mathematical model previously formulated by us predicts that limit-cycle oscillations (LCO) in nephron flow are mediated by tubuloglomerular feedback (TGF) and that the LCO arise from a bifurcation that depends heavily on the feedback gain magnitude, ␥, and on its relationship to a theoretically determined critical value of gain, ␥ c. In this study, we used that model to show how sustained perturbations in proximal tubule flow, a common experimental maneuver, can initiate or terminate LCO by changing the values of ␥ and ␥c, thus changing the sign of ␥ Ϫ ␥ c. This result may help explain experiments in which intratubular pressure oscillations were initiated by the sustained introduction or removal of fluid from the proximal tubule (Leyssac PP and Baumbach L. Acta Physiol Scand 117: 415-419, 1983). In addition, our model predicts that, for a range of TGF sensitivities, sustained perturbations that initiate or terminate LCO can yield substantial and abrupt changes in both distal NaCl delivery and NaCl delivery compensation, changes that may play an important role in the response to physiological challenge. kidney; renal hemodynamics; autoregulation; mathematical model; nonlinear dynamics THE TUBULOGLOMERULAR FEEDBACK (TGF) SYSTEM is a key moment-to-moment regulator of the single-nephron glomerular filtration rate (SNGFR). A large body of experimental and theoretical evidence indicates that TGF can mediate sustained, regular oscillations of 20-47 mHz in tubular flow, pressure, and intratubular thick ascending limb (TAL) NaCl concentration (4,6,7,12,18). These regular oscillations are called limit-cycle oscillations (LCO) because, after initiation, they tend to more and more closely approximate a fixed cycle, provided that system parameters do not change. Spontaneous LCO appear to occur in large numbers of nephrons, as they have been detected in recordings of renal blood flow and pressure taken in conscious, chronically instrumented dogs (8).A common and useful method of investigating TGF is to impose sustained perturbations of proximal tubule (PT) fluid flow in a freely flowing nephron where the TGF feedback loop is closed and functional (3,5,6,20,21,26). Using this technique, Leyssac and collaborators (5, 17, 18) have demonstrated that LCO can be initiated or extinguished in halothane-anesthetized rats by insertion or removal of PT fluid, findings that indicate that PT fluid flow can have a substantial effect on the stability of the TGF system. Some insight into the basis of this phenomenon is provided by our previous investigations of the TGF-mediated 22). These modeling studies indicate that LCO will emerge for sufficiently large feedback loop gain magnitude (12), that the parameter regime that supports LCO may overlap the parameter regime of normal TGF operation, that a gain magnitude near that needed for LCO will produce maximal feedback compensation (16), and that LCO may augment NaCl delivery to the distal nephron (16). A finding of fundamental importance is that the emergence of LCO depends on key TGF syst...

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A mathematical model that describes the effects of acute radiation exposure on thrombopoiesis in primates and humans is presented. Thrombopoiesis is a complex multistage dynamic process with potential differences between species. Due to known differences in cellular radiosensitivities, nadir times, and cytopenia durations, direct extrapolation from rhesus to human platelet dynamics is unrealistic. Developing mathematical models of thrombopoiesis for both humans and primates allows for the comparison of the system's response across species. Thus, data obtained in primate experiments can be extrapolated to predictions in humans. Parameter values for rhesus macaques and humans were obtained either from direct experimental measurements or through optimization procedures using dynamic data on platelet counts following radiation exposure. Model simulations accurately predict trends observed in platelet dynamics: at low radiation doses platelet counts decline after a time lag, and nadir depth is dose dependent. The models were validated using data that was not used during the parameterization process. In particular, additional experimental data was used for rhesus, and accident and platelet donor data was used for humans. The model aims to simulate the average response in rhesus and humans following irradiation. Variation in platelet dynamics due to individual variability can be modeled using Monte Carlo simulations in which parameter values are sampled from distributions. This model provides insight into the time course of the physiological effects of radiation exposure, information which could be valuable for disaster planning and survivability analysis and help in drug development of radiation medical countermeasures.

DISTRIBUTION A. Approved for public release: distribution is unlimited.This report provides an overview of the technical and scientific basis of the models incorporated in the Health Effects from Nuclear and Radiological Environments (HENRE) code for casualty estimation. The approach for each new model developed for HENRE included is presented. The models from HENRE include blast injury criteria models which are included in the Basic Casualty Estimation tool and the physiologically-based mathematical models included in the Advanced Casualty Estimation tool. In the discussion of the later tool, the aim is to provide the physiological basis for the mechanistic models included in HENRE and to highlight their application and value in casualty estimation, such as in the application to understanding the pathophysiological interactions of combined injury.

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