Analyzing Model Misspecification in Quantitative MRI: Application to Perfusion ASL
Quantitative MRI (qMRI) involves parameter estimation governed by an explicit signal model. However, these models are often confounded and difficult to validate in vivo. A model is misspecified when the assumed signal model differs from the true data-generating process. Under misspecification, the variance of any unbiased estimator is lower-bounded by the misspecified Cramer-Rao bound (MCRB), and maximum-likelihood estimates (MLE) may exhibit bias and inconsistency. Based on these principles, we assess misspecification in qMRI using two tests: (i) examining whether empirical MCRB asymptotically approaches the CRB as repeated measurements increase; (ii) comparing MLE estimates from two equal-sized subsets and evaluating whether their empirical variance aligns with theoretical CRB predictions. We demonstrate the framework using arterial spin labeling (ASL) as an illustrative example. Our result shows the commonly used ASL signal model appears to be specified in the brain and moderately misspecified in the kidney. The proposed framework offers a general, theoretically grounded approach for assessing model validity in quantitative MRI.