Dense electrical map reconstruction from ECG/MCG measurements with known fiber structure and standard

activation sequence

É. Debreuve, G.T. GullbergMedical Imaging Research LaboratoryThe University of Utah, Salt Lake City

Electrical activity of the myocardium

Myocardium contraction:

Electrical activity of the myocardium Signal propagation (integral equations)

Electrical potential on the thorax

Magnetic field close to the thorax

MCG

ECG

Electrodes

SQUIDs

Signal acquisition

Non-invasive measurements:

ECG (electrical potential) Standard clinical exam: 12 electrodes

MCG (magnetic field) E.g., 30 measurement sites

Analysis of the measurements

Diagnosis of heart diseases:

Analysis of the ECG curves Coarse defect localizations

Analysis of the MCG curves ?

Reconstruction of the electrical activity Electrical model of the myocardium Geometrical model of the thorax Discretization of the propagation equations Resolution of a system of equations

Analysis of the reconstructed electrical activity

or

Forward model: General

Electrical model of the myocardium:

Equivalent current dipoles Location, direction, magnitude (variable over time)

Tissue conductivities

Geometrical model of the thorax:

Piecewise constant isotropic conductivity volume Triangulation of the boundaries

Forward model: Based on NCAT

NCAT phantom:

With myocardium+cavities, liver, lungs Isotropic conductivities:

Blood, myocardium, liver, lungs, soft tissues

Discretization:

2900 triangles 1500 nodes

BEM of the NCAT phantom,The University of North Carolina,Chapel Hill

Electrical activity reconstruction

Ill-posed inverse problem:

Too many unknowns Location, direction, magnitude of each dipole

Too few measurements Too much noise

Reconstruction of many dipoles

Need for regularization

Fiber structure Dipole directions

Regularization of the problem

Use of known (or a priori) information:

Voxelization of the myocardium Known locations

Cardiac fibers Known directions

Activation sequence +Action potential shape

Standard magnitudesat anytime during the cycle

Unknowns with a priori: Dipole magnitudes

BioengineeringResearch Group,Auckland

Activation sequence Action potential

Regularized reconstruction

Implementation:

System of equations: RX = M– R: Transformation matrix from dipole magnitudes to measurements– X: Unknown dipole magnitudes– M: Electrical potential and magnetic field measurements

Solution close to standard magnitudes: ( X - X ) = 0 ( ): Function allowing half-quadratic regularization (commonly

used for support or edge-preserving smoothing constraints)– X: Standard magnitudes

Criterion to be minimized: |RX - M|2 + ( X - X )

Polak-Ribiere conjugate gradient algorithm

Preliminary results: Data simulated w/o noise

Dipoles: 700+ Locations: Spaced every 3 mm in x, y, and z inside the myocardium Directions & magnitudes: variations around a given dipole

configuration Magnitude interval:

[0.75, 1.25]

Measurement sites: Electrical potential: 250 (each node of the outer surface) Magnetic field: 250 (close to each potential measurement sites)

Front Back

Without regularization:

With regularization:

Preliminary results: Reconstruction

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Relative error Relative errorhistogram

Relative errorhistogram

Relative error

Future works

Using this forward model: Measurements with noise

Improved forward model: Bi-domain representation Coupled boundary-element/finite-element model

Real data