Arunn Narasimhan

Arunn Narasimhan

Bio-Fluid Dynamics of Human Eye

Created Last modified 9 min read

About this note

A plain-language summary of the 4 publications listed under this topic on Academic Publications (Topic-wise). Full citations are under References.

How this research began

This line of work began at home. Some years ago my father noticed black spots in the vision of his right eye, and a check-up at an eye hospital in Chennai found a retinal tear. The human eye is an imperfect sphere about 24 mm (just under an inch) across, from the cornea at the front to the retina at the back. Behind the lens, the large chamber holds the vitreous humour, which in a young eye is a jelly-like, non-Newtonian gel that keeps the eye’s shape and holds the lens and retina at the right distance apart. With age the gel changes, and as it contracts within its confined space it can pull on the retina. In some of us this pull tears it.

The remedy is to stick the retina back in place. The surgeon opens the eye behind the lens, removes the vitreous gel, seals the retina with targeted laser heating, and closes the eye. Over the following weeks, body fluids seep in to fill the space the gel occupied. My father’s surgery went well and his vision returned to normal.

Having studied retinal laser surgery through computer simulation earlier (see Bio-Heat Transfer in Human Eye), I knew what to expect from the laser step. What caught my attention was the aftermath. The fluid that replaces the gel is watery, like the aqueous humour at the front of the eye, so it can circulate. But will it, and under what conditions? Stirring is not an option inside an eye. Heating is: warmed fluid becomes lighter and rises, cooler fluid sinks, and a natural convection loop forms, stronger the larger the temperature difference.

A realistic heating situation does exist. Transpupillary thermotherapy (TTT) is, simply put, a thermal massage of the retina. Instead of the intense, focused dose used to seal a tear, the laser energy is spread over a larger spot, so temperatures stay lower. TTT sets up a temperature difference of about 5 to 10 °C across the eye, from the cooler cornea to the warmed retina, with the vitreous in between. Eye doctors at a premier eye institute in Chennai confirmed that many patients, as they age, first have a retinal tear repaired and then, in later years, need TTT. Such an eye has a liquid vitreous sitting in a thermal gradient, which is exactly the case worth simulating.

My research student, C. Sundarraj, was not convinced at first. The eye is small, the circulation might be fleeting, and the application seemed remote. Every research student meets this moment, when one has to put faith in something not yet within one’s grasp: the adviser’s experience, the promise of a risky problem, or one’s own abilities. He came round, first to me and then to the problem, and about a year and a few months after my father’s diagnosis the results described below were published (Narasimhan and Sundarraj, 2013).

Why this matters

The large chamber behind the lens of the eye is filled with the vitreous humour, a clear, jelly-like substance that is about 99.9% water. Being a gel, it resists flow, so models of heat transfer in the eye have usually treated it as stagnant. That picture does not always hold. In some retinal surgeries the gel is removed and replaced by a watery substitute, and with age (beyond about 45 to 50 years) the gel itself gradually gives way to a less viscous liquid (Narasimhan and Sundarraj, 2013). A liquid vitreous can move. Just behind the retina lies the choroid, a layer packed with blood vessels, whose blood flow carries heat and dissolved molecules away from the back of the eye.

Doctors treat several retinal diseases by heating the retina with a laser, and they deliver drugs into or around the eye. Both depend on how heat and molecules move inside the eye. Our research on this topic asks a physics question: what flows exist inside the eye, what drives them, and how much do they change temperatures and concentrations at the retina?

What we did

Natural convection in the vitreous during laser therapy

The starting point, with C. Sundarraj, was transpupillary thermotherapy (TTT), a treatment in which a long-pulse infrared diode laser is shone through the pupil to treat eye tumours and abnormal growth of choroidal blood vessels in age-related macular degeneration (Narasimhan and Sundarraj, 2013). We built a two-dimensional model of the human eye with seven regions (cornea, aqueous humour, lens, vitreous, retinal pigmented epithelium, choroid and sclera) and simulated 60 seconds of heating by a 300 mW laser over a 4 mm spot. In the vitreous we solved the equations of natural convection, the flow that arises when warmer fluid becomes lighter and rises while cooler fluid sinks. In the choroid we used the Pennes bio-heat equation, which adds a term for heat exchanged with blood arriving at body temperature (blood perfusion).

Putting the flow to work

We then asked whether this laser-driven circulation in an eye whose vitreous has been replaced by a fluid could carry an injected drug faster than diffusion alone, adding a drug transport equation to the same model (Narasimhan and Sundarraj, 2015). That question, and the delivery results, are the subject of Drug Delivery in Human Eye; here the interest is in the flow pattern itself.

