  The numerically dominant QED contributions to the anomalous magnetic moment
of the muon stem from Feynman diagrams with internal electron loops. We
consider such corrections and present a calculation of the four-loop
light-by-light-type corrections where the external photon couples to a closed
electron or muon loop. We perform an asymptotic expansion in the ratio of
electron and muon mass and reduce the resulting integrals to master integrals
which we evaluate using analytical and numerical methods. We confirm the
results present in the literature which are based on different computational
methods.
