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. Author manuscript; available in PMC: 2011 May 10.
Published in final edited form as: Scr Med (Brno). 2010;83(1):16–32.

BLOOD PRESSURE, HEART RATE AND MELATONIN CYCLES SYNCHRONIZATION WITH THE SEASON, EARTH MAGNETISM AND SOLAR FLARES

G Cornélissen 1, F Halberg 1, RB Sothern 1, DC Hillman 1, J Siegelová 2
PMCID: PMC3091818  NIHMSID: NIHMS248149  PMID: 21566725

Abstract

Three spectral components with periods of about (~) 0.41, ~0.5 and ~1.0 year had been found with serially independent sampling in human circulating melatonin. The time series consisted of around-the-clock samples collected for 24 hours at 4-hour intervals from different patients over several years. Some of these components had been found to be circadian stage-dependent, the daytime measurements following mostly a circannual variation, whereas a half-year characterized the nighttime samples. The latter were incorporated into a circasemiannual map. The relative brevity of the series prevented a check for the coexistence of all three spectral components, even if each component seemed to have a raison d’être. In time series of transdisciplinary data, a 1.00-year synchronized component is interpreted as representing the seasons. The half-year may qualify the circannual waveform, but it is also a signature of geomagnetics. An ~0.41-year (~5-month) component is the signature of solar flares. It has been called a cis-half-year (cis = on this side of a half-year) and may be detected only intermittently. Charles L. Wolff predicted the existence, among others, of ~0.42- and ~0.56-year components as beat periods of rotations at different solar latitudes.

The multiple components characterizing circulating melatonin could also be found in a (to our knowledge unique) data set of a clinically healthy scientist (RBS). Herein, we focus on vascular data self-measured by RBS as he aged from ~20 to ~60 years. A multi-component model consisting of cosine curves with periods of 0.41, 0.50 and 1.00 year was fitted to weekly means of systolic (S) and diastolic (D) blood pressure (BP) and heart rate (HR) collected ~5 times a day over 39 years by RBS. All three components can coexist for a while, although all of them are nonstationary in their characteristics and come and go by the criterion of statistical significance.

Intermittently, BP and HR are synchronized selectively with one or the other aspect of RBS′ physical environment, namely the seasons (at ~1.0 year), earth magnetism (at ~0.5 year) and/or solar flares (at ~0.42 year). Cosmic-biotic transfer of information, albeit hardly of energy (the biospheric amplitudes are very small) may be mediated in this set of frequency windows. As found earlier, RBS′ circulation is also frequency-trapped environmentally in multidecadal windows, HR being locked into the transtridecadal Brückner, or rather Brückner-Egeson-Lockyer, BEL sunspot and terrestrial weather cycle, while his BP follows Hale’s didecadal cycle in the changing polarity of sunspots.

The ~0.41-year HR cycle may be associated with changes in solar flares, the cis-half-year amplitude of HR showing a cross-correlation coefficient of 0.79 with the total solar flare index (from both solar hemispheres) at a lag of ~3.2 years. The superposed time courses of these two variables indicate the presence of a shared Horrebow-Arago-Schwabe sunspot cycle of ~11 years, the cis-half-year in HR being more prominent after the total solar flare index reaches its ~11-year peak. Differences in the time-varying behavior of BP vs. HR are also described.

Keywords: Blood pressure variability, Heart rate variability, Melatonin cycles, Earth magnetism

AN ANALOGY BETWEEN EXTERNAL SCRUBBING AND SELF-SURVEILLANCE OF INTERNAL RHYTHMS

With respect to preventive measures for maintaining cardiac and mental health and preventing morbid events such as strokes and criminality in individuals and terrorism in society, we are in the same situation today as Ignaz Semmelweis [1] and Oliver Holmes [2] were with respect to antisepsis. In our case, a broad spectrum of rhythms in us and around us, albeit already mapped, has not yet been recognized in terms of pertinence to everyday life. Like circadians [3–5], now a fashion in molecular biology, the many different more or less periodic extra-circadians [6] evolved and were adaptively built into human physiology under the influence of the nonphotic cycles of our cosmos. Infradians are apparent in military-political affairs, including aggression, notably crime, international battles and terrorism, in economics, in opinion polls, in education and, most important, in health and disease, including infection (7–10). Like circadians, infradians also tip the scale between life and death.

