  The inclusive radiative decay of the B meson is known to provide strong
constraints on many popular extensions of the Standard Model. Such constraints
crucially depend on precision of the Standard Model predictions. One of the
main contributions to the theoretical uncertainty is due to certain
Next-to-Next-to-Leading Order QCD corrections whose values at the physical
charm quark mass m_c have been estimated using interpolation between the m_c=0
and m_c >> m_b limits. A direct determination of such corrections at the
physical value of m_c requires calculating hundreds of two-scale four-loop
propagator diagrams with unitarity cuts. Applying the integration-by-parts
method, we express the corrections in terms of master integrals. Asymptotic
expansions of these integrals at m_c >> m_b serve as boundary conditions for
differential equations in z=m_c^2/m_b^2 that are being numerically solved.
Here, we present our final results for the diagrams involving massless and
massive fermion loops on the gluon lines. For the two-body cuts, we confirm the
analytical expressions and/or numerical fits that are already present in the
literature. In the four-body case, we make the correction complete by including
several diagrams that have previously been only estimated using interpolation
in m_c. We also report the status of the ongoing calculation of the remaining
diagrams where no closed fermion loops on the gluon lines are present.
