Journal of Refractive Surgery

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New Idea 

The Theory of "Other Than Round" Cornea Transplantation

David M Lieberman, MD, FACS; Richard C Troutman, MD, FACS

Abstract

The purpose of this opinion piece is to outline certain directions that research could take to achieve a more perfect cornea transplant and to point out the possible refractive advantages of 'other than round" corneal transplantation. The thesis is somewhat speculative, but we hope it will give the reader "food for thought* The primary author's (D.M. L.) observation of the structure and orientation of the posterior stroma in the dog should be repeated. No one should draw a conclusion from a single observation.

ELLIPTICAL CORNEAL TRANSPLANTATION

Rarely is anything truly new. Although Lang and coworkers1 introduced the concept of using an excimer laser to make an "other than round" cornea transplant, one of us (R.C.T.) used a mechanical cutter, a modified single point cam guided trephine (US patent #4,423,718 issued to D.M.L.)2 to perform the first elliptical recipient opening in one human patient in 1974. A round donor button was obtained by punching from the endothelial side. The donor button was sutured into the elliptical recipient bed, purposefully distorting the host and the donor tissue. This planned deforming procedure induced about 24.00 diopters of corneal astigmatism. R.C.T. reported the results at the 1976 American Academy of Ophthalmology meeting. D.M.L. first reported his trephine in 1976.3 Lang et al point out that the elliptical window wherein the long axis of the ellipse is horizontal may afford superior dimensional stability.1 Pallikaris described oval grafts in 1980.4 Additionally, because the surface area of the ellipse is smaller than the area of a round, less tissue is transplanted. Transplanting less tissue may imply the possible advantage of less risk of allograft rejection.

CURRENT ASSUMPTIONS ABOUT CORNEAL SHAPE AND STRUCTURE

The current assumptions made by the cornea surgeon are as follows: (1) the donor and the recipient corneas are perfectly spherical; (2) these corneas are of equal height and tnickness in all meridians; (3) each stromal bundle is identical to its neighbor both chemically and physically; (4) the central optical zones are of equal dimensions and keratometric values; (5) the optical zones are exactly at the geometric center of the cornea; (6) astigmatism is solely a function of the central optical cap and is not related to the peripheral zone; and (7) there is perfect wound healing. If these assumptions were true, a round donor placed into a round recipient opening would result in a graft that is stable and with no induced astigmatism. Furthermore, if the donor button were undersized, the patient's cornea would symmetrically flatten. Conversely, if the donor were oversized, the cornea would steepen equally in all meridians. Because (a) the cornea does not symmetrically steepen or flatten in these examples, (b) grafts are not predictably stable, and (c) the amount of induced astigmatism is significant, the cornea surgeon's assumptions are not valid. The human cornea, unfortunately, is neither spherical nor equally thick in every location: it is radially asymmetrically aspheric. Additionally, the anterior limbus, which defines the junction of the cornea and the sclera, is oval rather than round, which further complicates the geometry; examples of complications would include horizontal vs vertical chord differences and variation in the location of the optical center. The sclera applies stresses to the graft interface which most likely influence the eventual shape of the transplanted donor cornea. The rare case of a transplanted cornea without astigmatism probably occurs when the compounded errors of assumption just happen to cancel each other.

Figure 2 is an artist's depiction of D.M.L.'s single observation of the anatomy of the dog's cornea. The more superficial stromal fibers are less well defined and appear randomly orientated. The deep stromal lamellar fibers…

The purpose of this opinion piece is to outline certain directions that research could take to achieve a more perfect cornea transplant and to point out the possible refractive advantages of 'other than round" corneal transplantation. The thesis is somewhat speculative, but we hope it will give the reader "food for thought* The primary author's (D.M. L.) observation of the structure and orientation of the posterior stroma in the dog should be repeated. No one should draw a conclusion from a single observation.

