Improved initial value estimation for short echo time magnetic resonance spectroscopy spectral analysis using short T₂ signal attenuation

Abstract

Robust spectral analysis of magnetic resonance spectroscopy data frequently uses a spectral model with prior metabolite signal information within a nonlinear least squares optimization algorithm. Starting values for the spectral model greatly influence the final results. Short echo time magnetic resonance spectroscopy contains broad signals that overlap with metabolite signals, complicating the estimation of starting values. We describe a method for more robust initial value estimation using a filter to attenuate short T₂ signal contributions (e.g., macromolecules or residual lipids). The method attenuates signals by truncating early points in the data set. Metabolite peak estimation is simplified by the removal of broad, short T₂ signals, and corrections for metabolite signal truncation are described. Short echo time simulated Monte Carlo data and in vivo data were used to validate the method. Areas for metabolite signals in the Monte Carlo data with singlet (N-acetylaspartate, creatine, choline) and singlet-like (myo-inositol) resonances were estimated within 10% of actual value for various metabolite line widths, signal-to-noise ratios, and underlying broad signal contributions. Initial value estimates of in vivo magnetic resonance spectroscopy data were within 14% of metabolite area ratios relative to the creatine peak fitted using established magnetic resonance spectroscopy spectral analysis software.

INTRODUCTION

Proton magnetic resonance spectroscopy (1H MRS) is an important tool for investigating a number of pathologies of the brain, including epilepsy, multiple sclerosis, stroke, and cancer (1). For most of these investigations, the goal is to quantify metabolite concentrations that underlie a large water signal from one or more locations in the brain. This is often complicated by overlapping signals from multiple sources in the data, inherently low signal-to-noise ratio (SNR), and field inhomogeneities (2).

Metabolite quantification is generally achieved by estimating the signal areas of metabolite resonance groups in the spectrum where the area is proportional to the metabolite concentrations (3). However, the accuracy of metabolite peak area estimation is affected by all signals in a spectrum. Underlying nuisance signal contributions from residual water, lipids, and macromolecules typically have broad line widths, overlap with metabolite signals, and complicate the estimation of accurate metabolite concentrations (4). Short echo time (TE; <70 ms) MRS data has generally higher SNR and provides the most information about brain metabolites but also larger nuisance signals. Nuisance signals often have shorter T₂ decays and can be minimized by long TE (>70 ms) data acquisition, but metabolite signals are reduced as well, and in some cases not present (5).

A number of fitting algorithms have been described for estimating metabolite areas and in some cases nuisance signals from macromolecules. The most robust methods rely on fitting a spectral model to the data. Spectral models may have both parameterized and nonparameterized parts, to make use of prior information about well-characterized signal contributions and account for less well behaved nuisance signals, respectively. Various global or iterative nonlinear least squares algorithms are used to estimate an optimal fit of the model to MRS data (6–12). It is important to note that a good fit of the spectral model, indicated by a minimized least squares difference between the model and data, does not always mean that metabolite and macromolecular signal contributions were correctly estimated.

Accurate modeling of macromolecular signals is important for robust estimates of short TE data metabolites. Macromolecular signals have short T₂ values resulting in broad peaks that underlie narrower metabolite peaks. Works by Behar et al. (13) and Hofmann et al. (14) have demonstrated that macromolecular signal contributions can be identified and removed from short TE data using inversion and saturation techniques, respectively. Both techniques require additional MR scanning time, which may not be practical for clinical single voxel or spectroscopic imaging acquisitions. Based on this study, number of spectral analysis models have been introduced that include simple broad signal contributions at frequencies that correspond to macromolecular signal locations (4,15,16). Hoffman et al. also demonstrated that macromolecular peak patterns differ between tissue types thus suggesting that parameterized macromolecular signal models should allow peaks to vary independently. However, this can result in a much larger and more complex spectral model and one in which small changes in one parameter can affect other parameter estimates globally. In this case, constrained optimization techniques can be used to ensure that results are within reasonable ranges. But, these methods depend on accurate prior knowledge of signal contributions and parameter ranges.

