Method for noninvasive imaging of cardiac electrophysiological based on low rank and sparse constraints

Abstract

The present invention discloses a method for noninvasive imaging of cardiac electrophysiological based on low rank and sparse constraints. This method decomposes the spatio-temporal distribution of endocardial and epicardial potentials into a low-rank matrix representing smooth potential components and a sparse matrix representing the details of potential salience according to the prior condition of spatio-temporal correlation of the endocardial and epicardial potential distribution of the heart. By introducing low rank and sparse constraints, the solution of the ill-conditioned inverse problem of ECG is constrained to the unique optimal solution. The invention combines the individualized three-dimensional heart model of the subject to obtain a three-dimensional dynamic distribution image of the cardiac endocardial and epicardial potential of the subject, which has important practical application value.

Claims

1. A method for noninvasive imaging of cardiac electrophysiology, comprising the following steps: (1) recording a subject's surface potential data and thoracic tomography image data; (2) based on the thoracic tomographic image data, establishing a 3D torso geometric model of the object and a 3D cardiac geometry model, respectively, then unifying the 3D torso geometry model and the 3D cardiac geometry model into the same coordinate system to obtain a 3D heart-torso model; (3) establishing a quasi-static electric field model of the subject's heart-torso based on the geometric relationship between heart and trunk of the subject, wherein the boundary element method is used to solve an electric field model to calculate a positive problem of an electrocardiogram, and a mapping relationship between endocardial and epicardial potential of the heart and body surface potential is obtained as =HU, H is a transfer matrix, U is a cardiac endocardial and epicardial potential matrix, and is a body surface potential matrix; (4) pretreating a 64-lead body surface potential data; and (5) according to the transfer matrix H, establishing an inverse problem solving model of the body surface potential to the cardiac potential, and then performing an inverse operation of a pre-processed body surface potential data to solve an inverse problem of the electrocardiogram; finally, reconstructing a distribution of cardiac endocardial and epicardial potential in the geometric model of the three-dimensional heart.

2. The method for noninvasive imaging of cardiac electrophysiology according to claim 1, characterized in that: the specific operation process of collecting 64-lead body surface potential data and the thoracic tomographic image data of the study subject of the step (1) is as follows: first, putting the subject on a body surface potential recording device with 64 electrode leads distributed to collect the subject's 64-lead body surface potential data; then subjecting the subject with a wearable device to a computed tomography scan to acquire the thoracic tomographic image data of the recording electrode positions.

3. The method for noninvasive imaging of cardiac electrophysiology according to claim 1, characterized in that: the concrete realization process of establishing a three-dimensional trunk geometric model of the step (2) is as follows: first, manually marking the position of each electrode point in the thoracic tomography image to acquire the three-dimensional coordinates of each electrode point, and then performing triangulation of electrode points in three-dimensional space to obtain a three-dimensional torso geometric model of the study object.

4. The method for noninvasive imaging of cardiac electrophysiology according to claim 1, characterized in that: the concrete realization process of establishing a three-dimensional heart geometric model of the step (2) is as follows: first, intercepting several slices in the direction of the short axis of the heart in the thoracic tomographic image by imaging, and at least the apical position should be included downward, and at least the position of the right ventricular outflow tract should be upward; then, dividing the slices in the short axis direction of the heart to obtain the boundary contours of the epicardium, the left endocardium, and the right endocardium; finally, connecting the above-mentioned series of parallel boundary contours with a triangular mesh, which means, obtaining a three-dimensional heart geometry model.

5. The method for noninvasive imaging of cardiac electrophysiology according to claim 1, characterized in that: unifying 3D geometric model and 3D heart torso geometry model into one coordinate system due to the digital image space and cardiac physiological space in each orthogonal direction difference of the step (2), by concretely correcting the 3D geometric model of heart size and space position basing on the key field information, then fusing corrected 3D geometric model of heart and 3D geometric model of torso to obtain the 3D heart torso model.

6. The method for noninvasive imaging of cardiac electrophysiology according to claim 1, characterized in that: the concrete method for establishing a quasi-static electric field model of the heart and trunk of the step (3) is as follows: assuming that heart electric field is quasi static electric field, the ion circulation of cardiac myocytes provides a field source for the cardiac electric field, there are no other electric field sources in the thoracic cavity except the myocardium; a quasi static electric field model of the heart and trunk is established as follows:
.sup.2(r)=.Math.(D.sub.iu(r)) where means conductivity, means gradient operator, r means the 3D coordinates of any point in the electric field, (r) means the electric potential of r, D.sub.i means electrical conductivity tensor in the myocardium, u(r) means endocardial and epicardial potential of r, .Math.( ) means the divergence of the results in parentheses.

