AUTOMATED MULTI-MODALITY REGISTRATION OF 64-SLICE CORONARY CT ANGIOGRAPHY WITH MYOCARDIAL PERFUSION SPECT

Abstract

A multi-modality image registration algorithm for the alignment of myocardial perfusion SPECT (MPS) and coronary computed tomography angiography (CTA) scans is presented in this work. Coronary CTA and MPS provides clinically complementary information in the diagnosis of coronary artery disease. An automated registration algorithm is proposed utilizing segmentation results of MPS volumes, where regions of myocardium and blood pools are extracted and used as an anatomical mask. Using a variational framework, we adopt an energy functional with a piecewise constant image model and optimize it numerically with a gradient descent algorithm. The computational efficiency and robustness of the proposed automatic registration of CTA with MPS have been demonstrated by the experiments that yielded an average error smaller than an MPS voxel size.

1. INTRODUCTION

Both coronary computed tomography angiography (CTA) and myocardial perfusion SPECT (MPS) can be used to diagnose coronary artery disease. Coronary CTA allows precise localization of coronary artery plaques and depiction of coronary anatomy [1]. Coronary lesions are responsible for hypoperfusion of myocardium. Myocardial MPS is a mainstream imaging technique used to estimate hypoperfusion in the myocardium caused by coronary lesions, which however cannot be observed by MPS directly. Thus, it is requested to combine different imaging modalities that provide clinically complementary information in the diagnosis and this can be achieved by registration.

In general, registration algorithms can be categorized as “feature-based” and “intensity-based” methods depending on the characteristic information that is used in the computation of dissimilarity measure. Feature-based methods are performed based on local image features such as edges or relevant anatomical structures, whereas “intensity-based” methods directly use image intensity that does not require any additional function for characterizing structures in image. A number of different measures have been applied for the computation of dissimilarity and mutual information is one of the most popular approaches specially for multi-modality image registration [2, 3]. However, in multi-modality registration problems, intensity alone is often insufficient and additional prior knowledge is desired to be incorporated. This is especially true for images from abnormal subjects that have inherent physiological variations between different modalities. In such circumstances, image segmentation can be of great use for registration incorporating the hybrid information such as the boundaries and the intensity distribution in the regions of interest [4].

In this work, we aim to develop a fully automated multimodality image registration technique for aligning functional MPS with anatomical coronary CTA scans. To provide robust registration results, we utilize the segmented MPS volume and estimate intensity values in the myocardial and blood pool region simultaneously with a variational framework. The rest of this paper is organized as follows. Previous work is reviewed in Sec. 2. The proposed registration method with segmented MPS volume and its minimization is described in Sec. 3 followed by experimental results presented in Sec. 4. Finally, discussion and concluding remarks are given in Sec. 5.

2. REVIEW OF PREVIOUS WORK

Visual analysis of fused MPS and coronary CTA images can synergistically improve the diagnostic value of sequential combined imaging [5], and manual tools for CTA-MPS fusion have been developed [6]. However, manual alignment is tedious and observer-dependent, which complicates clinical protocols and reduces the practicality of such tools. The difficulty in accurate registration of MPS with coronary CTA lies in the fact that different anatomical features are visible in different images. For example, the CTA image is created by the attenuation of external photons throughout the thoracic volume while MPS is created by emissions of photons located primarily in the myocardium. Furthermore, although myocardium is visible from both CTA and MPS, there could be severe perfusion defects present on MPS images which do not have equivalent appearance on CTA as shown in Fig. 1. In addition, variations in the intravenous contrast distribution for different patients cause intensity variations on CTA images within the blood pool region. As a result, standard automated registration procedures, such as mutual information without specialized pre-processing may not be most effective.

Fig. 1.

Examples of mid-myocardial short-axis images from CTA and MPS: (a) a CTA image which looks similar for normal and abnormal arteries, (b) a normal MPS image and (c) an abnormal MPS image.

