Cosine Curve Fitting Research Articles

Direction Estimates for Short-Period P-Waves on Three-Component Stations and Arrays

Abstract P-arrival backazimuth estimates can be crucial in locating poorly constrained seismic events. Correlating short windows of the vertical waveform with corresponding windows of the radial rotation for different backazimuths can provide estimates, but these are often uncertain and biased due to skewness in the Z–R correlation functions. Assessing how well cosine curves centered on different backazimuths match the Z–R correlation functions provides more reliable estimates that depend less upon the time-window used. Stacking best-fit-cosine curves from neighboring three-component stations improves stability further in a form of array-processing that does not require coherence between the waveforms themselves. We demonstrate for recordings of North Korean nuclear tests at the Pilbara 3C array in Australia that the biases in the Z–R correlation functions vary greatly between adjacent stations. This bias is reduced both by the cosine curve fitting and stacking operations. We advocate obtaining backazimuth estimates for all P arrivals at three-component stations globally. This could improve phase association and event location, identify sensor orientation problems, and provide baseline backazimuth corrections and uncertainty estimates. We propose two benchmark datasets for developing, documenting, and comparing backazimuth estimation algorithms and codes. All the data and code used to generate the results presented here are open.

0015 A circadian-informed lighting intervention markedly accelerates circadian adjustment to a night shift-work schedule

Abstract Introduction Night shift-work results in misalignment between circadian timing and the sleep/wake schedule, negatively impacting sleep and performance. In encapsulated environments (e.g., submarines), the lack of strong daily solar lighting cues may impair circadian entrainment to the night shift-work schedule. This study designed and tested a circadian-informed lighting strategy to promote faster circadian phase delays to adjust to night shift-work compared to standard lighting. Methods Nineteen healthy sleepers (12 males/7 females, mean±SD aged 28.7±10.4 years) underwent two separate 8-day experimental conditions (circadian-informed lighting versus standard lighting). After a baseline sleep from 22:00 – 07:00 (day 1) and salivary dim light melatonin onset assessment ([DLMO], day 2), participants undertook simulated night shift-work (00:00 - 08:00) and slept during the day (10:00 - 19:00) for days 3-7 followed by a post-DLMO assessment on day 8. Ingestible capsules collected core body temperature (CBT) continuously throughout days 2-8, and cosine curve fitting was applied to estimate the timing of each daily temperature minima. The standard lighting condition mimicked current lighting on submarines (largely dim, blue-depleted light), while the circadian-informed lighting administered bright, blue-enriched and dim, blue-depleted lighting at times estimated to facilitate rapid circadian delay. The magnitude of daily CBT minima changes and the delay in pre- vs. post-DLMO were compared across conditions. Results There were significant day-by-condition interactions on CBT minima timing and DLMO timing (both p< 0.001). After 4 days of simulated night-shift work there was a mean [95%CI] 4.5 [3.4 to 5.7] hour greater delay in CBT minima and a 4.6 [3.6 to 5.6] hour greater delay in DLMO timing compared to standard lighting, equating to 3.6 and 2.4-fold faster delays in DLMO and CBT minima timing shifts, respectively. Conclusion Circadian-informed lighting substantially accelerates circadian re-adjustment to night shift-work. Lighting interventions could usefully improve sleep, performance, and safety in shift-workers. Support (if any) This research is supported by the Commonwealth of Australia as represented by the Defence Science and Technology Group of the Department of Defence through the Research Network for Undersea Decision Superiority (research agreement number: 9334), with additional financial support from Flinders University and lighting provision support from REDARC.

O021 Investigation of a novel LED lighting strategy designed to accelerate circadian entrainment to night shift-work in an encapsulated environment

