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The thermal and electrical conductivities of the normal matrix of LTS wires have a remarkable influence on the wire stability. In particular, in Nb3Sn wires, a bronze matrix in the region of the superconducting filaments may act as a thermal and electrical barrier between the filaments and the copper matrix. This phenomenon is analyzed here through a numerical model accounting for these thermal and electrical transverse resistances. The model is applied to a parametric analysis of the effect of the main properties of the wire matrix on the quench energy and velocity. A 2D analysis of the wire cross section is applied to investigate how a configuration change could improve the wire stability.