) for overcoming the intrinsic sensitivity limitation and improving spectral resolution (20–23). However, the achievable signal-to-noise ratio (SNR) (24) of ³¹P resonance measured in a fixed acquisition time depends not only on B₀ and its power term (defined as β and its value is expected to be in the range of 1–1.5 (25,26)), but also on many field-dependent parameters according to the following relationship (20,27):

$$\mathrm{S}\mathrm{N}\mathrm{R}(\text{in a fixed acquisition time})\propto B_0^{\beta }{Q}^{1/2}{(\frac{1}{T_1·\mathrm{\Delta }{\mathrm{\nu }}_{1/2}})}^{1/2}{(1-E_2^2)}^{1/2}G(x)$$ [1]

where Q is the radiofrequency (RF) coil quality factor (under the sample loaded condition), T₁ is the longitudinal relaxation time, Δν_1/2 is the resonance linewidth at half peak height (in Hz, which is inversely proportional to the apparent transverse relaxation time (T₂^*)), $E_2^2=e^{(-2·\mathit{\text{at}}·\pi ·\mathrm{\Delta }{\nu }_{1/2})}$ (at is the time for acquiring the ³¹P free induction decay signal), and $G(x)={(2·\frac{1-e^{-x}}{x(1+e^{-x})})}^{1/2}$ (x = TR/T₁ and TR is the repetition time) (20,25–27). Therefore, in order to evaluate the quantitative relationship between the field strength and the sensitivity of the in vivo brain ³¹P MRS as defined by the SNR per fixed acquisition time, it is necessary to consider all relevant field-dependent and acquisition parameters as expressed in Equation [1] at different fields.

It is known that resonance linewidth (in Hz unit) broadens with increasing B₀, which could reduce the SNR and affect the spectral resolution. Thus, the field dependence of the resonance linewidth is another key factor in determining the improvement of in vivo ³¹P MR spectral quality at higher field. Moreover, for phosphorus metabolites such as ATP and PCr, both dipole-dipole interactions and chemical shift anisotropy (CSA) contribute to the T₁ relaxation processes, and their relative contributions depend on B₀ and the molecular structure (28). At high/ultrahigh field, the CSA contribution to T₁ relaxation (T_1(CSA)) can become dominant due to the dependence of 1/T_1(CSA) on the square power of B₀ (29,30), thus shortening the ³¹P T₁ values of ATP and PCr.

To quantitatively understand the field-dependence of in vivo ³¹P MRS, the following experiments were designed and conducted. Firstly, the ³¹P NMR sensitivity of the PCr signal was compared in rat brains at the ultrahigh fields of 9.4 T and 16.4 T with identical experimental setups. Secondly, the resonance linewidths (in Hz units) and spectral resolutions (in ppm units) of PCr, α-ATP, and γ-ATP resonances obtained from human and animal brains covering a wide B₀ range up to 16.4 T were quantitatively compared to determine their field dependences. Thirdly, the field dependence of the PCr and ATP T₁ relaxation times in human and animal brains was investigated. Finally, the quantitative relationships between the SNR of the PCr and ATP resonances and the B₀ from 4 T to 16.4 T were deduced based on the experimental results of multiple field-dependent parameters.

Instead of investigating and predicting the theoretical field-dependence of intrinsic SNR and natural linewidth, the purpose of this study was to understand the practically achievable SNR and spectral resolution at a given field strength and their relative improvements with increasing B₀ field, since this information is most relevant to the majority of in vivo ³¹P MRS brain applications.

METHODS

Comparison study of in vivo ³¹P MRS sensitivity at 9.4 T and 16.4 T

The in vivo ³¹P SNR comparison study was conducted on 9.4 T/31 cm bore and 16.4 T/26 cm bore magnets (Magnex Scientific) interfaced to VNMRJ consoles from the same vendor (Agilent, CA). Passively decoupled dual-coil RF probes with identical geometry were constructed for 9.4 T and 16.4 T experiments and placed over the rat brains to obtain optimum detection sensitivity. Each probe consisted of a one-turn, oval (14 mm × 20 mm) shaped single-loop ³¹P surface coil for ³¹P MRS and a butterfly ¹H surface coil (28 mm × 20 mm) for shimming and anatomical images.

