Single-Shot Diffusion Trace-Weighted MR Spectroscopy: Comparison with Unipolar and Bipolar DW-PRESS

Abstract

This study demonstrates the feasibility and performance of the PRESS-based, single-shot diffusion trace-weighted sequence in quantifying the trace apparent diffusion coefficient (ADC) in phantom and in vivo using a 3T MRI/MRS scanner. The single-shot diffusion trace-weighted PRESS sequence was implemented and compared to conventional DW-PRESS variants using bipolar and unipolar diffusion-sensitizing gradients. Nine phantom data sets were acquired using each sequence, and seven volunteers were scanned in three different brain regions to determine the range and variability of trace ADC values, and to allow a comparison of trace ADCs among the sequences. This sequence results in relatively stable range of trace ADC values that are statistically significantly higher than those produced from unipolar and bipolar DW-PRESS sequences. Only tNAA, tCr, and tCho were reliably estimated in all sequences with CRLBs of at most 20%. The larger trace ADC from the single-shot sequences are likely due to the shorter diffusion time relative to the other sequences. Overall, this study presents the first demonstration of the single-shot diffusion trace-weighted sequence in a clinical scanner at 3T. Results show excellent agreement of phantom trace ADCs computed with all sequences, and in vivo ADCs agree well with the expected differences between gray and white matter. The diffusion trace-weighted sequence could provide an estimate of the trace ADC in a much shorter scan time (by nearly a factor of three) compared to conventional DW-PRESS approaches that require three separate orthogonal directions.

Graphical Abstract

This study presents the first demonstration of the single-shot diffusion trace-weighted sequence in a clinical scanner at 3T, and we compare the trace apparent diffusion coefficient (ADC) values obtained with this sequence to those computed from conventional DW-PRESS sequences with bipolar and unipolar diffusion gradients, both in phantom and in vivo.

1. INTRODUCTION

Diffusion-weighted magnetic resonance spectroscopy (DW-MRS) is a powerful tool that is capable of non-invasively measuring the diffusion properties of various intra-cellular metabolites in vivo. Unlike water, which permeates both the intra- and extra-cellular spaces, most metabolites are confined within the intracellular space, so that their diffusion reflects the structure and function of tissues at the microscopic scale. Quantifying metabolite diffusion therefore provides information pertaining to cellular compartment size and chemical transport, and the degree of tissue tortuosity and viscosity^1,2. Single voxel DW-MRS has shown changes in the apparent diffusion coefficients (ADC) of metabolites due to various pathologies such as ischemia and brain tumors^3–6, multiple sclerosis^7,8, and psychiatric disorders⁹.

One of the major confounding factors in measuring the ADC is the effect of diffusion anisotropy. Generally, the ADC along any diffusion direction depends on the orientation of the subject with respect to the scanner frame of reference. To eliminate this orientation dependence, several studies have instead reported the trace of the diffusion tensor, which is an invariant quantity.^10–12. Conventional DW-MRS methods require at least three separate measurements along orthogonal diffusion directions to determine the trace ADC. This can be accomplished by applying the diffusion-sensitizing gradients (DSGs) separately along each gradient axis or by scaling the amplitude simultaneously along multiple axes according to the desired directions^5,10–13.

The additional diffusion-weighting from cross-term interactions between the diffusion-sensitizing, localization, and other background gradients can bias the ADC quantitation^14,15. One straightforward, although time-consuming, technique for removing this bias is to acquire an additional measurement with DSG amplitudes of opposite polarities ¹³. The geometric mean of the diffusion-weighted signal from both polarities eliminates the cross-term contribution to the signal attenuation¹⁵, thus improving the accuracy of the estimated ADC. This approach can be used for any conventional DW-MRS sequence, including those incorporating bipolar (Figure 1(A)) or unipolar (Figure 1(B)) DSGs within the PRESS¹⁶ localization module. The bipolar scheme is known to minimize the cross-term contributions as well as eddy current effects, whereas the unipolar configuration (Figure 1(B)) generally does not share the same benefits^17–19. A variant of the Bipolar DW-MRS sequence has also been implemented using semi-LASER localization¹².

Figure 1:

Pulse sequence diagrams for the (A) Bipolar, (B) Unipolar, and (C) the single-shot diffusion trace-weighted (Trace) DW-PRESS sequences. The configuration for direction 1 ([1.0, 1.0, −0.5]) is shown here for the Bipolar and Unipolar DW-PRESS sequences. In general, TE = TE₁ + TE₂ for PRESS sequences. For the Bipolar and Trace DW-PRESS sequences, TE₁ = TE₂ = TE/2. The unipolar sequence was implemented with the minimum TE₁ and the rest of the time evenly distributed within the TE₂ period. The gradient ramp time is ζ, the duration is δ, and the separation between the start time of the dephasing and rephrasing lobes is Δ.

DW-MRS sequences based on PRESS, as opposed to sequences that use other localization schemes such as STEAM²⁰, are of particular interest because this class of sequences allows for a DSG configuration that generates a signal weighted by the trace of the diffusion tensor, within a single shot or TR. This single-shot diffusion trace-weighted scheme, originally proposed by Mori et al. for DW-MRI²¹, was later extended for DW-MRS by de Graaf et al.²². The single-shot diffusion trace-weighted MRS sequence (Figure 1(C), from here on also referred to as “Trace DW-PRESS”) is able to eliminate all cross terms between DSGs and any static background gradients while providing a diffusion trace-weighted signal that is suitable for directly estimating the trace ADC, without any additional measurements along orthogonal diffusion directions. A version of this sequence using localization by adiabatic selective refocusing (LASER) was proposed by Valette et al.²³. More recently, another variant using semi-LASER and tetrahedral encoding has been explored in human brain at 7T²⁴. However, the validation and performance of Trace DW-PRESS in humans has not been shown, although similar isotropic diffusion-weighted schemes have been implemented on a clinical scanner for DW-MRI only^25,26.

Another important consideration in DW-MRS is the dependence of the measured ADC on the diffusion time. As the diffusion time decreases, the mean displacement of diffusing metabolites increases due to the reduced impact of structural restrictions on diffusion occurring during short time scales, leading to higher estimates of metabolite ADC’s in vivo²⁷. Several reports have explored DW-MRS at short diffusion times (typically ≤ 10 ms) using oscillating sinusoidal gradients and have measured this relative increase in the trace ADC compared to DW-MRS with long diffusion times^{10–12,28–30}. For DW-MRS using pulsed gradients, the Trace DW-MRS sequence is constrained to have shorter diffusion times compared to the bipolar and unipolar alternatives which have a more flexible range of diffusion times, especially at long TE’s. Generally, the echo times for Trace DW-PRESS must be relatively long (~140 ms) in order to accommodate the DSGs, and consequently the number of reliably detected metabolites is limited to the main groups of total n-acetylaspartate (tNAA), total creatine (tCr), and total choline (tCho).

In this work, we validated Trace DW-PRESS in vivo and in a phantom on a clinical 3T scanner. This study presents the first demonstration of DW-MRS using the single-shot diffusion trace sequence proposed by de Graaf et al.²², but which until recently had not been testable in humans due to earlier hardware limitations of clinical scanners. We report the in vivo trace ADC values of three main metabolite groups – total NAA, total Cr, and total Cho – and water, as well as six metabolites (NAA, Cr, Cho, Glu, mI, Lac) from a brain phantom, and compare these values to those measured with Unipolar and Bipolar DW-PRESS schemes acquired with three orthogonal diffusion directions and positive and negative gradient polarities. In vivo results are shown from three different brain regions, and we tested for differences in trace ADC values among these regions and pulse sequence variants.

