Development of a scoring function for comparing simulated and experimental tumor spheroids
Fig 5
Feature comparison for spheroid point clouds resulting from four different transformation functions.
Shown are the standardized metric distances between the un-transformed reference spheroid and an increasingly transformed version for each data feature. In addition, the combined deviation score is depicted in gray crosses for each transformation (see Section 2.4). Below each subfigure, we provide a top-down view snapshot of the spheroid at three levels of transformation. Blue cells are classified as non-gaslike, and red cells are classified as gaslike. a) Rotation. Except for negligible changes in the spheroid surface deformation feature, we observe no change at increasing rotation angle. This supports rotational invariance of our features. b) Noise. For each feature, the distance increases at increasing noise level. Due to the loss of a solid core at high noise levels, the spheroid surface area and deformation features are no longer sensible, and were therefore cut. The deviation score increases approximately linearly up to a noise level of 200, at which point the features related to the spheroid surface area were cut. c) Deformation. Similar behavior to b) is observed here. Above a deformation amplitude of 120 the spheroid point cloud still contains cells classified as non-gaslike but loses its solid core. Surface area and deformation values were therefore cut above this threshold. The deviation score increases approximately linearly up to a deformation amplitude of 120. d) Scaling. We observe increased distances both for scale factors below and above 1. Due to the fixed values of Dcrit and dcrit (see Eq 1), the gaslike distribution feature is scale-dependent, and also varies here. For scale factors below 1.0, no gaslikes were found, and therefore the values of this feature remained constant. The deviation score increases approximately linearly both for scale factors smaller and larger than 1.