*
Gozd Martuljek,
Slovenia
September 29-30, 1995*

Forward
and inverse computation in
ECG and MCG.
(T. Oostendorp,
Nijmegen)

Modelling
of current sources in
cardiology.
(J. Nenonen,
Helsinki)

Volume conductors, volume currents
in cardiology - modelling.
(V. Jazbinsek,
Ljubljana)

Clinical multichannel measurements
of cardiac magnetic
field and electric potential.
(M. Burghoff,
Berlin)

Anatomic picture: 3-D cardiac
image processing.
(I. Magnin,
Lyon)

Software for MCG.
(S.N. Erné
, Ulm)

Localization of arrhythmogenic
substrate - validation by successful catheter ablation
procedures.
(M. Oeff, Berlin)

Analysis of depolarization and
repolarization for the characterization of the
arrhythmogenic substrate of the myocardium
(P. Stevens, Berlin)

The software package CURRY ^{TM}
and its application in cardiography
(U. Katscher,
Hamburg)

Effects of source extension on electric and magnetic
location: A simulation study (C. Del
Gratta,
Chieti)

Department of Medical Physics Biophysics

University of Nijmegen, Netherlands

In order to evaluate the condition of the heart from
measured ECG or MCG
signals, the relation between the current sources at the
heart and the electric
and magnetic fields they generate has to be known. The
problem of the
estimation of the source from measured fields is called
the *inverse problem*. In order to solve the
inverse problem, an
expression is needed for
the fields generated by current sources of known
properties, as obtained by *forward computations*.

The forward problem can only be solved analytically for simple volume conductor geometries (semi-infinite space, spheres etc.). The two most commonly used methods to solve the forward problem numerically for volume conductors of arbitrary shape are the Boundary Element Method (BEM) and the Finite Element Method (FEM). The BEM [1] is only applicable to isotropic, piecewise homogeneous volume conductors. The computations involve discretization nodes at the interfaces of the homogeneous compartments only. This makes the BEM much more computational efficient than the FEM [2], in which the complete 3D volume conductor is discretized. The FEM however can handle anisotropic conductivities.

There is no unique solution to the inverse problem. As a
consequence, the
current source distribution generating the external
field can not be
determined without the use of additional information.
Commonly, this additional
information follows implicitly from the choice of a
*source model*.
For example, if a dipolar source model is used, the
source distribution is
implicitly constrained to a point-like, dipolar nature,
and the solution is
unique. For the solution to make sense, however, it is
vital that the
additional information corresponds to physiological
properties of the source.
As the current source generating the ECG and MCG is
essentially distributed,
the dipole source model is not an appropriate model for
the cardiac sources.

The two most popular models for the cardiac sources are
the *epicardial potential* model [1] and the *
double layer
model* [3]. In the first model, the source is
described as the equivalent
boundary potential impressed at the epicardium for each
time instant
separately. The solution of the inverse problem for this
source model is a
series of epicardial potential distributions. In the
double layer model the
spreading of depolarization over the epicardium is
modeled. The epicardium is
discretized into a large number of elements that, from
the moment the
depolarization wave front reaches them, act as dipole
layer sources of a
certain strength. For this model, the inverse
computations results in a map of
the activation sequence at the epicardium.

Both the epicardial potential and the double layer model
are two dimensional
distributed source models, with many degrees of freedom.
In the external field,
not all of the degrees of freedom are expressed, as many
different source
patterns generate fields that differ less the noise level
(remote sensing
problem).
As a consequence, the inverse problem involving these
source model is
mathematically *ill-posed*, i.e: small differences
in
the recorded fields
will yield completely different solutions. The
ill-posedness is overcome by -
again - including additional information by means of
*regularization*.
In regularization a penalty function, expressing some
undesired property of the solution, is included in the
inverse procedure.
Popular penalty functions (commonly called regularization
operators) are the norm of the norm of the solution (i.e. small source strength
is prefferd) and the surface Laplacian of the solution
(i.e. smooth solution are preferred).

Regularization is effectively a method to select the most desirable solution from the range of possible solutions. Obviously, this only makes sense if the regularization operator expresses a realistic physiological property of the source. For instance, for the double layer model Laplacian regularization is quite suitable, as the mean Laplacian of the activation times is a measure for the velocity with which the depolarization spreads over the epicardium, which is a well-described physiological quantity. The amount of regularization can be chosen such that this quantity reaches a realistic value.

