Crying time: Modeling tear formation

The tear that coats the ocular surface (cornea plus adjacent conjunctival epithelium) provides critical protection for the underlying cornea. This tear is largely an electrolyte solution from lacrimal glands, and to some extent, the ocular surface itself provides fluid and electrolytes; the tear includes lipid from meibomian glands and glycoprotein from ocular surface cells (Willcox et al., 2017). Undisturbed, the tear would undergo progressive evaporative water loss, leaving the cornea to desiccate and thus compromising vision. However, with repetitive blinking every couple of seconds the tear is refreshed with new lacrimal fluid that has accumulated as eyelid-adjacent menisci. Dry eye disease (DED) had been defined by a National Eye Institute/Industry Workshop in 1995 as “… a disorder of the tear film due to tear deficiency or excessive tear evaporation…,” and they acknowledged the spectrum of symptoms ranging from annoyance to pain to compromised vision (Craig et al., 2017). This definition provided a natural taxonomy for DED etiologies: aqueous-deficient states (e.g., lacrimal gland disorders) and enhanced evaporation (which included meibomian gland dysfunction and eyelid-related disorders). At the time of that definition, tear lipid at the air–water interface was thought to provide some evaporative protection. That pathophysiological taxonomy was supported by clinical data, which identified distinct DED groups and proved to be useful in fashioning diagnostic testing and in guiding treatment (Tomlinson et al., 2009). It also provided guidance to those undertaking mathematical models of tear formation, to focus on the quantitative determinants of tear volume (or height) and tear osmolality. The subsequent explosion in investigation of eye pathophysiology ultimately led to a reformulation of the DED definition to “… a multifactorial disease of the ocular surface characterized by a loss of homeostasis of the tear film…” (Bron et al., 2017). While more general, it seems arguable that this 2017 definition of DED provides less guidance for eye scientists.

There have been several mathematical models of tear formation, each focused on predicting tear height and tear osmolality, and formulating a variety of mathematical structures that could be used to capture different aspects of eye function. An important model was that of Gaffney et al. (2010), who represented the tear as two compartments, a tear film and meniscus, each containing a single solute. The tear was subject to evaporative water loss, and the meniscus was fed from pockets of lacrimal accumulation under the eyelid. During a blink, there was mixing of these two fluids so that their initial osmolalities at the start of the interblink interval were reset. Thus, the model was a set of ordinary differential equations, piecewise continuous, which could be carried forward indefinitely to provide asymptotic solutions (i.e., independent of initial conditions) for tear and meniscal osmolality and volume. A notable feature of this model was that citing experiments of others, fluid secretion via the corneal epithelium was assumed negligible, and with this assumption, it was found that tear film osmolality could be substantially greater than in the meniscus fluid. An important conclusion from that work was that increasing blink frequency could mitigate evaporative DED, but not aqueous-deficient DED. Perhaps the model of greatest mathematical complexity is that of Li et al. (2016), who represented actual two-dimensional geometry of the visible ocular surface, along with a single nonelectrolyte solute. Their mathematical tools were the Navier–Stokes equations and convection–diffusion equations, with accommodation for surface tension, viscosity, and ocular surface wettability. Boundary conditions were lacrimal gland sources at the temporal aspect of the eye and nasolacrimal drainage at the medial aspect; a single extended blink cycle (25 s) was represented in the model solution. Of note, their model did provide for osmotic water transport through the ocular surface, with the corneal surface less permeable than the conjunctival epithelium. One finding from their calculations was apparent regionality, with distinct osmolalities for meniscus and supracorneal tear, and over the prolonged time of the interblink period, substantial tear-to-meniscus concentration differences developed.

Into this context comes the paper of Verma et al. (2026), which presents a mathematical model of the mouse ocular surface epithelium, which represents volume and composition of its overlying tear. Their scheme is that of Fig. 1 in which the whole tear is a well-stirred compartment abutting an epithelium, and is thus a simplification of the two-compartment model of Gaffney et al. (2010). Implicit in this simplification, blinking is absent, and in that case, the input sources of water and solutes must be considered as time-averaged and steady over the blink cycle. With respect to mass fluxes, there is a spigot (from the lacrimal gland) and a drain (the nasolacrimal duct), with additional entry across the epithelium and water loss through evaporation. In this regard, their assignment of ocular surface water permeability is about an order of magnitude greater than that used by Li et al. (2016), and this choice predictably provides additional tear water, which can blunt swings in tear concentrations. The model innovation of Verma et al. (2026) is its representation of specific tear solutes, rather than their osmotic sum. Their inclusion was motivated by identification of specific cell membrane transporters responsible for corneal fluxes: NKCC1, CFTR, and ENaC. Model solutes are Na⁺, K⁺, and Cl⁻, and glucose and electrical potentials are computed; time-dependent conservation equations are included and applied in simulation of eye drop instillation over extended periods of time (1 h). This model builds on an earlier model of corneal epithelium by Levin et al. (2006), and the calculations follow the template of prior epithelial models by the senior author (Verkman and Alpern, 1987; Hartmann and Verkman, 1990). Lacrimal gland flow and evaporative loss are specified, whereas tear duct flow varies in response to tear volume. What makes this work special, however, is the depth of focus of the paper. The authors are interested in DED pathophysiology, and in rationalizing the efficacy of approaches to treatment, in states of aqueous deficiency and evaporative excess (their Figure 7). In short, the paper offers a comprehensive approach to understanding tear physiology, dry eye pathophysiology, and therapeutics.

