An Optimal Scalp Rotation Flap Design: Mathematical and Bio-Mechanical Analysis

The design and implementation of successful rotational flaps of the scalp remains a complex process. There are several described techniques, all of which are based on a two-dimension surface, absent consideration of the convexity, and thereby three-dimensional nature of the scalp. This has contributed to flaps that are either too small or unnecessarily large in a bid to compensate. Mathematical analysis using trigonometric and algebraic formulas was used to derive the relationship between the defect, triangulation, the contour of the scalp, the radius of the arc of rotation for the flap, and scalp skin tension. Polyurethane models were used to test the applicability of the resultant formula, and a consecutive clinical case series is presented. Rotation flap dimensions were calculated using an apex angle of 30° depicted as a two-dimensional construct. The contour of the defect was then measured as the depth of depression with radius of the rotation flap calculated based on the changes in flap surface area across the defect. Finite element analysis was used to measure redistribution of tension along the flap reconstructing the defect, and the efficacy of the approach was confirmed in the consecutive clinical series. This study provides a reliable flap design based on mathematical analysis, with evidence-based application to the clinical setting.