2. THEORY

2.1. The b-matrix and the Diffusion Tensor

The b-value is primarily a function of the durations, amplitudes and temporal separations of the DSGs. A key component of its computation is the gradient moment $\stackrel{⃑}{F}\left(t^{\prime }\right)$:

$$\stackrel{⃑}{F}\left(t^{\prime }\right)=\underset{0}{\overset{t^{\prime }}{\int }}\stackrel{⃑}{G}\left(t\right)dt$$ [1]

where $\stackrel{⃑}{G}\left(t\right)≔〈G_x\left(t\right),G_y\left(t\right),G_z\left(t\right)〉$ is defined as the vector of the applied time-varying gradients³¹. The matrix of b-values, $\mathit{b}$, can then be defined as

$$\mathit{b}={\gamma }^2{\int }_0^{\tau }\stackrel{⃑}{F}\left(t^{\prime }\right)⨂\stackrel{⃑}{F}(t^{\prime }){dt}^{\prime }$$ [2]

where $⨂$ denotes the outer product operation. Using this definition, the signal attenuation $S\left(\tau \right)$, after a time $\tau$, can be described as

$$\ln \left(\frac{S\left(\tau \right)}{S_0}\right)=-\sum _{\alpha ,\beta }{\mathit{b}}_{\alpha \beta }{\mathit{D}}_{\alpha \beta }\alpha ,\beta \in \{x,y,z\}$$ [3]

where $S_0$ is the signal amplitude without diffusion-weighting and $\mathit{D}$ is the diffusion tensor. Both $\mathit{b}$ and $\mathit{D}$ are defined with respect to the same reference frame. For any arbitrary rotation, the trace of the diffusion tensor is preserved. Hence, the trace ADC value is an orientation independent quantity.

2.2. Cross Term Contribution to Diffusion-weighting

Any non-diffusion-sensitizing gradients, including localization and crusher gradients, as well as any background gradients, can cause an additional unwanted diffusion-weighting. In this case, the total b-matrix becomes $\mathit{b}={\mathit{b}}_d+{\mathit{b}}_{ct}$, where ${\mathit{b}}_d$ originates from the DSGs only and ${\mathit{b}}_{ct}$ contains cross terms between the DSGs and any other applied or (static and non-static) background gradients. The contribution from the non-diffusion-sensitizing gradients alone is usually relatively small and is considered negligible in practice³². By computing the geometric mean of the signals (peak integrals) acquired with positive and negative DSG polarities, the extra ${\mathit{b}}_{ct}$ term is cancelled from the total b-value. The effective b-value for the geometric mean becomes the average of the b-values from the negative and positive DSG polarities, $b_d^{-}$ and $b_d^{+}$, respectively.

2.3. Diffusion Trace-weighted PRESS

Within a single TR, the particular configuration of 12 pairs of bipolar gradient lobes interleaved within the PRESS localization leads to the cancellation of signal weighted by the off-diagonal terms of the diffusion tensor in Equation. 3. Further details and examples of how these off-diagonal terms are cancelled in the computation in Equation. 3 can be found in the aforementioned reports^21–23.

Since the bipolar DSG pairs in the Trace DW-PRESS sequence are isolated from the localization and crusher gradients, and the gradient-induced phase is rebalanced after each pair, the diffusion-weighting originating from cross-terms due to localization and crusher gradients is effectively null. Another key feature of Trace DW-PRESS is that the inclusion of a second refocusing pulse allows for the elimination of any cross-terms originating between static background gradients and the DSGs. The Bipolar DW-MRS sequence (Figure 1(A)) also is known to minimize (not eliminate) these cross terms³³, while the Unipolar DW-MRS retains a large contribution from cross-terms due to any static background gradients (Figure 3 ).

Figure 3:

Effect of cross-terms originating from the interaction of the diffusion-sensitizing gradients with a static background gradient G₀ (shown in green). The diffusion direction corresponding to the vector [1.0, 1.0, −0.5] is shown. The gradient moments (F₀, F_x, F_y, and F_z) are plotted along with the cross terms (F₀F_x, F₀F_y, and F₀F_z), for the Bipolar, Unipolar, and Trace (diffusion trace-weighted) DW-PRESS sequences. The cross terms F_xF_y, F_yF_z, and F_xF_z that contribute to off-diagonal elements in the b-matrix are also shown. Note that the Bipolar and Trace DW-PRESS sequences have equal contributions of negative and positive areas in the F₀F_x, F₀F_y, and F₀F_z plots, leading to cancellation of cross terms originating from the G₀. The Unipolar DW-PRESS sequences, in contrast, retains a large net cross term contribution. For simplicity, the localization and crusher gradients were omitted in the computation of F₀, F_j, and F₀F_j (j = x, y, z).

2.4. Computing the b-matrix with respect to a given reference frame

For a given DSG amplitude $G_d$, a particular diffusion direction is achieved by scaling this amplitude along each gradient axis according to a directional vector, $\stackrel{⃑}{n}=(n_x,n_y,n_z$). The DSG along the direction specified by $\stackrel{⃑}{n}$ is then written as ${\stackrel{⃑}{G}}_d=G_d·\stackrel{⃑}{n}$. Usually, the three directional vectors are chosen to be an orthogonal basis, with a common set being $\beta =\left\{\right(1.0,1.0,-0.5),(1,-0.5,1),(-0.5,1.0,1.0\left)\right\}$. This set makes more efficient use of the gradients to reach a given b-value compared to other choices such as the standard basis ${\beta }_0=\left\{\right(\mathrm{1,0},0),(\mathrm{0,1},0),(\mathrm{0,0},1\left)\right\}$, for which the DSG is applied only along a single gradient axis per measurement. In comparison, each direction in $\beta$ uses smaller gradient amplitudes along all axes to reach the same b-value.

In the Supporting Information Section 1.2, it is shown that the b-matrix for Trace DW-PRESS is diagonal and is preserved under any unitary transformation. In general, this invariance does not hold for the b-matrices computed for Unipolar and Bipolar DW-PRESS – the b-matrix for these sequences have diagonal and off-diagonal entries when computed in the standard ${\beta }_0$ frame, although these matrices naturally become diagonal in the $\beta$ frame, with only one diagonal entry, depending on the particular diffusion direction $\overrightarrow{n}\in \beta$ assumed in Equation 2.

2.5. Diffusion times and b-values for the Bipolar, Unipolar, and Trace DW-MRS sequences

Referring to Figure 1(A), the analytic b-value for Bipolar DW-PRESS can be derived (see Supporting Information Section 1.3) as

$$b={\gamma }^2{‖{\stackrel{⃑}{G}}_d‖}^2{\left(2\delta \right)}^2\left[\mathrm{\Delta }-\frac{2\delta }{3}-\frac{(\tau +\zeta )}{2}-\frac{1}{12}{\left(\frac{\zeta }{\delta }\right)}^2\left(\delta -\frac{\zeta }{5}\right)\right]$$ [4]

where $‖{\stackrel{⃑}{G}}_d‖$ is the magnitude of the diffusion gradient vector applied along the direction specified by $\stackrel{⃑}{n}({\stackrel{⃑}{G}}_d=G_d·\stackrel{⃑}{n})$, and $G_d$ is the amplitude. The effective diffusion time is

$$t_d=\mathrm{\Delta }-\frac{2\delta }{3}-\frac{(\tau +\zeta )}{2}-\frac{1}{12}{\left(\frac{\zeta }{\delta }\right)}^2\left(\delta -\frac{\zeta }{5}\right)$$ [5]

The following formula

$$b=N{\gamma }^2{‖{\stackrel{⃑}{G}}_d‖}^2{\delta }^2\left[\mathrm{\Delta }-\frac{\delta }{3}-\frac{1}{6}{\left(\frac{\zeta }{\delta }\right)}^2\left(\delta -\frac{\zeta }{5}\right)\right]$$ [6]

gives the analytic b-value for Unipolar (N = 1) and Trace (N = 4) DW-PRESS. For the trace-weighted sequence, the directional vector is always $\stackrel{⃑}{n}=\left(1.0,1.0,1.0\right)$, since the DSG amplitudes are the same along all axes. For Unipolar and Trace DW-PRESS (Figure 1, (B)–(C)), the diffusion time can be derived analytically from the generic b-value equation for a pair of trapezoidal gradients³⁴:

$$t_d=\mathrm{\Delta }-\frac{\delta }{3}-\frac{1}{6}{\left(\frac{\zeta }{\delta }\right)}^2\left(\delta -\frac{\zeta }{5}\right)$$ [7]

The b-value formulas presented above assume no localization and crusher gradients. The diffusion times given above are effectively the “reduced” diffusion times that are appropriate for trapezoidal DSGs^35,36.

