Blood pressure (BP) values (systolic BP = Ps, diastolic BP = Pd, heart rate = HR) fluctuate widely throughout the day, and are at their lowest levels during sleep (sleep-Ps = PS0, sleep-Pd = Pd0, sleep-HR = HR0). We analyzed the relationships among these values using the Windkessel model (logarithmic gradient of diastolic pressure decay A = E/R, E = elastic modulus, R = vascular resistance). Intra-arterial BP and ECG were recorded throughout 24 hours in 23 patients with mild essential hypertension (EH) by telemetry, and EEG was monitored during the night. The waveform of each BP pulse was analyzed by computer. The dye-function method was used to obtain the cardiac output while the subjects were awake, recumbent and during slow-wave sleep on the EEG. A high correlation coefficient (r) was observed between mean BP and square root of E x square root of R during sleep (r = 0.88, p < 0.001). Sleep-HR was determined from the waveform that most effectively permitted peripheral blood flow. Furthermore, the simple algebraic relationships Pd not equal to phi x Pd0 and phi not equal to FI + a1(BI) + b1 (a1, b1 = constant) were observed between Pd0 and different 24 h Pd values [FI = eA(RR0-RR); BI = baroreflex index = RR x Pd(RR0 x Pd0)-1, which was significantly correlated with the baroreflex sensitivity, r = 0.79; RR0 and RR are the RR intervals in Pd0 and Pd waves]. The mean r between Pd0 x phi and the actual Pd over 24 h was 0.91 +/- 0.02 (SD). We conclude that sleep-BP and sleep-HR depend mainly on square root of E x square root of R, m [m = log(e)(Ps/Pd)] and E/R, whereas BP variability (phi) over a 24 h period is related to HR variation, the baroreflex index and E/R in mild EH patients.