Intracardiac Inverse Potential Mapping Using the Method of Fundamental Solutions.

Introduction: Atrial fibrillation (AF) is the most prevalent cardiac dysrhythmia and percutaneous catheter ablation is widely used to treat it. Panoramic mapping with multi-electrode catheters can identify ablation targets in persistent AF, but is limited by poor contact and inadequate coverage. Objective: To investigate the accuracy of inverse mapping of endocardial surface potentials from electrograms sampled with noncontact basket catheters. Methods: Our group has developed a computationally efficient inverse 3D mapping technique using a meshless method that employs the Method of Fundamental Solutions (MFS). An in-silico test bed was used to compare ground-truth surface potentials with corresponding inverse maps reconstructed from noncontact potentials sampled with virtual catheters. Ground-truth surface potentials were derived from high-density clinical contact mapping data and computer models. Results: Solutions of the intracardiac potential inverse problem with the MFS are robust, fast and accurate. Endocardial surface potentials can be faithfully reconstructed from noncontact recordings in real-time if the geometry of cardiac surface and the location of electrodes relative to it are known. Larger catheters with appropriate electrode density are needed to resolve complex reentrant atrial rhythms. Conclusion: Real-time panoramic potential mapping is feasible with noncontact intracardiac catheters using the MFS. Significance: Accurate endocardial potential maps can be reconstructed in AF with appropriately designed noncontact multi-electrode catheters.

Non-Contact Intracardiac Potential Mapping Using Mesh-Based and Meshless Inverse Solvers.

Atrial fibrillation (AF) is the most common cardiac dysrhythmia and percutaneous catheter ablation is widely used to treat it. Panoramic mapping with multi-electrode catheters has been used to identify ablation targets in persistent AF but is limited by poor contact and inadequate coverage of the left atrial cavity. In this paper, we investigate the accuracy with which atrial endocardial surface potentials can be reconstructed from electrograms recorded with non-contact catheters. An in-silico approach was employed in which "ground-truth" surface potentials from experimental contact mapping studies and computer models were compared with inverse potential maps constructed by sampling the corresponding intracardiac field using virtual basket catheters. We demonstrate that it is possible to 1) specify the mixed boundary conditions required for mesh-based formulations of the potential inverse problem fully, and 2) reconstruct accurate inverse potential maps from recordings made with appropriately designed catheters. Accuracy improved when catheter dimensions were increased but was relatively stable when the catheter occupied >30% of atrial cavity volume. Independent of this, the capacity of non-contact catheters to resolve the complex atrial potential fields seen in reentrant atrial arrhythmia depended on the spatial distribution of electrodes on the surface bounding the catheter. Finally, we have shown that reliable inverse potential mapping is possible in near real-time with meshless methods that use the Method of Fundamental Solutions.

Feasibility of U-curve method to select the regularization parameter for fluorescence diffuse optical tomography in phantom and small animal studies.

When dealing with ill-posed problems such as fluorescence diffuse optical tomography (fDOT) the choice of the regularization parameter is extremely important for computing a reliable reconstruction. Several automatic methods for the selection of the regularization parameter have been introduced over the years and their performance depends on the particular inverse problem. Herein a U-curve-based algorithm for the selection of regularization parameter has been applied for the first time to fDOT. To increase the computational efficiency for large systems an interval of the regularization parameter is desirable. The U-curve provided a suitable selection of the regularization parameter in terms of Picard's condition, image resolution and image noise. Results are shown both on phantom and mouse data.

Electrocardiographic Imaging: A Comparison of Iterative Solvers.

Cardiac disease is a leading cause of morbidity and mortality in developed countries. Currently, non-invasive techniques that can identify patients at risk and provide accurate diagnosis and ablation guidance therapy are under development. One of these is electrocardiographic imaging (ECGI). In ECGI, the first step is to formulate a forward problem that relates the unknown potential sources on the cardiac surface to the measured body surface potentials. Then, the unknown potential sources on the cardiac surface are reconstructed through the solution of an inverse problem. Unfortunately, ECGI still lacks accuracy due to the underlying inverse problem being ill-posed, and this consequently imposes limitations on the understanding and treatment of many cardiac diseases. Therefore, it is necessary to improve the solution of the inverse problem. In this work, we transfer and adapt four inverse problem methods to the ECGI setting: algebraic reconstruction technique (ART), random ART, ART Split Bregman (ART-SB) and range restricted generalized minimal residual (RRGMRES) method. We test all these methods with data from the Experimental Data and Geometric Analysis Repository (EDGAR) and compare their solution with the recorded epicardial potentials provided by EDGAR and a generalized minimal residual (GMRES) iterative method computed solution. Activation maps are also computed and compared. The results show that ART achieved the most stable solutions and, for some datasets, returned the best reconstruction. Differences between the solutions derived from ART and random ART are almost negligible, and the accuracy of their solutions is followed by RRGMRES, ART-SB and finally the GMRES (which returned the worst reconstructions). The RRGMRES method provided the best reconstruction for some datasets but appeared to be less stable than ART when comparing different datasets. In conclusion, we show that the proposed methods (ART, random ART, and RRGMRES) improve the GMRES solution, which has been suggested as inverse problem solution for ECGI.

Considering New Regularization Parameter-Choice Techniques for the Tikhonov Method to Improve the Accuracy of Electrocardiographic Imaging.

