  An important tool for the analysis of results of numerical simulations of
lattice QCD is chiral perturbation theory. In Wilson chiral perturbation theory
the effects of the finite lattice spacing $a$ are taken into account. In recent
years the effects of isospin splitting on the masses of hadrons have been
investigated in Monte Carlo simulations. Correspondingly, in this article we
derive the expansions of the masses of the pseudoscalar mesons in chiral
perturbation theory at next-to-leading order for twisted mass lattice QCD with
three light quark flavours, taking the mass difference between the up and down
quarks into account. The results include terms up to orders $m_q^2$ in the
quark masses, $\Delta m^2$ in the mass splitting between up- and down quarks,
and $a^2$ in the lattice spacing, respectively.
