WO2009073811A2

WO2009073811A2 - System and method to quantify circadian entrainment disruption

Info

Publication number: WO2009073811A2
Application number: PCT/US2008/085579
Authority: WO
Inventors: Andrew Bierman; Mark Rea; Mariana Figueiro; John Bullough
Original assignee: Rensselaer Polytechnic Institute
Priority date: 2007-12-04
Filing date: 2008-12-04
Publication date: 2009-06-11
Also published as: WO2009073811A3

Abstract

A method of quantifying circadian entrainment disruption is disclosed. At least one time series set of activity information is obtained. At least one time series set of light-dose information is obtained which corresponds to the at least one set of activity information. The at least one set of light-dose information is transformed with a logistic stimulus response function. The transformed activity information and the transformed light-dose information are circularly cross-correlated to yield an entrainment correlation function. The entrainment correlation function is spectrally analyzed. A phasor analysis of the entrainment correlation function is completed based at least in part on the spectral analysis of the entrainment correlation function. A system for quantifying circadian entrainment disruption is also disclosed.

Description

SYSTEM AND METHOD TO QUANTIFY CIRCADIAN ENTRAINMENT DISRUPTION

RELATED APPLICATIONS

[0001] This patent application claims priority to provisional U.S. patent application 60/992,135 filed on December 4, 2007 and entitled, "METHOD TO QUANTIFY CIRCADIAN ENTRAINMENT-DISRUPTION." The 60/992,135 provisional patent application is hereby incorporated by reference in its entirety.

[0002] This invention was made with government support under contract 1RO1OH008171 awarded by the National Institute of Environmental Health Sciences (NIEHS) and under contract 1UO1DA023822-01 awarded by the National Institute on Drug Abuse (NIDA). The government has certain rights in the invention.

FIELD

[0003] The claimed invention relates to the quantification of circadian-related data, and more specifically to methods and systems for quantifying circadian entrainment-disruption and circadian time.

BACKGROUND

[0004] As the Earth rotates, all species on the surface of the planet are exposed to twenty-four-hour patterns of light and darkness. In response to these regular, daily oscillations to the natural light-dark cycle, we have evolved endogenous circadian rhythms that repeat approximately every twenty- four hours. Examples of circadian rhythms include oscillations in core body temperature, hormone secretion, sleep, and alertness. Circadian oscillations exist at a cellular level, including cell mitosis and DNA repair. These oscillations are a result of a small group of clock genes inside the cell nuclei creating interlocked transcriptional and post-translational feedback loops. The timing of these circadian genes is generally orchestrated by a master biological clock located in the suprachiasmatic nuclei (SCN) of the hypothalamus of the brain. The master clock in the SCN provides precise time cues throughout the body to regulate these diverse physiological, hormonal, and behavioral circadian patterns. However, in total darkness the timing of the SCN will become asynchronous with the solar day because the period of the master clock in humans is slightly longer than twenty- four hours. To maintain synchrony with the external world, the light-dark HRFM Docket 0094.142AWO RPI OTC case 1197 pattern incident on the retina resets the timing of the SCN every day, so that as seasons change or as we travel across time zones, we can entrain our biological functions to the local environment. If the period of the light-dark pattern is too long or too short, or if the light and dark exposures become aperiodic, the master clock can lose control of the timing of peripheral circadian clocks.

[0005] Maintaining the phase-relation ordering of the various circadian rhythms from molecular to behavioral levels is crucial for coordinated function throughout the human body. Lack of synchrony between the master clock and the peripheral clocks can lead to asynchronies within cells (e.g., cell cycle) and between organ systems (e.g., liver and pancreas). This breakdown in synchrony, as demonstrated most profoundly with jet lag, disrupts sleep, digestion, and alertness. Chronic disruptions can contribute to cardiovascular anomalies and accelerated cancerous tumor growth in animal models. In humans, epidemiological studies have shown that rotating-shift nurses, who experience a marked lack of synchrony between activity-rest patterns and light-dark cycles, are at higher risk of having breast cancer compared to day-shift nurses. In fact, the World Health Organization has identified nightshift work as a probable cause of cancer. In addition to heightened cancer risks, other disorders have been associated with nightshift work, such as diabetes and obesity, suggesting again a role for circadian disruption in the development and progression of diseases.

[0006] Despite the growing evidence that circadian disruption negatively affects human health, the logical chain linking light-induced circadian disruption to morbidity and mortality still has not been established. If the impact of circadian disruption is to be studied with any degree of accuracy, it is important to quantitatively characterize light and dark as it affects the human circadian system because the light-dark pattern is the primary synchronizing stimulus for our circadian system. It is also necessary to quantify the temporal characteristics of circadian light and dark exposures actually experienced by people. Without quantification of the actual circadian light and dark exposures experienced by people, it will be difficult to relate the findings from controlled laboratory studies of light-induced circadian disruption in humans to the expected health of any human sub-population, including nightshift workers. These actual circadian light and dark exposures in human populations must also be incorporated into parametric studies using animal models as surrogates for particular human diseases or maladies if we are to gain any detailed insight into the role of circadian disruption on human health. Since nocturnal species are used almost exclusively as animal models in this research, a method needs to be established to relate actual circadian light and dark HRFM Docket 0094.142AWO RPI OTC case 1197 exposures in humans to parametrically controlled exposures of light and dark using animal models.

[0007] Therefore, a methodology to quantify circadian entrainment-disruption in both diurnal and nocturnal species is needed, so as to allow researchers to make direct comparisons of circadian entrainment and disruption across species.

