Prof. John H. Frenster, Rockefeller Institute, New York, NY 10021 

For the purpose of analysis, a system may be defined as an integrated assembly of components which, by their interaction, effect some characteristic change on a substrate presented to them (6). Implicit in this definition is the concept of a flow of matter, energy or information first being presented to the system as an input load, then undergoing some characteristic transformation within the system, and finally emerging from the system as an output. Because of the flow or traffic characteristics of such substrates, they are recognized as throughputs, and the systems effecting their transformation as throughput systems (7). Most, if not all, of the human systems of medical interest have been shown to be examples of throughput systems (8), each with its own specific type of throughput units and with its own characteristic transformation of such units (8).

In the identification of the variables within such human throughput systems, three general categories of independent variables have been recognized (9). These are the input load of throughput units presented to the system for transformation, the available capacity of the system to effect transformation of these units, and the resistance opposing the exit of the transformed units from the system. By contrast, the output rate of transformed units from the system is a dependent variable, being determined by the interaction of the input load, the system capacity, and the resistance to output from the system (7).

Under pathological circumstances the system capacity may decrease or the input load or the resistance to output may increase (10), so that the rate of arrival of throughput units into the system will exceed the rate of departure of transformed units from the system. In such a situation, the capacity of the system may become saturated and limiting, and waiting lines or pools of arriving throughput units may accumulate before the active service channels of the system (Fig. 1). 
This congested state of the system can be conveniently analysed by a deterministic form of queueing theory (4, 7).

Fig. 1. Analytic model of queueing and renewal within human throughput systems.

Fig. 1. Analytic model of queueing and renewal within human throughput systems. Throughput units awaiting transformation form waiting lines or pools before the service channels. An orderly and continuous turnover of service channels is mediated by a renewal mechanism which permits adaptive changes in the number of existing channels. Not all the existing channels need be in an active state nor be operating at a maximal rate of transformation per channel.

The length in units (L) of the waiting line formed in the buffer storage area of such a congested system is the sum of the initial waiting line-length (L_o) and the integral of the difference in the rates of arrival (A) and departure (D) of throughput units from the system during the time-interval being examined:

Equation 1.

Within most human systems, a waiting line of some finite length exists in the normal state (8). The presence of such a normal waiting line permits the smooth continuous flow of throughput units that is characteristic of these systems. In pathological circumstances, in which either system capacity is reduced or system input load or resistance to output is increased (9, 10), the length of the waiting line increases to exceed some value (L_path) that is characteristic for each system, and which has been recognized statistically as a boundary value (7) correlating clinically with the transition from latent disease to overt disease (8). Individual systems in which the length of the waiting line exceeds the value of (L_path) under basal conditions are recognized as being in a state of overt failure (8). Conversely, systems in which the length of the waiting line under basal conditions is less than the value of (L_path) are recognized as being either in a state of health or in a state of latent failure (8). The clinical use of load-tolerance tests (11) has been useful in distinguishing and quantitating these states in the health-disease continuum (8).

If under basal conditions a test input load is administered to a particular system at a rate (A_test) which is just sufficient to lengthen the existing waiting line length (L) to the known boundary value (L_path), and if (D_test) be the additional system output resulting from such a test load beyond that of the existing system output (D), then:

Equation 2, where the magnitude of the test administration rate (A_test) is a quantitative measure of the load-tolerance of the system at the existing levels of system capacity, input load, and resistance to output (7). Such load-tolerance of a human throughput system is a dependent variable determined by the degree to which the available system capacity is in excess of that needed at the existing basal levels of input load and resistance to output (8). In latent disease, the load-tolerance of the affected system is less than in the normal state, while in overt disease load-tolerance is reduced to zero and usually assumes a negative value (7). A state of health within a particular system is thus characterized by a high load-tolerance within the system, and by measuring its load-tolerance, the magnitude of health or disease of a throughput system may be quantitatively determined (8).

The capacity of a human throughput system is usually not constant, but rather is variable and responsive to demands placed on the system (9, 10). Thus, pathological increases in the length of the system waiting line or decreases in the rate of system often result in adaptive increases in the capacity of the system (10). These throughput system changes are mediated by superimposed control systems which continuously sample the throughput system waiting lines and output rates (7), as well as communicate changes in other distant systems. Adaptive increases in system capacity are achieved by either an acceleration, an activation, or a hypertrophy of existing service capacity (7). In the context of queueing theory (4, 7), acceleration involves a decreased service time needed to effect a unit transformation within a service channel; activation involves a conversion of existing idle service channels to the active state; and hypertrophy involves a net increase in the total number of existing service channels (Fig. 1).

The service channels of nearly all human throughput systems are being constantly formed and broken down in an orderly turnover that can be conveniently analysed by renewal theory (5). Hypertrophy of system capacity could be achieved during such channel turnover by either an increased rate of new channel formation or by a decreased rate of old channel breakdown. It is now evident that either or both of these renewal mechanisms are used by diverse human throughput systems in the adaptive hypertrophy of their system capacity (12).

The net increase (delta N) in the number of service channels in such a hypertrophy response is a dependent variable determined by the rate of new channel formation (F) and the rate of old channel breakdown (B) within the system during the time-interval being examined:

Equation 3.

Conversely, when system waiting lines decrease or when system output rates increase for a sustained period, these renewal mechanisms effect a corresponding atrophy of the system capacity, with (delta N) assuming negative values, the effect of such adaptive atrophy being to restore the balance between system capacity and the reduced demand placed on the system (9).

Such adaptive changes within human throughput systems play a decisive part during the onset, course and therapy of many disease states (8, 10). A quantitative analysis of the queueing and renewal mechanisms which underlie these adaptive changes permits both greater insight (12) and more effective control (11) of these pathological states.

I thank Prof. Mark Kac and (the late) Prof. Norbert Wiener for their kind encouragement, and Dr. William R. Best for his advice.

This work was carried out during the tenure of a Research Career Development Award (CA-17857) from the
U. S. Public Health Service.

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7. Frenster JH, "Human Throughput Systems", Proc. 16th Annual Conf. Engineering in Medicine and Biology 16, 164-165 (Nov. 1963); Clinical Research 12, 298 (1964).

8. Frenster JH, "Load Tolerance as a Quantitative Estimate of Health", Annals of Internal Medicine 57, 788-794 (November, 1962).

9. Frenster JH, "Interaction of Load, Capacity, and Resistance in Body Processes", Perspectives in Biology and Medicine 4, 152-158 (Winter, 1961).

10. Frenster JH, "Limits to Functional Hypertrophy in High-Output Failure", Annals of Internal Medicine 53, 647-655 (October, 1960).

11. Frenster JH, "The Magnitude of Disease as Measured by Tolerance Tests", Journal of Theoretical Biology 2, 159-164 (1962).

12. Frenster JH, "An Introduction to Human Throughput Systems Analysis", in preparation.

1. Editorial, "Medical Feudalism", J. Am. Med. Assoc. 184: 1039 (June 29, 1963).

2. Frenster JH, "Human Throughput Systems", Proc. 16th Ann. Conf. Engin. Biol. Med. 16: 164-165 (Nov. 18, 1963).

3. Frenster JH, "Medicine 275: Systems Analysis of Latent Disease".

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