Mutual-Information Based Optimal Experimental Design for Hyperpolarized $^{13}$C-Pyruvate MRI

Abstract

Background. Hyperpolarized (HP) 13 C-Pyruvate MR imaging provides unique information about metabolic alterations indicative of the aggressiveness of certain cancer types. The information content of the HP-MRI data is fundamentally limited by the physics and chemistry of specific processes that take place at an atomic scale during a well-defined chemical reaction. The HP signal (magnetization of pyruvate and lactate) is a fixed resource that is established at the polarizer and naturally decays over time, and cannot be renewed after injection. The signal is further reduced with every radio-frequency excitation by the MR pulse sequence. Therefore, optimal experimental design (OED) for data acquisition is fundamentally important. A key parameter of interest recovered from HP-MRI measurements is the apparent pyruvate-to-lactate exchange rate, kP L, for measuring tumor metabolism. This manuscript presents an information-theory-based OED approach that minimizes the uncertainty in the rate parameter, kP L, recovered from the HP-MRI measurements.Methods. Mutual information (MI) is a statistical property employed here to measure the information content of the HP measurements with respect to the first-order exchange kinetics of the pyruvate conversion to lactate. An optimal experimental design formulation based on the maximization of the mutual information as a function of the MRI design parameters is proposed. The optimized MRI design parameters include flip angles of the pulse sequence acquisition. Further, a spatially varying model (high-fidelity) based on the Block -Torrey equations is proposed and utilized as a control for the OED formulation.Results. Within the mutual-information-based optimal experimental design formulation, a time-varying flip angle scheme is seen to provide significant differences in the flip angles compared to when excitation angles are fixed to a constant value. The varying flip angle scheme leads to a higher parameter optimization that can further improve the quantitative value of mutual information over the constant flip angle scheme. However, the constant flip angle scheme leads to the best accuracy and precision when considering inference from noise-corrupted data. Conclusion.Results suggest that the mutual information-based optimal data acquisition strategy is likely to improve the precision of the measurements. For the particular MRI data examined here, pyruvate and lactate flip angles of 35 and 28 degrees, respectively, were the best choice in terms of accuracy and precision of the parameter recovery. Moreover, the recovery of rate parameter kP L from the data generated from the high-fidelity model highlights the influence of diffusion and strength of vascular source on the recovered rate parameter. Since the existing pharmacokinetic models for HP-MRI do not account for spatial variation, the optimized design parameters may not be fully optimal in a more general 3D setting.

High-dimensional nonlinear Bayesian inference of poroelastic fields from pressure data

“…Many problems in science and engineering problems can be modeled by partial differential equations (PDEs). Inverse problems constrained by PDEs are a challenging class of these problems, which play an essential role in investigating many physical systems, including geomechanical engineering, medical engineering, and astrophysics [1][2][3][4][5][6][7][8][9][10][11]. Inverse problems aim at inferring the unknown model parameters of a physical system from observations, which may be limited, indirectly related to the parameters, and affected by noise.…”