CT to MR registration of complex deformations in the knee joint through dual quaternion interpolation of rigid transforms

Purpose. To develop a method that enables computed tomography (CT) to magnetic resonance (MR) image registration of complex deformations typically encountered in rotating joints such as the knee joint. Methods. We propose a workflow, denoted quaternion interpolated registration (QIR), consisting of three steps, which makes use of prior knowledge of tissue properties to initialise deformable registration. In the first step, the rigid skeletal components were individually registered. Next, the deformation of soft tissue was estimated using a dual quaternion-based interpolation method. In the final step, the registration was fine-tuned with a rigidity-constrained deformable registration step. The method was applied to paired, unregistered CT and MR images of the knee of 92 patients. It was compared to registration using B-Splines (BS) and B-Splines with a rigidity penalty (BSRP). Registration accuracy was evaluated using mutual information, and by calculating Dice similarity coefficient (DSC), mean absolute surface distance (MASD) and 95th percentile Hausdorff distance (HD95) on bone, and DSC on water and fat dominated tissue. To evaluate the rigidity of bone in the registration, the Jacobian determinant (JD) was calculated. Results. QIR achieved improved results with 0.93, 0.76 mm and 1.88 mm on the DSC, MASD and HD95 metrics on bone, compared to 0.87, 1.40 mm and 4.99 mm for method and 0.87, 1.40 mm and 3.56 mm for the BSRP method. The average DSC of water and fat was 0.77 and 0.86 for the QIR, 0.75 and 0.84 for BS and 0.74 and 0.84 for BSRP. Comparison of the median JD and median interquartile (IQR) ranges of the JD indicated that the QIR (1.00 median, 0.03 IQR) resulted in higher rigidity in the rigid skeletal tissues compared to the BS (0.98 median, 0.19 IQR) and BSRP (1.00 median, 0.05 IQR) methods. Conclusion. This study showed that QIR could improve the outcome of complex registration problems, encountered in joints involving rigid and non-rigid bodies such as occur in the knee, as compared to a conventional registration approach.