I would like to begin this post with a public service announcement. If you see the following happening in your eye, go immediately to an emergency room. A grey shadow creeps up from the bottom of the eye. You may have retina detachment. Like I did. Three times. You have hours to respond, not days.
The retina may be considered, not so much a part of the eye, as a part of the brain that has snuck into the back of the eye. It is held in place by the fluid pressure in the eye. If a tear in the retina occurs, then the eye fluid (aqueous humor) may leak into the back of the retina and the top of the retina may begin to float downward. There are several ways to repair this condition. A common one is called pneumatic retinopexy. That involves first getting the retina back in place, then holding it there with a bubble of gas (propane in my case) injected into the eye. The bubble gas dissolves away over time. You may not fly in an airplane with a gas bubble in your eye. Flying is not the problem, possibly losing cabin pressure is the problem.
That was my problem on retina detachment #2. I was scheduled to co-chair a conference in San Francisco two months following my surgery. My retina surgeon concerned himself with the condition of my eye, and not with my professional life and my agenda. Good for him. I didn’t know if I could get to the conference or not.
The gas bubble at the outset occupies more than half the eye. Vision through gas doesn’t work, only through liquid. But when the bubble occupies less than half the eye volume, you begin to see again. The brain reverses the image on the retina, so the gas bubble appears to lie in the bottom of the eye volume. When you’re underwater and look up, the surface (from below) appears as a silvery shimmering tableau of color, half reflecting, half transmitting, all very pretty. You see the same image when you look at the gas bubble, except this time you’re looking down.
With retina detachment #1, I amused myself away from work measuring my gas bubble and loosely tracking its decay. I took a ruler (30 cm) stuck one end on the bridge of my nose, the other end on a bathroom mirror, and I marked where on the mirror the edge of the bubble appeared. It doesn’t matter if you’re looking straight ahead or slightly down—the bubble doesn’t care. When the bubble got too small for this approach, I placed paper on my desk, and spaced myself once again 30 cm from the horizontal surface of my desk. I could mark the edges of the circular bubble image. I took maybe a dozen measurements, just for fun.
The fun stopped with detachment #2. I needed to track bubble size to see if I would buy a plane ticket. So I designed a research project. I would measure my bubble size twice a day, try to see a pattern in bubble diminution, and make a scientific decision. I figured, heck, maybe I could get a paper in an ophthalmology journal, or a patent for a measuring device, or something. I was ambitious back then.
The figure below shows the eye geometry I was working with. That figure shows a bubble whose edge is midway up the back of the eye, making what I called a bubble angle of 45 degrees. I considered my eye to have typical dimensions, or an eye radius of 1.2 cm. What I did not know was the focal length of my eye, which varies widely with peoples’ vision. My measurement techniques permitted me to determine my focal length. What I found was that, at the midpoint shown, I had the same edge measurement using both techniques. The edge measurement was 17 cm with a 30 cm ruler. 17/30 just happens to be about the tangent of a 30 degree angle. That led to a focal length measurement of 1.7 cm, a typical figure.
I plotted my results, shown in the figure below. It showed that the bubble angle varies linearly with time. In terms of predicting a time when the bubble would be extinguished, these data and this plot provide answers that are most helpful. Will I be rich and famous?
As scientists we are called upon to provide physical explanations for the phenomena we measure. And here the project falls flat. The dissolving or decay of a gas bubble is expected to be an exponential function, with an exponent slightly less than 1. This is true for all functions where the amount lost is proportional to the amount on hand; in other words it loses a certain percent of its mass in each time step. The gas may also dissipate at a fixed rate across the gas-liquid boundary, and vary as a function of the area. There probably is not a pressure factor. None of these interpretations gave output anywhere near as clean as the bubble angle results. Those results don’t explain bubble dissipation, they simply record it.
The conference planner in me was quite happy with the results. I had time to spare to make a plane reservation. The scientist in me, much less so. The builder in me is pleased as punch. Anyone who wants to do bubble measurements can now reach in their toolbag, pull out a digital laser level, hold it at their temple, tilt it until the laser dot lines up with the edge of the bubble, and have someone record the angle. If ophthalmologists and retina surgeons visit this site looking for more information, they will be disappointed—this is all I have to say on the subject. Except take care of your eyes.