In vivo validation of Cramer-Rao lower bounds for evaluating the reproducibility of Tofts kinetic modeling of DCE-MRI data
Authors: Naeyer Dieter De , Ceelen Wim P. , Verdonck Pascal 
Published: May 2015

Abstract
Introduction: Pharmacokinetic modeling (PKM) of dynamic contrast enhanced MRI-data (DCE-MRI) is increasingly used for in vivo monitoring of drug response or in the evaluation of novel antiangiogenic therapies. Several studies have shown a strong correlation between the Tofts kinetic parameter Ktrans and histological tumor grade or a significant reduction in Ktrans after successful therapy. The prognostic value of pre- and posttreatment Ktrans-change, is however strongly dependent on its reproducibility. Up to now, therapy induced microvascular changes are considered to be statistical significant when procentual Ktrans-change exceeds an experimental threshold, determined from paired DCE-MRI examinations. This threshold depends on study design, patient population and tumor type, but is independent of the values of the kinetic parameters, Ktrans and νe, themselves. In previous work we have developed a statistical framework, based on Cramer-Rao lower bounds (CRLB), to determine the standard deviation of Ktrans for a given DCE-MRI protocol. In this study, it is aimed to perform an in vivo validation of the CRLB and to investigate the current method of statistical significance testing.
Methods: Three groups of 2 test animals (mice with induced ht29-tumor) were scanned in paired examinations (48 hours in between) with a inversion recovery spoiled gradient echo sequence (Ti = 422-560-680 ms, flip angle = 10-12-15°, Te = 4.12 ms, Tr = Δt = 1-3-5 s) after injection of Gd-DTPA (Dose = 0.1 mM kg−1), for a total of 500 images. Arterial input function was taken as the average concentration curve over both examinations in the femoral artery. Tissue concentration curves in tumor tissue and muscle were fit pixelwise to the Tofts kinetic model without vascular term. In muscle, experimental procentual standard deviation σexp was calculated from spatial variation in Ktrans over the region of interest (ROI) for both examinations. In tumor the coefficient of within patient variation (CWV) between examinations was calculated in both tumor rim and tumor core. For the three protocols, the theoretical standard deviation σth was calculated with the CRLB, evaluated in the mean Ktrans and νe-values of the corresponding ROI.
Results: Simulations show that Ktrans-reproducibility is higher in tissue with increasing extravascular extracellullar space (increasing νe). In muscle, the correlation coefficient between σexp and σth is 87%, showing experimental validity of CRLB for a given protocol. In tumor the correlation coefficient between σth and CWV is 76% and 79% in tumor core and tumor rim respectively, indicating that CRLB can explain the major part of the Ktrans-variation between paired scans. Other errors, as improper scan-rescan positioning or natural microvascular changes, can account for the remaining part.
Conclusion: When using a fixed threshold for treatment evaluation by means of Ktrans-change, statistical significance will be concluded more often in tissues with small EES-volumes. CRLB have been validated in vivo and can be used in combination with standard statistical test to evaluate statistical significance of Ktrans-change for in vivo monitoring of drug response.