[2] Y. Yamashita et al. Source-field relationships for cardiac generators on the heart surface based on their transfer coefficients.

[3] G.J.M. Huiskamp et al. The depolarization sequence of the human heart surface computed from measured body surface potentials.

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Helsinki University of Technology, Laboratory of Biomedical Engineering

Rakentajanaukio 2C, 02150 Espoo, Finland

dvi source of this abstract (TeX), ps source of this abstract (Post Script)

Electrocardiograms (ECGs) and magnetocardiograms (MCGs) arise primarily from electric currents in the body associated with flow of charged ions (such as ${\rm Na}^+,\;{\rm K}^+,\;{\rm Ca}^{2+}$) in the myocardium. Ionic currents across the membrane of a myocardial muscle cell give rise to a time-dependent {\it impressed} current density ${\bf J}^i$, which could be described in terms of modified Hodgkin-Huxley differential equations. Impressed currents give rise to an electric potential $\phi({\bf r}')$, which in turn generates ohmic volume currents ${\bf J}_v({\bf r}') = -\sigma'\nabla\phi$ everywhere in the body ($\sigma$' is the microscopic conductivity inside $v'$). Because the volume of the actual cell membranes is very small as compared to the whole myocardium, their direct contribution to the external electromagnetic fields is also small. In fact, the active source regions are usually characterized with the concept of the {\it primary} current density ${\bf J}_p$. It can be expressed as ${\bf J}_p({\bf r}') = {\bf J} + \sigma\nabla\phi$, i.e., as a difference between the total current density ${\bf J}$ and the passive volume currents ${\bf J}_v$. The time variation of ${\bf J}^i$ is relatively slow (below 100~Hz), which means that the source currents and external electromagnetic fields can be treated in a {\it quasistatic} approximation (the true time-dependent terms in Maxwell's equations vanish). A very large number of cells has to be excited to get a measurable signal; thus it is convenient to introduce a macroscopic equivalent current dipole ${\bf P} = \int_{v'} {\bf J}_p({\bf r}')dv'$. One can also derive higher order equivalent generators by using various multipole expansions.

In the ECG and MCG {\it inverse} problem the aim is to characterize the primary current density on the basis of the measured signals. For this purpose various equivalent generators are usually applied. The current dipole ${\bf P}$ or quadrupole generators are applicable only to sources which are confined to a small restricted volume, such as the initial atrial or ventricular activation or the starting point of a focal arrhythmia. A more realistic description of actual excitation wavefronts can be achieved by using uniform dipole (or double) layers, e.g. confined onto the endo- and epicardial surfaces. The influence of anisotropic electric conductivity can be accounted for by adding an oblique component to the dipole layer. Different techniques have been developed to find the parameters of the equivalent dipole and/or quadrupole sources, multiple dipoles, double layers, epicardial potential distributions, and (continuous or discrete) current densities characterizing the primary currents.

Top of this pageInstitute of Mathematics, Physics and Mechanics

University of Ljubljana

Deriving the information on the current sources from the measured electric potential on the body surface and magnetic field distribution in vicinity of the body is the subject of the electrocardiographic (ECG) and magnetocardiographic (MCG) inverse problem. In order to solve the inverse problem, one has to introduce models for the current sources as well as models of the human body. In this paper the volume conductor modelling is discussed. Human body is a complex volume conductor consisting of several compartments, characterized by different conductivities, which can be in general anisotropic, such as myocardium and skeletal muscle. Properties of volume conductor model are determined by its shape and conductivity distribution. Volume currents, driven by the primary current sources within the heart, are influenced by the volume conductor structure which in turn affect the measured ECG and MCG signals. First attempts to the inverse problem solutions have neglected the contribution of irregular torso shape and its internal structure. This approach still plays an important role in qualitative interpretation of measured ECG and MCG data, however, for quantitative evaluation more realistic volume conductor model has to be introduced. The most common approach is a piece-wise homogeneous volume conductor composed of torso and some internal inhomogeneities, like lungs and heart cavities. In this model, bioelectric current sources and measured quantities (ECG, MCG) are related by integral equations, which can be solved numerically by the Boundary Element Method (BEM). When using BEM, surfaces between different compartments are tessellated. The integral equation for the electric potential becomes in discrete form a system of linear equations which is defined by a large matrix. This matrix is determined by the material and geometric properties of the volume conductor model. The electric potential distribution on the body surface due to an arbitrary source within the body is then calculated rather fast once the inverse of the matrix is found. The contribution of volume currents to the magnetic field is determined by the geometrical transfer matrix connecting the geometry of the volume conductor model with the position of magnetic sensors which is also computationally efficient what is necessary for the inverse problem solution.

