Narrow Results

Background: When performing partial toe-transfer flaps with a short vascular pedicle, as the flap becomes smaller, the likelihood of securing veins in the flap decreases. The purpose of this study was to clarify how frequently the partial toe-transfer flap with a short pedicle (free vascularized half-big toenail flap) contains veins and elucidate how frequently we can secure the veins with an artery via the first web space approach alone, using the Genial Viewer (a near-infrared light transmission imaging device).

Methods: We observed the dorsal vein images of the bilateral big toes of 250 volunteers (male, n = 125; female, n = 125) using the device. We counted the total number of dorsal veins in the big toe, the veins that crossed the margin of the region equivalent to the half-big toenail flap, and the veins that branched off from the fibular side of the flap area. An unpaired Student’s t-test was used for the statistical analyses.

Results: All of the dorsal big toes contained veins. The mean number of the veins was 2.3 (range, 1–4). Branched-off veins were observed in the area equivalent to the half-big toenail flap in 496 (99.2%) of the big toes, and the mean number of veins was 1.9 (range, 0–4). In four cases, the region contained no veins (unilaterally). Branched-off veins were observed in the first web space in 440 (88.0%) of the big toes, and the mean number of veins was 0.9 (range, 0–2).

Conclusions: The present study indicated high consistency of the veins in partial toe-transfer flaps with a short vascular pedicle and the high possibility of harvesting a flap with only exposing the first web space. In addition, in most cases, the flap will include one or, at most, two veins in the first web space.

Submultiplicativity, an analytic property generalizing the Strengthened Hanna Neumann Conjecture (SHNC) to complexes was proved in [2] assuming the deep-fall property. This in particular implied SHNC. The purpose of this note is to write the proof of the original SHNC and purely in terms of groups and graphs. We also give explicit examples showing that the upper bound in SHNC is sharp.