A triphasic analysis of corneal swelling and hydration control.

Physiological studies strongly support the view that hydration control in the cornea is dependent on active ion transport at the corneal endothelium. However, the mechanism by which endothelial ion transport regulates corneal thickness has not been elaborated in detail. In this study, the corneal stroma is modeled as a triphasic material under steady-state conditions. An ion flux boundary condition is developed to represent active transport at the endothelium. The equations are solved in cylindrical coordinates for confined compression and in spherical coordinates to represent an intact cornea. The model provides a mechanism by which active ion transport at the endothelium regulates corneal hydration and provides a basis for explaining the origin of the "imbibition pressure" and stromal "swelling pressure." The model encapsulates the Donnan view of corneal swelling as well as the "pump-leak hypothesis."

[1]  D. Maurice,et al.  The inbibition pressure of the corneal stroma. , 1963, Experimental eye research.

[2]  D Pflaster,et al.  A poroelastic finite element formulation including transport and swelling in soft tissue structures. , 1996, Journal of biomechanical engineering.

[3]  S. Hodson Why the cornea swells. , 1971, Journal of theoretical biology.

[4]  A. Katchalsky,et al.  Nonequilibrium Thermodynamics in Biophysics , 1965 .

[5]  W M Lai,et al.  A triphasic theory for the swelling and deformation behaviors of articular cartilage. , 1991, Journal of biomechanical engineering.

[6]  M. H. Friedman,et al.  General theory of tissue swelling with application to the corneal stroma. , 1971, Journal of theoretical biology.

[7]  D. Hoeltzel,et al.  Strip Extensiometry for Comparison of the Mechanical Response of Bovine, Rabbit, and Human Corneas , 1992 .

[8]  A. Grodzinsky,et al.  The kinetics of chemically induced nonequilibrium swelling of articular cartilage and corneal stroma. , 1987, Journal of biomechanical engineering.

[9]  M. Wiederholt,et al.  Ion transport mechanisms in cultured bovine corneal endothelial cells. , 1985, Current eye research.

[10]  B. Preston,et al.  Model connective tissue system: The effect of proteoglycans on the distribution of small non‐electrolytes and micro‐ions , 1972, Biopolymers.

[11]  W M Lai,et al.  Transport of fluid and ions through a porous-permeable charged-hydrated tissue, and streaming potential data on normal bovine articular cartilage. , 1993, Journal of biomechanics.

[12]  J. Ytteborg,et al.  Corneal edema and intraocular pressure. II. Clinical results. , 1965, Archives of ophthalmology.

[13]  Y Lanir,et al.  Biorheology and fluid flux in swelling tissues. I. Bicomponent theory for small deformations, including concentration effects. , 1987, Biorheology.

[14]  R D Kamm,et al.  Measurements of the compressive properties of scleral tissue. , 1984, Investigative ophthalmology & visual science.

[15]  D. Maurice,et al.  Chapter 1 – The Cornea and Sclera , 1984 .

[16]  J. Fischbarg,et al.  Effects of ambient bicarbonate, phosphate and carbonic anhydrase inhibitors on fluid transport across rabbit corneal endothelium. , 1990, Experimental eye research.

[17]  J P Laible,et al.  A Poroelastic-Swelling Finite Element Model With Application to the Intervertebral Disc , 1993, Spine.

[18]  Steven A. Velinsky,et al.  Design of Keratorefractive Surgical Procedures: Radial Keratotomy , 1989, DAC 1989.

[19]  D. Maurice The permeability to sodium ions of the living rabbit's cornea , 1951, The Journal of physiology.

[20]  V. Mow,et al.  Biphasic creep and stress relaxation of articular cartilage in compression? Theory and experiments. , 1980, Journal of biomechanical engineering.

[21]  S. Klyce,et al.  Numerical solution of coupled transport equations applied to corneal hydration dynamics. , 1979, The Journal of physiology.

[22]  P M Pinsky,et al.  Numerical modeling of radial, astigmatic, and hexagonal keratotomy. , 1992, Refractive & corneal surgery.

[23]  J. Fischbarg,et al.  Role of cations, anions and carbonic anhydrase in fluid transport across rabbit corneal endothelium , 1974, The Journal of physiology.

[24]  G O Waring,et al.  Computer simulation of arcuate keratotomy for astigmatism. , 1992, Refractive & corneal surgery.

[25]  C. Dohlman,et al.  A new method for the determination of the swelling pressure of the corneal stroma in vitro. , 1963, Experimental eye research.

[26]  A. Maroudas,et al.  Swelling pressures of proteoglycans at the concentrations found in cartilaginous tissues. , 1979, Biorheology.

[27]  G. S. Manning Limiting laws and counterion condensation in polyelectrolyte solutions. IV. The approach to the limit and the extraordinary stability of the charge fraction. , 1977, Biophysical chemistry.

[28]  J. Douglas Faires,et al.  Numerical Analysis , 1981 .

[29]  S. Timoshenko,et al.  Theory of elasticity , 1975 .

[30]  C. Gans,et al.  Biomechanics: Motion, Flow, Stress, and Growth , 1990 .

[31]  A. Grodzinsky,et al.  A molecular model of proteoglycan-associated electrostatic forces in cartilage mechanics. , 1995, Journal of biomechanical engineering.

[32]  A. Maroudas,et al.  Measurement of swelling pressure in cartilage and comparison with the osmotic pressure of constituent proteoglycans. , 1981, Biorheology.

[33]  D. Maurice,et al.  The metabolic basis to the fluid pump in the cornea , 1972, The Journal of physiology.

[34]  M. Reim,et al.  Glucose Concentration and Hydration of the Corneal Stroma , 1971 .

[35]  Computational models of the effects of hydration on corneal biomechanics and the results of radial keratotomy. , 1996, Journal of biomechanical engineering.

[36]  Gerald S. Manning,et al.  Limiting Laws and Counterion Condensation in Polyelectrolyte Solutions I. Colligative Properties , 1969 .

[37]  W M Lai,et al.  A continuum theory and an experiment for the ion-induced swelling behavior of articular cartilage. , 1984, Journal of biomechanical engineering.