Abstract
Dynamic contrast enhanced MRI and pharmacokinetic modelling provide a powerful tool for tumour diagnosis and treatment evaluation. However, several studies show low reproducibility of the technique and poor precision of the transendothelial transfer constant K (trans). This work proposes a theoretical framework describing how finite signal-noise-ratio (SNR) in the MR images is propagated throughout the measurement protocol to uncertainty on the kinetic parameter estimates. After deriving a distribution for the contrast agent concentration, a maximum likelihood estimator (MLM) is proposed that exhibits Cramer-Rao lower bounds (CRLB). An analytical expression is derived for the CRLB that can be used to determine confidence intervals for kinetic parameters and to investigate the influence of protocol parameters as scan time and temporal resolution on K (trans)-precision. K (trans)-uncertainty can be reduced up to 30% by using MLM in comparison with least square estimator. K (trans)-precision is proportional to the SNR and depends strongly on the kinetic parameter values themselves. Minimal scan time and temporal resolution were found to be 15 min and 15 s, respectively, for Gd-DTPA. Temporal resolution should be enhanced by decreasing the NEX parameter (NEX ≤ 1). CRLB provide a golden standard to construct 95% confidence intervals, which can be used to perform protocol optimization and to test the statistical significance of K (trans)-changes in treatment evaluation.
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