MULTIVARIATE LINEAR REGRESSION BASED SYNTHESIS

OF 12-LEAD ECG FROM THREE BIPOLAR LEADS

Ivan Tomasic, Roman Trobec and Viktor Avbelj

Department of Communication Systems, Jozef Stefan Institute, Ljubljana, Slovenia

Keywords: ECG, MECG, Multivariate Linear Regression, Synthesis, Derivation, Bipolar leads, Wireless electrodes.

Abstract: The development of new technologies for electrocardiographic (ECG) monitoring enables the optimization

of ECG recording strategy, in terms of a number and a position of body electrodes. Emerging wireless

technology, together with requirements for improved wearing comfort, dictates a special design of a

wireless bipolar ECG lead, which is composed of two closely placed electrodes. The measurements from a

set of wireless electrodes, can serve for the reconstruction of the standard 12-lead ECG, which is directly

applicable for the current medical knowledge. We present a method for synthesizing 12-lead ECG from

only three bipolar leads. The result of the proposed method, based on multivariate linear regression, is a

coefficients vector that transforms the data from three bipolar leads to a synthesized 12-leads ECG with

minimum loss of diagnostic information. Two presented test cases show that a linear combination of only

three bipolar leads, each obtained from two electrodes on a distance of 5 cm, suffices for a reliable

synthesis of a standard 12-lead ECG. Wireless ECG leads can constitute a body sensor network that

eliminates the need for additional wires and therefore improves the applicability of ECG device technology.

1 INTRODUCTION

Initial breakthrough in recording electrical activity

of the hearth came from Willem Einthoven, at the

beginning of 20

century. He was first to assigned

the letters to the various deflections in the

electrocardiogram (ECG), and described the

electrocardiographic features of a number of

cardiovascular disorders. Since Einthoven's time

there have been many advances in electro-

cardiography. Over the years, 12-lead ECG became

the golden standard with its diagnostic foundation

recognized by most cardiologists. The measurement

of ECG is simple and non-invasive, and therefore

widely used for diagnostic purposes in cardiology.

The conventional 12-lead ECG is obtained from

ten electrodes placed strategically on a patient's

body. The emergence of new hardware technologies

however, made possible the development of personal

and wireless ECG devices. These new technologies

impose the optimization of electrocardiographic

devices in terms of a number and a position of body

electrodes. Minimization of the required wire

lengths between electrodes and improved wearing

comfort of investigated person also became

important issues. These requirements are in partial

contradiction with the 12-lead ECG, which is the

golden standard; even that it contains an amount of

redundant information.

Several research and experimental projects have

shown (Finlay, Nugent, Kellett, Donnelly,

McCullagh, & Black, 2007) that the number of

electrodes can be reduced and their optimal placing,

that differs from the standard 12-lead ECG placing,

can be found. The measurements from reduced

electrode sets, can serve for the reconstruction (i.e.

synthesis) of the standard 12-lead ECG, which is

directly applicable for the current medical

knowledge.

There are several approaches to the introduction

of wireless technology in ECG measurements. One

of the most promising is the wireless electrode

(Valchinov & Pallikarakis, 2007) which enables the

minimal usage of wires on the body, and

consequently the maximal wearing comfort.

Since wireless electrode is bipolar (it enables the

measurements and transmission of only local

potential differences), we investigated in more

details the reconstruction of the standard 12-lead

ECG, from a set of bipolar leads with closely placed

electrodes. The distance between electrodes should

be small in order to minimize the wire length;

216

Tomasic I., Trobec R. and Avbelj V. (2010).

MULTIVARIATE LINEAR REGRESSION BASED SYNTHESIS OF 12-LEAD ECG FROM THREE BIPOLAR LEADS.

In Proceedings of the Third International Conference on Health Informatics, pages 216-221

DOI: 10.5220/0002697702160221

 SciTePress

however, electrodes cannot be too close because of

increased noise-to-signal ratio (Puurtinen, Viik, &

Hyttinen, 2009). Our investigation showed that a set

of only three bipolar leads, each obtained from two

electrodes on a distance of 5 cm, is sufficient for a

reliable synthesis of 12-lead ECG.

