A Personal View on Energy, Heat, and Entropy Dissipation in Corneal Tissue
The cornea, the eye's transparent outermost layer, serves as a crucial protective barrier against external stressors such as electromagnetic radiation, pathogens, and desiccation. While appearing macroscopically static and ordered, the cornea is, characteristic of living tissue, metabolically active at the microscopic level. It absorbs oxygen from its external surface and receives nutrients from the aqueous humor of the anterior chamber. This metabolic activity inevitably generates byproducts, which are thought to be eliminated both anteriorly, via the tear film over the epithelial surface, and posteriorly, through the aqueous humor on the endothelial side.
The quantum physicist Erwin Schrödinger, in his seminal work What is Life?, based on lectures delivered in Dublin, introduced thermodynamics to the study of living systems, notably the concept of entropy. He posited that living organisms sustain their internal order by importing "negative entropy" (negentropy) to counteract the natural increase in entropy stemming from their metabolic processes (1). Although "negentropy" remains a debated concept, the second law of thermodynamics—the inherent tendency towards increasing entropy—is universally accepted as applicable to living systems. In this framework, the excretion of waste products can be interpreted as a mechanism for expelling internally generated entropy, analogous to "consuming negentropy" to preserve biological order.
Anatomically, the cornea comprises three primary layers: the superficial epithelium, the intermediate stroma, and the innermost endothelium. These layers are separated by two distinct acellular membranes: Bowman's membrane, between the epithelium and stroma, and Descemet's membrane, between the stroma and endothelium. The corneal epithelium consists of multiple layers of stratified squamous cells that shield the ocular surface from mechanical, microbial, and environmental insults. In contrast, the corneal endothelium is a single layer of hexagonal cells in direct contact with the aqueous humor (Figure).
Corneal epithelial cells maintain their function and transparency by constantly eliminating from the eye the accumulation of waste molecules and unwanted/mutated antigens resulting from biological activity, along with the associated disorganization of biological information (i.e., an increase in entropy). This elimination occurs through apoptosis, phagocytosis, and tear fluid, and the cells are renewed by a supply from stem cells. In contrast, corneal endothelial cells are non-dividing cells that are arrested in the cell cycle in vivo. Therefore, unlike corneal epithelial cells, they do not expel increased entropy from the eye through a cycle of repeated apoptosis and regeneration.
Within the corneal stroma, continuous energy metabolism generates high-entropy molecules. To maintain homeostasis, a system for expelling these molecules is essential. While autophagy, a recently highlighted intracellular process, contributes to managing cellular waste (primarily by processing internal components rather than expelling them from the cell), the primary outflow pathways for entropy generated within the cornea are believed to be the tear fluid, conjunctival blood and lymphatic vessels, and, critically, the aqueous humor. Anatomically, the anterior chamber, interfacing with the hexagonally arranged endothelial cells (potentially a manifestation of dissipative structures), is considered the principal route for entropy outflow from the stroma.
Living organisms are generally understood as non-equilibrium open systems, a concept extensively explored by Ilya Prigogine in his theory of dissipative structures (2). This theory describes how, under conditions of thermodynamic entropy dissipation, characteristic self-organizing structures can emerge. Prominent examples include Bénard convection, where hexagonal convection cells (Bénard cells) spontaneously form under specific conditions, and Bénard-Marangoni convection, which can also produce such hexagonal patterns. The morphology of these cells bears a notable resemblance to the hexagonal arrangement of corneal endothelial cells.
We speculate that a horizontally stratified "High Entropy Zone"—a region of consistently elevated entropy production relative to its surroundings—exists in the anterior corneal stroma, likely just beneath Bowman's layer. This zone, presumed to have a high density of metabolically active corneal stromal cells, would consequently exhibit relatively high local temperature and entropy. This would establish a temperature and entropy gradient across the corneal stroma, driving the dissipation of this entropy towards the anterior chamber via the corneal endothelial cells, thereby maintaining corneal transparency and overall function (Figure). These interconnected processes of cellular activity, metabolism, and entropy dissipation within the stroma and endothelium may play pivotal roles in preserving corneal clarity, modulating autoimmune responses (e.g., corneal autoantigen dynamics), influencing corneal transplant immunology, and promoting corneal cell regeneration following injury or disease.
Supporting the concept of dynamic stromal fluid movement, a notable experiment demonstrated a horizontal, swirling flow of fluorescein dye injected into the corneal stroma (3). This flow of water, moving from the central to the outer parts of the cornea and eventually spreading dye throughout, was linked to the activity of the corneal endothelium. The pattern of this flow also hinted at a spiral movement in the vertical direction. Significantly, when endothelial cells were damaged by injecting a preservative into the anterior chamber, this migration ceased, underscoring the necessity of intact endothelial function for this phenomenon. These findings strongly suggest the existence of dynamic convection within the corneal stroma. Furthermore, it is conceivable, though speculative, that such convective flows could induce the very slow migration of corneal stromal cells.
Classical Bénard convection alone might not fully account for the high-density hexagonal cell patterns observed in the endothelium under certain conditions. However, it is plausible that Bénard convection (or a Bénard-Marangoni stage dominated by buoyancy) acts as an initial trigger. The resultant temperature and flow fields could then induce and amplify other self-organization mechanisms, particularly surface tension effects (the Marangoni effect), leading to the formation of more stable, high-density hexagonal patterns. If the corneal endothelial layer, approximately 5µm thick, is considered as a thin liquid film, the Marangoni effect could plausibly drive the formation of such a dense hexagonal cell population. A recent insightful report also suggests that dissipative structures can form at the nanoscale, implying that entropy dissipation at this scale might contribute to extended interpretations of classical thermodynamic convection models.
We propose that a laminar zone of high entropy is continuously and spontaneously generated in the anterior corneal stroma. To dissipate this entropy towards the anterior chamber, we hypothesize the involvement of convective phenomena analogous to Bénard or Bénard-Marangoni convection, or an alternative intra-tissue flow initiated by such mechanisms. We further propose that both stromal and endothelial entropy are consistently discharged into the anterior chamber, crucial for maintaining corneal homeostasis. The amount of entropy ejected from the endothelial surface (ΔS out) must not be less than the entropy generated within the stroma and endothelium (ΔS in), such that ΔS in−ΔS out ≤ 0 must always hold. If this balance is disrupted, the accumulation of waste molecules and the resulting equilibration (loss of order) would lead to corneal cell dysfunction, irreversible corneal damage, corneal allograft rejection, and loss of transparency. Efficient entropy dissipation from healthy stromal cells likely promotes similar dissipation from endothelial cells, contributing to the maintenance of endothelial function and the self-organization of corneal tissue. While this perspective is our own, its validation could pave the way for extending these concepts to include the role of nanoscale dissipative structures, potentially offering new insights into the thermodynamic foundations of corneal tissue homeostasis.
References
1) Schrödinger, E: What is life ? The physical aspect of the living cell. Order, disorder and entropy. Reprint edition, Cambridge University Press,
Cambridge, 67-75, 1992
2) Prigogine, I: Time, structure and fluctuations. Science 201(4358):777-785, 1978
3) Inoue, T et al: Horizontal intracorneal swirling water migration indicative of corneal endothelial function. Invest Ophthalmol Vis Sci 55: 8006-8014, 2014
May 07, 2025
Mejiro Dori Clinic (Ophthalmology)
Yasushi Sonoda, MD.