3. METHODS

All measurements were made using a 3T scanner (Prisma, Siemens Healthcare, Munich, Germany) with a maximum net slew rate limit of 200 mT/m/ms and a maximum gradient amplitude limit of 80 mT/m per axis. A 16-channel receive head coil was used for both the phantom and in vivo acquisitions. Localization of the entire phantom or brain volume was achieved with T₁-weighted axial, coronal, and sagittal two-dimensional MRI’s acquired with TR/TE = 250 ms/2.49 ms, FOV = 240 × 240 mm², 1.25 × 1.25 mm² in-plane resolution, and 35 slices of 4 mm thickness each.

For all DW-PRESS acquisitions, the voxel size was 25 × 25 × 25 mm³, TR = 2 s, and TE = 140 ms. The spectral width was 1250 Hz with 1024 time points. The offset frequency for the RF pulses was set at −2.3 ppm relative to water to minimize chemical shift misregistration. Global water suppression was achieved using a WET module³⁷. Non-water suppressed data was acquired for eddy current phase correction³⁸, coil sensitivity estimation, and for computing the water ADC.

3.1. Diffusion-sensitizing gradient parameters and b-values

For Unipolar and Bipolar DW-PRESS, three orthogonal diffusion directions were measured: [1.0, 1.0, −0.5] (direction 1), [1.0, −0.5, 1.0] (direction 2), and [−0.5, 1.0, 1.0] (direction 3). Data from both negative and positive DSG polarities were acquired. The average of the b-values from the negative and positive gradient polarities was taken for calculating the cross-term compensated trace ADCs from the geometric means of the signals. All b-values were computed with numerical integration using the actual chronograms and gradient parameters implemented in the sequences.

Three b-values – null (b₀), medium (b₁), and high (b₂) – were considered in this study: b₀ = 4 s/mm², b₁ = 994 – 1,021 s/mm², and b₂ = 1,697 – 1,718 s/mm². For these b-values, the corresponding diffusion-sensitizing gradient amplitudes for each sequence were as follows: (i) Bipolar: 0, 24.9, 32.4 mT/m; (ii) Unipolar: 0, 52, and 68 mT/m; (iii) Trace: 0, 51, 66 mT/m. The diffusion gradient timing parameters for each sequence (Figure 1) were as follows: (i) Bipolar: ζ = 700 μs, δ = 6.7 ms, Δ = 70 ms, τ = 17.6 ms; (ii) Unipolar: ζ = 1.5 ms, δ = 9.5 ms, Δ = 28.6 ms; (iii) Trace: ζ = 1.5 ms, δ = 6.5 ms, Δ = 13 ms. The diffusion times for the Bipolar, Unipolar, and Trace DW-PRESS sequences were 58.8 ms, 25.2 ms, and 10.8 ms, respectively.

At the largest b-value, the Bipolar and Unipolar DW-PRESS sequences had net slew rates of 69.4 mT/m/ms and 68 mT/m/ms, respectively, while the trace-weighted sequence had a net slew rate of 76.2 mT/m/ms. Ramp times were chosen to in order to limit the slew rate of the Unipolar and Trace DW-PRESS sequences, which could not exceed 79.6 mT/m/ms due to scanner-imposed nerve stimulation limits.

For a fixed TE, the trace-weighted sequence is less efficient at reaching higher b-values than the other sequences. The unipolar sequence has marked differences in the b-values computed with negative and positive DSG polarities (Table 1) because of cross term contributions from the localizer and crusher gradients, which can be additive or subtractive depending on the polarities of the DSGs. In the Supporting Information Section 1.1, the conditions and limitations of each sequence for reaching higher b-values is further examined. In particular, at the given TE of 140 ms, the Trace DW-PRESS is capable of b-values up to approximately 3,300 s/mm², however, only when employing the maximum gradient limit of 80 mT/m per axis. In contrast, Bipolar and Unipolar DW-PRESS can reach this higher range more efficiently because the Δ and ζ parameters can be more freely adjusted to reach ~3,300 s/mm² without having to increase the gradient amplitude to its maximum, while keeping the TE ≤ 140 ms. Additionally, due to its dependence on the closely spaced bipolar DSG pairs, Trace DW-PRESS is constrained to shorter diffusion times compared to the other sequences, which can attain more flexible b-value ranges in diffusion time by varying Δ and/or τ.

Table 1:

Table of b-values for each sequence used in this study. Note the relatively large difference in the computed b-values between the positive and negative diffusion-sensitizing gradient polarities for the Unipolar DW-PRESS sequence. For calculating the ADC in each direction, the average of the b-values from the positive and negative gradient polarities were used for fitting the geometric mean of the corresponding diffusion-weighted signals.

		b-values (s/mm2)
		b0	b1		b2
			pos	neg	pos	neg
BIPOLAR	dir 1	4	1006	1026	1704	1731
	dir 2		1005	1027	1703	1732
	dir 3		1006	1026	1705	1731
UNIPOLAR	dir 1	4	1034	954	1749	1644
	dir 2		1034	953	1750	1643
	dir 3		1034	953	1750	1644
TRACE		4	1020		1707

3.2. Phantom Experiments

The GE “Braino” phantom (GE Medical Systems, Milwaukee, WI, USA), containing N-acetylasparate (NAA, 12.5 mM), creatine (Cr, 10.0 mM), choline (Cho, 3.0 mM), Glutamate (Glu, 12.5 mM), myo-inositol (mI, 5.0 mM), and Lactate (Lac, 5.0 mM) was used for all phantom acquisitions. The ADC’s of the GE Braino metabolites were reported by Landheer et al. ³⁹. The voxel was positioned at the center of the phantom which was placed at isocenter.

The water-suppressed acquisitions had 20, 36, and 52 averages with corresponding non-water-suppressed averages of 4, 6, and 8 averages, for the null (b₀), medium (b₁), and high b-values (b₂), respectively. The average full width at half maximum (FWHM) of the magnitude water peak after manual shimming was 4.6 Hz.

3.3. In Vivo Experiments

A total of 14 healthy volunteers (6 females and 8 males, ages = 39.9 ± 16 years) were recruited and each participant in this study gave informed consent according to local institutional review board guidelines. A subset of these volunteers was scanned no more than two times but in different brain regions. Three voxel locations (Figure 2), in predominantly white or gray matter regions, were probed with each sequence – the frontal gray (FG) matter in the prefrontal lobe, occipital gray (OG) matter, and occipital (subcortical) white (OW) matter. Due to the large voxel size of 15.6 mL, the voxels in each region contain partial volumes of gray and white matter.

Figure 2:

In vivo localization images for voxel locations in (A) frontal gray matter (FG) (B) occipital gray matter (OG), and (C) occipital (subcortical) white matter (OW). Due to the relatively large voxel size of 15.6 mL, the voxels in each region actually contain partial volumes of white and gray matter. The panel in (D) shows voxel placement in the GE Braino phantom.

Data from all three sequences were acquired during the same scan session. Only two b-values – b₀ and b₂ – were acquired from the Bipolar and Unipolar DW-PRESS sequences, due to scan time limitations. The null b-value (b₀) data were acquired with 28 and 4 averages for water-suppressed and non-water-suppressed data, respectively. Diffusion-weighted spectra at b₂ were acquired with 56 and 8 averages for the water-suppressed and non-water-suppressed data, respectively. For Bipolar or Unipolar DW-PRESS, spectra from three directions and two gradient polarities were acquired, resulting in a scan time of 13 minutes, 52 seconds for 7 measurements (1 null and 6 diffusion-weighted).

