Synopsis

Pharmacokinetic modelling of DCE-MRI data allows characterisation of tumour response to anti-angiogenic therapies by estimating the volume transfer constant K^trans and the plasma volume fraction Vp. This work assesses the impact on K^trans and Vp of treatment changes in an early clinical trial cohort by comparing 4 models: Kety, extended Kety (with two lower limits on Vp), and a new model with Vp proportional to K^trans. When K^trans is the endpoint of interest, use of the Kety model is sufficient to depict cohort response. If Vp is also of interest, the new model improves the significance of Vp treatment effects.

INTRODUCTION

Pharmacokinetic modelling of DCE-MRI data allows characterisation of tumour response to anti-angiogenic therapies by analysing the temporal biodistribution of a contrast agent within the imaged tumour¹. In clinical trials, it is recommended² that the primary endpoints are the volume transfer constant K^trans and the integrated area under Gadolinium concentration curve over 60s (IAUGC₆₀). Additional endpoints, such as the plasma volume fraction (Vp), can also be reported, but the quality of such estimates is often sub-optimal.

The extended Kety/Tofts model^3,4 gives estimates of K^trans and Vp. In practice it is often found that this model yields non-zero K^trans estimates but with Vp=0, which is not logically consistent. We propose a new model (presented in more detail in a separate abstract⁵) that uses the fact that Vp=T_c/E∙K^trans for a wide range of compartmental models (T_c=capillary transit time, E=extraction fraction). The new model assumes that T_c/E is the same for all pixels in each tumour, and an estimate of T_c/E is obtained for each DCE-MRI study using a Bayesian approach⁵. Here we evaluate the impact of this new model on K^trans and Vp treatment changes compared with the standard Extended Kety model usage in a clinical trial cohort.

PATIENTS AND METHODS

25 liver and 2 pelvic metastases from patients enrolled in a novel anti-angiogenic drug trial were scanned pre/post-treatment (Table 1; ⁶).

Data from liver patients were manually registered (in-plane technique) prior to any post-processing, the pelvic data were not registered. Volumes of interest (VOI) of the target lesion were drawn on all pre- and post-treatment data by a radiologist. Pixel-wise analysis was performed for each tumour using in-house software⁷, and median values were reported for every patient at each visit.

The pharmacokinetic analysis compared four models: NonExtKety: Kety model (Vp=0), ExtKety: extended Kety with Vp≥0, LimExtKety: extended Kety with Vp≥4×10^-5, and VpPropKtrans: the proposed new model⁵. The limit for the LimExtKety model was the lowest non-zero median Vp from the ExtKety results from these data. A population-averaged arterial input function^8,9 was used for all patients and median K^trans, Vp and IAUGC₆₀ were reported for each tumour.

Lilliefors test for normality (MATLAB 2016a) of all three parameters indicated that the treatment differences in Vp were not normally distributed, whereas differences of its log-transformed estimates were normally distributed; transformed and un-transformed differences of K^trans and IAUGC₆₀ were normally distributed. For completeness, treatment effects were therefore assessed using paired t-tests (MATLAB 2016a) on both un-transformed and log-transformed data. Pearson’s correlation coefficient was calculated to compare changes in log(K^trans) and log(Vp).

RESULTS AND DISCUSSION

A cohort treatment response to the anti-angiogenic agent was observed for all parameters with all models, see Figure 1. Treatment response t-tests are summarised in Table 2.

When the parameters of interest are IAUGC₆₀ and K^trans, highly significant treatment effects were observed for log-transformed and un-transformed estimates from all models, suggesting that under these conditions the simpler NonExtKety model performs just as well as the more complicated models. The treatment significance was greater for the log-transformed estimates of IAUGC₆₀ and K^trans, though in these data the level of significance is sufficiently high that this difference is not important.

For Vp, however, use of the log-transform is important as the Lilliefors test indicates its use, and treatment effects are significant for all models when the log-transform is used, but are non-significant for the un-transformed data. For the ExtKety model 6/54 datasets returned median Vp values of zero, which makes use of the log-transform impossible. For this study, the 6 patients were excluded from the ExtKety statistics, but this is not an acceptable approach in general, hence the evaluation of the LimExtKety and VpPropKtrans models. The most significant Vp changes were found with VpPropKtrans (p=0.0006) compared to a non-significant effect observed with the ExtKety (p=0.0659). Although LimExtKety changes reach significance (p=0.003) and despite this model being simpler to implement, the selection of the lower limit is unacceptably ad hoc. On the other hand, the VpPropKtrans model implies an assumption that T_c/E is equal for all pixels, and so further work is needed to assess the veracity and applicability of this assumption. Vp vs. K^trans changes had very low correlation for all models, see Table 2 (correlation for ExtKety was computed by excluding the 6 patients with Vp=0).

CONCLUSION

Acknowledgements

References

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