The electrocardiographic imaging (ECGI) inverse problem highly relies on adding constraints, a process called regularization, as the problem is ill-posed. When there are no prior information provided about the unknown epicardial potentials, the Tikhonov regularization method seems to be the most commonly used technique. In the Tikhonov approach the weight of the constraints is determined by the regularization parameter. However, the regularization parameter is problem and data dependent, meaning that different numerical models or different clinical data may require different regularization parameters. Then, we need to have as many regularization parameter-choice methods as techniques to validate them. In this work, we addressed this issue by showing that the Discrete Picard Condition (DPC) can guide a good regularization parameter choice for the two-norm Tikhonov method. We also studied the feasibility of two techniques: The U-curve method (not yet used in the cardiac field) and a novel automatic method, called ADPC due its basis on the DPC. Both techniques were tested with simulated and experimental data when using the method of fundamental solutions as a numerical model. Their efficacy was compared with the efficacy of two widely used techniques in the literature, the L-curve and the CRESO methods. These solutions showed the feasibility of the new techniques in the cardiac setting, an improvement of the morphology of the reconstructed epicardial potentials, and in most of the cases of their amplitude.

Performance and limitations of noninvasive cardiac activation mapping.

BACKGROUND: Activation mapping using noninvasive electrocardiographic imaging (ECGi) has recently been used to describe the physiology of different cardiac abnormalities. These descriptions differ from prior invasive studies, and both methods have not been thoroughly confronted in a clinical setting. OBJECTIVE: The goal of the present study was to provide validation of noninvasive activation mapping in a clinical setting through direct confrontation with invasive epicardial contact measures. METHODS: Fifty-nine maps were obtained in 55 patients and aligned on a common geometry. Nearest-neighbor interpolation was used to avoid map smoothing. Quantitative comparison was performed by computing between-map correlation coefficients and absolute activation time errors. RESULTS: The mean activation time error was 20.4 ± 8.6 ms, and the between-map correlation was poor (0.03 ± 0.43). The results suggested high interpatient variability (correlation -0.68 to 0.82), wide QRS patterns, and paced rhythms demonstrating significantly better mean correlation (0.68 ± 0.17). Errors were greater in scarred regions (21.9 ± 10.8 ms vs 17.5 ± 6.7 ms; P < .01). Fewer epicardial breakthroughs were imaged using noninvasive mapping (1.3 ± 0.5 vs 2.3 ± 0.7; P < .01). Primary breakthrough locations were imaged 75.7 ± 38.1 mm apart. Lines of conduction block (jumps of ≥50 ms between contiguous points) due to structural anomalies were recorded in 27 of 59 contact maps and were not visualized at these same sites noninvasively. Instead, artificial lines appeared in 33 of 59 noninvasive maps in regions of reduced bipolar voltage amplitudes (P = .03). An in silico model confirms these artificial constructs. CONCLUSION: Overall, agreement of ECGi activation mapping and contact mapping is poor and heterogeneous. The between-map correlation is good for wide QRS patterns. Lines of block and epicardial breakthrough sites imaged using ECGi are inaccurate. Further work is required to improve the accuracy of the technique.

Use of Split Bregman denoising for iterative reconstruction in fluorescence diffuse optical tomography.

Fluorescence diffuse optical tomography (fDOT) is a noninvasive imaging technique that makes it possible to quantify the spatial distribution of fluorescent tracers in small animals. fDOT image reconstruction is commonly performed by means of iterative methods such as the algebraic reconstruction technique (ART). The useful results yielded by more advanced l1-regularized techniques for signal recovery and image reconstruction, together with the recent publication of Split Bregman (SB) procedure, led us to propose a new approach to the fDOT inverse problem, namely, ART-SB. This method alternates a cost-efficient reconstruction step (ART iteration) with a denoising filtering step based on minimization of total variation of the image using the SB method, which can be solved efficiently and quickly. We applied this method to simulated and experimental fDOT data and found that ART-SB provides substantial benefits over conventional ART.

Influence of absorption and scattering on the quantification of fluorescence diffuse optical tomography using normalized data.

Reconstruction algorithms for imaging fluorescence in near infrared ranges usually normalize fluorescence light with respect to excitation light. Using this approach, we investigated the influence of absorption and scattering heterogeneities on quantification accuracy when assuming a homogeneous model and explored possible reconstruction improvements by using a heterogeneous model. To do so, we created several computer-simulated phantoms: a homogeneous slab phantom (P1), slab phantoms including a region with a two- to six-fold increase in scattering (P2) and in absorption (P3), and an atlas-based mouse phantom that modeled different liver and lung scattering (P4). For P1, reconstruction with the wrong optical properties yielded quantification errors that increased almost linearly with the scattering coefficient while they were mostly negligible regarding the absorption coefficient. This observation agreed with the theoretical results. Taking the quantification of a homogeneous phantom as a reference, relative quantification errors obtained when wrongly assuming homogeneous media were in the range +41 to +94% (P2), 0.1 to -7% (P3), and -39 to +44% (P4). Using a heterogeneous model, the overall error ranged from -7 to 7%. In conclusion, this work demonstrates that assuming homogeneous media leads to noticeable quantification errors that can be improved by adopting heterogeneous models.

Split operator method for fluorescence diffuse optical tomography using anisotropic diffusion regularisation with prior anatomical information.

Fluorescence diffuse optical tomography (fDOT) is an imaging modality that provides images of the fluorochrome distribution within the object of study. The image reconstruction problem is ill-posed and highly underdetermined and, therefore, regularisation techniques need to be used. In this paper we use a nonlinear anisotropic diffusion regularisation term that incorporates anatomical prior information. We introduce a split operator method that reduces the nonlinear inverse problem to two simpler problems, allowing fast and efficient solution of the fDOT problem. We tested our method using simulated, phantom and ex-vivo mouse data, and found that it provides reconstructions with better spatial localisation and size of fluorochrome inclusions than using the standard Tikhonov penalty term.