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The conditions for activation transmission across a region of extracellular space was demonstrated in two-dimensional preparations with results consistent with those previously seen in the one-dimensional fiber studies. In addition, one sees changes in action potential morphology which occur in the tissue nearest the connective-tissue border as well as changes in conduction velocity along the border. These results hinge on an adequate representation of the connective-tissue region achieved by careful implementation of the boundary conditions in the intracellular and interstitial spaces and the expansion of the connective-tissue discretization to a "double-tier network" description. Through a series of simulations, a clear dependence on fiber orientation is illustrated in the efficacy to transmit activation. The collision of a front with an embedded connective-tissue region was also examined. The results revealed that fibers aligned normal to a planar stimulus would more greatly disrupt the advancement of a planar front. Such pronounced disruptions have been shown to be proarrhythmic in the literature. The increasing evidence of the ability of connective tissue to transmit activation has implications in understanding spread of activation through infarcted tissues and through the healthy ventricular wall in the presence of connective-tissue sheets.