CARDIAC MAGNETIC FIELD MAP TOPOLOGY QUANTIFIED

BY KULLBACK-LEIBLER ENTROPY IDENTIFIES PATIENTS

WITH HYPERTROPHIC CARDIOMYOPATHY

A. Schirdewan, A. Gapelyuk, R. Fischer, L. Koch, H. Schütt, U. Zacharzowsky

R. Dietz, L. Thierfelder

Medical Faculty of the Charité, Franz-Volhard-Klinik, Helios Klinikum-Berlin, Wiltbergstr. 50, D-13125 Berlin, Germany

N. Wessel

Department of Physics, University of Potsdam, Am Neuen Palais 10, D-14415 Potsdam, Germany

Keywords: Patient screening, Cardiac magnetic field mapping, Kullback-Leibler entropy; Hypertrophic

cardiomyopathy.

Abstract: Hypertrophic Cardiomyopathy (HCM) is defined clinically

by the growing/thickening of especially the left

heart muscle. In up to 70 % of cases, there is a family history of this condition. The individual risk for

affected patients strongly varies and depends on the individual manifestation of the disease. Therefore, an

early detection of the disease and identification of high-risk subforms is desirable. In this study we

investigated the capability of cardiac magnetic field mapping (CMFM) to detect patients suffering from

HCM (n=33, 43.8 ± 13 years, 13 women, 20 men; vs. a control group of healthy subjects, n=57, 39.6 ± 8.9

years; 22 women, 35 men; vs. patients with confirmed cardiac hypertrophy due to arterial hypertension,

n=42, 49.7 ± 7.9 years, 15 women, 27 men). We introduce for the first time a combined diagnostic approach

based on map topology quantification using Kullback-Leibler (KL) entropy and regional magnetic field

strength parameters. The cardiac magnetic field was recorded over the anterior chest wall using a

multichannel-LT-SQUID system. We show that our diagnostic approach allows not only detecting HCM

affected individuals, but also discriminates different forms of the disease. Thus, CMFM including KL

entropy based topology quantifications is a suitable tool for HCM screening.

1 INTRODUCTION

Hypertrophic cardiomyopathy (HCM) is a primary

inherited cardiac muscle disorder characterized by

hypertrophy, usually in the absence of other loading

conditions, such as hypertension. In the general

population, familial hypertrophic cardiomyopathy

(FHCM) is the most common cardiovascular genetic

disorder with a prevalence of about 1 in 500 adults.

HCM is caused by mutations in several cardiac

sarcomeric contractile protein genes. So far

mutations in 11 different genes, including the

cardiac ß-myosin heavy chain (ß-MHC), myosin-

binding protein C (MyBP-C), cardiac troponins T

and I, α-tropomyosin, myosin light chains and, more

recently, titin and actin genes, have been identified

(Seidman 1998, Thierfelder 1994). Histo-

pathological hallmarks of HCM are myocyte

hypertrophy with disarray and increased cardiac

fibrosis, leading to electrical remodeling processes

in the myocardium (Maron, 2004). The clinical

course of the disease is heterogeneous. Clinical

presentation of HCM ranges from minimal or no

symptoms to the development of the most serious

complications, including atrial fibrillation, heart

failure, and sudden death, often at a young age and

in the absence of previous symptoms (Spirito, 1989).

One of the strongest predictors of disease

progression to heart failure and finally death is the

existence of a hemodynamic obstruction of the left

ventricular outflow tract during systole, which per

convention is defined by a pressure gradient ≥30

mmHg measured by continuous wave doppler

echocardiography. Therefore, it is of clinical

importance to distinguish between the obstructive

(HOCM) and non obstructive (HNCM) form of the

disease. Familial hypertrophic cardiomyopathy is

445

Schirdewan A., Gapelyuk A., Fischer R., Koch L., Schütt H., Zacharzowsky U., Dietz R., Thierfelder L. and Wessel N. (2008).

CARDIAC MAGNETIC FIELD MAP TOPOLOGY QUANTIFIED BY KULLBACK-LEIBLER ENTROPY IDENTIFIES PATIENTS WITH HYPERTROPHIC

CARDIOMYOPATHY.

