This repository contains a C++ implementation of the MATLAB software provided by Riccardo Barbieri and Luca Citi here.

Refer to the following papers for more details:

• A point-process model of human heartbeat intervals: new definitions of heart rate and heart rate variability
• The time-rescaling theorem and its application to neural spike train data analysis

Requirements

The project can be built with CMake, the only dependencies are Eigen and Boost.

Check here for information on how to install these two packages.

Documentation

The technical and scientific documentation for this repository is available here. (WIP)

In order to build the project you should follow the instructions in the build.sh script.

Quick Tour

This brief tutorial shows how to fit a history-dependent Inverse Gaussian point process model to a temporal series of RR events.

You can find this example as a Jupyter Notebook in the examples/ directory.

Note: In order to call the Python bindings you need to first build the library.

# Basic imports
import sys
import os
import numpy as np
import matplotlib.pyplot as plt

# Path to the generated .so library (MacOs or Linux) or .dll (Windows)
# Should be "build/src/" if you built the project with build.sh
PATH_TO_LIB = "path/to/library/" 

sys.path.append(PATH_TO_LIB)

# Now we can import the Python byndings from the pointprocess library
from pointprocess import (
    compute_single_regression,
    compute_full_regression,
    compute_spectral_analysis,
    Distributions,
    Result,
    RegressionResult,
    get_ks_coords
)

# Example: load and plot a series of RR events
rr = np.load("events.npy")
events = np.array(rr[75:301])
plt.plot(events[1:], 1000*np.diff(events),"b")
plt.xlabel('time [s]')
plt.ylabel('RR [ms]')

Single Regression

# Compute single regression on a subset of the RR intervals
result_single_regression = compute_single_regression(
    events = rr[75:301],
    ar_order = 9,
    has_theta0 = True,
    right_censoring = False,
    alpha = 0.02,
    distribution=Distributions.InverseGaussian,
    max_iter=10000
    )

# You can now access to elements as:
# result_single_regression.thetap
# result_single_regression.theta0
# result_single_regression.kappa
# result_single_regression.likelihood
# result_single_regression.mean_interval

Get Spectral info

thetap = result_single_regression.thetap
mean_interval = result_single_regression.mean_interval
kappa = result_single_regression.kappa
variance = result_single_regression.sigma**2


# Retrieve spectral info
analysis = compute_spectral_analysis(thetap, mean_interval, variance, aggregate=False)

# Plot stuff
plt.figure(figsize=(8,6),dpi=100)
colors = []
for comp in analysis.comps:
    p = plt.plot(analysis.frequencies, np.real(comp),linewidth=0.7)
    colors.append(p[-1].get_color())
    
for i in range(len(analysis.poles)):
    plt.vlines(analysis.poles[i].frequency,0,10000,colors[i],"--")
    
plt.plot(analysis.frequencies, analysis.powers, "k-",linewidth=0.8,label="Total PSD")
plt.xlabel("f [Hz]")
plt.ylabel("PSD [$ms^2$/Hz]")
plt.legend()

Full Regression

# Fit Inverse Gaussian distribution to RR by moving a 60.0 seconds windows and shifting it by 0.005 s at each step.
# The mean of the ditribution will bi given by a 9th order AR model
result = compute_full_regression(
    events=rr,
    window_length=60.0,
    delta=0.005,
    ar_order=9,
    has_theta0=True,
    right_censoring=True,
    alpha = 0.02,
    distribution=Distributions.InverseGaussian,
    max_iter = 1000
)

# Compute spectral info
result.compute_hrv_indices()

# Convert result to dictionary...
d = result.to_dict()

# Plot first moment of the distribution in time, along with the discrete RR intervals 
plt.figure(figsize=(6,4),dpi=120)
plt.plot(d["Time"],d["Mu"],"b",linewidth=0.5,label="First moment of IG regression")
plt.xlabel("Time [s]")
plt.ylabel("$\mu$ [s]")
plt.plot(rr[1:],np.diff(rr),"r*",mew=0.01,label="RR interval")
plt.legend()

# Plot hazard rate
plt.figure(figsize=(6,4),dpi=120)
plt.plot(d["Time"],d["lambda"],"firebrick",linewidth=0.15,label="Hazard rate ($\lambda$)")
plt.xlabel("Time [s]")
plt.ylabel("Hazard rate ($\lambda$)")
plt.legend()

# Same but just for a smaller number of samples...
plt.figure(figsize=(6,4),dpi=120)
s,e = 30200,31000
plt.plot(d["Time"][s:e],d["lambda"][s:e],"firebrick",linewidth=0.5,label="Hazard rate ($\lambda$)")
plt.xlabel("Time [s]")
plt.ylabel("Hazard rate ($\lambda$)")
plt.legend()

# Plot LF/HF ration
plt.figure(figsize=(8,8))
bal = d["powLF"] / d["powHF"]
plt.plot(d["Time"],bal,"blue",linewidth=0.5)
plt.ylim(-1,20)
plt.ylabel("LF/HF")
plt.xlabel("Time [s]")

# Build KS plot to assess goodness of fit
coords = get_ks_coords(result.taus)
plt.figure(figsize=(5,5),dpi=100)
plt.plot(coords.z, coords.inner, "k", linewidth=0.8)
plt.plot(coords.lower, coords.inner, "b", linewidth=0.5)
plt.plot(coords.upper, coords.inner, "b", linewidth=0.5)
plt.plot(coords.inner, coords.inner, "r", linewidth=0.5)