Male Sprague Dawley rats were anesthetized with 2% (v/v) isoflurane in a mixture of O₂ and N₂O gases (~2:3), and scanned at 9.4 T and 16.4 T (five rats for each field strength). All animal procedures for rat preparation, anesthesia, and maintenance under physiological conditions during the measurements were the same as described in a previous report (31).

A single-pulse-acquisition sequence was applied to obtain the brain ³¹P signal and to calibrate the nominal 90° of the RF excitation pulse (where a maximum ³¹P signal was approached) with the following acquisition parameters: 200µs hard pulse, 8 kHz spectral width (SW), 1024 number of points (NP) for each free induction decay (FID), 10 s repetition time (TR) and 8 signal averages (NT). The raw ³¹P MRS signal was processed by exponential filtering with a line broadening (LB) of 20 Hz to enhance apparent SNR, followed by Fourier transformation. The ³¹P NMR sensitivity was evaluated using the SNR of the PCr resonance calculated by dividing the PCr resonance height by the peak-to-peak spectral noise, and multiplying it by 2.5 to minimize the errors of noise measurement caused by spectral baseline drifting (20,31–33).

Practically, several factors, which are not included in Equation [1], can also influence the SNR values measured at different fields, and their possible confounding effects were carefully considered when conducting the SNR comparison study at 9.4 T and 16.4 T. For example, the same RF coil size and geometry, same pulse flip angle, as well as the same position between the coil and rat head were used to ensure identical RF excitation and reception profiles at these two fields. In addition, the same acquisition parameters including the spectral width were applied, and a similar receiver noise figure was confirmed at 9.4T and 16.4T.

In vivo ³¹P MRS studies of field dependence of PCr and ATP linewidths and spectral resolution

For studying the field dependence of PCr and ATP resonance linewidths and spectral resolution, in vivo ³¹P spectra were acquired from either human brains at 4 T/90 cm bore (Oxford) and 7 T/90 cm bore (Magnex Scientific) magnets interfaced with Varian consoles (Agilent, CA), or cat brains at 9.4 T and 16.4 T. Nine healthy human adults (19–50 years old; four for 4 T and five for 7 T) and eight adolescent cats (weight 0.8–1.6 kg; four for 9.4 T and another four for 16.4 T) were used. More information about cat preparation and maintenance can be found in a previous report (34).

A set of home-built and passively decoupled ³¹P/¹H RF dual surface coils were applied to collect the ³¹P signals with a single-pulse-acquisition sequence, without the use of ¹H decoupling, from the human and cat visual cortices at various field strengths of 4 T, 7 T, 9.4 T and 16.4 T. B₀ field homogeneity was achieved by shimming the water ¹H resonance of the occipital brain region using the FASTMAP algorithm (35). A relatively long repetition time (TR: 3–16 s) and a high signal average (NT: 40–320) were used for achieving sufficient SNR. All ³¹P spectra were processed without a line broadening before Fourier transformation to measure resonance linewidths. The resonance linewidths of PCr, γ-ATP, and α-ATP at half peak height were regressed and quantified for each spectrum acquired at different magnetic field strengths using the VNMRJ software package. The linewidth results of 1.5 T and 2 T taken from the literature (21) were also included in this study to further extend the B₀ range for comparison.

