Dr Rheza Maulana and Anggie Rassly discuss an adjusted measurement technique as a new proposed method for eyebrow correction based on the golden ratio

The eyebrow region is one of the most important parts in facial aesthetics^{1}. Eyebrow appearance and its position play an important role in forming facial expressions and aesthetic perception, therefore, it plays an integral role in overall facial beauty^{2}.

Eyebrows are responsible for revealing emotions by creating facial expressions through the change of their shape and position. Disproportional eyebrows in terms of size, shape, and proportion may alter the overall appearance and characters of the face cosmetically, making the face look less attractive^{3}.

Many factors can cause disproportional eyebrows, some of which include congenital eyebrow anomalies, post-procedure trauma, tumour, following chemotherapy, iatrogenic, and functional (age-related)^{4}. Functional or age-related alteration of the eyebrow is usually caused by prolonged hyperactivity of the upper facial musculature^{5}.

With such aesthetic importance, correction of an eyebrow alteration, such as asymmetry, deformity, disproportional, or absence of the eyebrow is a common procedure in aesthetic practice and remains an important procedure for facial rejuvenation.

Numerous techniques can be used to correct eyebrow shape and position, including nonsurgical and surgical approaches^{2}. Each of the methods has to be considered and tailored individually to patient conditions, goals, and needs by addressing the symmetry, elevation, contour, and wrinkle reduction of the eyebrow perimeter in order to achieve satisfactory results^{2}. There are two key components in achieving satisfactory eyebrow correction and reconstruction^{4}. The first component is the recognition of any eyebrow alteration using a comprehensive facial evaluation, resulting in the ideal measurement and the position of the eyebrow. The second component is the selection of the appropriate procedure that will give an optimal result for the patient individually^{4}.

One of the most popular measurements to determine the ideal shape and position of the eyebrow is the standard brow measurement, which states that the relative positions and distances of eyebrows to facial landmarks might be more important than the absolute measurement of the eyebrow^{5}. The established universal brow measurement of the eyebrow and forehead is based on a 2D frontal facial image of the subject. This measurement bestows a bias advantage to those individuals with faces that align with the golden ratio standard. While more people tend to have unique features that deviate from this perfect measurement, the use of the established standard brow measurement can result in less than satisfactory results. Therefore, there is a need for a breakthrough measurement that can be applied universally for every patient with their own distinct and unique facial features.

# Case study

A 36-year-old woman visited the practice centre for eyebrow correction. The patient wanted an eyebrow alteration because of her low self-esteem due to a disproportional eyebrow–forehead ratio caused by a prominent forehead. The operator then conducted a face and eyebrow metric using Facegrid™. The procedure begins with the operator focused on measuring the patient’s forehead length (right, left, combined) and continued with measuring the patient’s left and right eyebrow, respectively.

The operator then calculated the individual ratio between the patient’s right eyebrow compared with right half forehead and left eyebrow compared with the left half forehead. The step then continued by measuring the ratio between the right and left brow combined with the total forehead length. After conducting the pre-procedure measurements, the operator sketches the eyebrow by using standard brow measurement methods, the patient was then documented, and the measurement was conducted similarly as the previous step. Lastly, the operator applied the sketch of the new adjusted golden ratio (Anggie Rassly Method) to the patient and conducted the same measurement. The patient was then presented both standard universal brow measurement and adjusted golden ratio sketch images of her eyebrow for her to decide which one was more suitable and aesthetic. The patient preferred the adjusted golden ratio method (Anggie Rassly Method) for her eyebrow alteration sketch.