In Proceedings of the First International Conference on Bio-inspired Systems and Signal Processing, pages 445-452

DOI: 10.5220/0001064504450452

 SciTePress

the most common structural cause of sudden cardiac

death in individuals aged less than 35 years,

especially in competitive athletes. Thus, an early

recognition of the disease is useful for risk

assessment and starting drug therapy and non-

pharmacological treatment options to prevent

prognostic fatal heart failure and mortality. The

detection of affected patients remains still

challenging. Genetic testing allows accurate

diagnosis of HCM and its causing mutations, but has

some limitations. First, DNA screening is not part of

routine clinical evaluation, and identifies the

mutation actually only in 50-60 % of patients.

Secondly, as shown by DNA genotype-phenotype

correlation studies, the disease expression varies not

only between unrelated individuals but also within

the same family. At present, clinical screening and

risk stratification includes medical history, clinical

examination, 12-lead ECG at rest and under physical

exercise, Holter-ECG, echocardiography and cardiac

magnetic resonance imaging. Follow-up

examinations should be encouraged in affected

patients on a 12-18 month basis. For their first

degree relatives annual evaluations are

recommended in the adolescence period and every 5

years beyond the age of 18.

Noninvasive electrophysiological diagnosis in

patients suffering from HCM is usually done by

electrocardiography, rarely by body surface potential

mapping studies. However, information content

from ECG signals seems to be limited and not

disease specific (Maron, 1990). As an alternative to

electrocardiography, magnetocardiography can be

used for a study of cardiac electrophysiological

phenomena, especially myocardial electrical

remodeling processes. Changes in myocardial

electrical properties were shown to be associated

with the development of hypertrophic

cardiomyopathy (Fananapazir, 1989). Multi channel

cardiac magnetic field mapping (CMFM) reflects the

magnetic fields generated by the myocardial

electrical currents occurring during the cardiac

cycle. CMFM signals have several advantages: (1)

they are little influenced by the tissues between skin

and heart; (2) they are sensitive to tangential

currents that arise in the border zones of cardiac

tissue with different electrophysiological properties;

(3) they consider the track of electrical vortex

currents; and (4) their properties make it possible to

accurately localize intracardiac sources (Fenici,

2003).

We therefore investigated the capability of

CMFM to detect patients suffering from HCM,

including those who have a very mild phenotype or

are asymptomatic. The purpose of the study was to

develop a CMFM based diagnostic approach to

improve screening/diagnosis of HCM. We

introduced the calculation of Kullback-Leibler

entropy as a parameter to quantify the topology of

cardiac magnetic field distribution. We use the term

map topology as a synonym for the two-dimensional

distribution of cardiac magnetic field strength. Note

that this term is therefore independent from field

strength amplitudes. The mathematical method, first

described by Kullback and Leibler in 1951, provides

a value of the similarity between two probability

distributions (Kullback).

We further analyzed, whether a combination of

KL based topology quantification with regional field

strength parameters improves the discrimination

power of the automatic diagnostic algorithm.

Our study was done to address three questions:

1. Can CMFM distinguish between HCM

individuals and healthy control subjects or patients

with cardiac hypertrophy of other causes?

2. Is it possible to discriminate between the two

main phenotype subgroups of HCM; patients with

(HOCM) and without (HNCM) obstruction of the

left ventricular outflow tract?

3. How do CMFM based classification algorithms

perform, when prospectively applied for screening in

HCM families with known genetic status?

2 METHODS

2.1 Patients

Thirty three patients (HCM, n=33, 43.8 ± 13 years,

13 women, 20 men) affected by hypertrophic

cardiomyopathy were recruited from our hospital

based cardiomyopathy-outpatient center. The

diagnosis was confirmed by complex diagnostic

tests including echocardiography and magnetic

resonance imaging established on evidence-based

guidelines. HCM was diagnosed by the presence of a

non-dilated and hypertrophied left ventricle in the

absence of another cardiac or systemic disease (e.g.

hypertension or aortic stenosis) capable of producing

the magnitude of hypertrophy observed. Nineteen

patients suffered from the obstructive form and 14

patients from hypertrophic non obstructive

cardiomyopathy.

The total number of subjects in the control group

(NoHCM) was n=99. We recruited a healthy

volunteers group from an occupational health center.

