Associative memory networks based on quaternionic Hopfield neural network are investigated in this paper. These networks are composed of quaternionic neurons, and input, output, threshold, and connection weights are represented in quaternions, which is a class of hypercomplex number systems. The energy function of the network and the Hebbian rule for embedding patterns are introduced. The stable states and their basins are explored for the networks with three neurons and four neurons. It is clarified that there exist at most 16 stable states, called multiplet components, as the degenerated stored patterns, and each of these states has its basin in the quaternionic networks.

The present study aimed to conduct a real-time automatic analysis of two important surgical phases, which are continuous curvilinear capsulorrhexis (CCC), nuclear extraction, and three other surgical phases of cataract surgery using artificial intelligence technology. A total of 303 cases of cataract surgery registered in the clinical database of the Ophthalmology Department of Tsukazaki Hospital were used as a dataset. Surgical videos were downsampled to a resolution of 299 × 168 at 1 FPS to image each frame. Next, based on the start and end times of each surgical phase recorded by an ophthalmologist, the obtained images were labeled correctly. Using the data, a neural network model, known as InceptionV3, was developed to identify the given surgical phase for each image. Then, the obtained images were processed in chronological order using the neural network model, where the moving average of the output result of five consecutive images was derived. The class with the maximum output value was defined as the surgical phase. For each surgical phase, the time at which a phase was first identified was defined as the start time, and the time at which a phase was last identified was defined as the end time. The performance was evaluated by finding the mean absolute error between the start and end times of each important phase recorded by the ophthalmologist as well as the start and end times determined by the model. The correct response rate of the cataract surgical phase classification was 90.7% for CCC, 94.5% for nuclear extraction, and 97.9% for other phases, with a mean correct response rate of 96.5%. The errors between each phase’s start and end times recorded by the ophthalmologist and those determined by the neural network model were as follows: CCC’s start and end times, 3.34 seconds and 4.43 seconds, respectively and nuclear extraction’s start and end times, 7.21 seconds and 6.04 seconds, respectively, with a mean of 5.25 seconds. The neural network model used in this study was able to perform the classification of the surgical phase by only referring to the last 5 seconds of video images. Therefore, our method has performed like a real-time classification.

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Surgical skill levels of young ophthalmologists tend to be instinctively judged by ophthalmologists in practice, and hence a stable evaluation is not always made for a single ophthalmologist. Although it has been said that standardizing skill levels presents difficulty as surgical methods vary greatly, approaches based on machine learning seem to be promising for this objective. In this study, we propose a method for displaying the information necessary to quantify the surgical techniques of cataract surgery in real-time. The proposed method consists of two steps. First, we use InceptionV3, an image classification network, to extract important surgical phases and to detect surgical problems. Next, one of the segmentation networks, scSE-FC-DenseNet, is used to detect the cornea and the tip of the surgical instrument and the incisional site in the continuous curvilinear capsulorrhexis, a particularly important phase in cataract surgery. The first and second steps are evaluated in terms of the area under curve (i.e., AUC) of the figure of the true positive rate versus (1—false positive rate) and the intersection over union (i.e., IoU) obtained by the ground truth and prediction associated with the region of interest. As a result, in the first step, the network was able to detect surgical problems with an AUC of 0.97. In the second step, the detection rate of the cornea was 99.7% when the IoU was 0.8 or more, and the detection rates of the tips of the forceps and the incisional site were 86.9% and 94.9% when the IoU was 0.1 or more, respectively. It was thus expected that the proposed method is one of the basic techniques to achieve the standardization of surgical skill levels.

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