ELLIPTICAL CORNEAL TRANSPLANTATION

Rarely is anything truly new. Although Lang and coworkers1 introduced the concept of using an excimer laser to make an "other than round" cornea transplant, one of us (R.C.T.) used a mechanical cutter, a modified single point cam guided trephine (US patent #4,423,718 issued to D.M.L.)2 to perform the first elliptical recipient opening in one human patient in 1974. A round donor button was obtained by punching from the endothelial side. The donor button was sutured into the elliptical recipient bed, purposefully distorting the host and the donor tissue. This planned deforming procedure induced about 24.00 diopters of corneal astigmatism. R.C.T. reported the results at the 1976 American Academy of Ophthalmology meeting. D.M.L. first reported his trephine in 1976.3 Lang et al point out that the elliptical window wherein the long axis of the ellipse is horizontal may afford superior dimensional stability.1 Pallikaris described oval grafts in 1980.4 Additionally, because the surface area of the ellipse is smaller than the area of a round, less tissue is transplanted. Transplanting less tissue may imply the possible advantage of less risk of allograft rejection.

CURRENT ASSUMPTIONS ABOUT CORNEAL SHAPE AND STRUCTURE

The current assumptions made by the cornea surgeon are as follows: (1) the donor and the recipient corneas are perfectly spherical; (2) these corneas are of equal height and tnickness in all meridians; (3) each stromal bundle is identical to its neighbor both chemically and physically; (4) the central optical zones are of equal dimensions and keratometric values; (5) the optical zones are exactly at the geometric center of the cornea; (6) astigmatism is solely a function of the central optical cap and is not related to the peripheral zone; and (7) there is perfect wound healing. If these assumptions were true, a round donor placed into a round recipient opening would result in a graft that is stable and with no induced astigmatism. Furthermore, if the donor button were undersized, the patient's cornea would symmetrically flatten. Conversely, if the donor were oversized, the cornea would steepen equally in all meridians. Because (a) the cornea does not symmetrically steepen or flatten in these examples, (b) grafts are not predictably stable, and (c) the amount of induced astigmatism is significant, the cornea surgeon's assumptions are not valid. The human cornea, unfortunately, is neither spherical nor equally thick in every location: it is radially asymmetrically aspheric. Additionally, the anterior limbus, which defines the junction of the cornea and the sclera, is oval rather than round, which further complicates the geometry; examples of complications would include horizontal vs vertical chord differences and variation in the location of the optical center. The sclera applies stresses to the graft interface which most likely influence the eventual shape of the transplanted donor cornea. The rare case of a transplanted cornea without astigmatism probably occurs when the compounded errors of assumption just happen to cancel each other.

Figure 1: Placement of round donor buttons into defined oval recipient openings and resultant induced astigmatism. The left column describes what would happen If the donor were punched at 7.50 mm and placed into an elliptical window of a given dimension. The right column represents the mathematical relationship to an 8.00-milllmeter donor.

Figure 1: Placement of round donor buttons into defined oval recipient openings and resultant induced astigmatism. The left column describes what would happen If the donor were punched at 7.50 mm and placed into an elliptical window of a given dimension. The right column represents the mathematical relationship to an 8.00-milllmeter donor.

The following simphfying assumptions are, however, probably more descriptive of the cornea:

* The cornea is the same thickness in every meridian;

* The cornea (both host and donor) is regularly aspheric, implying that the rate of peripheral flattening is the same for each semimeridian;

* Astigmatism is solely a function of the central optical cap and is not related to the peripheral zone; and

* The surface area and the total volume of tissue removed from the recipient is equal to the donor's tissue.

As a circle is defined by a single radius, an ellipse is defined by two radii. In such a case, preexisting astigmatism of 2.00 D with the rule (plus axis cylinder at 90°) theoretically could be corrected by placing a 3.75-millimeter radius round donor into a 3.80-millimeter × 3.70-millimeter elliptical recipient opening (Fig 1). In this example, the two radii of the ellipse are 3.80 mm and 3.70 mm. Similarly, recipient astigmatism of 13.40 D could theoretically be corrected by placement of a 3.75-millimeter radius donor into an elliptical recipient opening of 4.10 mm × 3.43 mm. A 4.00-millimeter radius round donor button placed into a 4.30-millimeter × 3.72-millimeter host elliptical opening would eliminate 11.60 D of astigmatism.