DOUBLE PURPOSE OF PHYSIOLOGICAL SURVEILLANCE: SELF-HELP IN HEALTHCARE AND PHOTIC-NONPHOTIC ENVIRONMENTAL MONITORING

Chronobiologically interpreted systolic (S) and diastolic (D) blood pressure (BP) and heart rate (HR) monitoring detects pre-hypertension, pre-diabetes, and a pre-metabolic syndrome in Vascular Variability Disorders (VVDs), as conditions of increased vascular disease risk [11–14] and as complications of a (reliably diagnosed) MESOR-hypertension, a VVD in its own right. Another VVD is an excessive circadian amplitude of BP (CHAT, short for Circadian Hyper-Amplitude-Tension). This condition carries a risk of cerebral ischemic event greater than a high BP. It can coexist with other VVDs to form Vascular Variability Syndromes (VVSs). VVDs are not being screened for in our current conventional health care system. Once diagnosed, some VVDs can be treated.

It is not yet generally known that in the human newborn, variables such as BP and HR have infradians such as an about-weekly component, which is usually more prominent than the 24-hour variation, awaiting testing as a gauge of risk. It is also not generally known that the incidence patterns of sudden cardiac death (ICD10, code I46.1) is characterized by ~5-month (cis-half-year) and ~17-month (far-trans-year) components, cyclic signatures of space weather, in the absence of yearly changes, notwithstanding the large difference between Minnesota’s mid-continental winters and summers. A host of spectral components is shared between natural physical environmental variables, such as the solar wind and other aspects of space weather, and biological variables, such as those of the human circulation, electrical accidents of the heart [15], and suicides [16]. They are said to be congruent when the 95% confidence intervals (CIs) of their (shared) periods are overlying or overlapping. (Congruence is a similarity in characteristics such as the period or phase of a spectral component in two or more concomitantly sampled time series of variables when 95% CIs are overlying or overlapping.) When cardiovascular and mental health and their relation to the cosmos are viewed in 40 years of self-measurements by RBS, there is selective congruence of the ~5-month component between RBS′ HR and the total solar flare index (SFI). An ~0.41-year cis-half-year component in HR is modulated by solar flares, and both solar flares and the cis-half-year amplitudes of RBS′ HR show the Horrebow-Arago-Schwabe pattern of sunspot numbers (Figure 1, left). Their cross-correlation function (Figure 1, section D) reaches a maximum of r=0.79 at a 3.16-year lag, raising the question whether the effect of solar flares is direct or indirect, perhaps mediated by terrestrial magnetism. Congruence of an ~33-year cycle between RBS′ HR and Wolf’s sunspot numbers (Figure 2) was reported earlier [17], as were other congruences of RBS′ HR and BP with space weather (Figure 3).

Figure 1.

Figure 1

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Horrebow-Arago-Schwabe pattern of solar flares (top and bottom, left) and of Wolf numbers (middle, left) is shared with changes in cis-half-year amplitude of RBS′ HR (bottom, left). The cross-correlation function of the latter with the total solar flare index reaches a maximum of 0.79 at a 3.16-year lag (top, right). © Halberg.

Figure 2.

Figure 2

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Congruences were reported earlier [17] at a period of ~33 years between RBS′ HR and Wolf’s sunspot numbers. Whereas this component is rather weak in the physical variable, it is much more prominent in HR, as apparent from the least squares spectra. © Halberg.

Figure 3.

Figure 3

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Summary of relative congruences between RBS′ HR and BP and nonphotic environmental variables, including the one shown in Figure 2 (top left). Note a didecadal congruence between RBS′ BP and Hale’s bipolarity cycle of sunspots. © Halberg.

HORREBOW-ARAGO-SCHWABE MODULATION OF CIS-HALF- YEAR IN AND AROUND US

Both solar flares (Figure 1, left, top and bottom) and Wolf sunspot numbers (Figure 1, left, middle) are characterized by a prominent ~11-year cycle. The prominence of the cis-half-year in RBS′ HR, gauged by the 0.41-year amplitude estimated over a 4-year interval displaced in 2.5-month increments, also follows a similar ~11-year cycle (Figure 1, left, bottom). It is detected with statistical significance (filled rectangles) only part of the time, usually following a peak in solar flares and sunspot numbers. The cross-correlation function between the cis-half-year amplitude of HR versus the total solar flare index reaches a maximum of 0.79 at a 3.16-year lag (Figure 1, right, top). Whether the effect is direct or indirect should be examined further, beyond the congruence of periods and phases, as they change with time, against the background of already demonstrated prior global congruences at a trial period of ~33 years, Figures 2 and 3. Congruences can be selective, as noted in Figure 3: RBS′ HR displays a transtridecadal congruence with Wolf numbers, while RBS′ BP responds to Hale’s sunspot bipolarity cycle.