The 57 healthy volunteers (age 39.6 ± 8.9 years; 35

men and 22 women) had normal findings in

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echocardiography, bicycle ergometry, ECG and

Holter-ECG for many years. No control subject had

a history of cardiac diseases or symptoms. Forty two

patients with essential arterial hypertension (HYP,

n=42, 49.7 ± 7.9 years, 15 women and 27 men) were

also included in this study, fulfilling the following

criteria: known hypertension on pharmacological

therapy; echocardiographicly estimated left

ventricular hypertrophy (Framingham heart study

classification FHC 1-2); no prior clinical

manifestation or angiographic documentation of

coronary artery disease; no evidence of prior

myocardial infarction. The NoHCM group consists

of both healthy volunteers and hypertensives

(together n=99) to get a more realistic control group

for familiar HCM screening.

Two families with genetically proofed HCM (ß-

MHC, α-Tropomyosin; 4 HNCM, 1 HOCM, 22

family members in total) were investigated

prospectively to check the accuracy of the MFM

screening tool.

Our internal review board approved the study

and written informed consent was obtained.

2.2 Magnetocardiographic

Measurements

The cardiac magnetic field was recorded over the

anterior chest wall using a seven channel magnetic

measurement system (Cryoton Ltd, Moscow) based

on low temperature Superconducting Quantum

Interference Device (LT-SQUID), coupled with an

axial second order gradiometer (baseline 5.5 cm,

pickup coil diameter 2 cm). The component of the

magnetic field perpendicular to the chest wall was

registered in a 38 point grid (Fig. 1a). To improve

the signal to noise ratio all measurements were done

in a magnetically shielded room (VAC Akb3b) with

a shielded factor better than 10000 at 10 Hz. Typical

system performance in this environment was 7 fT in

unit band. The measurements were done sequentially

at six measurement positions (Fig. 1a) to cover a

mapping area of 20x20 cm. Recording time was 30

seconds per point with an acquisition rate of 1000

Hz and a bandwidth of 0.01 – 130 Hz. The ECG lead

II was recorded simultaneously as a time reference

signal for further processing. Thereafter, signal

averaging techniques and offset corrections were

applied. Averaged data were then transformed from

irregular measurement grid to the regular 6x6 point

grid (20 cm width and height) using thin-plate-spline

surface. Fig.1b shows averaged cardiac magnetic

Figure 1: The layout of cardiac magnetic field map

(CMFM) measurement: (a) CMFM measurement grid

based on a seven channel system. The dashed lines denote

six sequential measurement positions. (b) Cardiac

magnetic field waveforms transformed into a regular grid

(6x6) corresponding to the light grey square in panel (a).

signals for the regular grid. The strength of the

cardiac magnetic field was in the range of 10 – 100

pT (picotesla, 10-12 Tesla). The MFM amplitude

depends on the distance between measurement plane

and patient heart. To compensate this effect we

normalized magnetic field strength by the mean

absolute value during QRS averaged over 36 points

of rectangular grid.

2.3 Cardiac Magnetic Field Map

Quantification

After averaging we obtained 1000 samples for each

of the 36 measurement positions (Fig 1b), leading to

1000 different CMFM. Thus, the dimensionality of

measured data is very high and therefore, we have to

reduce it. One solution we present here is based on

the concept of Kullback-Leibler entropy to quantify

the topology of each map. Suppose that Q={Q

}

(i=1,..,36 – the number of measurement positions; 1:

A1, …, 6: A6, 7: B1, …, 12: B6, …36: F6 in Fig 1b)

is a given reference well-behaved probability

distribution (all Q

>0) and that P={P

} (i=1,..,36) is

some trial probability distribution. The difference of

information content of P compared to the reference

distribution Q is quantified by the Kullback-Leibler

entropy

PP,QKL ln )(

∗=

∑

(1)

The Kullback-Leibler (KL) entropy can be

considered as a kind of distance between the two

probability distributions, though it is not a real

distance measure because it is not symmetric. In our

study, KL entropy was used to quantify differences

in topology between magnetic field maps of a single

subject compared with a reference maps. For each

CARDIAC MAGNETIC FIELD MAP TOPOLOGY QUANTIFIED BY KULLBACK-LEIBLER ENTROPY IDENTIFIES

PATIENTS WITH HYPERTROPHIC CARDIOMYOPATHY

447

time point, the group mean CMFMs of subjects

without HCM was used as a reference map. To

quantify topology independent from amplitudes,

each CMFM was normalized to get a probability

distribution. For maps very similar to the reference

we obtain a KL entropy value near zero, differences

in topology lead to higher KL entropy values.