Since the outcome of linewidth measurements is subject to the quality of shimming, it is essential to optimize the B₀ homogeneity within the sample volume covered by the ³¹P RF coil. Extra cautions were taken in this study to minimize the possible confounding effect due to shimming variation. For instance, ³¹P linewidths were measured from the visual cortex of human and cat, which approximates a spherical shape favorable for optimal shimming; the ³¹P RF coil sizes (5 cm diameter for human and oval shaped 1.4 cm × 2 cm for cat) were optimized to ensure that the ³¹P signals were mainly detected from the visual cortex with negligible muscle contribution. Also, both first and second-order FASTMAP shimming (35) was applied for further improving the B₀ homogeneity and the resonance linewidths.

In vivo measurements of PCr and ATP T₁ relaxation times at different fields

The T₁ values of PCr in rat brains at both 9.4 T and 16.4 T (four rats for each field strength) were measured using an inversion recovery pulse sequence under the fully relaxed condition with a long pre-inversion delay (d1) of 16 s with 8 signal averages. A B₁-insensitive hyperbolic secant inversion pulse (36,37) was used to compensate the B₁ inhomogeneity of the ³¹P surface coil followed by magnetization dephasing gradients. T₁ values were determined by a three-parameter least-square fitting of a single exponential function to the PCr signals with a total of nine different inversion times (TI: 0.012–20 s) at each field.

Similarly, the T₁ values of PCr, γ-ATP, and α-ATP were also determined in the cat visual cortex at 9.4T (seven cats with d1 of 20 s and 12–16 signal averages, TI: 0.08–20.48 s) and 16.4T (six cats with d1 of 16 s and 16–24 signal averages, TI: 0.012–20 s), and in the human visual cortex at 4T (twelve subjects with d1 of 16 s and 16 signal averages, TI: 0.025–32 s) and 7T (ten subjects with d1 of 16 s and 8–12 signal averages, TI: 0.008–20 s).

The experimental procedures of human studies were approved by the Institutional Review Board of the University of Minnesota with written informed consent obtained from all subjects prior to study. The Institutional Animal Care and Use Committee of the University of Minnesota approved the animal procedures and experimental protocols.

All results presented in this study are shown as mean standard deviation.

RESULTS

The averaged PCr ³¹P SNR obtained at 16.4 T was 1.74 fold higher than that at 9.4 T for the rat brains, as shown in Table 1. Similar SNR improvements were also observed in a phantom solution containing Pi and from localized in vivo ³¹P spectra of the rat brains measured at these two fields (data not shown herein). The overall results demonstrate an excellent sensitivity at both high fields for obtaining ³¹P signals; nevertheless, the 16.4 T scanner offers a remarkable improvement in the ³¹P NMR sensitivity.

Table 1.

Summary of field-dependent parameters for the sensitivity comparison study of rat brain between 9.4 T and 16.4 T using the single-pulse-acquisition approach

B0	Rat Brain SNR (N=5) (8 averages)	T1 (S), N=4	Δν1/2 (Hz), N=5	Coil Q	G (TR/T1)	(1-E22)1/2
16.4 T	80.2 ± 4.7	1.56 ± 0.05	32.8 ± 1.62	353.5	0.56	1
9.4 T	46.1 ± 6.0	2.95 ± 0.11	21.8 ± 0.9	405	0.74	1
Ratio	1.74	0.529	1.505	0.873	0.757	1

For calculation of the G and E₂² factors, at=0.064 s and TR=10 s were used for both field strengths. Coil Q values were measured experimentally with rat brain loading.

Figure 1 displays typical in vivo ³¹P spectra obtained either from human visual cortex at 4 T (Fig. 1a) and 7 T (Fig. 1b) or from cat visual cortex at 9.4 T (Fig. 1c) and 16.4 T (Fig. 1d). It clearly indicates that the linewidths of metabolite resonances in ppm scale reduced substantially when the field strength was increased from 4 T to 16.4 T, thus significantly improving the spectral resolution and the separation of adjacent resonances. The linewidth dependences of three major high-energy phosphate resonances (PCr, γ-ATP, and α-ATP) on B₀ from the human and cat brains are shown in Fig. 2. When using Hz as the unit of linewidth, linear correlations according to the following regressed equations were observed for all resonances studied (Fig. 2a):