SUMMARY

[0008] A method of quantifying circadian entrainment disruption and time is disclosed. At least one time series set of activity information is obtained. At least one time series set of light-dose information is obtained which corresponds to the at least one set of activity information. The at least one set of light-dose information is transformed with a logistic stimulus response function. The activity information and the transformed light-dose information are cross-correlated to yield an entrainment correlation function. The entrainment correlation function is spectrally analyzed. A phasor analysis of the entrainment correlation function is completed based at least in part on the spectral analysis of the entrainment correlation function.

[0009] A system for quantifying circadian entrainment disruption is also disclosed. The system has a processor configured to complete a phasor analysis of an entrainment correlation function based at least in part on a spectral analysis of the entrainment correlation function which is the result of cross-correlating activity information and light-dose information which has been transformed with a logistic stimulus response function. The system also has a data input coupled to the processor and configured to provide the processor with the light-dose information and the activity information. The system further has a user interface coupled to either the processor or the data input.

[00010] A new framework is provided for the study of the effects of circadian entrainment-disruption on human health, emphasizing three important links in the logical chain, relating circadian disruption to maladies such as breast cancer, obesity, and sleep disorders. First, circadian light (and dark) for humans and for animal models can now be quantitatively defined to such a degree that meaningful studies of light as a stimulus for circadian disruption can now be undertaken, not only in humans but in nocturnal rodents as well. Without quantitative definitions of the light stimuli, it would simply be impossible to understand the results of any ecological study of circadian disruption on human health or how laboratory studies using animal models relate to the human condition. Second, with an understanding of circadian light, it is now possible to measure the synchrony between light- HRFM Docket 0094.142AWO RPI OTC case 1197 dark and activity-rest patterns in actual human living environments using tools which collect activity and light-dose data. These ecological light and activity data are necessary to develop the essential insights into circadian entrainment and disruption actually experienced by people affected by modern maladies. Third, it is now possible to simply and quantitatively characterize degrees of circadian entrainment-disruption; that is, the levels of synchrony between light-dark exposures and activity-rest, in both humans and animal models. A focus on entrainment, rather than light per se or activity alone, makes it possible to relate ecological studies of diurnal humans to parametric studies of diseases using nocturnal animal models. In other words, parametric studies of circadian disruption employing animal models for human diseases can now be designed and conducted so as to more accurately reflect their relevance to the actual living conditions in humans.

[00011] It should be emphasized, too, that the methods presented here are not limited to the study of behavioral entrainment. Rather, this analysis provides the basis for assessing entrainment of other outcome measures from the circadian system, such as core body temperature or melatonin synthesis, to light-dark patterns. From these envisioned studies, modern maladies like diabetes, obesity, and poor sleep, as well as breast cancer and cardiovascular disease, can be meaningfully and systematically investigated. More important perhaps, forging the links identified herein will significantly accelerate our understanding of the role of circadian disruption on human health and thereby may accelerate medical treatment of these maladies with light and with drugs. The techniques identified here also imply that, in the future, it will be possible to examine circadian entrainment and disruption on an individual basis so that each person can be treated with the appropriate light-dark exposure and/or with the appropriate pharmaceutical interventions at the optimum circadian time.

BRIEF DESCRIPTION OF THE DRAWINGS

[00012] FIG. 1 schematically illustrates an embodiment of an activity and light-dose sensing device.

[00013] FIG. 2 illustrates an embodiment of a spectral-opponent subadditive response of a circadian system to polychromatic light.

[00014] FIG. 3 illustrates an embodiment of a transfer function relating a circadian light stimulus to nocturnal melatonin suppression.

[00015] FIG. 4A illustrates activity data for a day shift nurse plotted as a function of time. HRFM Docket 0094.142AWO RPI OTC case 1197

[00016] FIG. 4B illustrates activity data for a rotating shift nurse plotted as a function of time.

[00017] FIG. 4C illustrates light exposure data for the day shift nurse of FIG. 4A plotted as a function of time.

[00018] FIG. 4D illustrates light exposure data for the rotating shift nurse of FIG. 4B plotted as a function of time.

[00019] FIG. 5A illustrates one embodiment of an entrainment correlation function relating activity and light exposures for an example day-shift nurse.

[00020] FIG. 5B illustrates one embodiment of an entrainment correlation function relating activity and light exposures for an example rotating shift nurse.

[00021] FIG. 6A illustrates one embodiment of an entrainment correlation function relating activity and light exposures for an example rat exposed to a regular twelve hours of light followed by twelve hours of darkness pattern (12L: 12D).

[00022] FIG. 6B illustrates one embodiment of an entrainment correlation function relating activity and light exposures for an example rat exposed to a 12L: 12D cycle that was phase-reversed every forty-eight hours.

[00023] FIG. 7 illustrates example phasor amplitudes as a function of fundamental phasor period for a group of day-shift nurses.

[00024] FIG. 8 illustrates peak phasor amplitudes calculated from quadratic curve fits shown in FIG. 7 as plotted against the fundamental phasor period.

[00025] FIG. 9A illustrates an embodiment of a phasor diagram quantifying circadian entrainment disruption for a group of day shift nurses.

[00026] FIG. 9B illustrates an embodiment of a phasor diagram quantifying circadian entrainment disruption for a group of rotating shift nurses.

[00027] FIG. 1OA illustrates an embodiment of a phasor diagram quantifying circadian entrainment disruption for a group of entrained nocturnal rats.

[00028] FIG. 1 OB illustrates an embodiment of a phasor diagram quantifying circadian entrainment disruption for a group of disrupted nocturnal rats.

[00029] FIG. 11 illustrates an embodiment of mean phasors for the nurses and rats of

FIGS. 9A-10B.

[00030] FIG. 12A illustrates an example plot of the phasor magnitudes for the day-shift nurses and rotating- shift nurses of FIGS. 9A-9B.

