The standard model (SM) has been proposed as an appropriate diffusion MRI microstructural model for brain white matter. Using the cumulant expansion up to 2nd order in the b-tensor, it has been recently shown that multidimensional diffusion encoding makes the model parameter estimation problem well-posed. However, the tensorial properties of the expansion and their relationship with the SM assumptions have not been exploited. We reformulate the solution of the SM in an elegant tensorial form and analyse the constraints the SM imposes, showing how they can potentially falsify the model. Some simulations show the test feasibility for high-quality signals ($$$\text{SNR}\geq 50$$$).
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