Three-dimensional (3D) computer-assisted planning is increasingly used for long bone osteotomies. However, creating an optimal pre-surgical plan remains challenging due to the procedure’s many degrees of freedom, leading to high human workload and associated costs. To address this, we present a fast, interactive surgical planning tool that maximises bone contact and minimises bone protrusion, while favouring wedge-type corrections. It employs an evolutionary multi-objective optimisation algorithm to generate a set of Pareto-optimal osteotomy solutions. This allows users to choose an optimal trade-off solution based on clinical experience. The approach proposed in this work generates optimised plans in under fifteen minutes. It features a user interface, integrated in Siemens NX, making it readily integrable into existing pre-operative workflows. Quantitative validation on past cases showed that our tool produced solutions with better or equal objective values compared to manual plans in 10 of 12 cases, with an average increase of bone contact of 3 % (range: –0.7 % to 31 %). A blinded assessment by surgeons and experiments with 3D printed bones confirmed the clinical relevance and feasibility of the automatic plans. Incorporating this automatic osteotomy planning tool can therefore improve the quality of the selected pre-surgical plan, speed up the workflow and increase the volume of cases handled by the 3D lab.

Background Dynamic SPECT scanning provides a non-invasive way to image the time-dependent distribution of radio-labelled tracers inside living tissue. Beside human medicine, dynamic SPECT also finds its applications in pre-clinical research on small animals. In pre-clinical research, multi-pinhole collimators are used to enable high-resolution sub-millimeter imaging. Conventional iterative reconstruction methods, such as Maximum Likelihood Expectation Maximisation (MLEM) perform poorly in reconstructing the noisy and low-count scans in dynamic SPECT. This limits the temporal resolution that can be achieved.
Method The reconstruction of noisy, low-count time-frames can be aided by incorporating information from earlier and later time-frames. Wang and Qi (2015) published the paper 'PET Image Reconstruction Using Kernel Method', with a proposed method entitled Kernelised Expectation Maximisation (KEM) for dynamic PET, a method that uses principles from Machine Learning, such as Support Vector Machines and the 'kernel trick' to incorporate prior information in the reconstruction algorithm. This method is highly adjustable due to a number of input parameters of the method. In this paper, KEM is implemented for dynamic multi-pinhole SPECT. The effects of the KEM parameters are explored in computer simulations. Two different dynamic phantoms are used, one of the striata in a mouse brain which were adapted from a paper by Vastenhouw et al. (2007) and one of the hepatobiliary system adapted from Vaissier et al. (2012). The results of KEM are benchmarked against conventional MLEM with a Gaussian post-filter. 
Results In high-count simulations, the MLEM reconstructions had a lower mean-squared-error than the KEM image, while the signal-to-noise ratio of KEM was better than MLEM. The images produced after 200 iterations were indistinguishable, however. In the low-count regime, KEM was shown to be more resistant to noise than MLEM. Varying the input parameters of KEM gave rise to differences in performance, such as (over-)smoothing effects and a different level of noise-suppresion in the reconstructed image. 
Conclusions In the simulations used in this paper, KEM was shown to outperform conventional MLEM with a Gaussian post-filter from low-count projections. The optimal input parameters of the KEM algorithm, however, need to be found ad hoc by searching the parameter space. Further research should look into finding a set of rules or guidelines for finding the optimal parameters.