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The geometric evolution of aortic dissections: Predicting surgical success using fluctuations in integrated Gaussian curvature
Fig 9
Clustering Analysis in 
Geometric Feature Space Shows Superior Accuracy and Stability Compared to Size Alone.
The 
geometric feature space improves upon current sized-based methods. The clinical paradigm relies on size metrics alone to classify aortic disease states (green for normal aortas, blue for successful TEVAR, and red for failed TEVAR). However, broad within-group size distributions indicate considerable variability in aortic sizes within the general population. Clinicians routinely utilize statistical means of these distributions as thresholds for classifying disease states, but linear decision boundaries are highly sensitive to small changes in model setup. A. A 73.0% accuracy for classifying the 3 states is obtained when each threshold is defined as the mean 〈C1/2〉 of the two neighboring distributions. B. An 83.9% accuracy is achieved when the threshold is defined as the midpoint of the means of individual class distributions. C. An 87.0% accuracy is obtained when a logistic regression classifier is used. Thus, small changes in how a threshold is defined dramatically alter the perceived utility of size. D. The 
shape and size-based geometric feature space allows for the utilization of two independent parameters to characterize aortic disease state. A 90.3% classification accuracy is obtained when defining thresholds according to the mean δK and 〈C1/2〉 of each patient group. E. A 92.8% mean accuracy with a standard deviation of only 1.7% is obtained using a logistic regression classifier with varying regularization parameters. The shaded region indicates the interquartile range of decision boundaries and demonstrates the robustness of the two-parameter space. Unlike the single parameter space, the presence of two physically interpretable and orthogonal asymptotic limits ensures more effective classification.
doi: https://doi.org/10.1371/journal.pcbi.1011815.g009