SCIENCE AND ENGINEERING FAIR
Research Plan and/or Abstract for 2013

Category Award:   4 (Blue - Outstanding)

Research Plan:

Abstract:
Novel methods of early detection of diseases are becoming more important as the sciences progress. Early detection allows early treatment and provides time that can often make the difference between a disease that is treatable and one that has progressed beyond the opportunity for a cure. In this project, a mathematical method is being explored as a potential tool for early detection of certain diseases.
Researchers have noted that shapes of healthy human organs such as the lungs and the brain are irregular; time dependent responses of many healthy organs such as the human heart are irregular as well [1]. The degree of these irregularities is affected by disease and can be quantified through fractal dimension analysis. A technique to determine fractal dimension for image data is the box-count method [2], and a technique to determine fractal dimension for time-series data is through use of the Hurst exponent [3,4]. In the box-count method, boxes of a specific size are overlaid on an image and then the number of boxes with pieces of the image in them is counted. The process is repeated with boxes of smaller sizes, and the ratio of boxes used to boxes counted is graphed to determine the fractal dimension. This technique is very useful for spatial data such as image files. The Hurst exponent measures statistical self-similarity in time-series data; self-similarity in a time-series implies how similar a smaller portion of a time-series is to the entire time-series. This method is used for temporal data such as time dependent fluctuations.
In this project, the box-count method is used on images of blood vessels from the retina of human eyes [5,6] and the Hurst exponent is used on heartbeat rate time-series data [7]. The goal is to demonstrate that there are quantifiable differences in the fractal dimensions of healthy and diseased eye images and healthy and diseased heart rate data. These techniques, if implemented, could assist in earlier detection of diabetic retinopathy and heart disease (e.g. arrhythmia) and thus allow patients to get faster treatment, attention, and possibly corrective actions for their conditions. All data used in this project were taken from online databases managed by research institutions. These databases have been made freely available to the public to be used in research [5,6,7].