Almost all spectral optimization algorithms also require initial estimates of model parameters (17–19). Variations in these initial estimates can greatly influence the final optimized model parameters for both metabolite and macromolecular signals (10). Spectral model optimizations can often end up at different local minima with only slightly different starting values (9). Because many of the signal contributions overlap, an inaccurate starting value of one signal may affect many other signal estimates, regardless of whether those other signals have accurate starting estimates. Often, the search for good starting values results in a circular approach: with good macromolecular signal starting values it is easier to estimate metabolite signals, but we need good metabolite signal starting values to estimate macromolecular signals.

In this report, we describe a method for more robust metabolite signal initial value estimation from short TE MRS data using a filtering method that attenuates short T₂ signal contributions such as those from macromolecules or residual lipid. The filtering method attenuates these signals by truncating, or kissing off (KO), early points in the MRS dataset, and is hence referred to as the KO-filter. The resulting MRS spectrum is greatly simplified by the removal of the underlying broad, short T₂, signals. This makes metabolite peak estimation more straightforward and robust.

THEORY

The mechanism for the KO-filter method is based on the fact that short T₂ nuisance signals decay more rapidly than longer T₂ metabolite signals. Metabolite and macromolecule signals can be separated by removing sufficient early time points of the raw free induction decay (FID) data to remove a significant percentage of the short T₂ signal contributions from the resultant spectrum. In practice, the filter is applied as:

$$s\left(t^{\prime }\right)=s(t-t_n)\times \mathrm{\Pi }\left(t_n\right(t-t_n\left)\right)$$ [1]

where s(t’) is the modified time domain data, s(t−t_n) is the original time domain data shifted by n points, and Π(t_n(t−t_n)) is a scaled boxcar function shifted by n points. By applying the shift theorem and convolution theorem from Bracewell’s book on Fourier transformations (17), the fast Fourier transform (FFT) of the data this results in:

$$FFT\left(s\right(t^{\prime }\left)\right)=FFT\left(s\right(t-t_n\left)\right)\otimes FFT\left(\mathrm{\Pi }\right(t_n(t-t_n)\left)\right)=e^{-i2\pi t_n\omega }s\left(\omega \right)\otimes FFT\left(\mathrm{\Pi }\right(t_n(t-t_n)\left)\right)$$ [2]

The FFT of the rectangular function, Π(t), is equal to the sinc function, sinc(πω), for when they are symmetric around the origin and scaled to ±½. Equation 1 contains a rectangular function shifted by t_n and scaled to ± t_n, so using the shift theorem and substitution,

$$s\left({\omega }^{\prime }\right)=FFT\left(s\right(t^{\prime }\left)\right)=s\left(\omega \right)\times e^{-i2\pi t_n\omega }\otimes \left(\frac{1}{t_n}\text{sinc}\left(\frac{\pi \omega }{t_n}\right)\times e^{-i2\pi \omega t_n/2}\right)$$ [3]

where s(ω’) is the FFT of s(t’).

As shown in Equation 2, removing points from the beginning of an FID has consequences. First, metabolite and macromolecular peak areas are reduced due to the effective decrease in the “first point” of each time domain signal due to T₂ decay. T₂* effects are also present in the FID but can be corrected for by using the same estimate of spectral peak line width for both KO-filtered and unfiltered spectra in our analysis. Subsequent changes in peak height, which is proportional to area, are thus due to T₂ decay in the FID. Second, a phase roll is introduced into the spectral data as defined by the Fourier shift theorem. This effect can be calculated based on the number of points removed and corrected. However, as will be described below, it is generally more useful to use the magnitude spectrum for initial value calculations, which obviates the need for phase correction. Finally, zeroing the initial points in the FID effectively multiplies the time domain signal by a boxcar function. This causes the signals in the frequency domain to be convolved and broadened by a sinc function due to the Fourier convolution theorem. The artifacts caused by this effect and their corrections are described and demonstrated in more detail below.

