Assessing Parameter Identifiability for Tissue Microstructure Characterization with Optimized Impulsed Diffusion MRI Acquisition Protocol
Abstract
Purpose
Accurate estimation of microstructural parameters by Imaging Microstructural Parameters Using Limited Spectrally Edited Diffusion (IMPULSED) diffusion MRI, including cell size and intracellular volume fraction, is promising for monitoring radiation treatment response. However, parameter identifiability remains a challenge in model fitting, where multiple parameter combinations can produce similar signal curves despite representing different tissue properties. This study determines which IMPULSED model parameters can be reliably estimated from signals measured by an optimized protocol.
Methods
An acquisition protocol optimized using Bayesian experimental design at SNR = 20 was implemented for three pulse types (PGSE, OGSEn1, and OGSEn2). Forward modeling generated 10,000 synthetic observations by uniformly sampling five biophysical parameters (cell radius r, intracellular volume fraction vin, intracellular diffusivity Din, and extracellular diffusion parameters Dex and betaex) from physiologically plausible priors. Linear regression models were independently applied to each pulse type to quantify parameter sensitivity. Singular value decomposition (SVD) was applied to the resulting coefficient matrix to evaluate identifiable parameter combinations and their contributions to measurement variance. A variance significance threshold was calculated as 0.04 at SNR=20.
Results
Linear regression models achieved excellent fit (R² = 0.910/0.837/0.823 for PGSE/OGSEn1/OGSEn2). SVD analysis revealed two resolvable degrees of freedom. The dominant principal direction explains 93.2% of the measurement variance, composed of Dex (weight -0.71), vin (weight +0.54) and r (weight -0.44). The second principal direction explains 6.2% of the variance, contributed from r (weight +0.63), vin (weight +0.59) and Din (weight +0.50).
Conclusion
Our analysis determined a strongly identifiable combination of parameters (r, vin, and Dex). This dominant parameter combination represents a fundamental constraint imposed by clinically achievable SNRs. We recommend fitting only these three parameters while applying strong prior constraints with other two parameters (Dex and betaex) fixed.