Complexity and some of its applications in health sciences
Authors: Erjaei G. Hussien 
Published: November 2013

In recent years, the field of applied nonlinear dynamics has attracted scientists and engineers across many different disciplines to develop innovative ideas and methods to study complex behavior exhibited by relatively simple tools. In this study, we have investigated some of these tools together with some its applications. Among these applications, here we have chosen one of our resent research work in heart rate complexity (HRC). It seems classical vital signs information such as heart rate and blood pressure to identify critically injured patients eventually replaced by complexity exist in the heart rate. Indeed, HRC is a measure of the beat-to-beat variations in heart rate which can be used in patients to identify their physiologic deterioration caused by critical injury. This measurement is the results of nonlinear analysis to the R-to-R interval (RRI) of the electrocardiogram (ECG) of pre-hospital trauma patients. Entropy, Lyapunov exponent and capacity dimension are some tools for this nonlinear analysis of ECG signal. These measurements as a nonlinear analysis tools, play an important role in this study. Indeed, biologic processes, as a highly complex system, cannot be described by analysis of the simple calculation. In the cardiovascular system, one consequence of this complexity is the irregularity and chaotic behavior in RRI. Perrier to use these tools for human RRI analysis Batchinsky and his co-workers have used them in two animal models of hemorrhagic shock [A.I. Batchinsky, W.H. Cooke, T. Kuusela & et al., Loss of complexity characterizes the heart-rate response to experimental hemorrhagic shock in swine. Crit Care Med., 35:519 -525, 2007]. They have used Entropy technique to measure RRI complexity on which was decreasing during the shock and was restoring by fluid resuscitation. Similar study have reported in decreasing of RRI complexity in human volunteers subjected to central hypovolemia by means of lower body negative pressure. In this study, we have used the same methodology in this and some other articles, with some different chaotic measurements for real data, to discriminate between survivors and non-survivors of trauma in the pre-hospital setting. We hypothesized that loss of RRI complexity is associated with mortality after trauma. In order to do our data analyze, among the 65 available data recorded by ECG from trauma patients brought to hospital prior to any medication, we were screened for presence of ECG recordings free of electromechanical noise, free of ectopic beats, and at least 270 heart beats in length of 45 patients were selected. Evaluating entropy, Lyapunov exponents and capacity dimension of these data the results are showed in tables 1 and 2. Table 1 shows the results for 5 (out of 37) survivals and Table 2 for 5 (out of 8) non-survival patients. As we expected, by comparing the average values, all values correspond to survival patients are more than the values corresponds to non-survivals. Therefore, in average the chaos measurements, entropy, Lyapunov exponents and capacity dimension in survival patients are higher than non-survival, which proof our assertion.