A new model for diurnal blood pressure profiling. Square wave fit compared with conventional methods.

Abstract

For the characterization of diurnal blood pressure variation, we developed a simple mathematical model that nevertheless does justice to the specific form characteristics of individual blood pressure registrations. Analysis was based on 24-hour continuous intra-arterial measurement of blood pressure obtained in 23 hospitalized patients with mild-to-moderate untreated essential hypertension (mean±SD, 112 ±13 mm Hg). The day-night difference for mean arterial pressure varied markedly (mean, 18.6 mm Hg; range, 6.8-36.0). Inspection of profiles suggested a model of blood pressure as two contiguous, complementary periods of constant pressure, a so-called square wave. Determination of the times of transience between both periods (segmentation) was performed individually using a least-square error criterion. Results were compared with those obtained by conventional methods, including analysis by Fourier modeling. The square wave fit accounted for a larger fraction (66%) of circadian variance of mean arterial pressure than modeling based on segmentation by visual inspection (59%, considerable observer bias) or by clock time (50%). Application of the Minnesota Cosinor Method resulted in the poorest description (47%). Segmentation based on harmonic modeling (61%) appeared to be cumbersome (10 harmonics needed), and the significance of additional information offered over the square wave fit is dubious. Observer bias makes segmentation by visual inspection unsuitable for assessment of the circadian variance of blood pressure. Even when daily activities are strictly regulated (hospital environment), circadian variance is not well modeled by clock time. As compared with harmonic analysis, square wave fitting is simple, and it appears to best model the circadian variance. The method can also be applied to data obtained from noninvasive ambulatory blood pressure monitoring. Nevertheless, a constant and prominent feature in normotensive men is a fall of blood pressure during the night, which constitutes a major fraction of the total diurnal blood pressure variation.3 The question as to whether there is an internal biological "blood pressure clock" analogous to the one responsible for the circadian variation of certain hormone levels and body temperature is still open. Various pathologies have been shown to alter circadian blood pressure fluctuations. For instance, a paradoxical rise in blood pressure at

Sleep and cardiovascular regulation

“…The sleep-related variation in blood pressure (BP) has been described as a square wave function with abrupt falls in association with sleep onset and increases at morning awakening, with relatively constant values during sustained sleep [25]. The fall in BP during the sleep period is referred to as a "dipping BP profile", its occurrence being considered important for cardiovascular health, as it is thought to provide what has been referred to as a "cardiovascular holiday".…”

Misclassification and discordance of measured blood pressure from patient’s true blood pressure in current clinical practice: a clinical trial simulation case study

“…Several other models were also available in the literature to describe the daily based variability of BP. Some models focused on the BP deference between daytime and nighttime BP such as the square wave fit model [27], some model focused on the transit phase between day time and night-time BP changes such as double logistic model [20,28,29]. The limitation of these models is the lack of description of the important features regarding BP fluctuations.…”

Nonsymmetrical double logistic analysis of ambulatory blood pressure recordings

“…By comparing the slopes, a measure of symmetry or nonsymmetry can be made. It does not assume a continuous transition of data between a high and low peak value as does the cosinor method (19) or an abrupt transition as does the square-wave analysis (5). Inspection of 24-h data obtained from humans showed that transitions occur differently, in different parameters, in different groups and vary depending on whether it is an increase or decrease.…”

“…To automate the fitting procedure and minimize user intervention, a series of constraints was imposed on the parameters. The constraints for P1 and P2 were established with an initial "square-wave" fit of the data that determined the mean values and standard deviation (SD) for the "light time" and the "dark time" (5). The light time mean ϩ 2SD was taken as y max, and the dark time mean Ϫ 2SD was taken as y min.…”

“…An extension of this approach has been to apply a Fourier analysis, which constitutes the superposition of multiple cosine functions of different amplitude and frequency (2). A recent method has involved the application of a simple square-wave mathematical model that involves the estimation of the daytime and nighttime plateau with a vertical transition between the two periods, resulting in a square-wave pattern (5). Although this method has been shown to be better than the cosinor method, it assumes an abrupt and complete transition within one time point, which is clearly not the case in practice.…”