[00031] FIG. 12B illustrates an example plot of the phasor magnitudes for the entrained and disrupted nocturnal rats of FIGS. 10A-10B. HRFM Docket 0094.142AWO RPI OTC case 1197

[00032] FIG. 13 illustrates one embodiment of a method of quantifying circadian entrainment disruption.

[00033] FIG. 14 illustrates one embodiment of a system for quantifying circadian entrainment disruption.

[00034] It will be appreciated that for purposes of clarity and where deemed appropriate, reference numerals have been repeated in the figures to indicate corresponding features, and that the various elements in the drawings have not necessarily been drawn to scale in order to better show the features.

DETAILED DESCRIPTION

[00035] FIG. 1 schematically illustrates an embodiment of an activity and light-dose sensing device 20. An activity and light-dose sensing device 20 measures and characterizes light available for entering a person's eye. The light-dose sensing aspect of the device 20 may be configured to measure and characterize a variety of conditions, for example, but not limited to light intensity, light spectrum, light spatial distribution, and timing / duration of the light. Although in the illustrated embodiment, photosensors 22 for sensing a light-dose are mounted substantially at eye-level, in other embodiments, the one or more photosensors could be mounted in other locations, such as on a different location of the person, on a work surface, or remote from the person. The device 20 also has an activity sensor 24 for recording head movements to differentiate between rest/sleep periods and active/awake periods. In other embodiments, the activity sensor could be mounted on a different location of the person or be located remotely from the person as in the case of an infrared motion sensor. Embodiments of activity sensors 24 which are mounted or worn on a person may utilize accelerometers, mercury switches, or the like to sense motion. Depending on the embodiment, the activity and light dose sensing device 20 may have one or more light sensors 22 which are coupled to the one or more activity sensors 24, such as the embodiment illustrated in FIG. 1. In other embodiments, however, the one or more light sensors 22 and the one or more activity sensors may exist as separate devices. Depending on the embodiment, the activity and light dose sensing device 20 may have one or more of signal filtering circuitry, signal processing circuitry, storage circuitry for storing data locally or on a removable storage device, and wired or wireless communication circuitry for transferring stored, buffered, or live data which is collected to a remote processor for analysis or to a remote database for storage. The circuitry may include a computer, a microprocessor, an HRFM Docket 0094.142AWO RPI OTC case 1197 application specific integrated circuit (ASIC), digital electronics, analog electronics, or any combination or plurality thereof.

[00036] A device called a Daysimeter, available from Rensselaer Polytechnic Institute is one example of an activity and light-dose sensing device 20. The Daysimeter was developed as a head-worn light-dosimeter and activity monitor to address measurements of the spectral and spatial response of the human circadian system. As with the device illustrated in FIG. 1, with the Daysimeter, two photosensors are used to characterize the spectral-opponent, subadditive response of the circadian system to polychromatic light and thereby provide measurements of the circadian light stimulus (CS) for humans. FIG. 2 illustrates an embodiment of such a spectral-opponent subadditive response of a circadian system to some polychromatic light. [00037] A transfer function relating CS to nocturnal melatonin suppression was also developed to characterize the effective stimulus for non-visual responses associated with optical radiation on the retina (illustrated in FIG. 3). Entrainment to the circadian light-dark pattern is not directly related to nocturnal melatonin suppression, however as demonstrated by Zeitzer et al in J. Physiol. 526,695 (2000), both light-induced phase shifting and nocturnal melatonin suppression appear to have similar, if not identical, functional relationships to optical radiation of the same spectral power distribution. The Daysimeter also measures head movements with solid-state accelerometers to characterize behavioral activity. More detailed information about the Daysimeter is available elsewhere, for example: A. Bierman, T. R Klein, M. S. Rea, Meas. Sci. Technol. volume 16, 2292 (2005). For simplicity, the Daysimeter will be referred to throughout the specification, however it should be understood that other types of activity and light-dose sensing devices 20 may be used.

[00038] Activity as measured by the Daysimeter is not a direct measure of the endogenous clock in the SCN. Like every downstream measure of circadian function, behavioral activity can only yield partial insight into circadian entrainment. For this reason, the synchrony between light-dark and activity-rest as measured by the Daysimeter should be more precisely operationally defined as "behavioral entrainment." Since, however, it is presently impossible to directly measure SCN activity, and thus entrainment in the purest sense in living and active humans, the term "entrainment" will be used in this document to describe the observed levels of synchrony between light- dark exposures and activity-rest responses as measured by an activity and light-dose sensing device 20. HRFM Docket 0094.142AWO RPI OTC case 1197

[00039] A head-worn light-dosimeter and activity monitor, the Daysimeter, was sent to thirty-two day-shift and eleven rotating- shift nurses throughout the United States to measure their actual circadian light stimulus (CS) exposures and activity. The Daysimeter was worn while nurses were awake. The nurses were instructed to place the Daysimeter next to them when they slept or bathed. After the seven-day recording session, they returned the device for data analysis. In addition to wearing the Daysimeter, participating nurses provided urine samples, obtained every four hours, for subsequent melatonin assay and filled out a Chronotype questionnaire [Horne-Ostberg Morningness-Eveningness Questionnaire (MEQ)] and a lighting survey. The nurses were also asked to keep a sleep log, writing down the times they went to bed and any other information about their sleep schedules. These sleep logs were used to match the exact time nurses started wearing the device.

