MicroKAN: Mapping human brain microstructure using diffusion MRI and adaptive nonlinear modeling

Diffusion magnetic resonance imaging (dMRI) provides powerful insights into brain microstructure, but conventional microstructural modeling methods require long acquisition times for covering sufficient diffusion directions and are computationally intensive. While deep learning has shown promise in reducing the direction requirement and accelerating the modeling, traditional architectures such as CNNs often struggle to capture the highly nonlinear relationships between multi-shell diffusion signals and microstructural properties. We present MicroKAN, a novel framework built upon Kolmogorov-Arnold Networks with adaptive spline-based activations, specifically designed to represent complex biophysical models with enhanced flexibility and efficiency. MicroKAN supports both supervised and self-supervised paradigms: the supervised variant learns mappings from data to reference metrics, while the self-supervised variant estimates model parameters directly by reconstructing signals through the forward diffusion process, eliminating the need for ground-truth labels. Evaluated on diffusion tensor imaging (DTI) and neurite orientation dispersion and density imaging (NODDI) across multiple datasets, MicroKAN substantially accelerates acquisition and improves the fidelity of microstructural parameter estimation. Beyond supervised training, its self-supervised formulation shows strong robustness to distribution shifts, enabling reliable performance even without annotations. Furthermore, transfer learning with minimal labeled data preserves high accuracy, underscoring the framework's adaptability to diverse scenarios. These advances establish MicroKAN as a versatile and efficient tool for dMRI analysis, offering new opportunities to accelerate neuroscience research and expand the clinical utility of microstructural imaging. Our source code is available at https://github.com/JustlfC03/MicroKAN.