Enhancing accuracy of magnetic resonance image fusion by defining a volume of interest

Abstract

We compared the registration accuracy for corresponding anatomical landmarks in two MR images after fusing the complete volume (CV) and a defined volume of interest (VOI) of both MRI data sets. We carried out contrast-enhanced T1-weighted gradient-echo and T2-weighted fast spin-echo MRI (matrix 256×256) in 39 cases. The CV and a defined VOI data set were each fused using prototype software. We measured and analysed the distance between 25 anatomical landmarks in predefined areas identified at levels L₁–L₅ corresponding to defined axial sections. Fusion technique, landmark areas and level of fusion were further processed using a feed-forward neural network to calculate the difference which can be expected based on the measurements. We identified 975 landmarks for both T1- and T2-weighted images and found a significant difference in registration accuracy (P<0.01) for all landmarks between CV (1.6±1.2 mm) and VOI (0.7±1.0 mm). From cranial (L₁) to caudal (L₅), mean deviations were: L₁ CV 1.5 mm, VOI 0.5 mm; L₂ CV 1.8 mm, VOI 0.4 mm; L₃ CV 1.7 mm, VOI 0.4 mm; L₄ CV 1.6 mm, VOI 0.6 mm; and L₅ CV 1.6 mm, VOI 1.6 mm. Neural network analysis predicted a higher accuracy for VOI (0.05–0.15 mm) than for CV fusion (0.9–1.6 mm). Deviations due to magnetic susceptibility changes between air and tissue seen on gradient-echo images can decrease fusion accuracy. Our VOI fusion technique improves image fusion accuracy to <0.5 mm by excluding areas with marked susceptibility changes.

Appendix

1. The rigid transformation algorithm

A 3D image co-ordinate transformation is termed rigid if it consists only of rotations and translations. One of the images is termed fixed, the other floating image. Subscripts "fix" (fixed image) and "float" (floating image) refer to quantities of the fixed and the floating images, respectively. Any rigid 3D transformation from the co-ordinate system of the fixed to that of the floating image can be described by a single matrix-vector equation

$${{\left( {\matrix{ {{x_{{float}} }} \cr {{y_{{float}} }} \cr {{z_{{float}} }} \cr } } \right)} = R \cdot {\left( {\matrix{ {{x_{{fix}} }} \cr {{y_{{fix}} }} \cr {{z_{{fix}} }} \cr } } \right)} + t}$$

(2)

where

$${t=(t_{x},t_{y},t_{z})^{T}}$$

(3)

is a constant arbitrary translation vector and R a constant orthogonal rotation matrix

$${R = {\left( {\matrix{ {{\cos \varphi _{y} \cos \varphi _{z} }} & {{\cos \varphi _{y} \sin \varphi _{z} }} & {{ - \sin \varphi _{y} }} \cr {{\sin \varphi _{x} \sin \varphi _{y} \cos \varphi _{z} - \cos \varphi _{x} \sin \varphi _{z} }} & {{\sin \varphi _{x} \sin \varphi _{y} \sin \varphi _{z} + \cos \varphi _{x} \cos \varphi _{z} }} & {{\sin \varphi _{x} \cos \varphi _{y} }} \cr {{\cos \varphi _{x} \sin \varphi _{y} \cos \varphi _{z} + \sin \varphi _{x} \sin \varphi _{z} }} & {{\cos \varphi _{x} \sin \varphi _{y} \sin \varphi _{z} - \sin \varphi _{x} \cos \varphi _{z} }} & {{\cos \varphi _{x} \cos \varphi _{y} }} \cr } } \right)}}$$

(4)

Here, φ_X, φ_z, φ_y (Euler angles) denote the rotation angles around the x, y and z axis, respectively. Altogether, any rigid transformation can be represented by a particular instance of the six transformation parameters ${t_{x} ,t_{y} ,t_{z} ,\varphi _{x} ,\varphi _{y} ,\varphi _{z} }$.

This Euler angle representation is just one of several possible representations. Alternatively, there exist different representations based on, e.g., quaternions. Usually, fixed image voxel positions ${x_{{fix}} ,y_{{fix}} ,z_{{fix}} }$ will not transform to integer positions in the floating image. Hence, some interpolation scheme is required to extract the intensity at the transformed position.

2. The similarity measure

Mutual information (MI) is based on the shared information or relative entropy between the overlapping regions of the two images, which at registration should be maximised. The MI between an image A and an image B is given by

$${MI(A,B) = H(A) + H(B) - H(A,B).}$$

(5)

Here, H(A) and H(A) denote the entropies of the overlapping portions of the images A and B, respectively. H(A, B) denotes the joint entropy of the image overlap. Equivalently, the MI between the (fixed) image A and the (transformed floating) image B computes as

$${MI(A,B) = {\sum\limits_{i_{A} }^{} {} }{\sum\limits_{i_{B} }^{} {p(i_{A} ,i_{B} ) \cdot \log {\left( {{{p(i_{A} ,i_{B} )} \over {p(i_{A} ) \cdot p(i_{B} )}}} \right)}} }}$$

(6)

where ${p(i_{A} )}$; ${p(i_{B} )}$ and ${p(i_{A} ,i_{B} )}$ denote the probabilities of occurrence of intensities i_A and i_B in the histograms of A, B and the joint histogram, respectively. Voxels which do not lie in the overlapping image portions are excluded from the computation of the histograms. Note that MI is a complicated, non-linear function of the transformation parameters ${t_{x} ,t_{y} ,t_{z} ,\varphi _{x} ,\varphi _{y} ,\varphi _{z} }$.

Evaluations of the mutual information measure are quite "expensive" since they require looping through all voxels for histogram computations.