For each time point between the onset of QRS

and the offset of T-wave, KL values describing

differences in topology were calculated. In order to

avoid inadequate comparisons due to interindividual

differences in QRS and STT duration, we limited the

considered time intervals to the shortest QRS and

STT lengths in the study population. To identify sub

segments with the highest differences in KL values

between compared groups, we calculated the

discriminant index (DI) for every time point as

follows: the absolute differences of mean KL values

in both groups were divided by the standard

deviation of all cases. Mean KL values during QRS

and STT subintervals with a DI value greater than

0.8 were considered as classification parameters

KLQRS(DI>0.8) and KLSTT(DI>0.8).

Figure 2: Mean group Kullback-Leibler (KL) entropy

values over time during QRS (a) and STT (b). NoHCM

group values are denoted with solid (blue) lines and HCM

group values with dashed (red) lines (reference maps:

NoHCM group). Lower panels give discriminant index

(DI) values during QRS (a) and STT (b) intervals

respectively: KL values for time intervals where DI was

higher than 0.8 (dashed lines) are considered for

KLQRS(DI>0.8) and KLSTT(DI>0.8) calculation.

To assess regional differences in magnetic field

strength, which cannot be captured by topology, we

calculated 36 regional parameters (QRSA1-F6, for

positions see Fig. 1b) as mean values of magnetic

field strength during QRS complex. Data processing

was performed in two steps: classification rules were

determined, firstly to discriminate between groups

with and without HCM, and secondly to

discriminate patients with different forms of HCM.

For each step classification performance was tested

for KL parameters, regional features and then for

their combinations. Finally, the best set of predictors

was prospectively applied to identify members of

HCM families affected by the disease.

3 RESULTS

Discrimination of HCM Individuals from Healthy

Control Subjects and Patients with Cardiac

Hypertrophy of other Causes (NoHCM). The

mean KL values of the HCM and NoHCM groups

during QRS and STT interval are given in Fig. 2

(upper panels), with the corresponding DI values in

the lower panels. Only the beginning and parts of the

second half of the QRS are discriminating (DI>0.8)

for these groups, whereas for STT almost the whole

segment is distinctive. These subintervals were used

to calculate KLQRS(DI>0.8) and KLSTT(DI>0.8).

Mean values of these parameters differed

significantly between the two groups (Tab. 1). LDA

based on these two features yielded a sensitivity of

78.8 % and specificity of 86.9 % (Tab. 1) with an

overall correct classification rate of 84.8 %. Next,

we estimated discrimination power of regional

parameters based on mean values of magnetic field

strength in each grid position. Forward stepwise

discriminant analysis was performed to select the

best two feature set: QRSB3 and QRSF3. QRSB3

was positive in the NoHCM and negative in the

HCM group (Tab. 1, p < 10-8). For QRSF3 mean

values of both groups were comparable and not

significantly different. However, this parameter was

automatically selected by LDA because it provides

orthogonal information to QRSB3 to separate both

groups. The overall classification rate based on these

two regional parameters was lower than with KL

based: The specificity of 85.9 % was comparable

with KL features but the sensitivity of 66.7 %

(cross-validated only 63.6 %) was substantially

lower (Tab. 1).

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Table 1: Descriptive statistics of patient groups without

HCM (NoHCM) and with HCM as well as their

separability. Data are given as mean values ± SE and

percentage of correctly classified (CC) cases. If ‘leave one

out’ crossvalidated results of discriminant function

analysis differ from the original results, they are shown in

parentheses. P-values were obtained with the Mann-

Whitney-U-test (univariate cases) and the Wilks-Lambda

test (linear discriminant function). Three classification

approaches were used: (a) KL: based on Kullback-Leibler

entropy mean values for QRS and STT time intervals

where discriminant index (DI) was higher than 0.8, (b)

Regional: based on selected regional parameters, (c)

KL+Regional: based on selected KL and regional

parameters.