Abstract Introduction Shift-work results in misalignment between circadian timing and the sleep/wake schedule, negatively impacting sleep and performance. In encapsulated environments (e.g., submarines), the lack of strong daily lighting cues impairs circadian entrainment. This study tested whether circadian-informed LED lighting promotes greater circadian phase delays to adjust to night shift-work compared to standard lighting. Method To date, 11 healthy sleepers (7 males, mean±SD age27.6±8.5 y, N=24 anticipated) have completed two separate 8-day experimental conditions (circadian-informed lighting versus standard lighting). After a baseline sleep from 22:00 – 07:00 (day 1) and salivary dim light melatonin onset ([DLMO], day 2), participants undertook simulated night shift-work (00:00 - 08:00) and slept during the daytime (10:00 - 19:00) for days 3-7 followed by a post-DLMO assessment on day 8. Ingestible capsules collected core body temperature (CBT) continuously throughout days 2-8. The standard lighting condition mimicked current lighting on submarines (largely dim, blue-depleted light), while the circadian-informed lighting administered bright, blue-enriched and dim, blue-depleted lighting at times estimated to facilitate rapid circadian delay. Cosine curve fitting was applied to the CBT data to estimate temperature minima (CBTmin) and determine phase delay magnitude for comparison across conditions. Results There was a significant day-by-condition interaction on CBTmin (F4, 88=2.82, p=0.030). By day 6, the CBTmin delay was (mean±SD) 3.2±.97 hours greater in the circadian-informed lighting versus standard lighting, p=0.001. Conclusions These preliminary analyses support that circadian-informed lighting accelerates circadian re-adjustment to night shift-work. Such interventions could improve sleep, performance, and safety in shift-workers who work in encapsulated environments.

Neuraxial analgesia interfered with the circadian rhythm of labor: a propensity score matched cohort study

ObjectivesTo investigate whether neuraxial analgesia and other medical interventions have effects on the circadian rhythm of labor.MethodsIt was a retrospective propensity score matched cohort study. Parturients were recruited, who delivered term singletons in cephalic position, from seven hospitals in Harvard University Partners Healthcare Systems, 2016–2018. The parturients were divided into two groups, neuraxial analgesia delivery and spontaneous vaginal delivery, the stratification was performed according to labor induction, oxytocin, operative delivery. The parturients in each group were divided into 12 periods in every 2 h based on the birth time of babies. Cosine function fitting was used to verify whether the birth time had the characteristic of circadian rhythm.ResultsIn spontaneous vaginal deliveries, the peak of birth time was at 2:00–4:00, and the nadir was at 14:00–16:00, this showed a circadian rhythm presented by a cosine curve fitting with the formula (y = 0.0847 + 0.01711 × cos(− 0.2138 × x + 0.4471). The labor rhythm of NAD (Neuraxial Analgesia Delivery) group changed completely, inconsistent with the cosine curve fitting of the circadian rhythm. The intervention of induction and oxytocin blurred the circadian rhythm of SVD (Spontaneous Vaginal Delivery) group and increased the amplitude of the fluctuation in NAD (Neuraxial Analgesia Delivery) group. The intervention of operative delivery had changed the distribution curve completely both in the SVD (Spontaneous Vaginal Delivery) group and the NAD (Neuraxial Analgesia Delivery) group.ConclusionsNeuraxial analgesia did affect on circadian rhythm of labor, changed the cosine rhythm of labor with spontaneous vaginal delivery, and this trend was aggravated by the use of induction, oxytocin and operative delivery.

Annual rhythm in filgrastim use in southeast Florida.

e20697 Background: Circadian, seasonal and annual temporal organization characterizes earth-evolved life forms. Cellular proliferation in human bone marrow shares this temporal organization. Careful clinical trials have documented that bone marrow damage from a range of cytotoxic anti-cancer drugs is predictably greater and lesser when these drugs are given at specific times of day and seasons of the year to human beings with cancer. Filgrastim is a human growth factor, which is given to stimulate the production of neutrophils that have been depressed to low levels by cancer chemotherapy, in order to prevent infectious complications. We hypothesized that administration of filgrastim, stimulated by dangerously low neutrophil counts, would be initiated non-randomly with reproducible seasonality and annual rhythmicity. Methods: All claims from contracted healthplans submitted by oncologists in southeast Florida were tabulated by month of service date, during the calendar years of 2010, 2011, and 2012 (n=2,506). These numbers were de-trended, tested by linear regression, ANOVA and multi-component least squares cosine curve fitting for annual rhythmicity. Results: Similar stable annual time structures characterize filgrastim use in this population for each of these three years. An overall increasing trend (p 0.004) was present in its use during this three year span. Time of year effects were present (ANOVA p<0.058), demonstrating a prominent annual rhythm (p 0.006). The annual use pattern peaks during late winter and early spring and is lower in summer and fall. Conclusions: A large literature documents expected annual rhythmicity of cytotoxic drug bone marrow damage as reflected in circulating neutrophil count. Substantial annual rhythms characterize the clinical use of filgrastim in southeast Florida for this indication. The relative contributions of “snowbird” migration and the temporal organization of hematopoiesis remain to be fully elucidated. [Table: see text]

