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