$$\mathrm{\Delta }{\mathrm{\nu }}_{1/2,\mathrm{P}\mathrm{C}\mathrm{r}}=0.41{\mathrm{B}}_0+10.6,{\mathrm{R}}^2=0.50$$ [2a]

$$\mathrm{\Delta }{\mathrm{\nu }}_{1/2,\mathrm{\alpha }-\mathrm{A}\mathrm{T}\mathrm{P}}=1.45{\mathrm{B}}_0+28.7,{\mathrm{R}}^2=0.99$$ [2b]

$$\mathrm{\Delta }{\mathrm{\nu }}_{1/2,\mathrm{\gamma }-\mathrm{A}\mathrm{T}\mathrm{P}}=3.02{\mathrm{B}}_0+22.3,{\mathrm{R}}^2=0.99$$ [2c]

However, such linear correlations between linewidth and B₀ became approximately inverse relationships when the unit of the linewidth was converted from Hz to ppm as shown in Fig. 2b, indicating a drastic improvement in ³¹P spectral resolution at high/ultrahigh fields.

Figure 1.

In vivo ³¹P spectra of visual cortex acquired at (a) 4 T (TR=6s, NT=192) and (b) 7 T (TR=16s, NT=128) from human brains, and at (c) 9.4 T (TR=16s, NT=64) and (d) 16.4 T (TR=5s, NT=40) from cat brains and processed without any line broadening (LB=0). PE: phosphoethanolamine; PC: phosphocholine; GPE: glycerophosphoethanolamine; GPC: glycerophosphocholine; NAD⁺ & NADH: oxidized and reduced forms of nicotinamide adenine dinucleotide.

Figure 2.

Field dependences of PCr (○), γ-ATP (□) and α-ATP (Δ) linewidths display in the unit of Hz (a) and ppm (b). Dashed lines demonstrate the regression curves and correlations between linewidths and B₀. The data of 1.5 T and 2 T were taken from the literature (21). (c) ³¹P T₁ relaxation time measurements of PCr in the rat brains at 9.4 T and 16.4 T. Solid and dashed lines are the exponential fittings of the T₁ data at 16.4 T and 9.4 T, respectively. (T₁ = 2.95 ± 0.11 s for 9.4 T and 1.56 ± 0.05 s for 16.4 T) (d) Field dependence of PCr T₁. Solid line indicates the regression curve and correlation between PCr T₁ and B₀.

Figure 2c illustrates the exponential fittings of the in vivo ³¹P signals as a function of the inversion times at either 9.4 T or 16.4 T for the T₁ measurements of PCr in the rat brain. The measured PCr T₁ values were 2.95 ± 0.11 s (N = 4) and 1.56 ± 0.05 s (N = 4) for 9.4 T and 16.4 T, respectively. For the T₁ comparisons between different species, PCr T₁ values of cat brains were also measured at 9.4 T (T₁ = 2.60 ± 0.07 s; N = 7) and 16.4 T (T₁ = 1.50 ± 0.03 s; N = 6). The slightly longer T₁ values of PCr in the rat brains could be due to partial signal contribution from surrounding muscle. To extend the B₀ range, T₁ values of PCr from human brains at 4 T (T₁ = 4.36 ± 0.25 s; N = 12) and 7 T (T₁ = 3.54 ± 0.21 s; N = 10) were also included and compared in this study. Figure 2d shows an approximately exponential decay dependence of PCr T₁ values on the field strength between 4 T and 16.4 T according to the following regressed equation with an excellent regression coefficient:

$$T_{1,PCr}=6.248·e^{-0.086·B_0}{\mathrm{R}}^2=0.99$$ [3a]

