Synthesizing 3D axon morphology: springs are all we need

The realism of digital phantoms for the white matter microstructure is highly valued. Realistic synthesis provides reliable input to generate synthetic diffusion MRI signals for evaluating biophysical models or training machine learning models of microstructure features, such as axon diameter, shapes, and cellular structures. Inspired by the popular spring-mass systems used in physical simulation, we propose a novel and flexible method for synthesizing axon morphology and its dynamics with physical constraints. Specifically, starting with an initial axon configuration, our method constructs a spring-mass system based on specific sampling rules inspired by the real 3D axons and cell morphology observed in X-ray synchrotron imaging. By minimizing the spring potential energy, our method optimizes the positions of sampled mass points, thereby deforming the axon morphology from its physical surroundings. After the optimization, a triangle mesh of the axon surfaces is obtained and can be used as input for Monte Carlo diffusion MRI simulations. Experimental results demonstrate that our approach successfully mimics a range of axon morphologies and the dynamic environment.