Mathematical analysis in the design of digital artery-based V–Y advancement flap in treating proximal interphalangeal joint flexion contracture

BACKGROUND: The digital artery-based V–Y advancement flap is a widely used flap for soft tissue coverage in the treatment of flexion contracture of the proximal interphalangeal (PIP) joint. A standard method for the flap design and a mathematical method to predict the advance distance have not been well established. In this study, we proposed a simplified method for the design of V–Y advancement flaps based on digital arteries and used a geometric model to predict the advance distance for the flexion contracture correction surgery. METHODS: According to the general concept of hand flap design and law of cosine, we proposed three principles in the design of the digital artery-based V–Y advancement flap that should be followed. Since 2021 to 2022, finger geometric data of 120 fingers (index, middle, ring, and small fingers) from 30 healthy participants were collected and analysed to evaluate the necessary advance distance and flap tip angle for PIP flexion contracture correction of different fingers by our flap design method. RESULTS: The middle finger needed a significantly longer advance distance compared to other fingers in the same degree flexion contracture correction. The ring finger had the largest length-to width ratio and smallest flap tip angle among the four fingers in the V–Y flap design. No vertical scar crossed the flexion creases and flap tip angle < 20° was found in the tentative V–Y flap design for the 120 fingers. CONCLUSIONS: Our flap design method provides a proper advance distance and flap length-to-width ratio without common skin complications in the flap design for PIP flexion contracture of index, middle, ring and small fingers. This geometric model provides a mathematical basis for prediction of advance distance and flap tip angle in the design of a digital artery-based V–Y advancement flap. SUPPLEMENTARY INFORMATION: The online version contains supplementary material available at 10.1186/s12891-023-06158-7.