[00040] FIGS. 4A and 4B show activity for two representative nurses, one day-shift nurse (FIG. 4A) and one rotating- shift nurse (FIG. 4B), for seven consecutive days. FIGS. 4C and 4D illustrate the measured CS exposure values obtained directly from the Daysimeter and subsequently transformed using a logistic stimulus-response function representing the entire response range of the circadian system, from threshold to saturation (as shown in FIG. 3). In this embodiment, the logistic stimulus-response function can be represented as:

cs_logιstιc

where:

CS = [(a,lM_λP_λdλ -b, )< a₂ ($S_λP_λdλ - klv_wλP_λdλ)-b₂ ]- _ai l -

foτ

- kj V_WλP_λdλ < 0

and where: HRFM Docket 0094.142AWO RPI OTC case 1197

Mλ is the melanopsin-containing retinal ganglion cell spectral efficiency function peaking at 480 nm [67],

Vioλ is the large-field L+M cone spectral efficiency function [16,64], VV is the rod spectral efficiency function [16], Sλ is the S-cone spectral efficiency function [66], Pλ is the spectral irradiance at the eye (W/m²/nm), the parameters k = 0.31, ai = 0.285, a₂ = 0.2, a₃ = 0.72 represent the interactions among photoreceptor types, the constants bi = 0.01, b₂ = 0.001, and rodsat = 6.5 represent the thresholds and dynamic characteristics of the photoreceptor types as described below, and CS (circadian stimulus) is in units of circadian spectrally weighted irradiance (weighted

W/m²).

[00041] The transformation was employed to estimate the functional input to the circadian system, which appears to apply to both light-induced nocturnal melatonin suppression and phase shifting.

[00042] Examination of FIGS. 4A-4D reveals subtle but important differences in the activity and transformed CS data for these two nurses. In the case of the day-shift nurse (FIGS. 4A and 4C), there appears to be a consistent relationship between the activity and transformed CS values over the course of the seven-day measurement session. For the rotating- shift nurse (FIGS. 4B and 4D), however, this synchrony is much less pronounced. Qualitatively then, these two example sets of data suggest that the day- shift nurse is much more entrained to the light-dark cycle than the rotating- shift nurse. Parenthetically, FIGS. 4A-4D also reveal "flat" periods for both nurses over the course of the seven-day measurement period, which indicate prolonged times of rest and, usually, darkness.

[00043] The data in FIGS. 4A-4D were used to develop a quantitative measure of behavioral entrainment-disruption for day-shift and for rotating-shift nurses. Although the quantitative measure is applied to nurses in this embodiment, it should be understood that the quantitative measure can be applied to people in any number of different professions or situations. The entrainment analysis in this embodiment was based on the cross-correlation of activity and light exposure data. Cross-correlation, an analysis technique commonly used in the field of signal processing, involves the HRFM Docket 0094.142AWO RPI OTC case 1197 concept of time-shifting one signal relative to another to determine relationships between signals that might otherwise be obscured due to relative timing differences. The activity and the transformed CS data can be considered as two time varying signals whose time-matched values can be multiplied together and then the products at every time of data acquisition integrated into a single value. This value is proportional to the covariance of the two signals. When normalized by dividing by the number of data samples, subtracting the product of the individual signal means, and dividing by the product of the standard deviations of each signal, the result will always be limited to values between -1 and 1 (i.e., a correlation coefficient). The multiply-and-integrate operation can be repeated following a small shift in time by one of the signals (e.g., the activity trace, FIG. 4A) with respect to the other (e.g., the transformed CS trace, FIG. 4C) and a new correlation coefficient computed. Continuously repeating this process for the entire recording period yields a new time-varying function, bounded by -1 and 1, that reveals the degree to which the two signals are systematically related to one another for all possible alignments of phase between the two signals. [00044] For continuous functions/and g the cross-correlation is defined as:

(/ * <?)(*) r(τ) 9{t * τ) dτ<

where/* denotes the complex conjugate of/ [00045] Similarly, for discrete functions, the cross-correlation is defined as:

en

[00046] For our analysis we are working with a finite data set of N samples and we want the circular cross correlation which is defined similarly, but treats the functions as periodic, extending from - infinity to + infinity. The equation for the circular cross correlation of a finite sample is computed as:

HRFM Docket 0094.142AWO RPI OTC case 1197 where the subscript N in g[(n-m)N] signifies the periodic extension of the function such that g[ih = g[i+N] =g[i-N].

[00047] The computation of the circular cross correlation can be more readily and efficiently performed by Fourier transform techniques. Making use of the convolution theorem, the circular cross correlation is computed by taking the product of the Fourier transform of/ and g, then taking the inverse Fourier transform of the product.

f ® g = invF{F{f)F{g)) where F and invF represent the Fourier and inverse Fourier transforms respectively. [00048] The following equation scales the cross correlation to range from -1 to 1 which is what we are calling the entrainment correlation function (ECF).

ECF = f ® g fg

N σ_fσ_g where N is the number of data samples, fb_ar and gb_ar are the mean values of data series/and g, Gf and σ_g are the standard deviations of/ and g respectively.

[00049] This operation is adapted from signal processing techniques, and when performed on a periodic representation of the light and activity data, yields what are termed, for the purposes of this paper, entrainment-correlation functions. [00050] FIGS. 5A and 5B show two entrainment-correlation functions for nurses relating the transformed CS data to the activity data: one (FIG. 5A) for the day-shift nurse and one (FIG. 5B) for the rotating-shift nurse. As can be readily appreciated from FIG. 5A, the activity of the day-shift nurse is highly entrained to her light-dark pattern throughout the seven days, as exhibited by the regularly oscillating, twenty-four-hour period of her entrainment-correlation function. More specifically, this nurse, typical of almost all dayshift nurses in the study, has a peak correlation near the zero-phase marker and again at every twenty-four-hour phase marker. This day-shift pattern is in marked contrast to the entrainment-correlation pattern for the rotating-shift nurse illustrated in FIG. 5B. The pattern for the rotating shift nurse in FIG. 5B is aperiodic, exhibiting minor correlation peaks at times other than at the twenty-four-hour phase markers. The pattern of the rotating-shift nurse is of much lower amplitude and very HRFM Docket 0094.142AWO RPI OTC case 1197 distorted compared to the smoothly varying and periodic entrainment-correlation pattern of the day-shift nurse.

