Normalizing Flow-Based Distribution Estimation of Pharmacokinetic Parameters in Dynamic Contrast-Enhanced Magnetic Resonance Imaging

Engineering Medical Laboratory Science Electrical Engineering Information Science Artificial Intelligence Oncology Medical Imaging Medicine
normalizing flow pharmacokinetic parameters dynamic contrast-enhanced MRI maximum likelihood estimation posterior distribution

In modern medical diagnostics and clinical research, Dynamic Contrast-Enhanced Magnetic Resonance Imaging (DCE-MRI) technology provides significant information regarding tissue pathophysiology. By fitting a Tracer-Kinetic (TK) model, pharmacokinetic (PK) parameters can be extracted from time-series MRI signals. However, these estimated PK parameters are susceptible to various unavoidable sources of variability, such as Signal-to-Noise Ratio (SNR), baseline T1 time, initiation time, Arterial Input Function (AIF), and fitting algorithms. These factors lead to uncertainty in PK parameter estimation. Therefore, estimating the posterior distribution of these PK parameters will help simultaneously quantify the values of PK parameters and the uncertainty of their estimation.

Source of the Paper

This paper, written by Ke Fang, Zejun Wang, Qi Xia, Yingchao Liu, Bao Wang, Zhaowei Cheng, Jian Cheng, Xinyu Jin, Ruiliang Bai, and Lanjuan Li, originates from several research institutions including the College of Information Science and Electronic Engineering of Zhejiang University. The paper was published in the March 2024 issue of the IEEE Transactions on Biomedical Engineering journal.

Research Process and Methods

This paper proposes a Flow-based Parameter Distribution Estimation Neural network (FPDEN). The model aims to adaptively learn and estimate the posterior distribution of PK parameters to improve estimation accuracy and quantify estimation uncertainty. The specific research process includes the following steps:

Research Process

  1. Data Acquisition and Preprocessing:

    • Using DCE-MRI technology, DCE-MRI data from 57 patients with brain glioma were acquired.
    • Various denoising methods, such as rigid transformation, were employed to ensure data quality.

  2. Simulation Data Generation:

    • Using the extended Tofts model to generate DCE-MRI time-series data, thus obtaining strictly controlled “ground truth” data.

  3. Model Construction and Training:

    • Constructed a regression network based on LSTM to extract high-dimensional features and estimate the mean and variance of PK parameters.
    • Utilized a regularized flow model to map simple distributions to complex distributions, performing the learning and estimation of parameter distributions.

  4. Model Evaluation:

    • Trained the model using a loss function based on Maximum Likelihood Estimation (MLE).
    • Compared the model’s performance in estimating PK parameter values and uncertainty against traditional linear regression and predefined distribution assumption methods.

  5. Clinical Application:

    • Applied the model to actual patient data for clinical tasks in glioma grading, and introduced an uncertainty filtering mechanism to improve classification performance.

Research Results

  1. Model Performance:

    • On simulation datasets, the FPDEN model significantly outperformed traditional regression methods (such as L1 and L2 loss) and MLE methods based on predefined distributions.
    • On actual patient data, the FPDEN method effectively distinguished tumor boundaries, improving the accuracy of PK parameter estimation.

  2. Uncertainty Analysis:

    • The model can adaptively adjust the estimation uncertainty based on the input data’s SNR, and there is a significant correlation between uncertainty and estimation error.
    • Under fixed SNR conditions, the interdependence of different PK parameters is revealed through uncertainty.

  3. Glioma Grading Task:

    • After introducing the uncertainty filtering mechanism, the classification performance of the glioma grading task significantly improved, especially in distinguishing between low-grade and high-grade gliomas, with the AUC increasing from 0.168 to 0.662.

Research Conclusion

The FPDEN method proposed in this paper improves the accuracy of parameter estimation by learning the posterior distribution of PK parameters while quantifying the uncertainty of the estimation. Compared with traditional methods, FPDEN not only optimizes parameter estimation but also provides more reliable and accurate data support for subsequent medical applications. In the analysis of DCE-MRI data, this method shows significant potential, particularly in improving classification performance in glioma grading tasks. Furthermore, this method is highly flexible and can be extended to other dynamic imaging technologies and clinical tasks.

Research Highlights

  1. Innovative Approach: For the first time, a regularized flow model is used to learn and estimate the posterior distribution of PK parameters, overcoming the errors introduced by predefined distribution assumptions.
  2. Accurate Estimation: Optimized the loss function through MLE, improving the accuracy of PK parameter estimation.
  3. Uncertainty Analysis: The model can quantify the uncertainty of the estimation and enhance classification performance in clinical tasks through the uncertainty filtering mechanism.
  4. Clinical Application: Validated the effectiveness of this method in glioma grading, providing new research directions and application prospects.