7. The method for noninvasive imaging of cardiac electrophysiology according to claim 1, characterized in that: concrete step for preprocessing of body surface potential data of the step (4) is as follows: first, denoising the body surface potential data by Fourier transform or Wavelet transform, retaining the main information in the potential signal and removing the redundant interference; then, smoothing the signal of all cardiac cycle after denoising, so that the baseline is pulled to a horizontal level, and the error of baseline migration is avoided.

8. The method for noninvasive imaging of cardiac electrophysiology according to claim 1, characterized in that: in step (5), the specific process is as follows: first, decomposing the cardiac endocardial and epicardial potential matrix U into a matrix L and a matrix S, representing smooth component and highlight detail of endocardial and epicardial potential respectively, that is U=L+S; then, the solution to the inverse problem of establishing the body surface potential to the cardiac potential is as follows: $\underset{U}{\min }\left\{{.Math.L.Math.}_{*}+{.Math.S.Math.}_1+{.Math.\mathrm{HU}-.Math.}_F\right\}$ $s.t.U=L+S$ where .sub.* means nuclear norm, .sub.l means L1 norm, .sub.F means Frobenius norm, and presents weight parameters; finally, the above model is optimized by augmented Lagrangian algorithm, and the distribution data of the endocardial and epicardial potential in the three-dimensional heart geometry model is obtained.

Description

BRIEF DESCRIPTION OF THE DRAWINGS

(1) FIG. 1 is a location diagram of the 64-lead electrode on the body surface

(2) FIG. 2 is a schematic diagram of ventricular slicing in 3D cardiac modeling

(3) FIG. 3 is a schematic diagram of the outline of the heart

(4) FIG. 4 is a schematic diagram of heart contour data stacking

(5) FIG. 5 is a schematic diagram of a three-dimensional heart grid model.

(6) FIG. 6 is a schematic diagram of the 64-lead electrode distribution on the body surface.

(7) FIG. 7 is a schematic diagram of a heart-torso model in the same coordinate system.

(8) FIG. 8(a) and FIG. 8(b) are schematic diagrams of body surface potential signal waveforms before and after pretreatment, respectively.

(9) FIG. 9(a) is a schematic diagram showing the true result of endocardial and epicardial potential data of the heart.

(10) FIG. 9(b) is a schematic diagram of inversion reconstruction results of cardiac endocardial and epicardial potential data.

DESCRIPTION OF THE PREFERRED EMBODIMENTS

(11) In order to more specifically describe the present invention, the technical solutions of the present invention will be described in detail below in conjunction with the accompanying drawings and specific embodiments.

(12) The present invention is based on a low rank and sparse constraint non-invasive ECG imaging method, and the specific implementation steps are as follows:

(13) S1. Collecting the subject's 64-lead ECG and chest CT images.

(14) First, we let the subject put on a 64-lead vest and collected the subject's 64-lead electrocardiogram to record the surface potential data of multiple cardiac cycles. The distribution of 64 leads on the body surface is shown in FIG. 1. Then, we removed the wire on the vest and retained the detection electrode only. We performed a computed tomography scan of the human chest and acquired enhanced CT image data of the subject's trunk and heart. The subject's personalized torso was recorded with the heart geometry and spatial location.

(15) S2. Creating a personalized three-dimensional heart model.

(16) First, from the CT image data of the thorax, we sliced along the short axis of the heart from the top of the ventricle to the apex of the heart, as shown in FIG. 2; then, we extracted the outline of the heart in each slice (the left heart chamber membrane, the right heart chamber membrane, Epicardium), as shown in FIG. 3; then we stacked the heart contour data extracted from all sections, as shown in FIG. 4; finally, we connected the data to the heart contour with the triangle network to obtain a personalized heart three-dimensional grid model as shown in FIG. 5.

(17) S3. Creating a personalized joint heart-torso model.

(18) We marked the position of the 64-lead electrocardiogram in the computed tomography data and recorded the three-dimensional coordinates of 64 electrodes. The distribution of the 64-lead electrodes on the human body surface is shown in FIG. 6. The protruding point in FIG. 6 is the detection electrode. Finally, we got a personalized torso three-dimensional model by Delaunay triangulation. The three-dimensional heart model and torso model were calibrated to a unified global coordinate, resulting in a personalized heart-torso model as shown in FIG. 7.

(19) S4. Establishment of quasi-static electric field model of heart-torso.

(20) Assuming that the electric field is a quasi-electrostatic field, the ion flow of myocardial cells provides a field source for the cardiac electric field, and there is no other electric field source in the thoracic cavity besides the myocardium. In the present invention, the heart surface includes the endocardium and the epicardium and is considered as an exiting closed surface. Therefore, a quasi-static electric field model between the heart surface to the torso surface is established as a Laplace equation:
.sup.2(r)=0
Where means conductivity, means gradient operator, r means the 3D coordinates of any point in the electric field, (r) means the electric potential of r.

