Personalized Prediction of Glioma Growth Using Bayesian Inference

Introduction

Glioblastoma is the most aggressive type of primary brain tumor, characterized by highly invasive tumor cells that spread to surrounding tissues. Conventional medical imaging techniques cannot precisely identify these diffuse tumor boundaries, leading to suboptimal clinical interventions and poor prognosis. Due to these challenges, reliable computational predictions of tumor spatial and temporal development based on medical images can provide valuable insights, assisting physicians in devising optimal treatment plans for each individual.

In recent years, several biophysical models of tumor growth have been developed and calibrated using non-invasive imaging measurement data, aiming to predict future tumor growth and treatment outcomes. However, to achieve accurate tumor development predictions, two key challenges must be addressed: First, the uncertainty in model predictions needs to be quantified to improve individualized treatment outcomes; second, the spatial heterogeneity of tumors and host tissues must be characterized, as this significantly impacts treatment design.

Research Background and Motivation

The core motivation of this study is to address the aforementioned challenges by introducing a Bayesian framework, thereby calibrating parameter distributions within the tumor growth model and validating its effectiveness through MRI data. The Bayesian framework uses gray and white matter atlas segmentation to establish individual-specific prior information and adjust the spatially dependent model parameters. The study is based on quantitative MRI data from four Wistar rats, calibrating tumor parameters in the early stages and predicting their spatial development in later stages.

Research Source

This study was authored by Baoshan Liang, Jingye Tan, Luke Lozenski, David A. Hormuth II, Thomas E. Yankeelov, Umberto Villa, and Danial Faghihi, from University at Buffalo, Washington University in St. Louis, University of Texas at Austin, and their affiliated institutions. The article was published in the October 2023 issue of IEEE Transactions on Medical Imaging.

Research Process

Experimental Data Collection and Processing

1. MRI Data Acquisition: The study used glioma growth data from four female Wistar rats, employing MRI imaging. Specifically, T2-weighted MR images were used to define the simulation domain and tumor segmentation, diffusion-weighted MRI (DW-MRI) was used to calculate the apparent diffusion coefficient (ADC) maps, and the tumor volume fraction d(x, ti) was determined at each time point.
2. Automated Tissue Segmentation: An atlas-based automated method was used to segment the brain tissue of the rats, distinguishing between gray and white matter. This method enhances the accuracy of tissue segmentation by combining atlas and local image registration algorithms.

Tumor Growth Model

A classical single-species reaction-diffusion partial differential equation (PDE) was used to represent tumor diffusion and proliferation. The parameter d(x) denotes the tumor diffusion coefficient in the tissue, and g(x) represents the tumor proliferation rate. The model parameters θ = (log d(x), log g(x)) account for subjective heterogeneity and spatial variation.

High-dimensional Bayesian Calibration

Bayesian inference was used to calibrate the model parameters utilizing sample-specific MRI data. The process includes: 1. Establishing sample-specific prior distributions, represented by Gaussian random fields and assuming different diffusion and proliferation rates in gray and white matter. 2. Constructing a likelihood function that incorporates data uncertainty and model errors through an additive noise model. 3. Optimizing the posterior density function (PDF) to determine the posterior distributions.

Research Results

Data Analysis

Through Bayesian calibration of MRI data from four rats, the model accurately captured the tumor diffusion patterns and was able to predict tumor morphology at unobserved time points, achieving a Dice coefficient exceeding 0.9. The study found that the accuracy and reliability of tumor morphology predictions depended on the number of early imaging sessions used for model calibration.

Comparison of Different Calibration Scenarios

Comparisons of different amounts of calibration data and time points revealed that the predictive ability of the model significantly improved with the use of more early imaging data. Specifically, when using the complete training set for calibration, the relative error between predicted tumor regions and actual data was lower.

Comparison with Other Methods

Compared to two other simple calibration methods, the high-dimensional Bayesian framework demonstrated superior tumor prediction capabilities in terms of accuracy and confidence. The proposed framework, in particular, was able to provide higher resolution predictions of tumor heterogeneity.

Three-dimensional Bayesian Inference

The study also demonstrated the scalability of the three-dimensional tumor model calibration. Through Bayesian calibration of three-dimensional MRI data, the framework was able to accurately predict three-dimensional tumor morphology, indicating good scalability and potential for clinical application.

Conclusion

The proposed Bayesian framework effectively achieved individualized predictions of glioma morphology development, further enhancing model accuracy through automated atlas segmentation and cross-validation methods. The results indicate that the framework can accurately predict individual tumor morphology developments within the constraints of quantitative MRI data. Additionally, the computational efficiency and high-precision predictions of the framework offer inspiration and potential optimization directions for clinical treatment.

Future research will further extend this approach by including more complex PDE models to more realistically describe tumor growth mechanisms and integrating more imaging data (such as tissue stiffness maps from MRI elastography and blood volume distributions from dynamic contrast-enhanced MRI). In a clinical setting, the potential applications of this method will greatly assist in optimizing personalized treatment plans.