Balancing Bias and Variance in Deep Learning-Based Tumor Microstructural Parameter Mapping.

Area of Science:

• Biomedical Imaging
• Machine Learning in Medical Imaging
• Quantitative MRI

Background:

• Time-dependent diffusion MRI is crucial for tumor microstructural parameter quantification.
• Current methods like nonlinear least squares fitting (NLLS) and mean squared error deep learning (MSE-Net) present challenges with bias-variance trade-offs.
• NLLS offers low bias but high variance, while MSE-Net provides low variance but high bias.

Purpose of the Study:

• To investigate the bias-variance characteristics of NLLS and MSE-Net in diffusion MRI model fitting.
• To propose a novel method for controlling the bias-variance trade-off in quantitative MRI.
• To enhance the accuracy and reliability of tumor microstructural parameter estimation.

Main Methods:

• Reformulated NLLS and MSE-Net within a Bayesian framework to understand bias-variance behavior.
• Introduced B2V-Net, a supervised learning approach with an adjustable bias-variance weighting loss function.
• Evaluated B2V-Net against NLLS and MSE-Net using numerical simulations across various parameters and noise levels, and in vivo in head and neck cancer patients.

Main Results:

• Explained NLLS and MSE-Net behaviors through flat posterior distributions in Bayesian analysis.
• B2V-Net successfully controlled the bias-variance trade-off, reducing standard deviation by 56% versus NLLS.
• B2V-Net achieved an 18% reduction in bias compared to MSE-Net, with in vivo parameter maps showing balanced smoothness and accuracy.

Conclusions:

• Demonstrated and explained the inherent bias-variance issues in NLLS and MSE-Net.
• The proposed B2V-Net effectively balances bias and variance in diffusion MRI analysis.
• This work offers valuable insights and methods for designing customized loss functions for specific clinical imaging applications.