  We consider the issues of stability and reconstruction of the electrical
anisotropic conductivity of biological tissues in a domain
$\Omega\subset\mathbb{R}^3$ by means of the hybrid inverse problem of
magneto-acoustic tomography with magnetic induction (MAT-MI). The class of
anisotropic conductivities considered here is of type
$\sigma(\cdot)=A(\cdot,\gamma(\cdot))$ in $\Omega$, where $[\lambda^{-1},
\lambda]\ni t\mapsto A(\cdot, t)$ is a one-parameter family of matrix-valued
functions which are \textit{a-priori} known to be $C^{1,\beta}$, allowing us to
stably reconstruct $\gamma$ in $\Omega$ in terms of an internal functional
$F(\sigma)$. Our results also extend previous results in MAT-MI where
$\sigma(\cdot) = \gamma(\cdot) D(\cdot)$, with $D$ an \textit{a-priori} known
matrix-valued function on $\Omega$ to a more general anisotropic structure
which depends non-linearly on the scalar function $\gamma$ to be reconstructed.