CAN BIOSPHERIC BEHAVIOR TEACH PHYSICAL LESSONS?

The original task was to examine the degree of ubiquity and, in this sense, the consistency in different variables, if any, of an ~0.42-year cis-half-year component. It had been found to characterize sudden cardiac death (ICD10, code I46.1) in Minnesota and in a number of other geographic locations (15; cf. 18–20), Figure 4. It was also detected in the SBP of an elderly subject (FH) during nearly 16 years of monitoring, at 70–86 years of age [15], and in a 10-year DBP record (analyzed by gliding spectrum) of another elderly man (GSK) [21]. The 39-year BP and HR record of RBS, at 20–59 years of age, lent itself well to the examination of the cis-half-year as it may change as a function of time.

Figure 4.

Figure 4

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A cis-half-year (cY/2) had been found in the incidence patterns of sudden cardiac death in Minnesota [15] and in some other geographic locations, as summarized in this map. © Halberg.

LOOKING FOR INTERMITTENTLY COEXISTING CYCLES

Linear least-squares spectra of weekly means of SBP, DBP and HR of RBS showed only a small peak at a period of ~0.42 year that was not statistically significant, contrasting with its detection in the BP of two elderly men (FH and GSK). The task was to determine whether the cis-half-year was definitively absent in RBS during his 39 years of self-measurements or whether its detection was obscured by the presence of other larger neighboring spectral peaks and/or by its non-stationary Aeolian nature. (The intermittent and otherwise nonstationary waxing and waning in amplitude was dubbed “Aeolian”.). Prominent yearly and half-yearly variations indeed characterized the BP and HR of RBS. The half-year may be an expression of the non-sinusoidality of the circannual component, but it may also represent the expression of a geomagnetic signature of its own right. The ~0.42-year cis-half-year was anticipated from its detection in two other long-term series, being congruent with solar flares, where this component was documented by Rieger et al. [22] and others, Table 1. An ~0.56-year component in solar activity, also of interest as another beat period of the solar rotation according to Charles L. Wolff (23, cf. 16), remains beyond the scope of this analysis. In order to answer the above question, multiple-component serial sections were carried out, including with the 0.42-year cis-half-year the other two major neighboring components with periods of 0.5 and 1.0 year. Specifically, a 3-component model was fitted by cosinor, consisting of cosine curves with periods of 1.0, 0.5, and 0.41 year (or 8766, 4383, and 3615 hours), to data in a 209-week (~4-year) interval displaced throughout the time series by increments of 11 weeks (~0.21 year or a half cis-half-year cycle).

Like many other nonphotic components, the cis-half-year in the BP and HR of RBS was found to be present only intermittently and with characteristics that varied as a function of time. Specifically, based on this moving 3-component model, the following results were obtained. For SBP, the 1.0-year component reached statistical significance (P<0.05) in 157 of 167 (partly overlapping) intervals (94.0%). The 0.5-year and 0.41-year components were statistically significant in 110 (65.9%) and 39 (23.4%) intervals, respectively. In the case of DBP, the 1.0-year, 0.5-year, and 0.41-year components reached statistical significance in 152 (91.0%), 61 (36.5%), and 38 (22.8%) intervals, respectively, and in the case of HR, statistical significance was reached in 112 (67.1%), 61 (36.5%), and 37 (22.2%) intervals, respectively. Whereas in RBS (but not in FH and GSK), the yearly component and its second harmonic are undoubtedly the most consistent and the most prominent, the cis-half-year is also detected with statistical significance at a rate higher than would be expected by chance alone and according to a non-random pattern in time that prompts the search for a similar clustering in environmental variables (Figure 1, left, bottom). All three components could be detected concomitantly in 33 (19.8%), 18 (10.8%), and 10 (6.0%) intervals for SBP, DBP, and HR, respectively.

The results are illustrated in Figures 5–7, where statistical significance (P<0.05) is represented as dark-filled symbols, borderline statistical significance (0.05<P<0.10) as lightly-filled symbols, and non-significance (P>0.10) as open symbols. It can readily be seen that instances when the cis-half-year reaches statistical significance do not occur at random but mostly as clusters in time. Large changes in the amplitude of all three components are also observed for all three variables.

