FIGURES AND TABLES
FROM:
A mathematical modelling tool for predicting survival of individual patients following resection of glioblastoma: a proof of principle
K R Swanson, R C Rostomily and E C Alvord Jr
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Figure 1.
Scatter graphs defining some of the major characteristics of the 70 patients with correlations of duration of survival for BX/STR patients (asterisks) and for the GTR patients (squares) with age, KPS and KPS-age. Note the broad ranges, illustrating the variety of the patients. Note also that none of these data enter into the mathematical model.
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Figure 2.
The actual data used for the present analysis: average radii of spheres equivalent to the T1-Gd and T2-weighted MRI volumes for glioblastomas of 70 actual patients subjected to biopsy or subtotal resection (BX/STR, asterisks, N=38), or to gross total resection (GTR, squares, N=32) as defined by the absence of tumour on post-operative enhanced CT.
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Figure 3.
Schematic representations of the relationships between T1-Gd and T2 images and the concentrations of tumour cells and of the effects of increasing the net rates of diffusion (D) and proliferation (
) on the 'traveling wave' of the 'edge' of an enlarging glioblastoma. The thresholds of detection for T1-Gd and T2 MR images (solid lines) are estimated at 80 and 16%, respectively, of the maximum cell density K in Equation (1).
Figure 4.
Distributions (%) of actual values of D/, in (A) for 22 patients having had steroid (asterisks) and for 45 patients not having had steroid (circles) before their MRIs, and in (B) for 38 patients having had biopsy or subtotal resection (circles) and 32 patients having had gross total resection (asterisks), as defined by the presence or absence of residual tumour in post-operative enhanced CT.
Figure 5.
Actual survival curves for 7 patients subjected to biopsy (BX, pluses), for 31 subjected to subtotal resection (STR, triangles) and for 32 subjected to gross total resection (GTR, asterisks) as defined by presence or absence of residual tumour on post-operative enhanced CT. Inset shows a close-up of the survival curves near the median survival times of 36.5 and 62 weeks, respectively.
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Figure 6.
(A) Survival curves for actual patients (asterisks) and virtual patients (squares) subjected to biopsy or subtotal resection (BX/STR, N=38). Inset shows a close-up of the survival curves near the median survival times of 32.4 and 36.5 weeks. (B) Survival curves on a longer time scaling following gross total resection (GTR, N=32) in actual patients (asterisks) defined by the absence of residual tumour on post-operative enhanced CT. The virtual patients (matched to actual pre-operative T1-Gd volume and D/ ratio derived from the T1-Gd and T2 volumes) were subjected to no resection (BX/STR, squares), to resection of 100% of the T1-Gd volumes or radii, r
T1 (circles) and to resection of 125% of the T1-Gd volumes or radii, 1.25 r
T1 (diamonds). Inset shows a close-up of the survival curves near the median survival times of 44.9, 55, 62 and 66.9 weeks.