Seeing the circulation in a glass eye

With Shrinivas Vibhute, we tested the idea in the laboratory (Shrinivas and Narasimhan, 2023). A glass orb with the proportions of a real eye was filled with water or silicone oil as vitreous substitutes, a small heater on the retinal surface stood in for the laser, and a dye stood in for the drug. The heating produced temperature differences of 6 to 12 K across the chamber, which correspond to Rayleigh numbers (a measure of how strongly buoyancy drives flow against viscosity and heat diffusion) of 75,000 to 180,000.

Blood flow through the choroid

The choroid is the other important flow. With Ramanathan Vishnampet, we treated the sclera and choroid as porous media, materials made of a solid matrix with fluid-filled pores, and computed the blood flow through the choroid alongside the movement of a drug placed outside the sclera (Narasimhan and Ramanathan, 2012).

What we found

The vitreous flow is significant. In the TTT simulations, the heated retina set the liquid vitreous moving at up to about 2.2 mm/s near the laser spot, with the flow concentrated in the upper half of the chamber. Along the pupillary axis the velocity profile resembles natural convection next to a heated vertical plate, and near the lens the flow reverses to complete the circulation. Compared with a stagnant vitreous, this convection lowered the peak retinal temperature by 15 K at steady state and 12.5 K after 60 seconds of heating; choroidal blood perfusion on its own lowered it by 6 K and 1.5 K respectively. The flow also carries heat sideways, warming the retina next to the laser spot by about 2 K. Treating the vitreous as stagnant can therefore misjudge both the peak temperature and the region at risk of thermal damage (Narasimhan and Sundarraj, 2013).

In plain terms, a temperature difference of about 5 °C across the vitreous is enough to set up a steady circulation, and that circulation shifts the hot spot a few millimetres up the retinal surface from its centre. Compared with a still vitreous, more of the retina is heated during TTT, so thermal damage could appear at spots the surgeon does not expect.

The circulation has the classic structure of natural convection in an enclosure: strong flow in thin layers along the walls and a cooler, nearly stagnant core in the middle. This explains why, in both the simulations and the experiments, material released near the bottom of the chamber spread to the retina better than material released at the centre or near the lens (Narasimhan and Sundarraj, 2015; Shrinivas and Narasimhan, 2023). The simulations also showed that the body force direction matters: with the patient lying down, the velocity field became uniform in the two halves of the chamber. In the glass eye the Peclet number, the ratio of transport by flow to transport by diffusion, reached about 146,000, so convection overwhelmed diffusion. We expect weaker flow in a real eye, which is why we describe the effect as convection-assisted diffusion rather than pure convection (Shrinivas and Narasimhan, 2023).

In the choroid, the Peclet number was about 148,000, so blood flow, not diffusion, controls what happens there. The flowing blood sweeps drug away from the back of the eye, and over the normal range of choroidal blood speeds this circulation loss is the main route by which drug is lost inside the eye (Narasimhan and Ramanathan, 2012).

Together these studies show that the eye is not a still container. Buoyant flow in a liquid vitreous and blood flow in the choroid both shape how heat and molecules move at the back of the eye, and both need to be in any model used to plan laser treatment or drug delivery.

References

  1. Shrinivas, V. and Narasimhan, A., (2023) “Convection-assisted intra-vitreous drug delivery in human eye: An experimental investigation,” Heat Transfer May 2023, 1-13. [ DOI: 10.1002/htj.22899 | Abstract | IITM Tech Talk News | BioVoice News ]
  2. Narasimhan, A. and Sundarraj, C., (2015) “Convection-Enhanced Intravitreous Drug Delivery in Human Eye”   ASME J. of Heat Transfer 137(12), 121003 (Aug 11, 2015) (7 pages) [DOI: 10.1115/1.4030916 | Abstract ]
  3. Narasimhan, A. and Sundarraj, C., (2013), “Effect of choroidal blood perfusion and natural convection in vitreous humor during transpupillary thermotherapy (TTT),”  Int. J. Numer. Meth. Biomed. Engng., 29 (4), 530–541. [DOI: 10.1002/cnm.2538 | Abstract]
  4. Narasimhan, A. and Ramanathan, V. G., (2012), “Effect of choroidal blood flow on transscleral retinal drug delivery using a porous medium model,”  Int. J. Heat and Mass Transfer, 55 (21), 5665–5672.[DOI: 10.1016/j.ijheatmasstransfer.2012.05.060].

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