Examples and simulations of different volume conductor models will be discussed. Further information of volume conductor studies will be illustrated with Wolff-Parkinson-White (WPW) case study of 12 patients.

Top of this pagePhysikalische-Tehnische Bundesanstalt, Institut Berlin

Abbestr. 2-12, 15879 Berlin, Germany

Requirements for clinical multichannel cardiac measurements are:

- multichannel MCG system (more than 30 channels)
- electrical potential measurement system (12 leads and or 3 Frank)
- 1 channel for recording of breathing
- magnetic and electric shielding to reduce influence of the clinical environment
- coupling with imaging methods such as MRI, CT or other imaging systems within the clinic for two reasons: modelling of the volume conductor and the source space and anatomic related presentation of the results
- coupling with clinical data bases for full description of the patient
- immediate analysis of the data is required in some cases of VT patients to prepare a catheter ablation
- positioning system for MCG, MRI, CT and other imaging systems
- interdisciplinary group is necessary: physicians, physicists, mathematicians, computer specialists

Each system has another configuration --> the signals and calculated parameters such as QRS length cannot be compared without recalculation into a virtual sensor configuration --> programs for recalculation are designed in Helsinki and Berlin

Berlin experience with the Steglitz MCG multichannel system:

- standard measurement takes no more than 30 minutes
- standard recording during 100 seconds
- MCG + 3 Frank leads + breathing
- goals: risc stratification, localization (WPW, VT), stress MCG

Trends for the near future:

- Multicentre studies to compare the results
- Use of more components of the magnetic field (not only Bz)
- Analysis of non-averaged data

CREATIS, Lyon, France

A large variety of techniques exist to investigate the anatomic shape and the functional behaviour of the moving heart. The information content issued from them is roughly complementary and directly related to the physical phenomena involved. They can be divided into two classes called passive and active techniques.

Passive techniques record the natural activity of the beating heart. It mainly concerns the electrocardiography (ECG) which measures the variations of the electric field (along the cardiac cycle) and the magnetocardiography (MCG) which provides the magnetic field variations. The cardiac signals are recorded using electrodes (ECG) or SQUIDs (MCG) located on the body. When placed in particular positions, they can provide orthogonal projections of the ECG (vectorcardiography) or spatio-temporal information (MCG). The resulting recorded signals give functional information. Active techniques consist in using some external wave or excitation to get information back. It mainly includes imaging techniques using X-Rays, magnetic resonance imaging (MRI), ultrasound (US) and isotopic imaging (SPECT and PET). Both anatomical and functional information cam be extracted from such 2-D or 3-D sequences.

The heart experiences a complex motion that is only partially captured by the previously mentioned acquisition techniques. The inverse problem which consists in extracting global and local motion and metabolism information from these data is a quite difficult task because it is an ill-posed inverse problem. Moreover, according to the diversity of data, various mathematical approaches will be necessary. Studying the true 4-D behaviour of the heart, implies to be able to efficiently mix such heterogeneous information in a fusion process.

Top of this pageZentralinstitut für Biomedizinische Technik

Universität Ulm, Ulm, Germany

This talk has been designed as an introduction to a fruitful discussion to define what is needed, what is desirable, and what is available in the MCG analysis. This talk will be organized in the following sections:

- data formats and standardization for the integration of imaging and the MCG data and the exchange of data between different research and clinical sites.
- data acquisition software - a brief excursion on different acquisition modalities and consequences for data formats and analysis.
- preprocessing: triggering, quality assesment, cathegorized data analysis, averaging.
- registration of patient coordinate system.
- torso models.

One of the main aspects discussed will be the problem of computational speed or analysis time, being this one of the main problems in the design of biomagnetic cardiac systems for clinical use.

Top of this pageCardiopulmonary Department, Klinikum Benjamin Franklin

Freie Universität Berlin, Germany

High-resolution magnetocardiographic mapping is used for non-invasive measurements of the the dynamic magnetic field distribution generated by the electrical activation of the heart. The magnetic field propagation is much less influenced by the tissue conductive inhomogeneities than the electrical propagation. The isomagnetic line of the precordial magnetic field represents the position and the direction of the current source generated by the electric myocardial activity, the equivalent current dipole (ECD). The analysis of the distance of the extrema allows the determination of the sources depth and the quantitative three-dimensional calculation of the ECD position. In addition, with cardiac imaging techniques (Magnetic Resonance Imaging) the functional abnormalities as measured magnetocardiographycally can be projected into anatomical structures which may be of particular value for ablative techniques.