[00051] A circadian light stimulus was also applied to forty albino female Sprague- Dawley rats (Rattus norvegicus). The rats were housed in individual cages illuminated by a lighting system previously developed by Bullough et al as disclosed in, Zoolog. Sci. 22, 223 (2005), to determine the spectral and absolute sensitivities of another nocturnal rodent (murine). Based upon the mouse phase response curve (PRC) obtained in that study, a spectral power distribution (nearly monochromatic green light; λ_max=525 nm, half-bandwidth = 35 nm) and irradiance (approximately 5 μW/cm² on the cage floor) were selected to provide the circadian light stimulus to the Sprague-Dawley rats. This particular circadian light stimulus for nocturnal rodents was estimated to be above threshold and below saturation for stimulation of the rat circadian system. This more biologically relevant light stimulus for the rats was precisely controlled using a light- emitting diode (LED) light-delivery system fabricated and installed in every cage. The light-delivery system provided better controlled and more biologically meaningful circadian light stimulation to the rats than the fluorescent ceiling lighting traditionally used to provide bright, ambient illumination throughout an animal colony. [00052] As with the nurse data, the rat data were obtained from two experimental groups: twenty rats were exposed to a consistently repeating pattern of twelve hours of light (12L) followed by twelve hours of darkness (12D), and another twenty rats (the "jet-lagged" group) were exposed to a light-dark pattern where the phase of the light- dark cycle was reversed every forty-eight hours (as if this group of rats instantly traveled back and forth from Asia to the Americas every other day). Animals were housed individually and allowed to eat and drink ad libidum. Wheel running was measured continuously throughout the experimental session and used as measure of rest-activity in these animals.

[00053] The wheel running data (a measure of rest-activity) from the rats were typical of those collected in innumerable studies of nocturnal animals, with the more active periods associated with darkness and less active periods in the light. The two groups differed considerably, however, in the apparent degree of association. For those rats in the 12L: 12D group, almost all of their wheel running occurred in darkness; although, as is usually the case, there was some activity in the light, particularly near the transition times from light to dark, and there were intervals of quiescence sporadically occurring during the dark periods. In the "jet lagged" group of rats, the HRFM Docket 0094.142AWO RPI OTC case 1197 association between wheel running and darkness was markedly less pronounced. Indeed, after several reversals of the light-dark cycle, the wheel running appeared to be disassociated with either light or dark.

[00054] The same analysis of the entrainment-correlation functions that was performed with the nurse data for FIGS. 5A and 5B was also applied to the data from the two groups of nocturnal rodents. An entrainment-correlation function from one typical rat in the 12L: 12D group is shown in FIG. 6A. The similarity between the entrainment-correlation function for the sample day-shift nurse and thel2L: 12D rat are remarkable; the only apparent difference is that the latter function is shifted approximately twelve hours with respect to the former. This shift reflects the expected difference between a diurnal and a nocturnal species; diurnal nurses are active during the day and inactive at night, whereas nocturnal rats are inactive during the light phase and active in the dark. FIG. 6B shows a typical entrainment-correlation function for one rat in the 'Jet-lagged" group. Again, there is marked similarity between the entrainment-correlation functions for the rotating-shift nurse in FIG. 5B and for the "jet lagged" rat in FIG. 6B.

[00055] Plots of the entrainment-correlation functions of day-shift nurses and the 12L: 12D rats generally exhibit smooth, oscillating curves from which estimates of phase, frequency, and magnitude can be determined. Spectral analysis using Fourier transform techniques can arrive at a quantitative description of the entrainment- correlation functions. Spectral analysis becomes especially important for the entrainment-correlation curves exhibited by the poorly entrained rotating-shift nurses and "jet-lagged" rats. Often, no regular cyclic pattern is visually discernible in the entrainment-correlation functions from these individuals and it is only with spectral analysis, such as Fourier decomposition, that estimates of circadian phase, frequency, and magnitude can be made.

[00056] The discrete Fourier transform (DFT) of the entrainment-correlation function provides the spectral components of the entrainment-correlation function given as complex numbers at frequency increments defined by the length of the data sample. For data sample lengths that are twenty- four hours, or integer multiples of twenty- four hours, the twenty-four-hour spectral component is the fundamental frequency, or the corresponding multiple of the fundamental respectively. For data lengths that are not multiples of twenty- four hours there exists several widely used spectral power HRFM Docket 0094.142AWO RPI OTC case 1197 estimation techniques for determining the spectral power and phase at a given frequency which are familiar to those skilled in the art.

[00057] A phasor analysis of the entrainment-correlation functions presented above was performed whereby the multi-day recordings were divided into twenty-four-hour periods for the calculation of entrainment-correlation curves and for subsequent spectral analysis. The resulting phasors represent the average for the number of continuous days being studied, seven days for the nurses and eight days for the rats. The twenty-four- hour parsing of the data for the disrupted rat analysis avoids complete cancellation of the twenty-hour fundamental [f(24)] phasors due to the phase reversal of the lighting scheme that occurred every forty-eight hours. Although parsing the data produces phasors of moderate magnitude and varying phase representing each twenty-four-hour period of data, when averaged across multiple days, the mean phasors tend toward zero magnitude because of the phase reversed lighting pattern. The same result occurs when all eight days are considered together. For consistency of analysis, all light and activity recordings were parsed into twenty-four-hour segments for the phasor analysis. For example, if the data sample represents seventy-two hours of continuous data logging, then the sample can be divided into three twenty-four-hour periods. A phasor analysis can be performed on each twenty-four-hour segment resulting in, for example, three twenty-four-hour phasors. These resulting phasors can then be statistically analyzed (mean, standard deviation, etc.), or evaluated for trends over the three-day period. As another example, the same seventy-two hours of data can be divided into forty-eight twenty-four-hour periods each displaced by one hour relative to the previous period. In effect this produces a sliding twenty-four-hour window of data for phasor analysis with subsequent statistical and trend analysis. A benefit of parsing the data into twenty-four- hour segments is that the same calculation procedures can be applied to any set of data with a recording period of at least twenty-four hours.

