This chapter deals with the author’s original finding that the natural tilt of the eyelid’s tarsal segment is at approximately 45° when the eyelids are open. The crease height is inaccurate when measured vertically and actually corresponds to the true anatomic crease height through a factor of √2 ÷1.0, assuming a 45° isosceles triangle, or is 1.41 X, with X being the frontally measured vertical extent. In other words, the vertical measurement with opened eye underestimates the true crease height by a factor of 1/√2. Inaccuracy in discussion and measurement of crease height are a major cause of problematic suboptimal outcomes.
Figure 20-1A shows the author’s concept of tarsal tilt, with the sloping angle of the tarsal plate and pretarsal segment (where the crease is located) varying between 45 and 50°. This angle can be investigated through mathematical modeling and clinical measurements using photography and MRI.
Proper understanding of the effect of the tarsal tilt and its effect on apparent crease height is critical for any practitioner contemplating eyelid surgery. The tarsal tilting reduces the apparent crease height as well as influencing Caucasians’ and Asians’ anatomy differentially in both normal state and various conditions of eyelid malpositions. Using mathematical modeling as well as clinical examples, this chapter will relate the effects of this with respect to common errors seen in aesthetic upper blepharoplasty.
Discrepancy between Observed Apparent Crease Height and True Anatomic Crease Height
We often see teaching staff demonstrating to house staff the nuances of measuring levator function (excursion) by placing a millimeter ruler along the face and eyelid, perhaps at the central portion of the upper lid margin. The measurement of the crease height is often taken in a similar position. To get the true anatomic crease height, we should have the patient looking downward, such that the upper lid pretarsal zone is almost vertical, or measure the eyelid crease height with the lids closed; we then obtain the true anatomic crease height, which is usually located at and corresponds to the height of the central tarsus.
In the figure we see here of a young adult ( Figure 20-2 ), the upper tarsus is measured to be at a tilt angle of 41° from the horizontal axis.
Asian Anatomy
Take for example a natural 7 mm crease for an Asian upper eyelid. Figure 20-3A shows the upper lid in a closed or down-turned position, while Figure 20-3B illustrates the lid in its normal, open position looking ahead. When the face is vertical and the eyes are looking ahead, the crease is optimally manifested and tucked in under its eyelid fold. The superior tarsal platform is angled supero-posteriorly in a tilted direction, close to a tilted incline angle (I) of 45°. The tarsus therefore manifests tarsal tilt.
Inclined crease height (Ich) or ‘tilted crease height’ (Tch) (blue in Figure 20-1 ) is the crease height as seen and measured vertically by an observer sitting across from the subject (eyes are open), and is always less than the true anatomic crease height.
An anatomic crease height of 7 mm (pretarsal skin or tarsus, red line in Figure 20-1 ) can be thought of as being aligned on the hypotenuse of a 45° isosceles triangle, while the two remaining sides of this hypothetical triangle are the vertical axis and the horizontal axis (each of the two sides will be approximately 7 mm × (1/√2), equaling 5 mm vertically and horizontally). Therefore a natural 7 mm crease will appear to the examiner as occupying 5 mm in vertical height from the most indented part of the crease to the eyelash margin (inclined or ‘tilted’ crease height, Tch), and about 3 mm only if there is 2 mm of eyelid fold overhanging it (the portion showing below the edge of the lid fold will be the clinically ‘apparent crease height’). Therefore it is quite normal for a single-eyelid patient to ask for a 3 mm crease for an end result; the practitioner should realize that it needs to come from a 7 mm anatomic crease placement.
Apparent crease height < Inclined crease height ( often measured vertically ) < Anatomic crease height
Anatomic crease height > Inclined crease height > Apparent crease height
The apparent height of the crease is less than the tilted crease height we see, by the millimeters of overhanging lid fold:
Tilted crease height − Fold = Apparent crease height
Apparent crease height + Fold = Tilted crease height
Another crude method of measuring the tarsal tilt in an open eye is through MRI scan. In Figure 20-4 we see an image of a patient showing the measured angle of the open eyelid’s tarsal segment to be 44.45°.
