I. General issues

A. Why study periodic physiological activity

Periodic physiological activity has been observed and interpreted since antiquity when physicians assessed health by listening to heart rhythms and breathing rhythms. In more contemporary models of physiology, the concept of periodic activity has been associated with life defining processes such as homeostasis. In spite of this interest, there is a paucity of research evaluating periodic physiological activity.

It is perplexing to try to understand why the study of periodic physiological activity has been neglected in psychophysiological research. The history of psychophysiology, with its interest in accurately monitoring central nervous system function, would seem to provide the appropriate motivation. For example, researchers for approximately 100 years have justified the placement of electrodes on the surface of the body (e.g., scalp, chest, palms, etc) as a method to provide information regarding central mediation of emotional or cognitive states. Yet, the measurement of physiological activity in these studies has seldom measured Periodic Processes.

Quantification of physiological activity, even in the physiology literature, has generally consisted of counting events or evaluating a mean level of activity within a time period. The study of periodic physiological activity seems to be lacking. This is remarkable, because the study of living systems has always emphasized temporal and periodic characteristics. There are numerous reasons for this lack of research. Perhaps, the most imposing factor has been the statistical sophistication necessary to accurately quantify periodic activity. This chapter has been written in response to this need.

The chapter has been written to serve as a two-way bridge between the psychophysiologist and the statistician. We have intended this chapter to aid the psychophysiologist by introducing time-series concepts without mathematical jargon and to aid the statistician by introducing the unique problems associated with physiological data.

Periodicities in physiological activity convey important information regarding central nervous system regulation. This is true not only for the study of electro-cortical activity like the EEG, but also for peripheral systems such as heart rate and EMG. In our research the amplitude of heart rate rhythms has provided reliable diagnostic information regarding the status of the central nervous system. Similarly, there have been clinical reports that muscle tone changes (i.e., EMG) following brain insult. These changes in periodic activity are not an epiphenomenon, but are a direct manifestation of the peripheral component of a peripheral-central-peripheral feedback system. In the healthy individual this feedback system has a characteristic frequency and gain which is reflected by a periodicity with a relatively stable duration and amplitude. When brain function is compromised by a variety of insults including tissue damage, hemorrhage, increased intra-cranial pressure, drugs, anoxia, severe exercise, or even psychological stress, the feedback system is disrupted and there are changes in the periodic nature of these measures.

B. One researcher's data is another researcher's error

With the exception of the EEG literature, which historically has emphasized rhythmicity, psychophysiological research usually has treated oscillations in physiological activity as recording error or irrelevant background physiological activity. This decision is based upon two interdependent assumptions: one, that oscillations in physiological activity reflect homeostatic activity; and two, that event-related physiological responses are manifest as short latency trends.

Physiological systems are continuously changing, reflecting the dynamic regulatory function of the nervous system. It would be naive to believe that these systems are sensitive solely to the variables we choose to manipulate in our experiments. Paradoxically, the physiological systems that may be the most sensitive to psychological processes also may manifest neurophysiological regulation. Thus, we are faced with a problem of how to quantify the component of physiological activity related to the experimental manipulation, when the same physiological system is also indexing the continuous neural modulation of primary homeostatic function.

In the study of short latency event-related responses (e. g., evoked potentials, directional heart rate responses, and stimulus specific electrodermal activity) the spontaneous oscillations characteristic of most physiological systems are bothersome and need to be removed. In the conceptual models underlying this style of research, oscillations or "jitter" are treated as experimental error and can be removed through a variety of averaging and smoothing procedures.

These averaging procedures are insensitive both to the possibility that the signal is encoded in a parameter other than level and to the possibility that the signal is encoded in the background noise. In contrast to methods which minimize background activity, this chapter will identify problems, provide an overview of methods, and propose a series of rules for analyzing and interpreting rhythmic physiological data.

