ANALYSIS

OF ECG DATA, FOR DATA

M. SHRIDHAR andM.F.

COMPRESSION

STEVENS

Electrical Engineering Department, University of Windsor, Windsor, Ontario (Canada)

(Received: 9 April. 1978)

SUMMARY

A number of papers on the subject of data reduction techniques applied to ECG Data have recently been published; however, the authors found that most of these articles did not consider quantization techniques, which can be eflectively applied to ECG data without any complex parameter extraction procedures. In this paper the authors have looked at the ejj?ects of quantization on ECG data and techniques of reducing the amount of data needed to represent these signals. Basically, 3 data reduction techniques, linear prediction using differential pulse code modulation, spectral analysis and slope change detection are investigated and a relative assessment of their performance is presented. lhis analysis revealed that a slope change detection, as applied to prefiltered data, can be used to represent ECG data at a rate of 2 bits/sample, while maintaining the mean squared error and peak error below 1 yO anJ 5% respectively. This technique therefore gives an effective 3 to 1 reduction over the original sampled data, since it was found that the original data could be quantized to 6 bits without signij?cant loss of waveform information.

SOMMAIRE

On a publid rtkemment de nombreux articles sur les methodes de relluction des don&es appliqutes aux ECG. Neanmoins les auteurs ont observe que la plupart de ces articles ne s’interessent pas aux mtthodes de quantification applicables aux ECG sans intervention de procedures compliquees Xextraction de parametres. Dans cet article les auteurs ont &w&t les efits de la quantification sur les ECG et les methodes de reduction du volume de don&es nkcessaire pour repressenter ces 113

ht. J. Bio-Medical Computing (10) (1979) 113-128 @Elsevier/North-Holland

Scientific Publishers Ltd.

114

M. SHRIDHAR,

M. F. STEVENS

signaux. Fondamentalement trois mtthodes de rduction des don&es ont ttt examinies: p&vision linkaire par modulation di@rentielle, analyse spectrale et dttection de changement de pente. Puis leurs performances ont ktk comparies. Cette analyse a r&Ye qu’une mtthode par de’tection de changement de pente, appliqude h Jes donnkes dPjd jilt&es, peut &tre utiliske pour reprtsenter des don&es dectrocardiographiques au taux de 2 bitslkchantillon, tout en maintenant l’erreur moyenne quadratique et l’erreur maximale en dessous de 1% et de 5% respectivement. Par suite cette mtthode permet de rduire de 3 d 1 les donraPesinitiales, compte tenu du fait que ces donntes peuvent &tre quantijkfes, au niveau de 6 bits, suns perte significative d’information.

I.

INTRODUCTION

Minicomputers are beginning to play a major role in the monitoring, storage and diagnosis of electrocardiogram (ECG) data. These computer methods are being adapted because of the ever increasing number of ECG’s taken yearly. Therefore efficient means of representing the ECG’s in a computer are needed, in order to make these automatic systems financially feasible. In the past a wide range of data compression techniques have been applied to ECG data, and the results of many of these methods have been outlined in papers by Andrevvs ef al. (1967) and McFee and Baule (1972). These techniques can be divided into 3 main groups, transformation, parameter extraction and direct data techniques. It was found that most of the authors working in this area have evaluated their techniques by comparing their parameter representation and the original sampled data, assuming each number is stored in a fixed length word of memory. Thus they have not taken advantage of any quantization techniques to make optimal use of the available storage. By directly quantizing the original data one finds that a considerable reduction can be achieved, while maintaining an acceptable degree of fidelity. Now if the model parameters are also quantized one can calculate the reduction factors on a bits/sample basis, rather than simply using the number of model parameters versus the number of original sample points. In this paper the effects of quantization on ECG data are analyzed and techniques to improve data reduction over those obtainable by direct quantization are discussed. Basically, 3 data reduction techniques, linear prediction with differential pulse code modulation, spectral analysis and slope change detection, are considered and a relative assessment of their performance is presented. The results of our investigation reveal that a reduction of 3 to 1 is obtainable if a slope change detection technique is applied to prefiltered ECG data. This claim is based on the number of bits/sample required for the slope technique as compared to the number of bits/sample required when ECG data is directly quantized. The mean squared

ANALYSIS OF ECG DATA

115

error was less than 1% in all cases and the maximum percentage error between the original and reconstructed samples was less than 5%.