In contrast, all three b-values – b₀, b₁, and b₂ – were acquired for Trace DW-PRESS. The same number of averages were acquired as for the Bipolar and Unipolar DW-PRESS sequences for b₀ and b₂. For b₁, 44 and 6 averages were acquired for the water-suppressed and non-water-suppressed data, respectively. The Trace DW-PRESS scan time was 4 minutes, 45 seconds.

The average FWHM of the magnitude water peak after manual shimming was 18.2 Hz, 13.8 Hz, and 12.8 Hz, for the frontal gray, occipital gray, and occipital (subcortical) white matter brain regions, respectively.

The total scan time for one in vivo session (Bipolar, Unipolar, and Trace DW-PRESS acquisitions) - including localization, shimming, and other sequence preparations – was approximately 50 minutes.

3.4. Determining the effects of eddy-currents

As a metric for determining eddy current effects on the signal, we measured the standard deviation (SD) of the zero-order phase correction for the NAA singlet at 2.01 ppm in phantom at the highest b-value. This phase was estimated before applying eddy current phase correction using the water data, and before coil combination. The spectrum from the dominant coil element, which was determined as the coil with the largest water peak integral from the non-water-suppressed data, was used since it had sufficient NAA SNR to allow a reliable phase determination. A similar approach for measuring eddy current effects was taken by Hanstock et al.⁴⁰, in which a single n-octanol peak was used as a reference. Instead of the water peak, the NAA singlet was chosen as a reference since this was the dominant peak in the phantom spectrum and is not J-coupled, serving as a reliable peak for estimating the SD of the zero-order phase correction from all 52 averages of the highest b-value acquisition, as opposed to the water data which only had at most 8 averages.

This analysis was done on phantom data, as it was not influenced by confounding factors such as thermal noise, motion, and variability in localization – all of which could present additional sources of phase variation in vivo. Using a least-squares algorithm, the optimal phase ${\phi }_0$ for placing the real part of the NAA peak in absorptive mode was formulated as the minimization

$${\phi }_0=\underset{\phi }{\mathrm{argmin}}\frac{1}{2}{‖|Y|-Y{e}^{i\phi }‖}_2^2$$ [8]

where $\mathrm{Y}$ is the portion of the measured spectrum in the range of the NAA singlet (1.8 – 2.2 ppm) and $\left|Y\right|$ is the magnitude. Prior to the least-squares procedure, linear baseline was subtracted. The SD of the zero-order phase ${\phi }_0$ was computed from across all measurement for each type of sequence and for each b-value.

3.5. Determining the effects of diffusion-weighting from cross terms

The non-water suppressed phantom data from the Bipolar and Unipolar DW-PRESS sequences were used for determining the degree to which cross-terms from static background gradients may cause additional signal attenuation, as reflected in decreases of the water peak area. The sensitivity to these cross terms was compared between these two sequences. The water peak in magnitude mode was integrated over a frequency range containing a water signal level above at least 1% the maximum peak height. This integral was computed for all three directions and for both polarities. Large differences in the water peak area between negative and positive polarities would indicate a strong contribution from cross terms. This approach for determining the effects due to cross terms is similar to those found in other reports ^13,41.

3.6. Post-Processing

Diffusion-sensitizing gradients, along with pulsatile motion in the brain, render the signal more susceptible to large phase variations from shot to shot. Therefore, it is crucial to apply 0^th order phase corrections as well as frequency drift corrections to the data before signal averaging^{10,11,42–47}. The residual water or another dominant peak, such as the NAA singlet, can serve as a reference for phasing the signal and determining the frequency drift. No cardiac gating or ECG triggering was used in this study, similar to other reports^10,11,40.

Initially, eddy current phase correction was implemented using the non-water-suppressed data³⁸. Using a least squares algorithm (Equation 8), the optimal zero-order phase for the NAA peak was determined for each average and coil, and this constant phase was subsequently applied to the entire spectrum. The coil sensitivities were estimated from the water peak integrals of the water-unsuppressed data. Generalized least squares coil combination⁴⁸ was then applied. Using a cross-correlation algorithm with the NAA peak from the first average as a reference, an initial frequency drift correction was applied. This correction allowed for a better SNR estimation of NAA and improved the initialization for the non-linear least-squares algorithm in Equation 9. Individual averages with NAA peak SNR’s less than 90% of the average NAA peak SNR were removed, thus excluding spectra overly affected by motion and other artifacts. Before averaging, a final frequency drift ${\mathrm{\Delta }f}_i$ and zero-order phase ${\phi }_i$ correction for each average were computed by solving⁴⁹

$${\mathrm{\Delta }f}_i,{\phi }_i=\underset{\mathrm{\Delta }f,\phi }{\mathrm{argmin}}\frac{1}{2}{‖\tilde{y}-y_i{e}^{i\phi +i2\pi \mathrm{\Delta }ft}‖}_2^2$$ [9]

where $y_i$ is the time signal of the $i^{th}$ average, and $\tilde{y}$ is the average that is most similar (in terms of room mean square error) to the other averages within the same set.

Finally, the signals were averaged and the residual water was removed using the Hankel-Lanczos singular value decomposition algorithm⁵⁰. All spectra were processed using MATLAB (MathWorks, Natick, MA, USA).

3.7. Signal Quantitation and Determination of ADC

Prior-knowledge basis spectra were simulated with VESPA⁵¹. For in vivo data sets, the basis set included the following metabolites: alanine, ascorbate, aspartate, choline (Cho), creatine (Cr), γ-aminobutyric acid, glucose, glutamine (Gln), glutamate (Glu), glycerophosphorylcholine, glutathione, lactate (Lac), myo-inositol (mI), N-acetylaspartate (NAA), N-acetylaspartylglutamate (NAAG), phosphorylcholine (PCh), phosphocreatine (PCr), phosphorylethanolamine, scyllo-inositol, and taurine.

The post-processed MRS signal was quantified using LC Model (version 6.2–0T)⁵² and the resulting LC model concentration estimates, which are proportional to the metabolite peak integrals, were assumed to fit the general model:

$$S\left(b_k^{\pm }\right)=S(b_0)e^{-b_k^{\pm }·{ADC}_k^{\pm }}$$ [10]

where $b_k^{\pm }$ and ${ADC}_k^{\pm }$ is the b-value and the ADC in the $k^{th}$ direction, for either the positive or negative polarities, respectively. Only estimates with Cramer-Rao lower bounds (CRLB’s) ≤ 20% were considered for further analysis. For DW-PRESS acquisitions with three directions and two polarities, the trace ADC’s from the negative (ADC−), positive (ADC+), and geometric means of the two polarities (ADC_geo) were also determined.$ete$ For estimation of water ADC’s, the water peak from the non-water suppressed data was first zero-order phased into absorptive mode. The water spectrum was then 4× interpolated to produce a smoother profile of the peak for better estimation of the area with numerical integration. These water peak areas were subsequently used for computing the ADC using the same model stated above.

3.8. Statistical Analysis

Phantom

A repeated measures analysis of variance (ANOVA) with Bonferroni correction was performed to determine any significant differences in the trace ADC values of NAA, Cr, Cho, Glu, mI, and Lac, among the Bipolar, Unipolar and Trace DW-PRESS sequences. For Unipolar and Bipolar DW-PRESS, paired samples t-test were conducted to determine any statistically significant differences between the values of ADC− and ADC+ for each of these metabolites. A significance level of α = 0.05 was adopted.

In vivo

A repeated measures analysis of variance with Bonferroni correction was conducted to determine any significant differences in the trace ADC values of tNAA, tCr, tCho and water, for each brain region (FG, OG, and OW), among the Bipolar, Unipolar and Trace DW-PRESS sequences.

Paired samples t-tests were conducted to determine any statistically significant differences in the trace ADC values of tNAA, tCr, tCho, and water between the occipital gray (OG) and occipital white (OW) matter, for each type of pulse sequence.

For the Bipolar and Unipolar sequences, and for each brain region (FG, OG, and OW), paired samples t-test were conducted to determine any statistically significant differences between the values of ADC− and ADC+ for tNAA, tCr, tCho, and water.