Rapid phase adjustment of melatonin and core body temperature rhythms following a 6-h advance of the light/dark cycle in the horse

BackgroundRapid displacement across multiple time zones results in a conflict between the new cycle of light and dark and the previously entrained program of the internal circadian clock, a phenomenon known as jet lag. In humans, jet lag is often characterized by malaise, appetite loss, fatigue, disturbed sleep and performance deficit, the consequences of which are of particular concern to athletes hoping to perform optimally at an international destination. As a species renowned for its capacity for athletic performance, the consequences of jet lag are also relevant for the horse. However, the duration and severity of jet lag related circadian disruption is presently unknown in this species. We investigated the rates of re-entrainment of serum melatonin and core body temperature (BT) rhythms following an abrupt 6-h phase advance of the LD cycle in the horse.MethodsSix healthy, 2 yr old mares entrained to a 12 h light/12 h dark (LD 12:12) natural photoperiod were housed in a light-proofed barn under a lighting schedule that mimicked the external LD cycle. Following baseline sampling on Day 0, an advance shift of the LD cycle was accomplished by ending the subsequent dark period 6 h early. Blood sampling for serum melatonin analysis and BT readings were taken at 3-h intervals for 24 h on alternate days for 11 days. Disturbances to the subsequent melatonin and BT 24-h rhythms were assessed using repeated measures ANOVA and analysis of Cosine curve fitting parameters.ResultsWe demonstrate that the equine melatonin rhythm re-entrains rapidly to a 6-h phase advance of an LD12:12 photocycle. The phase shift in melatonin was fully complete on the first day of the new schedule and rhythm phase and waveform were stable thereafter. In comparison, the advance in the BT rhythm was achieved by the third day, however BT rhythm waveform, especially its mesor, was altered for many days following the LD shift.ConclusionAside from the temperature rhythm disruption, rapid resynchronization of the melatonin rhythm suggests that the central circadian pacemaker of the horse may possess a particularly robust entrainment response. The consequences for athletic performance remain unknown.

Prognostic significance of circadian variability of RR and QT intervals and QT dynamicity in patients with chronic heart failure

In patients with chronic heart failure (CHF), circadian variability of RR and QT intervals may be altered because of neurohumoral activation and functional and structural remodeling of the heart. The aim of this study was to evaluate the prognostic significance of circadian variability of the RR and QT intervals and QT dynamicity (QT/RR slope) in CHF patients. We prospectively enrolled 121 patients with stable CHF in sinus rhythm (age 67 +/- 14 years, mean +/- SD; range 34 to 87 years). The RR, QT, and rate-corrected QT (QTc) intervals and the QT/RR slope measured from 24-hour Holter electrocardiogram were fitted by cosine curves. During the follow-up period of 34 +/- 17 months, 40 (33%) patients died of cardiac causes, 10 of which were sudden. All patients showed significant circadian rhythms in the RR, QT, and QTc intervals and the QT/RR slope by cosine-curve fitting. In addition to the expected higher heart rate, longer QT interval, and steeper QT/RR slope, we found that patient who died of cardiac causes had reduced circadian variability of QT interval (10 +/- 10 ms vs 21 +/- 13 ms) and a later maximum RR interval (4.1 +/- 0.9 AM vs 2.3 +/- 2.1 AM) compared with survivors, among many other statistically significant circadian parameter differences. These 2 parameters were independent predictors of cardiac death in multivariate Cox proportional hazards regression analysis. Circadian variability analyses of Holter-derived RR and QT intervals may provide prognostic information beyond that provided by 24-hour averages of these parameters.

Stability of Melatonin and Temperature as Circadian Phase Markers and Their Relation to Sleep Times in Humans

