Introduction

Few biological systems are as functionally sensitive to changes in tissue geometry as the eye. Even with significant advances in refractive error measurement and surgical precision, discrepancies between intended and actual optical outcomes still occur. Accordingly, corneal refractive surgery has evolved to the degree that its precision is limited primarily by the innate biological and biophysical responses of the patient.

The shape-subtraction paradigm of refractive keratectomy assumes that the cornea is biologically and biomechanically inert1. This assumption ignores a large body of experience with incisional refractive surgeries such as radial keratotomy, astigmatic keratotomy, and anterior lamellar keratomileusis. Biomechanics figure prominently in any surgery in which corneal tissue is removed or incised, including routine LASIK, and the effect is more pronounced in corneas altered by previous surgery. Surgeon nomograms to reduce systematic errors do little to prevent refractive errors attributable to patient-to-patient biological and biomechanical variations, particularly if we lack critical preoperative predictors and the means to measure them. This chapter surveys corneal biomechanical behavior and its role in improving the safety and predictability of refractive surgery.

Anatomic considerations

The cornea is a complex biomechanical composite whose behavior depends on its structural subcomponents and their organizational motifs (Fig. 28.1). Bowman’s layer and the stroma provide the majority of the cornea’s tensile strength. The low stiffness of Descemet’s membrane ensure its laxity over a broad range of intraocular pressures (IOP)2 and may serve to buffer the endothelium from stromal stresses. The role of Bowman’s layer, an 8–12 µm thick acellular condensation of stroma with more randomly oriented collagen fibrils3, has been a subject of controversy4,5. Although some have proposed a structural role distinct from that of the stroma, extensiometry studies in normal corneas suggest that removal of Bowman’s layer does not measurably alter the bulk mechanical properties of the cornea5. The biomechanical importance of Bowman’s layer in abnormally thin or ectatic corneas is suggested by its fragmentation during histological examination of keratoconic tissue.

Fig. 28.1 Major biomechanical forces in the cornea (A) and a model of biomechanical central flattening associated with disruption of central lamellar segments (B). A reduction in lamellar tension in the peripheral stroma reduces resistance to swelling, and an acute expansion of peripheral stromal volume results10. Interlamellar cohesive forces11 and collagen interweaving12, indicated by gray shading, are greater in the anterior and peripheral stroma and provide a means of transmitting centripetal forces to underlying lamellae. Because the central portions of these lamellae constitute the immediate postoperative surface, flattening of the optical surface occurs, resulting in hyperopic shift. The degree of flattening is associated with the amount of peripheral thickening10. This phenomenon is exemplified clinically by PTK-induced hyperopic shift but is important in any central keratectomy, including PRK and LASIK. Simultaneous elastic weakening of the RSB may occur13, and the threshold for irreversible (plastic) deformation is a matter of great clinical concern.

The mechanical response of the cornea to injury is dominated by the stroma. On a weight basis, the stroma is approximately 78% water, 15% collagen, and 7% non-collagenous proteins, proteoglycans, and salts6. A total of 300–500 lamellae run from limbus to limbus and are stacked with angular offsets; this orientation becomes increasingly random in the anterior stroma where significantly more oblique branching and interweaving are noted3. Interlamellar branching is also more extensive in the corneal periphery (see Fig. 28.1)7,8. Interweaving of collagen bundles between neighboring lamellae provides a mechanism for shear resistance9 and sharing of tensile loads1,10. In addition, X-ray diffraction studies provide evidence of a predominantly circumferential fibril orientation in the corneal periphery11 that may favor conservation of limbal circumferential dimensions even in ectatic disease12,13. Proteoglycans play a critical role in collagen fibril assembly and spacing14, and their importance in promoting lamellar cohesion may be greater than currently recognized.

Fundamental principles

The cornea’s constituent material properties provide the link between its structure and its mechanical behavior under the stresses of surgery or disease. The cornea is a complex anisotropic composite with non-linear elastic and viscoelastic properties. It is a composite because its properties are determined by the interaction of disparate materials like collagen and a polyanionic ground substance, and anisotropic because its properties are not directionally uniform. The cornea is highly heterogeneous in the central to peripheral, anterior to posterior, and rotational dimensions.