We tested for potential bias resulting from the systematic difference of using 3 b-values for Trace DW-PRESS versus 2 b-values for Bipolar and Unipolar DW-PRESS by applying Wilcoxon signed rank tests to determine if the ADCs for Trace DW-PRESS estimated from 2-bvalues were significantly different from those estimated from 3 b-values. Statistical tests and comparisons with Unipolar and Bipolar DW-PRESS were redone for those metabolites whose ADCs computed from 2 vs.3 b-value were significantly different. Further details on this statistical analysis is described in the Supporting Information Section 1.4.

To test for repeatability, two volunteers were each scanned three separate times – one in the frontal gray (FG) matter and the other in the occipital gray (OG) matter. The means, standard deviations, and coefficients of variance (CV) of the trace ADC’s of tNAA, tCr, tCho, and water were computed across the three sessions.

4. RESULTS

4.1. Cross terms due to a static background gradient

As seen in Figure 3, cross terms due to static background gradients are compensated for in the Bipolar and Trace DW-PRESS sequences. However, the b-value for the Unipolar sequence has an inherent greater dependence on cross terms from the localization and crusher gradients. This effect explains the large differences in the computed b-value between the negative and positive DSG polarities in the Unipolar DW-PRESS sequences (Table 1). The terms F_xF_y, F_xF_z, and F_yF_z correspond to the off-diagonal elements of the b-matrix. Evidently, the time integrals of these terms are essentially nulled only for the Trace DW-PRESS sequence.

4.2. Phantom

Figure 4(A) presents representative spectra acquired with Bipolar, Unipolar, and Trace DW-PRESS in phantom. The amplitudes of the NAA peaks in the unipolar sequences tend to vary more compared to the NAA spectra from the Bipolar sequence, both as a function of direction and polarity. In Figure 4(B), the standard deviation of the zero-order phase correction on the NAA singlet show that the Bipolar sequence experiences a lower degree of eddy current-induced phase fluctuations. However, the Unipolar and Trace sequences have a larger standard deviation, indicating greater influence of eddy currents, as expected since these sequences require larger gradient amplitudes to reach a given b-value, compared to the Bipolar sequence. Figure 4(C) also shows that the Unipolar sequence does not compensate for cross-terms as well as the Bipolar sequence, as the percent differences between the water peaks acquired with positive and negative DSG polarities are greater than for the Bipolar sequence.

Figure 4:

(A) Representative spectra acquired with the Bipolar, Unipolar, and diffusion-trace weighted (Trace) DW-PRESS sequences. Spectra from all three b-values (b₀, b₁, b₂) are shown. The spectra from the Bipolar and Unipolar DW-PRESS sequences acquired at all three directions with positive (d₁₊, d₂₊, d₃₊) and negative (d₁₋, d₂₋, d₃₋) polarities are shown. (B) The standard deviations (SD) of the zero-order phase corrections for the NAA peak (before application of eddy current phase correction). This SD is a measure of the effect of eddy currents on the acquired signal. (C) Percent difference of the water peak integral values between water spectra acquired with negative and positive polarities – mean and standard deviations (error bars) are shown for all three directions and for the two b-values greater than the b₀. The unipolar sequence has markedly higher differences in b-values between the two polarities.

Statistical Analysis

No significant differences were found in the trace ADC values of NAA, Cr, Cho, Lac, and mI among the Bipolar, Unipolar, and Trace DW-PRESS phantom acquisitions (Table 2). The trace ADC values of Glu were significantly different only between the Bipolar (0.78 ± 0.05 μm²/ms) and Unipolar (0.64 ± 0.06 μm²/ms) sequences (p = 0.006). For Unipolar DW-PRESS, the trace ADC of Glu from the negative gradient polarities (ADC− = 0.64 ± 0.06 μm²/ms) is significantly different (p < 0.001) from the one from the positive polarities (ADC+ = 0.65 ± 0.07 μm²/ms). For the Bipolar sequence, the trace ADC+ of Glu (0.77 ± 0.04 μm²/ms) was also significantly different from the trace ADC− (0.78 ± 0.07 μm²/ms). All other trace ADC+ and ADC− values were not significantly different for any other metabolites from either the Unipolar or Bipolar sequences.

Table 2:

GE Braino trace ADC values averaged over 9 measurements from DW-PRESS acquisitions using the Bipolar, Unipolar, and Single-shot Trace-weighted sequences. All phantom measurements agree well with reference values³⁹.

	GE Braino Trace ADC values: mean ± standard deviation [μm2/ms]
	Bipolar			Unipolar			Trace	Reference Values
	ADC−	ADC+	ADC (geo)	ADC−	ADC+	ADC (geo)	ADC
NAA	0.59 ± 0.01	0.61 ± 0.02	0.6 ± 0.01	0.6 ± 0.02	0.6 ± 0.02	0.6 ± 0.02	0.6 ± 0.02	0.59 ± 0.01
Cr	0.77 ± 0.01	0.78 ± 0.01	0.78 ± 0.01	0.78 ± 0.03	0.78 ± 0.02	0.78 ± 0.02	0.78 ± 0.02	0.78 ± 0.02/0.84 ± 0.1
Cho	0.93 ± 0.01	0.94 ± 0.02	0.93 ± 0.01	0.95 ± 0.04	0.95 ± 0.03	0.95 ± 0.03	0.93 ± 0.03	0.91 ± 0.03
Glu	0.78 ± 0.06	0.77 ± 0.04 #	0.78 ± 0.04 *	0.64 ± 0.06	0.65 ± 0.06 #	0.64 ± 0.06	0.73 ± 0.07	0.76 ± 0.03
Lac	0.75 ± 0.13	0.8 ± 0.14	0.78 ± 0.12	0.82 ± 0.08	0.8 ± 0.08	0.81 ± 0.06	0.76 ± 0.1	0.64 ± 0.13
mI	0.78 ± 0.16	0.79 ± 0.13	0.79 ± 0.14	0.72 ± 0.12	0.72 ± 0.14	0.72 ± 0.13	0.76 ± 0.11	0.76 ± 0.1

^*significantly different with respect to Unipolar ADC (p < 0.05); repeated measured ANOVA with Bonferroni correction

^#significantly different with respect to ADC− (p < 0.05); paired samples t-test

Coefficients of variance percentages (CV%) are largest for the trace ADC estimates of Glu (6 – 10%), Lac (8 – 18%), and mI (15 – 21%) in all sequences, while the CV%’s of NAA, Cr, and Cho are all below 4%. The CV%’s of trace ADC estimates of Lac and mI are largest from the Bipolar acquisitions (16–19% and 19–21%, respectively). The CV% value for Lac is lowest from the Unipolar sequence (8–10%).

4.3. In Vivo

Post-processing procedures are illustrated in Figure 5 with in vivo data. Recent studies, such as by Genovese et al.¹², have reported the use of cardiac triggering to avoid further signal reduction due to pulsatile motion. Without triggering, large shot-to-shot phase and SNR variations are measured (Figure 5C & 5D), which, if uncorrected, could result in significant net signal loss upon averaging (Figure 5G). In this study, SNR-based thresholding was key in retrospectively excluding averages significantly affected by large SNR losses from pulsatile motion (Figure 5C). Across all sequences, for the highest b-value, 10±2 of 56 averages were removed and, for the lowest b-value, approximately 5±1 were excluded, resulting in a rejection percentage range of 14 – 21%. Frequency drift and phase corrections prior to averaging also ensured that the diffusion-weighted signal was not overly biased towards higher ADCs.

Figure 5:

Post-processing procedures demonstrated from in vivo data: (A) Separation of the low- and high-SNR averages. (B) Comparison of the averaged spectra from the sets of low-SNR and high-SNR averages, showing that a reduction in peak intensities will result if the low-SNR averages are not removed. (C) The threshold criterion based on the SNR of the NAA singlet determines which specific averages to remove. (D) Raw spectra before zero-order phase correction. (E) The spectra after zero-order phase correction. (F) Frequency-drift correction after zero-order phasing. (G) Comparison between the uncorrected and corrected spectra.