Circadian rhythms of core body temperature and melatonin are commonly used as phase markers of the circadian clock. Melatonin is a more stable marker of circadian phase when measured under constant routine conditions. However, little is known about the variability of these phase markers under less controlled conditions. Moreover, there is little consensus about the preferred method of analysis. The objective of this study was to assess various methods of calculating melatonin and temperature phase in subjects with regular sleep schedules living in their natural environment. Baseline data were analyzed from 42 healthy young subjects who were studied on at least two occasions. Each hospital admission was separated by at least 3 weeks. Subjects were instructed to maintain a regular sleep schedule, which was monitored for 1 week before admission by sleep logs and actigraphy. Subjects spent one habituation night under controlled conditions prior to collecting baseline temperature and melatonin measurements. The phase of the melatonin rhythm was assessed by 9 different methods. The temperature nadir (Tmin) was estimated using both Cleveland and Cosine curve fitting procedures, with and without demasking. Variability between admissions was assessed by correlation analysis and by the mean absolute difference in timing of the phase estimates. The relationship to sleep times was assessed by correlation of sleep onset or sleep offset with the various phase markers. Melatonin phase markers were more stable and more highly correlated with the timing of sleep than estimates of Tmin. Of the methods for estimating Tmin, simple cosine analysis was the least variable. In addition, sleep offset was more strongly correlated with the various phase markers than sleep onset. The relative measures of melatonin offset had the highest correlation coefficients, the lowest study-to-study variability, and were more strongly associated with sleep timing than melatonin onsets. Concordance of the methods of analysis suggests a tendency for the declining phase of the melatonin profile to be more stable and reliable than either markers of melatonin onset or measures of the termination of melatonin synthesis.

Chronic exposure to ELF magnetic fields during night sleep with electric sheet: effects on diurnal melatonin rhythms in men.

The possible effects of repeated night-time exposure to an extremely low frequency magnetic field (ELF-MF) on melatonin were investigated in nine healthy male subjects aged 23-37 yr. The 16-week experiment consisted of 3 weeks of pre-exposure, 11 weeks of night-time exposure to MF generated from a nonheated electric sheet (ES), and 2 weeks of post-exposure recovery observation. The average MF intensity (rms, mainly 50 Hz AC) on the surface of the sheet was 0.7 microT at the head, 8.3 microT at the waist, and 3.5 microT at the feet of the subject. For each of the urine samples collected 5 times a day on scheduled sampling days, the urinary excretion rate (ng/h) of melatonin was determined, and 24 h rhythms were extracted for each subject and each experimental period (pre-exposure, first half and latter half exposure, and post-exposure periods) by the method of complex cosine curve fitting. Although estimates of the peak height, acrophase, and total daily amount of melatonin were characterized by significant variations among individual subjects, they did not reveal any statistically significant difference between exposure periods and nonexposure periods. Thus, the present study indicates that any profound effect of the MF originating from an ES on nocturnal melatonin production and its circadian rhythm is unlikely.

Circadian rhythms of lipoprotein lipase and hepatic lipase activities in intermediate metabolism of adult rat.

Although intermediate metabolism is known to follow circadian rhythms, little information is available on the variations in lipoprotein lipase (LPL) and hepatic lipase (HL) activities during the 24-h period, and there is also a lack of adequate statistical analysis. Here, adult male rats were fed ad libitum and kept at 21 degrees C under 12:12-h light-dark cycles. They were killed in batches every 3 h over a 24-h period. Lipase activities were determined in plasma and fresh homogenates of epididymal white adipose tissue (EWAT), interscapular brown adipose tissue (IBAT), heart, skeletal muscle, and liver. Plasma insulin, corticosterone, glucose, triacylglycerol (TAG), cholesterol, glycerol, beta-hydroxybutyrate, and liver and muscle glycogen were determined. Cosinor analysis was used to evaluate the presence (significance of fit of cosine curve to data and variance explained by rhythm) and characteristics of possible circadian rhythms [acrophase (phi), mesor, and amplitude]. Statistically significant circadian rhythms were detected for 1) all metabolites studied, except TAG, cholesterol, and liver HL activity; 2) LPL and HL activity in plasma (both phi in light phase); and 3) LPL activity in all tissues studied (phi: heart in light phase; skeletal muscle, IBAT, and EWAT in dark phase). Liver also showed a circadian rhythm of LPL activity, with phi near that in plasma. These findings demonstrate for the first time that, in physiological conditions, LPL activities in plasma and various tissues, including liver, and HL activity in plasma follow circadian rhythms. Their metabolic significance is discussed.

