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Hybrid PET/CT scanners can simultaneously visualize coronary artery disease as revealed by computed tomography (CT) and myocardial perfusion as measured by positron emission tomography (PET). Manual registration is usually required in clinical practice to compensate spatial mismatch between datasets. In this paper, we present a registration algorithm that is able to automatically align PET/CT cardiac images. The algorithm bases on mutual information (MI) as registration metric and on genetic algorithm as optimization method. A multiresolution approach was used to optimize the processing time. The algorithm was tested on computerized models of volumetric PET/CT cardiac data and on real PET/CT datasets. The proposed automatic registration algorithm smoothes the pattern of the MI and allows it to reach the global maximum of the similarity function. The implemented method also allows the definition of the correct spatial transformation that matches both synthetic and real PET and CT volumetric datasets.

Cardiac images acquired via different modalities can provide complementary information. Therefore, the fusion of two or more coregistered multimodal datasets into a single representation can provide important support for a medical diagnosis or for the therapeutic evaluation in cardiology. However, the use of a multimodal imaging approach in clinical practice is limited by drawbacks in accurate image alignment. Several approaches have been developed to register 3D cardiac datasets [

Recently, the clinical need to merge complementary information has been emphasized by the success of the hybrid scanners, which are able to acquire in a single imaging session multimodal data that provide complementary information. The most important examples are the PET/CT devices [

In this work, we describe an automatic method to register functional PET and anatomical CT 3D cardiac datasets. The developed registration algorithm is based on a rigid transformation described by three translational and three rotational parameters. The mutual information (MI) measure has been used as the similarity metric, and a multiresolution optimization algorithm based on existing genetic algorithms has been implemented that defines the optimal transformation that makes maximum use of the MI value. One real PET and CT dataset has been used to build a registered synthetic model exploited for the development of the registration algorithm and for the evaluation of the similarity metric function and of the optimization approach. The registration algorithm presented here has also been applied to real PET and CT datasets.

Three CT-PET datasets were acquired with PET/CT Discovery-RX (GE Healthcare) from patients scheduled for simultaneous assessment of myocardial perfusion and coronary artery disease. The first dataset was used as the reference when developing the registration algorithm, while the other datasets were used to test the algorithm. The CT datasets were acquired during ECG gating and end-expiratory breath holds and consisted of 411 transaxial slices of _{3 }and reconstructed as 47 transaxial slices of

The registration algorithm has been developed in MATLAB 7.0 and the genetic algorithm has been implemented by using the Genetic algorithm and Direct Search Toolbox. The development and the evaluation of the registration algorithm has been done by using an Intel Core i3-530-2.93 GHz 4 MB cache and Windows XP OS.

Two isotropic 3D cardiac models were built to simulate registered PET and CT short axis image volumes. Both models were developed using an elliptical geometry and a previously described image model [

The CT model was described by the following equation:

The PET model was described by the following equation:

In comparison to the CT model, the PET model contained only the gray value

As for the CT model, the PET noise, described by the last term

Image fusion was based on the 3D registration process used to define the spatial and temporal alignment of the volumetric datasets involved. The aim of the registration process was to define a transformation to map voxels from the reference image volume

As previously noted, the entire registration process can be described by considering three linked components: the domain where the transformation

The transformation definition is based on the geometrical operations required for the process. The 3D rigid transformation has six degrees of freedom (three translational and three rotational parameters), while the affine transformation adds scaling and shearing parameters. The most general transformation is the elastic or nonrigid registration. In theory, it has infinite degrees of freedom and can be represented by a polynomial function. The elastic registration should be used for cardiac image registration, but its clinical application is limited by its high computational load and by the long time needed to perform the registration [

The similarity metric used to evaluate alignment must be robust and must be performed in a reasonable time. In our registration method, the mutual information metric was used because it does not make any assumptions about the relationship between various image intensities [

The NN, PV, and GPVE were evaluated in the present study. The ability of the optimization algorithm to reach the global maximum of MI was strongly related to the pattern of MI over the search space. A “smooth” MI pattern allows convergence to an optimal solution, while a “rough” pattern was likely to trap the optimization algorithm in local. We calculated the smoothness parameter si of the MI pattern curve by