To the best of our knowledge, a fully automated multimodality image registration of MPS with coronary CTA scans obtained from stand-alone systems has not been developed previously. Previous studies on fusion between MPS and coronary CTA required laborious manual alignment of image data [5, 6]. Several studies on the registration of MPS with other modalities were conducted. Faber et al. [7] proposed a point-based registration of the MPS surface with 3D coronary anatomy reconstructed from invasive 2D coronary angiography. Guetter et al. [8] developed a registration method for MPS and non-contrast CT data to improve the attenuation correction. In their studies, images were however obtained by the hybrid SPECT-CT scanner (in contrast with different stand-alone scanners) where images are already in approximate alignment, requiring only small correction. Guetter et al. [8] proposed a learning-based method based on the mutual information and an intensity co-occurrence prior. However, this approach used an off-line training process that is computationally inefficient. Besides, all data sets have to be provided a priori; otherwise, the prior model may not be incrementally extended as new image data (e.g. different vendors or abnormal data) are available. In related development, Aladl et al. [9] proposed an MRI-MPS volume registration technique which utilized the MRI motion to pre-segment the heart for registration with MPS. However, this approach is not practical for CTA since typically only one phase is reconstructed and available for analysis while the use of all frames is computationally intractable.

3. DESCRIPTION OF PROPOSED METHOD

3.1. Pre-processing

In our registration method, a fully automatic segmentation algorithm [10] for the left ventricle (LV) with additional segmentation of the blood pool regions is first adopted to extract structures of interest, including myocardium and the blood pool, in the MPS volume. Segmentation of MPS volumes is of great importance since it can provide the anatomical information to guide registration. Those regions to be extracted from MPS volumes usually do not present distinguished boundary features due to severe perfusion defects, resulting in an inhomogeneous intensity distribution despite within the same anatomical region as shown in Fig. 2.

Fig. 2.

An example of myocardial segmentation (white contours) from MPS: (a) the 2D slice of segmented normal MPS, (b) abnormal segmented MPS, and (c) the 3D segmented MPS volume with endocardial boundary (gray) and epicardium boundary (orange mesh).

Let I and J be segmented MPS and coronary CTA volumes, respectively, in Ω which correspond to an open and bounded domain in ℝ³. The segmented MPS volume, I, is the union of three disjoint regions; namely, the blood pool, myocardium, and extracardiac structures. We denote regions of blood pool, myocardium, and extracardiac structures by D₁, D₂, and D₃ respectively, and Ω = D₁ ∪ D₂ ∪ D₃.

Besides the segmentation procedure, it is necessary to match cardiac phases between these two modalities. To achieve this goal, we perform the alignment of coronary CTA with end-diastolic (ED) images as selected for coronary artery analysis with segmented “motion-frozen” MPS created from gated images [11]. In the motion-frozen technique, derived LV contours are used in combination with a thin-plate spline image warping [12] to create the MPS volume in enddistolic phase matching with CTA. For both CTA and MPS, transverse image orientation is used during the registration process.

3.2. Registration Model Using Segmented MPS Volume

The goal of registration is to find the transformation, T(x), that maps the source volume into the corresponding target volume. In this application, we consider 3D rigid registration with 6 parameters (3 for the translation and 3 for the rotation). The energy functional based on the segmented MPS volume can be defined as

$$E(c_1,c_2,c_3,\mathrm{\Theta })={\displaystyle {\int }_{D_1}}{|c_1-G_{\sigma }*(J\circ T_{\mathrm{\Theta }})(x)|}^2\mathit{\text{dx}}+{\displaystyle {\int }_{D_2}}{|c_2-G_{\sigma }*(J\circ T_{\mathrm{\Theta }})(x)|}^2\mathit{\text{dx}}+{\displaystyle {\int }_{D_3}}{|c_3-G_{\sigma }*(J\circ T_{\mathrm{\Theta }})(x)|}^2\mathit{\text{dx}}={\displaystyle {\int }_{\mathrm{\Omega }}}{\chi }_{D_1}(x)·{|c_1-G_{\sigma }*(J\circ T_{\mathrm{\Theta }})(x)|}^2\mathit{\text{dx}}+{\displaystyle {\int }_{\mathrm{\Omega }}}{\chi }_{D_2}(x)·{|c_2-G_{\sigma }*(J\circ T_{\mathrm{\Theta }})(x)|}^2\mathit{\text{dx}}+{\displaystyle {\int }_{\mathrm{\Omega }}}{\chi }_{D_3}(x)·{|c_3-G_{\sigma }*(J\circ T_{\mathrm{\Theta }})(x)|}^2\mathit{\text{dx}},$$ (1)

