The schematic of the inhomogeneity correction in the CCC_MR algorithm. The left image shows the volume segment, and the right image shows the EDK_ms generated in each arbitrary mass density. s is the interaction point, and the thick arrow from s indicates the energy transportation direction. |${\overline{\rho}}_i$| and |${p}_i$| (i = 1, 2, 3) indicate the average mass density and the radiological path length from s to each cross plane, respectively. The image shows cases where |${\overline{\rho}}_1$|⁠, |${\overline{\rho}}_2$| and |${\overline{\rho}}_3$| are equal to 0.25, 1.0 and 2.0 g·cm⁻³, respectively. The energy depositions from s to |${p}_1$|⁠, |${p}_2$| and |${p}_3$| are obtained from |${p}_1$|⁠, |${p}_2$| and |${p}_3$| in the EDKs_ms generated at 0.25, 1.0 and 2.0 g·cm⁻³, respectively. When the EDK_ms is not preobtained for the mass density corresponding to |${\overline{\rho}}_i$|⁠, the EDK_ms corresponding to that mass density is calculated by linear interpolation and is used to obtain the energy deposition. In inhomogeneity correction in the CCC_MR algorithm, the referenced EDK_ms is determined or interpolated according to the average mass density from the interaction point to the calculation point.