Comparing Regularized Kelvinlet Functions and the Finite Element Method for Registration of Medical Images to Sparse Organ Data

Image-guided surgery collocates patient-specific data with the physical environment to facilitate surgical decision making in real-time. Unfortunately, these guidance systems commonly become compromised by intraoperative soft-tissue deformations. Nonrigid image-to-physical registration methods have been proposed to compensate for these deformations, but intraoperative clinical utility requires compatibility of these techniques with data sparsity and temporal constraints in the operating room. While linear elastic finite element models are effective in sparse data scenarios, the computation time for finite element simulation remains a limitation to widespread deployment. This paper proposes a registration algorithm that uses regularized Kelvinlets, which are analytical solutions to linear elasticity in an infinite domain, to overcome these barriers. This algorithm is demonstrated and compared to finite element-based registration on two datasets: a phantom dataset representing liver deformations and an in vivo dataset representing breast deformations. The regularized Kelvinlets algorithm resulted in a significant reduction in computation time compared to the finite element method. Accuracy as evaluated by target registration error was comparable between both methods. Average target registration errors were 4.6 +/- 1.0 and 3.2 +/- 0.8 mm on the liver dataset and 5.4 +/- 1.4 and 6.4 +/- 1.5 mm on the breast dataset for the regularized Kelvinlets and finite element method models, respectively. This work demonstrates the generalizability of using a regularized Kelvinlets registration algorithm on multiple soft tissue elastic organs. This method may improve and accelerate registration for image-guided surgery applications, and it shows the potential of using regularized Kelvinlets solutions on medical imaging data.