Introduction “That is the essence of science: ask an impertinent question, and you are on the way to a pertinent answer.” Jacob Bronowski (The Ascent of Man) The author wishes to express his thanks to Kurt Buzard, MD for allowing him to cadge some material from his published paper for inclusion in this section. e eye surgeons have done rather well in our attempts to modify the corneal shape — despite our abysmal ignorance of the properties of the tissue we incise with aplomb. It was ever thus, however. Ignorance of the true state of nature has seldom held physicians back since the time of the ancients. Albeit, such hubris has never prevented us getting into trouble either. In the past we have not sought to change the corneal curvature in any precise way, however. Rather we have been content with either outright replacement of tissue, letting the corneal shape take what form it may; or by tweaking incisions reduce the severity of natural or induced astigmatism. Since the advent of refractive surgery, however, we can no longer make do with approximations. The quest for excellence — engendered in us all as physicians — and the quest for order — imbued in us all as humans — encourages the practitioner to get all his “ducks in a row”. We have lathed, incised, ablated and overlaid tissue using empirical formulas as guides, and have made some progress in predicting the outcome of the surgery. Nevertheless, these predictions have much the same accuracy (not to say messiness) of a hand grenade. While close will do with a grenade, it will not do with refractive surgery and therein lies the rub. We know very little about the true shape of the surface responsible for 80% of the refractive power of the eye and still less of its biomechanical properties — yet we seek to change it. Nonetheless, whether these factors are known or unknown to the surgeon — they do affect the outcome of such surgery and they do impinge upon the decision making process. It is, therefore, incumbent upon us to learn more about such things — natural curiosity aside -and to that end some advances have been made. Topography of the cornea, a recent development, is helping in this regard.[1, 2] While precise knowledge of shape is essential in modeling any mechanical system, including the cornea, it is clear that this cannot be the sole determinant of the results of refractive surgery.[3] Still less is known about the internal structural properties of the cornea than is understood of its surface. The ultrastructure of the cornea has been detailed in many publications.[4-6] However, the mechanical role of these elements has not been conclusively established. Moreover, morphologic examination of corneal wound healing has not included extensive quantification of this process, and has shed little light on constituent properties.[7-10] The tools for measuring these processes are available, however, in a subspecialty of physical science — biomechanics — which has been successfully applied in other medical specialties, such as orthopedics, to evaluate the requirements for prosthetic devices.[11, 12] Whether anyone of us means to or not, as ophthalmologists we are taking into account biomechanical properties of the eye on a daily basis. Historically, tonometry is an example that first comes to mind.[13-17] As a matter of fact, Friedenwald dealt with the “rigidity" of the cornea when he established his coefficients.[18] Constitutive properties have been linked, albeit loosely, to parameters of age, sex, and medical health. Fyodorov and Bores, in their earlier work have emphasized the importance of a rigidity factor in predicting the outcome of radial keratotomy.[19-21] Others have attempted to account for the same elements by factoring in age, IOP, and/or gender in various ways.[22, 23] Figure 1. Finite element analysis model of stress pattern in incised cornea. Interest in refractive corneal surgery, particularly radial keratotomy, has resulted in several published mechanical models of the cornea which attempt to simulate the effects of this surgery.[27, 30-32] Many of these use the finite element method, primarily because this approach holds promise for systematically dealing with the complexities of modeling corneal surgery (Figure 1).[33] The predictions of even relatively simple finite element models are in qualitative agreement with certain observations on patients when surgical parameters, such as incision length and depth, are varied.[34] Unfortunately, the assumptions inherent in biomechanical modeling of the cornea have not been rigorously tied to experimental observation — clearly the key to the use of such models by refractive surgeons for quantitative rather than qualitative purposes. In this treatise, we will explore these topics and attempt to clarify the steps necessary to create a quantitative model of the cornea using the finite element method. We will examine finite element mechanical models of the cornea based on several possible assumptions concerning key aspects of these models. We will then compare the results to determine the significance of factors such as the choice of boundary conditions at the limbus, thickness, and number of corneal layers. We will extend earlier studies of tonometry to test the validity of our corneal model. Specifically, we will consider a layered model to show that ad hoc assumptions about material properties are not needed to simulate tonometry — not the case in surgical models. Finally, we will examine the technique of tensor analysis applied to the examination of an impaired thin-shell model which incorporates properties omitted with other methods. It is hoped that this treatise will — at the very least — impart some working understanding of biomechanics to the reader and allow them to communicate with a structural engineer with some lucidity. Some mathematics is inevitable in a discussion of this sort, however, but we will endeavor not to “pepper the pot” excessively. Suggestions for further and more extensive reading are given at the end for the more adventuresome among the readers. © Leo D. Bores, MD - 2002