Figure 6 shows representative spectra in the OG voxel, indicating good linewidths (averages of 12–18 Hz for the magnitude water peak in vivo) and SNR’s suitable for quantitation, as well as Cramer-Rao lower bound (CRLB) values of the LC Model metabolite concentration estimates no greater than 20% (Supporting Information Table S1). Spectra from the voxels in FG and OW are shown in Supporting Information Figures S1 and S2, respectively. The highest average CRLB value was 13.2% for tCho from the Trace DW-PRESS acquisitions in OG. Due to metabolite CRLB exceeding 20% at the highest b-value, three data sets were discarded from the frontal gray matter, and one data set was discarded from the occipital white matter. The CRLB’s for all datasets in occipital gray voxels did not exceed 20% for any b-value. Spectra from Trace DW-PRESS experienced the largest drop in signal amplitude at the highest b-value tested, compared to the Bipolar and Unipolar DW-PRESS acquisitions.

Figure 6:

In vivo spectra from Bipolar, Unipolar, and Trace DW-PRESS sequences, shown from acquisitions in occipital gray matter (OG). For Bipolar and Unipolar DW-PRESS, spectra are shown at b₀ (null) and b₂, for both gradient polarities (+, −) and all three directions (d₁, d₂, d₃). An additional b-value (b₁) was acquired for Trace DW-PRESS.

Figure 7 demonstrates the average trace ADC’s computed from the three sequences in each brain region. The differences in ADCs between the Trace and Unipolar and Bipolar DW-PRESS sequences were significant for most metabolites (see statistical analysis subsection below). The significantly increased trace ADC values of water is quite evident in the Trace DW-PRESS acquisitions, indicating the effect of the shorter diffusion time. This effect is also seen in Supporting Information Figure S3, where the signal ratios S(b)/S₀ in the Trace DW-PRESS sequence are evidently lower than the Bipolar and Unipolar DW-PRESS acquisitions, for any given b-value.

Figure 7:

Average trace ADC values for the three main metabolite groups (tNAA, tCr, and tCho) in (A) frontal gray (FG) matter, (B) occipital gray (OG) matter, and (C) occipital (subcortical) white (OW) matter. (D) Average trace ADC value of water ADC in FG, OG, and OW. Note the overall larger trace ADC’s of water and metabolites from Trace DW-PRESS compared to the other sequences (Bipolar and Unipolar). * significantly different with respect to the Bipolar ADC (p < 0.05); ^# significantly different with respect to the Unipolar ADC (p < 0.05); ^† significantly different with respect to ADC− (p < 0.05); ^‡ significantly different with respect to ADC in OW (p < 0.05).

Figure 8 illustrates representative spectra for each sequence in the occipital gray matter region of the brain. The difference in the spectra from negative and positive polarities, as well as from different diffusion directions, is quite small, as seen from the NAA singlet from the Bipolar and Unipolar DW-PRESS acquisitions. However, the extent of signal attenuation is less than that of the Trace DW-PRESS sequence, which shows more reduction at the highest b-value (1707 s/mm²) compared to the other sequences. This effect is largely due to the shorter diffusion time of the Trace DW-PRESS sequences. In contrast to the in vivo spectra, the phantom spectra from all sequences experience a similar reduction of signal intensity as a function of b-value, as seen in Supporting Information Figure S4(A). In vivo, these relative signal intensity reductions are not the same as a function of the lowest (b₀) and highest (b₂) b-value, between the Bipolar and Unipolar and the Trace DW-PRESS sequence (Supporting Information Figure S4(B)), showing that the restriction of the metabolites is affected differently depending on the diffusion time.

Figure 8:

(A) Representative spectra from the Bipolar, Unipolar and Trace DW-PRESS acquisitions, from a healthy volunteer in the occipital gray (OG) matter region. (B) Plots of the NAA singlet at 2.01 ppm. For the Unipolar and Bipolar DW-PRESS sequences, the various spectra from two b-values (b₀, b₂), both gradient polarities (+, −), and three diffusion directions (d₁, d₂, d₃) are overlaid. The NAA singlet is shown for the Trace DW-PRESS sequence at three b-values. (C) The water peak from the null to the highest diffusion-weighting. Note the greater degree of signal attenuation in the Trace DW-PRESS acquisitions, for the same b-value range (b₀ and b₂) as those shown for the Unipolar and Bipolar DW-PRESS spectra. (D) Zoom-in on the water spectra, indicating the greater reduction in water signal in the Trace DW-PRESS acquisitions.

Statistical Analysis

Within all brain regions, nearly all in vivo ADCs measured with Trace DW-PRESS were significantly different from those measured with the Bipolar and Unipolar sequences (Table 3). Only the ADC of tCho in FG measured with Unipolar DW-PRESS (0.18 ± 0.07 μm²/ms) was not significantly different from the corresponding value (0.23 ± 0.04 μm²/ms) measured with Trace DW-PRESS. None of the ADCs between Bipolar and Unipolar DW-PRESS were significantly different, except for water ADC in frontal gray matter.

Table 3:

Table of in vivo ADC values for the Bipolar, Unipolar, and Trace DW-PRESS sequences. For the Bipolar and Unipolar DW-PRESS sequences, the trace ADC’s from negative (ADC−) and positive (ADC+) polarities were computed, as well as the trace ADC from the geometric mean, ADC (geo), of the signals from positive and negative diffusion gradient polarities. In the rightmost column, the trace ADC values from the Trace DW-PRESS sequence are shown.

		In Vivo Trace ADC values: mean ± standard deviation [μm2/ms]
		BIPOLAR			UNIPOLAR			TRACE
		ADC−	ADC+	ADC (geo)	ADC−	ADC+	ADC (geo)	ADC
FG	tNAA	0.11 ± 0.04	0.11 ± 0.04	0.11 ± 0.04	0.12 ± 0.03	0.15 ± 0.04 †	0.13 ± 0.03	0.26 ± 0.04 *, #
	tCr	0.11 ± 0.06	0.12 ± 0.06	0.12 ± 0.06	0.12 ± 0.04	0.14 ± 0.06	0.13 ± 0.05	0.23 ± 0.03 *, #
	tCho	0.12 ± 0.05	0.14 ± 0.05	0.13 ± 0.04	0.18 ± 0.08	0.18 ± 0.07	0.18 ± 0.07	0.23 ± 0.04 *
	Water	1.03 ± 0.06	1.05 ± 0.06 †	1.04 ± 0.06 #	1.02 ± 0.07	1.02 ± 0.07	1.02 ± 0.07	1.19 ± 0.08 *, #
OG	tNAA	0.13 ± 0.05	0.13 ± 0.04	0.13 ± 0.04	0.16 ± 0.03	0.17 ± 0.03	0.16 ± 0.03	0.27 ± 0.03 *, #, ‡
	tCr	0.14 ± 0.05	0.14 ± 0.05	0.14 ± 0.05	0.15 ± 0.03	0.15 ± 0.05	0.15 ± 0.04	0.30 ± 0.05 *, #
	tCho	0.11 ± 0.05	0.11 ± 0.04	0.11 ± 0.04	0.14 ± 0.04	0.11 ± 0.06	0.12 ± 0.05	0.29 ± 0.06 *, #
	Water	1.02 ± 0.05	1.04 ± 0.06	1.03 ± 0.05 ‡	1.01 ± 0.04	0.99 ± 0.03 †	1.00 ± 0.03 ‡	1.20 ± 0.06 *, #, ‡
OW	tNAA	0.16 ± 0.02	0.17 ± 0.02	0.16 ± 0.02	0.16 ± 0.04	0.17 ± 0.04	0.17 ± 0.03	0.34 ± 0.05 *, #
	tCr	0.17 ± 0.03	0.17 ± 0.04	0.17 ± 0.03	0.17 ± 0.03	0.17 ± 0.02	0.17 ± 0.02	0.35 ± 0.06 *, #
	tCho	0.11 ± 0.04	0.11 ± 0.03	0.11 ± 0.03	0.10 ± 0.04	0.11 ± 0.03	0.1 ± 0.03	0.29 ± 0.05 *, #
	Water	0.77 ± 0.06	0.77 ± 0.06 †	0.77 ± 0.06	0.78 ± 0.07	0.76 ± 0.07 †	0.77 ± 0.07	1.06 ± 0.08 *, #

^*significantly different with respect to Bipolar ADC (p < 0.05)

^#significantly different with respect to Unipolar ADC (p <0.05)

(Repeated measures ANOVA with Bonferroni correction)

^†significantly different with respect to ADC− (p < 0.05)

^‡significantly different with respect to OW ADC (p < 0.05)

(Paired samples t-tests)

When comparing the trace ADC’s between the OG and OW regions, statistically significant differences were found in the trace ADC’s of water in OG vs. OW, measured with all three sequences (Table 3). Only the trace ADC of tNAA measured with Trace DW-PRESS was significantly different in OW vs. OG (0.34 ± 0.05 vs. 0.27 ± 0.03, p = 0.040).