II.

ACQUISITION AND PREPROCESSING OF ECG DATA

The standard lead II configuration was used for recording the data. The data was obtained from the output monitor terminal of a Burdick model EK2 electrocardiograph machine. Now in order to sample the analog signal, one must decide on a bandwidth for the ECG signal. The bandwidth should be as small as possible without excluding any important frequency components. It was found that a wide range of bandwidths have been proposed by various authors, ranging from 5 Hz to 40 Hz (Swenne et al., 1973), to DC to 1477 Hz (Burton et al., 1975). In the former case the author was dealing with the QRS portion of the ECG only, while in the latter case the author was using Fourier coefficients in order to detect ECG waveform changes. The choice of bandwidth can significantly affect one’s reduction factor, since the number of samples needed to represent a set amount of data is directly proportional to the sampling rate. It was decided to use a bandwidth from DC to 100 Hz for our analysis since it was found that any significant reduction below this value showed visual distortion in the waveform. This upper limit was also recommended by Pipberger et al. (1967) and Wartak (1970). Therefore the signal was low pass filtered to 100 Hz and the sampling rate was set to 250 Hz, so that any aliasing affects would be insignificant. The analog to digital convertor used was a Tustin X-1500,14 bit convertor and all the analysis was done using a Nova 840 computer with 32k core memory and 2 Diablo discs with a total capacity of 2.5 million words.

III.

LINEAR PREDICTION MODEL

Let the sample sequence of the ECG signal be represented by: Si,

i=l,2,3

,...,

N

(3.1)

linear prediction attempts to estimate the present sample by a linear combination of past samples. The estimate is of the form:

c ”

c

sic

UjSi- j

(3.2)

j=l

where aj, j= 1, 2, . . . , p are the prediction parameters and Si represents the estimate of Si. The system is represented by an all pole model which has a transfer

116

M. SHRIDHAR,

M. F. STEVENi

function in the z-domain as follows: H(z)=

p’ l+ 7

(3.3)

ajZ-j

where a0 has been normalized to unity. The zeros and excitation function have not been included in the expressions because of the way in which the model was implemented using the first p samples as starting values. Now in order to calculate the als one Amust minimize the mean squared error between the samples Si and the estimate Si. Therefore: ei=Sl-~i P

ei=Si-

ajSi_

7

(3.4)

j

u

i= 1

Now the sum of the squared error is: ~Z~C$=Q2ii-~CZjSi_j) j=l

i=l

i=l

(3.5)

Now one can calculate the als by differentiating with respect to the aj’s and set the results equal to zero, giving: EC-2

tki-2 i=l

ajSi_j)Si-,=O,

k=l,2,3,.*.,p

j=l

=~~ajSi_jSi_~=~SiSi_., i=r j=r

k=l,2,3,*.*,p i=

(3.6)

1

Now using matrix notation:

(Djk

=

c

Si_jSi_k

(3.7)

i=l

N $k=

c

SiSi-k

i=l

The solution of the set of linear eqs. (3.7) yields the optimum (in the mean squared

117

ANALYSIS OF ECG DATA

error sense) parameters, j= 1, 2, 3, . . . , p. There are many methods of solving these linear equations. Levinson (Robinson, 1967) derived a recursive procedure for solving for the als, j= 1,2,3, . . . , p, which takes advantage of the symmetrical and positive definite characteristics of the matrix @jb Now if the estimate using lmear prediction is accurate, one can expect that the error between the estimate Si and the sample points Si, can be encoded using fewer bits than the original samples. Therefore by using the linear prediction model along with the coded error one can obtain a better reconstruction of the signal. When this model is implemented directly one finds that the output is subject to error build up, which can cause unacceptable errors in the reconstruction. For this analysis differential pulse code modulation (DPCM) was used, so that this error build up problem could be alleviated. The DPCM predictive quantizing scheme is shown in Fig. 1. A one bit quantizer was used and the quantizer level Q is chosen to be, (Cirjanic, 1973): M tlj,

Q=b

ISi-iil

(3.8)

c

i=l

where

P gi=

@i-k c k=l

and M is the number of samples over which Q is constant. Therefore the estimated sample points are given by D

c

ajSi_j+Q

ii=

sgn ei

(3.9)

j=l

where Sgnei=+l,

=- 1,

f?i>O ei