The elastic (Young’s) modulus provides an indicator of stiffness and is a critical material property in understanding the corneal response to refractive surgery. An elastic material regains its original geometry along the same stress–strain pathway when an imposed stress is removed. The elastic modulus is traditionally measured in excised tissue with an extensiometer that measures force generation during steady axial elongations of the sample. The slope of stress (force per unit area, N/m²) over strain (a dimensionless quantity defined by the current length divided by the starting length) is calculated for a representative portion of the curve. A high modulus indicates a stiff or low compliance material. While most biological soft tissues approximate linear elastic behavior over a small range of stresses, their overall elastic behavior is highly non-linear, as exemplified in Figure 28.2A. The reported range of ex vivo human cornea elastic modulus values spans orders of magnitude15. Although some biological variability is expected, this variability also reflects the challenges of obtaining representative data under highly variable experimental conditions ex vivo. Membrane inflation experiments in normohydrated donor globes provide a more physiological alternative to extensiometry16 but do not abrogate the need for in vivo measurement techniques.

Fig. 28.2 Experiments illustrating elastic (A) and viscoelastic (B) behavior in a 7 mm, full-thickness horizontal corneal strip from a 63-year-old donor. (A) Non-linear elastic behavior arises from an initially slow uptake of load as the collagen takes up slack, followed by stiffening as maximal fibril recruitment is approached. (B) A second experiment in which a constant displacement is imposed in the same sample demonstrates time-dependent stress–relaxation, a viscoelastic property of soft tissues.

Viscoelastic properties arise from the time-dependent nature of biomechanical responses and are a feature of all biological soft tissues. Viscoelastic materials return to their pre-stress configuration via different stress–strain pathways that depend on loading rates. This discordance between loading and unloading behavior can be partially characterized by hysteresis, which reflects the capacity of a tissue to dissipate energy. Viscoelastic creep and stress–relaxation (Fig. 28.2B) also describe time-dependent responses to sustained stress or strain that may be important in the mechanics of ectasia and post-refractive surgery instability17.

Preoperative assessment: clinical measurement of corneal biomechanical properties

Traditional extensiometry has revealed deficits in elastic tensile strength in keratoconus18 and suggests a diagnostic role for elastic modulus determination in the clinical setting. The obvious unsuitability of extensiometry for in vivo testing, however, has led to accelerated efforts to develop non-destructive, non-invasive tools for clinical biomechanical property measurement.

In sonic wave propagation velocimetry, an acoustic perturbation is emitted at one point on the ocular surface and detected by a receiver positioned at a fixed distance from the emitter. Young’s modulus is related to the corneal density and the wave velocity measured between the two transducer tips, that are positioned along the corneal arc. Stiffness is measured in the plane of the lamellae, similar to traditional extensiometry. Experiments with a prototype handheld device have explored directional and regional stiffness differences in porcine19 and human donor globes20, corneal stiffness changes with keratotomy, and increases in stiffness with stromal collagen cross-linking that lead to artifactually high applanation pressures19. Signal attenuation in the presence of the precorneal tear film is the primary challenge to clinical implementation.

The Ocular Response Analyzer (ORA, Reichert, Inc., Depew, NY) utilizes a high speed air-puff to quantify the dynamics of central corneal deformation and recovery21. Figure 28.3 illustrates a response waveform where the corneal hysteresis (CH) is the difference between the higher ingoing (P₁) and lower outgoing (P₂) applanation pressures. A high CH may indicate a greater capacity for absorption or dissipation of kinetic energy, which reflects viscoelastic behavior. The corneal resistance factor (CRF) is derived from the same dual-applanation signal with a linear factor emphasizing P_1, the pressure required to achieve the first near-applanation endpoint, and thus reflects the overall corneal resistance. The ORA does not have regional or out-of-plane directional sensitivity, and the values are not directly comparable to the corneal elastic modulus. The ORA also reports two IOP values: Goldmann-correlated (IOP_G) and cornea-compensated (IOP_CC), where the latter was derived empirically to be less affected by LASIK than traditional applanation tonometry.

Fig. 28.3 A response waveform for the Reichert Ocular Response Analyzer. In- and outgoing applanation events are indicated by the two peak intensities of reflected infrared light (in red). The air pressures (in green) intersecting these two applanation events are recorded as P₁ and P₂. Corneal hysteresis (CH) is the difference between the inward and outgoing applanation pressures (P₁ − P₂). Eyes with more viscoelastic damping capacity result in greater dissipation of perturbation energy and a delay in applanation, shifting the applanation peaks to the right, and resulting in a higher P₁, a lower P₂, and an increase in CH. CRF incorporates an empirical adjustment (kCRF) to P₂ (CRF = P₁ − kCRFP₂).

Modified from Luce DA. Determining in vivo biomechanical properties of the cornea with an ocular response analyzer. J Cataract Refract Surg 2005;31(1):156–62.