NoHCM HCM P - value

QRS(DI>0.8)

0.14 ± 0.007 0.27 ± 0.019 4.8*10

-10

STT(DI>0.8)

0.11 ± 0.015 0.33 ± 0.03 1.1*10

-10

CC 86.9 % 78.8 % 3.9*10

-17

QRS

0.45 ± 0.07 -0.59 ± 0.14 7.8*10

-9

QRS

0.7 ± 0.05 0.68 ± 0.12 0.34

Regional

CC 85.9 % 66.7 % (63.6 %) 6.2*10

-12

QRS

* -0.46 ± 0.02 -0.37 ± 0.06 0.44

KL+Regional

CC 88.9 % 84.8 % 6.9*10

-19

As a last step, we combined KL and regional

features and applied forward stepwise LDA to find

the best set of three parameters. This set included the

KL parameters KLQRS(DI>0.8), KLSTT(DI>0.8)

and the regional parameter QRSA6. The mean

values of the latter parameter again did not

significantly differ between both groups, but the

combination of these three parameters improved the

overall classification rate from 84.8 % to 87.9 %

(sensitivity: 84.8 %, specificity: 88.9 %, area under

ROC curve: 0.94). The correct classification rates

for the subgroups included were 98.2 % in normal

subjects, 76.2 % in hypertensive patients, 85.7 % in

patients with HNCM and 84.2 % in patients with

HOCM.

Discrimination of Obstructive from non

Obstructive Forms of HCM. For this analysis, KL

entropy was calculated using the averaged maps of

the HOCM group as the reference. The mean KL

values of HOCM and HNCM groups during QRS

and STT interval are given in Fig. 3 (upper panels),

with the corresponding DI values in the lower

panels. Obviously, the only informative part to

separate HOCM from HNCM is the time interval

between 57 and 77 ms of the QRS (DI>0.8). Mean

values of KLQRS(DI>0.8) differed significantly

(p<10

-4

) between both groups (Tab. 2). Using only

this parameter, 78.8 % of patients were correctly

classified (78.9 % from HOCM group and 78.6 %

from HNCM group).

Figure 3: Mean group Kullback-Leibler (KL) entropy

values over time during QRS (a) and STT (b). HOCM

group values are denoted with solid (blue) lines and

HNCM group values with dashed (red) lines (reference

maps: HOCM group). Lower panels give discriminant

index (DI) values during QRS (a) and STT (b) intervals

respectively: KL values for time intervals where DI was

higher than 0.8 (dashed lines) are considered for

KLQRS(DI>0.8) calculation.

Table 2: Descriptive statistics of patients with HNCM and

HOCM as well as their separability. Data are given as

mean values ± SE and percentage of correctly classified

(CC) cases. If ‘leave one out’ cross-validated results of

discriminant function analysis differ from the original

results, they are shown in parentheses. P-values were

obtained with the Mann-Whitney-U-test (univariate cases)

and the Wilks-Lambda test (linear discriminant function).

Three classification approaches were used: (a) KL: based

on Kullback-Leibler entropy mean values for QRS where

discriminant index (DI) was higher than 0.8, (b) Regional:

based on selected regional parameters, (c) KL+Regional:

based on selected KL and regional parameters.

HNCM HOCM P - value

QRS(DI>0.8)

0. 4 ± 0.04 0.16 ± 0.03 5.1*10

-5

CC 78.6 % 78.9 % 3.8*10

-5

QRS

0.67 ± 0.28 2.26 ± 0.34 2*10

-3

Regional

CC 71.4 % 63.2 % 1*10

-3

QRS

* -0.73 ± 0.3 -1.31 ± 0.3 0.08

KL+Regional

CC 100 % (92.9 %) 94.7 % (89.5 %) 1.5*10

-7

Next, we estimated discrimination power of regional

parameters, which were calculated for the same time

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PATIENTS WITH HYPERTROPHIC CARDIOMYOPATHY

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interval (57-77 ms of QRS). Forward stepwise

discriminant analysis found QRSF5 to be the best

discriminating parameter (Tab. 2). Overall

classification rate using QRSF5 was 66.7 % (63.2 %

patients from the HOCM group and 71.4 % from the

HNCM group were correctly classified). Again,

regional parameters demonstrated a lower

classification power.

As the last step, we combined KL and regional

parameters and performed a forward stepwise LDA.

KLQRS(DI>0.8) and QRSA3 were selected. Overall

classification rate for this parameter set was 97 %

(94.7 % of HOCM and 100 % of HNCM patients

were correctly classified, area under ROC curve:

0.97).

Prospective Screening of Two HCM Families.