[00058] The precision and accuracy of Fourier spectral analysis are constrained by the number of cycles captured in a data set. To preserve the full frequency resolution afforded by application of the fast Fourier transform (FFT), simple periodograms were used. A periodogram provides an estimate of the spectral power at different frequencies; however, a periodogram is an uncertain estimator of spectral content due to the finite length of the data. The lowest temporal frequency that can be analyzed is determined by the length of the period of time for one complete cycle; in the present case, this is twenty-four hours. Choosing a data length that is an integral number of HRFM Docket 0094.142AWO RPI OTC case 1197 twenty-four-hour periods will inadvertently favor the detection of a twenty-four-hour spectral component. Other nearby frequency components, naturally, will not be resolved because their power will be only partially contained in the twenty-four-hour component, the remainder of power being distributed over the rest of the spectrum. Other embodiments may utilize other methods for different optimizations of frequency resolution and amplitude accuracy for spectral analysis. One option is to collect the data at higher sample rates and over longer time periods.

[00059] The entrainment-correlation function analysis places no restrictions or biases on the resulting wave shapes, and in principle, a better description of the entrainment period might be with a fundamental other than twenty- four hours, say, twenty-three or twenty- four and a half hours. To answer this question, the spectral analysis for the day- shift nurses was repeatedly recalculated using different length data sets, The data length periods ranged from sixty-six (=22*3) to seventy-eight (=26*3) hours in ten-minute increments, which provided exactly three cycles of fundamental frequencies ranging from twenty-two to twenty-six hours in ten minute increments (FIG. 7). [00060] Quadratic functions were fitted to each nurse's amplitude series in order to determine the optimum fundamental period (FIG. 8). Peak pliasor amplitudes for all day- shift nurses calculated from quadratic curve fits shown in FlG, 7 were plotted against the fundamental pliaser period. The mean (broken line) and one standard deviation from the mean (dotted lines) of the phasor period are shown. The abscissa location of the peak amplitude indicates the period having the highest correlation with the data, or in other words, the period that best describes the waveform. Other techniques to determine the optimum fundamental period are known to those skilled in the art and are may be used in other embodiments. For example, see the techniques disclosed in J.T. Enright's publication in the Journal of Theoretical Biology, volume 8, pages 426-468 (1965) which is hereby incorporated by reference in its entirety.

[00061] While the range of peak amplitudes occurred for periods ranging from 23.73 to 24.56 hours, the mean was 24.035, just two minutes longer than twenty-four hours, with a standard deviation of 10.6 minutes. The closeness to an exact twenty-four-hour period is remarkable considering that the light exposure and activity for each day-shift nurse results entirely from that nurse's natural behavior; again, the correlation- entrainment functions have no inherent bias for twenty-four-hour periods. A corresponding analysis of the laboratory rat data (not shown) shows a similarly exact HRFM Docket 0094.142AWO RPI OTC case 1197 twenty-four-hour optimum period, but this result is less surprising because the laboratory lighting was precisely controlled in twenty-four-hour cycles. [00062] This analysis supports using a twenty-four-hour entrainment period for the analyses of the nurse data for two reasons. First, the nurses' mean period is empirically almost exactly twenty- four hours, and second, choosing slightly different length periods for the analysis of the data results in only small differences in the phasor magnitudes, at least for this sample of nurses. The nurse with the largest difference in optimal period from a twenty-four-hour period has a less than four percent drop in phasor magnitude by using a twenty-four-hour period instead of the period of her maximum amplitude occurring at 24.56 hours. It should be noted that in some embodiments, this curve fitting exercise is not part of the phasor analysis proper, but rather it was done in this embodiment to validate the use of a twenty-four-hour frequency for further analysis of the particular data sets discussed in the paper. Any frequency can be used for phasor analysis with the choice depending on the experimental hypotheses or purpose of the analysis. For example, an eighteen-hour phasor might be useful for investigating how well sailors tolerate eighteen-hour watch schedules on naval submarines. [00063] FIG. 9A illustrates an embodiment of a phasor diagram quantifying circadian entrainment disruption for a group of day shift nurses. FIG. 9B illustrates an embodiment of a phasor diagram quantifying circadian entrainment disruption for a group of rotating shift nurses. The length of each phasor is the magnitude of f(24) and reveals how well light and activity are correlated in the seven-day, twenty-four-hour pattern. Recall that the ordinate of the entrainment-correlation curves is the correlation between activity-rest and light-dark for all seven days. Consistent with a diurnal species, all the phasor directions for the nurses are to the right, meaning that activity and light exposure occur at nearly the same time. The angular direction of a phasor indicates the phase relationship between light and activity for an individual, or in other words, the circadian time difference between light exposure and activity. Greater amounts of activity in the morning than in the evening would produce a phasor extending below the horizontal line (the 3 o'clock position for a diurnal species), where the horizontal line corresponds to zero phase. Conversely, greater amounts of activity in the evening produce phasors extending above the zero-phase line. Other studies have used the terms "larks" and "owls" to refer to people with circadian rhythms shifted either to the morning or evening, respectively. The phasor analysis precisely reveals this behavioral characteristic. Interestingly, there are more owls than larks among the day-shift nurses HRFM Docket 0094.142AWO RPI OTC case 1197

(FIG. 9A), as is also true for the rotating-shift nurses (FIG. 9B), indicating that these people tend to be more active after sunrise and sunset than before sunrise and sunset. As a group, the day-shift nurses (FIG. 9A) also have larger phasor lengths than the rotating-shift nurses (FIG. 9B), implying that they have a much higher degree of behavioral entrainment.

