**Purpose**:
The purpose of this study was to determine if it is possible for the macula to remain attached if a bullous retinal detachment blocks the examiner's view to the macula.

**Methods**:
A mathematical analysis compared the arc length of the attached retina versus the length of a detached retina necessary to obscure the macula (hang over the visual axis). The shape (oblate ellipsoid) and dimensions of the retina were based on a published study. The complete path of the hanging retina was calculated as a static catenary so as to depict the lowest possible position (“worst case scenario”).

**Results**:
The measured and calculated angle between the fovea and ora serrata was 105 degrees. When considering a catenary shape of the hanging retina, the macula could, mathematically, still be attached despite the retina hanging down 1.03 mm below the visual axis for an emmetropic eye. The maximal distance calculated was 1.095 mm for a −12 diopter (D) myopic eye.

**Conclusions**:
If the macular center cannot be viewed due to a bullous superior retinal detachment hanging into the examiner's view, it is unlikely but possible that the macula remains attached. If the view is obscured by at least 1 mm below the fovea, it is not mathematically possible for the fovea to be attached.

**Translational Relevance**:
The status of the macula being detached is subject to mathematical constraints, which, explored herein, offer a higher certainty of clinical decision making that could inform management for better clinical results.

^{1}Thus, the accuracy of discerning the macular status has important implications regarding the visual prognosis and urgency of necessary attempted repair.

^{2}Although this works well in most instances, especially for optic calculations, it is an oversimplification of the true shape of the retina; this might yield incorrect results when trying to answer mathematically a question as just introduced above.

^{3}Atchison tabulated many enhanced measurements and concluded that the retina more closely approximates an ellipsoid – more specifically, an oblate ellipsoid where the sagittal and transverse dimensions are similar and slightly longer than the transverse (i.e. optical) axis.

^{3}deduced), and that the detached retina assumes a catenary shape as for any freely hanging, weighted cable.

^{4}We assumed a static situation, so that fluid shifts were not a factor. Moreover, we considered an average sized retinal break so that additional extension of the detached retina was not created. We also did not consider the possibility of the retina stretching, because little is known about that possibility or its extent.

^{5}Subtracting the angles corresponding to those measurable chord lengths, and subtracting from 180, gives an approximation of θ. This yielded about 105 degrees. Applying a protractor to measure published gross pathology section photographs determined that the arc, θ, from the ora to the fovea is also about 105 degrees. However, a range from 100 degrees to 120 degrees was evaluated in our analysis.

^{3}was simplified to an ellipse taken in the sagittal plane (we will refer to this as the yz-plane) to model the hanging retina (see Fig. 1). They set the fovea as the posterior extent along the z-axis; the current study was based on that same reference point. The radii of the retina in these dimensions for an emmetrope were 11.18 mm vertically (the y-axis, b in the ensuing equations) and 10.04 mm horizontally (the z-axis, the approximate optical axis, a in the ensuing equations). In addition, the Atchison model determined that these dimensions (mm) vary with diopters of myopia (m, up to 12 diopter [D]) as z = 10.04 + 0.16 m, and y =11.18 + 0.09 m.

^{2}/b

^{2}+ z

^{2}/a

^{2}= 1, where a is the length of the corresponding minor axis in the z direction (optical axis) and b is the corresponding major axis in the y direction (vertical axis). The upper half of the ellipse is the graph of the function \(y = f( z ) = b\sqrt {1 - {z^2}/{a^2}} \). Another convenient parametrization is

*z*= −

*a*cos

*t*and

*y*=

*b*sin

*t*, where

*t*runs from 0 to π. With it, the arc length along the portion of the ellipse from the fovea (z-intercept which is [−a,0] where θ = 0) to the prescribed position (

*z*

_{1},

*y*

_{1}) on the ellipse (corresponding to some θ) is expressed by Equation 1:

*s*of the catenary (Equation 2)

*z*

_{0},

*y*

_{0}) and (

*z*

_{1},

*y*

_{1}) on the ellipse, and, in addition, the arc length of the portion of the ellipse between those points and the arc length of the catenary must be equal.

^{o}degrees, which most closely depicts the human eye, it will hang 1.03mm below the axis (for an emmetrope, i.e. when

*m*= 0; see Fig. 1). This distance increased such that if θ was 120 degrees the distance would be 2.41 mm.

^{3}The principal finding is that it is mathematically possible for the retina to hang below the visual axis sufficiently to obscure the view to the fovea without the fovea becoming detached. Hence, if the fovea cannot be seen, it is not necessarily detached. This has implications for prognosis and the urgency of pursuing definitive repair.

^{6}). Our presumption for this is that the magnitude of the change in the length of the eye (approximating a sphere, and in the extreme case becoming a prolate ellipsoid) simply did not yield enough dimensional change to alter the (relatively imprecise) clinical observational implications meaningfully.

^{3}Distantly, a hanging cable was thought to have assumed a shape of parabola. With its axis of symmetry parallel to the y axis, a parabola is defined by three parameters, which can be determined to satisfy the boundary conditions and the path length. However, the computation is more complex than with the catenary and no closed form solutions can be obtained. The parabola is “slimmer” than the catenary and dips deeper. Looking for a triangular shape, one would find even lower minimum point (and no uniqueness). We posit that the catenary is physically the most appropriate shape in our case.

^{7}The elasticity of the retina has been evaluated using acoustic radiation force optical coherence elastography (in ex vivo porcine retina) finding the outer retina layers to be more elastic than the inner layers.

^{8}Another study used Brillouin microscopy in ex vivo murine retinal, but did not find a difference between the inner and outer retinal layers.

^{9}The retina is a nonhomogeneous solid, and we are suspicious that in vivo it would likely demonstrate neoHookean characteristics

^{10}due to its more complex, interlocking, and cellular structure. We hypothesize, however, that the tiny differences in specific gravity of subretinal fluid (minimally different from vitreous fluid in the acute retinal detachment, because the protein concentration, which determines of specific gravity

^{11}– about 1.02 g/cm

^{3})

^{12}the retina (1.04)

^{13}and vitreous (1.0053–1.008)

^{14}would seem to be of minimal gravitational impact to effect stretching. If the retina did stretch, it could hang down even further below the optical axis before peeling off at the fovea.

**W.E. Smiddy,**None;

**L. Kapitanski,**None;

**H.W. Flynn,**None

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