Conversely, if the cutting procedure were reversed and we cut the donor as an ellipse and sutured it into a round recipient, we would theoretically achieve the same distorted effect.

IMPLICATIONS OF CORNEAL TOPOGRAPHY FOR SURGICAL MANAGEMENT

The 1980s witnessed the introduction of computer-assisted videokeratography for topographical analysis of the cornea. We now know that the assumption of sphericity is incorrect. The rate of progressive flattening of each semimeridian of the cornea is different from a semimeridian only 10° away. If a relatively steep meridian of a recipient happens to abut on a flat donor meridian, the net effect after healing should be a radius somewhere between the two; the recipient side will flatten and the donor side will steepen. We think that, to create the best optics, assuming only that the volume of the removed recipient tissue is equal to that of the donor cornea being placed, the radius of curvature of the recipient and donor should be approximately the same at the wound interface. Hence, the optimal incision will not be a well-defined oval or ellipse, but rather one in which each point of the perimeter of the donor and recipient will have a different radius.

During the 1980s, optical pachymetry was further refined to allow us to recognize that the human cornea is of unequal thickness from its relatively thin center to the thicker periphery. Additionally, each meridian of the cornea has a different rate of central-peripheral thickening. For example, at the same point on the diameter, the inferior-nasal cornea typically is thicker than the opposite superiortemporal area. Despite universal acceptance of unequal thickness in each cornea, most cornea surgeons today continue to treat the cornea as a uniformly similar structure. No attempt is made by these surgeons to orient the inferior-nasal meridian of the donor to the same point in the recipient. We believe that in the future both stromal thickness and meridional asphericity will be given consideration.

Polack5 states that the "collagen that forms the stroma of the cornea is arranged in parallel fibrils, these in turn arrange themselves in bundles and form lamellae. Collagen bundles criss-cross in various directions from limbus to limbus while moving from one layer to another, as in the weave of a basket." The cornea surgeon assumes all stroma are universally the same. He assumes that the anterior stromal layers have the similar physical (and chemical) structure as the posterior stromal layers. Similarly, he makes no attempt to differentiate between the various quadrants or sectors of the cornea.

OBSERVATIONS ABOUT CORNEAL STROMAL STRUCTURE

As described in more detail below, D.M.L.'s recent observation of the structure of the dog's cornea suggests that the embryology of the human cornea is more specific and differentiated than previously considered. The surface ectoderm contributes the epithelium and its basement membrane, and the mesoderm makes up the remainder of the cornea.6 At about the 12-millimeter stage of embryonic development (5 weeks), the mesoderm penetrates between the surface ectoderm and the lens vesicle, forming the lens. The mesoderm begins as a single cell layer, representing the endothelium. By the 22-millimeter (7 weeks) stage, the stroma is formed as the mesoderm continues to thicken. The mesothelium secretes Descement's membrane which is easily seen at 12 weeks or the 76-millimeter stage. The stroma secrets Bowman's layer at the 105millimeter stage (13) weeks. We assume that the mesothelium in the intervening 5 weeks continues to lay down identical tissue. D.M.L.'s observation raises the possibility that the mesothelium is more specific over time. During the 8 weeks between the mesoderm's first appearance and the final differentiation of Bowman's membrane, the mesothelium may form physically distinct collagen structures.