# Pre-procedure measurement method

Measuring the patient’s natural eyebrow ratio

- The following steps were taken to acquire an accurate measurement:
- The patient was asked to cover her hair in order for her forehead and hairline to be seen clearly
- The Facegrid™ was applied to the patient with the central vertical line of the grid running through an imaginary line that divides the face into two exact parts, and the horizontal line lies on the nasal root (the most depressed, superior portion of the nose along the nasal ridge)
- The patient was then documented from the front side angle (0°), right oblique (45° right), right side (90° right), left-oblique (45° left) and left side (90° left)
- The operator then measures the starting point (the most medial point of the eyebrow) of the right eyebrow and left eyebrow from the front side angle (0°)
- The operator measures the total length of the eyebrow using the Facegrid™ from the medial point of the eyebrow to the lateral end of the eyebrow
- The operator then measures the length of the right segment forehead from the right angle (90°) of where the patient hairline grows, the same procedure is then applied on the left side. The total forehead length was the average of the sum from the length of the upper margin level of the eyebrow to the hairline with the length of the lower margin level eyebrow to the hairline
- The full forehead length was calculated by adding the left and right forehead length
- The calculation for the right ratio was created by dividing the length of the right forehead with the length of the right brow. The same calculation is applied to the left ratio
- The calculation for the whole eyebrow — the forehead ratio was made by dividing total forehead length with the sum of right and left forehead length
- The deviation was then calculated by subtracting the golden ratio with the measurement.

### Measuring the standard brow ratio

The operator sketches the standard golden ratio by using the standard universal brow measurement. After the sketch was drawn, the operator calculated the measurement with the same step as the pre-procedure measurement.

### Measuring the adjusted golden ratio

(Anggie Rassly Method)

- The operator draws the adjusted golden ratio sketch with the steps below:

- The medial part of the eyebrow (
*Figure 2a*) begins from anywhere in the imaginary line, which divides the patient’s nostril in the midline to the canthus medialis of the eye (adjusted onsite based on patient preference) - The end part of the eyebrow (
*Figure 2b*) ends within an area from the canthus lateralis of the eye to the midpoint between hairline and canthus lateralis of the respective eye (can be adjusted based on user preference) - The arch of the eyebrow follows the natural shape of the patient eyebrow or can be adjusted by locating the linear line between lateral nostril to the lateral part of the iris as the arch point.

- After the sketch was drawn, the operator calculated the measurement with the same step as the pre-procedure measurement. The measurement for both pre-procedure eyebrow-forehead, universal eyebrow ratio, and adjusted golden ratio are then recorded in
*Table 1*.

The measurements shows that each of the measurements are not precisely resulting in the same number as the golden ratio measurement of (1.618). The pre-procedure measurement (natural eyebrow) shows that both the left and right side forehead-brow ratio are 1.737 and 1.721, respectively, while the total forehead-brow ratio is 1.729. These ratios show a deviation of 0.119, 0.103, and 0.111 from the natural golden ratio, respectively, for the left side, right side, and total forehead-brow.

Using the standard brow measurement methods, which are taken only via a 2D frontal image, the measurement of forehead-brow ratio are 1.864, 1.875, and 1.869, respectively, for the left side, right side, and total forehead-brow ratio.

The measurement shows a deviation of 0.246, 0.257, and 0.251. The adjusted golden ratio (Anggie Rassly Method) resulting in a ratio measurement of 1.627, 1.615, and 1.621 with a deviation of 0.009, 0.003, and 0.003, respectively, for the left side, right side, and total forehead-brow ratio. To strengthen the aesthetic result of both measurements, we gave the images of the preprocedural eyebrows, standard universal brow measurement sketch, and adjusted golden ratio sketch to 30 responders in order to choose the most aesthetic eyebrow for the subject.

The result shows that 25 of the 30 (84%) responders chose the adjusted golden ratio measurement result (Anggie Rassly Method) as the most aesthetic eyebrow (both from the front or oblique side) compared with the standard universal brow measurement (3 of 30; 10%) and preprocedure measurement (2 of 30; 6%).