Figure 5.

Figure 5

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Statistical significance (P<0.05) of 1.0-year (top), 0.5-year (middle), and 0.41-year (cis-half-year, bottom) components fitted concomitantly to the SBP data of RBS is represented as dark-filled symbols, borderline statistical significance (0.05<P<0.10) as lightly-filled symbols, and non-significance (P>0.10) as open symbols. It can readily be seen that instances when the cis-half-year reaches statistical significance do not occur at random but mostly as clusters in time. Large changes in the amplitude of all three components are also observed for all three variables. © Halberg.

Figure 7.

Figure 7

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Statistical significance (P<0.05) of 1.0-year (top), 0.5-year (middle), and 0.41-year (cis-half-year, bottom) components fitted concomitantly to the HR data of RBS is represented as dark-filled symbols, borderline statistical significance (0.05<P<0.10) as lightly-filled symbols, and non-significance (P>0.10) as open symbols. It can readily be seen that instances when the cis-half-year reaches statistical significance do not occur at random but mostly as clusters in time. Large changes in the amplitude of all three components are also observed for all three variables. © Halberg.

The occasional (intermittent) presence of all three components coexisting concomitantly in the BP and HR data of RBS was of interest in relation to another study in Florence, Italy, on circulating melatonin, offering a fresh interpretation to results obtained earlier. In the course of ~4 years, blood samples had been obtained at 4-hour intervals for 24 hours from each of 172 subjects for the determination of melatonin [24]. Original analyses of the serially-independent data pooled from all subjects stacked over an idealized year had reported the presence of a circannual variation characterizing daytime samples, contrasting with the detection of a half-yearly component in nighttime samples [24]. A recent reanalysis of these data without stacking revealed the presence of a cis-half-year instead of the originally reported half-year, Figure 8 [25].

Figure 8.

Figure 8

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In melatonin data that were serially-dependent along the 24-hour scale, each person providing blood at 4-hour intervals for 24 hours, but serially-independent after pooling across 172 subjects examined in the course of ~4 years, a cis-half-year rather than half-year is invariably detected observed, characterizing the individual MESORs and circadian amplitudes as well as both daytime and nighttime samples considered separately. A map of the nonlinear estimates of cis-half-year periods and their CIs (bottom) is provided with an abstract definition of congruence (top). © Halberg.

PHASE BEHAVIOR OF THE YEAR, HALF-YEAR, AND CIS-HALF- YEAR COMPONENTS IN BP AND HR

Figures 9–11 illustrate the time course of the acrophases of the three components with periods of 1.0, 0.5, and 0.41 year, fitted concomitantly in ~4-year intervals displaced in ~0.21-year increments. The acrophases are shown only when the zero-amplitude test could be rejected at P<0.10. The yearly component is detected most of the time for SBP and DBP, but less often for HR. There are large changes in the circannual acrophases as a function of time, with a range larger than 4 and 5.5 months for SBP and DBP, respectively, and exceeding 7.5 months for HR, indicating that this component is much less stable than could be anticipated from the strong seasonal changes in the environmental temperature of Minnesota. The 1.0-year component may be modulated by lower-frequency components. The 0.5-year and 0.41-year components are only sporadically detected and their time course shows an intermittency contrasting with the relative consistency of the yearly component.

Figure 9.

Figure 9

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Time course of the acrophases of the three components (with periods of 1.0, 0.5, and 0.41 year) fitted concomitantly to the SBP data of RBS. Acrophases are shown only when the zero-amplitude test could be rejected at P<0.10. The 1.0-year component is detected most of the time, and all three components are occasionally detected concomitantly, albeit only intermittently. © Halberg.

Figure 11.

Figure 11

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Time course of the acrophases of the three components (with periods of 1.0, 0.5, and 0.41 year) fitted concomitantly to the HR data of RBS. Acrophases are shown only when the zero-amplitude test could be rejected at P<0.10. The 1.0-year component detected most of the time in the case of SBP and DBP is less consistent for HR. All three components are occasionally detected concomitantly, albeit only intermittently. © Halberg.

