# Performance of recurrent neural networks with Monte Carlo dropout for predicting pharmacokinetic parameters from dynamic contrast‐enhanced magnetic resonance imaging data

## TL;DR

This study compares LSTM and GRU neural networks with Monte Carlo dropout for predicting drug behavior from MRI data, finding that dropout improves accuracy but increases computational cost.

## Contribution

Demonstrates the effectiveness of Monte Carlo dropout in improving pharmacokinetic parameter prediction from DCE-MRI data using RNNs.

## Key findings

- LSTM showed stable performance while GRU accuracy dropped with fewer training samples.
- MCD reduced prediction errors at low signal-to-noise ratios but increased computational cost.
- Optimal dropout rates varied with signal quality and network type.

## Abstract

To quantitatively evaluate the performance of two types of recurrent neural networks (RNNs), long short‐term memory (LSTM) and gated recurrent units (GRU), using Monte Carlo dropout (MCD) to predict pharmacokinetic (PK) parameters from dynamic contrast‐enhanced magnetic resonance imaging (DCE‐MRI) data.

DCE‐MRI data for simulation studies were synthesized using the extended Tofts model and a population‐averaged arterial input function (AIF). The ranges of PK parameters for training the RNNs were determined from data of patients with brain tumors. The effects of the number of training samples, number of hidden units, dropout rate (DR), and bolus arrival time delay and dispersion in AIF on the accuracy of the PK parameters were investigated, and the uncertainties for different DRs and peak signal‐to‐noise ratios (PSNRs) were quantified. For comparison, PK parameters were estimated using the nonlinear least‐squares method. In the clinical studies, the PK parameter and uncertainty images were generated by applying the trained RNNs to DCE‐MRI data.

Compared with GRU, the computational cost for training the LSTM was significantly higher. The prediction accuracy of GRU decreased with decreasing numbers of training samples and hidden units, whereas the performance of LSTM remained stable. Despite an increased computational cost, MCD reduced the prediction error at low PSNR and improved the quality of PK parameter images. The simulation results recommended using a DR of 0.25–0.5 at low PSNR and ≤ 0.25 for other PSNRs. The clinical studies recommended using a DR of 0.25 and 0.5 for LSTM and GRU, respectively.

MCD is effective in quantifying uncertainty in PK parameter prediction from DCE‐MRI data and improves their performance, particularly at low PSNR; however, at the expense of increased computational cost. This study helps deepen our understanding of RNNs with MCD and select suitable hyperparameters for creating an RNN architecture for DCE‐MRI studies.