where c₁, c₂ and c₃ are constants that approximate the average intensities of regions D₁, D₂, and D₃, respectively, G_σ is a Gaussian kernel with standard deviation σ, and T_Θ is a rigid transformation of parameters Θ = (θ_x, θ_y, θ_z, t_x, t_y, t_z) that denote rotations with respect to x, y and z directions and translations in x, y and z directions, respectively. The characteristic function χ_D is defined by

$${\chi }_D(x)=\{\begin{array}{cc}\hfill 1,\hfill & x\in D\hfill \\ \hfill 0,\hfill & x\notin D.\hfill \end{array}$$ (2)

We apply a Gaussian filtering (with a standard deviation of 3mm) to the CTA volume to ensure homogeneous intensity levels, to suppress noise and to lower the CTA image resolution closer to that of the MPS image.

3.3. Minimization

The optimal values of parameters (c₁, c₂, c₃, Θ) to minimize the given energy functional are obtained by solving the associated Euler-Lagrange equations. As a numerical scheme, a gradient descent method is performed. The derivation of the Euler-Lagrange equations is given as below:

$$\frac{\partial {\mathrm{\Theta }}_i}{\partial t}=-\frac{\partial E}{\partial {\mathrm{\Theta }}_i}(i=1,2,\cdots ,6).$$

In the derivation, we consider only one term for a single region in the energy functional for simplicity, which is given by

$$-\frac{1}{2}\frac{\partial E}{\partial {\mathrm{\Theta }}_i}={\displaystyle {\int }_{\mathrm{\Omega }}}\{{\chi }_D(x)·(c-G_{\sigma }*(J\circ T_{\mathrm{\Theta }})(x))\}\left(\frac{\partial }{\partial {\mathrm{\Theta }}_i}(c-G_{\sigma }*(J\circ T_{\mathrm{\Theta }})(x)\right)\mathit{\text{ dx}}$$ (3)

By setting T_Θ(x) = T(Θ, x), we get

$$\frac{\partial }{\partial {\mathrm{\Theta }}_i}(G_{\sigma }*(J\circ T_{\mathrm{\Theta }})(x))={\displaystyle {\int }_{{ℝ}^2}}{G}_{\sigma }(y)\frac{\partial }{\partial {\mathrm{\Theta }}_i}\{J(T(\mathrm{\Theta },x-y))\}\mathit{\text{dy}}={\displaystyle {\int }_{{ℝ}^2}}{G}_{\sigma }(y)\nabla J(T(\mathrm{\Theta },x-y))·\frac{\partial T(\mathrm{\Theta },x-y)}{\partial {\mathrm{\Theta }}_i}\mathit{\text{dy}}.$$ (4)

Furthermore, by setting $\frac{\partial J\circ T_{\mathrm{\Theta }}(x)}{\partial {\mathrm{\Theta }}_i}=L_i(\mathrm{\Theta },x)=\nabla J(T(\mathrm{\Theta },x))·\frac{\partial T(\mathrm{\Theta },x)}{\partial {\mathrm{\Theta }}_i}$, we obtain

$$\frac{\partial }{\partial {\mathrm{\Theta }}_i}(G_{\sigma }*(J\circ T_{\mathrm{\Theta }})(x))={\displaystyle {\int }_{{ℝ}^2}}{G}_{\sigma }(y)L_i(\mathrm{\Theta },x-y)\mathit{\text{dy}}=G_{\sigma }*L_i(\mathrm{\Theta },x).$$ (5)

Hence, Eq. (3) becomes

$$-\frac{1}{2}\frac{\partial E}{\partial {\mathrm{\Theta }}_i}={\displaystyle {\int }_{\mathrm{\Omega }}}\{{\chi }_D(x)·(c-G_{\sigma }*(J\circ T_{\mathrm{\Theta }})(x))\}{G}_{\sigma }*L_i(\mathrm{\Theta },x)\mathit{\text{dx}}.$$ (6)