On one occasion, one of us (D.M.L.) removed a circumferential wedge of the dog's cornea and quite by accident allowed the tissue to desiccate. We emphasize that this observation has not been repeated and needs to be confirmed. He was testing an early prototype of his device intended for the surgical correction of high myopia and noted under the surgical microscope that the dog's dried stroma is not homogeneous. He observed that the dog's cornea, and, by extension, the cornea of the human (not yet confirmed), reveals a stroma wherein the deep stromal layers are not a collection of random fibers. Rather the layers of deep stroma appeared well organized and oriented. The fibers appeared wrapped together or "bundled" and each bundle seemed to have the shape of "drawn" wire. An analogy is a thick core of multiple strands of wire which was heated and subsequently stretched. Each strand comprising the core within the bundle appeared oval at its limbal base. Each core as well as the aggregate cores comprising the bundle gradually taper within the core centrally. Each symmetrically-placed bundle about the limbus appeared separated from the adjacent one by a fiber-poor zone. The more anterior stromal fibers appeared much less differentiated, more random, and much less organized. Another mesodermal structure is striated muscle. Individual striated muscle fibers are bundled together and each muscle bundle is separated by connective tissue.

Figure 2: Artist's depiction of the dried deep stromal bundles of the dog's cornea with a single bundle highlighted and the displaced optical center. The drawing is not to scale and is intended to be representative. The surface drawing shows each bundle's symmetrical placement about the ovoid limbus and each bundle's common width. Each bundle gradually thins as It progresses toward the geometric center of the ellipse. The highlighted 5 o'clock bundle loses its definition centrally but appears to be continuous with the opposite 11 o'clock bundle. Note that the bundles are crossing toward the optical center and not the geometric center. The area of the optical center is purposefully drawn much smaller and not to scale to emphasize the nonradial direction of the deep stromal bundles. The cross section drawing represents the deep lamellar bundle as rt approaches the tightly knit nonoriented optical center.

Figure 2: Artist's depiction of the dried deep stromal bundles of the dog's cornea with a single bundle highlighted and the displaced optical center. The drawing is not to scale and is intended to be representative. The surface drawing shows each bundle's symmetrical placement about the ovoid limbus and each bundle's common width. Each bundle gradually thins as It progresses toward the geometric center of the ellipse. The highlighted 5 o'clock bundle loses its definition centrally but appears to be continuous with the opposite 11 o'clock bundle. Note that the bundles are crossing toward the optical center and not the geometric center. The area of the optical center is purposefully drawn much smaller and not to scale to emphasize the nonradial direction of the deep stromal bundles. The cross section drawing represents the deep lamellar bundle as rt approaches the tightly knit nonoriented optical center.

Figure 2 is an artist's depiction of D.M.L.'s single observation of the anatomy of the dog's cornea. The more superficial stromal fibers are less well defined and appear randomly orientated. The deep stromal lamellar fibers seem bundled with a relatively fiberpoor space between each bundle. These bundles seem to be symmetrically placed about the limbus and each bundle appears to radiate exactly toward the geometric (not the optical) center. Each peripheral bundle appears equally thick, ie, the bundle at 12 o'clock is the same as the bundle at 6 o'clock. As the fiber bundles approach the geometric center, the fibers lose their horizontal orientation and scatter in all directions, ie, anteriorly, posteriorly, and radially. At the geometric center of the cornea, the stromal fibers are blended in a random, but tightly knit, pattern.

The anatomy of the stroma may explain why human peripheral lamellar dissection is relatively easy. The peripheral bundles are oriented and distinct from each other. However, as the dissection progresses centrally, the splitting of the stroma is more difficult because the bundles have blended together.

FUTURE DIRECTIONS FOR CORNEAL TRANSPLANT SURGERY

As stated above, the purpose of this communication is to deal with those aspects of corneal transplantation limited to the cutting of the tissue. As our accuracy and ability to cut the cornea improves, the issue of volume of tissue transplanted will lessen. Additionally, we will continue to improve our suturing techniques to insure accurate apposition of recipient Bowman's membrane to donor Bowman's membrane.