A simple demonstration of KO-filtering is obtained by considering two simulated peaks with the same areas, one broad peak (T₂ = 20 ms) underlying a narrow peak (T₂ = 250 ms). After removing 20 points from the FID (20 ms), the broad peak height is reduced by 88%, while the narrow peak height is reduced by 12%. After removing 40 points (40 ms), almost no broad signal remains. The broad underlying signals can be removed with only a slight reduction in metabolite signals.

The artifacts caused by the Fourier shift and convolution effects differ depending on the number of metabolite peaks and the width of the boxcar function. When there is one line present in a simulated spectrum, the convolution with the sinc function results in an apparent baseline ripple that depends on the width of the boxcar function (Fig. 1a). This artifact can be eliminated in this case by using the magnitude spectrum of the KO-filtered data for initial value calculation. While the full width at half maximum (FWHM) line width of magnitude peaks are broadened, the maximum peak height is not affected. This is demonstrated by the plot of the magnitude peak maximum height decaying smoothly as KO-filtering points increase in Fig. 1b. When a second peak is added 0.2 ppm to the left of the original peak, phase roll effects can still be calculated and corrected for or ignored by using the magnitude data (Fig. 1c). However, the apparent baseline ripple caused by the convolution is increased. Furthermore, the baseline effects from the second peak affect the magnitude plot of the peak amplitude of the first peak (Fig. 1d) as the number of KO-filtering points increase. This occurs because of destructive interference between the two complex signals that occurs prior to the magnitude spectrum calculation. The amount of destructive or constructive interference depends on the frequency separation of the peaks and area under each peak. Thus, as will be shown, the decay patterns of various peaks in simulated brain spectra differ greatly as the KO-filter number increases depending on the spectral neighborhood.

Figure 1.

The effect of removing points from the FID. a: The magnitude (top) and real (bottom) spectra of a single simulated peak after 20 points have been removed. b: Decay in the magnitude of peak amplitude as a function of the number of points removed in single peak. c: The magnitude (top) and real (bottom) spectra of two simulated peaks after 20 points have been removed. d: Decay in the magnitude of peak amplitude as a function of the number of points removed for the right peak in the two peak spectrum.

MATERIALS AND METHODS

Simulated and In Vivo Brain Data

The KO-filter method for determining spectral model starting peak values was validated for simulated brain spectra under a number of conditions and demonstrated for typical in vivo 3 T single voxel PRESS data. Simulated spectra contained signals from eight metabolites, choline (Cho), creatine (Cr), N-acetylaspartate (NAA), gamma-aminobutyric acid, glutamate (Glu), glutamine (Gln), lactate (Lac), and myo-inositol (mIns), and simulated macromolecular peaks at seven locations. Brain metabolite basis functions were created using the GAVA spectral simulation program (21) for PRESS data on a 3 T scanner at a TE of 30 ms which were then used as input for a second in-house application called Prior that created simulated MRS data with user-specified spectral width, spectral points, and peak line widths and areas. Prior also simulated macromolecular peaks using a Gaussian lineshape with user-defined areas and line widths at expected frequencies (1). Prior was used to create matrices of simulated spectra with added noise at given SNR levels for use as Monte Carlo test cases for various simulated spectral data conditions.

Simulated metabolite spectra were created using the metabolite area ratios and T₂ decay values are listed in Table 1. Metabolite area ratios were scaled against NAA, and the simulations had 2000 spectral points and a spectral width of 2000 Hz. Metabolite line widths were set at 6 Hz FWHM in all cases except for the test set for the effects of line width change. Metabolite line widths in a spectrum were set by measuring the FWHM for the NAA singlet resonance group without any underlying signals. The metabolite line widths were applied as Voigt functions (22) by multiplying the combined basis set representing metabolite peaks by both an exponential decay function, representative of the T₂ decays of the signals of individual metabolites, as well as a gaussian decay function, representative of the global T₂* effects. Sufficient gaussian broadening was added to the fixed Lorentzian (T₂) decay to increase the NAA singlet group FWHM line width to the user-specified amount. This global T₂* setting was then applied to all other metabolite signals. Thus, metabolite signals with shorter T₂ values, such as mIns and Glu, will have slightly greater effective FWHM line widths. SNR values were calculated relative to root-mean-squared noise values of the NAA singlet peak height without any underlying signals and a spectral line width of 6 Hz.