(21) Since there are no conductors outside the body surface, the derivative of the body surface potential in the direction perpendicular to the body surface outward is 0, and the body surface potential is the potential recorded by the 64-lead electrocardiogram, thereby obtaining the boundary condition:

(22) $\frac{\left(r\right)}{n}=0\mathrm{on}{S}_b$$\left(r\right)=\left(r\right)\mathrm{on}{S}_b$$\left(r\right)=u\left(r\right)\mathrm{on}{S}_h$

(23) Where n means the direction perpendicular to the body surface outward, S.sub.b means the body surface, S.sub.h means the heart surface. (r) means the body surface potential data recorded by 64-lead. u(r) means the heart surface potential.

(24) S5. Establishment of mapping relationship between endocardial and epicardial potential of heart and body surface potential.

(25) Using the boundary element method to solve the quasi-static electric field model of the heart-to-torso, the model for transecting the endocardial and epicardial current of the heart through the transfer matrix to the body surface potential can be expressed:
=HU
Where is body surface potential matrix, U is endocardial and epicardial potential matrix, H is transfer matrix and only relates to the heart-torso geometry and conductivity.

(26) S6. Pretreatment of body surface potential data.

(27) First, we used the Fourier transform or wavelet transform to de-noise the 64-lead body surface potential signal, preserved the main information of the signal, removed the redundant interference, then flattened the baseline of ECG signals for all cardiac cycles. In this implementation, wavelet transform was used to filter the body surface potential signal. The frequency threshold is selected from 0.3 to 0.5, and the decomposition level is selected from 7 to 8. The comparison before and after the signal processing is shown in FIG. 8(a) and FIG. 8(b).

(28) S7. Solving Model of Inverse Problem Based on Low-Rank Sparsity Constraints.

(29) First, we decomposed the endocardial and epicardial potential matrix into a low-rank matrix and a sparse matrix, which represent the smooth background of the endocardial and epicardial potential and highlight the details:
U=L+S
Where L means the low-rank matrix, S means the sparse matrix.

(30) Then, we forced the L matrix to be a low-rank matrix and the S matrix to be a sparse matrix by iteration, so that the solution to the ill-conditioned inverse problem tends to be optimal. The target expression is as follows:

(31) $\min {.Math.L.Math.}_{*}+{.Math.S.Math.}_1+{.Math.\mathrm{HU}-.Math.}_F$$s.t.U=L+S$
Where L.sub.* means the nuclear norm of the matrix L, that is the sum of all singular values of the L matrix, and it is the convex relaxation of the matrix rank. S.sub.l means the L1-norm of the S matrix and the solution to the L1 optimization is a sparse solution; HU.sub.F is a fidelity item which guarantees that the obtained endocardial and epicardial potential has the least error between the positive mapping of the body surface and the actual measured body surface potential; and are weight parameters.

(32) We used the augmented Lagrangian method to solve the target equation to obtain the best estimate of the endocardial and epicardial potential of the heart:

(33) $L\left(L,S,U\right)={.Math.L.Math.}_{*}+{.Math.S.Math.}_1-.Math.Z,U-\left(L+S\right).Math.+\frac{}{2}{.Math.U-\left(L+S\right).Math.}_F^2+\frac{}{2}{.Math.\mathrm{HU}-.Math.}_F^2$
Where Z means Lagrange multiplier, means inner product, , and are weight parameters.

(34) Combined with the three-dimensional cardiac model, we obtained a three-dimensional distribution of the endocardial and epicardial potential on the heart, thereby diagnosing the specific location and shape of the corresponding disease and lesion area.

(35) Then we validated the proposed method through experiments, the computer operating environment is: 8G memory, CPU is intel i7, frequency 3.47 GHz; Through the above-mentioned implementation process, the cardiac endocardial and epicardial potential of the myocardial infarction subject is simulated and reconstructed. Under the interference of the Gaussian noise level of 30 dB to 10 dB, the above implementation can restore the position and shape of the infarct scar to different degrees. FIG. 9 shows the reconstruction results with a noise level of 25 dB, where FIG. 9(a) is a true value and FIG. 9(b) is a calculation inversion result. The reconstruction of the endocardial and epicardial potential of subjects with real ventricular premature beats was performed. The inversion of the premature beat point was the same as the position of the premature beat point reconstructed by Ensite3000 by the invasive method.

(36) The foregoing description of the embodiments is provided to facilitate those skilled in the art in understanding and applying the present invention. It will be apparent to those skilled in the art that various modifications to the above described embodiments may be readily made, and that the general principles described herein may be applied to other embodiments without inventive step. Therefore, the present invention is not limited to the above embodiments, and those skilled in the art, based on the disclosure of the present invention, should make improvements and modifications to the present invention within the protection scope of the present invention.