D-optimal designs are frequently used in controlled experiments to obtain the most accurate estimate of model parameters at minimal cost. Finding them can be a challenging task, especially when there are many factors in a nonlinear model. As the number of factors becomes large and interact with one another, there are many more variables to optimize and the D-optimal design problem becomes high-dimensional and non-separable. Consequently, premature convergence issues arise. Candidate solutions get trapped in local optima and the classical gradient-based optimization approaches to search for the D-optimal designs rarely succeed. We propose a specially designed version of differential evolution (DE) which is a representative gradient-free optimization approach to solve such high-dimensional optimization problems. The proposed specially designed DE uses a new novelty-based mutation strategy to explore the various regions in the search space. The exploration of the regions will be carried out differently from the previously explored regions and the diversity of the population can be preserved. The proposed novelty-based mutation strategy is collaborated with two common DE mutation strategies to balance exploration and exploitation at the early or medium stage of the evolution. Additionally, we adapt the control parameters of DE as the evolution proceeds. Using logistic models with several factors on various design spaces as examples, our simulation results show our algorithm can find D-optimal designs efficiently and the algorithm outperforms its competitors. As an application, we apply our algorithm and re-design a 10-factor car refueling experiment with discrete and continuous factors and selected pairwise interactions. Our proposed algorithm was able to consistently outperform the other algorithms and find a more efficient D-optimal design for the problem.
Magnetoencephalography (MEG) can non-invasively measure the electromagnetic activity of the brain. A new type of MEG, on-scalp MEG, has attracted the attention of researchers recently. Compared to the conventional SQUID-MEG, on-scalp MEG constructed with optically pumped magnetometers is wearable and has a high signal-to-noise ratio. While the co-registration between MEG and magnetic resonance imaging (MRI) significantly influences the source localization accuracy, co-registration error requires assessment, and quantification. Recent studies have evaluated the co-registration error of on-scalp MEG mainly based on the surface fit error or the repeatability error of different measurements, which do not reflect the true co-registration error. In this study, a three-dimensional-printed reference phantom was constructed to provide the ground truth of MEG sensor locations and orientations relative to MRI. The co-registration performances of commonly used three devices—electromagnetic digitization system, structured-light scanner, and laser scanner—were compared and quantified by the indices of final co-registration errors in the reference phantom and human experiments. Furthermore, the influence of the co-registration error on the performance of source localization was analyzed via simulations. The laser scanner had the best co-registration accuracy (rotation error of 0.23° and translation error of 0.76 mm based on the phantom experiment), whereas the structured-light scanner had the best cost performance. The results of this study provide recommendations and precautions for researchers regarding selecting and using an appropriate device for the co-registration of on-scalp MEG and MRI.
Summary
In recent years, optically pumped magnetometer (OPM)-based magnetoencephalography (MEG) has shown potential for analyzing brain activity. It has a flexible sensor configuration and comparable sensitivity to conventional SQUID-MEG. We constructed a 32-channel OPM-MEG system and used it to measure cortical responses to median and ulnar nerve stimulations. Traditional magnetic source imaging methods tend to blur the spatial extent of sources. Accurate estimation of the spatial size of the source is important for studying the organization of brain somatotopy and for pre-surgical functional mapping. We proposed a new method called variational free energy-based spatial smoothing estimation (FESSE) to enhance the accuracy of mapping somatosensory cortex responses. A series of computer simulations based on the OPM-MEG showed better performance than the three types of competing methods under different levels of signal-to-noise ratios, source patch sizes, and co-registration errors. FESSE was then applied to the source imaging of the OPM-MEG experimental data.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.