**Patients**

For localization of the accessory pathway, 21 patients
with
Wolff-Parkinson-White syndrome were investigated.
Patients with dual
pathways were excluded. The accessory pathway position
was localized
according to standard electrophysiologic techniques or by
successful
catheter ablation (9 consecutive patients). The
intrathoracic position of
the catheter at the pathway was measured in the biplane
cine-fluoroscopy.
For analysis of the magnetocardiographic "late fields" 12
patients with
coronary heart disease and spontaneous and inducible
ventricular
tachycardia were investigated.

**Localization of ventricular preexcitation**

The dynamic isofield contours of the high resolution
magnetocardiogram
were used to determine the position and strength of the
three-dimensional
propagation of the equivalent current source, which
represents the center
of the electrical activity for the chosen time and is by
definition the
current source whose magnetic field distribution at a
specified time
instant matches according to least square fit the
measured field
distribution. The initial 1 to 3 msec of the
magnetocardiographic delta
wave were analyzed; the progression of the ventricular
preexcitation
during the delta-wave in space was followed by the
calculation of the ECD
in steps of 1 - 2 msec. Standardized values of the
overlay of the atrial
repolarization were subtracted.

**Comparison of magnetocardiographic and
electrophysiologic localization**

The differences between magnetocardiographic and invasive
localization
was (0.7 cm,1.0 cm,0.9 cm) in the X-plane, (0.9 cm,1.0
cm,1.0 cm)
in the Y-plane and (1.2 cm,1.0 cm,1.0 cm)
in depth (Z-plane). The correlation coefficients of these
positions were 0.89 (p < 0.0001), 0.92 (p < 0.0001)
and 0.84 (p < 0.0003), respectively. The difference
between both
positions in space was (1.9 cm,1.0 cm,1.3 cm).

**Magnetocardiographic localization and catheter
ablation**

Magnetocardiographic localization of the accessory
pathway was made in 9
consecutive patients before catheter ablation. This
position was
projected into the MR image, and the ablation catheter
was
advanced to that site.
The final catheter position was chosen according to
criteria of the endocardial electrograms i.e. the
recording of the
accessory pathway
potential, with changes of catheter position in the range
of millimeters.
However, the gross position was reliably predicted by the
magnetocardiographic mapping even in differentiating
right and left paraseptal pathways.

**Conclusions**

In conclusion, the high-resolution magnetocardiographic
mapping is a new
and promising diagnostic method for quantitative
3-dimensional
localization of ventricular preexcitation. The
localization of other
abnormal arrhythmogenic activation of the heart may also
be suitable. In combination with cardiac imaging it
provides an accurate
functional and anatomical picture of the heart.

Cardiopulmonary Department, Klinikum Benjamin Franklin

Freie Universität Berlin, Germany

**Introduction**

Post-myocardial infarction mortality is largaely related
to the incidence
of malignant tachyarrhythmias like sustained ventricular
tachycardia or
ventricular fibrillation; reinfarction does not play an
important part in
its causation. Their prevalence is dependant on multiple
factors
including abnormal de- and repolarization, which can be
identified by
various tests characterizing pathological
electrophysiological states.

**Concept of arrhythmogenesis**

It is important to recognize the interdependency of the
factors that lead
to the appearance of ventricular tachycardia: The
cellular
electrophysiology of the organic substrate (the diseased
myocardium) is
irritated by repetitive ventricular premature beats
(trigger events)
towards a (further) slowing of conduction and a change in
the membrane
potential, which in turn leads to a micro-reentry
circuit, the origin of
ventricular tachycardia. This process itself is
influenced by modulating
factors.

**The organic substrate**

Most of the organic cardiac diseases carry an elevated
risk of
ventricular tachycardia and it is debated whether the
so-called idiopathic
vetricular tachycardia is the symptom of an undiagnosed
underlying
condition. Left ventricular ejection fraction quantifies
the left
ventricular function and is well recognized as predictor
of outcome. In
electrophysiologic testing, premature beats are applied
in a standardized
fashion to mimic trigger events that may lead to the
induction of
ventricular tachycardia and consequently to the
identification of the
patients at risk. Ventricular late potentials (as
recorded by high
resolution signal averaged ECG) represent areas of slow
conduction due to
myocardial damage and are of prognostic significance.
Magnetocardiographic mapping is a more sensitive and
sophisticated method
for quantification and even localization of abnormal
cardiac
electrophysiological phenomena. Its value in diagnostics
of various
states of different cardiac diseases is well recognized,
but needs
further evaluation.