Table 1.

Simulated macromolecular signals used in the simulation with their frequencies in parts per million (ppm), areas, line widths, and corresponding decay times.

Macromolecule	PPM	Relative Area (to NAA)	Line Width [Hz]	T2 [ms]
1	0.9	2.5	40.0	13.0
2	1.4	3.0	40.0	13.0
3	1.8	2.0	40.0	13.0
4	2.1	3.0	30.0	18.0
5	2.4	2.0	40.0	13.0
6	3.0	2.0	50.0	11.0
7	3.8	8.0	80.0	9.0

The following values (area ratio/T₂ decays) were used for simulated spectra where area ratios were relative to NAA: NAA 1.0/300 ms, Cr 0.6/300 ms, Cho 0.6/300 ms, gamma-aminobutyric acid 0.15/200 ms, Glu 0.75/150 ms, Gln 0.15/150 ms, Lac 0.1/200 ms, and mIns 0.7/200 ms. Simulated macromolecular signal contributions are shown in Table 1 where line width was based on actual FWHM of each Gaussian peak that composed the macromolecular signal contribution.

Application of the KO-filter initial values technique was also demonstrated for an in vivo single voxel PRESS dataset (512 averages, repetition time = 1500 ms, TE = 30 ms, spectral width = 2500 Hz, 2048 points, 2 × 2 × 2 cm³ voxel). The voxel was positioned in the posterior occipital cortex along the superior sagittal sinus. The voxel was intentionally positioned to excite subcutaneous lipid signals to demonstrate the efficacy of the algorithm in the presence of nuisance signals.

KO-filter Initial value Algorithm

The goal of the KO-filter initial value algorithm was to improve accuracy in metabolite peak area initial value estimation. By using the magnitude spectrum result from the KO-filter, zero and first order phase corrections were not required. However, an estimate of peak line width was needed for accurate peak area estimation since initial value were estimated by creating a simulated initial value spectrum and comparing the KO-filtered simulated data to the original KO-filtered data. For all tests performed in this report, we assumed that an accurate estimate of peak line width was available and that no B₀ shift artifacts were present.

An example of simulated brain data (SNR = 30, frequency = 124 MHz) is shown in Figure 2a (top), and the spectrum after KO-filtering of 40 points (20 ms) is shown in Figure 2a (bottom). We shall refer to these spectra from here on as KO(0) and KO(40) respectively. As expected from the theory a significant amount of broad nuisance signals have been removed, but at the cost of broadened and shortened peaks. In developing a robust initial value estimate from this sort of filtering, two immediate concerns had to be addressed: 1) how many points to KO-filter and 2) how to correct for peak area reduction.

Figure 2.

a: The simulated spectrum (top) before filtering and KO(40) filtered spectrum (bottom). b: The original simulated spectrum (grey/red) with the KO-filtering method showing the initial estimation (top), first iteration (middle), and second/last iteration (bottom).

To address the first issue of determining the number of points to KO-filter, the decay of metabolites and macromolecules as a function of the number of points removed is needed. Figure 3a–d demonstrate the complexity of the normalized decay of the maximum peak height for simulated NAA, Cho, Cr, and mIns signals with and without any underlying signals. After 40 points removed, the black line indicating the decay of the metabolites only spectrum and the red line indicating the decay of the metabolites and macromolecules spectrum nearly converge. Removal of more than 40 points will reduce macromolecular signals even more but at the expense of further reduction in metabolite signals. Based on this, we derived an empirical KO-filtering threshold of 40 points for subsequent validations.

Figure 3.

The decay in magnitude of the peak value for (a) NAA, (b) choline, (c) creatine, and (d) myo-inositol as a function of the number of points removed. The black line indicates a simulation with metabolite signals only and the grey/red line indicates a simulation with metabolite and macromolecular signals.

