# Non-Linear HRV

Time and frequency domain measures of HRV quantify HRV on various time scales. Nonlinear HRV quantifies the structure or complexity of the heart rate pattern. For example, a random series of heart beats, a series of heart beats from a normal person and a totally periodic series of heart beats that goes up and down like a wave the exact same standard deviation (SDNN, a time domain measure of HRV), but their underlying organization would be clearly be completely different. A large number of nonlinear measures of HRV have been studied, but only a few been able to identify people at higher risk for a bad outcome.

## Non-linear HRV measures

### Power law slope

- Normally the amount of variance in HRV increases exponentially as the underlying frequency goes down (see Frequency Domain HRV)
- This means that the variance in HRV is self-similar over different time scales
- When two things are related exponentially, a plot of the log of one vs. the log of the other is a straight line.
- To calculate power law slope, the log of HRV spectral power (see Frequency Domain HRV) is plotted against the log of the underlying frequency (See below)
- Power law slope is measured as the slope of the log:log plot between 10 -2 and 10-4 Hz (cycles per second)
- This slope reflects the degree of self-similarity of heart rate patterns over different time scales.
- A more negative number means more abnormal organization of heart rate patterns.
- Decreased power law slope has been show to identify people at higher risk of dying after a heart attack.
- Log:log plot of spectral power vs. underlying frequency. Power law slope is best fit line between 0.01 and 0.0001 Hz.
**Detrended Fractal Scaling Exponent (DFA1 or Î±1)** - Measures degree to which heart rate pattern is random at one extreme or highly correlated (i.e., repeating the same pattern over and over) at the other extreme.
- Calculated using sequences of 4-11 beats (detailed calculations can be found on PhysioNet)
- Normal heart rate patterns are in between, neither random nor correlated.
- DFA1 is about 0.5 for an extremely random heart rate pattern.
- DFA1 is about 1.5 for an extremely correlated one.
- Normal values are about 1.05-1.10
- Decreased DFA1 very strong predictor of outcome after a heart attack and of mortality in older adults.
- DFA can be calculated on other scales. For example DFA2 or Î±2 is calculated from sequences of 12-20 beats. However DFA2 has not been very useful in predicting outcomes.

### SD12 or the Poincaré ratio

- A Poincaré plot graphs each interval between heart beats vs. the interval between the next two heart beats.
- Poincaré plot is an excellent way to visualize heart rate patterns.
- Normal plot is fan-shaped or torpedo-shaped.
- Often plotted for entire recording (e.g. 24 hours) but hourly plots are a good way to see changing heart rate patterns.
- Abnormal heart rate patterns are disorganized and referred to as complex.
- If HRV is very low, Poincaré plot may look like a small ball.
- If an ellipse is fitted to the plot, the dimensions of that ellipse can be measured.
- Short-axis of fitted ellipse is called SD1.
- Long-axis of fitted ellipse is called SD2.
- Poincaré ratio is SD1/SD2.
- Abnormalities in the plot will make SD1/SD2 higher.
- Poincaré plot useful for identifying abnormal HRV and for finding errors in the beat file.