Probabilistic Nested Model Selection in Pharmacokinetic Analysis of DCE-MRI Data in Animal Model of Cerebral Tumor

Purpose: Best current practice in the analysis of dynamic contrast enhanced (DCE)-MRI is to employ a voxel-by-voxel model selection from a hierarchy of nested models. This nested model selection (NMS) assumes that the observed time-trace of contrast-agent (CA) concentration within a voxel, corresponds to a singular physiologically nested model. However, admixtures of different models may exist within a voxel's CA time-trace. This study introduces an unsupervised feature engineering technique (Kohonen-Self-Organizing-Map (K-SOM)) to estimate the voxel-wise probability of each nested model.

Methods: Sixty-six immune-compromised-RNU rats were implanted with human U-251N cancer cells, and DCE-MRI data were acquired from all the rat brains. The time-trace of change in the longitudinalrelaxivity $\left(\Delta R_1\right)$ for all animals' brain voxels was calculated. DCE-MRI pharmacokinetic (PK) analysis was performed using NMS to estimate three model regions: Model-1: normal vasculature without leakage, Model-2: tumor tissues with leakage without back-flux to the vasculature, Model-3: tumor vessels with leakage and back-flux. Approximately two hundred thirty thousand (229,314) normalized $\Delta R_1$ profiles of animals' brain voxels along with their NMS results were used to build a K-SOM (topology-size: 8×8, with competitive-learning algorithm) and probability map of each model. K-fold nested-cross-validation (NCV, k=10) was used to evaluate the performance of the K-SOM probabilistic-NMS (PNMS) technique against the NMS technique.

Results: The K-SOM PNMS's estimation for the leaky tumor regions were strongly similar (Dice-Similarity-Coefficient, DSC=0.774 [CI: 0.731-0.823], and 0.866 [CI: 0.828-0.912] for Models 2 and 3, respectively) to their respective NMS regions. The mean-percent-differences (MPDs, NCV, k=10) for the estimated permeability parameters by the two techniques were: -28%, +18%, and +24%, for $v_p,K^{\text{trans}}$ , and $v_e$ , respectively. The KSOM-PNMS technique produced microvasculature parameters and NMS regions less impacted by the arterial-input-function dispersion effect.

Conclusion: This study introduces an unsupervised model-averaging technique (K-SOM) to estimate the contribution of different nested-models in PK analysis and provides a faster estimate of permeability parameters.