Even if different methods can be used to reduce the possibility of local peaks in the MI pattern, a robust optimization method is required to reach the global similarity metric maximum that corresponds to the correct spatial alignment. Different optimization algorithms can be used as a search strategy, but not all techniques are able to reach the global maximum. For instance, depending on the starting condition, local optimization methods are affected by the similarity metric pattern such that they can obtain a local solution. The use of a global optimization method in the registration process assures that the optimal solution is reached and that the correct spatial transformation parameters are defined. Some widely used global optimization techniques are the genetic algorithms (GAs). These are based on Darwin’s theory of biological evolution and are implemented using stochastic information [

In this work, we have developed a search strategy based on a multiresolution approach. Two primary steps have been defined. The first step is based on a global optimization method that uses GAs to reach a solution near the global maximum. The second step is based on a local, computationally efficient optimization method (the downhill simplex algorithm). This step originates from the solution given by the GAs and achieves the global maximum for the MI.

First, the GAs require an initial definition of a population of individuals, each containing a possible solution to the problem defined in their chromosomes. In the present problem, the chromosomes included six values (

Each solution was associated with two values used to describe the new population: a fitness score corresponding to the MI value, and a reproduction probability proportional to the fitness score. Because of the high computational load of the GA method, in this step we used the NN interpolation method to calculate the MI and applied an optimal downsampling to the floating dataset. Several methods were employed to generate the new population. The first was the

As shown in Figure

Roulette wheel selection method (a) and crossover strategy (b).

Starting from the global solution, the local downhill simplex method was used to calculate the optimal solution. Because the main purpose of using the local method was to obtain excellent accuracy and precision within a reasonable time, the downsampled value of the floating volume was reduced in this step, and the PV interpolation method was used. The local optimization process was stopped when the maximum number of iterations was reached or when no more improvement in the best fitness value could be obtained.

The MI pattern has been defined as a function of independent translational (

Figure

Typical MI translational pattern obtained by using different interpolation methods and strategies. Translational results for the PV method are shown in the range ±10 mm to illustrate the interpolation artifacts. Translational results for the GPVE, PV + downsampling and PV + upsampling methods are shown in the range ±10 mm for comparison of the pattern obtained against the PV curve. When the second strategy is applied, the downsampling produced a new voxel dimensions =

To set a correct downsampling factor (DF), we also evaluated the MI patterns for each transformation parameter by applying a different DF, defined as the voxel volume measured in mm^{3} (the voxel volume of the reference dataset is 1 mm^{3}), and by calculating the corresponding SI value. As shown in Figure

SI values for different DF values. The first row shows the SI values corresponding to the translational

The PET signal in pathological conditions, as a perfusion deficit, can be missed in some regions. This aspect can affect the robustness of the registration algorithm and the MI pattern. We evaluated the influence of intensity of the PET signal on the MI pattern by varying the multiplicative kernel

MI translational (

The application of the GAs as the first step of the optimization algorithm allowed us to reach a solution near the global maximum. The optimal initial population size was determined by considering the accuracy of the algorithm and the computational time. We introduced a new parameter defined as

By using an initial population number = 75, we varied the percentage of the new generation created by the elite method (

The registration algorithm presented here has been evaluated by applying it 150 times to the PET and CT cardiac models, which were randomly misaligned in ranges of ±40 mm and ±20° for translational and rotational parameters, respectively. The mean error and standard deviation for each rigid transformation parameter are shown in Table

Accuracy of the registration algorithm applied to the synthetic (a) and real (b) datasets. When the real dataset is considered, the results of the manual registration are also shown. The manual registration has been performed by an expert operator blinded to the results of the automatic registration and used as reference for the error computation.

