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Purpose: To introduce a method to create 3D-printed axon-mimetic phantoms with complex fibre orientations to characterise the performance of diffusion magnetic resonance imaging (MRI) models and representations in the presence of orientation dispersion., Methods: An extension to an open-source 3D printing package was created to produce a set of five 3D-printed axon-mimetic (3AM) phantoms with various combinations of bending and crossing fibre orientations. A two-shell diffusion MRI scan of the five phantoms in water was performed at 9.4T. Diffusion tensor imaging (DTI), diffusion kurtosis imaging (DKI), the ball and stick model, neurite orientation density and dispersion imaging (NODDI), and Bingham-NODDI were all fit to the resulting diffusion MRI data. A ground truth map of that phantom's crossing angles and/or arc radius was registered to the diffusion-weighted images. Metrics from each model and representation were compared to the ground-truth maps, and a quadratic regression model was fit to each combination of output metric and ground-truth metric., Results: The mean diffusivity (MD) metric defined by DTI was insensitive to crossing angle but increased with fibre curvature. Axial diffusivity (AD) decreased with increasing crossing angle. DKI's diffusivity metrics replicated the trends seen in DTI, and its mean kurtosis (MK) metric decreased with fibre curvature, except in regions with high crossing angles. The estimated stick volume fraction in the ball and stick model decreased with increasing fibre curvature and crossing angle. NODDI's intra-neurite volume fraction was insensitive to crossing angle, and its orientation dispersion index (ODI) was correlated to crossing angle. Bingham-NODDI's intra-neurite volume fraction was also insensitive to crossing angle, while its primary ODI (ODI P ) was also correlated to crossing angle and its secondary ODI (ODI S ) was insensitive to crossing angle. For both NODDI models, the volume fractions of the extra-neurite and CSF compartments had low reliability with no clear relationship to crossing angle., Conclusion: Inexpensive 3D-printed axon-mimetic phantoms can be used to investigate the effect of fibre curvature and crossings on diffusion MRI representations and models of diffusion signal. The dependence of several representations and models on fibre dispersion/crossing was investigated. As expected, Bingham-NODDI was best able to characterise planar fibre dispersion in the phantoms., Competing Interests: The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest., (Copyright © 2022 Kuehn, Mushtaha, Khan and Baron.)