# Designing Flaps for Closure of Circular and Semicircular Skin Defects: Erratum

Plastic and Reconstructive Surgery – Global Open: May 2016 - Volume 4 - Issue 5 - p 2
doi: 10.1097/GOX.0000000000000794
Erratum
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The article by Alvarado (Designing Flaps for Closure of Circular and Semicircular Skin Defects. Plast Reconstr Surg Glob Open 2016;4:e607; doi: 10.1097/GOX.0000000000000583), contained a number of mathematical errors in the sections titled “GEOMETRICAL ANALYSIS” and “Detailed Geometric Calculations.” There were six places in which a number raised to the second power was printed incorrectly, without superscript; for example, 1.5 squared was rendered as 1.52 rather than 1.52. Also in those sections, several formulas and percentages were incorrect. For instance, 7.08/7.06 = 1.03 should have been 7.34/7.08 = 1.03. Additionally, the equation in Figure 10 below the representation of the goblet incision should read 2.18 cm2 (19%). In the legend, 29% should be 19%. Finally, the last sentence of the section titled “Geometrical Analysis” should have been omitted. All errors have been corrected in the passage presented here (changes indicated by bold italic font):

The half moon incision and the goblet incision do not have a basic extension but have a complementary extension at the curved side of the defect (Fig. 4). The axis of the incision (axis X–X), representing the minimal tension lines, is centered at its upper corner and measures 30 degrees in relation to the straight side of the incision. The wastage for the half moon incision is 21% and for the goblet incision is 19% (Fig. 10). These calculations were made comparing the size of the complementary excision with the whole excised area.

## DETAILED GEOMETRIC CALCULATIONS

Details for these calculations are given here for the rhombus, circular, and semicircular incisions (Figs. 8, 10). The calculation for the rhombus incision was based on a rhombus ABC measuring 3.2 × 9 cm resulting in 14.4 cm2 (3.2 × 9/2 = 14.4) where A is a circular defect of 1.5 radius (π × 1.52= 7.06), so the total wastage would be ABC minus A (14.4 – 7.06 = 7.34), which represents a wastage of 103% (7.34/7.06=1.03). The calculation for the beak of the bird’s beak incision was made based on a parallelogram ABC measuring 3.5 by 3.0 cm (3.5 × 3.0 = 10.5) and subtracting the circular defect A (π × 1.52= 7.06), so wastage B would be 1.72 cm2 (10.5 – 7.06/2=1.72), which represents a wastage of 24% (1.72/7.06 = 0.24). The triangular defect (C) of the cat’s ear incision was calculated using the formula for an equilateral triangle measuring 1.6 by 1.5 (1.6 × 1.5/2 = 1.2). The total wastage for the cat’s ear incision would be the sum of ear B (1.72) plus triangular defect C (1.2), which equals to 2.92 cm2, and this represents a wastage of 41% (2.92/7.06 = 0.41).

The calculation for the half moon incision (Fig. 10) was made using the semicircle ABC that measures 14.14 cm2 (π × 32/2=14.14) and the semicircle Defghi, which is equal to semicircle ABC. Segment i is equal to ABC divided by 3 that is 4.71 (14.14/3= 4.71), segment h is equal to 3.89 (32 × √3/4 = 3.89), g equals to i minus h that is 0.82 (4.71 − 3.89 = 0.82), and g is equal to e and f (0.82). Segments e plus f equals to 1.64 (0.82 + 0.82=1.64), and D is equal to i minus fe that is 3.07 (4.71 − 1.64 = 3.07), so the total waste would be D divided by ABC (3.07/ 14.14=0.21), which represents a wastage of 21%.

The calculation for the goblet incision (Fig. 10) was made using the area of a robust semicircle ABC formed by a quadrilateral measuring 0.75 by 4.5 (0.75 × 4.5 = 3.37) plus a semicircle with a radius of 2.25 measuring 7.94 (π × 2.252/2 = 7.94), so the total area for this robust semicircle would be 11.31 (7.94 + 3.37 = 11.31). The quadrilateral Def equals to 10.12 (2.25 × 4.5 = 10.12) where e equals to 3.97 (π × 2.252/ 4 = 3.97) and f is equal to e, so e plus f equals to 7.94 (3.97 + 3.97 = 7.94), and D is equal to Def minus ef that is 2.18 (10.12 − 7.94 = 2.18), which represents wastage of 19% (2.18/11.31 = 0.19).

## REFERENCE

Alvarado A. Designing flaps for closure of circular and semicircular skin defects. Plast Reconstr Surg Glob Open 2016;4:e607DOI: 10.1097/GOX.0000000000000583.