3 RESULTS
The cosinor analysis method is often used to
estimate biorhythms with regular cycle length from
biological time series data (Nelson et al., 1979). We
determine the optimal parameter set (M, A, ω, φ) to
approximate the detrended mode data using a cosine
function f(t
i
), as showed in the equation (1), by
minimizing the residual sum of squared (RSS) errors
between the detrended mode data and the
corresponding value generated by the function f(t
i
).
ii
tAMtf cos
(1)
where t
i
represents the time of measurement of the i
th
data, M is the mean level (MESOR) of the cosine
curve, A is the amplitude of the function, ω is the
angular frequency (reciprocal of the cycle length) of
the curve, and φ is the acrophase (horizontal shift) of
the curve.
The optimal length of the average menstrual
cycle is estimated 24.9 days. This compares with the
average self-recorded menstrual cycle length of
27.5±1.3 days which is derived from total 16 cycles
ranging from 25 to 30 days during the data
collection period. The estimated length has an error
about 9.5%.
The estimation procedure and its outcomes with
overlapped self-record are showed in Figure 4. The
upper subplot shows daily mode value and its
standard deviation profiles, the markers “o” and
vertical bars “|”, terminated at the upper and lower
ends by short horizontal lines “-”, show the mode
values and standard deviation of the pulse rate data
in daily sleep episodes. The lower subplot
demonstrates the menstrual cycle estimation
procedure, the bold blue line shows the smoothed
profile of the daily mode values, and the black
dotted line shows the detrended result of the
smoothed mode profile. The cyan line is the cosinor-
fitting result to the black dotted line. Red horizontal
bars denote the menses periods that were recorded
by the subject.
Data are plotted on the day-by-day basis along
the x-axis. The y-axis denotes pulse rate in the unit
of beat per minute (bpm). Some sporadic
discontinuities can be seen, as no data were collected
during those days.
4 DISCUSSION
Purposes of this study aim mainly at developing a
user-friendly and convenient system available for
daily physiological information collection over long-
term period, and providing more reliable data for
further analysis.
Data collection rate can be used as one of the
indicators for evaluating the usability of the system.
It seems promising to achieve fairly high rate in data
collection over 15 months. We examined the
reliability of these data by applying the cosinor
analysis method to estimate the menstrual cycle, and
achieved reasonable accuracy with estimation error
smaller than 10%.
Although the cosinor analysis method does not
require that the data be sampled at equal intervals,
and it also tolerates incidents of missing data, it
provides an accessible means of estimating the
periodic signature in physiological data. However,
the cosinor analysis method postulates that the data
should be reasonably represented in a deterministic
cyclic form with a constant period. This prerequisite
is not always suitable in female menstrual cycles. To
deal with irregular cycle cases and explore other
intrinsic biorhythms, more data mining methods will
be conducted to extract various features in time
domain, frequency domain and chaotic domain in
the future.
Further interpretation for the physiological
significance such as health condition change and
biorhythmic fluctuation from these long-term data
will be one of the most important tasks in the
coming data analysis. Deep data mining on different
temporal scales, such as daily, weekly, monthly,
seasonal and even yearly, will be conducted to
reveal the statistical links among health condition
change and various data signatures over a long-term
period.
5 CONCLUSIONS
The system was examined by a female volunteer in
more than 15 months and confirmed its friendly
usability, performance and reliability in systematic
aspects such as data collection and data analysis.
Higher rate in data collection over a long-term
period, and more reliable outcome from the long-
term data were confirmed and achieved. This study
is expected to be served as a part of SHIP (Scalable
Healthcare Integrated Platform) project (Chen et al.,
2008).
ACKNOWLEDGEMENTS
The authors thank the volunteer for her cooperative
DevelopmentofanAutomaticSystemforPersistentCollectionofPhysiologicalInformation-TowardLong-Term
ApplicationinBiorhythmMonitoringandHealthcare
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