C. Problems in the quantification of periodic processes

There are three basic statistical problems in quantification of the periodic components of physiological processes. First, physiological data are non-stationary. Non-stationarity implies that the expected values of the mean and variance are not constant throughout the data set. In physiological data this is characterized by aperiodic components and slow trend shifts in level. All traditional time series methods for quantifying periodicities assume that the data are stationary. When data are non-stationary and aperiodic, the analyses will distort the values for frequency and amplitude of the periodicity of interest. Second, physiological periodicities are non-sinusoidal. Most of the methods for describing periodicities assume that the periodic process may be fit with a sine or cosine wave. When periodic activity can not be fit with a sine or cosine function, the analyses produce harmonic variances at frequencies higher than the true periodic process. This, confounds the interpretation of the analyses by distributing harmonic variances at frequencies higher than the true periodic process. Third, physiological data are complex and consist of numerous periodic and aperiodic components. Not only must the researcher be cognizant of the non-stationary component, but when there is more than one periodic component the researcher must be aware that the non-sinusoidal characteristic of slow periodic processes inflates the estimates of faster periodic activity. Later in this chapter we will elaborate on the statistical characteristics of these problems and describe methods for minimizing their impact on data analyses.

There are a number of other problems associated with the description of specific periodic processes within complex physiological patterns. Based upon the above statistical problems, it is difficult to quantify a low amplitude signal when it is embedded within a complex signal. Not only are there statistical problems, but amplification equipment and filters used to enhance low amplitude signals may influence the amplitude and frequency components of the periodic process being studied.

The quantification of rhythmicity is confounded by the complexity of some physiological response systems. Obviously, it is easiest to quantify periodic activity, when most of the variance of the physiological process may be described by one sinusoid. For example, recordings of respiration using measures of chest circumference or nasal airflow exhibit a predominant rhythmicity, synchronously waxing and waning with inhalation and exhalation. Unfortunately, not all physiological processes exhibit an observable periodicity which accounts for most of the variance.

In many response systems the periodic component of interest may account for a very small proportion of the variance of the process. In these situations the experimenter is attempting to accurately quantify a low amplitude periodic process which is embedded in a complex signal composed of other periodic and aperiodic components. Examples of this problem can be seen in the monitoring of EEG rhythmicity or fetal heart rate. In the analyses of the periodic components of the EEG, it is important to note that the amplitude of alpha and other periodic activity is in the microvolt range, although the background skin potential from the scalp is in the millivolt range. Similarly, in the human fetus, vagal influences on the heart are modulated by central respiratory drive and manifested as an oscillation of heart period. This oscillation, fetal respiratory sinus arrhythmia, is embedded in a very complex signal of high beat-to-beat variability with identifiable contributions from blood pressure, thermoregulation, metabolic demands, and reactivity to uterine contractions. In many situations the fetal respiratory sinus arrhythmia may have an amplitude between two to five msec and the heart period reaction to uterine contractions may at times be as great 500 or 600 msec. In these two examples, the rhythmicity of interest (i.e., alpha in the EEG study; respiratory sinus arrhythmia in the fetal heart rate study) represents an extremely small proportion of the variance of the process.

The characteristics of amplifiers contribute to difficulties in the analysis and interpretation of physiological signals. In early EEG research it was necessary to use high gain AC amplifiers to achieve the necessary amplification to observe the low amplitude rhythmicity emanating from the scalp. The AC amplifier provided a method for filtering slow periodic and aperiodic influences associated with skin potential and allowed the observation and quantification of low amplitude oscillations characteristic of the EEG. Although solid state electronics provide contemporary amplifiers with higher gain and greater stability, the basic methods used in this field have changed little over the past 50 years.

Researchers modify the signal for their research objectives by using a combination of hardware (e.g., amplifier characteristics and filter settings) and software manipulations (e.g., statistical procedures). For example, the same input signal is used for both evoked potential and EEG research. Evoked potential research emphasizes the low frequency influence of the voltage shifts associated with stimulus processing by expanding the low frequencies passed by the amplifier via longer time constants. In contrast, EEG research emphasizes the high frequency content by attenuating the low frequency activity via short time constants.

In most situations, the time-constants on AC amplifiers do not perform their assumed task of removing the variance of physiological processes below or above a specific frequency. Since physiological activity is composed of periodic and aperiodic components and the periodic components are never a perfect sine wave, the time-constant filters pass variance of the processes in the frequencies assumed to be filtered. Therefore, AC amplifiers may distort the specific output characteristics of interest: frequency and amplitude of the EEG or latency and magnitude of evoked potential.

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