Biology Reference
In-Depth Information
the lower right panel is the average of the 2nd, 48th, 94th, and 140th data
points. The third is the average of the 3rd, 49th, 95th, and 141st
data points, and so on. This process is repeated for a series of different
assumed periods from three data points to N/3 data points, where N is
the total number of data points. The repeated waveform shown in the
lower right panel is clearly not a single sine or cosine wave. The upper
right panel is the percent of the variance remaining after the waveform
of period L is removed from the data plotted as a function of L. The
dominant periodicities occur at periods of 230 and 460 minutes. The
460-minute waveform is essentially two cycles of the 230-minute
waveform with slightly different amplitudes. The 230-minute waveform
accommodates 63.7% of the variance, and the 460-minute periodic
waveform describes 72% of the variance. Although this approach clearly
provides a much better description of the data than does the Fourier
approach shown in Figure 9-14, it is not perfect. Note that the alignment
of the peaks of the data and the peaks of the periodic waveform is not
exact. This method assumes the secretion events (i.e., the peaks) are
equally spaced, whereas in reality they are not.
The corresponding analysis for the growth hormone example is not
shown; however, as is evident from Figures 9-13 and 9-15, the GH is
substantially less periodic, with dominant periods of 190 minutes and
400 minutes describing only 8.3% and 26.6% of the variance,
respectively.
The analysis of the LH and GH data sets clearly indicates the functions
describing the secretion of these hormones are not entirely, or even
predominantly, periodic. This is a common feature of virtually every
hormone concentration time series ever measured. Thus, Fourier and
other algorithms which assume periodic events are not the best
analytical methods for this type of data. In general, the objectives of
hormone time series data analyses are to characterize the number, times,
masses, and shapes of the pulsatile secretory events that increase the
hormone concentration in the blood. The amount of basal (nonpulsatile)
secretion is also of interest, as is the description of the time course of the
removal of the hormones from the blood. The Fourier and signal-
averaging approaches presented above cannot evaluate these
characteristics well. Consequently, a group of statistically based
algorithms, called deconvolution methods, have been developed to provide
this information. Some of these methods do not require a constant
measurement uncertainty, can accommodate missing values, and do not
assume periodic secretion events.
t
−
statistic
STEP 1
t
−
statistic
STEP 2
FIGURE 9-17.
Schematic illustration of the CLUSTER
algorithm. (From Urban, R. J., Evans, W.
S., Rogol, A. D., Kaiser, D. L., Johnson, M.
L. and Veldhuis, J. D. [1988].
Contemporary aspects of discrete peak
detection algorithms: I. The paradigm of
the luteinizing hormone pulse signal in
men. Endocrine Reviews, 9(1), 3-37.
#
1988 The Endocrine Society. Used by
permission.)
D. CLUSTER Hormone Pulse Analysis Algorithm
One of the first statistically based algorithms was the CLUSTER
algorithm (Veldhuis and Johnson [1986]; Urban et al. [1988]) depicted
schematically in Figure 9-17. The CLUSTER algorithm functions as a