Methods of Investigation and Analysis: Mathematical Modeling
Mathematical modeling is often used by engineers and physicists to simulate real life scenarios when it is not feasible to measure complex events at the current stage of technology available, for example weather patterns, earthquake predictions, nuclear weapon testings, or aerodynamics of rocketry. Next to feasible actual measurement, it is considered the gold standard when it comes to accuracy; I will attempt to do the same here using basic geometry and trigonometry.
When the eyes are open, the tilt angle of the pretarsal segment of the upper lid (including skin, orbicularis, tarsal plate) as it lies on the eyeball may vary between 40 and 50° (assuming that the upper lid margin, hence tarsus, rests at the location of the upper corneal limbus and the tarsal plate extends superiorly beyond this point); we shall designate this tarsal resting angle as the incline angle, I.
Normal Eye Schema
The human eye has an axial diameter of 25 mm, with a radius of 12.5 mm and a circumference of 78.5 mm. Each millimeter on the globe surface will subtend 4.6° as measured from the center point of the eye (360° ÷ 78.5 mm = 4.6° per millimeter of circumference).
[Optional reading: We will make several assumptions . Although various eye specialists may consider the resting position of the upper lid in an open eye as between superior corneal limbus (in youngsters) and one millimeter below superior corneal limbus (adults), we will assume it is at superior limbus to eliminate the difference in corneal and scleral curvatures affecting the calculations, if there is any. We will also discuss the two abnormal clinical conditions of upper lid retraction of 2 mm above limbus (2 mm scleral show), as well as ptosis when the upper lid covers 4 mm down from limbus (4 mm of superior cornea covered). This is similar to if we should adopt that 1 mm coverage of superior cornea is the natural position of the upper lid in the open eye position, and then these two abnormal clinical conditions stated above will be equal to 3 mm of retraction from the original resting upper lid position (of 1 mm covering cornea) with a resultant 2 mm scleral show; while the 4 mm ptosis down from superior limbus is essentially a 3 mm ptosis from the defined resting upper lid margin at 1 mm corneal coverage. You can also think of this as trying to simulate what happens with a non-linear function like sine function, when we deviate upward and downward an equal amount of 3 mm in each direction, if we assume the resting upper lid margin is located at 1 mm below the superior limbus.]
Caucasian with 10 mm Tarsus ( Figure 20-5 )
Let us consider a Caucasian adult with the upper tarsus measuring 10 mm in vertical size (height), measured from the widest (central) portion of the tarsal plate. With the upper lid completely opened, assume the eyelid margin rests at the superior corneal limbus. Its crease will be 10 mm from the ciliary margin. The tarsus itself will subtend 46°of the circumference of the eye. The upper half of the cornea, which is 5 mm, will subtend 23°. The tarsus subtends 46°. From the knowledge that the two radii connecting from center of the globe to the lid margin and similarly to the crease indentation are equal, we can calculate the incline angle (I) relative to the horizontal axis for a Caucasian to be I = (180° − 46°)/2 − 23° = 44° (see Figure 20-5 ).
Figure 20-5 shows a model of a Caucasian eye with a 10 mm upper tarsus. The solid circle is the eyeball. The upper lid is not drawn here but its margin lies from the top of the superior corneal limbus on upward. The blue outline is an average clear cornea of 10 mm diameter. The 10 mm arc represents the upper lid tarsus when the eyelid is opened. (The horizontal line with the arrow is drawn parallel to the axial line that runs from the center of cornea to the back of the eyeball.) The dotted line is the slope of the tarsus rather than its true location in space (hence the tilt of the tarsus is I° when it indents to form the crease at the blue arrow where the upper border of the tarsus is located).
The magnitude of the tilt angle I (based on the lid position) can be used to relate what we apparently see (Tch) versus what we measure correctly when the lids are looking down (or closed): we may recall from trigonometry that {sine function of an angle = opposite/hypotenuse}.
Therefore, the sine function of value I (incline angle from tarsal tilt) is equal to the observed vertical component of the crease in space (Tch, which is not yet known), divided by the anatomic height (the hypotenuse) of the tarsus (whose superior tarsal border usually correspond to the location of the eyelid crease), which is known to be usually 10 mm in Caucasians (see also Figure 20-3 ):
Sine 44 ° = Tch / 10 mm Sine 44 ° = 0.69 Therefore Tch = 10 mm × 0.69 = 6.9 mm for Caucasians .
