A quantitative model for differential motility of gliomas in grey and white matter

Abstract

We have extended a mathematical model of gliomas based on proliferation and diffusion rates to incorporate the effects of augmented cell motility in white matter as compared to grey matter. Using a detailed mapping of the white and grey matter in the brain developed for a MRI simulator, we have been able to simulate model tumours on an anatomically accurate brain domain. Our simulations show good agreement with clinically observed tumour geometries and suggest paths of submicroscopic tumour invasion not detectable on CT or MRI images. We expect this model to give insight into microscopic and submicroscopic invasion of the human brain by glioma cells. This method gives insight in microscopic and submicroscopic invasion of the human brain by glioma cells. Additionally, the model can be useful in defining expected pathways of invasion by glioma cells and thereby identify regions of the brain on which to focus treatments.

Virtual brain tumours (gliomas) enhance the reality of medical imaging and highlight inadequacies of current therapy

“…Previous studies of the motility of gliomas have demonstrated that diffusion is an accurate estimation for the spread of gliomas (Woodward et al, 1996;Swanson, 1999). A consequence of modeling cellular motility by Fickian or gradient-driven diffusion, is the lack of a definitive interface between malignant and normal tissue.…”

“…Previous two-dimensional models have suggested that tumour location can have a significant impact on survival time based simply on the local invasion abilities of the tumour (Swanson, 1999;Swanson et al, 2000). Figure 3 shows the survival times (time between diagnosis at 3 cm diameter and death at 6 cm diameter) predicted by the model for a range of values of the ratio of the tumour cell migration rate in white matter to that in grey matter (g= D w /D g ).…”

“…The difference in the diffusion coefficients in grey and white matter has been estimated to range from 2 -100-fold (Swanson, 1999), but we have chosen 5 as an arbitrary first approximation to illustrate the model's potential. To complete the model formulation, we impose a 'zero-flux' of cells across the brain boundaries defined by cerebrospinal fluid in the ventricular and subarachnoid space.…”

“…For high-grade gliomas (glioblastomas) previous reports, based on extant data, have suggested a net proliferation rate of r&0.012/day (Alvord and Shaw, 1991; Swanson, 1999;Swanson et al, 2000), corresponding to a volume-doubling time of 60 days, and a diffusion coefficient of D&0.0013 cm 2 day 71 (Swanson, 1999;Swanson et al, 2000). The actual ranges of these values are quite extreme but real values for any actual patient could be substituted.…”

“…By defining a virtual human brain with the anatomical distribution of grey and white matter (the two primary tissue components of the brain) to a voxel resolution of 1 mm 3 , we can model the differential motility of glioma cells in grey and white matter to accommodate reports (Giese et al, 1996) that such differences are biologically significant. Specifically, since glioma cells are reported to migrate more rapidly in white matter than in grey matter (Giese et al, 1996;Silbergeld and Chicoine, 1997;Swanson, 1999) we allow the motility coefficient to differ depending on the local tissue composition.…”