  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.