When a round host opening is cut out of the elliptical (ie, oval) limbus, healing will be uneven because of bundle retraction. If a full thickness round donor button is placed inside an oval recipient opening, the recipient's remaining stromal bundles are of unequal length because a round shape has been cut out of an elliptical structure. Each bundle will retract at a different rate, making for a structure that dimensionally is not predictable. If our surgery is based on anatomy, the logical transplant to perform is an oval.

The optical center of the human cornea is usually not the geometrìe center; the optical center is usually displaced toward the inferior-temporal direction. It follows logically that placement of a donor's optical center at the superior-temporal location of the recipient will induce astigmatism. If the presumed anatomy of the dog's cornea is true in the human, and because the circle or ellipse has 360°, the surgeon has a 1 in 360 chance of aligning the deep stroma of the recipient to the donor. The fact that the incisions of radial keratotomy give little, if any, effect until the incisions are at least to a depth of 75% of the cornea implies that the structure holding the cornea together is the very deep stroma. The authors believe that the deep stromal bundles give the cornea its strength and significantly contribute to its ultimate surface characteristics. The surgeon should align the deep stromal bundles of recipient and donor tissues exactly. He should orient his tissue and approximate a thick bundle to a thick bundle producing consistent tension at the interface. The problem is obviously compounded by right- and left-eye differences. The chances of error increase dramatically if a right donor button is placed into a left recipient opening. If continued investigation of the human cornea shows it to have the same structure as that of the dog, it is important to match right- (or left-) eye donor to right(or left-) eye recipient and to orient each tissue appropriately to decrease induced astigmatism.

The authors' belief is that, in the future, the shape of both recipient openings and donor buttons will be anything but round. Each surgery will be customtailored for that specific pair of tissues. The scenario might be the foUcwing: The donor eye will be identified as right or left eye. A suture will be placed (perhaps under the superior rectus muscle) at the 12 o'clock location on the donor eye. As a first step, the oriented donor's right eye will be cut on a punching block that is a statistical average of the "normal" right eye. The donor's left eye will be cut on a corresponding "normal" left-eye punching block. The second step will be that the topographical information of the donor tissue will be digitized and correlated with the topography of the recipient's tissue. The computer-guided trephine will suggest a proposed cutting path for each tissue which the surgeon can modify. If the donor is to be punched from the endothelial side, a cutting block will be made specifically for that cornea. The round (or oval) punched donor will necessitate one set of calculations. That round (or oval) donor will be purposefully distorted into the recipient window. On the other hand, if the donor tissue is to be cut from the epithelial surface, a different mathematical calculation would be utilized.

Optimally, both donor and recipient tissues will be cut from the anterior (epithelial) surface at an angle more perpendicular to the stroma. To accomplish this, the current method of cutting vertical to the axis of the eye will be replaced by a cut at 20° off the vertical axis. After cutting the tissue, the surgeon will carefully place the oriented donor tissue into the recipient opening and suture (glue, staple, weld, etc) the tissues together. The excimer laser cutting technique is one possibility. Another is the mechanical single point cam guided trephine. Until such time, the ophthalmologist will continue to do transplant surgery knowing he will have residual astigmatism, which he will correct secondarily.

REFERENCES

1. Lang GK, Naumann G, Koch J. A new elliptical excision for corneal transplantation using an excimer laser. Arch Ophthalmol. 1990;108:914-915.

2. Lieberman DM. The single point cam guided trephine: an interim report. Ophthalmic Surg. 1981;12:185-189.

3. Lieberman DM. A new corneal trephine. Am J Ophthalmol. 1976;81:684.

4. Pallikaris I. Preoperative Placido photography in keratoconus and its meaning in conjunction with postoperative astigmatism (author's translation). Albrecht von GraefksArch Klin Exp Ophthalmol. 1980;213:87-89.

5. Polack FM. Corneal Transplantation. New York, NY: Grane & Stratton, Inc;1977:13.

6. Grayson M, Keates R. Manual of Diseases of the Cornea. Boston, Mass: Little Brown & Co, Ine; 1969:2.

10.3928/1081-597X-19920101-19

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