Method for determining cardiac potentials

A computer-implemented method for determining cardiac potentials of a subject, the method comprising the following steps:

• a) providing as input data a torso model of the subject comprising a plurality of nodes, a cardiac model of the subject comprising a plurality of nodes, a cardiac activation sequence at the plurality of nodes of the cardiac model, and body surface potentials recorded on the torso of the subject;
• b) assigning to each node of the cardiac model a time-dependent weighting regularization coefficient Ψi based on the cardiac activation sequence, wherein the weighting regularization coefficient Ψi takes a value from a range of values with a minimum when a node has the highest probability of being depolarized and a maximum when a node has the lowest probability of being depolarized, wherein i denotes the i-th node of the cardiac model, with i=1, . . . Nnodes, Nnodes being the number of nodes in the cardiac model;
• c) obtaining estimated cardiac potentials as result of minimizing:
• X
• ^
• (
• t
• )
• =
• arg
• ⁢
• min
• [
• 
• AX
• ⁡
• (
• t
• )
• -
• Y
• ⁡
• (
• t
• )
• 
• 2
• 2
• +
• λ
• 2
• (
• t
• )
• ⁢
• 
• βΨ
• ⁡
• (
• t
• )
• ⁢
• RX
• ⁡
• (
• t
• )
• 
• 2
• 2
• ]
• wherein:
• {circumflex over (X)}(t) is the estimated cardiac potentials,
• A is the transfer matrix that relates the cardiac potentials and the body surface potentials,
• X(t) is a variable that represents the cardiac potentials to be determined,
• Y(t) is the body surface potentials provided as input data,
• λ(t) is a regularization function common to all the nodes of the cardiac model,
• R is a square matrix that defines the order of the regularization,
• β is a vector having a component with value between 0 and 1 for each node of the cardiac model, wherein the value represents a weight for the maximum magnitude of the electrical activity at each node,
• Ψ(t) is a diagonal matrix with the time-dependent weighting regularization coefficients Ψi assigned to the nodes of the cardiac model, and
• ∥·∥2 is the Euclidean norm;
• d) obtaining estimated body surface potentials Ŷ(t) as:
• Y
• ^
• (
• t
• )
• =
• A
• ⁢
• X
• ^
• (
• t
• )
• wherein A is the transfer matrix and {circumflex over (X)}(t) is the estimated cardiac potentials;
• e) determining a correlation coefficient between the estimated body surface potentials Ŷ(t) and the body surface potentials Y(t) provided as input data;
• f) determining if a predefined stop condition is reached based on the determined correlation coefficient;
• and
• if the stop condition is reached, providing the estimated cardiac potentials {circumflex over (X)}(t) as output;
• if the stop condition is not reached, updating the cardiac activation sequence based on the estimated cardiac potentials {circumflex over (X)}(t) and performing steps b) to f);
• wherein in step b) the time-dependent weighting regularization coefficients Ψi assigned to the nodes of the cardiac model are updated based on the updated cardiac activation sequence and in step c) the regularization function λ(t) is updated based on the updated weighting regularization coefficients Ψi.