ABSTRACT
In the last two chapters, we introduced several interesting dynamical phenomena in various biological systems. We saw that the complex observed behaviour could be described in a variety of ways and that under certain situations, external changes can affect the behaviour of the system — even to the extent of altering the fundamental type of behaviour. In Chapter 2 the logistic map gave us a neat toy example of just this type of behaviour. But, one very important fundamental question remains: How do we know? How do we know what the system is doing when we cannot measure exactly
what type of behaviour is being exhibited. In certain, very simple cases, it is possible to measure all the relevant information: in the case of the rabbits, for example, it is possible to have a fairly complete picture of the population1. But, in general this is not enough. How do we know that by simply measuring the movement of the abdomen of a sleeping infant that one has enough information to describe the state of respiration. Moreover, how can one go about making measurements that are sufficient? In this chapter we will address both these questions: both the engineering challenges of measuring biophysical system parameters and the mathematical problems of how much measurement is enough. Fortunately, the human body is an electrical machine. When muscles con-
tract, they do so in response to electrical signals conducted along nerve cells. When the heart pumps — creating mechanical force — it does so as a result of muscle contraction, and the electrical activity that causes this is relatively easy to measure. The brain too is an electrical system (well, actually it is an electrochemical system with signals being transmitted both electrically as well as chemically — with the help of neurotransmitters). Within the brain the individual neuronal cells generate small electrical potentials (of the order of ±70 mV) and the result of the massive orchestration of billions of these cells can then be measured as a changing electrical potential — either from the exterior surface of the head or by placing electrodes internally. Similarly, the
activities of all other muscles can be measured electronically. As we will see in Chapter 5.1, this is essentially a result of electrical activity — due to the movement of chemical ions carrying electrical charge across cell boundaries — in various cellular systems in the body. In addition to measuring bioelectric phenomena directly (by measuring elec-
trical potential), it is also quite common to measure the result of the bioelectric phenomena. Usually this means physical movement, and usually this can be measured with some simple form of displacement transducer — the effect of which is to convert the physical movement back into an electrical signal. In Section 3.2, we will consider in a little more detail the various different techniques for measuring a variety of bioelectric phenomena in which we are interested. In Section 3.6 we briefly discuss the vast topic of biomedical imaging. At the end of this chapter, in Section 3.7, we will return to the deeper mathematical problem of how much measurement is sufficient.
