Simulating Healthy Humans Heart Rate: A Model Using Symbolic Dynamics And Probabilistic Automaton
C.C. Yang, C.H. Chang, S.S. Hseu, H.W. Yien
Taipei Veterans General Hospital
Objectives: This study is performed within the scope of Computers in Cardiology Challenge 2002 on simulating 24 hours RR interval time series. Based on the ideas of symbolic dynamics and probabilistic automaton, we construct a computational model to characterized complex dynamics of healthy human heart rate.
Methods: Human cardiac dynamics are driven by complex nonlinear interactions of two competing forces: sympathetic regulation increases the heart rate and parasympathetic regulation decreases the heart rate. For this type of intrinsically noisy system, it is useful to simplify the dynamics via mapping the output to binary sequences, where the increase and decrease of the interbeat interval are denoted by 1 and 0, respectively. We further define a m-bit symbolic sequence to characterize transition of symbolic dynamics. For simplest model of 2-bits sequence, it has 4 possible symbolic sequences including 11, 10, 00, and 01. Moreover, each symbolic sequence has 2 possible transitions, for example, 1(0) can be transited to (0)0 which results in decreasing RR intervals, or (0)1 in vice versa. To define the mechanism of symbolic transition, we utilize concept of probabilistic automaton in which the transition from current symbolic sequence to next state takes place with a certain probability in a given range of RR intervals. In final version of this model, we use 8-bits sequences and a probability table according to RR time series of healthy humans from Taipei Veterans General Hospital and PhysioNet. The resulting generator comprises of the following major components: (1) the symbolic sequence as state of RR dynamics, (2) the probability table defines transitions between 2 sequences and (3) an absolute Gaussian noise as increment of RR intervals.
Results: The generator reached a score of 0.689 in event 1 (entry 142), and we further achieved a score of 100 in event 2 (entry 20020425.062810)
In summary, our preliminary study on the model lends hope for using ideas from symbolic dynamics and probabilistic automaton. Further study is needed to examine the correlation with physiologic mechanisms.