PURPOSE: The nonmonotonic dependence of diffusion kurtosis on diffusion time has been observed in biological tissues, yet its relation to membrane integrity and cellular geometry remains to be clarified. Here we establish and explain the characteristic asymmetric shape of the kurtosis peak. We also derive the relation between the peak time METHODS: The peak shape and its position RESULTS: We establish that CONCLUSION: Numerical simulations and theory provide an interpretation of a specific feature of kurtosis time-dependence, offering a potential biomarker for in vivo evaluation of pathology by disentangling the functional (permeability) and structural (cell size) integrity in tissues. This is relevant as the time-dependent diffusion cumulants are sensitive to pathological changes in membrane integrity and cellular structure in diseases, such as ischemic stroke, tumors, and Alzheimer's disease.