Introduction

The assessment of myelin content in white matter (WM) provides valuable information regarding neurodegenerative diseases, as well as insights on neuronal maturation and development^1,2–5. Myelin water fraction (MWF) is a proxy for myelin content, which can be estimated using multicomponent analysis of T₂ relaxation times (mcT₂). This estimation is done through a fitting process where a weighted sum of different T₂ components (i.e. spectra) is matched to multi-echo spin-echo (MESE) signal decay curve. However, the detection of the true T₂ distribution is a highly ill-posed problem^6,7, especially at low-to-moderate signal-to-noise ratios (SNRs)⁸. In this study we present a new approach to mcT₂ analysis from MESE signals. To overcome the problem’s non-uniqueness we generate a dictionary of possible T₂ distributions of different tissue types, and exploit correlation between local and global features to choose a small set of basis-functions for the fitting process. The algorithm can be applied to clinical MESE data and the resultant spectra can be further analyzed to identify different tissue microenvironments, as well as, to quantify MWF.

Methods

Fitting algorithm
The proposed signal-deconvolution algorithm begins with fitting a single T₂ to each MESE signal. To compensate for the non-exponential signal decay due to stimulated and indirect echoes¹⁰ we employ the echo modulation curve (EMC) algorithm. This technique was previously shown to produce accurate and reproducible T₂ values¹¹, by accounting for specific protocol implementation, hardware imperfections, and scan parameters to form a simulated MESE signal. Next, we used the same model to simulate a series of multi-T₂ signals each containing 1-3 components with relative fractions between 0.1-1: $${S_{mc}= \sum_{i=1}^3w_i\cdot S_{T_{2}}}, s.t. \sum_1^3w_{i} = 1$$ where: $$$S_{T_{2}}$$$ is the MESE relaxation pattern for the i^th T₂, $$$w_i$$$ is the relative fraction of the T₂ component, and $$$S_{mc}$$$ is the simulated multicomponent-MESE signal. Next, a score is calculated for each simulated signal based on its L₂-norm correlation to each of the pixels in the segment of interest. These scores are summed up, producing a global similarity score for each simulated multi-T₂ signal. Lastly, we choose the 50 multi-T₂ signal options with the highest score and consider those basis-function for the subsequent optimization process. The problem is defined as a quadratic least-squares⁶ and a quadratic programming solver with L₁ regularization term is applied on the set for the fitting task.

Validation
Numeric simulation: A 2D Shepp–Logan numerical phantom was generated, consisting of 5 tissue types (Fig. 1). Each type reflected a different distribution of three T₂ components (detailed in Fig. 1) with varying fractions (detailed in Fig. 2). The MESE signal from each compartment was simulated using a weighted-sum of the components at each pixels in the phantom. To simulate realistic condition, Gaussian noise, and natural variation of 20% in T₂ values were added to the signals prior to analysis.

Phantom scans: A unique multi-compartment T₂ phantom was prepared from 3 MnCl₂ solutions inducing different T₂ values. A 50ms solution was filled within a 5mm tube with a varying number of 1mm tubes filled with T₂={13 and 80ms}. Smaller tubes were consecutively inserted between scans into the 5mm tube. The phantom was scanned 7 times on a Bruker,9.4T scanner with a different number of small tubes inducing varying fractions. This phantom’s design allowed us to map high-resolution T₂ values in all three environments and to perform a low resolution scan where all three compartments occupied a single pixel. Low resolution data was deconvolved using our mcT₂ algorithm and the resulting T₂ spectra validated against ground-truth values. To estimate MWF, the area under the short T₂ component were calculated from the resultant T₂ spectra¹².

In vivo: MESE brain data (30 echoes and 2 averages) were acquired from healthy mouse (Bruker, 7T) and human volunteer (Siemens, 3T). T₂ spectra were fitted to all voxels and MWF were estimated in selected WM pixels.

Results

T₂ spectra of numerical phantom were perfectly reconstructed with 1, 2 and 3 compartments respectively, and at SNR level of 60 and above (Fig. 2). Fig. 3 presents the goodness-of-fit for the phantom, demonstrating high accuracy between calculated and actual MWF (p<0.01, R-square=0.98). Applying the algorithm on in vivo mouse and human data produced the T₂ spectra seen in Fig. 4-5, having 2 and 3 distinct compartments and T₂ values and fractions within physiological range²: T₂ mouse: {20ms, 40ms 50ms} and T₂ human: {20ms 50ms 78ms}. Although no ground truth was available for this data, the estimated MWF at 3 different locations were consistent with literature^12,13: mouse {8%, 8.9%,10%}, and human {10%, 18%, 20%}.

Discussion and Conclusion

Presented results attest to our mcT₂ algorithm’s ability to probe distinct sub-voxel compartments at realistic scan conditions. The excellent agreement shown for the MWF phantom suggests that the method has the potential to accurately quantify myelin content. The presented algorithm has three notable advantages: first, it learns the anatomy prior to analyzing each specific voxel; secondly, it does not impose prior distribution of T₂ values; and third, and most importantly, it does not use a predefined fixed number of components, but rather manages to accurately identify this number based on the acquired data. Further validations are now begin conducted, comparing MWF values to ground-truth myelin content extracted from histology.

Acknowledgements

ISF Grant 2009/17