Article Figures & Data
Figures
- FIG 1.
Schematic of each of the 3 main stages of the model-building procedure. A, The data are partitioned into 5 homogeneous folds, each comprising 80% of the data for training and 20% for validation, repeated 5 times. Within each round of cross-validation (CV) 1 fold is held out for validation while the other 4 (80%) are pooled to form a training set. B, A random forest (RF) model was fit to the training data, and the best predictor variable from each imaging family was selected. Because there are 5 rounds of CV, this procedure was repeated 5 times and the selections (listed in Online Tables 4 and 5) were combined by voting. C, Using the consensus subset of predictor variables after feature selection, we trained another random forest on each training set and made predictions on the corresponding holdout set. The average correlations between predicted and observed values across all rounds of CV are given in Table 4. Kep indicates reverse transfer constant from DCE imaging.
- FIG 2.
Predicted and observed cell density (nuclei/square millimeter) for the random forest model using 4 fixed inputs from conventional-plus-advanced imaging. A, The solid line is the best fit for all predictions (R2 = 0.56), and the dashed black line is the best fit for real-sample predictions only (R2 = 0.39), that is, excluding virtual samples (red points). B, The predictions using conventional imaging only. The model performance decreased slightly with R2 = 0.50 for all observations and R2 = 0.30 for real observations only. Blue points are real tissue biopsies that were graded as histologically normal-appearing. The cell density for these points is generally lower than the CD for tumor samples and falls within the range of the virtual biopsies.
- FIG 3.
Estimated map of cell density using machine learning models. A, The T2-weighted image of a glioblastoma. B, The estimated cell density map using the 4 inputs to the final model (T2, fractional anisotropy, CBF, and AUC) selected from all the available imaging data (conventional and advanced) and smoothed by a 1-mm radius filter. The profiles shown in C correspond to the dashed blue line in A, B, and E. We can see in C that the predicted CD is strongly related to the AUC and CBF within the tumor volume. E, The estimated cell density map using conventional imaging only with the analogous profiles shown in F. The model predicts less extreme values than seen with the model using advanced imaging. D, The whole axial section of the T2-weighted image for reference with the cropped area for A, B, and E is outlined in red. PA indicates posteroanterior distance.
- FIG 4.
Sample cell density maps for a low-grade glioma (World Health Organization II, left images) and a high-grade glioblastoma (World Health Organization IV, images). The T2-weighted or T1-weighted postcontrast images are shown for reference. As expected, the low-grade tumor shows lower and more homogeneous cell density estimates.
Tables
Demographics No. (Sex) 23 Patients (14 women, 9 men) Age (mean) (range) (yr) 43.9 [SD, 16.9] range, 21–80 WHO grade (I/II/III/IV) 0/7/9/7 Biopsy samples/patient (mean) 2.26 [SD, 0.54] No. of biopsy samples in final analysis 52 real + 52 virtual Note:—WHO indicates World Health Organization.
Sample Grade No. of Samples Cell Density (Mean) (SD) Normalb 3 1777 [SD, 371] II 39 5790 [SD, 2667] II/III 3 6085 [SD, 2022] IIIc 2 2584, 14,634 IV 5 11,547 [SD, 4252] ↵a The grade of a sample is not necessarily the same as the patient’s clinical grade. As expected, the cell density of the samples increases with increasing sample grade.
↵b These samples appeared histologically tumor-free but showed Ki-67-positive endothelial cells.
↵c Because only 2 samples were grade III, the values are listed.
All Variables (23 Inputs) Variables Selected by RF Importance (4 Inputs) All Conventional Variables (6 Inputs) Variables Selected by RF Importance: Conventional Only (4 Inputs) Random forest 0.572 0.586 0.513 0.523 Linear 0.542 0.572 0.444 0.475 Neural network 0.265 0.460 0.382 0.379 Decision tree 0.301 0.325 0.376 0.376 ↵a The columns list variables used to train the predictive model. “All Variables” is simply using all 23 imaging parameters of all 6 conventional sequences, whereas “RF Importance” and “RF Importance, Conventional” use the final 4 variable sets shown in Online Tables 4 and 5. A larger average R2 indicated better performance.
