Diagnostic medical imaging plays an imperative role in clinical assessment and treatment of medical abnormalities. The fusion of multimodal medical images merges complementary information present in the multi-source images and provides a better interpretation with improved diagnostic accuracy. This paper presents a CT-MR neurological image fusion method using an optimised biologically inspired neural network in nonsubsampled shearlet (NSST) domain. NSST decomposed coefficients are utilised to activate the optimised neural model using particle swarm optimisation method and to generate the firing maps. Low and high-frequency NSST subbands get fused using max-rule based on firing maps. In the optimisation process, a fitness function is evaluated based on spatial frequency and edge index of the resultant fused image. To analyse the fusion performance, extensive experiments are conducted on the different CT-MR neurological image dataset. Objective performance is evaluated based on different metrics to highlight the clarity, contrast, correlation, visual quality, complementary information, salient information, and edge information present in the fused images. Experimental results show that the proposed method is able to provide better-fused images and outperforms other existing methods in both visual and quantitative assessments.