Validation of the VERDICT MRI Framework using a Novel Computational Model of Diffusion and Flow in Real-World Tumours.
Ben Hipwell1, Tom Roberts1, Paul Sweeney2, Morium Ali2, Angela D'Esposito3, Eleftheria Panagiotaki2, Mark Lythgoe2, Daniel Alexander2, Rebecca Shipley2, and Simon Walker-Samuel2

1Centre for Advanced Biomedical Imaging, University College London, London, United Kingdom, 2University College London, London, United Kingdom, 3University of Bologna, Bologna, Italy


Compartmental models are increasingly being used to quantify diffusion MRI signals from tumours. We have developed a complex, multiscale mathematical modelling platform for simulating tumour pathophysiology, using high-resolution optical imaging data from complete tumour samples. Diffusion MRI signals from these tumours were simulated, including vascular flow and intra- and extracellular diffusion. These data were fitted to the VERDICT compartmental model, and the resulting parameters compared against ground truth simulation values. Cell radius and intra/extracellular fractional volume parameters and respective ground truth values were strongly correlated. A more complex relationship was found in vascular volume fractions.


Compartmental diffusion models are becoming increasingly popular for studying the microstructural properties of tissue. Recently-developed models such as VERDICT (Vascular, Extracellular and Restricted Diffusion for Cytometry in Tumours) provide powerful tools for accessing histologic features such as cell radius, intracellular volume fraction and vascular volume fraction1–3. The increasingly complex nature of such models makes thorough validation essential. We have developed a complex, multiscale mathematical modelling platform for simulating tumour pathophysiology, using high-resolution optical imaging data from complete tumour samples. The multi-bvalue, multi-direction diffusion MRI signal from these tissue simulations was synthesised using Monte Carlo simulations, which were then fitted to the VERDICT model. This allowed us to evaluate the accuracy of VERDICT model parameters, in a realistic and controlled setting, which we compare with previously acquired in-vivo data from the same tumours.


Substrate Generation: The vascular compartment of the simulation substrates (figure 1) was generated from optical projection tomography data (5-10μm resolution) acquired from optically-cleared LS174T tumours grown subcutaneously on balb/c nu/nu mice, with vessels labelled with fluorescently conjugated lectin4,5. Optical clearing was performed with benzyl alcohol benzyl benzoate (BABB). The vessel structures were segmented by applying a Frangi vesselness filter6, binary threshold and skeletonisation algorithm. Volumetric blood flow values were estimated throughout the networks using a discrete-network model simulating Poiseuille flow with conservation of flux at network bifurcations7. Four voxel-sized sections were randomly isolated for separate Monte Carlo simulations. The intracellular and extracellular compartments of the simulation were created by randomly generating spherical cells with a sphere-packing algorithm, which packed non-overlapping cells of a specified radii around the vessel network.

Synthetic MRI Data Generation: Walkers, representing water molecules, were initialised in one of the three compartments within the substrate, with the total in each compartment weighted by pre-specified volume fractions. In the intra/extracellular space the walker position was updated at each time-step using a random-walk protocol8 (figure 2(c)). In the vascular compartment, the walkers followed the flow velocity of their current vessel segment. Once all the walkers had been propagated, synthetic VERDICT data (46 b-value, 3 direction PGSE) was generated from their recorded trajectories using the Camino Diffusion MRI Toolkit9.

VERDICT Parameter Validation: The VERDICT models ‘BallSphereStick’ (Anisotropic vascular compartment) and ‘BallSphereAstrosticks’ (Isotropic vascular compartment) were each fitted to the synthetic data. The model parameters produced from these fits were then compared against the ground truth values specified in the simulation. This process was repeated for a range of simulation parameters to ascertain the correspondence between the VERDICT parameter estimates and the ground truth, over a wide range of values. The synthetic data produced by the simulation was also compared against subject-matched in-vivo¬≠ data acquired previously.


Plots of subject-matched (vascular structure) in-vivo¬≠ data, averaged over an ROI (figure 2(b)) and the synthetic MR data generated shows a good level of agreement between the simulated and real data. A strong correlation is shown between the ground truth and measured values of cell radius and intracellular volume fraction (figure 3), with a close to 1-1 correspondence in many cases. The ‘BallSphereAstrosticks’ model performed better that the ‘BallSphereStick’ in most cases. Ground truth and VERDICT estimates of vascular volume fraction showed a more complex relationship, and a poorer correlation(figure 4(a)). A similarly complex relationship can be seen in figure 4(b), in which results from a single vascular structure are shown, and where the average flow velocity was varied in each batch of simulations.


This study aimed to demonstrate the utility of a novel computational model of diffusion and flow for validating the mathematical models used by the VERDICT MRI framework. The results presented above show that the parameters produced by the VERDICT method, such as cell radius and intra/extracellular volume fractions, are strongly correlated with the ground truth values and suggest that these are truly representative measures. The discrepancies seen in the vascular volume fraction estimates and ground truth values require further investigation. The result shown in figure 4(b) shows that the mean blood-flow velocity is a possible reason for this discrepancy.


This work was supported by a Wellcome Trust Senior Research Fellowship (grant WT100247MA), KCL and UCL Comprehensive Cancer Imaging Centre CR-UK & EPSRC (In association with the DoH England), the EPSRC-funded UCL Centre for Doctoral Training in Medical Imaging (EP/L016478/1) and the Department of Health’s NIHR-funded Biomedical Research Centre at University College London Hospitals.


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Figure 1: (a) An image showing a 2D projection of the segmented and graph-converted vessel structure from an LS174T tumour overlaid on the structural MR image of the tumour. (b) 3D representations of the sub-voxels that were selected from the vessel structure, colour-coded according to the blood-flow velocity estimated by the finite network model. The thickness of the graph segments corresponds to the radius of the blood vessel calculated from the OPT data.

Figure 2: (a) Graph showing the normalised signal curves from subject-matched in-vivo data and simulated data (The vessel structure used for the substrate in the simulations was taken from the same tumour). The solid lines represent fitting the 'BallSphereAstrosticks' model to both datasets. (b) b0 image of a subcutaneous LS174T tumour, with a representation of a ROI overlaid (imaged using parameters of Panagiotaki et al1). (c) 3D plot of the trajectories from a typical Monte Carlo simulation.

Figure 3: Plots showing the correlation between the measured and simulation ground-truth values of the cell radius and intracellular volume fraction parameters produced using two different VERDICT models. The different colours represent different simulation voxels with different vessel structures. The black lines represent identity (a 1-1 correspondence). (a) Correlation between ground truth and measured cell radius using the ‘BallSphereStick’ model. (b) Correlation between ground truth and measured cell radius using the ‘BallSphereAstrosticks’ model. (c) Intracellular volume fraction correlation using ‘BallSphereStick’ model. (d) Intracellular volume fraction correlation using ‘BallSphereAstrosticks’ model.

Figure 4: (a) Shows the correlation between the ground truth and measured values of vascular volume fraction produced by the ‘BallSphereAstrosticks’ model. The different colours represent different simulation voxels with different vascular structures and blood-flow velocity distributions. (b) Shows the vascular volume fraction correlations produced from a single simulation voxel while varying the blood-flow velocity by a scalar factor between 0 and 2. The colour of the points represent the flow-adjustment factor.

Proc. Intl. Soc. Mag. Reson. Med. 26 (2018)