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.

Figure 1

Computational domain with tumour locations. Grey matter appears grey and white matter appears white. Position 1 is the location of an inferior fronto‐parietal tumour, position 2 is the location for a superior fronto‐parietal tumour, position 3 is the location for a temporal lobe tumour.

Figure 2

Simulation of tumour invasion of a high‐grade glioma in position 2 in the superior cerebral hemisphere: (a) (b) at diagnosis; (c) (d) at death; (a) (c) as seen by our standard threshold of detection; (b) (d) as calculated out to 1.25% of the threshold (boundary) cell concentration defining the sensitive threshold of detection.

Figure 3

Simulation of tumour invasion of a high‐grade glioma in position 1 in the inferior cerebral hemisphere: (a) (b) at diagnosis; (c) (d) at death; (a) (c) as seen by our standard threshold of detection; (b) (d) as calculated out to 1.25% of the threshold (boundary) cell concentration defining the sensitive threshold of detection.

Figure 4

Simulation of tumour invasion of a high‐grade glioma in position 3 in the temporal lobe: (a) (b) at diagnosis; (c) (d) at death; (a) (c) as seen by our standard threshold of detection; (b) (d) as calculated out to 1.25% of the threshold (boundary) cell concentration defining the sensitive threshold of detection.)

Figure 5

Percentage of position 1 tumour detectable by our standard threshold of detection at diagnosis vs. the growth rate ρ and the diffusion coefficient in grey matter D_g. Note that the greatest proportion of detectable tumour occurs with high growth rate and low diffusion coefficient; conversely, the least proportion is seen with gliomas having low growth rate and high diffusion coefficient.

Figure 6

Percentage of detectable volume of tumour vs. the threshold of detection at various positions. The 40 000 cells/cm² represents our standard, the threshold of detection for an enhanced CT scan.