Mathematical modelling of corneal swelling

Measurement of postmortem outflow facility using iPerfusion

The key risk factor for glaucoma is elevation of intraocular pressure (IOP) and alleviating it is the only effective therapeutic approach to inhibit further vision loss. IOP is regulated by the flow of aqueous humour across resistive tissues, and a reduction in outflow facility C, is responsible for the IOP elevation in glaucoma. Measurement of C is therefore important when investigating the pathophysiology of glaucoma and testing candidate treatments for lowering IOP. Due to similar anatomy and response to pharmacological treatments, mouse eyes are a common model of human aqueous humour dynamics. The ex vivo preparation, in which an enucleated mouse eye is mounted in a temperature controlled bath and cannulated, has been well characterised and is widely used. The postmortem in situ model, in which the eyes are perfused within the cadaver, has received relatively little attention. In this study, we investigate the postmortem in situ model using the iPerfusion system, with a particular focus on i) the presence or absence of pressure-independent flow, ii) the effect of evaporation on measured flow rates and iii) the magnitude and pressure dependence of outflow facility and how these properties are affected by postmortem changes. Measurements immediately after cannulation and following multi-pressure facility measurement demonstrated negligible pressure-independent flow in postmortem eyes, in contrast to assumptions made in previous studies. Using a humidity chamber, we investigated whether the humidity of the surrounding air would influence measured flow rates. We found that at room levels of humidity, evaporation of saline droplets on the eye resulted in artefactual flow rates with a magnitude comparable to outflow, which were eliminated by a high relative humidity (>85%) environment. Average postmortem outflow facility was ∼4 nl/min/mmHg, similar to values observed ex vivo, irrespective of whether a postmortem delay was introduced prior to cannulation. The intra-animal variability of measured outflow facility values was also reduced relative to previous ex vivo data. The pressure-dependence of outflow facility was reduced in the postmortem relative to ex vivo model, and practically eliminated when eyes were cannulated >40 min after euthanisation. Overall, our results indicate that the moderately increased technical complexity associated with postmortem perfusion provides reduced variability and reduced pressure-dependence in outflow facility, when experimental conditions are properly controlled.

Deformation velocity imaging using optical coherence tomography and its applications to the cornea

Optical coherence tomography (OCT) can monitor human donor corneas non-invasively during the de-swelling process following storage for corneal transplantation, but currently only resultant thickness as a function of time is extracted. To visualize and quantify the mechanism of de-swelling, we present a method exploiting the nanometer sensitivity of the Fourier phase in OCT data to image deformation velocities. The technique was demonstrated by non-invasively showing during de-swelling that osmotic flow through an intact epithelium is negligible and removing the endothelium approximately doubled the initial flow at that interface. The increased functional data further enabled the validation of a mathematical model of the cornea. Included is an efficient method of measuring high temporal resolution (1 minute demonstrated) corneal thickness, using automated collection and semi-automated graph search segmentation. These methods expand OCT capabilities to measure volume change processes for tissues and materials.

Corneal biomechanics and biomaterials

The ability to clearly observe one's environment in the visible spectrum provides a tremendous evolutionary advantage in most of the world's habitats. The complex optical processing system that has evolved in higher vertebrate animals gathers, focuses, detects, transduces, and interprets incoming visible light. The cornea resides at the front end of this imaging system, where it provides a clear optical aperture, substantial refractive power, and the structural stability required to protect the fragile intraocular components. Nature has resolved these simultaneous design requirements through an exceedingly clever manipulation of common extracellular-matrix structural materials (e.g., collagen and proteoglycans). In this review, we (a) examine the biophysical and optical roles of the cornea, (b) discuss increasingly popular approaches to altering its natural refractive properties with an emphasis on biomechanics, and (c) investigate the fast-rising science of corneal replacement via synthetic biomaterials. We close by considering relevant open problems that would benefit from the increased attention of bioengineers.

Oxygen-deficient metabolism and corneal edema

Wear of low-oxygen-transmissible soft contact lenses swells the cornea significantly, even during open eye. Although oxygen-deficient corneal edema is well-documented, a self-consistent quantitative prediction based on the underlying metabolic reactions is not available. We present a biochemical description of the human cornea that quantifies hypoxic swelling through the coupled transport of water, salt, and respiratory metabolites. Aerobic and anaerobic consumption of glucose, as well as acidosis and pH buffering, are incorporated in a seven-layer corneal model (anterior chamber, endothelium, stroma, epithelium, postlens tear film, contact lens, and prelens tear film). Corneal swelling is predicted from coupled transport of water, dissolved salts, and especially metabolites, along with membrane-transport resistances at the endothelium and epithelium. At the endothelium, the Na+/K+ - ATPase electrogenic channel actively transports bicarbonate ion from the stroma into the anterior chamber. As captured by the Kedem-Katchalsky membrane-transport formalism, the active bicarbonate-ion flux provides the driving force for corneal fluid pump-out needed to match the leak-in tendency of the stroma. Increased lactate-ion production during hypoxia osmotically lowers the pump-out rate requiring the stroma to swell to higher water content. Concentration profiles are predicted for glucose, water, oxygen, carbon dioxide, and hydronium, lactate, bicarbonate, sodium, and chloride ions, along with electrostatic potential and pressure profiles. Although the active bicarbonate-ion pump at the endothelium drives bicarbonate into the aqueous humor, we find a net flux of bicarbonate ion into the cornea that safeguards against acidosis. For the first time, we predict corneal swelling upon soft-contact-lens wear from fundamental biophysico-chemical principles. We also successfully predict that hypertonic tear alleviates contact-lens-induced edema.

Microfluidics for cryopreservation

Minimizing cell damage throughout the cryopreservation process is critical to enhance the overall outcome. Osmotic shock sustained during the loading and unloading of cryoprotectants (CPAs) is a major source of cell damage during the cryopreservation process. We introduce a microfluidic approach to minimize osmotic shock to cells during cryopreservation. This approach allows us to control the loading and unloading of CPAs in microfluidic channels using diffusion and laminar flow. We provide a theoretical explanation of how the microfluidic approach minimizes osmotic shock in comparison to conventional cryopreservation protocols via cell membrane transport modeling. Finally, we show that biological experiments are consistent with the proposed mathematical model. The results indicate that our novel microfluidic-based approach improves post-thaw cell survivability by up to 25% on average over conventional cryopreservation protocols. The method developed in this study provides a platform to cryopreserve cells with higher viability, functionality, and minimal inter-technician variability. This method introduces microfluidic technologies to the field of biopreservation, opening the door to future advancements at the interface of these fields.

Numerical simulation of corneal transport processes

This paper presents a numerical study on the transport of ions and ionic solution in human corneas and the corresponding influences on corneal hydration. The transport equations for each ionic species and ionic solution within the corneal stroma are derived based on the transport processes developed for electrolytic solutions, whereas the transport across epithelial and endothelial membranes is modelled by using phenomenological equations derived from the thermodynamics of irreversible processes. Numerical examples are provided for both human and rabbit corneas, from which some important features are highlighted.