a) Predictions of normalized individual CellDen for each of the 54 ADNI test subjects using the individually trained high-smoothing ANN model. Cubic Gaussian-smoothing sigma |${\sigma}^3$| used for the network are 0, 1, 8, 64, and 512. Order of ADNI subjects same as in Supplementary Table S1. As with the SynDen predictions, the same ANN architecture predicts the range and spatial patterns expected for CellDen. Predictions were closer to the mean with lower standard deviation than in the reference standard, to a greater degree than present in the SynDen predictions, with standard deviations ranging from 0.063 to 0.093, compared to 0.16 in the reference standard dataset, reflecting the challenge of predicting the same CellDen reference standard regardless of ADNI subject and demonstrating low overfitting. Similar to the SynDen results, we normalized the data to correct for mean and standard deviation, presumably low as a result of our lack of individualized reference standards for each subject. This achieves predictions that are qualitatively very similar to our ex vivo histology-based reference standard. Overall, spatial correlations of the subject predictions with our reference standard range from 0.44 to 0.65, averaging 0.58 across subjects. b) Absolute differences in CellDen predictions for the 54 subjects compared to the reference standard. The patterns of over- and under-predictions with respect to the reference standard seem to show more similar patterns to each other than for the SynDen predictions. For example, patterns of over- and under-predictions in the visual cortex area (bottom of the slices shown near the visual cortex area) are highly conserved between subjects. On the one hand, this is evidence that our ANN is not overfitting the data due to spatial information inadvertently provided in the training datasets, in addition to MPRAGE, ADC, and FA information, since then the network could have learned away these systematic deviations correcting its prediction in the visual cortex area. One possible reason for these systematic deviations from the reference standard is that the CellDen reference standard, which was from a single subject, is not representative of the population at large (a problem which was not present with the SynDen reference standard, which was a group average). It could be that the network did indeed learn the appropriate relationships to predict CellDen from the limited data that it was provided, and systematically predicts “individual differences” from the reference standard for the 54 subjects, when in reality the individual differences is present in the single subject reference standard. c) The associated CellDen histograms for the individual predictions with the continuous red lines showing the reference standard histogram, with individual subjects presented in the same order. The x axis is in the original (relative) scale of image intensities before normalization for ANN training. The fractional overlap of the prediction histogram for each subject with the reference standard is displayed on each histogram. The overlap between subject CellDen histogram predictions with the reference standard range from 0.79 to 0.91, averaging 0.85 across subjects, demonstrating that, similar to our SynDen predictions, our CellDen predictions achieve the range and spatial patterns expected.
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