Similar dependences were also observed for α-ATP and γ-ATP (data and regression curves are not shown herein) across a wide B₀ range from 4T to 16.4T:

$$T_{1,\alpha -ATP}=1.846·e^{-0.073·B_0}{\mathrm{R}}^2=1.00$$ [3b]

$$T_{1,\gamma -ATP}=1.754·e^{-0.046·B_0}{\mathrm{R}}^2=0.99$$ [3c]

When applying all field-dependent parameters obtained from rat brain at 9.4 T and 16.4 T (including the values of Δν_1/2, Q, T₁, at, TR, E₂² and G(x) as summarized in Table 1) into Equation [1], a power (β) dependence of PCr SNR on B₀ of approximately 1.42 was deduced using Equation [4],

$$\frac{SN{R}_{16.4T}}{SN{R}_{9.4T}}=1.74={(B_0\text{ratio})}^{\beta }\sqrt{Q\text{ratio}}\sqrt{\frac{1}{T_1\text{ratio}}}\sqrt{\frac{1}{\mathrm{\Delta }{\nu }_{1/2}\text{ratio}}\times }(G\text{ratio})={(\frac{16.4}{9.4})}^{\beta }\sqrt{0.873}\sqrt{\frac{1}{0.529}}\sqrt{\frac{1}{1.505}}\times 0.757$$ [4]

This result is in excellent agreement with the theoretical prediction of β=1.5 when the coil noise is dominate (25,26), and with the comparison result of human brain at 4 T and 7 T (β=1.4) as previously reported (20).

Equation [1] can be further simplified using the key parameters that are sensitive to B₀ to estimate the SNR ratio (R_SNR) at higher field relative to 4 T, while term E₂² (≈ 0 for most cases) can be omitted:

$$R_{SNR}={\left(\frac{B_0}{4}\right)}^{1.5}{\left(\frac{Q}{Q_{4T}}\right)}^{\frac{1}{2}}\sqrt{\frac{T_{1,4T}·\mathrm{\Delta }{\nu }_{1/2,4T}}{T_1·\mathrm{\Delta }{\nu }_{1/2}}}\left(\frac{G(x)}{G{(x)}_{4T}}\right)=\sqrt{\frac{Q}{Q_{4T}}}\left(\frac{G(x)}{G{(x)}_{4T}}\right)·R{\prime }_{SNR}$$ [5]

and

$$R{\prime }_{SNR}={\left(\frac{B_0}{4}\right)}^{1.5}\sqrt{\frac{T_{1,4T}·\mathrm{\Delta }{\nu }_{1/2,4T}}{T_1·\mathrm{\Delta }{\nu }_{1/2}}}$$ [6]

In Equation [5], the relative SNR contribution from the G(x) term depends on the TR and T₁ values, and it is close to 1 for most in vivo ³¹P MRS applications with a TR/T₁ ratio of < 1 (20), although it was offset from 1 in this study due to the application of a much longer TR (Table 1). Nevertheless, the SNR contribution of the G term can be readily calculated if the T₁ and TR values are known. There is not a simple way, however, to provide a priori estimation of the relative SNR contribution from the Q term since it is difficult to predict the loaded Q value of a particular RF coil at a given field strength. The Q value of a RF coil depends on many factors including its operating Larmor frequency, coil geometry and size, the sample size and loading property, etc., and it has to be determined experimentally under the sample loaded conditions. Therefore, based on the field dependent relationships (i.e., Eqs. [2] and [3]) deduced in the present study), Equation [6] was used to estimate the relative SNR improvement at higher fields to that of 4T. As a result, Figure 3 quantitatively shows the contributions from the B₀, T₁, and Δν_1/2 terms (either individual or combined effect) to the ³¹P SNR gain for PCr, α-ATP, and γ-ATP resonances, at high/ultrahigh fields.

Figure 3.

Field dependences of relative contributions from T₁ and Δν_1/2 (a, b and c), and from T₁, Δν_1/2 and B₀ (d, e and f) to the brain ³¹P SNR (normalized to 4 T) determined for the PCr (a and d), α-ATP (b and e), and γ-ATP (c and f) resonances, respectively.

