We consider the effect of tissue heterogeneity on diffusion acquisitions with multiple encodings. Previously, these signals were analyzed in Gaussian compartments, or disconnected pores. Here we assume a more realistic situation where a compartment cannot be considered Gaussian (uniform) at finite diffusion times, and derive the 4th-order contributions in the diffusion weightings, that distinguish the double-diffusion-encoding (DDE) signal from its single-encoding counterpart. We specifically identify terms odd in the DDE diffusion wave-vectors, which emerge due to local tissue heterogeneity but absent when compartments are Gaussian. Our results are expressed via the dynamical exponent related to the disorder universality class, and agree with Monte Carlo simulations.
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