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Image-guided percutaneous interventions have successfully replaced invasive surgical methods in some cardiologic practice, where the use of 3D-reconstructed cardiac images, generated by magnetic resonance imaging (MRI) and computed tomography (CT), plays an important role. To conduct computer-aided catheter ablation of atrial fibrillation accurately, multimodal information integration with electroanatomic mapping (EAM) data and MRI/CT images is considered in this work. Specifically, we propose a variational formulation for surface reconstruction and incorporate the prior shape knowledge, which results in a level set method. The proposed method enables simultaneous reconstruction and registration under nonrigid deformation. Promising experimental results show the potential of the proposed approach.

Current treatment of cardiac arrhythmias ranges from noninvasive
strategies, such as pharmacological therapy, to minimally invasive techniques,
such as catheter-based ablation, and to open surgical techniques. While medical
therapy can mitigate the occurrence of arrhythmias, these treatments may have
significant side effects since most drugs used have some toxicity that is not
suitable for long-term therapy. The catheter-based procedure is proven to be an
effective method in treating patients with certain cardiac arrhythmias [

AF is the most common sustained cardiac arrhythmia
encountered in clinical practice. In the United States alone, there are over
3.5 million patients with this disorder [

The procedure of interventional AF treatment entails
mapping the left atrium and the attached pulmonary veins using an
electroanatomic mapping (EAM) system. This mapping information can be used to
deliver lesions as well. This electrical approach is suitable for the heart
since it is an electromechanical organ, where mechanical contractions are
driven by electrical stimulus. However, there is a serious limitation of the
EAM system in that it is not able to provide an accurate anatomical information
of heart. Typically, a virtual shell is used to represent the atrial wall and
the vein. The points on the atrial wall, where the catheter is manually
touched, are used to create this shell [

The catheter-based ablation process can be greatly improved if a real anatomy is used instead of the virtual shell. To ensure safe catheter maneuverability and enable delivery of effective lesions with minimal collateral damage and complications, it is critical to have both the anatomical information and the electrical information available to the operator. This is particularly important for performing ablation in a complex structure such as the left atrium that is surrounded by important organs, which are vulnerable to damage if lesions are not appropriately directed with close anatomical guidance. Furthermore, even the pulmonary veins themselves are liable to be damaged with grave long-term consequences if the lesions extend deeply into the veins instead of being restricted to the ostia.

The use of a multimodal data integration process can provide an anatomical, physiological, and functional representation simultaneously. In practice, this can be achieved by combining an anatomical surface model acquired by MRI/CT images and the localized electrical information measured by an EAM system. In the registration process, one obvious difficulty stems from the noise and/or outliers that are inevitably associated with the MRI/CT imaging process and the EAM data collection procedure. Unlike other organs in the body, heart undergoes contractile motion, apart from respiratory motion, thus making it unique and very challenging to register and integrate data of different modalities. In addition to physiological variations such as changes in the heart rate, the heart rhythm, and the respiratory effect, various types of heart motion are the source of outliers.

The main contribution of this work is to provide enhanced imaging of the anatomical heart surface from sparse and noisy EAM data in combination with a heart-shape model obtained from MRI/CT reconstruction as a prior knowledge. For 3D surface reconstruction, we propose a variational formulation in the level set framework that is an efficient numerical scheme. The level set method is particularly of great use in representing a shape due to its topology-free and implicit characteristics. By leveraging the 3D heart-shape model, we can compensate incomplete EAM data, thereby representing the anatomical heart more accurately. The proposed method has two important advantages. First, it is robust against nonrigid deformation caused by cardiac motion and noise. Second, it can construct the optimal surface without an explicit correspondence between the MRI/CT surface and EAM data due to the implicit surface representation.

The rest of this paper is organized as follows.
Previous related work is reviewed in Section

Developing a computer-guided system for ablative heart
surgery involves image registration or integration techniques. They are usually
performed under a rigid transformation between preoperative MRI/CT
reconstruction and intraoperative EAM data points [

The ICP algorithm begins with two meshes and an
initial guess for their relative rigid-body transform. It refines the transform
iteratively by generating pairs of corresponding points on the meshes and
minimizing an error metric repeatedly [

Most of previous schemes used an ICP-based method
without addressing the above-mentioned problem. Instead, they focused on
clinical registration. For example, Reddy et al. [

The rigid transformation assumption made by existing
schemes is simple yet insufficient in most cases. It often yields
unsatisfactory results since a nonrigid deformation is involved between the
anatomical heart model reconstructed by MRI/CT images and temporal instances of
the heart at the collection of EAM data points. This physiological and
anatomical variation that occurs in the formation of the heart surface model
and the collection of EAM data points demands a nonrigid transformation (or
equivalently diffeomorphism) between the model and the data. Woo et al. proposed a novel image integration
technique by incorporating nonrigid deformation using the level set method in
[

To overcome the limitation of the traditional
registration approach based on the rigid-transformation assumption, we
formulate this problem as a 3D surface reconstruction problem from EAM data
points with a given surface prior. A similar context arises in surface
reconstruction from point clouds in a scanned noisy image. Surface reconstruction
using an explicit representation has been considered by researchers, for example, [

Surface reconstruction based on an implicit shape
representation using the level set technique has been studied for almost two
decades by applied mathematicians, for example, [

The problem of insufficient EAM data encountered in the 3D heart surface construction, including the left atrium and its pulmonary veins, can be mitigated by incorporating a heart-shape prior provided by MRI/CT imaging. Then, the optimal surface can be obtained by minimizing the energy functional that consists of a data-fitting term and a prior knowledge term as detailed in the next section.

