Monte Carlo simulation was performed in 1D space to study the spin diffusion, kurtosis characteristics, spin dephasing and MR signal attenuation in compartment-restricted diffusion environment. The apparent kurtosis was computed based on DKI formulation and compared to the true kurtosis and calculated from the actual diffusion displacement profiles. The simple results revealed that errors can be present in estimating true diffusion kurtosis by the apparent kurtosis. Choices of diffusion weighting parameters affect the outcomes. Both apparent diffusion kurtosis measurement and true diffusion kurtosis are not entirely intrinsic to the tissue structures because they also depend on the MR parameters. Therefore, cautions must be taken in the quantitative interpretation of kurtosis measurements in DKI experiments.