**Modulating factors**

The extent of coronary artery disease is a main predictor
of outcome in
patients with this condition. But detection of silent or
overt ischemia
by noninvasive techniques (resting ECG, holter
monitoring, exercise ECG)
did not show to be useful in stratifying high risk
patients.
Stress-magnetocardiography may particularily be suitable
in detecting
ischemic conditions.
More recently, research has focussed on the autonomous
innervation of the
heart, i.e. the system responsible for heart-rate and
pressure control.
Reduced heart rate variability as well as reduced
baroreflex sensitivity
as indicators of vago-sympathetical dysbalance seem to
proof promising in
stratifying patients at risk.
QT-dispersion indicates an imbalance of the heart's
sympathetic
innervation which results in abnormal spatial
distribution of
repolarization and, thus, can be recorded excellently by
mapping
techniques, including magnetocardiographic mapping.

Philips GmbH Forschungslaboratorien

Forschungsabteilung Technische Systeme Hamburg

Hamburg, Germany

CURRY ^{TM} is a software package for scanning
and analysing
magnetic
and/or electric signals of the human body, for example,
the human
heart. Supported reconstruction modes are the fitting of
single dipole(s) and
the current density reconstruction. Results can be
overlayed with the
anatomic information.

Besides scientific research, possible applications of
CURRY ^{TM} in
cardiography are the family of arrhythmias and all kind
of myocardial
infarctions. In the first case, a single dipole can be
fitted using
Nelder-Mead simplex to localize arrhythmic center and to
determine the
strength of the arrhythmic impulse. In the case of
infarction, a current density can be reconstructed on the
myocardium
yielding information about position, size, and vitality
of the injured
tissue. Several concepts to restrict the
underdetermination of the
problem are offered to the user (e.g., L1/L2 norm
criterion, SVD
regularization).

CURRY ^{TM} is able to read and visualize
anatomic images,
e.g., from
the magnetic resonance or computer tomography
measurements. A toolkit
helps the user to segment anatomic surfaces like thorax,
lungs, or
myocardium out of these images. The surfaces can be used
to determine
the position of the current sources to be reconstructed
and to illustrate the
anatomic context of the reconstruction result. Moreover,
the surfaces
can be used to model a realistic volume conductor for the forward
problem using the boundary element method.

One of the difficulties in source localisation lies in the choice of a model for the source. Due to the fact that the real source is extended, the use of a pointlike model source (e.g. a current dipole) in an inverse calculation may lead to localisation errors due to incorrectness of the model. Reconstruction of current distribution does not assume a pointlike source but still requires that the sources be constrained in an a priori determined surface. On the other hand, dipole localisation is still useful because it is fast, easy to interpret, and provides an error estimate. We have compared the location of the ECD obtained by means of a standard single dipole localization technique, when the source is an array of dipoles simulating an extended source, both for electric and magnetic data. The forward calculations were performed according to a simple mathematical model for the conductor: the homogeneous half-space. The sensor was a square array of 11 x 11 = 121 sensors both for the electric and for the magnetic data. Magnetic sensors were in turn: magnetometers, first order vertical gradiometers, and first order planar gradiometers. Sources consisted of arrays of dipoles in various geometrical configurations: pointlike sources like multiple dipoles, linear sources like stripes of dipoles. Gaussian noise was added to the field and potential distribution at a constant level (independent of source depth) and without correlation among channels. The inverse calculations were performed using the single current dipole model by minimising the usual cost functions i.e. the sum of squared differences between theoretical and experimental electric and magnetic data. In the case of combination of electric and magnetic data, the respective cost functions were added together after separate normalisation to take into account differences in value and in signal-to-noise ratio. The best localisation error was taken as the mean of 100 localisations; localisation error was taken as the standard deviation. Comparison of electric and magnetic localisations shows that the two techniques give markedly different source location, the mismatch of which may be as large as the source dimensions. Combination of electric and magnetic data does not necessarily improve the localisation accuracy compared to either one of the data type alone.