Improving nonlinear search with Self-Organizing Maps - Application to Magnetic Resonance Relaxometry

Quantification of myelin in vivo is crucial for the understanding of neurological diseases, like multiple sclerosis (MS). Multi-Component Driven Equilibrium Single Pulse Observation T1 and T2 (mcDESPOT) is a rapid and precise method for determination of the longitudinal and transverse relaxation times in a voxel wise fashion. Briefly, mcDESPOT couples sets of SPGR (spoiled gradient-recalled echo) and bSSFP (fully balance steady-state free precession) data acquired over a range of flip angles (α) with constant interpulse spacing (TR) to derive 6 parameters (free-water T1 and T2, myelin-associated water T1 and T2, relative myelin-associated water volume fraction, and the myelin-associated water proton residence time) based on water exchange models. However, this procedure is computationally expensive and extremely difficult due to the need to find the best fit to the 24 MRI signals volumes in a search of nonlinear 6 dimensional space of model parameters. In this context, the aim of this work is to improve mcDESPOT efficiency and accuracy using tissue information contained in the sets of signals (SPGR and bSSFP) acquired. The basic hypothesis is that similar acquired signals are referred to tissue portions with close features, which translate in similar parameters. This similarity could be used to drive the nonlinear mcDESPOT fitting, leading the optimization algorithm (that is based on a stochastic region contraction approach) to look for a solution (i.e. the 6 parameters vector) also in regions defined by previously computed solutions of others voxels with similar signals. For this reason, we clustered the sets of SPGR and bSSFP using the neural network called Self Organizing Map (SOM), which uses a competitive learning technique to train itself in an unsupervised manner. The similarity information obtained from the SOM was then used to accordingly suggest solutions to the optimization algorithm. A first validation phase with in silico data was performed to evaluate the performances of the SOM and of the modified method, SOM+mcDESPOT. The latter was further validated using real magnetic resonance images. The last step consisted of applying the SOM+mcDESPOT to a group of healthy subjects ( ) and a group of MS patients ( ) to look for differences in myelin-associated water fractions values between the two groups. The validation phases with in silico data verified the initial hypothesis: in more the 74% of the times, the correct solution of a certain voxel is in the space dictated by the cluster which that voxel is mapped to. Adding the information of similar solutions extracted from that cluster helps to improve the signals fitting and the accuracy in the determination of the 7 parameters. This result is still present even if the data are corrupted by a high level of noise (SNR=50). Using real images allowed to confirm the power of SOM+mcDESPOT underlined through the in silico data. The application of SOM+mcDESPOT to the controls and to the MS patients allowed firstly obtaining more feasible results than the traditional mcDESPOT. Moreover, a statistically significant difference of the myelin-associated water fraction values in the normal appearing white matter was found between the two groups: the MS patients, in fact, show lower fraction values compared to the normal subjects, indicating an abnormal presence of myelin in the normal appearing white matter of MS patients. In conclusion, we proposed the novel method SOM+mcDESPOT that is able to extract and exploit the information contained in the MRI signals to drive appropriately the optimization algorithm implemented in mcDESPOT. In so doing, the overall accuracy of the method in both the signals fitting and in the determination of the 7 parameters improves. Thus, the outstanding potentiality of SOM+mcDESPOT could assume a crucial role in improving the indirect quantification of myelin in both healthy subjects and patients.