_{x} | _{y } | _{y } | _{y} | _{z} | ||||
---|---|---|---|---|---|---|---|---|

(a) Synthetic | ||||||||

Automatic | Mean Error | 0.083 | 0.054 | 0.037 | 0.117 | 0.286 | 0.201 | |

standard deviation (SD) | 0.108 | 0.089 | 0.097 | 0.215 | 0.2718 | 0.397 | ||

(b) Real | ||||||||

Manual | −25.61 | 18.51 | −4.9 | −9.45 | 0.86 | −2.01 | ||

Automatic | Mean error | −25.89 | 18.485 | −5.157 | −9.59 | 0.89 | −2.29 | |

standard deviation (SD) | 0.238 | 0.146 | — | — | 0.825 |

In order to also evaluate our multiresolution optimization algorithm, the local and global methods were also applied separately 150 times to the PET and CT cardiac models, starting from a random initial parameter value in the ranges previously defined. As shown in Figure

Accuracy of local, global and multiresolution optimization approaches when applied separately to the PET and CT cardiac models.

Two real PET and CT datasets (datasets 1 and 2) were also used to evaluate the registration algorithm. First, the two datasets were manually aligned by an expert operator blinded to the results of the automatic registration, using a state-of-the-art image analysis package meant for a clinical environment (GE Healthcare, CardIQ Fusion software). These manually defined translation and rotation parameters were recorded.

The limited regions manually defined around the heart of the dataset 1 and 2 were used in the validation process to reduce the effect of the surrounding structures on the MI calculation and then on the registration algorithm. Table

For rotational parameters

Example of misaligned (a) and aligned (b) transaxial PET and CT images corresponding to dataset 1.

The registration algorithm presented here was applied to dataset 2, which contained an artifact in the CT image volume caused by a metallic object (Figure

A transaxial image of the CT data volume in which an artifact caused by a metallic object is present.

Example of misaligned (a) and aligned (b) transaxial PET and CT images in which an artifact caused by a metallic object is present.

Registration of PET/CT volumetric datasets is an important issue in cardiac applications in which complementary PET/CT information is utilized to find the correct diagnosis. The hardware fusion obtained by hybrid PET and CT scanners does not completely solve the misalignment problem. In the current clinical practice CT, and PET images are transferred to a proprietary workstation where the two datasets are manually registered. This task is affected by inter and intraobserver variability and requires a long processing time. Our method may replace the manual registration saving image analysis time and reducing at the same time the inter- and intraobserver variability inherent in the manual procedure. The registration algorithm is based on a rigid transformation and on the MI measurement used as the similarity metric. The optimization algorithm implemented here defines the optimal transformation that maximizes the MI value and is based on a combination of global (genetic algorithms) and local (downhill simplex) optimization methods.

MI is generally recognized as a powerful metric for registration of multimodal images, thanks to its ability to capture the similarity of datasets with different gray-lever distributions, such as in CT and PET images. However, the effectiveness of the search for the global maximum in the MI similarity function could be affected by the presence of local peaks in the MI pattern.

We have demonstrated that the MI pattern is related to the interpolation method used in the joint histogram calculation, confirming findings from earlier studies [

A possible limitation of the proposed approach is the use of a rigid transformation, that cannot take into account either the complex nonrigid motion of the heart during the cardiac cycle or the various image distortions present in the CT and PET acquisition processes. However, rigid registration is commonly used in clinical practice and is considered to be acceptable for reaching the correct diagnosis, particularly when electrocardiographic gating is not used in PET imaging to save acquisition time. In this case, the borders of the left ventricle in PET images appear to have been too “smoothed” to obtain a voxel-to-voxel registration. Our expectation is that a nonrigid registration procedure can be inserted into the local optimization step of the proposed algorithm, via one of the several approaches available.

We have demonstrated that cardiac PET/CT image registration can be effectively and automatically performed using a two-step approach. The first step consists of identification of a global maximum of mutual information by using a genetic algorithm which in turn utilizes downsampled data and a fast interpolation algorithm. The second step completes the registration with a high-resolution local optimization algorithm. The method proposed here may improve the effectiveness of hybrid PET/CT scanners for use in the joint assessment of CAD and myocardial perfusion in cardiac disease.

This research was partly supported by EVINCI European Project: Evaluation of INtegrated Cardiac Imaging for the Detection, Characterization and Monitoring of Ischemic Heart Disease (EVINCI-STUDY), 7th FWP, reference number 222915.

^{18}F-FDG whole-body PET with CT