The use of strength-duration curves for system identification
Foltz, James Monroe
Master of Science
The inputs to systems which exhibit threshold behavior can be characterized by a strength-duration curve. In its most basic form, this curve gives the amplitude (strength) of an input required to exceed threshold as a function of the duration of that input. These curves have historically been used to identify physical characteristics of certain biological systems. E.g., in the nervous system, how are the position and shape of the curve related to nerve conduction velocity or membrane time constant; in the visual system, how are these characteristics of the curve related to rod and cone function, etc. In this thesis, methods of analysis are developed in an attempt to solve the more general problem of how the properties of a strength-duration curve for a general system, defined mathematically, relate to the parameters of that system. The approach used to gain insight into this problem is to investigate the effect of a change in a linear, time-invariant system on its strength-duration curve. Two system changes are considered: addition of a pole, and addition of a zero, to the transfer function. The effect of these changes on ^reai;, a parameter of the curve, is investigated. It is found that, in certain cases where rather severe restrictions are imposed on the system impulse response always increases with addition of a pole, and always decreases with addition of a zero. The special case of a system with transfer function is solved numerically. The impulse response of this system does not satisfy the severe restrictions mentioned above, but the results are the same, indicating that will shift in this manner when a pole or zero is added to the transfer function of any system. In an attempt to demonstrate the feasibility of the theoretical analysis, strength-duration curves are plotted from data taken from stimulating the frog sciatic nerve with rectangular voltage pulses. The experimental error involved in these plots is estimated. Two different experimental conditions produce curves with a significant difference, which can be explained by the above theoretical results. Since the strength-duration curve analysis discussed in this thesis is not unique, i.e., different linear, time-invariant systems may produce identical strength-duration curves, an experimental observation can be explained in more than one way.