Friday, April 26, 2019

Neurological Control Systems

In Section 10.12 of Intermediate Physics for Medicine and Biology, Russ Hobbie and I provide examples of negative feedback. One of these examples analyzes how pupil size is controlled by the light impinging on the retina.
The pupil changes diameter in response to the amount of light entering the eye. This is one of the most easily studied feedback systems in the body, because it is possible to break the loop and to change the gain of the system…. [This feedback loop] has been studied extensively by Stark (see Stark 1957, 1968, 1984).
Neurological Control Systems, by Lawrence Stark, on top of Intermediate Physics for Medicine and Biology.
Neurological Control Systems,
by Lawrence Stark.
The 1968 reference is to Lawrence Stark’s book Neurological Control Systems: Studies in Bioengineering. In the introduction, Stark outlines his philosophy of science, which is similar to the approach in IPMB.
Science proceeds by alternate steps: formulation of an intuitive concept for a new phenomenon, incorporation of the new and other related phenomena into a mathematical structure, and finally, again, development of intuitive concepts of further phenomena utilizing the added perspective obtained with the formal elegance of the mathematical model or theory.
I like how he emphasizes the connection between mathematics and intuition.

In Neurological Control Systems, Stark describes his motivation for choosing the pupil of the eye as his model system.
The pupil was chosen for study from a host of possible examples of biological servosystems for several reasons... First, its motor mechanism, the iris, lies exposed behind the transparent cornea for possible measurement without prior dissection. This had previously been exploited for scientific and clinical researches by using high-speed motion picture cameras. Further, by employing invisible infrared photographic techniques, measurements can be made without disturbing the system, because its sensitivity is limited (by definition) to the visible spectrum. Second, the system can be disturbed or driven by changes in intensity of visible light, a form of energy fairly easy to control, and painless in its administration to the subject. The first two advantages lead to still a third: the possibility of performing experiments on awake, unanesthetized animals whose nervous system is fully intact and functional. In fact, all of the experiments to be discussed below have been performed on human subjects. Last, the system responds with a movement having only one degree of freedom, a change in pupil size, which simplifies the system equation analysis.
A photograph of Fig. 6 from Section II, Chapter 1
of Neurological Control Systems, by Lawrence Stark.
In Stark’s system you can break the feedback loop by restricting the light to a small dot at the center of the pupil, so changes in pupil area do not affect the amount of light impinging on the retina. Figure 10.34 in IPMB illustrates this point, as does Fig. 6 in Section II, Chapter 1 of Neurological Control Systems (shown at the right).

Stark goes on to analyze the transfer function (how the pupil area responds to an oscillating light intensity), oscillations induced by focusing the light on the border of the iris and pupil to increase the gain (in this case the light intensity is constant but the pupil area oscillates), random fluctuations of pupil noise (using many of the techniques discussed in Chapter 11 of IPMB), and nonlinearities in the pupil feedback loop.

After this exhaustive discussion of pupil area, Stark moves on to another feedback system: accommodation of the lens of the eye. But that’s another story.

Below, listen to Stark describe his life and work.

Listen to Lawrence Stark describe his research.

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