In occipital white matter, statistically significant differences were found between water ADC+ and ADC− values, for both Bipolar and Unipolar DW-PRESS). In occipital gray matter, only the water ADC+ and ADC− values were significantly different for Unipolar DW-PRESS, although the water ADC+ and ADC− values were nearly significantly different in the Bipolar DW-PRESS acquisitions (p = 0.066). In frontal gray matter, the difference in the ADC+ and ADC− values of water measured with Bipolar DW-PRESS was significant, and only the trace ADC+ and ADC− values of tNAA were significantly different in the Unipolar DW-PRESS measurements.

In occipital gray matter, the results of Wilcoxon signed ranks tests showed that the Trace DW-PRESS ADCs of tCr and water estimated with 2 b-values were significantly different from those estimated with 3 b-values. No differences in the ADC values of Trace DW-PRESS were found in frontal gray matter, whether estimated with 3 or 2 b-values. In occipital white matter, only the water ADC of Trace DW-PRESS, estimated with 2 b-values, was significantly different from the one estimated with 3 b-values (Supporting Information Table S3). Hence, comparisons with Unipolar and Bipolar DW-PRESS were redone for these particular metabolites and brain regions. However, the results of the statistical analysis assuming 2 b-values for Trace DW-PRESS yielded the same significant differences as the previous analysis that used Trace DW-PRESS ADCs estimated from 3 b-values (Supporting Information Table S4). Therefore, no significant bias was introduced by using 3 b-values for Trace DW-PRESS versus 2 b-values for Unipolar and Bipolar DW-PRESS (see Supporting Information Table S5 and Supporting Information Section 1.4 for further details).

Repeatability of three in vivo measurements in two volunteers

The repeatability of measuring the trace ADC’s of tNAA, tCr, tCho, and water was estimated with the coefficient of variance (CV). Supporting Information Table S2 lists the means, standard deviations, and CV’s (%) of these metabolites measured across three sessions in two volunteers, one in the frontal gray and the other in the occipital gray matter. Water has the lowest CV’s (3–4%) in all methods and regions. The FG region generally had higher CV’s compared to the OG region for nearly all metabolites, except tCho. The trace ADC of tCho also carried the highest CV within both the FG (45–58%) and OG (15–62%) regions. In the FG region, the Trace DW-PRESS measurements had the lowest CV’s except for water, while in the OG region, they were also lowest except for tNAA, where Bipolar DW-PRESS resulted in the lowest CV (8% vs. 11%).

5. DISCUSSION

5.1. Phantom validation

All sequence variants are generally in agreement with one another in terms of the average trace ADC values measured in phantom, except for Glu for which the Bipolar and Unipolar sequence have slightly different ADC’s (Table 2). Overall, the trace ADCs in phantom also agree remarkably well with those reported previously in the same standardized phantom³⁹, except for mI, Lac, and Glu, since the report by Landheer et al. used shorter TE values (minimum of 74 ms) at which the signals from these metabolites are more distinguishable and have higher SNR’s. The phantom trace ADC values for NAA, Cr, Cho have low coefficients of variance while those for mI, Glu, and Lac are higher, due to long TE.

Differences in the water peak integral between acquisitions with negative and positive diffusion gradients indicated a greater cross-term contribution in the Unipolar DW-PRESS sequence compared to the Bipolar variant. The higher standard deviations of the zero-order phase correction indicate that the Trace and Unipolar sequences are more susceptible to eddy-current induced phase fluctuations. The report by Hanstock et al.⁴⁰ did not use a water reference in order to reduce the scan time and because of the high b-values tested which greatly attenuate the water signal. In that report, the phase variation was also measured via the standard deviation of the zero-order phase correction on a reference peak in phantom. However, in our study, the eddy current phase correction³⁸ using the water data apparently corrects for these effects in all the sequences, since the phantom data remains relatively stable (low CV%) for all sequences. Additionally, for the Unipolar DW-PRESS acquisitions, the taking of the geometric mean of the signals from both polarities evidently reduces the effect of the cross terms, as the trace ADC values in the phantom show low variation and are comparable to those from the Bipolar and Trace DW-PRESS acquisitions.

5.2. In vivo validation and comparison with other studies

In vivo experiments show that the trace ADC of water in white matter is significantly lower than the trace ADC of water in gray matter, as measured with the Unipolar, Bipolar, and Trace DW-PRESS. Higher ADCs in white versus gray matter have been reported in DW-MRI⁵³ and DW-MRS studies^10,13. The report by Najac et al.¹³ measured water trace ADCs of 0.47 ± 0.02 and 0.69 ± 0.02 μm²/ms in white and gray matter, respectively, using a maximum b-value of approximately 2,850 s/mm², while Ellegood et al.¹⁰ reported 0.78 ± 0.06 μm²/ms in subcortical white matter and 1.05 ± 0.23 μm²/ms in occipital gray, using a maximum b-value of 1,517 s/mm². Najac et al. attributed the large discrepancy in these values to the much higher maximum b-value used in their report. In our study, the water trace ADC values are much closer to the ones reported by Ellegood et al. likely due to the similarity of their b-value range with ours.

In white matter, the tNAA trace ADC is significantly higher than the one in gray matter for Trace DW-PRESS acquisitions only. The tCr trace ADC value measured with Unipolar DW-PRESS is nearly significantly higher in OW vs. OG (p = 0.088), indicating that more subjects are needed to establish this difference. The difference in ADCs in OW and OG are due to structural differences in the composition between gray and white matter, and higher ADC’s of the three main metabolite groups in white matter compared to gray matter have been reported ⁴¹. The trace ADCs in frontal gray matter have greater coefficients of variation (CV%), likely due to challenges experienced with acquiring the spectra near the sinus regions, where B₀ inhomogeneity is greater and water suppression is less effective. Datasets in FG with large residual water shoulders (usually occurring at the low b-value) were discarded as the quantitation was adversely affected, particularly for peaks close to water such as tCho. Differences in CV’s among the sequence variation could also reflect the longer scan times necessary to acquire the Bipolar and Unipolar DW-PRESS data, during which effects from temporal fluctuations in shimming, water suppression and patient motion are more likely to accumulate.

It is known that tCho tends to have lower trace ADC’s than tCr and tNAA⁴¹. This trend can be seen from all acquisitions in occipital gray and white matter, as the trace ADC of tCho are lower in those regions, except for Trace DW-PRESS in OG where it is comparable to the values for tNAA and tCr. The trend is also apparent in the frontal gray matter for Trace DW-PRESS, but not for the Bipolar or Unipolar measurements, likely partly due to the complicating factors in frontal lobe MRS acquisitions mentioned above. However, it is also important to note that partial volumes of gray and white matter are present in all voxels and therefore the final estimated ADC represents a mixture of these tissue types. White matter is largely composed of axonal bundles that can be oriented along a predominant direction, so the measured ADC would ideally reflect the diffusion along this direction. Similarly, in other anisotropic tissue types such as pure gray matter, equivalent results to the trace ADC could be obtained by a one measurement along a single diffusion direction. Nonetheless, the large voxel size used in this study (15.6 mL) makes it difficult to study any directionality effects on the ADC.

