Modeling meibum secretion: Alternatives for obstructive Meibomian Gland Dysfunction (MGD).

PURPOSE: While changes in meibum quality are correlated with severity of meibomian gland dysfunction (MGD) and dry eye disease, little is known regarding the mechanics of meibum secretion. The purpose of this study was to develop a finite element model of meibum secretion and evaluate the effect of various factors that might impact meibum delivery to the ocular surface. METHODS: A finite element analysis in COMSOL 6.0 was used to simulate the flow of meibum within the gland's terminal excretory duct. Historical normal human meibum rheology data taken over the meibum melting range from fluid (35-40 °C) to solid (25-30 °C) were then used to calculate the minimum yield stress and plastic viscosity of meibum. The effects of meibum melting state, eyelid pressure and terminal duct diameter on meibum flow rates were then systematically investigated. RESULTS: The melting state of meibum from liquid to solid was associated with an increase in the minimum yield stress and plastic viscosity that caused an exponential decrease in meibum flow. Modeling also established that there was a linear correlation between meibum flow rate and eyelid pressure needed to express meibum and the 4th power of the terminal duct radius. CONCLUSIONS: Our results suggest that changes in the melting state of meibum from fluid to solid, as well as changes in the radius of the terminal excretory duct and the force exerted by the eyelid can lead to dramatic decreases in the flow of meibum. Together these findings suggest alternative mechanisms for meibomian gland obstruction.

Finite-element modeling of posterior lamellar keratoplasty: construction of theoretical nomograms for induced refractive errors.

PURPOSE: To estimate the theoretical corneal refractive error induced by mechanical weakening effects from posterior lamellar keratoplasty (PLKP) in the human cornea. METHODS: The refractive effects of PLKP are simulated by finite-element modeling (FEM) as a mathematical function of the thickness of the excised posterior lamellar corneal button, with a nonlinear formulation of stress-strain relation for the corneal material. A theoretical nomogram was developed to correlate the refractive changes to button thickness. RESULTS: The predicted refractive change after PLKP is less than 1 dpt for a 170-microm thickness posterior corneal button over a broad range of Young's modulus. Thicker buttons result in greater surgically induced refractive errors. CONCLUSIONS: According to FEM analysis, the excision of a posterior lamellar button of less than 170 microm thickness produces a minimal predicted refractive change (< 1 dpt) in the cornea after PLKP.