[00064] FIG. 1OA illustrates an embodiment of a phasor diagram quantifying circadian entrainment disruption for a group of entrained nocturnal rats. FIG. 1OB illustrates an embodiment of a phasor diagram quantifying circadian entrainment disruption for a group of disrupted nocturnal rats. The rats exposed to the consistent 12L: 12D light-dark cycle (FIG. 10A) produced phasors with magnitudes similar to the day-shift nurses (FIG. 9A), but with directions to the left, clustered around a twelve-hour phase shift between light and activity, as would be expected for an entrained nocturnal animal (FIG. 10A). The "jet-lagged" rats (FIG. 10B) experiencing the continually changing light-dark exposures have short, low magnitude phasors with no consistent direction across individuals. Whereas the somewhat disrupted rotating-shift nurses (FIG. 9B) have phasors of intermediate magnitude, the rats exposed to the more extreme alternating light-dark cycles (FIG. 10B) show a nearly complete loss of entrainment. These data indicate that the phasor analysis provides a useful measure of the degree of entrainment, as well as tendencies towards nocturnal or diurnal behavior and the degree to which these individuals are phase-delayed (owls) or phase-advanced (larks). [00065] The phasors of each individual within a group can be combined using statistical analysis to arrive at an average magnitude and direction representing the behavior of the group (FIG. 11).

[00066] Considering only the degree of entrainment, FIGS. 12A and 12B show the spread of the f(24) phasor magnitudes for the two groups of nurses and for the two groups of rats. FIG. 12A shows a clear difference between the day-shift and rotating- shift nurse groups with widely separated group means and medians. Nevertheless, there is some overlap of the distributions, perhaps reflecting a true continuum of the degree of circadian entrainment among individuals. In FIG. 12B, the rats also show a clear separation, but undoubtedly because of the two radically different light-dark patterns, there is no overlap in the phasor amplitudes for these two groups of rats. [00067] FIG. 13 illustrates one embodiment of a method of quantifying circadian entrainment disruption. At least one set of activity information is obtained 26. The activity information can represent a wide variety of activities, including motion of a person; HRFM Docket 0094.142AWO RPI OTC case 1197 cardiovascular information, such as heart rate, QT interval, and blood pressure; hormonal information, such as specific hormone levels as measured in- vitro or in-vivo; blood information, such as glucose concentration; clotting capacity, platelet count, white blood cell count, red blood cell count, and the presence of one or more virus, bacteria, or cancerous tissue; urine information; agility information; cognitive information; motor skill information; and neurological information. The activity information may be obtained directly from a variety of sensors or tests, or it may be obtained from a database where such data has been stored.

[00068] At least one set of light-dose information which corresponds to the at least one set of activity information is also obtained 28. The corresponding light-dose information may be obtained by a photosensor as discussed previously with regard to the Daysimeter example, or the light information may be obtained from a database where such data has been stored. The light-dose information may be obtained at the exact same time as the activity information is obtained or the two sets of information may be obtained in an interleaved or partially overlapping fashion.

[00069] The at least one set of light-dose information is transformed 30 with a logistic stimulus response function. Embodiments of this transformation have been discussed above. The transformed light-dose information are circularly cross-correlated 32 to yield an entrainment correlation function. Embodiments of this circular cross-correlation have been discussed above. The entrainment correlation function is spectrally analyzed 34, and embodiments of this spectral analysis have been described above. A phasor analysis of the entrainment correlation function is completed 36 based at least in part on the spectral analysis of the entrainment correlation function.

[00070] FIG. 14 schematically illustrates a system 38 for quantifying circadian entrainment disruption. The system has a processor 40 which is configured to complete a phasor analysis of an entrainment correlation function based at least in part on a spectral analysis of the entrainment correlation function which is the result of circularly cross- correlating activity information and light-dose information which has been transformed with a logistic stimulus response function. Embodiments of suitable processes and method steps to complete the phasor analysis of the entrainment correlation function have already been discussed above. The processor 40 may be a computer executing machine readable instructions which are stored on a CD, a magnetic tape, an optical drive, a DVD, a hard drive, a flash drive, a memory card, a memory chip, or any other computer readable medium. The processor 40 may alternatively or additionally include a laptop, a microprocessor, an HRFM Docket 0094.142AWO RPI OTC case 1197 application specific integrated circuit (ASIC), digital components, analog components, or any combination or plurality thereof. The processor 40 may be a stand-alone unit, or it may be a distributed set of devices.

[00071] A data input 42 is coupled to the processor 40 and configured to provide the processor with the light-dose information and the activity information. A photosensor 44 may optionally be coupled to the data input 42 to enable the live capture of light-dose information. Similarly, an activity sensor 46 may optionally be coupled to the data input 42 to enable the live capture of activity information.

[00072] A database 48 may optionally be coupled to the data input 42 to provide previously captured light-dose and activity information to the processor 40. Database 48 can be as simple as a memory device holding raw data or formatted files, or database 48 can be a complex relational database. Depending on the embodiment, none, one, or multiple databases 48 and/or photosensors 44 and/or activity sensors 46 may be coupled to the data input 42. The photosensor 44 and the activity sensor 46 may be coupled to the data input 42 by a wired connection, an optical connection, or by a wireless connection. Suitable examples of wireless connections may include, but are not limited to, RF connections using an 802.1 Ix protocol or the Bluetooth ® protocol. Furthermore, in embodiments having a database 48, the processor 40 may be coupled to the database 48 for storing results or accessing data by bypassing the data input 42.