As a data source for the construction of bipolar

measurements, we used multichannel ECG (MECG)

measurements (Trobec, 2003), offering 31 unipolar

measurements. Potential differences between two

unipolar measurements were regarded as bipolar

leads. We used multivariate linear regression (MLR)

to calculate coefficients vector that transforms three

bipolar leads to the standard 12-lead ECG. For the

purpose of having minimum loss of diagnostic

information, the process is personalized in terms of

obtaining a transformation vector for each

investigated person.

2 METHODS

The 12-lead ECG is synthesized from only three

bipolar leads. Since the development of the bipolar

leads is still in an experimental phase, we emulated

them from the available MECG measurements. The

target 12-lead ECG can be reliably obtained from

MECG. Together with the emulated bipolar leads

they are used as the input data to MLR algorithm,

which computes a personalized coefficients vector

that transforms bipolar leads to a synthesized 12-

lead ECG. The target and synthesised 12-lead ECGs

can be now compared in order to evaluate the

proposed method.

2.1 Input Data

Input data sets were segments from 31-channel

MECG measurements, 10 seconds long (1000

samples/second/channel), and obtained from

different volunteers.

Currently, MECGs are mostly experimental

research devices with no common accepted standard

about the number of electrodes and their placing.

The number of MECG electrodes differs from 10 to

300 electrodes (Lux, Smith, Wyatt, & Abildskov,

1978). Their placing is mostly based on the

equidistant four neighbours mesh. We have

developed a custom MECG with 31 electrodes

placed as shown in Figure 1, and all referenced to

the Wilson’s central terminal potential (see (Trobec,

2003) for details).

Figure 1: MECG's placement of 31 electrodes.

Note, that a MECG measurement has enough

leads, placed on appropriate positions, to exactly

reproduce the standard 12-lead ECG.

We will denote each MECG measurement in the

following way:







,…,







,…,







,…,,

(1)

where X(i), and X(j) are the i

and j

leads

respectively, referenced to the Wilson's central

terminal potential, and m is the total number of

leads. The Wilson's central terminal potential is an

average of limb electrodes (Okamoto & Mashima,

1998).

For an evaluation of the proposed method we

will present two test 31-channel MECG

measurements, first in a normal sinus rhythm and

second with a single supraventricular extrasystole.

Such a measurement is particularly useful because

the synthesis of the 12-lead ECG can be additionally

evaluated with the extrasystole reconstruction

ability.

2.2 Bipolar Leads

A bipolar ECG lead is composed of two connected

electrodes with appropriate electronics for

digitalization and transmission of the measured

results (Valchinov & Pallikarakis, 2007). Wireless

bipolar leads can constitute a body sensor network

that eliminates the need for additional wires and

therefore improves the applicability of mobile ECG

devices. Moreover, there is increased safety due to

the complete isolation from the power-line network

and consequently less noise. Additionally, the

influence of body movement on wireless bipolar

electrodes is much smaller than by conventional

electrodes.

A bipolar lead is a potential difference between

two unipolar electrodes i and j:









(2)

MULTIVARIATE LINEAR REGRESSION BASED SYNTHESIS OF 12-LEAD ECG FROM THREE BIPOLAR LEADS

217

If we denote the Wilson's central terminal potential

as φ

WCT

and subtract it from both unipolar potentials

in equation (2), we get:























,

(3)

and finally:













.

(4)

Equation (4) is used to calculate a bipolar lead from

two MECG unipolar leads.

For 31-electrode MECG from Figure 1, 465

bipolar leads can be obtained. However, bipolar

lead's wireless hardware implementation tends to

become smaller and smaller. Hence, such devices

could benefit from a small inter-electrode distance,

which restricts the set of all useful bipolar leads

from MECG, to the set of bipolar leads formed only

from nearest neighbouring electrodes. In the case of

31-electrode MECG the useful set contains just 81

bipolar leads with 85320 possible combinations of

three bipolar leads.

Since the reduction in inter-electrode distance

inevitably reduces signal strength, three bipolar

leads for synthesis of 12-lead ECG may be selected

by means of evaluating signal strength from various

bipolar leads (Puurtinen et al., 2009).

2.3 Multivariate Linear Regression

To model the relationship between a 12-lead ECG

and a set of three approximation leads we used

MLR.

First, a MECG dataset is divided into two

approximately equal intervals. Chronologically first

interval is used by MLR algorithm to calculate

transformation coefficients, and the second interval,

not known to the MLR algorithm, is used for the

estimation of algorithm's efficiency.

