Shmueli Gilad & Freund Eyal Supervisor: Prof. Dan Adam

1. Technion - Israel Institute of TechnologyDepartment of Electrical EngineeringThe Vision Research and Image Science Laboratory Infant Heart Rate Variability (IHRV) Shmueli Gilad & Freund Eyal Supervisor: Prof. Dan Adam February 1999

2. Index • Abstract • Goals • Method • Averaged Periodogram (Algorithm) • Averaged Periodogram (results) • Auto Regression (Algorithm) • Auto Regression (results) • summary & conclussions

3. Abstract • The Heart Rate (HR) is modulated by different systems , which cause fluctuations in HR which are called Heart Rate Variability (HRV). • HRV has been shown to reflect the behavior and development of different parts in the autonomous nervous system. • Spectral analysis of HRV has contributed to the understanding of the sympathetic and para-Sympathetic systems. • Fetal HRV shows properties similar to adult HRV . • Spectral analysis of fetal HRV can be of use in monitoring the fetal development.

4. Goals • Get a clean and steady digitized HR signal of mature infants (~36 weeks of gestation), saved and formatted to fit matlab software. • Provide fast and easy-to-use mechanism, that performs strong and reliable spectral analysis, on any HR signal, in order to detect the variance in the HR of a healthy infant. • Test two different algorithms, based on different approaches, and view the differences and common.

5. Method • 2 infants HR signals were monitored, using an ultra-sound transducer (HP8040A 2.7Mhz). • The continuos time signals were digitized at 200Hz, 21 minutes long each (total of 250000 digitized points for each signal). • Digitizing was done by using codas A/D converter and a PC (Hardware & Software by Codas). • The digitized signals were saved in matlab format. • Wrote 2 different Algorithms, using matlab mathematical software : • Averaged periodogram based on Fourier transform • Auto Regression parametric model

6. Method (cont.) • The two methods was tested and debugged in order to find the best model parameters, length of stationary segments, number of poles for AR, weight of overlapping for periodograms etc.

7. Averaged Periodogram (Algorithm) • Welsh's Averaged Peiodogram is based on averaging the periodograms of overlapping segments of the signal. • The discrete time signal is divided into overlapping segments for whom the Power Spectral Density (PSD) will be calculated, using the periodogram algorithm, and then all the calculated PSD's will be averaged, in order to reduce the variance (statistical error). X[n] - The original signal 50% Overlapping segments of x[n]

8. Averaged Periodogram (Algorithm - cont.) • According to the periodogram theory, the PSD is calculated using the following formula : w[n] - the time window U - normalizing factor L - segment length - segment p PSD • For getting less variance in the PSD estimations we will average the PSD's of overlapping segments as follows : P - number of segments - The total PSD estimation

9. Averaged Periodogram (results) • Graph A - Averaged periodogram PSD estimations of HR signal of a mature infant (36 weeks of gestation). The signal was digitized in 200Hz, for 10 minutes, total signal length of 150000 points, divided into 5 segments of 50000 points, 50% overlapping, hann window. Graph A 25 20 15 PSD 10 5 0 0.1 0.22 0.34 0.004 0.028 0.052 0.076 0.124 0.148 0.172 0.196 0.244 0.268 0.292 0.316 Hz

10. Auto Regression (Algorithm) • Auto regression is based on the consumption that the given random signal is the output of a gauss white noise, passing through a linear, causal and time invariant filter. • x[n], the random signal, can be expressed as follows : • bk are the model paramets, are calculated as follows : b - the model parameters p - number of poles r - estimated autocorrelation valus N - the length of x

11. Auto Regression (Algorithm - cont.) • After we find the model parameters (bk), we can calculate the estimated PSD of the random signal (HR signal in our case) : b - the model parameters p - number of poles r - estimated autocorrelation valus N - the length of x

12. Auto Regression (results) • Graph A - Auto regression PSD estimations of HR signal of a mature infant (36 weeks of gestation). The signal was digitized in 8Hz, for 10 minutes, total signal length of 4800 points, divided into 5 segments of 50000 points, 50% overlapping, hann window. Graph B 160 PSD 140 120 100 80 60 40 20 0 0.00 0.02 0.03 0.05 0.06 0.08 0.10 0.11 0.13 0.14 0.16 0.17 0.19 0.21 0.22 0.24 0.25 0.27 0.29 0.30 Hz

13. Summary & Conclusions • As written in the articles, we got PSD estimation with 2 peaks in the low frequency band (<0.125Hz), and in the AR results, we can even see the 3rd high frequency peak. • Which of the techniques is better ? • The periodogram technique is more robust, and the results are more objective (less sensitive to parameters we decide on), its disadvantages are the need for relativly big amount of data (long signal), energy leakage because of the window, but as said, its much more • The AR thechnique can be used with a small amount of data ints, it estimates the future autocorellation so no windowing effects, and the results were much more smooth. Its disadvantages are the need to apply a model that is subjective, and may bias the results according to our interference.

14. Summary & Conclusions (cont.) • Segmentation and averaging must be done, due to non-stationarity in long intervals, and to reduce PSD variance.