Initial area estimations were calculated for only NAA, Cr, Cho, mIns, and Glu because they had sufficient signal intensity to be observable at reasonable SNR levels after KO(40) filtering was applied. For all peaks, the ppm location of the maximum peak height (MaxPpm) was measured from a normalized simulated basis function. Metabolite peak heights were located in the KO(40) simulated brain spectrum by doing a peak search at ±0.02 ppm around MaxPpm as underlying signals can shift the maximum peak height.

To address the second issue of reduction of metabolite signal after KO(40), an iterative bootstrap method was used to convert the peak heights in the KO(40) spectrum back to KO(0) values. A simulated dataset, called InitialValue0, composed of basis functions for the five metabolite signals of interest was scaled until the MaxPpm basis function peak heights were equal to the original data KO(40) values. These were then summed and a KO(40) filter was applied to create a dataset InitialValue40. The difference between the MaxPpm peak heights of the original dataset at KO(40) and InitialValue40 data was used to modify the scaling of the InitialValue0 data. A KO(40) filter was then applied to the new scaled InitialValue0 to create the InitialValue40 data. This process of scaling InitialValue0 data based on InitialValue40 data was repeated until the difference between all MaxPpm locations was less than 1%. Typically this took three to four iterations. The final scaling value for each InitialValue0 metabolite basis function was used as the metabolite area initial value. Three iterations of this process are demonstrated in Fig. 2b, top, middle, and bottom, respectively.

KO-filtered Initial Value Validation

The effects of SNR, peak line width and underlying nuisance signal amplitudes on the KO-filter initial value algorithm were investigated using Monte Carlo methods. For SNR, 14 levels from 2:1 to 60:1 were investigated. The same simulated brain spectrum described above (with 6 Hz line width) was combined with different levels of noise to create 100 spectra at each SNR level. Initial values were normalized and mean and standard deviations compared. For line width, nine levels from 2–10 Hz were investigated for a simulated brain spectrum with fixed SNR of 60. Finally, four nuisance signal levels were investigated. Starting with a fixed 6 Hz line width at 60:1 SNR simulated metabolite plus macromolecules spectrum as listed above, three additional datasets were created where the macromolecular component amplitudes were multiplied as a group by 0.0, 0.5 and 2.0. Normalized initial values were compared to known values for all line width and macromolecule variations.

RESULTS

Initial values for NAA, Cr, and Cho and for NAA, Glu, and mIns are shown in Fig. 4a and b, respectively, as a function of 14 SNR values and a metabolite line width of 6 Hz. The initial value estimates are averaged over 100 sets at each SNR, and the mean and standard deviation for each metabolite signal at each SNR is shown. As the SNR is lowered, the estimate of the metabolites is increased. We assume that initial value estimates are good if estimates are within 20% of known values. In this case, good estimates were acquired for NAA down to an SNR of four, Cr and Cho down to 10, mIns down to 16, and glutamate down to 30. Below the SNR thresholds mentioned, the root-mean-squared noise value becomes a significant contribution to the normalized peak area estimate.

Figure 4.

Initial value estimates for (a) creatine, choline, and NAA, and (b) glutamate, myo-inositol, and NAA as a function of SNR. Each point and error bar is calculated from the results of 100 simulations at the same SNR but different distribution of noise. The normalized area is the metabolite area divided by the known area for each metabolite signal.

The algorithm was also tested for different line widths at an SNR of 60. The simulated data imposes a line width by using a static, assumed exponential T₂ decay for each metabolite signal as well as a dynamic Gaussian decay representing T₂* effects to achieve the desired FWHM. The accuracy of estimate of the initial models as a function of line width is shown in Fig. 5. The line width listed is the FWHM of the NAA singlet with a 300 ms T₂ exponential decay. Thus, as myo-inositol and glutamate have shorter T₂ values, their line widths will be slightly larger. The figure shows the ratio of the initial values to the known values for each of five metabolite signals. Choline, creatine, myo-inositol, and NAA are consistently between 1% and 16% of known values between 3 and 7 Hz line width. Above 7 Hz, myo-inositol estimates are 31–54% overestimated. However, at 8 to 9 Hz line width, creatine, choline, and NAA still have reasonably accurate estimates of 1–13%. At 10 Hz, the choline peak is seriously underestimated probably due to its proximity to the overestimated myo-inositol peak after KO-filtering at that line width. Glutamate estimates vary greatly with line width, indicating that the initial value method does not give robust estimates for glutamate at any line width.

