Non-uniform noise correction in dynamic contrast-enhanced MR images reveals superiority of the two compartmental exchange model over the extended Tofts and the adiabatic approximation to the tissue homogeneity models in glioma patients
Georgios Krokos1, Neil Thacker1, Ibrahim Djoukhadar1, David Morris1, Alan Jackson1, and Marie-Claude Asselin1

1Medical and Human Sciences, University of Manchester, Manchester, United Kingdom

Synopsis

Variability in the underlying assumptions and mathematical formulations of the commonly used models for pharmacokinetic analysis of dynamic contrast-enhanced (DCE) MRI data make model selection not straightforward[1]. The variable noise in DCE-MR images affects the precision of parameters such that correcting the chi-square for the non-uniform noise is required for model comparison[2]. After noise correction, the two-compartmental exchange model fitted the data better, particularly in grade IV glioma, compared to the extended Tofts and adiabatic approximation to the tissue homogeneity models. Lengthening the acquisition duration not only provided more precise parameter estimates but also reduced the mathematical correlations between parameters.

Purpose

This work aims to incorporate a non-uniform noise correction into the pharmacokinetic analysis of DCE-MR images in patients with glioma in order (i) to compare the fit quality of the three commonly used models, (ii) to evaluate the impact of the acquisition duration on the parameter values and precision and (iii) to estimate the parameter correlations for each model.

Methods

Seven patients with glioma (three grade II, three grade III and one grade IV) underwent a pre-surgical DCE-MRI examination on a 1.5T Philips Achieva MR scanner with a SENSE coil. A low dose acquisition (pre-bolus, 0.025mmol/kg) was performed in the sagittal orientation for 3min with 1.7s temporal resolution followed by an axial acquisition covering the whole brain for 15min with 3.4s temporal resolution after injection of the main bolus (0.075mmol/kg). The images were acquired into a 128x128x20 matrix (pre-bolus) or 128x128x40 (main bolus), using slice oversampling with voxel sizes 1.9x1.9x2.5mm3. The peak of the arterial input function was generated from the internal carotid artery using the pre-bolus acquisition and combined with the tail from the superior sagittal sinus using the main bolus acquisition[3]. Kinetic analysis was performed at the voxel level using the extended Tofts (ETM), the two-compartmental exchange (2CXM)[4] and the adiabatic approximation to the tissue homogeneity (AATHM) models with the bolus arrival time included as an additional fitted parameter on 6 and 15min of data from the main bolus acquisition. All parameters in all models were constrained to be non-negative; additionally, the extraction fraction was constrained below 1 and the mean transit time below 1.5min in the AATHM[5]. Parametric maps were generated and corrected for the non-uniform noise distribution[2]. The tumour region was manually delineated by a radiologist using the post contrast T1-weighted and FLAIR images while the grey (GM) and white matter (WM) regions were automatically segmented using FSL/FAST after masking the tumour and oedema.

Results

Before correction for non-uniform noise, all tissues had much broader chi-square (χ2) per degree of freedom (DOF) distributions than theoretically predicted for all model used (figure 1). Applying the noise correction narrowed down and aligned the distributions of the three tissues, except for the grade IV tumour when fitted to the ETM and AATHM, revealing poorer fits. Some parameters are not common to all models and vp is also defined differently between models (figure 3). Nonetheless comparing the parameters estimated from the 15min data (table 1), ve estimates were similar between all models in all tissues whereas vp estimates from the AATHM were twice higher compared to the other models except in grade IV glioma where they agreed with the 2CXM estimates FE estimates from the 2CXM were comparable to Ktrans, and both parameters were an order of magnitude lower than Fp estimated from either the 2CXM or AATHM. Except in grade IV glioma, SEs on all parameters other than ve were twice higher for the 2CXM than the other two models despite having similar χ2/DOF values. When 6min of data were used (table 2), Ktrans and FE increased by a factor of two while ve decreased by ~30%, Fp increased by ~20%, and vp remained relatively unaffected. Strong inverse correlations were observed in all tissues between Ktrans and vp (ETM), FE and vp (2CXM) and E with Fp and vp (AATHM) which were weaker when using 15min instead of 6min of data (figure 2). The other parameters were weakly correlated.

Discussion

The distinct broad non-Gaussian χ2/DOF distributions arising from the non-uniform noise make it impossible to appraise model performance. After noise correction, only the 2CXM was able to fit the fast and slow kinetics, more clearly measured in grade IV glioma. In GM, WM and grades II and III glioma where the contrast agent leakage is limited and thus time-activity curves noisier, all models fitted the data similarly well. The slow kinetics are partially captured in the short acquisitions, explaining the higher exchange rate constants returned by all models compared to longer acquisitions. Furthermore, fewer frames are available with short acquisitions for the estimation of the noise variance, making the noise correction, χ2 and SE estimates less accurate.

Conclusion

Non-uniform noise correction allowed assessment of the performance of pharmacokinetic models and their comparison. The three models provided comparable fits to GM/WM but only the 2CXM fitted the data from the grade IV glioma equally well. More precise estimates of the pharmacokinetic parameters were obtained by lengthening the acquisition duration. Strong inverse correlations were found in all tissues between vp and Ktrans (ETM), FE (2CXM) and E (AATHM) which were weakened with longer acquisition durations.

Acknowledgements

The research leading to these results was supported by the Cancer Research UK and EPSRC Cancer Imaging Centre in Cambridge and Manchester (grant C8742/A18097).

References

[1] Sourbron and Buckley (2012) Phys. Med. Biol. 57:R1-R33

[2] Krokos et al ISMRM 2016 abstract in submission

[3] Li et al (2012) Magn. Reson. Imaging 68:452-62

[4] Sourbron et al (2009) Magn. Reson. Med. 62:672-81

[5] Kersaw et al (2010) Magn. Reson. Med. 64:1772-80

Figures

Figure 1: Distribution of the χ2/DOF values in all tissues for all three models before (left column) and after (right column) noise correction for a patient with grade IV (upper row) and a patient with grade II (lower row) glioma. Distributions were generated using 15min of data.



Figure 2: Correlations between Ktrans and vp in ETM (upper row), FE and vp in 2CXM (middle row) and E with vp (lower row) in grey matter (left column), white matter (middle column) and tumour (right column). The median values and the standard deviations across all 7 patients are displayed.

Figure 3: Theoretical tissue time-activity curves for 4 plausible vp values in all models. An arterial input function from a real patient was used to generate the simulated curves.



Proc. Intl. Soc. Mag. Reson. Med. 24 (2016)
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