Caucasian with 4 mm Ptosis ( Figure 20-6 )
We will now model a Caucasian eye with 4 mm ptosis. The solid circle is the eyeball. The upper lid is not drawn here but its margin lies on the cornea with ptosis covering 4 mm of the upper cornea and is only 1 mm from totally occluding the central optical axis. The blue outline is an average clear cornea of 10 mm diameter. The 10 mm arc (that covers the dotted line) represents the upper lid tarsus. The dotted line is the congruent slope of the tarsus at its mid-height (hence the tilt of the eyelid crease is I° when it indents to form the crease at the blue arrow where the upper border of the tarsus is located).
If this Caucasian had a 4 mm ptosis, the upper lid would be covering 4 mm of the upper cornea. (Note that ophthalmologists usually measure from a reference point of normal upper lid margin as covering 1 mm of the cornea, so 4 mm on the cornea would actually be a 3 mm ptosis. For simplicity’s sake and modeling purpose, we shall use this position of 4 mm ptosis from the superior corneal limbus. See previous discussions on assumptions in mathematical modeling. )
Using a similar calculation as previously shown, we know that each millimeter on the globe’s surface will subtend 4.6°. When the lid is down 4 mm, it is only 1 mm above the equator of the eye, so that angle is 4.6° as labeled in the model of the globe.
I (incline angle) = 67° − 4.6° = 62°, sine I = 0.89 = Tch/10 mm, with a Tch of 8.9 mm. We will therefore see more of the true crease height (Tch approaches closer to 10 mm) with a moderate ptosis; in this case, the value of Tch is 8.9 mm. Stated similarly, when the upper lid drops down, we see a greater pretarsal zone and it shows closer to its true anatomic crease dimension.
Caucasian with 2 mm of Upper Lid Retraction ( Figure 20-7 )
Now we model a Caucasian eye with 2 mm of upper lid retraction. The solid circle is the eyeball. The upper lid is not drawn here but its retracted margin lies above the superior corneal limbus with 2 mm of white sclera showing. The blue outline is an average clear cornea of 10 mm diameter. The 10 mm arc (peripheral to the dotted line) represents the upper lid tarsus when the eyelid is opened. The dotted line is the congruent slope of the tarsus at its mid-height (hence the tilt of the eyelid crease is I° when it indents to form the crease at the blue arrow where the upper border of the tarsus is located). With 2 mm of retracted upper lid margin beyond the superior corneal limbus (or 3 mm retraction according to ophthalmologists’ convention of 1mm covering the upper cornea as normal upper lid position with an open eye), the upper lid margin now rests 7 mm from the optical center of the cornea or the equator of the globe.
We know that each millimeter on the globe’s surface will subtend 4.6°. An upper lid margin at 7 mm above equator will subtend 32°. This allows us to calculate: I value = 67° − 32° = 35°.
Sine I = sine 35 ° = Tch / 10 mm = 0.57 Tch is 10 mm × 0.57 = 5.7 mm .
Asian with Upper Lid Tarsus of 7 mm ( Figure 20-8 )
We will apply analogous calculations to Asian anatomy for normal resting position, ptosis of 4 mm, and upper lid retraction of 2 mm above superior limbus.
Figure 20-8 shows an Asian eye with upper lid tarsus of 7 mm vertical height. The eyeball is still 25 mm diameter. The 7 mm arc represents the upper lid tarsus when the eyelid is opened and its lid margin is right along the superior corneal limbus (top of the cornea). The dotted line is the congruent slope of the tarsus at its mid-height (hence the tilt of the eyelid crease is I° when it indents to form the crease at the brown arrow where the upper border of the tarsus rests).
The average Asian tarsal plate measures between 6.5 and 7.5 mm, with the majority averaging 7 mm centrally ( Figure 20-8 ). Remember that 4.6° is the angle subtended (covered) by each millimeter of the globe’s circumference. A 7 mm tarsus therefore covers 32°, and 5 mm of the cornea (upper half) covers 23°.
With the lids opened, the tarsus has an incline angle (I) of (180−32)/2, then minus 23°: 74 − 23 = 51°.
Sine I = sine 51 ° = 0.77 = Tch / 7 mm Tch ( vertical component of the crease height ) = 0.77 × 7 mm = 5.4 mm for Asians .
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