Application of the two classification algorithms

based on the selected sets of combined KL and

regional features yielded a correct classification of

all 22 family members. This was true not only for

detection of HCM affected individuals (5 out of 22

family members), but also for discrimination

between different forms of the disease (1 HOCM vs.

4 HNCM).

4 CONCLUSIONS

This study investigated the capability of CMFM to

detect patients affected by HCM. The most

important findings are, that a KL based topology

quantification of cardiac magnetic field distribution

discriminates HCM from non HCM and

distinguishes between different forms of HCM

(HOCM and HNCM), and that a combination with

regional field strength parameters improves the

discrimination results to a level relevant for clinical

application.

Discrimination of HCM Individuals from Healthy

Control Subjects and Patients with Cardiac

Hypertrophy of other Causes (NoHCM). Both the

large variability of the disease expression and the

resulting complexity of the CMFM raise difficulties

for the magnetophysiologic diagnostic evaluation of

HCM. The present paper proposes a new

diagnostical approach based on CMFM. Different

analysis techniques are currently used for evaluation

of cardiac magnetic field maps. This includes for

example the estimation of changes in magnetic field

orientation through the cardiac cycle and the

calculation of QRS-ST-T wave integrals (Van

Leeuwen, 2006). We applied for the first time the

methodology of Kullback-Leibler entropy for

analysis of CMFM to investigate the diagnostic

information content in topology related to the status

“HCM affected or not”. As we could show, KL

values increase with the deviation of map topology

compared to the reference field distribution. The

idea to use relative entropy measures to classify

medical data had already successfully been applied

to EEG, HRV and MRI-analyses. Using the KL

approach, we found significant differences in map

topology during QRS and STT interval between

HCM patients and the mixed control group of

healthy volunteers and hypertensives. For the

process of depolarization the most significant

differences were found during the early part (5-20

ms) and within the second half (62-75 ms) of this

time period. In contrast, the same was true for nearly

the whole repolarization period (STT interval) with

marked map topology deviations of the HCM group,

revealed by the discriminant index. The analysis of

the CMFM using two parameters based on the

Kullback-Leibler entropy measures correctly

classified 84.8 % of the tested groups. As the control

group contained also patients with cardiac

hypertrophy due to arterial hypertension, our results

strongly suggest that Kullback-Leibler based map

quantification revealed specific topological features

in HCM patients. They may originate from the

pathognomonic ventricular remodeling process,

which includes myocardial disarray, left ventricular

hypertrophy (LV) and fibrosis. Typically, the LV

hypertrophy shows asymmetric distribution with

diffuse or segmental pattern of left ventricular wall

thickening, most involving the septal region

(Saumarez, 1992). This is accompanied by changes

in the electrical properties especially at the initial

and the last part of QRS, both due to a loss of

electrical forces because of transmural myocardial

fibrosis and abnormal electrical activation of

hypertrophied ventricular septum (Dumont, 2006).

Echocardiographic and MRI studies showed that the

balance of these electrical forces is primarily a

function of the relation of upper anterior septal

thickness to right ventricular wall thickness and to

upper left ventricular posterior wall thickness. In a

non-invasive electrocardiographic imaging study of

ventricular activation, Ramanathan et al. (2006)

demonstrated an epicardial right ventricular

breakthrough in the anterior paraseptal region during

the earliest ventricular activation under

physiological conditions in healthy volunteers. At

the end of the ventricular activation sequence, an

apex-to-base activation of the posterior left ventricle

was displayed. Based on this description of the

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ventricular activation sequence, our findings suggest

that within the first 20 ms of the ventricular

activation paraseptal parts of the right ventricle

could contribute to the observed differences in

CMFM topology. In contrast, the map topology

differences at the end of the QRS could reflect the

influence of regional LV wall hypertrophy and

myocardial fibrosis on the electrophysiological

myocardial properties, especially if the propagation

wave front turns from apical to posterior basal LV.

These findings are consistent with those from

invasive electrophysiological and morphological LV

studies (Schumacher, 2005). Myocardial scarring

and its electrophysiological consequences like

slowed and fragmented intraventricular conduction

also contributed to the specific magneto-

physiological HCM phenotype.

