Tight closure of parameter ideals in local rings F-rational on the punctured spectrum

Let $(R,\mathfrak{m},k)$ be an equidimensional excellent local ring of characteristic $p>0$. The aim of this paper is to show that ${?}_R({\mathfrak{q}}^{?}/\mathfrak{q})$ does not depend on the choice of parameter ideal $\mathfrak{q}$ provided R is an F-injective local ring that is F-rational on the punctured spectrum.