GLOBAL ANALYSES ASSESS ADDITIONAL COMPONENTS CHARACTERIZING BP AND HR

Apart from the cis-half-year, other nonphotic components characterize RBS’s data. One of these components has an anticipated period of ~0.55 year, too close to 0.5 and 0.41 year to be reliably resolved in ~4-year intervals. Additional global analyses were hence performed on the entire 39-year series (1968–2006). Because some low-frequency components account for a much larger portion of the overall variance, analyses were processed in two steps. In the first step, components with periods longer than ~4 years were assessed nonlinearly together with a fixed yearly component and its second harmonic of 6 months. The model was then subtracted from the weekly means. In the second step, residuals were nonlinearly analyzed (allowing the period to vary as a parameter to be estimated) to try to resolve the remaining components of interest and to determine their (period) length. A composite model using the nonlinearly estimated periods was then fitted linearly to determine the extent of their statistical significance.

Low-frequency components considered had trial periods of 25, 11.1, 6.5, and 4 years. They were fitted concomitantly with fixed 1.0- and 0.5-year harmonically-related components. Nonlinear results indicated that all components could be resolved for SBP, the periods and their CIs being estimated as 22.56 [21.20, 23.92], 11.44 [10.92, 11.96], 6.66 [6.44, 6.88], and 4.03 [3.91, 4.15] years. In the case of DBP, all infra-annual components were also validated nonlinearly conservatively, whereas the half-year could only be assessed on the basis of a (more “liberal”) 1-parameter CI of the amplitude that did not overlap zero. The period estimates for DBP were 20.55 [19.00, 22.10], 10.75 [10.14, 11.37], 6.70 [6.38, 7.03], and 3.96 [3.82, 4.10] years. In the case of HR as well, only the half-year had only a 1-parameter CI of the amplitude that did not overlap zero. The period estimates for HR were 32.68, 13.59 [13.03, 14.15], 5.82 [5.71, 5.93], and 3.99 [3.91, 4.08] years. The selective multidecadal congruence is visualized in Figure 3.

Residuals from the above models indicated the presence of components with trial periods of 1.65, 1.38, 1.25, 0.55, and 0.41 year(s), corresponding to spectral peaklets in the global spectra of the weekly means. Nonlinearly, the three transyearly components were validated for SBP. Albeit the conservative approach yielded CIs of the amplitude that overlapped zero, the 1-parameter CI of the ~0.55-year and 0.41-year amplitudes did not overlap zero. With this qualification, period estimates and their CIs were 1.682 [1.646, 1.718], 1.400 [1.371, 1.428], 1.245 [1.226, 1.263], 0.548 [0.542, 0.555], and 0.413 [0.408, 0.417] year(s). In the case of DBP, the ~1.25-year component could not be validated and the other four components all had (if not conservative) 1-parameter CIs of the amplitude that did not overlap zero. With this qualification, the period estimates and their CIs were 1.695 [1.653, 1.738], 1.393 [1.339, 1.448], 1.235 [1.159, 1.310], 0.548 [0.537, 0.559], and 0.412 [0.407, 0.418] year(s). In the case of HR, a slightly different trial period had to be used for the first transyear: instead of a trial period of 1.65 years, one of 1.86 years was used. This component and the ~1.38-year component were both validated conservatively. The other three all had a 1-parameter (but not a conservative) CI of the amplitude that did not overlap zero. With this qualification, period estimates and their CIs were 1.806 [1.760, 1.851], 1.394 [1.371, 1.417], 1.247 [1.223, 1.271], 0.550 [0.541, 0.559], and 0.411 [0.408, 0.415] year(s).

A 5-component model using the periods estimated nonlinearly was then fitted, the periods differing slightly for each variable. This model and each of its constituent components was statistically significant for SBP and for HR, but in the case of DBP, only the ~1.69-year and ~1.39-year components reached statistical significance, whereas the 0.41-year component only reached borderline statistical significance (P=0.054). The other two components with periods of ~1.24 and ~0.55 year(s) were not statistically significant and had to be removed from the model.

INFRA-ANNUAL MODULATIONS OF THE 1.0-YEAR, 0.5-YEAR, AND 0.41-YEAR AMPLITUDES OF BP AND HR

In order to explore possible environmental influences underlying the changes in amplitude of the 1.0-year, 0.5-year, and 0.41-year components of SBP, DBP, and HR, the amplitude estimates from the 3-component serial sections were further analyzed by least squares spectra, with the understanding that P-values obtained in the following analyses cannot be taken at their face value since the serial sections were pergressive with an increment of 1/19 the length of the interval. With this qualification, Figure 12 summarizes the results, rough estimates of the periods corresponding to spectral peaks marked in each case. Apart from some low-frequency components that may contribute sidelobes in global spectra of the weekly means, the following two observations may deserve further investigation. First, perhaps because of the relatively large changes in amplitude and acrophase of the yearly component as a function of time, the 1.0-year amplitudes are characterized by an ~1.1-year component for SBP and DBP and by an ~1.2-year component for HR. Second, the cis-half-year amplitudes of HR are characterized by a prominent ~11-year component.

