This article discusses our approach for extending interactive Live-Wire segmentation on 3D for pre-segmented MRI volume data. We generate a mosaic image volume by region growing. Surfaces between two neighboring regions (called facets) are considered as nodes and the borders where two or more surfaces meet are defined as edges thus converting the mosaic image into a graph onto which the 3D-live-wire operates. Due to the pre-segmentation the graph is concentrated to the areas of strong gradients which are the regions of interest for finding object outlines. The cost optimal path between two graph nodes can be calculated by applying a standard Live-Wire algorithm to this graph data. To get a surface patch without holes from three user defined seeds, an initial frame is calculated in a first step. This frame consists of the three paths connecting the seeds. By calculating the paths between a few additional facets taken from the initial frame we obtain supporting paths which increase the quality of segmentation. The remaining gaps in the resulting grating are closed in three steps. Firstly, we detect object and background regions of the grating. Next, these regions are expanded by adding similar unlabeled regions. And finally, we add facets enclosed by object and background regions to the grating until all gaps are closed. The preprocessing is done in about 188 seconds and the interactive segmentation in our examples takes about 8.4 seconds. We achieve a mean deviation from the correct object boundary extracted from available model data of about 0.2 voxels.