In this section, we present a multimodal data integration algorithm for simultaneous surface reconstruction and registration. This algorithm reconstructs the heart surface from measured EAM data points and a heart-shape prior obtained by MRI/CT imaging using the level set method.

Under the level set framework [

For the representation of a surface model

The essential assumption in this surface
reconstruction application is that surface

The energy functional in (

The data fitting term can be written as

Combining (

For numerical implementation, we use the following
approximations for the heaviside function and the Dirac delta measure as
defined in [

The energy functional in (

To discretize the equation in

We first set

Solving the above partial differential equations numerically is challenging since the time step should be constrained to a small value in maintaining numerical stability. In addition, it is computationally expensive to find a high dimensional surface. Thus, it is desired to employ an efficient numerical scheme and we naturally use multigrid method that adopts a hierarchical representation of the data in multiple scales and propagates the solution from the coarse scale to the fine scale to achieve computational efficiency.

This variational approach presented in Sections

We begin with simple yet illustrative examples to demonstrate the efficiency and robustness of the proposed algorithm. We use synthetic geometric objects in 2D and 3D which have geometric features that aim to be preserved under reconstruction process. Then, the evaluation of the algorithm is performed based on real patient data.

We first compare the proposed scheme with the ICP
scheme in registration accuracy using a synthetic 2D star shape as shown in
Figure

The shape reconstruction results for a synthetic 2D star shape, (a) the original shape, (b)–(d) ICP results using different Gaussian noise levels, (e) the deformed shape, and (f)–(h) results of the proposed method using different Gaussian noise levels.

Original shape

ICP (2% noise)

ICP (6% noise)

ICP (10% noise)

Deformed shape

Proposed (2% noise)

Proposed (6% noise)

Proposed (10% noise)

Graphical illustration of the registration results
between deformed shape of different noise level and noisy contour points are
presented in Figures

Comparison of mean distances between the reconstructed surface and measured data points for the 2D star example at different noise levels using ICP and the proposed algorithm.

Next, we compare the proposed scheme with ICP using a
3D synthetic jar example. Experimental results are shown in Figure

The shape reconstruction results for a synthetic 3D image: (a) the original shape, (b)–(e) ICP results using different Gaussian noise levels, (f) the deformed shape, and (g)–(j) results of the proposed method using different Gaussian noise levels.

Original shape

ICP (3% noise)

ICP (6% noise)

ICP (9% noise)

ICP (12% noise)

Deformed shape

Proposed (3% noise)

Proposed (6% noise)

Proposed (9% noise)

Proposed (12% noise)

Comparison of mean distances between the reconstructed surface and measured data points for the 3D jar example at different noise levels using ICP and the proposed algorithm.

We can adjust the importance of both a data fitting
term and a prior knowledge term that includes a regularization and shape
similarity term by tuning the parameter

The final example is a set of real patient data. 3D
preoperative contrast-enhanced MR angiography (MRA) was performed to delineate
endocardial boundaries of the left atrium and pulmonary veins. The voxel size
was

After delineating and removing unwanted regions such
as the left ventricle (LV) and other small veins, we reconstruct the 3D model
as shown in Figure

The 3D patient data: (a) MRA of LV and (b) 3D reconstruction result of the given MRA.

MRA of LA

3D Reconstruction

The surface registration results for the patient data.

ICP

Proposed method

To validate the proposed algorithm, the optimal
surface is reconstructed using 250 EAM data points by incorporating a heart
shape prior from preoperative MRA. By minimizing the energy functional, the
final result is shown in Figure

Performance comparison of ICP and the proposed method.

ICP | Proposed | |
---|---|---|

EAM point mean distance | 4.5087 mm | 2.4113 mm |

Ablation point mean distance | 3.2046 mm | 2.0921 mm |

A novel multimodal data integration technique using the level set method for catheter ablation of AF was presented in this paper. This technique enables reconstruction and registration simultaneously using data fitting, regularization, and shape prior energy terms. It provides better performance than the existing ICP method in accuracy. In the proposed framework, the heart-shape model from MRA reconstruction is used as a prior shape knowledge. Thus, we can use the shape information to compensate for insufficient EAM data. Clinically, this technique can improve efficacy and safety of AF ablation by integrating EAM data and 3D imaging data.

Dynamic cardiac shape analysis will make the current integration method more precise and meaningful. We plan to incorporate a richer set of spatiotemporal shape models using dynamic shape information in the future. Besides, we may consider a localized regularization method around the point data to obtain more precise reconstruction.