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

Area of Science:

• Plastic Surgery
• Biomechanical Engineering
• Surgical Innovation

Background:

• Scalp rotational flap design is complex, often neglecting the scalp's 3D curvature.
• Existing 2D methods lead to inaccurate flap sizing (too small or large).
• This necessitates a more precise, mathematically-driven approach.

Purpose of the Study:

• To develop a reliable mathematical model for scalp rotational flap design.
• To incorporate the scalp's 3D contour and skin tension into flap calculations.
• To validate the model through physical and clinical testing.

Main Methods:

• Mathematical analysis using trigonometric and algebraic formulas to relate defect size, scalp contour, and flap rotation arc.
• Testing the derived formula using polyurethane models.
• Clinical case series to confirm the approach's efficacy.

Main Results:

• A formula was derived to calculate optimal rotation flap dimensions based on defect characteristics and scalp geometry.
• Polyurethane models demonstrated the formula's applicability.
• Clinical application confirmed the reliability and accuracy of the mathematically designed flaps.

Conclusions:

• The study presents a novel, mathematically derived method for designing scalp rotational flaps.
• This approach addresses the limitations of 2D design by considering scalp 3D convexity.
• The validated method offers evidence-based improvements for clinical reconstructive surgery.