In this paper, the application of 3-dimensional (3D) functional magnetic resonance imaging (FMRI) in the diagnosis of the 5th lumbar (L5) nerve root compression and brain functional areas in patients with lumbar disc herniation (LDH) was analyzed. The traditional fast independent component analysis (Fast ICA) algorithm was optimized based on the modified whitening matrix to establish a new type of Modified-Fast ICA (M-Fast ICA) algorithm that was compared with the introduced traditional Fast ICA and ICA. M-Fast ICA was applied to the 3D FMRI diffusion tensor imaging (DTI) evaluation of 65 patients with L5 nerve root pain due to LDH (group A) and 50 healthy volunteers (group B). The values of fractional anisotropy (FA) and apparent diffusion coefficient (ADC) in the lumbar nerve roots (L3, L4, L5, and the 1st sacral vertebra (S1)) were recorded among subjects from the two groups. Besides, the score of edema degree in the lumbar nerve roots (L5 and S1) and activity of brain functional areas were also recorded among all subjects of the two groups. The results showed that the mean square error of M-Fast ICA was smaller than that of traditional Fast ICA and ICA, while its signal-to-noise ratio (SNR) was greater than that of Fast ICA and ICA (P < 0.05). The FA of L5 and S1 nerve roots in patients of group A was sharply lower than the values of group B, while the ADC of patients in group A was greater than that of the control group (P < 0.05). Besides, the score of edema in L5 and S1 nerve roots of patients in group A increased in contrast to group B (P < 0.05). The brain areas were activated after surgery including bilateral temporal lobe, left thalamus, splenium of corpus callosum, and right internal capsule. In conclusion, the 3D image denoising performance of M-Fast ICA optimized and constructed in this study was superior to that of the traditional Fast ICA and ICA. The FA of patients with L5 nerve root pain due to LDH decreased steeply, while the ADC increased dramatically. L5 nerve root pain caused by LDH resulted in changes in brain functional areas of the patients to inhibit the resting state default network activity, and the corresponding brain functional areas could be activated through treatment.Copyright © 2021 Bofeng Zhao et al.