Spatio-Temporal Free-Form Registration of Cardiac MR Image Sequences Antonios Perperidis s /02/2006

MR-Imaging  Magnetic Resonance (MR) imaging allows the acquisition of: 3D images which describe the cardiac anatomy. 4D cardiac image sequences which describe the cardiac anatomy and function.  Advances in cardiac MR imaging are making it an important clinical tool: The improvement of the spatial and temporal resolution of the image sequences enabling the imaging of small cardiac structures. The development of tagged MR imaging which allow the study of cardiac motion.

Cardiac Image Registration  Currently increased need for cardiac registration methods.  Cardiac image registration is a very complex problem due to 4D nature of the cardiac data: Complicated non-rigid motion of the heart and the thorax. Low resolution with which cardiac images are usually acquired.  Recently, cardiac image registration has emerged as an important tool for a large number of applications such as: The construction of anatomical and functional atlases of the heart. The analysis of the myocardial motion. The segmentation of cardiac images. The fusion of information from different modalities such as CT, MR, PET, and SPECT. The comparison of images of the same subject. The comparisons between the cardiac anatomy and function of different subjects.

Background  There are currently many registration techniques for cardiac imaging.  Most techniques focus on 3D images ignoring any temporal misalignment between two image sequences.  One exception: an approach for the spatial and temporal registration of cardiac SPECT and MR images. Uses linear interpolation for the temporal mapping between the end-systolic and end-diastolic frames.  The heart has a complicated motion pattern.  This method ignores all the spatial information contained in the images between the end-systolic and end-diastolic frames.

Spatio-Temporal Registration Introduction  The heart is undergoing a spatially and temporally varying degree motion during the cardiac cycle.  Spatial alignment of corresponding frames of the image sequences not enough since frames may not correspond to the same position in the cardiac cycle of the hearts.  This is due to differences in: The acquisition parameters. The length of cardiac cycles. The dynamic properties of the hearts.

Spatio-Temporal Registration Introduction  Spatio-temporal alignment enables to find the temporal relationship between the 2 image sequences.  We present 2 spatio-temporal alignment methods using image information only.  The 4-D mapping can be described by the transformation:  Mapping can be resolved into decoupled spatial and temporal components: Spatial: Temporal:

Spatial Alignment  Aim: to relate each spatial point of an image to a point of the reference image.  T spatial can be written:  T spatial/global : 3D affine transformation:  Coefficients  parameterize the 12 degrees of freedom.  T spatial/local : Free-Form deformation (FFD) model based on B-Splines.

Temporal Alignment  T temporal can be written:  T temporal/global : affine transformation: a accounts for scaling differences. b accounts for translation differences.  T temporal/local : Free-Form deformation (FFD) using 1-D B-Splines.

Combined Optimization of the Spatial and Temporal Components  2 registration algorithms for finding the optimal transformation T: 1.Optimizes the spatial and temporal transformation components simultaneously using image information only 2.Optimizes the temporal transformation component before optimizing the spatial component.  In the 1 st algorithm: Optimal transformation T is found by maximizing a voxel based similarity measure.  Normalized Mutual Information (NMI): a measure of spatio-temporal alignment.  NMI is optimized as a function of T spatial/global and T temporal/global using: an iterative downhill descent algorithm. a simple iterative gradient descent method.

Separate Optimization of the Spatial and Temporal Components 1  Computational complexity of the previous method is very high.  Reduced by optimizing each transformation component separately.  T temporal/global : aligns the temporal ends of the image sequences  T temporal/local : aligns a limited temporal positions of the cardiac cycles.  Temporal positions detected by calculating the normalized cross-correlation coefficient between each frame of the sequence with the first frame.

Separate Optimization of the Spatial and Temporal Components 2  The idea behind this approach: during the contraction phase of the cardiac cycle each consecutive image will be less similar to the first image. during the relaxation phase of the cardiac cycle each consecutive image will be more similar to the first image

Results  Algorithm evaluation: 15 cardiac MR images from healthy volunteers.  Reference subject: 32 different time frames acquired.  14 4D cardiac MR images were registered to the reference subject.  Cardiac Cycle length: 300 to 800msec.  Qualitative evaluation through visual inspection.  Quality of registration in spatial domain measured by Calculating volume overlap for: The left and right ventricles. The myocardium.

Results – Separate optimization of the transformation components  Maximum contraction & and-diastole positions determined manually.  Positions compared with corresponding positions identified by the algorithm: Mean error in the detection of maximum contraction: 1.2 frames. Mean error of the end diastole detection: 0.93 frames.

Combined optimization of the transformation component - Qualitative Evaluation  Deformable temporal & spatial registration improves alignment of the image sequences in spatial and temporal domain

Combined optimization of the transformation component - Quantitative Evaluation  Optimising transformation components simultaneously provides better overlap measures the separate optimisation method.

 Approach achieves very good spatio temporal registration of the images.  Computational complexity is reduced by 25% (approximately) Results – Using cross correlation based method to calculate temporal alignment.

Applications of the Spatio-Temporal Registration Method.  Large number of applications for this Spatio- Temporal registration method: Comparison between image sequences from the same subject. Comparison between image sequences from different subjects, Building probabilistic and statistical atlases of the cardiac anatomy and function.

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