Oral Presentation Australian & New Zealand Society of Magnetic Resonance Conference 2017

Assessment of Model Fit in Experimental MRI Data: Application to ADC Estimation (#44)

Warda Syeda 1 , Amanda Ng 2 , David Wright 2 3 , Leigh Johnston 1 3
  1. Department of Biomedical Engineering, The University of Melbourne, Australia
  2. Department of Anatomy and Neuroscience, The University of Melbourne, Australia
  3. Florey Institute of Neuroscience and Mental Health, Australia

Self-diffusion of water in biological tissue leads to attenuation of the MRI signal, influenced by the microstructural geometry of the tissue.1 A variety of parametric diffusion models, such as mono-exponential, bi-exponential2, diffusion kurtosis (DK)3 and continuous distribution models4, have been widely applied to characterize the measured diffusion decay curves. Apparent diffusion coefficient (ADC) parameters are typically reported without due consideration given to model fit. In this work, we propose a statistical framework by which to evaluate the performance of these models applied to experimental diffusion-weighted MRI (DWI) data.

The goodness of a model fit is typically quantified by mean square error (MSE), a measurement of accuracy that does not take into account the variability associated with the parameter estimates. The Cramer Rao lower bound provides the lowest variance of a model estimator5, and has been well-employed in the MRI literature as a precision metric and in experimental design. The CRLB is only valid, however, when the data can be said to be generated from the given model. We, therefore, propose the use of an empirical variant of CRLB precision, known as the Observed Fished Information (OFI)6, for quantifying the precision of model fits to experimental MRI data.

PGSE-EPI acquisition of an ex-vivo rat brain embedded in agar was carried out on a 4.7T Bruker Biospec scanner, with parameters: TR/TE=5000/50ms, Resolution=166x166μm, b= [100,200,300,400,500,1000,1500,2000,…6000s/mm2]. Voxel-wise estimation of model parameters was achieved using nonlinear, iterative maximum likelihood estimation in MATLAB. Mono-exponential, bi-exponential, DK and gamma distribution models were fit to the DWI data.

Our results demonstrate that CRLB analysis of diffusion models provide extremely conservative measures of estimator precision compared to the measured performance of estimators applied to DWI data. Larger MSE was observed in the mono-exponential model with lower and comparable MSE in DK, gamma and bi-exponential models. Consistently higher OFI is observed in parameter estimates of the gamma model compared to the other diffusion models. Thus, robust assessment of model can be achieved using both MSE and OFI, measures of accuracy and precision, respectively.

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  6. B. Efron and D. Hinkley, “Assessing the Accuracy of the Maximum Likelihood Estimator : Observed Versus Expected Fisher Information,” Biometrika 65(3), 457–482 (1978).