DISCUSSION AND CONCLUSION

In this study, we first examined and compared the ³¹P NMR sensitivity in rat brain between 9.4 T and 16.4 T. The results show an approximately 1.74 fold ³¹P SNR gain at 16.4 T compared to that at 9.4 T, which is consistent with the previous ³¹P MR sensitivity comparison study in human brain at 7T vs. 4T (20). The T₁ relaxation times of PCr in rat brains at these two fields were also measured and a 47% decrease of PCr T₁ value was observed at 16.4T. Similar reductions in T₁ relaxation times of PCr and ATP were also observed in the cat and human brains across a wide range of B₀ from 4 T to 16.4 T as summarized in Fig. 2d and Equation [3]. Such field dependences of T₁ are presumably due to the fact that the CSA rather than the dipole-dipole interaction mechanism dominants the relaxation process of these phosphorus metabolites at high/ultrahigh field (28–30). This phenomenon is different from that observed in MRI, in which the ¹H T₁ of the tissue water has been found to increase with magnetic field strength since the proton relaxation is dominated by the dipole-dipole interaction mechanism. The shortened T₁ values of PCr and ATP resonances at higher field would allow more signal averaging within the same acquisition time, thus increasing the achievable SNR of ³¹P MRS. These findings indicate that increasing field strength not only significantly improves the in vivo ³¹P MRS detection sensitivity and quality, but also can shorten the total acquisition time for acquiring localized ³¹P MRS or three-dimensional imaging which usually requires a large number of k-space samples.

Another topic of interest in this study was the field dependence of PCr and ATP linewidths. Figures 2a and 2b summarize the field-dependent relationships of brain PCr and ATP linewidths across a very wide B₀ range from 1.5 T to 16.4 T. In general, all linewidths in Hz unit were positively correlated to B₀ with high linearity and very small error bars (Fig. 2a). However, the regression slopes were substantially different between different resonances, showing the smallest slope for PCr and largest slope for γ-ATP as described by Eq. [2]. Interestingly, the slope of γ-ATP was two times higher than that of α-ATP for the two phosphate spins within the same ATP molecule, and the two lines intersected at about 4 T where α-ATP and γ-ATP had equal linewidths (see Fig. 2a). These results suggest distinct relaxation behaviors between α-ATP and γ-ATP, which may reflect their different spin environments. As expected, we also observed that the intercepts for both γ-ATP and α-ATP lines at zero field strength were larger than that of the ³¹P-³¹P J-coupling constant (about 20 Hz). Both γ-ATP and α-ATP resonances are doublets separated by the ³¹P-³¹P J-coupling constant. The linewidths measured in this study are the apparent linewidths of the ATP resonances including the broadening effect caused by the ³¹P-³¹P J-coupling splitting. Nevertheless, the linewidths of their single resonances can be determined by subtracting the ³¹P-³¹P J-coupling constant from the apparent linewidth values (in Hz, as shown in Fig. 2a or summarized by Eqs. [2b] and [2c]). Importantly, the rates of the linewidth broadening (in the unit of Hz) as a function of B₀ were much slower than that of B₀ increasing for all resonances studied, e.g., increasing B₀ from 4 T to 16.4 T (> 4 times) only approximately doubles the linewidth for γ-ATP. Therefore, the “true” ³¹P spectral resolution (i.e., the linewidths in the ppm scale as demonstrated in Figs. 1 and 2b,) is significantly improved at high/ultrahigh fields, especially in the B₀ range of 1.5 T towards 9.4 T.

