Dose–response assessment by quantitative MRI in a phase 1 clinical study of the anti-cancer vascular disrupting agent crolibulin

The vascular disrupting agent crolibulin binds to the colchicine binding site and produces anti-vascular and apoptotic effects. In a multisite phase 1 clinical study of crolibulin (NCT00423410), we measured treatment-induced changes in tumor perfusion and water diffusivity (ADC) using dynamic contrast-enhanced MRI (DCE-MRI) and diffusion-weighted MRI (DW-MRI), and computed correlates of crolibulin pharmacokinetics. 11 subjects with advanced solid tumors were imaged by MRI at baseline and 2–3 days post-crolibulin (13–24 mg/m2). ADC maps were computed from DW-MRI. Pre-contrast T1 maps were computed, co-registered with the DCE-MRI series, and maps of area-under-the-gadolinium-concentration-curve-at-90 s (AUC90s) and the Extended Tofts Model parameters ktrans, ve, and vp were calculated. There was a strong correlation between higher plasma drug \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${C}^{max}$$\end{document}Cmax and a linear combination of (1) reduction in tumor fraction with \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${AUC}_{90s}>15.8$$\end{document}AUC90s>15.8 mM s, and, (2) increase in tumor fraction with \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${v}_{e}<0.3$$\end{document}ve<0.3. A higher plasma drug AUC was correlated with a linear combination of (1) increase in tumor fraction with \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\text{ADC}} < 1.1 \times 10^{ - 3} \;{\text{mm}}^{2} /{\text{s}}$$\end{document}ADC<1.1×10-3mm2/s, and, (2) increase in tumor fraction with \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$v_{e}<0.3$$\end{document}ve<0.3. These findings are suggestive of cell swelling and decreased tumor perfusion 2–3 days post-treatment with crolibulin. The multivariable linear regression models reported here can inform crolibulin dosing in future clinical studies of crolibulin combined with cytotoxic or immune-oncology agents.


T1 Parameter Fitting
The pre-contrast T 10 was obtained by fitting the variable flip angle T1w voxel intensities to the GRE signal equation 1 : where and α are the repetition time and flip angle, respectively; 0 is a function of the M 0 , , and T2 We have neglected the contribution of the T2 term ( − 2 → 1) so for these short echo time images: 0 = 0 − 2 ≈ 0 . From the pre-contrast T1w images acquired at different and α, we fit the T1w GRE signal equation to get the unknown parameters T1 without contrast (T10), and M 0 . M 0 is assumed to be invariant to the contrast agent 2 , however in practice pre and post-contrast images may have been acquired using different scanner gains (against study protocol imaging instructions).
Generally, in case is the same for all images, the variable flip angle method 7,8 which is a linearized model of Eq. A1 is commonly used for fitting; however in most visits variable and α were used for T1w acquisition, additionally trust-region non-linear fitting allows to constraint the solution to be inside a region which is useful to avoid unfeasible solutions.
For the pre-contrast parameter fitting, 0 is assumed to be the same for each T1w image, however in practice each image may have a different scanner gain. In some cases, this information can be extracted from the image metadata 9 . However, in case this information is not clearly defined in the image metadata, these gain factors should be also estimated. The gain factors are estimated such that model fitting on re-scaled mean intensities in healthy tissue ROIs results in closer T1 values to literature values (see Table A1). Normal and pathologic tissue ROIs were manually annotated.  To get the gain factors we used two approaches. In one approach, we make the assumption that the signal given by Eq. A1 using a T1 value from literature from a specific tissue is almost equal as the intensity in that tissue. This means the difference between intensities and resulting signal should be minimal. Therefore, to find the gain factors, we minimize a cost function based on the Sum of Squared Errors (SSE) between mean intensities and signal equation as a function of the gain factor plus a regularization to avoid unfeasible solutions. Having N precontrast registered T1w images { ⊂ 3 | ∈ 1, … , }, we define the mean intensity in image in the manually annotated tissue j as ̂. If per image, we assume the average M 0 in tissue j ( � 0 ) is multiplied by a gain factor , the cost function f is defined as: where 1 is the T1 time in tissue j as defined in Table A1, and the α and for image , and g is the regularization function defined by the step type expression: ( ) = ( ℎ( − ) + 1), which is a differentiable function with K → ∞ and the maximum allowed value for a gain factor. Finally, S in Eq. A1 is redefined using the gain factor by: Then, the gain factors are obtained by solving 1 ,…, , � 0 using a simplex search algorithm 10 .
In another method to get the gain factors, we use the principle that at higher α the T1weighting increases. Then, we use the average image intensity in tissue j with the highest α

Concentration Curves
The gadolinium concentration curves C were obtained by: where T1 times are calculated using Eq. A1, assuming S equal to the DCE-MRI image intensities: � ∈ 3 � ∈ , . . ,0, … }, where and are the first and last DCE-MRI images, and 0 the image at time of injection. Then, we can redefine Eq. A1 as The rationale behind this is that it is likely that the optimized gain factor for acquiring DCE-MRI is the same as the pre-contrast T1w image with the same flip angle. Approach 2: the rationale of this approach is that to get comparable concentrations between visits the mean 0 values between visits should be the same; to get this equal the ratio between 0 means.
In the three patients where no rescaling was applied to the T1w images, M 0 was not rescaled to get T1 at time t. In seven patients M 0 is rescaled such that we used the same scaling factor to scale the T1w image with α=30 ∘ , which is the same α used to acquire the DCE images. In one patient the concentration curves where still very different so M 0 was rescaled using approach 2 such that concentration curves in reference normal tissues became similar. The relaxivity to get concentrations was obtained depending of the employed contrast agent: Magnevist, Multihance, Optimark; and field strength 1 .

Kinetic model Parameters
From the concentration curves, we obtain the DCE-MRI parameter maps: AUC 90s , k trans , v p , and . To get 90 , concentration curves are interpolated to a higher resolution (Δt=0.5s) and integrated from time of injection (t=0s) to t=90s to get 90 . To get the other parameters we use the extended Tofts model. This model assumes two compartments in the tissue ( and ) that exchange contrast as: where C are the tissue concentrations defined by Eq. A4, and the plasma concentrations.
Then the parameters of the model are estimated by solving a linear system of equation as in Murase 1 . To get the plasma concentration , this is defined by is the artery contrast concentration (Arterial Input Function (AIF)), and H LV ≈ 0.45 the large vessel hematocrit fractional 3 . The AIF is defined as the contrast concentration in a feeding artery 4 . There are two main approaches in the literature to get the AIF: population based 3,5 where AIF is represented by an invariant functional form, and measuring C at artery locations in the image 4 . In this work we measured C at artery locations using the manually annotated ROIs, then we discarded incorrect concentration curves 6 , and finally AIF is given by the median curve from the remaining concentration curves.