Arrhythmia analysis (heart rate variability)

Johanna Uusvuori 25.11.2004

Contents

1. Introduction: one slide of autonomic nervous system 2. Why does heart rate vary?

3. Analysis methods a) Time domain measures b) Model of the heart rate c) Representations of heart rate d) Spectral methods (introduction) 4. Summary

Human nervous system

Somatic Autonomic Somatic nervous system: controls organs under voluntary control (mainly muscles) Autonomic nervous system: regulates individual organ function and homeostasis, and for the most part is not subject to voluntary control Parasympathetic: rest Sympathetic: Fight, fright, flight

Why does heart rate vary?

Why is the variation interesting?

Heart rhythm is due to the pacemaker cells in the sinus node Autonomic nervous system regulates the sinus node Analysis of the sinus rhythm provides information about the state of the autonomic nervous system

Starting point

of the analysis of the heart rate variability   sinus node → P-wave (hard to detect) analysis methods are based on measuring RR-intervals (RR-interval can be used instead of PP-interval, since PR interval ~ constant )  NN-intervals = RR-intervals but non-normal intervals excluded RR-interval

Problems in the analysis

In laboratory analysis is easy. 24 h measurement (Holter) → problems: wrong corrects, undetected beats, 100 000 RR-intervals Analysis methods are sensitive to errors (time domain methods less sensitive, spectral most sensitive)

Time domain measures of HR

 Long term variations in heart rate (due to parasympathetic activity) are described by: - SDNN = standard deviation of NN-intervals (1 value/ 24 h) - SDANN = standard deviation of NN-intervals in 5-minute segments (288 values / 24 h)  Short term variations in heart rate (due to sympathetic activity) rMSSD = standard deviation of successive interval differences - pNN50 = the proportion of intervals differing more than 50% from the previous interval (used clinically)

d IT

(

k

) 

t k



t k

 1 Successive interval differences: mean int.diff.

Intervals:

Time domain measures of HR…

Histogram approach: – has been used to study arrhyhtmias (in addition to spontane variations in HR) – possible to remove artefacts and ectopic beats – only for 24 h measurement – width of the peak determines the variation in the heart rate Peak of short intervals due to falsely detected T-waves

Model of the heart rate

Integral pulse frequency modulation (IPFM) model:  INTEGRATOR THRESHOLD Main idea: – We have the output: event series

d E u

(

t

) – We search for input m(t) that modulates the HR (=autonomic nervous system) – m 0 is the mean heart rate

IPFM-model…

 Bridge to physiology: pacemaker cells collect the charge until threshold. Then action potential if fired.

 When this equation is valid, produce a peak to the event series:

t



k t k

 1 (

m

0 

m

(  ))

d

 

R

m0 mean heart rate tk time of QRS-complex m(t) modulation of heart rate R threshold

Representations of the heart rate

Quantities to describe the heart rate:    Lengths of the RR-intervals Occurence times of the QRS-complexes Deviations of the QRS-complex times from the times predicted by a model With IPFM-model we can test which method is best in finding the modulation m(t).

Representations of the HR… 1. RR-interval series

* Interval tachogram & inverse

d IT

(

k

) 

t k



t k

 1

d IIT

(

k

) 

t k

 1

t k

 1 These are functions of k (# of heart beats). If they can be changed to functions of time, several methods from other fields can be used in the analysis. * Interval function & inverse (u=unevenly sampled)

u d IT

(

t

)  

K k

 1 (

t k



t k

 1 )  (

t



t k

) * Interpolated interval fuction & inverse (evenly sampled, function of t) - sample and hold – interpolation (and better methods) - sample & hold produces high frequency noise low pass filter → before resampling

Representations of the HR… 2. Event series

   Event series = QRS occurence times:

d E

(

t

) 

k K

  0  (

t



t k

) In low frequencies info of HR, in high frequencies noise → new representation: low-pass filter h

d LE

(

t

)  

h

(

t

  )

d E

(  )

d

 

K



h

(

t



t k

)

k

 0 h =sin(2piF c t)/t for example. After some limit the terms in the sum are allmost zero.

 If in the IPFM-model m(t)=sin(F 1 t), a proper low pass filter removes other stuff except the m(t) → estimate for m(t)=d LE (t)

-

Representations of the HR… 3. Heart timing

Unlike previous representations, this is based on the IPFM model.

The aim is to find modulation m(t).

Heart timing representation:

u d HT

(

t

) 

k K

  0 (

kT

0 

t k

)  (

t



t k

) k = # of heart beat T 0 = average RR-interval length d HT is the deviation of the event time tk from the expected time of occurence . The expected time of occurence is kT 0 .

By calculating Fourier transform of the d HT and m(t), one can see that the spectrum of d HT and m(t) are related, and spectrum of m(t) can be calculated from the spectrum of d HT .

Representation of the HR… Performance of the representations

 Best method to predict m(t) of IPFM-model is to use heart timing representation (which is based on this model…)  However: heart timing representation does not fully explain the heart rate variability of humans → the IPFM-model might not be accurate The End of the representation-part

Spectral methods

New topic: what kind of modulating signals do we have?

Which kind of information is gained?

Oscillation in heart rate is related to for example: body temperature changes 0.05 Hz (once in 20 seconds) blood pressure changes 0.1 Hz respiration 0.2-0.4 Hz Power of spectral peaks → information about pathologies in different autonomic funtions Power spectrum of a heart rate signal during rest

Spectral methods… Which kind of information is gained?

 Peaks of thermal and blood pressure regulation sometimes hard to detect → frequency ranges used: 0.04-0.15 Hz and 0.15-0.40 Hz  Sympathicus increase, low-frequency power increase  Parasympathicus increase, high-frequency power increase  Ratio between two spectral power describes autonomic balance

Spectral methods… Problems of spectral analysis

 Stationarity important  Extrabeats violate the stationarity, but they can be removed in the analysis  Undetected beats are a bigger problem → spectral analysis can not be conducted, if they are present  HR determines the highest frequency that can be analyzed: 0.5*mean hr

Summary

 Autonomic nervous system → heart rate varies  Measurment of HR → info about autonomic system  Analysis methods of HR: – Time domain methods  standard deviations – Representations of the heart rate (intervals, times, heart timing=model based) – Model that can predict heart rate: IPFM-model – Spectral analysis (to be continued in the next talk)