Bohyun Kim

2papers

2 Papers

IVAug 20, 2023
Developing a Machine Learning-Based Clinical Decision Support Tool for Uterine Tumor Imaging

Darryl E. Wright, Adriana V. Gregory, Deema Anaam et al.

Uterine leiomyosarcoma (LMS) is a rare but aggressive malignancy. On imaging, it is difficult to differentiate LMS from, for example, degenerated leiomyoma (LM), a prevalent but benign condition. We curated a data set of 115 axial T2-weighted MRI images from 110 patients (mean [range] age=45 [17-81] years) with UTs that included five different tumor types. These data were randomly split stratifying on tumor volume into training (n=85) and test sets (n=30). An independent second reader (reader 2) provided manual segmentations for all test set images. To automate segmentation, we applied nnU-Net and explored the effect of training set size on performance by randomly generating subsets with 25, 45, 65 and 85 training set images. We evaluated the ability of radiomic features to distinguish between types of UT individually and when combined through feature selection and machine learning. Using the entire training set the mean [95% CI] fibroid DSC was measured as 0.87 [0.59-1.00] and the agreement between the two readers was 0.89 [0.77-1.0] on the test set. When classifying degenerated LM from LMS we achieve a test set F1-score of 0.80. Classifying UTs based on radiomic features we identify classifiers achieving F1-scores of 0.53 [0.45, 0.61] and 0.80 [0.80, 0.80] on the test set for the benign versus malignant, and degenerated LM versus LMS tasks. We show that it is possible to develop an automated method for 3D segmentation of the uterus and UT that is close to human-level performance with fewer than 150 annotated images. For distinguishing UT types, while we train models that merit further investigation with additional data, reliable automatic differentiation of UTs remains a challenge.

14.1NAApr 15
Layer Potential Methods for Doubly-Periodic Harmonic Functions

Bohyun Kim, Braxton Osting

We develop and analyze layer potential methods to represent harmonic functions on finitely-connected tori (i.e., doubly-periodic harmonic functions). The layer potentials are expressed in terms of a doubly-periodic and non-harmonic Green's function that can be explicitly written in terms of the Jacobi theta function or a modified Weierstrass sigma function. Extending results for finitely-connected Euclidean domains, we prove that the single- and double-layer potential operators are compact linear operators and derive the relevant limiting properties at the boundary. We show that when the boundary has more than one connected component, the Fredholm operator of the second kind associated with the double-layer potential operator has a non-trivial null space, which can be explicitly constructed. Finally, we apply our developed theory to obtain solutions to the Dirichlet and Neumann boundary value problems, as well as the Steklov eigenvalue problem. We present numerical results using Nyström discretizations and find approximate solutions to these problems in several numerical examples. Our method avoids a lattice sum of the free-space Green's function, is shown to be spectrally convergent, and exhibits a faster convergence rate than the method of particular solutions for problems on tori with irregularly shaped holes.