Changes in repolarization in HCM patients were

also found in ECG studies (Barletta, 2005). The

most common abnormalities are related to the ST-

segment and the T-wave. This is in consistence with

our findings of differences in KL entropy values at

the STT interval. They probably emanate from

myocardial disarray, fibrosis and small vessel

disease leading to scarred myocardium due to

regional ischemia (Basso, 2000). HCM does not

affect the ventricles uniformly; it is likely that there

are areas of diseased myocardium with

abnormalities in conduction and refractoriness and

heterogeneity of refractoriness, especially related to

distal hypertrophy with craniocaudal asymmetry.

Compared with KL measurements, we also

found significant regional deviations of magnetic

field strengths during depolarization period (QRS),

especially in the superior (sensor position B3) and

inferior (sensor position F3) part of the mapped area.

However, the overall classification rate using only

these parameters was lower compared to the KL

based set. Specificity was comparable with KL

method but sensitivity was substantially lower. A

possible explanation for the lower classification rate

could be that regional parameters are more sensitive

to measurement conditions, especially to the position

of the patient’s heart relative to the measurement

system. Even with a presumed constant distance

between sensors and thorax surface, the variations in

patients’ anatomy result in different heart-sensor

distances. Automatic adjustments to solve this

problem are under investigation (Burghoff, 2000).

In contrast to the lower efficacy of the mean

values of magnetic field strength approach, the

classification rate improved adding a regional

parameter to the KL features. Since the

crossvalidation did not differ from the original

results the improvement in classification is due to a

higher information content of the combined

parameter set.

Discrimination of Obstructive from non

Obstructive Forms of HCM. In order to find a

discriminant function for separation of HCM

subforms (HOCM vs. HNCM), we applied the same

approach but now using the HOCM group maps as

the reference for KL entropy calculation. As shown

by high DI values, KL based topology differed only

in a short time interval within the second part of

depolarization process (57-77ms). The analysis of

regional magnetic field differences revealed that

most significant differences between these two

HCM subforms exist in the inferior part of the

mapped area (sensor position F5). HOCM is

characterized by a predominantly septal

hypertrophy, which leads to chronic obstruction of

the left ventricular outflow tract and consecutively to

an increase in wall stress, myocardial ischemia,

increased cell death and fibrosis.

Using gadolinium contrast-enhanced MRI,

Choudhury et al. found in asymptomatic or mildly

symptomatic patients with HCM that the extent of

scar increased significantly in relation to wall

thickness on a regional basis. The

electrophysiological consequences are regional

prolongation of the bipolar endocardial potentials

and the occurrence of fractionated and split

potentials, which directly point to an underlying

inhomogeneity of the myocardial excitation with a

shift to earlier activation of the lateral LV wall due

to septal conduction delay. This probably led to the

observed deviation in CMFM map topology between

HOCM and HNCM patients in the second part of the

QRS interval, which could be quantified by using

the KL entropy method. The alterations of regional

electrophysiological properties at hypertrophic

septal areas are responsible for the observed changes

in the inferior mapped area.

Intended to detect HCM subforms, KL entropy

measures were superior to the analysis of regional

map differences. But, adding a regional parameter

QRSA3 to KL entropy parameters, the classification

result improved to 97 % with a sensitivity of 100 %

for HNCM and a specificity of 94.7 % for HOCM.

Feasibility of the Approach and Conclusions. The

correct classification of 5 HOCM and HNCM

patients out of 22 family members, in which the

diagnosis was confirmed by genetic testing, showed

in a prospective part of the study the feasibility of

the presented diagnostic algorithm. Our results give

CARDIAC MAGNETIC FIELD MAP TOPOLOGY QUANTIFIED BY KULLBACK-LEIBLER ENTROPY IDENTIFIES

PATIENTS WITH HYPERTROPHIC CARDIOMYOPATHY

451

evidence, that KL entropy as a natural distance

measure between two probability distributions is an

effective tool to obtain discrimination information

from CMFM measurements. It is important to point

out that the KL tool is applicable to CMFM analysis

in a population characterized by a broad spectrum of

magnetophysiological and clinical phenotype

expression. Prospective screening of HCM family

members is strongly recommended, including serial

echocardiographic and electrocardiographic

examinations (Maron, 2004).

In conclusion, a combined diagnostic algorithm

based on KL entropy topology quantification and

regional parameters of cardiac magnetic field maps

is a suitable tool for HCM screening and

discrimination between different forms of the

disease.

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