The kidney has long been known as an organ of homeostasis, which has been taken to imply that the steady state is the most appropriate condition in which to view the kidney. However, the kidney has an intrinsic rhythm (Holstein-Rathlou and Leyssac, 1987; Holstein-Rathlou and Marsh, 1989), and it is known that disorders of these rhythms are associated with at least some cardiovascular diseases, such as renovascular hypertension (Yip et al. 1991), and in spontaneous hypertension in rats (Wagner et al. 1997). Renal blood flow (RBF) and pressure mechanisms have been modelled using a range of dynamic system models (Holstein-Rathlou and Marsh, 1994b). This has improved our understanding of the controlling mechanisms, enabling the evaluation of models, and has been of use in determining the relative importance of various inputs in the control of RBF. However, in a comprehensive review paper, Holstein-Rathlou and Marsh (1994b) reveal that, even using a combination of the best existing modelling approaches, there are some significant discrepancies between the predictions of such models and the actual behaviour of the kidney. One explanation for this may be that previous work has given no consideration to the importance of sympathetic nerve activity (SNA) in regulating RBF. Historically, it has been hypothesised that small variations in SNA occurring during normal daily events play little role in modulating renal blood flow RBF (Dibona and Kopp, 1997). This suggests that RBF, under basal conditions, is likely to be regulated by other factors such as arterial pressure, hormones and autoregulation. This hypothesis has been supported by a number of studies in both anaesthetised and conscious animals, in which RBF was generally estimated by the clearance of a substance across the kidney, and nerve activity increased and decreased in response to afferent stimuli (Hesse and Johns, 1984; Miki et al. 1989a,b). However, this approach does not take into account that SNA is an inherently dynamic signal, responding rapidly to 3425 The Journal of Experimental Biology 201, 3425–3430 (1998) Printed in Great Britain © The Company of Biologists Limited 1998 JEB1726 A linear autoregressive/moving-average model was developed to describe the dynamic relationship between mean arterial pressure (MAP), renal sympathetic nerve activity (SNA) and renal blood flow (RBF) in conscious rabbits. The RBF and SNA to the same kidney were measured under resting conditions in a group of eight rabbits. Spectral analysis of the data sampled at 0.4 Hz showed that the low-pass bandwidth of the signal power for RBF was approximately 0.05 Hz. An autoregressive/moving-average model with an exogenous input (ARMAX) was then derived (using the iterative Gauss–Newton algorithm provided by the MATLAB identification Toolbox), with MAP and SNA as inputs and RBF as output, to model the low-frequency fluctuations. The model step responses of RBF to changes in SNA and arterial pressure indicated an overdamped response with a settling time that was usually less than 2 s. Calculated residuals from the model indicated that 79±5 % (mean ± S.D., averaged over eight independent experiments) of the variation in RBF could be accounted for by the variations in arterial pressure and SNA. Two additional single-input models for each of the inputs were similarly obtained and showed conclusively that changes in RBF, in the conscious resting rabbit, are a function of both SNA and MAP and that the SNA signal has the predominant effect. These results indicate a strong reliance on SNA for the dynamic regulation of RBF. Such information is likely to be important in understanding the diminished renal function that occurs in a variety of disease conditions in which overactivity of the sympathetic nervous system occurs. Key words: mathematical model, ARMAX, spectral analysis, arterial pressure, blood flow, sympathetic nerve activity, rabbit. Summary Introduction MODELLING OF THE DYNAMIC RELATIONSHIP BETWEEN ARTERIAL PRESSURE, RENAL SYMPATHETIC NERVE ACTIVITY AND RENAL BLOOD FLOW IN CONSCIOUS RABBITS CLIVE S. BERGER 1 AND SIMON C. MALPAS 1,2, * 1 Department of Electrical Engineering and Computer Systems, Monash University, Clayton, Baker Medical Research Institute, Prahran, Victoria, Australia and 2 Department of Physiology, University of Auckland, PO Box 9201, New Zealand *Author for correspondence at address 2 (e-mail; s.malpas@auckland.ac.nz) Accepted 5 October; published on WWW 17 November 1998