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

## TL;DR

This paper introduces a new unsupervised method to improve pharmacokinetic analysis of DCE-MRI data in cerebral tumors by estimating the probability of different models per voxel.

## Contribution

The novel contribution is the use of Kohonen-Self-Organizing-Map (K-SOM) to estimate probabilistic model contributions in DCE-MRI pharmacokinetic analysis.

## Key findings

- The K-SOM probabilistic-NMS technique showed strong similarity to traditional NMS in identifying leaky tumor regions.
- The new method produced microvasculature parameters less affected by arterial-input-function dispersion.
- Estimated permeability parameters showed significant mean-percent-differences compared to traditional NMS.

## Abstract

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.

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 ΔR1 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 ΔR1 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.

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 vp,Ktrans, and ve, respectively. The KSOM-PNMS technique produced microvasculature parameters and NMS regions less impacted by the arterial-input-function dispersion effect.

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.