quantum mechanics - Deriving the optical Bloch equations as given in Wikipedia from the von Neumann equations

Different from my previousquestion, which dealt with a convention my professor used, I now want to derive the optical Bloch equations in a semiclassical model, but this time in the shape they are given in for example on Wikipedia:

$$ \begin{align} \frac{d \rho_{gg}}{dt} & = \frac i2 (\Omega^* \rho_{eg}-\Omega \rho_{ge}), \\ \frac{d \rho_{ee}}{dt} & = \frac i2 (\Omega \rho_{eg}-\Omega^* \rho_{ge}), \\ \frac{d \rho_{ge}}{dt} & =-\left(i\delta\right)\rho_{ge}+\frac i2\Omega^*(\rho_{ee}-\rho_{gg}), \\ \frac{d \rho_{eg}}{dt} & =-\left(i\delta\right)\rho_{eg}+\frac i2\Omega^*(\rho_{gg}-\rho_{ee}). \end{align} $$

I'm not interested in the attenuation terms, so I ommitted them. Problems arrise with the off-diagonal equations: Instead of $\delta$, the factor infront of $\rho_{ge}$ becomes $\omega_0$. Does anybody know where a semiclassical Model and the von Neumann equations are used to derive the optical Bloch equations? I have only found this derivation for pure states, but in my opinion this derivation lacks some generality.