Circadian rhythms of early morning awakening insomniacs

It has been suggested that two types of insomnia, sleep onset insomnia and early morning awakening insomnia, may be caused by delays and advances respectively of circadian rhythms. Evidence supports the circadian rhythm phase delay of sleep onset insomniacs. The present study investigated the phase timing of circadian rhythms of early morning awakening insomniacs compared with a group of age matched good sleepers. A 24-h bed rest laboratory session was used to evaluate the endogenous core body temperature and urinary melatonin rhythms. Objective and subjective sleepiness were also measured every 30 min across the session with 10 min multiple sleep latency tests and Stanford Sleepiness Scale. Maximum and minimum phases of each individual's rhythm were identified using two-component cosine curve fitting. Compared with the good sleepers, the insomniacs had significant phase advances of 2-4 h for the temperature and melatonin rhythms. However, the 0-4 h advances of the sleepiness rhythms were not significant. This latter unexpected result was explained on the basis of variability of sleepiness measures. It was suggested that early morning awakening insomnia arises from phase advanced circadian rhythms which evoke early arousal's from sleep.

Amplitude regulation of episodic release, in vitro biological to immunological ratio, and median charge of human chorionic gonadotropin in pregnancy.

In the present study, we examined the regulation of 24-h serum immunoreactive levels, in vitro biological to immunological (B/I) ratio, and median charge of circulating CG at the end of the first, second, and third trimesters of human gestation. Seven pregnant women were prospectively studied at 12-15, 23-26, and 35-38 weeks of gestation. Blood was sampled every 20 min over a 24-h period, and serum CG concentrations were determined by RIA. Pulse detection and analysis of the 24-h rhythm of serum immunoreactive CG concentrations were carried out by the program Cluster and cosine curve fitting, respectively. The in vitro biological activity of circulating CG was determined by the mouse Leydig cell-testosterone production bioassay, and the median charge of its isoforms was determined by zone electrophoresis in agarose suspension. The immunoreactive levels of CG present at the end of each trimester of gestation fluctuated over a 24-h period; such variability exceeded that of the within-assay coefficient of variation of the CG RIA and could be resolved into a series of CG peaks and valleys. Although no trend in the number of peaks or valleys was systematically found in relation to gestational age, comparisons between the amplitude and area of the CG peaks revealed that these pulse parameters were significantly higher at 12-15 weeks than at 23-26 and 35-38 weeks of gestation. Cosine fits for 24-h rhythms revealed the existence of significant nyctohemeral profiles of serum CG levels in all women studied at 12-15 weeks, in four subjects at 23-26 weeks, and in six women at 35-38 weeks gestation. The time of acrophase was highly homogeneous only between 12-15 weeks of gestation, occurring between 1057-1452 h in six of the women. The in vitro B/I ratio of CG contained in serum pools from 12-15 weeks was significantly (P < 0.05) higher than that exhibited by CG during later gestational periods (B/I ratio at the end of first trimester, 1.14 +/- 0.14; second trimester, 0.87 +/- 0.22; third trimester, 0.79 +/- 0.12). hCG isoforms at 12-15 weeks were more negatively charged than those circulating at 23-26 and 35-38 weeks of gestation. There were no significant differences between the B/I ratio and the median charge of CG molecules from the second and third trimesters. We conclude that serial serum concentrations of CG throughout pregnancy show significant amplitude-modulated pulsatile release and nyctohemeral variations.(ABSTRACT TRUNCATED AT 400 WORDS)

The Sleep-Evoked Decrease of Body Temperature

The circadian rhythm of deep body temperature consists of both an endogenous component and evoked components resulting from exogenous influences. Previous studies of the sleep-evoked effect have failed to control confounding influences, so that the effect of sleep per se has not been established. In the present study, eight good sleepers had their rectal temperatures recorded for 24 hours in each of two laboratory conditions employing a constant routine to control exogenous influences. Sleep was allowed at night in one condition. Following sleep onset, body temperature dropped more rapidly and remained lower than when wakefulness continued over the same time, resulting in a mean sleep-evoked decrease of 0.31 +/- 0.09 degree C. Fourier regression analysis showed a significant 24-hour (circadian) temperature rhythm, together with a 12-hour harmonic rhythm, in each condition. Circadian rhythm parameters were also altered by the sleep-evoked (or masking) effect, with the amplitude increased and the mean decreased when subjects slept at night in the constant routine. It was suggested that a constant routine methodology be used in studies of circadian rhythm differences and that Fourier regression be used in preference to simple cosine curve fitting to give a better approximation of the temperature rhythm.

Alteration of circadian rhythm in shift-working ambulance personnel. Monitoring of salivary cortisol rhythm.

