Exercise 3.1 Parameters of rhythmic processes

This simple exercise uses the program Wave. Wave is a short tutorial on the parameters of rhythmic processes (mean level, amplitude, phase, period, and waveform). The tutorial takes only about 6 minutes to complete, includes background music, and shuts itself down at the end. To start the program, double-click on the Circadian icon to open the program banner, then click on Wave (the eighth icon from the right).

Exercise 3.2 Smoothing a data set

This exercise uses the procedure of moving averages to smooth a data set (i.e., to filter out high-frequency oscillations). Section 3.2 explains the rationale for this procedure.

1. Double-click on the Circadian icon to open the program banner, then click on Plot (the first icon on the left). Select the Data subfolder by double-clicking on it in the Source panel, and select the sample data file A07 by single-clicking on it. This file contains values of metabolic heat production (in W) in a fat-tailed gerbil, collected in 6-minute intervals for 6 consecutive days.

2. The program's default values are appropriate for this data set, so click on the Cartesian plot button (the purple button) now. Browse through the entire data set (6 days). Note that there is a clear daily rhythm with higher values during the first part of each day. However, considerable "noise" (i.e., ultradian oscillations that do not seem to be regular and that obscure the daily oscillation) is also present.

3. To filter the data set, start the program Moving (the second icon from the left in the Circadian banner). If necessary, select the Data subfolder in the Source File panel and then choose the file A07. If the box Same as Source is checked, the program will automatically change the information in the Destination File panel. For this exercise, don't use the default file name (MAV-A07) provided; instead, delete MAV-A07.txt and type B07.txt. Accept the default values for Data Points or Pre-filters.

4. Because ultradian oscillations in A07 are particularly conspicuous in the range of a few minutes, set the Averaging Window size to 24 minutes. Type in 4 (i.e., 4 bins or 24 minutes) and click on Execute.

5. To eliminate the need to switch between programs, create a second filtered file before returning to Plot to look at the data. Type in a new Destination File name (e.g., C07), change the Averaging Window to 60 (i.e., 60 bins or 6 hours), and click on Execute.

6. Now, look at the results. Go back to Plot and load the first file that you created (B07, if you followed my suggestion). Note that the temporal pattern is very similar to that of the original file (A07), but the high-frequency oscillations have been filtered out. You may want to alternate between A07 and B07 a few times to observe the difference.

7. Next, look at the second file you created (C07). Open it now. The first thing you may notice is that the wave pattern is phase-advanced by 3 hours in comparison with A07. This is an artifact of the moving-averages procedure, which you can easily correct by starting the procedure 3 hours later. The important thing to note, however, is that C07 is a much smoother data set. It has only one major peak each day. The daily pattern present in A07 was preserved, but the ultradian oscillations were filtered out.

8. You may also have noticed that, although A07 was 6-days long, both B07 and C07 are only 5-days long. In actuality, B07 is 12 minutes shorter than A07, while C07 is 3 hours shorter than A07. Because Plot plots only full days, an entire day seems to be missing in both B07 and C07.

9. Next, you can practice with other source files. Note that you have the option of telling the program to discard data points at the beginning or end of the file (using the Data Points panel). You may also use the Pre-filter panels to eliminate outliers. You can set the Averaging Window size to 1 (and avoid the moving-averages filter) if you only want to extract a section from a long data set and eliminate outliers.

Exercise 3.3 Constructing an actogram

As explained in Section 3.2, the actogram is a classic graphic in circadian physiology. Originally used only for records of running-wheel activity, it now is used for practically any type of variable that is recorded over an extended period of time. Data sets must have equally spaced data points to generate a meaningful actogram. A few missing points are acceptable, but they must be filled in with a null value to preserve the temporal structure of the data set.

1. Start the program Plot.

2. In the Source panel, select the Data subfolder by double-clicking on it.

3. Select the data file A03 by clicking on it. This file contains the records of the running-wheel activity of a golden hamster maintained in constant darkness for 36 consecutive days. The number of wheel revolutions is accumulated in 6-minute bins (for a total of 8640 data points in the file). Because the data points are equally spaced, time tags are not needed.

4. For now, leave the default values in the Data panel. Click on the Actogram button (the green button) to display the data. You can see why golden hamsters are the preferred rodent for the study of circadian rhythms. The pattern of activity is very "clean," with wheel-running neatly restricted to a limited portion of each day. Also note that the onsets of activity are neatly arranged, one under the other, in an almost vertical line, which indicates a free-running period very close to 24.0 hours.

5. Now select the data file A04 by clicking on it. This file contains the records of running-wheel activity of another hamster maintained in constant darkness for 29 days.

6. Click on the Actogram button to display the data. The onsets for this animal clearly deviate from a vertical line, indicating a free-running period slightly longer than 24.0 hours. You will learn how to determine the exact period in future exercises. Note that you can switch to black-and-white display by clicking on the brush cup (under the display panel). Please do so now.

7. Next, select the data set A05. This file contains the body temperature records of a Long-Evans rat, measured by telemetry every 6 minutes for 6 weeks. A light-dark cycle was present for the first 4 weeks.

8. Click on the Actogram button. What do you see? If you are in black-and-white mode, you probably see 42 horizontal straight lines. Why? Because body temperature, unlike locomotor activity, does not go down to zero during the inactive phase of the circadian cycle. By plotting every value above zero, you end up plotting every single data point. Thus, in order to have a useful actogram, you must "clip off" the lower values. An arbitrary but convenient clipping level is the mean level of the rhythm. You will learn how to calculate the mean level later (Exercise 5.2). For now, click on the Clip box and type 36.2.

9. Click on the Actogram button. What a difference! You have created a very legible actogram of the rat's body temperature rhythm. You can clearly see that the animal exhibited a period of 24.0 hours during the 2 weeks under a light-dark cycle and that it freeran with a period longer than 24.0 hours when released into constant darkness.

10. Of course, you don't need to adjust the clipping level if you use different colors for different temperature values. Click on the Clip box, delete 36.2, and type 0. Then click on the brush cup to revert to color mode (the data will automatically be replotted). The resulting actogram is not as clear as the black-and-white version, but it is readable.

11. Finally, select the data set A06. This file contains the locomotor activity records of a pill bug (a small terrestrial crustacean), measured with an infrared photocell for 19 days in constant darkness. The data resolution is 6 minutes, and the file contains only the ordinate values.

12. Click on the Actogram button. You can see why pill bugs are not the preferred species in circadian physiology. The records are much "noisier" than those of the hamster or rat. You can still see, however, that the animal had a free-running period much shorter than 24.0 hours.

Exercise 3.4 Determining circadian period by

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