With a diffusion time of 10.8 ms, the trace-weighted sequence implemented for this study approaches the short diffusion time regime (t_d ≤ 10 ms), resulting in higher estimates of ADCs compared to those found with the Unipolar (t_d = 25.6 ms) and Bipolar (t_d = 58.8 ms) DW-PRESS. Figure 8 (and Supporting Information Figures S3 and S4) show that the in vivo metabolite and water spectra measured with Trace DW-PRESS sequence experience a larger signal drop compared to the other sequences, for the same b-value range. Previous reports have shown this trend in animals and to some extent in humans ^27–30,54. A recent study by Döring et al. used oscillating gradients to measure in vivo ADCs in human parieto-occipital gray matter with a short diffusion time of 8.3 ms along a single diffusion direction. Their ADC estimates for NAA, NAAG, tCr, and tCho at t_d = 8.3 ms were 0.19 ± 0.03, 0.19 ± 0.09, 0.19 ± 0.05, and 0.17 ± 0.04 μm²/ms, respectively, and these values were shown to be significantly higher than ADC’s measured at t_d = 155 ms. In rodent brain, the ADCs of tNAA, tCr, and tCho fall within a range of 0.10 – 0.15, 0.10 – 0.20, and 0.10 – 0.15 μm²/ms, respectively, at diffusion times between approximately 8 – 13 ms^27–30. However, a study by Najac et al.²⁴, which used a single-shot isotropic diffusion scheme with semi-LASER localization at 7T and a diffusion time of t_d = 26 ms, measured ADCs ranges comparable to our study. In that report, the ADCs for NAA, tCr, tCho, and water in the posterior cingulate cortex (gray matter dominant) were 0.23 ± 0.02, 0.25 ± 0.04, 0.20 ± 0.05, and 1.07 ± 0.07 μm²/ms, respectively; in the parietal white matter, these ADCs were 0.30 ± 0.03, 0.32 ± 0.02, 0.30 ± 0.03, and 0.87 ± 0.03 μm²/ms, respectively. By comparison, in our study, the ADCs for NAA, tCr, tCho, and water in OG, measured with Trace DW-PRESS, were 0.27 ± 0.03, 0.30 ± 0.05, 0.29 ± 0.06, and 1.20 ± 0.06 μm²/ms, respectively, and in OW these values were 0.34 ± 0.05, 0.35 ± 0.06, 0.29 ± 0.05, and 1.06 ± 0.08 μm²/ms, respectively. The discrepancies in ADC dependence on diffusion time, as shown between this study and the abovementioned reports, can be attributed to systemic differences in the experimental approaches, including choice of echo time, the range and number of b-values tested, the anatomical locations and voxel sizes probed, partial volume effects, and any remaining effects of motion. Indeed, uncompensated residual motion due to lack of cardiac triggering could be a one of the main effects contributing to these differences, since SNR thresholding only eliminates effects from outliers, not those from inherent amplitude effects present throughout most of the acquisition.

Although the diffusion time of the Unipolar sequence is only slightly greater than twice that of Trace DW-PRESS, the signal attenuation of the spectra more closely resembles that of the Bipolar sequence, even for water. This finding indicates a threshold in the diffusion time under which the metabolite diffusivity becomes less restricted by subcellular and cellular-scale structures. Therefore, the implication is that diffusion times shorter than 25.2 ms may be needed to measure ADCs significantly different from those measured at t_d = 58.8 ms, especially for water since it permeates both the intra- and extra-cellular space and its diffusion would reflect a lesser degree of restriction during shorter diffusion times.

5.3. Limitations

One of the limitations of Trace DW-PRESS is that the long TE leads to reliability in only tNAA, tCr, tCho. Strong diffusion gradients could potentially render any DW-MRS sequence more susceptible to motion, possibly leading to more signal loss and resulting in an overestimation of ADC. However, the phantom results indicate that eddy current effects may not be a significant factor for the particular sequence parameters used in the experiments, since the values from the Trace, Bipolar, and Unipolar DW-PRESS sequences are comparable and consistent with reference values. The combination of large gradients and long TE also puts a constraint on the highest achievable b-value for the Trace DW-PRESS. For a given TE, the Trace DW-PRESS also has a less flexible range of diffusion times, which is constrained by the short separation Δ of the gradients within a bipolar pair. In contrast, the Unipolar and Bipolar DW-PRESS can achieve a broader range of diffusion times for a given TE, although they can be shorter for the Unipolar sequence. The relatively short diffusion time constraint for Trace DW-PRESS is a limitation for this sequence as it cannot probe long-range morphologic features (e.g., axonal length and neuronal asymmetry) which can be done more accurately with long t_d⁵⁵_. In addition, it is important to note that DW-PRESS sequences that use true bipolar diffusion-sensitizing gradient pairs, such as those in the trace-weighted sequence, can also achieve the same relatively short diffusion times as Trace DW-PRESS, although only for a single diffusion direction.

A general limitation of this study is that no cardiac gating or ECG triggering was implemented, which could avoid further signal losses. Other DW-MRS reports ^10,11,40 have similarly excluded the use of triggering and gating while minimizing ADC overestimation by implementing careful post-processing procedures, as was done in this study. Another limitation is chemical shift displacement which is inherent to the basic PRESS sequence and causes misregistration of the metabolite signals with respect to the target volume-of-interest. Also, no more than two b-values were able to be practically acquired in one scan session for the Bipolar and Unipolar DW-PRESS in vivo measurements, as opposed to Trace DW-PRESS, for which there was sufficient time to acquire three b-values. A similar, two b-value approach for Bipolar DW-PRESS was taken in the report by Deelchand et al.¹¹, but three b-values could further improve the estimation of the ADC’s for the Bipolar and Unipolar DW-PRESS acquisitions, albeit at a considerable increase in scan duration. However, for this study, statistical tests showed no significant bias in the comparisons of the ADCs from Trace DW-PRESS, measured from three b-values, with those from Unipolar and Bipolar DW-PRESS measured with only two. Another limitation is quality filtering based on relative CRLB’s, which is acknowledged to introduce bias⁵⁶, and could be a contributing factor towards higher ADCs measured in this study. Error propagation on the ADC measurement due to the CRLB threshold of 20% may also be present, although our quantitation indicated average CRLB’s well below this threshold.

6. CONCLUSION

This study presents the first demonstration of the single-shot diffusion trace-weighted sequence in a clinical scanner at 3T, and we compare the trace ADC values obtained with this sequence to those computed from the conventional bipolar and unipolar DW-PRESS sequences acquired with three orthogonal directions and negative and positive diffusion gradient polarities. Results show excellent agreement of phantom trace ADC’s computed with all sequences, and in vivo ADC’s agree well in both the difference between OG and OW matter, as well as the overestimation of metabolite and water ADC’s due to a shorter diffusion time. The diffusion trace-weighted sequence could provide an estimate of the trace ADC of the main metabolite groups (tNAA, tCr, and tCho) in a much shorter scan time (by nearly a factor of three) compared to conventional DW-PRESS acquisitions.

Abbreviations used:

ADC

apparent diffusion coefficient

PRESS

point-resolved spectroscopy

DW

diffusion-weighted

DSG

diffusion-sensitizing gradient

STEAM

stimulated echo acquisition mode

semi-LASER

semi-localization by adiabatic selective refocusing

WET

water suppression enchanced through T1 effects

SNR

signal-to-noise ratio

CRLB

Cramer-Rao lower bound

ECG

electrocardiogram

NAA

n-acetylaspartate

Cr

creatine

Cho

choline

Glu

glutamate

mI

myo-inositol

Lac

lactate

tNAA

total NAA

tCr

total creatine

tCho

total choline

FG

frontal gray matter

OG

occipital gray matter

OW

occipital white matter

Data Availability Statement:

Data available from the authors upon request.