The present study shows that the cosinor method can be used to retrospectively analyze diurnal variation in clinical data, but that it is associated with a number of limitations. In two-thirds of the subjects, the rhythm was not reproducible in the long-term.
Technically, it was possible to fit a cosine curve to the data and the fit seemed well-constrained in the majority of cases. Generally, variations of IOP can be analyzed quantitatively using sophisticated mathematical methods. For some of these methods, like autocorrelation, Fourier analysis, or Enright periodograms, time intervals between measurements have to be evenly spaced and sufficiently short [16]. Thus, we performed cosinor analysis, a method which is based on the assumption that a cosine curve is an adequate mathematical model to describe diurnal fluctuation of IOP [13]; the superimposed IOP fluctuations that do not follow a 24-hour rhythm are then considered biological noise [17]. This method has been widely used in research on IOP variation [9, 11, 18]. We have not measured IOP between midnight and 7 am. Theoretically, if a cosine curve is a good model of rhythmic IOP variation and there is not too much sporadic fluctuation superimposed, cosine analysis still yields valid results, because the peak in the early morning hours can be inferred from the other data. However, due to the lacking measurements between midnight and 7 am, the risk of an inaccurate estimate increases disproportionately high if rhythmic variation of IOP deviates from a cosine curve or if large sporadic fluctuations are superimposed.
On average, the IOP was lowest at the last measurement at midnight. Moreover, the IOP peaks occurred mostly early during the day between 6 am and noon. These findings are in line with older clinical studies [19, 20], but they differ from results from prospective studies in sleep labs [9–11]. This indicates that we may have missed IOP peaks in the early morning hours due to the gap in our clinical data between midnight and 7 am. Another reason for the lower at night in our study may have been underestimation of nocturnal IOP by measuring in the sitting position. However, this cannot be the only reason because, contrary to our data, Liu et al. [10] have found higher IOP at night despite measuring in a sitting position, whereas Quaranta and coworkers [21] have not found a systematic increase of IOP at night even when measuring in a habitual position (i.e. sitting position during the day, supine at night). Therefore, the ultimate reason for the different timing of IOP peaks in different studies is not known – it may be associated with other details of the setting and the protocol of the measurements.
In our study, the IOP rhythms were not reproducible in the long-term. Thus, the notion of an individual IOP rhythm as it was postulated by Duke-Elder [5] cannot be confirmed by our data. Currently, it is not clear how robust the rhythm of this 24-h variation is in the long-term [16], that is how much the pattern of IOP curves changes over the years. The reproducibility of IOP rhythms, even in the short term, has recently been questioned [22–24]. This is supported by our data: only in one third of our subjects, the Rayleigh test showed statistically significant mean direction of acrophases over the years. This variability in the timing of IOP variation may be explained by synchronization of the internal clock to environmental influences, by external rhythmic influences on IOP, or by the inability of cosinor analysis to detect an underlying stable 24-hour rhythm in some cases due to superimposed non-rhythmic IOP variations, like physical activity, or intake of caffeine or alcohol. Newer studies that attempt a continuous measurement of IOP in primates and humans also show that the behavior of IOP is very dynamic [22, 25].
We were able to demonstrate that IOP rhythms were more reproducible when the environment was more strictly controlled. Only 16 of the 52 subjects were hospitalized each year for acquisition of the IOP curve. These subjects were significantly more likely to have a stable rhythm of IOP in the long term than subjects in whom ambulatory IOP profiles were performed on some occasions or even every single time. In other words, the more standardized the environment, the higher the stability of acrophase over the years. On the other hand, although a highly standardized environment is desirable in a scientific setting, it may limit the external validity of the resultant IOP curves.
Therefore, the interpretation of these results is limited by the study design, and the value of cosinor analysis for retrospective examination of IOP rhythms in longitudinal clinical data may be limited. However, in subjects with stable rhythm a phase lag in subjects with PDS was observed. This is an intriguing finding, although it does not seem to have any immediate clinical applications.
