A Mathematical Model of the Human External Respiratory System

A MATHEMATICAL MODEL OF THE HUMAN EXTERNAL RESPIRATORY SYSTEM GEORGE B. DANTZIG, JAMES C. DeHAVEN, IRWIN COOPER, SELMER M. JOHNSON, EDWARD C. DeLAND, HERSCHEL E. KANTER, Mathematics Division, The RAND Corporation, Santa Monica, California; and CRAWFORD F. SAMS, M.D., University ofCalifornia, Berkeley, California* The only way of real advance in biology lies in taking as our starting point, not the separated parts ofan organism and its environment, but the whole organism in its actual relation to environment, and defining the parts and activities in this whole in terms implying their existing relationships to the other parts and activities. J. B. S. Haldane I. The Rationale Traditionally, the doctor ofmedicine has been trained first in the basic sciences ofanatomy, biochemistry, physiology, pathology, and pharmacology . Subsequently, in his clinical years he has been trained to integrate and relate the knowledge obtained in these basic sciences of medicine as they apply to the individual patient. Since the turn of the century, the accumulation of knowledge—not only in the clinical fields but also in the basic sciences—has become so vast that there has necessarily developed a fragmentation into many specialties and subspecialties. The human body is perhaps the most complex chemical factory ever devised. It is a dynamic factory in which there are no absolute values. * The work described was undertaken at The RAND Corporation under the auspices of the United States Air Force. The contribution of Dr. Crawford F. Sams, University of California, to the planning and execution of this research was made possible by the support of the Office of Civil and Defense Mobilization through the Civil Defense Research Project at the university. The co-operation ofthe University ofCalifornia and OCDM in this arrangement is gratefully acknowledged. 324 George B. Dantzig et al. · Mathematical Model ofthe Respiratory System Perspectives in Biology and Medicine · Spring 1961 The recent introduction of isotope techniques into medicine has reemphasized the dynamic nature ofthe human body. Recognizing the dangers inherent in oversimplification, we might nevertheless say that in medicine we are dealing functionally with highly complex systems of oxidation-reduction reactions and with control mechanisms that affect the varying rates ofthese reactions. The hundreds ofparameters that we measure in medicine are, in fact, indexes ofrates of conversions at a given time. The availability of energy to control these rates may be a critical factor in such normal processes as growth and aging; and variations from these normal processes may be viewed as diseased states or pathological conditions. New approaches must be undertaken to assist in viewing the human body as a whole. These approaches must make it possible to integrate and evaluate the information that has been accumulated but not necessarily interrelated from a very large number ofparameters in the hundreds of special fields in which research has been undertaken in the study of the human body. Itnow appears feasible to use advanced techniques ofmathematicalprogramming and computers as one means ofgaining greater insight into the over-all complexities of the functioning human body in relation to its anatomical structure. The trial study to be described demonstrates the feasibility ofthis approach with regard to oxygen utilization. This study examines the thesis that a part of the human physiological system can be simulated by a suitably constructed mathematical model. The model employed derives from a class ofmathematical programming methods that were originally developed for representing complex military and industrial activities and have recently been used to represent involved chemical equilibria. The motivation for this research is the long-range view that a successful mathematical simulation of the human system or of human subsystems would provide an important tool for biological investigations. A sufficiently complex mathematical model—that is, a model that embodies sufficient chemical and biological detail to represent a whole, functioning human system or subsystem—could be used to explore biological hypotheses , environmental stress reactions, and the interplay of dependent subsystems, and it could serve as a pedagogical tool or even as an aid to medical diagnosis. 325 Ofcourse, such a long-range view is an ultimate goal. For the moment, only the techniques, concepts, and characteristics ofsuch a mathematical model are being explored. This paper presents the result ofa simulation ofthe external respiratory function...