Analysis of Time-Varying Biological Data Using Rainflow Cycle Counting

Abstract

A wide range of biological investigations lead to time-history data. The characterization of such data can be difficult particularly in the presence of signal noise or superimposed signals. Several methods are described which can be brought to bear including FFT, thresholding, peak counting, and range counting. However, each of these approaches has significant disadvantages. In this paper we describe a novel method, known as rainflow cycle counting, for characterizing time varying biological time-history data in terms of spiking or oscillation amplitude and frequency. Rainflow counting is a straightforward algorithm for identifying complete cycles in the data and determining their amplitudes. The approach is simple, reliable, easily lends itself to automation, and robust even in the presence of superimposed signals or background noise. After describing the method, its use and behavior are demonstrated on three sample histories of intracellular calcium concentration in chondrocytes exposed to fluid shear stress. The method is also applied to a more challenging data set that has had an artificial random error included. The results demonstrate that the rainflow counting algorithm identifies signal oscillations and appropriately determines their amplitudes even when superimposed or distorted by background noise. These attractive properties make rainflow counting a powerful approach for quantifying and characterizing biological time histories.

Keywords:

• Time-history
• filtering
• fluorescent imaging
• intracellular calcium
• fatigue analysis
• FFT