On the structural and practical identifiability of multi-echo BBB-ASL tracer kinetic models.

Purpose: Tracer kinetic models are used in arterial spin labeling (ASL); however, deciding which model parameters to fix or fit is not always trivial. The identifiability of the resultant system of equations is useful to consider, since it will likely impact parameter uncertainty. Here, we analyze the identifiability of two-compartment models used in multi-echo (ME) blood-brain-barrier (BBB)-ASL and evaluate the reliability of the fitted water-transfer rate $(k_w$ ).

Method: The identifiability of two variants of a two-compartment model (referred to here as "series" and "parallel") were analyzed using sensitivity matrix and Monte-Carlo simulation methods, the latter including the effects of noise and fixed-parameter error. ME-ASL data were collected at 3T in 25 cognitively normal participants (57-85 y). In one volunteer, additional scans were acquired to estimate noise. Fits for whole-gray-matter $k_w$ were performed with a theoretically identifiable version of the model.

Results: All models needed one or more fixed parameters to be structurally identifiable, with different combinations required for each. Practical identifiability analysis yielded $k_w$ estimates with a median absolute error of 29% (parallel model) and 33% (series model). Fits to data yielded median $k_w$ values of 0 (parallel) and 96 min^-1 (series).

Conclusion: We used identifiability analysis to determine an appropriate BBB-ASL model for acquired data. Through simulations we showed that parameter estimates depend on model selection and the value of fixed parameters. We demonstrated that fixed-parameter value and errors significantly impact the reliability of $k_w$ values obtained from acquired ME-ASL images, even with structurally identifiable models.