In order to investigate the relationship between internal desynchronization and clinical intolerance to shift work, a set of circadian rhythms including salivary cortisol rhythm were monitored in seven shift-working ambulance personnel. Oral temperature, grip strength of both hands, subjective assessment of drowsiness, fatigue and attention were recorded approximately every four hours except during sleep, for seven days. Self-sampling of salivary cortisol, which was suitable evaluation of endocrine rhythm in field studies, was also tried in this study. cosinor (cosine curve fitting) method and power spectral analysis were used for time series data analysis. The internal desynchronizations between rhythms of physiological variables and sleep-wake cycle were observed in shift-working ambulance personnel. The incidence of internal desynchronization seemed to be higher in intolerant subjects, although the difference between tolerant and intolerant subjects did not reach a statistically significant level. The peak time of salivary cortisol rhythm during a twenty-four hour shift was phase-advanced as intolerant to shift work showed apparently an atypical circadian pattern of salivary cortisol with an abnormal peak at 21.00 h. In this subject, the clinical intolerance to shift work seemed to be associated with internal desynchronization of circadian rhythms. The present study confirmed the internal desynchronization of the circadian rhythm in physiological rhythms like oral temperature and grip strengths, and was in favour of the hypothesis of an internal desynchronization and clinical intolerance to shift work. The clinical implication of impairment of salivary cortisol rhythm remains to be further investigated.

Age-related changes in circadian sleep-wakefulness rhythms in male rats isolated from time cues

Sleep-wakefulness rhythms were recorded for at least 5 consecutive days in young adult ( n=6; 5–8 months) and old ( n=4; 30–32 months) rats. During the continuous recordings the rats were maintained in isolated cabins under constant temperature and constant dim, red light. The period length and amplitude of the free-running circadian rhythms of wakefulness (W), slow wave sleep (SWS) and desynchronized sleep (DS) were estimated by means of a cosine curve fitting program. Age-related amplitude differences were absent under the constant recording conditions. The circadian period of the W- and DS-rhythms, however, was significantly shorter in the old rats. These results are consistent with the notion that circadian organization is changed in old age.

Circadian rhythms determined by cosine curve fitting: Analysis of continuous work and sleep-loss data

In this study, we report the effects of sleep loss upon circadian rhythm parameters analyzed by the cosine curve fitting (cosinor) method. Rhythm alterations are described as reductions in rhythm strength, increases in individual variations producing an increase in the 95% confidence limits, and reductions in rhythm amplitude. Subjects worked continuously at tasks for 45 h with time-of-day cues. Circadian cycles in physiological and mood variables remained intact, but rhythms in some task performance measures no longer showed significant 24-h/cycle activities. The relationship between oral temperature, mood, and pulse rhythms continued undisturbed during the continuous work period; however, the performance linkage to oral temperature was lost. These findings direct attention to individual difference in susceptibility to continuous work periods and suggest that 24-h rhythms in some performance and physiological measures perhaps are more readily responsive to an altered wake/sleep cycle than other circadian rhythms.

Non-circadian periodicity in the duration of the cell cycle and the G1 phase in the hindlimb epidermis of the anuran tadpole, Rana pipiens.

Using the percentage labeled mitoses method, seven cell cycle determinations were initiated at 6-hr intervals over a 36-hr span in order to see if the cell cycle in the tadpole hindlimb epidermis varied with time or showed rhythmicity. There was a pattern of two long cell cycles followed by a shorter one. Total cell cycle length (Tc) and the length of the G1 phase plus one-half of the mitotic time (TG1 + 1/2M) fluctuated the most, although only TG1 + 1/2M varied significantly with the Chi-square test. The proportion of TC spent in each phase was also calculated. Only TG1 + 1/2M/TC had statistically significant fluctuations with time. Rhythmicity was analyzed by a computer program using the method of least squares for cosine curve fitting. Statistically significant ultradian rhythms of 18.4 hr in TC, 18.5 hr in TG1 + 1/2M and 18.6 hr in TG1 + 1/2M/TC and the length of the DNA synthetic phase/total cell cycle length (TS/TC) were found. Circadian rhythmicity was not observed. The acrophases of the ultradian rhythms of TC and TG1 + 1/2M coincided, suggesting that the rhythm of TC was due mainly to variation in TG1 + 1/2M. In the absence of significant variation in TS, the longest phase of the cell cycle, whenever G1 + 1/2M was short, TS/TC increased, so that the 18.6 hr rhythm in TS/TC was also a result of the periodicity in TG1 + 1/2M.