Synopsis

Clinical proton MRS conventionally measures metabolites' concentrations, but neglects to acquire their relaxation constants, despite the fact that these are known to vary in many pathologies. Using computer simulations and literature values for n-acetyl-aspartate, we show that incorporating this additional information can greatly facilitate the detection of neurodegeneration in early stage multiple sclerosis (MS), increasing the area under the corresponding receiver operating characteristic curves from 0.68 to 0.91. These results strongly motivate the need for developing robust sequences for clinical multiparametric magnetic resonance spectroscopy .

Introduction

Proton Magnetic Resonance Spectroscopy (1H-MRS) can detect biochemical imbalances in brain tissue before structural abnormalities are observed on conventional MRI. In Multiple Sclerosis (MS), neurodegeneration precedes symptoms and determines patient outcome, and therefore there is high interest in using concentrations of the neuronal marker n-acetyl-aspartate (NAA) to follow treatment effects and disease progression in recently-diagnosed patients. Imaging protocols, however, usually do not acquire metabolites' and water’s relaxation constants (T1, T2), due to lack of time and an appropriate protocol/sequence. Our groups and others, however, have shown that these values in MS are not only different from controls’, but also exhibit regional and inter-subject variations [1-6]. This indicates that using average population values – as opposed to subject-specific values – results in substantial bias to the estimated concentrations. The results also suggest that relaxation times have the potential to provide independent markers of pathophysiology. Given recent interest in multiparametric MRS techniques [7,8], we sought to quantify the sensitivity and specificity gains that might be had by measuring these values for NAA in early stage MS. This is done using receiver operating characteristic (ROC) curves and areas underneath them (AUC). The AUC ranks the performance of a classifier and ranges from 0.5 (useless) to 1.0 (perfect).

Methods

A literature search was conducted on values of metabolite concentrations and relaxation times in MS. The following criteria were used:

1. Only data from cerebrum was used.
2. Where unavailable, a conservative ±10% population standard deviation was assumed.
3. Concentrations: Only values from statistically significant results (p<0.05) obtained by absolute quantification.
4. Only work in normal appearing white matter (NAWM) of early relapsing remitting MS was considered.
5. For relaxation times, only works at 3T were considered.

We estimated the ROC and AUC using NAA’s T1 [2], T2 [2,6] and concentration changes [1-6], averaged across publications: Controls: NAA=9.2±0.7 mM, T1=1860±200 ms, T2=312±32 ms; Early MS: NAA=8.4±0.6 mM, T1=1680±100 ms, T2=273±44 ms. Reference water values were adopted from [2, 9,10]. Three cases were considered for distinguishing between patients and controls:

1. Using NAA/water concentrations alone, corrected using population average values for NAA's and water's T1 and T2.
2. Using NAA/water concentrations alone, corrected using each subject’s specific NAA's and water's T1 and T2 values.
3. Using a multiparametric optimal linear-combination estimator [11], designed to maximize the AUC, comprised of NAA’s (true, unweighted) concentrations, T1 and T2 values (no reference to water values was used).

For all cases, the water reference signal was left uncorrected (we note The ROCs for each case were calculated using Monte Carlo simulations as follows: NAA and water concentrations, T1 and T2 values were randomly generated for 10,000 controls and 10,000 patients assuming normal distributions and using literature values. Weighted NAA/water ratios were generated assuming a simple spin-echo pulse sequence (with TR/TE=1500/40 ms, FA=90 degrees) and a perfectly homogeneous radiofrequency transmitter, via:

$$C_{NAA}^{Weighted}=(1-e^{-TR/T_{1,NAA}})e^{-TE/T_{2,NAA}} C_{NAA}$$

$$C_{Water}^{Weighted}=(1-e^{-TR/T_{1,Water}})e^{-TE/T_{2,Water}} C_{Water}$$

For cases (1-3), the weighted NAA and water values were corrected by dividing them by a correction factor of the form:

$$f=(1-e^{-TR/T_{1,c}})e^{-TE/T_{2,c}}$$

For case (1), population means were substituted for T_1,c, T_2,c, while for cases (2) and (3), subject-specific values were used. The NAA concentrations were estimated via:

$$C_{NAA}^{Est.} = \frac{C_{NAA}^{Weighted}}{C_{Water}^{Weighted}} \frac{f_{Water}}{f_{NAA}} \bar{C}_{Water}$$

with $$$\bar{C}_{Water}$$$ being the population mean value of the water concentration (i.e. as done in absolute quantification in MRS).

For case (3), the linear classifier $$$CLASS=a_1 C_{NAA} + a_2 T_{1,NAA} + a_3 T_{2, NAA}$$$ was formed for each subject, with a₁=1.0, a₂=0.0038 mM/ms, a₃=0.0093 mM/ms (as described in [11]). Using NAA (cases 1 & 2) or CLASS (case 3), the ROC was generated numerically by varying the classification threshold from -infinity to +infinity. The AUC was estimated via numerical integration of the ROC.

Results

Discussion & Conclusions

Acknowledgements

Assaf Tal acknowledges the support of the Monroy‐Marks Career Development Fund, the Carolito Stiftung Fund, the Leona M. and Harry B.Helmsley Charitable Trust and the historic generosity of the Harold Perlman Family. Ivan Kirov acknowledges the support of National Institutes of Health (NIH) funding grants R01 NS097494 and P41 EB017183.

References

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