To understand the relative improvement of the ³¹P SNR that is practically achievable at a given field strength as compare to that of 4T, Eq. [5] has been derived to account for the contributions from all B₀ dependent parameters shown in Eq. [1]. If the contributions from the experimentally specific terms such as Q and G(x), which need to be determined based on the actual coil and acquisition conditions used in a particular study, are excluded, then Eq. [6] can be used to estimate the apparent SNR ratio at high/ultrahigh fields relative to 4T. As a summary, Fig. 3 displays the SNR gains for the brain PCr, α-ATP and γ-ATP resonances at high/ultrahigh fields (> 4 T) due to the contributions from B₀, T_1, and/or Δν_1/2. The most significant SNR gain is from the increasing magnetic field strength with the β power of 1.4–1.5 (dashed lines in Fig. 3d–3f); the sample loading and the operating frequency of the RF coil will affect the actual value of the β power (25,26). The consistent β values of approximate 1.4 as observed in the rat brain and the human occipital cortex in vivo using surface coils suggest that the coil noise likely dominated the noise contribution to the measured SNR. In contrast, for a volume RF coil with a heavy sample loading (e.g., human head) or a large RF coil operated at very high frequency, the increasing sample noise contribution will reduce the SNR gain at higher fields and reduce the β value below 1.5 when the sample noise becomes dominant (25).

It is also worth noting that identical spectral widths (SW=8kHz) were applied in the present SNR comparison study of rat brain between 9.4T and 16.4T to exclude the confounding effect of SW on the overall SNR (inversely proportional to square root of SW). However, practically, the optimal SW at lower fields for covering the same chemical shift range (in ppm unit) can be reduced as compared to higher fields, which will slightly negate the SNR benefit at higher field.

The broadened lines (Δν_1/2) at higher fields could lead to a reduction in signal intensity (dashed lines in Fig.3a–3c), and thus a SNR loss. This loss, however, could be compensated completely (for the PCr and α-ATP resonances) or partially (for γ-ATP resonance) by the shortened T₁ values. As a result, the net effect of combined T₁ and Δν_1/2 contributions leads to a significant SNR enhancement of >40% for PCr and >20% for α-ATP at 16.4 T as compared to 4 T, or a small SNR loss of <5% for the γ-ATP resonance (solid lines in Fig. 3a–3c). It has been reported that, in a solution at 37°C, the relative contribution of CSA increases from 14% at 2.3T to 59% at 7T for α-ATP, in contrast to a lesser degree of increase for γ-ATP from 5% at 2.3T to 34% at 7T (28), indicating a stronger CSA effect for ±-ATP than γ-ATP at higher field. This finding on the field-dependent ³¹P CSA is consistent with the in vivo results of the present study, in which a relatively slower decay of γ-ATP T₁ with increasing B₀ (Eq. [3c]) was observed as compared to that of α-ATP (Eq. [3b]). Nevertheless, all three HEP resonances benefit significantly from increased magnetic field strength in terms of overall SNR gain and spectral resolution improvement as quantitatively illustrated in Figs. 2 and 3. Finally, the findings of the present work suggest that a comprehensive approach based on Eqs. [1] and [5] or [6] can be applied to robustly quantify the achievable SNR gain of in vivo ³¹P MRS for brain applications at different fields as demonstrated herein.

In conclusion, the overall results of this study quantitatively demonstrate the substantial sensitivity and quality improvements of in vivo ³¹P brain MRS at high/ultrahigh fields. Such improvements should greatly benefit many biomedical applications of in vivo ³¹P MRS in assessing altered bioenergetics and metabolic processes associated with brain function and neurological diseases.

Abbreviations

MRS

magnetic resonance spectroscopy

MRSI

magnetic resonance spectroscopy imaging

NMR

nuclear magnetic resonance

B₀

magnetic field strength

HEP

high-energy phosphate

Pi

inorganic phosphate

PCr

phosphocreatine

ATP

adenosine triphosphate

SNR

signal-to-noise ratio

T₁

longitudinal relaxation time

T₂^*

apparent transverse relaxation time

Δν_1/2

resonance linewidth at half peak height

RF

radiofrequency

Q

radiofrequency coil quality factor

CSA

chemical shift anisotropy