Figure 5.

The ratios of initial values to known values are shown for NAA, creatine, choline, glutamate, and myo-inositol as a function of the line width of the simulated spectra.

The initial value estimation was also tested for four simulated macromolecular baseline signal contributions. Figure 6 shows the initial value estimates versus the known metabolite areas for baseline signals scaled by 0.0, 0.5, 1.0, and 2.0. Despite the range of added baseline signals, the initial values of choline, creatine, myo-inositol, and NAA were within 3–12% of the known values. The glutamate peak showed significant variability among the four datasets. Of particular significance was the performance of the method for no added baseline signals. The range of over/underestimated peak areas is likely due solely to complex signal interactions in the InitialValue40 model, either due to incorrect peak estimates (Glu) or the fact that only five of the eight metabolite signals in the simulated data were incorporated into the model spectrum.

Figure 6.

The ratios of initial values to known values are shown for NAA, creatine, choline, glutamate, and myo-inositol as a function of the magnitude of the underlying macromolecular signals.

Finally, the KO-filtering method was applied to real data. A 30 ms 3T PRESS sequence using an 8 cm³ voxel in the occipital lobe of a healthy brain with 512 averages and water saturation was acquired. The resulting spectrum had approximately an SNR of 60 and metabolite line width of 7 Hz, but there was a large lipid signal overlapping the metabolite signals. Figure 7a shows the original magnitude spectrum (black line), the KO(50) filtered signal (grey/red line, 20 ms of points removed), and an insert MRI showing voxel location. As expected, the broad lipid peak decayed rapidly in the time domain. Figure 7b shows the original data absorption spectrum (black line) and the results of the initial value estimates for metabolite signals using the KO-filtering method (red/grey line). The initial values for metabolite signals relative to the creatine signal was estimated to be 0.63, 1.04, 0.98, and 1.35 for choline, glutamate, myoinositol, and NAA, respectively. As a comparison, we fitted the data using standard analysis software (11) and derived fitted ratios of 0.51, 1.16, 0.86, and 1.30 for choline, glutamate, myo-inositol, and NAA, respectively. Thus, the initial values calculated for the metabolite signals using KO-filtering were within 14% of the fitted values with the exception of choline which was at 22%.

Figure 7.

a: The original magnitude spectrum (black), the KO(50) filtered signal (grey/red) after 20 ms of points removed, and an axial MRI image of the brain showing voxel location. b: The original data absorption spectrum (black) and the results of the initial value estimates for metabolite signals using the KO-filtering method (grey/red).

DISCUSSION

The KO-filtering algorithm presented in this article demonstrates a robust ability for calculating metabolite peak initial values for singlet resonances across a variety of SNR, line width, and baseline signal conditions. However, there are some obvious limitations to the algorithm in its present form. The method depends on determining the maximum peak height for a metabolite signal, so metabolite signals that consist of multiplet resonance groups (e.g., glutamate and myo-inositol) were more affected by the noise because multiplet groups with the same area as singlets had lower effective peak heights and thus lower relative SNR than for the singlets. Metabolite areas for mIns and Glu were consistently overestimated at low SNR as the algorithm implemented for estimating starting values calculated the maximum amplitudes within a narrow range of the expected ppm value of each metabolite signal. This was partly mitigated for mIns by the multiplet resonance peak group at 3.54 ppm which behaves similarly to a singlet resonance in terms of maximum peak height signal decay due to T₂*and J-coupling effects.

