Epsilon dichotomy for twisted linear models

Let $E\mathrm{/}F$ be a quadratic extension of local nonarchimedean fields of characteristic zero and let $D$ be a quaternion algebra over $F$ containing $E$. In this paper, we study a relation between the existence of twisted linear models on ${\mathrm{G}\mathrm{L}}_n(D)$ and the local root numbers.