Abstract: Objective To discriminate the differences between normal appearing white matter(NAWM) in the patients with multiple sclerosis(MS) and normal white matter(NWM) in the healthy,and to set up a model to discriminate two classes.Methods The total sample set was 120 images with NAWM and NWM of 60 each.The NAWM sample set of 60 was randomly divided into training section and testing section by rate of 70% and 30% and the NWM was processed with the same way.Multiple fractal analysis was used to analyze regions of interest(ROI) which were gained from T2-weighted MR images of patients with MS and the healthy.Three eigenvectors were obtained,which were fractal box dimensions for 2D,3D surface and 3D volume.The sample was conversed to binary image firstly and different patterns of square were used to cover it.A data counting the covering squares was obtained from one pattern and a data set was achieved from all patterns.After logarithms of the square sizes and the data set gained were extracted,the linear fitting was conducted to calculate slope by these logarithms,i.e.fractal box dimension for 2D.Similarly to the fractal box dimension for 2D,a curved face was constructed based on the grey value of every pixel firstly,and then a 3D surface was achieved following by covering the face with different sizes of cube.After logarithms were applied to the cube sizes and the data set gained,linear fitting slope was acquired,i.e.fractal box dimension for 3D surface.When the whole volume was covered by different sizes of cube,fractal box dimension for 3D volume was then achieved.T-test was conducted to test if there were any significant differences in three eigenvectors of fractal box dimensions above between two groups of NAWM and NWM.The probabilistic neural network(PNN) was used to classify ROI based on significant eigenvectors.Results In two groups of NAWM and NWM,the mean values were 1.803 vs 1.833 for fractal box dimension for 2D(P=0.037),1.9751 vs 2.058 for fractal box dimension for 3D surface(P<0.001),2.6988 vs 2.7649 for fractal box dimension for 3D volume(P<0.001) respectively.The identification rates were 77.5% for NAWM and 65% for NWM based on these ROI.The rate of classification with fractal box dimension was close to that of other methods.Conclusion There were significant differences of fractal box dimensions between groups of NAWM and NWM,which indicated that the textures in MRI images of them could be different in a certain extent.Some microstructures change because of demyelination around nerve axes in NAWM,which perhaps leads to fractal box dimensions from NAWM a little less than those from NWM.But the pathological changes in NAWM were not macroscopic.Fractal dimension maybe becomes an effective tool used to observe images with MS of MRI.The result was affected by some factors,such asanatomization structure and the course of diseases.The data of our patients is limited,and bigger crowd is expected to confirm theconclusion above in further study.

Key words: fractal dimension, multiple sclerosis, normal appearing white matter