Figure 12.

Figure 12

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Least squares spectra of the amplitude estimates from the 3-component serial sections, with periods of 1.0-year (top), 0.5-year (middle), and 0.41-year (bottom) of SBP (left), DBP (middle), and HR (right) of RBS. P-values obtained in these analyses cannot be taken at their face value since the serial sections were pergressive with an increment of 1/19 the length of the interval. Perhaps because of the relatively large changes in amplitude and acrophase of the yearly component as a function of time, the 1.0-year amplitudes have an ~1.1-year spectral peak for SBP and DBP and by an ~1.2-year spectral peak for HR. The cis-half-year amplitudes of HR are characterized by a prominent ~11-year component. © Halberg.

Figure 13 (see also Figure 1) illustrates the ~11-year modulation of the cis-half-year amplitude of HR. Figure 14 shows that the cis-half-year amplitudes of DBP similarly lag after solar flares. RBS′ HR and DBP as well as the total solar flare index are in synchrony with a decadal Horrebow-Schwabe cycle. As shown in Figure 2 (and discussed elsewhere), HR and Wolf numbers are also modulated by the transtridecadal Brückner-Egeson-Lockyer (BEL) cycle (17, 26, 27).

Figure 13.

Figure 13

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As also summarized in Figure 1, the cis-half-year amplitude of HR (bottom) shares an ~11-year cycle with Wolf numbers (top). © Halberg.

Figure 14.

Figure 14

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Similarly to HR, the cis-half-year amplitudes of DBP are cross-correlated with solar flares, reaching a peak association of 0.564 at 3.37-year lag after the total solar flare index. © Halberg.

Methodologically and basically revealing is that the search for another biotic cis-half-year has not only validated the latter in the longest available series of BP and HR, but has found near-transyears in SBP and DBP, whose presence had also been documented in physics (prompted by their presence in the elderly’s BP). Whether the near-transyear is a nonlinear modulation by a lower frequency in physics, e.g., in solar magnetism or a component in its own right, it has a biological counterpart. Further, as to reciprocal periods of the beats of the rotations at different solar latitudes, Charles Wolff’s predicted periods have been found not only as a cis-half-year but also as a trans-half-year of 0.55 year. At one end of the CI, its period is within one decimal of Wolff’s 0.56-year prediction [23]. Moreover, both these periods have been validated along with a very likely geomagnetic component of 0.50 year.

CONCLUSION

Multiple spectral component signatures of time-varying solar activity are likely to characterize any time series covering years. When an anticipated component is not detected by the fit of a single component, a concomitant fit of several components is indicated. Apart from this methodologic truism that bears emphasis as the control information for any and all studies, we here demonstrate the intermittency of cis-half-years in the adult human circulation and their temporal association with an about 11-year cycle in solar flares, with a lag somewhat longer than 3 years.

Figure 6.

Figure 6

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Statistical significance (P<0.05) of 1.0-year (top), 0.5-year (middle), and 0.41-year (cis-half-year, bottom) components fitted concomitantly to the DBP data of RBS is represented as dark-filled symbols, borderline statistical significance (0.05<P<0.10) as lightly-filled symbols, and non-significance (P>0.10) as open symbols. It can readily be seen that instances when the cis-half-year reaches statistical significance do not occur at random but mostly as clusters in time. Large changes in the amplitude of all three components are also observed for all three variables. © Halberg.

Figure 10.

Figure 10

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Time course of the acrophases of the three components (with periods of 1.0, 0.5, and 0.41 year) fitted concomitantly to the DBP data of RBS. Acrophases are shown only when the zero-amplitude test could be rejected at P<0.10. The 1.0-year component is detected most of the time, and all three components are occasionally detected concomitantly, albeit only intermittently. © Halberg.

Acknowledgments

Support

GM–13981 (FH), University of Minnesota Supercomputing Institute (GC, FH), MSM0021622402

This paper is dedicated to the memory of Jean De Prins, a great teacher, an inspiring mentor, and above all, a dear friend

Support

U.S. National Institutes of Health (GM–13981) (FH), University of Minnesota Supercomputing Institute (GC, FH)

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