The algorithm is effective in separating signals from large SNR singlets, such as NAA, creatine, and choline, from the underlying baseline signals. However, metabolites with smaller concentrations, such as gamma-aminobutyric acid, glutamine, and lactate, will not benefit directly from this algorithm due to their low effective SNR. However, small concentration metabolite peak starting values are often estimated as a ratio to a larger peak, such as NAA. Thus, a more robust and stable estimate of NAA would also benefit the starting estimates for the low concentration peaks. Future work on this method may benefit from adding a second pass to the algorithm which incorporates these small metabolite signal estimates into the InitialValue0 model to more accurately simulate the metabolite signal interactions in the simulated spectrum while estimating starting values.

The algorithm also becomes significantly less accurate for multiplet resonances like Glu. This is most likely due to the use of peak heights to determine a ratio between the InitialValue40 model to the KO(40) of the original data. The fact that mIns, which has a multiplet resonance pattern but also a “pseudo-singlet” peak at 3.54 ppm, showed much more robust and stable estimates than Glu, is just one indication of this. This behavior might be mitigated by using a wider region of the multiplet group to estimate the peak height ratio of the KO(0) versus KO(40) spectra. However, as we have an estimate of metabolite basis functions for all metabolite signals, we will investigate modifying the iterative ratio estimation to use a root-mean-square metric normalized across a ppm range of a scaled basis function versus the KO(40) data, rather than just a difference in peak heights. Care would have to be taken in the selection of the ppm range to avoid resonance group overlap. As part of a multi-pass extension of this algorithm, subsequent iterations could be used to remove easily estimated signals (e.g., NAA, Cr, or Cho) by subtracting out scaled basis function estimates from the original complex data. This would reduce the interactions between these large metabolite signals and possibly simplify the estimation of multiplet resonance groups.

One final future application of the KO-filtering technique may be to apply it within an actual fitting method to achieve a pseudo-2D effect on the data. As subsequent FID points are removed, artifacts enter the metabolite model, but the overall signal is simplified as nonparameterized nuisance signals are minimized. The simplified signal model at KO(40) could serve as a constraint on the full model fit at KO(0) or even be fitted both at the same time with a full signal model at both KO-filter settings.

It is anticipated that using the initial values estimated with KO-filtering in an optimized fitting routine will result in more consistent and/or less variable estimates of the metabolite signals. This should be due to the starting values being relatively closer to the final result and perhaps less likely to get stuck in a local minima within the optimization search space than they would be if the nuisance signals had not been removed. This proximity of the initial values to the final results could also lead to a reduction in convergence time, which would hopefully reduce total computational time for large spectroscopic imaging datasets. However, a demonstration of these effects was beyond the scope of this article and may well vary considerably among the various fitting methods available for spectral analysis.

Finally, this algorithm used a fixed KO-filter setting of 40 points (20 ms of data) determined empirically. A future enhancement may be to determine this threshold automatically. A fit of the area under a ppm range (e.g., 3.7–1.9 ppm) for increasing KO-filtered spectra should demonstrate regions of quickly decaying signals and slowly decaying signal. While, this is not a simple bi- exponential decay, even a rough linear estimate of early KO-filter rates of decay versus later KO-filter rates could provide a sufficient estimate for a threshold. The most likely issue here would be to avoid setting the threshold so late that significant signal is lost due to T₂ decay.

CONCLUSION

KO-filtering provides a robust tool for estimating initial values for a spectral model by removing baseline contributions from short TE data. It uses prior information regarding the behavior of metabolite and macromolecular signal contributions without the need for additional scans. Even in the presence of a large lipid signal, KO-filtering provides a way to remove the nuisance signal and give reasonable initial estimates for the metabolite signals. While the in vivo example given was for short TE data, the KO-filtering method should be effective for removing unwanted lipid signals at any TE value so long as there is sufficient metabolite SNR to apply a sufficiently long KO-filter to remove the lipids. Overall, estimates of NAA, creatine, and choline can be consistently estimated well despite underlying baseline signals, and good estimates of myo-inositol are possible for data with high SNR. The results are promising for estimating signals from other metabolites, such as glutamate, but will require additional work.