## Friday, December 2, 2011

### Feedback Loops

Negative feedback is an important concept in physiology. Russ Hobbie and I discuss feedback loops in Chapter 10 of the 4th edition of Intermediate Physics for Medicine and Biology. In the text and homework problems, we discuss several examples of negative feedback, including the regulation of breathing rate by the concentration of carbon dioxide in the alveoli, the prevention of overheating of the body by sweating, and the control of blood glucose levels by insulin. You can never have enough of these examples. Therefore, here is another homework problem related to negative feedback: regulation of blood osmolarity by antidiuretic hormone. Warning: the model is greatly simplified. It should be correct qualitatively, but not accurate quantitatively.

Section 10.3

Problem 15 ½ The osmolarity of plasma (C, in mosmole) is regulated by the concentration of antidiuretic hormone (ADH, in pg/ml, also known as vasopressin). As antidiuretic hormone increases, the kidney reabsorbs more water and the plasma osmolarity decreases, C=700/ADH. When osmoreceptors in the hypothalamus detect an increase of plasma osmolarity, they stimulate the pituitary gland to produce more antidiuretic hormone, ADH = C-280 for C greater than 280, and zero otherwise.
(a) Draw a block diagram of the feedback loop, including accurate plots of the two relationships.
(b) Calculate the operating point and the open loop gain (you may need to use four to six significant figures to determine the operating point accurately).
(c) Suppose the behavior of the kidney changed so now C=750/ADH. First determine the new value of C if the regulation of ADH is not functioning (ADH is equal to that found in part b), and then determine the value of C taking regulation of ADH by the hypothalamus into account.

You should find that this feedback loop is very effective at holding the blood osmolarity constant. For more about osmotic effects, see Chapter 5 of Intermediate Physics for Medicine and Biology.

Here is how Guyton and Hall describe the physiological details of this feedback loop in their Textbook of Medical Physiology (11th edition):
“When osmolarity (plasma sodium concentration) increases above normal because of water deficit, for example, this feedback system operates as follows:

1. An increase in extracellular fluid osmolarity (which in practical terms means an increase in plasma sodium concentration) causes the special nerve cells called osmoreceptor cells, located in the anterior hypothalamus near the supraoptic nuclei, to shrink.

2. Shrinkage of the osmoreceptor cells casuse them to fire, sending nerve signals to additional nerve cells in the supraoptic nuclei, which then relay these signals down the stalk of the pituitary gland to the posterior pituitary.

3. These action potentials conducted to the posterior pituitary stimulate the release of ADH, which is stored in secretory granules (or vesicles) in the nerve endings.

4. ADH enters the blood stream and is transported to the kidneys, where it increases the water permeability of the late distal tubules, cortical collecting tubules, and the medullary collecting ducts.

5. The increased water permeability in the distal nephron segments causes increased water reabsorption and excretion of a small volume of concentrated urine.

Thus, water is conserved in the body while sodium and other solutes continue to be excreted in the urine. This causes dilution of the solutes in the extracellular fluid, thereby correcting the initial excessively concentrated extracellular fluid.”
Feedback loops are central to physiology. Guyton and Hall write in their first introductory chapter
“Thus, one can see how complex the feedback control systems of the body can be. A person’s life depends on all of them. Therefore, a major share of this text is devoted to discussing these life-giving mechanisms.”