Reprint & Copyright 9 by Aerospace Medical Association, Alexandria, VA TECHNICAL NOTE A Mathematical Model of G Time-Tolerance THOMAS W. MOORE, Ph.D.,* Dov JARON, Ph.D., LEONID HREBIEN, Ph.D., and DAVID BENDER, B.S.E.E. MOORE TW, JARON D, HREBIEN L, BENDER, D. A mathematical model of G time-tolerance. Aviat. Space Environ. Med. 1993;64:947- 51. We propose a model to explain experimentally observed ef- fects of Gz onset rotes and levels on the time of occurrence of loss of vision and/or consciousness. The model is based on the exis- tence of two generally accepted parameters: a G limit beyond which cerebral porfusion ceases, and a buffer time between loss of perfusion and loss of function. When applied to ramp onset G profiles, the model predicts a generally hyperbolic locus of end- points, similar to the well-known Stoll curve, except for the dip. The advantage of the model is its applicability to any G onset profile. Data from the literature support the assumption s of the model and its results, including the absence of the dip in the locus for a ramp onset. The results call into question some con- cepts used to design G avoidance inflight strategies and the use- fulness of some experimental centrifuge methods. The model may enable an increase in the accuracy of predictions of the time of visual or cerebral loss of function under various G profiles. T HE OBJECTIVE of this paper is to propose a model which can explain experimentally observed effects of Gz onset rate and level on the time of occur- rence of loss of vision and/or consciousness. The pro- posed model calls into question some of the existing concepts used in the design of inflight strategies to avoid G-induced loss of pilot function, and in the design of experimental methods for centrifuge determinations of G tolerance. Our model should increase the accuracy of predictions of the time at which loss of visual or cere- bral function occurs under various profiles of G stress. Most discussions of G tolerance refer to graphs pre- sented in a classic paper by Stoll (14), in which data from several human centrifuge studies were used to gen- erate curves of G tolerance vs. time. Physiologic end points (greyout, blackout, loss of consciousness), were plotted on a G vs. time graph. A line was drawn through these data points forming a generally hyperbolic curve, From the Biomedical Engineering and Science Institute, Drexel University, Philadelphia, PA. This manuscript was received for review in January 1992. It was revised in April, June, August 1992 and January 1993. It was accepted for publication in January 1993. Address reprint requests to Professor Dov Jaron, Biomedical En- gineering and Science Institute, Drexel University, Philadelphia, PA 19104. * Dr. Thomas W. Moore died July 2, 1993. except for a "dip" sketched just below the knee. This curve has since gained wide acceptance as a basis for predicting physiologic reaction to acceleration stress in general. It is often used as a basis in the design of strat- egies to avoid G-induced loss of pilot function (2,5,6,12). Unfortunately, the Stoll data were obtained using both ramp-to-plateau and pure ramp G profiles. These profiles result in quite different endpoint loci as ex- plained below. Further, the data consisted of 40 end- points taken from 15 subjects. Since two or three datapoints were produced by most runs, few subjects were involved in more than one plotted run. The use of dissimilar G profiles and the scatter of data from such a population makes the drawing of a single line and the assignment of a detail such as the dip very questionable. We propose that such static G vs. time curves, even if all data come from a single profile, are special cases and do not serve to illustrate the basic time course of physiologic G response in general. Instead, a dynamic model is required. Relaxed G tolerance is determined primarily by two physiologic parameters which vary among individuals. We have developed a model based on these parameters. The first parameter is the Gz stress beyond which the heart is unable to produce pres- sure at eye level sufficient for normal function. This parameter primarily depends on the pressure the left ventricle can develop and the vertical distance from heart-to-eye level. It has been demonstrated that when the heart-to-eye level distance of a subject is changed using a tilting seat, relaxed G tolerance also changes in inverse proportion to this distance (1). Under G stress, physiologic compensatory mechanisms may operate, over time, to increase this parameter. The second pa- rameter of our model is the time delay between cessa- tion of adequate blood flow to a region such as the retina or brain, and loss of function, This time delay has been called the functional buffer period (15). It may be a result of oxygen retention in the affected tissue (3,13). In this paper, we demonstrate that if these parameters are relatively fixed for a given individual, endpoints re- sulting from ramp onset G profiles yield smooth Stoll- like G vs. time curves. However, endpoints obtained from other profile types (ramp to profile, for example) Aviation, Space, and Environmental Medicine ~ October, 1993 947