Ultrasound (US) is a versatile, low cost, real-time, widely available imaging modality. Manual segmentation for volumetric US measurements can be difficult and very time consuming, requiring slice-by-slice segmentations. However, automatic segmentation of ultrasound images can prove challenging due to the presence of speckle, attenuation, missing boundaries, signal dropouts, and artefacts. Semi-automatic segmentation techniques can improve the speed and accuracy of such measurements, taking advantage of clinical expertise while allowing user interaction. This paper presents a novel solution for interactive image segmentation on B-mode ultrasound images. The proposed method builds on the Live Wire framework and introduces two new sets of Live Wire costs, namely a Feature Asymmetry (FA) cost to localise edges and a weak shape constraint cost to aid the selection of appropriate boundaries in the presence of missing information or artefacts. The resulting semi-automatic segmentation method follows edges based on structural relevance rather than intensity gradients, adapting the method to ultrasound images, where the object boundaries are normally fuzzy. The new method is applied in the context of fetal arm adipose tissue quantification, the adipose tissue being an indicator of the fetal nutritional state. A quantitative and qualitative evaluation is performed with respect to related segmentation techniques. The method was tested on 48 manually segmented ultrasound images of the fetal arm across gestation, showing similar accuracy to the intensity-based Live Wire approach but superior repeatability while requiring significantly less time and user interaction.