Although Verma et al. (2026) have gone to the trouble of individual solute bookkeeping, their most important conclusions relate to the osmotic issues of DED. These can be appreciated by rendering their model down to osmolar fluxes and water flows for a tear compartment, as summarized in Table 1. Solute secretion by the cornea into the tear is small in relation to inflow from the lacrimal glands. Thus, a secure finding from the analysis of Verma et al. was the limited efficacy of anti-absorptive and prosecretory drugs targeting epithelial ion transporters to mitigate DED. Rather, relief was more likely to be achieved by treatments that directly impact the four volume flows. More specifically, the authors note that changes in lacrimal fluid delivery or duct drainage could modulate tear height with little effect on tear osmolality, whereas changes in evaporative loss or cell membrane water permeability were necessary to achieve an osmolality effect. They refer to these divergent effects as “orthogonality” of the flows, which emerges as an empirical observation from their calculations. In that regard, it is natural to explore the robustness of this “common sense” conclusion, in terms of model scope and parameter choices. What is done below is to display a toy model of the tear, with volume and a single nonelectrolyte (osmoles) as the two independent variables. Its purpose is to capture the intuition of the electrolyte model in a very schematic version to see whether their empiric orthogonality holds up. The reference conditions for Table 1 are their baseline flows and osmolality, along with the corneal water permeability. The only condition or parameter used in the toy model not taken directly from the tables of Verma et al. is the dependence of duct drainage on tear height (m_D), which was estimated from the slope of their drainage function at the reference point. Ratification of the authors’ conclusion in this stripped-down analytic model will provide strong support that their observation is not contingent on some detail of their representation of corneal electrolyte transport, but likely generalizable to many other models of tear formation.

This calculation demonstrates that tear osmolality (C_T) is 25 times more sensitive to evaporative water loss than to altered lacrimal flow, and that tear height is (h_T) is 36 times more sensitive to lacrimal inflow than to evaporative loss. This supports the intuition of Verma et al. (2026) for control of tear osmolality and height. Ratification in the toy model affirms that this intuition depends upon overall osmotic accounting and is independent of specific electrolyte fluxes. In retrospect, the common sense of this orthogonality is that with lacrimal flow nearly isotonic to the tear it will have little impact on tear osmolality; evaporative water loss is substantial and concentrates the tear.

From a biological perspective, perhaps the most important experimental challenge from the model of Verma et al. (2026) is securing the magnitude of the ocular surface water permeability. In prior tear models, this permeability ranged from negligible to small. Verma et al. have posited a substantial permeability, such that osmotically driven water secretion across the ocular surface approximately balances evaporative loss (Table 1). In contrast to lacrimal fluid, the ocular surface secretion is hypotonic (J_sC/J_vC = 33 mOsm) so that this transcellular source of water can rescue the hyperosmotic tear. Absent this mechanism (i.e., with smaller epithelial L_p), the only osmotic relief can come from more vigorous rinsing from the isotonic meniscus (i.e., increased blinking frequency), as shown by Gaffney et al. (2010).

From a modeling perspective, a natural next step may be comparison between predictions from the compartment models from Verma et al. (2026) and from Gaffney et al. (2010), to see whether omission of explicit blinking (and mixing of tear and meniscus) has introduced any important inaccuracy over the timescale of hours. Going forward, acid/base transport can be introduced into the model of Verma et al. at little computational cost, in order to provide representation of ocular CO₂ concentrations and pH. Looking further, the model of Verma et al. is simple enough to be integrated into a comprehensive model of the ocular surface, in conjunction with representations of the corneal endothelium and the intervening stromal compartment. Models of corneal endothelium were devised with the aim of understanding the cellular mechanisms of stromal desiccation (e.g., Liebovitch and Weinbaum, 1981; Fischbarg, 2010). More recently, Vanone et al. (2025) developed an endothelial model, which includes an electrolyte model of the corneal endothelial cell. They concluded that the forces for water transport from stroma to anterior chamber can be understood in terms of cell solute transport and small osmotic gradients. Amalgamation of such compartment models of ocular surface and endothelium would not be computationally burdensome, and could aid translation of insights from the molecular basis of transport to strategies for ocular surface protection.