By keeping Θ fixed, the minimization of the energy E with respect to constants c₁, c₂ and c₃ leads to

$$\{\begin{array}{c}{c}_1=\frac{{\displaystyle {\int }_{\mathrm{\Omega }}}{\chi }_{D_1}(x)·(G_{\sigma }*(J\circ T_{\mathrm{\Theta }})(x))\mathit{\text{ dx}}}{{\displaystyle {\int }_{\mathrm{\Omega }}}{\chi }_{D_1}\mathit{\text{dx}}},\hfill \\ c_2=\frac{{\displaystyle {\int }_{\mathrm{\Omega }}}{\chi }_{D_2}(x)·(G_{\sigma }*(J\circ T_{\mathrm{\Theta }})(x))\mathit{\text{ dx}}}{{\displaystyle {\int }_{\mathrm{\Omega }}}{\chi }_{D_2}\mathit{\text{dx}}}\hfill \\ c_3=\frac{{\displaystyle {\int }_{\mathrm{\Omega }}}{\chi }_{D_3}(x)·(G_{\sigma }*(J\circ T_{\mathrm{\Theta }})(x))\mathit{\text{ dx}}}{{\displaystyle {\int }_{\mathrm{\Omega }}}{\chi }_{D_3}\mathit{\text{dx}}}.\hfill \end{array},$$ (7)

The constant intensity values and transformation parameters can be minimized using Eqs. (6) and (7) in an alternative manner.

4. EXPERIMENTAL RESULTS

Registration results using the proposed method and a conventional mutual information (MI) method have been compared with the manual alignment (n=40) obtained by two observers on 20 stress/rest MPS (64×64×24, 6.4×6.4×6.4mm) and CTA (512×512×260, 0.49×0.49×0.63mm) datasets acquired by two CT scanners (10 GE VCT 64-slice scanner and 10 Siemens 64-slice Dual Source CT scanner). An example of CTA and MPS pair and its registration result are shown in Fig. 3.

Fig. 3.

An example of registration results: images before (top) and after (bottom) registration are shown. Errors were (1, 2, 1) mm for the translation and (2, 0, 0) degrees for the rotation in this case.

Our registration of MPS with CTA achieved a success rate of 100% and the average registration time was 10±1.3 sec. The MI based registration method had a larger error than proposed one as shown in Fig. 4 and the average registration time was 24±2.2 sec. The translational and rotational registration results were not much different in inter-observer variability and in the stress and rest MPS (p=NS) as shown in Table 1. No significant difference between different types of scanners was observed. That is, 4.5±3.3 mm for translation and 1.2±2.1 degrees for rotation for Siemens and 4.6±3.5 mm for translation and 2.2±3.4 degrees for rotation for GE (p=NS).

Fig. 4.

Registration errors for stress and rest

Table 1.

Registration error and observer variability

		translation (mm)	rotation (degree)
MI based	Stress	9.0±7.0	1.5±3.1
Method	Rest	10.2±7.3	1.5±1.6
Proposed	Stress	4.6±3.3	1.7±2.6
Method	Rest	4.5±3.1	1.8±3.1
Observer	Stress	3.1±2.4	2.8±3.3
Variability	Rest	3.7±2.9	2.6±3.8

The preliminary studies show that the proposed approach fulfills fast and accurate results with the registration accuracy of less than an MPS voxel size, which is feasible to be used for clinical practice.

5. CONCLUSION

A multi-modality registration algorithm of coronary CTA with MPS in a variational framework was presented. A segmentation algorithm for extracting the blood pool, myocardium, and extracardiac structures from MPS was adopted before registration. In the registration process, segmented regions in MPS were aligned to the corresponding regions in coronary CTA by utilizing geometrically characteristic features obtained by MPS segmentation and the homogeneity property of intensities within regions of interest in coronary CTA. It was demonstrated by experimental results that the proposed algorithm outperformed a standard registration method based on the normalized mutual information. The potential of the proposed algorithm in clinical applications for integrated MPS analysis to resolve borderline cases is enhanced by its computational efficiency.