The reasons for the observed phase lag in IOP rhythm in subjects with PDS are not known, and they cannot be concluded from our data. Changes in biological rhythms are generally caused by one of three conditions: altered phase timing of the endogenous clock, alterations of the effector mechanisms, or external influences [26]. One possible explication that comes to mind in PDS are rhythmic changes in the release of pigment granules into the anterior chamber [27]. Rhythmic changes in the amount of pigment released may be caused either by increased physical activity during the day [28, 29], or by changes in diameter of the pupil [30]. Although no explanation can be given from our data, it may indicate that beside hormonal and neural mechanisms, local factors may modify the diurnal variation of IOP. Because of the limitations of the retrospective study design, this finding needs to be confirmed in a carefully designed clinical study. This finding may indicate that in some instances, cosinor analysis may in fact be applied to generate hypothesis from clinical data.
The importance of diurnal fluctuation of IOP for development or progression of glaucoma is subject to controversy and cannot be discussed in much detail here; please see Sultan et al. [31] and Quaranta et al. [4] for a thorough review of the literature. Most studies are concerned with the magnitude of IOP fluctuations, either completely disregarding the timing of these fluctuations [32, 33] or distinguishing mainly between peaks during and outside office hours [34, 35]. However, very little is known about the importance of IOP rhythms for progression. More important, clinical studies that do show association between changes in IOP rhythms and glaucoma [5, 6, 14, 36] cannot distinguish between cause and effect. Only Noël and coworkers [12] have not found any differences in IOP rhythm between healthy volunteers and glaucoma patients. Experimental studies, for example in an animal model, are needed to clarify this. It seems likely that the influence of IOP rhythms on glaucoma progression cannot be analyzed without looking at the circadian variation of other biological factors, especially blood pressure [4, 30].
Limitations
The presented study is a retrospective analysis of data that was not primarily intended for studying chronobiology of IOP. Measurements were not equally spaced throughout the 24 hours and no measurements were made between midnight and 08:00 h. Significant changes in IOP that may have occurred during this time period may have been systematically missed. Another limitation of the present study is the relatively small sample size. Thus, confirmation of the presented findings in a study with more subjects is desirable.
Furthermore, the time of sleep onset and offset was not recorded in our study, and no independent markers showing a circadian rhythm (such as body temperature or blood cortisol level) were monitored. As a result, we cannot be certain to what degree fluctuations were caused by circadian rhythms or by rhythmic environmental influences [26]. Short exposure of subjects to light may have taken place during the measurements at 21:00 h and 24:00 h. The influence of this exposure cannot be determined; however, in a study by Liu et al., short exposure to low levels of light did not seem to cause relevant disruption of the pattern of IOP fluctuation [37].
All IOP measurements, including those at midnight, were taken in a sitting position using Goldmann tonometry. It is known that posture does influence IOP, and there is a significant increase of IOP in the supine position [38]. Consequently, habitual variation of IOP (i.e. when all measurements are taken in the habitual position for that time of day) exhibits a different pattern due to the postural increase in IOP in the supine position at night [9, 10]. The lack of measurements in the supine position in our study may limit the validity of the absolute IOP measurements at night and may have lead to a different pattern of IOP variation, but it should not have influenced our primary end-point: the long-term stability of diurnal IOP curves.
In the final analysis, a bias may have been introduced by the exclusion of subjects with a non-significant Rayleigh test. On the other hand, the interpretation of long-term data from subjects with high variability in phase timing from year to year would have been difficult. Selection of any single IOP curve or comparison of accumulated individual IOP curves (that is individual mean acrophase) seemed pointless in subjects with an erratic pattern of IOP variation.
Further research
The interesting findings of our retrospective analysis should ideally be confirmed and further explored in prospective studies. These studies might include control of the wake-sleep-cycle as well as the light–dark-cycle and control of the activity of the subjects. The latter can be achieved with a wrist device. If possible, an independent marker of the circadian system, for example, body temperature or plasma cortisol levels, should also be determined several times per day.
Specific factors associated with PDS should be examined more closely. The role of physical activity on the diurnal fluctuation of IOP in subjects with PDS may be clarified by comparing IOP profiles under regular activity to IOP profiles under bedrest conditions, similar to the study by Buguet et al. [11]. In addition, the concentration of melanin granules in the anterior chamber using a laser flare-cell meter should be determined several times during the 24-h cycle [39, 40].
In the long term, continuous measurement of IOP would be desirable. Initial experiments have been conducted using a telemetry system with an intraocular manometer in non-human primates and a contact lens in humans [22, 25]. However, methods to analyze these complex IOP curves have not yet been established.