Let a set of three arbitrary bipolar leads from the

first interval of the MECG be denoted by:

1,2,3.

(5)

The 12-lead ECG from the first interval of the

MECG is represented as a set of 12-leads:

12,,,,,,

1,2,3,4,5,6.

(6)

As it was already mentioned, every MECG

measurement contains enough leads to exactly

reproduce the standard 12-lead ECG, so ECG12 is

produced from X (see equation (1)) and will

represent a target ECG for our approximation.

Generally, linear regression model represents the

relationship between a response (i.e. criterion

variable) ECG12 and a predictor B (Tabachnik &

Fidell, 2001, chap. 5):

12











































.

(7)

The response is modelled as a linear combination of

functions (not necessarily linear) of the predictor,

plus a random error ε. The expressions f

(B),

(j=1,…,p) are the terms of the model while the α

(j=1,…,p) are the coefficients. Errors ε are assumed

to be uncorrelated and distributed with mean 0 and

constant, but unknown, variance. Our problem can

be solved by the multivariate regression due to the

fact that the response variable ECG12 is

multidimensional, i.e. it is composed of 12 leads

(variables).

Given n independent observations (samples):

, ECG12

),…,(B

, ECG12

) of the predictor B

and the response ECG12, the linear regression

model becomes an n-by-p system of equations:



12





12

















…



























…











·



























, or

(8)

12·,

(9)

where M is the design matrix of the system. The

columns of M are the terms of the model evaluated

at the predictors. To fit the model to the input data,

the system must be solved for the p coefficient

values: [α

… α

], by applying the least-squares

solution, i.e. by minimizing the norm of the residual

vector: ECG12-M·α. We used MATLAB "regress"

function (The MathWorks, 2009) to solve the system

from equation (9).

The predictor B is multidimensional because it is

composed of three variables, so are the functions f

that form the terms of the model. For three

dimensional predictor B={B

, B

}, terms for the

model might include f

(B) =B

(or for example

(B)=B

), which are linear terms, f

(B)=B

(quadratic terms), and f

(B)=B

·B

(a pairwise

interaction term). Typically, the function f(B)=1 is

included among f

, so that the design matrix M

contains a column of ones and the model contains a

constant term.

We have explored the usage of linear additive

(straight-line) models with terms f(B) = 1 and f(B) =

HEALTHINF 2010 - International Conference on Health Informatics

218

Figure 2: The target (blue) and the synthesized (red) 12-leads ECG for the first test case.

B(i). In the case of three bipolar leads, linear

additive straight-line design matrix M becomes:



1

























1























,

(10)

with four coefficients in the vector α=[α

]

that are obtained after the system solution. If we

denote the solution coefficients by α

, then the result

of the M·α

is the best approximation of ECG12 in

the sense of the least-square solution.

Calculated transformation coefficients α

can be

used to synthesize 12-leads ECG from a new data,

measured on the bipolar leads for which the α

was

calculated.

To verify the quality of the synthesised 12-lead

ECG the second interval (not known to the

algorithm) of the input MECG is used as:

12







·



(11)

where M

is the design matrix with bipolar leads

data from the second interval of the MECG, and

ECG12

is the synthesized 12-lead ECG. To verify

the quality of ECG12

it can be compared with the

target 12-lead ECG.

2.4 Personalization

The transformation vector for the synthesized 12-

leads ECG is personalized in a sense of being

calculated for every patient. By studying a

sufficiently large number of cases for different

patients it would be possible to calculate a global

transformation, which gives, on average, for each

individual case the best possible fit (Horacek,

Warren, Field, & Feldman, 2002). Although

possible, such an approach is not necessary due to

the fact that MECG measurement can be easily

obtained for every patient.

3 RESULTS

We will illustrate the quality of the synthesized 12-

lead ECG on two MECG datasets. For each case we

will plot the target 12-lead ECG together with the

synthesized ECG for the purpose of visually

illustrating the quality of the synthesized 12-lead

ECG. Plots shown in Figures 2 and 3 are all referred

to the second intervals of MECGs that are not

known to the MLR algorithm.