# Discussion

Although there is no exact formula for beauty, yet we all know beauty when we see it. Many factors affect the perception of beauty, but most aestheticians agree that proportion and symmetry nearest to the golden ratio (1.618) acquires a key role in facial beauty, including with the eyebrows. The golden ratio of 1.618 gives us unique mathematical properties that no other number or formula can offer to create both reproducible proportionality and bilateral symmetry. The golden ratio is a representation of an irrational number of 1.618 and denoted by the Greek letter phi (φ) in mathematics^{6}. This Golden Ratio, also well known as the Golden proportion, contains unique properties and is considered as the most pleasing ratio to the human visual sensation^{7}.

This unique ratio is not only limited to aesthetic beauty but can also be found in many other aspects, such as the body proportions of human beings, the growth patterns of many plants, and even the model of the enigmatic universe^{7}.

One example of the use of the golden ratio in the human body is the standard universal brow measurement to measure the most aesthetically pleasing eyebrow. This established standard measurement, creates an aesthetic proportion of the eyebrow using a 2D measurement of the facial structure. Therefore, this standard measurement could give a very pleasing aesthetic eyebrow on paper or a 2D model that could be translated beautifully in a natural or symmetrical face; for example, for those who have a facial proportion near to the golden ratio, without any distinct or unique features in both the front or oblique side of the forehead. However, for individuals with unique features on the front or oblique side of the forehead, this established measurement could lead to a less than satisfactory result. One example of a unique feature that is commonly possessed by some people is a prominent forehead, which results in a wider distance between the end of the eyebrow with the hairline on the sides of the forehead, as possessed by the subject in our case. The use of the standard universal brow measurement, resulted in a less aesthetic result in the oblique view compared to the adjusted golden ratio measurement that we currently proposed as a new measurement method, proven by the broader deviation in standard universal brow measurement than the adjusted golden ratio or even with the preprocedural measurement from the 3D golden measurement. The result was then supported by the independent validation from 30 responders, whose tendency to choose the adjusted golden ratio measurement result as the most aesthetic eyebrow for the subject.

This result strengthens the overall golden ratio theory of proportion and symmetry, where all of the aesthetical proportions tend to follow the golden ratio rule of 1.618. The closer the proportion of the forehead-eyebrow to the 1.618, the more aesthetically pleasing the result will be. In addition to the rule, to get the most aesthetic result from eyebrow rejuvenation, what must be remembered is that the human being was made in the three-dimensional form. Therefore, the golden ratio must follow the three-dimensional form (as shown by the Anggie Rassly Method) and should not be forced into a two-dimensional state. The one side measurement and forehead-eyebrow ratio is required to identify the symmetrical appearance between the right side and the left side of the face. The more symmetrical the face, the more similar the measurement of the forehead-eyebrow ratio between the right side and the left side, resulting in the more aesthetic face. In this case, the adjusted golden ratio (Anggie-Rassly Method) measurement resulted in the more symmetrical face (right forehead-eyebrow ratio: 1.5214; left forehead-eyebrow ratio: 1.5147) if compared to the established golden ratio (1.9363 and 1.8727 for right and left ratio, respectively) and pre-procedural measurement (1.775 and 1.7167, respectively).

The use of three-dimensional facial grids will bring more advantages in achieving the most aesthetic result of the eyebrow closer to the 1.618 golden ratio.

# Summary

The standard universal brow measurement is a popular choice in the field as the guideline to attain the eyebrow correction ratio. However, due to its single two-dimensional consideration, the result could also lead to a less aesthetic result in some people with distinct properties of the forehead. Therefore, a more comprehensive measurement approach, with three-dimensional consideration of the forehead, is needed to achieve results that are more aesthetically pleasing. The Adjusted golden ratio (Anggie Rassly Method), could be a new approach to be used in the universal population, regardless of their unique facial properties. Moreover, the use of a 3D face grid could also lead to practitioners achieving an aesthetic result of the eyebrow closer to the 1.618 golden ratio with a more straightforward procedure.

Further research using a larger study population and valid procedural method is needed to support the evidence that the newly proposed adjusted golden ratio is a robust technique to achieve more favourable aesthetic eyebrow results in the general population.