Monte Carlo simulations are used to (1) investigate the accuracy of approximations that are implicit in first‐order stochastic dispersion theories and (2) identify the accuracy limits of first‐order dispersion theories in isotropic porous media. The Fickian theory of Gelhar and Axness (1983), as well as the Fickian and non‐Fickian theories of Dagan (1984) and Neuman and Zhang (1990) are investigated. All Monte Carlo simulations are in three dimensions. Confidence limits of ensemble‐averaged Monte Carlo results in isotropic porous media are established for 0.1 ≤ σY ≤ 1.5. These results showed that first‐order theoretical estimates of the Eulerian velocity covariance function are quite accurate for σY < 1; theoretical estimates of the non‐Fickian longitudinal dispersivity do not deviate significantly from theory for at least σY ≤ 1.5; theoretical estimation of the transverse dispersivity is limited to σY < 1; and, the Fickian longitudinal dispersivity is overestimated by the theory of Gelhar and Axness (1983). Of all first‐order dispersion theories, the theory of Dagan (1984) is most robust in estimating the dispersivity tensor.

The results of this meta-analysis suggested that serum glypican-3 was acceptable as a moderate diagnostic marker in the diagnosis of hepatocellular carcinoma compared with healthy individuals, which could elevate the sensitivity and specificity of diagnosis. Furthermore, more well-designed studies with large sample sizes are needed to show the effectiveness of glypican-3 in the differential diagnosis of hepatocellular carcinoma.

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