Critical Scale Invariance in a Healthy Human Heart Rate

Group project for Laboratory of Computational Physics - Module A Course, AA 2022/23

Description of the project

In this project you will analyse from a physics perspective time series of human heart rate. You will demonstrate the robust scale-invariance in the probability density function (PDF) of detrended healthy human heart rate increments. Moreover, you will show that such increments are not Gaussian distributed, but they display fat tails. This scale-independent and fractal structure supports the view that a healthy human heart rate is controlled to converge continually to a critical state.

Final result

The complete result can be found in the Critical-Scale-Invariance-LCP-Group2.ipynb file in the main branch. As an optional work, an attempt to implement the Detrended fluctuation analysis (DFA) has been done in the CleanCode_Combined.ipynb in the branch giuseppe. This analysis doesn't agree with the theory (reference 2), since healty and unhealty patients data show the same trend.

Original reference

1. Critical Scale Invariance in a Healthy Human Heart Rate, Kiyono, Oct 2004
2. Quantification of scaling exponents and crossover phenomena in nonstationary heartbeat time series, C.-K. Peng

Assignment steps

1. Build the cumulative time series $B(i)$ from the detrended and normalised heart beat time series $b(i)$
2. Do a polynomial fit of $B(i)$
3. Calculate the increments (fluctuation) from the polynomial fit
4. Build the increments PDF and fit it with Gaussian and non Gaussian distributions.
5. Test the scale invariance of the PDFs by collapse plot

Data sources

1. Fantasia
2. Normal Sinus Rhythm Database
3. Congestive Heart Failure Database

Members of Group 2

• Tommaso Bertola
• Giacomo Di Prima
• Giuseppe Viterbo
• Marco Zenari