[00073] The system 38 also has a user interface 50 which may be coupled to either the processor 40 and/or the data input 42. The user interface 50 can be configured to display the data and plots as discussed above. The user interface 50 may also be configured to allow a user to select light-dose and activity information from a database 48 coupled to the data input 42, or to start and stop collecting data from a photosensor 44 and an activity sensor 46 which may be coupled to the data input 42.

[00074] Attention to circadian entrainment-disruption, rather than to activity alone or to light and dark per se, makes it possible to circumvent the diurnal-nocturnal conundrum plaguing comparative studies of circadian entrainment-disruption using animal models, especially nocturnal animal models which are most common. We found that the circadian entrainment-disruption patterns for day-shift and rotating-shift nurses were remarkably different, but they were remarkably similar to the patterns for two parallel groups of nocturnal rodents. The marked differences in circadian entrainment-disruption patterns within species together with the marked similarities in circadian entrainment-disruption across species, in addition to the new method for quantifying circadian entrainment- HRFM Docket 0094.142AWO RPI OTC case 1197 disruption, strongly suggest that circadian disruption in humans can be parametrically studied using animal models.

[00075] The advantages of a method and system for quantifying circadian entrainment disruption and circadian time have been discussed herein. Embodiments discussed have been described by way of example in this specification. It will be apparent to those skilled in the art that the foregoing detailed disclosure is intended to be presented by way of example only, and is not limiting. Various alterations, improvements, and modifications will occur and are intended to those skilled in the art, though not expressly stated herein. These alterations, improvements, and modifications are intended to be suggested hereby, and are within the spirit and the scope of the claimed invention. Additionally, the recited order of processing elements or sequences, or the use of numbers, letters, or other designations therefore, is not intended to limit the claims to any order, except as may be specified in the claims. Accordingly, the invention is limited only by the following claims and equivalents thereto.

Claims

HRFM Docket 0094.142AWO RPI OTC case 1197What is claimed is:

1. A method of quantifying circadian entrainment disruption, comprising: obtaining at least one time series set of activity information; obtaining at least one time series set of light-dose information which corresponds in time to the at least one time series set of activity information; transforming the at least one set of light-dose information with a logistic stimulus response function; circularly cross-correlating the activity information and the transformed light-dose information to yield an entrainment correlation function; spectrally analyzing the entrainment correlation function; and completing a phasor analysis of the entrainment correlation function based at least in part on the spectral analysis of the entrainment correlation function.

2. The method of claim 1, wherein the at least one set of activity information comprises movement data from an accelerometer.

3. The method of claim 1, wherein the at least one set of activity information is selected from the group consisting of cardiovascular information, hormonal information, blood information, urine information, agility information, cognitive information, motor skill information, and neurological information.

4. The method of claim 1, wherein the at least one set of light-dose information corresponds the at least one set of activity information such that the at least one set of light- dose information is taken simultaneously with the at least one set of activity information.

5. The method of claim 1, further comprising plotting the at least one set of activity information versus time.

6. The method of claim 1, further comprising plotting the at least one set of light-dose information versus time.

7. The method of claim 1, wherein the logistic stimulus response function represents the entire response range of a circadian system. HRFM Docket 0094.142AWO RPI OTC case 1197

8. The method of claim 1, wherein the logistic stimulus response function is represented as:

9. The method of claim 1, further comprising plotting the at least one set of activity information versus time.

10. The method of claim 1, further comprising plotting the transformed at least one set of light-dose information versus time.

11. The method of claim 1, further comprising plotting the entrainment correlation function.

12. The method of claim 11, further comprising determining a degree to which the at least one set of activity information and the at least one set of light-dose information are systematically related to each other for all possible alignments of phase between the two signals by examining the plotted entrainment correlation function.

13. The method of claim 1, wherein the entrainment correlation function is scaled to a range from -1 to 1 as follows:

where N is a number of data samples, fb_ar and gb_ar are mean values of data series /and g, and Gf and σ_g are the standard deviations of/ and g respectively. HRFM Docket 0094.142AWO RPI OTC case 1197

14. The method of claim 1, wherein spectrally analyzing the entrainment correlation function comprises using Fourier transform techniques to determine at least one of a circadian phase, frequency, or magnitude.

15. The method of claim 1, wherein completing a phasor analysis of the entrainment correlation function comprises plotting a phasor diagram quantifying the circadian entrainment disruption, wherein: the length of each phasor is a magnitude revealing how well the at least one set of activity information and the at least one set of light-dose information are correlated; and the direction of each phasor indicates the circadian time.

16. A system for quantifying circadian entrainment disruption, comprising: a processor configured to complete a phasor analysis of an entrainment correlation function based at least in part on a spectral analysis of the entrainment correlation function which is the result of circularly cross-correlating activity information and light-dose information which have been transformed with a logistic stimulus response function; a data input coupled to the processor and configured to provide the processor with the light-dose information and the activity information; and a user interface coupled to either the processor or the data input.

17. The system of claim 16, further comprising a database coupled to the processor.

18. The system of claim 16, further comprising a database coupled to the data input.

19. The system of claim 16, further comprising a photosensor and an activity sensor coupled to the data input.

20. The system of claim 19, wherein the activity sensor is configured to sense cardiovascular information; hormonal information, blood information, urine information, agility information, cognitive information, motor skill information, and neurological information.

21. The system of claim 19, wherein at least one of the photosensor and the activity sensor is coupled to the data input by a wireless connection.