The first test case, shown in Figure 2, is a healthy

person with a normal sinus rhythm. Bipolar leads

used for the synthesis are electrode pairs: (17,15),

(11,8), (28,31). For the position of each electrode

please refer to Figure 1. The synthesized 12-lead

ECG is shown in red and the measured target ECG

in blue.

The second test case, shown in Figure 3, is a

measurement that contains, beside a normal sinus

rhythm, also a single supraventricular extrasystole.

Bipolar leads used for the synthesis, are: (13,10),

(10,15), (15,12). All other notations are the same as

MULTIVARIATE LINEAR REGRESSION BASED SYNTHESIS OF 12-LEAD ECG FROM THREE BIPOLAR LEADS

219

Figure 3: The target (blue) and the synthesized (red) 12-leads ECG for the second test case.

Table 1: Pearson's linear correlation coefficients between leads of synthesized and target ECG.

I II III aVR aVL aVF V1 V2 V3 V4 V5 V6

First case 0.976 0.985 0.98 0.983 0.953 0.985 0.981 0.979 0.982 0.983 0.983 0.99

Second case 0.891 0.962 0.942 0.941 0.842 0.95 0.996 0.988 0.939 0.991 0.984 0.942

in Figure 2. In this case the synthesis of the 12-lead

ECG can be additionally evaluated by the means of

the extrasystole reconstruction ability.

4 DISCUSSION

For a similarity measure between a synthesized and

a target ECG we used Pearson's linear correlation

coefficients (Kachigan, 1991, p. 130-133), which are

listed in Table 1, for all leads and for both test cases.

To investigate the differences between the two test

cases we calculated the mean (r) and standard

deviation (σ) of correlation coefficients of both test

cases, which are r



=0.98, σ1=0.009 and r



=0.947,

σ2=0.045 for the first and second test case,

respectively. The second test case is somewhat more

complex because of the extrasystole present;

therefore lower correlation coefficients have been

expected. However, visual examination of the

synthesized 12-lead ECGs reveals adequate

approximation in both test cases.

When synthesizing 12-leds ECG from

measurements obtained from electrodes placed

exclusively on patient's torso it is obviously easier to

synthesize the precordial leads than the limb leads.

To analyze the algorithm performance separately for

the limb and precordial leads we can calculate the

mean and standard deviations of correlation

coefficients separately as shown in Table 2.

The correlation results are somewhat better for

the precordial leads in both test cases as it was

expected. Nevertheless, the algorithm produces

synthesized 12-lead ECG with significant

correlations on limb and precordial leads in both test

cases. The definite diagnostic value of the

synthesized 12-lead ECG is left to be confirmed by

further experiments and their interpretation by

cardiologists.

Table 2: Mean and standard deviation of Pearson's linear

correlation coefficients for the limb and precordial leads.

Limb leads Precordial leads

mean st. dev. mean st. dev.

First case 0.977 0.012 0.983 0.004

Second case 0.921 0.046 0.973 0.026

5 CONCLUSIONS

The ECG monitoring is routinely useful in the early

HEALTHINF 2010 - International Conference on Health Informatics

220

detection of life threatening events. Currently

available medical instrumentation however, shows

limited abilities for continues, long-term ECG

monitoring. One of the key limitations of mobile

ECG devices (like Holter monitors) is a limited

number of lead measurements that they produce.

We have proposed a way to synthesize 12-lead

ECG from a small set of bipolar leads composed of

two electrodes with a distance of 5 cm. We emulated

bipolar measurements from 31 unipolar MECG's

leads. From the same MECG measurement the target

12-lead ECG is calculated and used, together with

three bipolar leads, as the inputs for MLR algorithm.

The MLR algorithm generates a coefficients vector

that transforms three bipolar leads to a synthesized

12-lead ECG.

We evaluated the quality of synthesized ECGs

on two test cases by visual comparison and by

analysing Pearson's linear correlation coefficient

calculated between the target and synthesized 12-

lead ECGs.

In the further work, we plan to evaluate and

verify the proposed approach on more test cases in

order to confirm its diagnostic value. The wireless

bipolar electrodes will be applied for the direct

bipolar measurement on patient's body. The

proposed methodology is widely applicable to the

emerging wireless body sensors technology because

it increases patient’s mobility and comfort.

ACKNOWLEDGEMENTS

This research was funded under Grant No. P2-0095

by the Ministry of Higher Education, Science and

Technology of Slovenia.

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