In this project, the investigators will develop a set of computational tools to investigate long sequences of continuous data from physiological systems. One interesting property exhibited by these data sets is called "fractal scaling." This means that the data are "self-similar" on different time scales, so that short sections of data, when rescaled properly, resemble larger sections of data and this scaling holds true over a large range of time intervals. This is a defining feature of a fractal. Another fractal property is that the data exhibit fluctuations on many different time scales. Not all physiological data sets show this attribute. Some show instead a particular time scale at which the variability is most prominent. Many analytical and computational tools to study fractals have been developed over the last two decades. However, the large number of these tools makes it difficult for many investigators to make the proper choice when analyzing any given data set. Furthermore, different computational tools are susceptible to different types of artifacts and different tools are valid for different data types. Erroneous or misleading results can be obtained when the tools are improperly applied. It is very difficult for a non-expert in fractal mathematics to understand and keep track of all of these issues, which can inhibit progress in the investigation of many physiological and behavioral systems. In this project, the research team will assemble a set of established computational tools for fractal time-series analysis, apply them to a variety of data sets with known and unknown properties (i.e., artificially generated data and real physiological data), and determine when different tools break down, when they are most effective, how to detect when erroneous results are being generated, and how to interpret the results. This will provide increased confidence in the application of these tools and encourage their widespread use.
Fractal fluctuations are common in the behavior of biological systems. They have been found in heartbeat intervals, stride intervals, firing rates of neurons, human reaction times, and many other cases. However, the source and significance of these characteristics are unclear. They could arise from fractal properties of ion channels in neurons and have no special role or relevance. On the other hand, they could be deliberately produced at the behavioral level and confer a physiological benefit. By developing and making freely available a standard set of computational tools that implement the most modern algorithms for assessing data for fractal properties, the current project can further our understanding of how sensorimotor systems organize, how behaviors are produced, how sensory information is processed and how perceptions emerge.
It is common, when investigating physiological and biological systems, to obtain recordings of various signals such as heart beats, eye movements, blood pressure, rate of walking, and others. When properly analyzed, these signals can provide important information on the state of health of the organism under study. In many of these measures, results over the last few decades have demonstrated the existence of long-term correlations: instead of each data value being independent of the others in the signal, the values are strongly dependent on each other, and this dependence can extend over long time periods. Proper analysis of these signals requires that the time order of the data values be maintained. In particular, missing data values can disrupt the correlations in the signal and yield erroneous results. This problem is made even more difficult by the fact that missing or corrupted data values are common in recordings of physiological data, due to instrumentation anomalies, movement of electrodes on the body, and other transient disturbances. In this project, the investigators developed computer algorithms to replace missing or corrupted data values in recordings of physiological data, with the goal of maintaining any long-term correlations that are present. These algorithms were applied to a wide range of data with known correlation structures, to determine which algorithms best retain the correlations when presented with different amounts of data that had to be replaced. Recommendations are made as to which methods are most useful in different circumstances. This work is important in helping to maintain the quality and integrity of studies that examine recordings of physiological signals, including signals that might be used for medical diagnosis.
