PMC3386273_01
Case 1 at diagnosis.. a) Coronal, b) Sagital and c) Axial view of T2 MRI real images of the tumor. d) and e) Corresponding simulated MRI images generated at a detection level of d) 400 cells/ and e) 1 cell/. In simulations, white areas represent the tumor mass and black ones, tumor infiltration.
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This figure should be compared with figure 1a and 1c from that shows the real MRI images from this patient. At diagnosis, real and simulated tumor mass radii are 8.9 and 8.7 mm; while tumor infiltration radii are 28.4 and 28.9 mm, respectively (compare figure 1a from with axial view from figure 6(a)). Eighteen days after diagnosis, real and simulated tumor mass radii are 11.4 and 10.6 mm; and tumor infiltration radii are 33.1 and 31.2 mm, respectively (compare figure 1c from with axial view from figure 6(c)). Real images show that tumor invasion through the corpus callosum is significantly augmented at that time (figures 1c and 1d from).
Case 1, 20 days after diagnosis.. a) Axial view of a T2 MRI real image of the tumor. b) and c) Simulated MRI images of central slices of the tumor generated at a detection level of b) 400 cells/ and c) 1 cell/. In simulations, white areas represent the tumor mass and black ones, tumor infiltration.
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 Figure 2 presents the tumor mass and infiltration 20 days after diagnosis time.
Case 1, 40 days after diagnosis.. a), b) and c): Different slices of T2 MRI real images of the tumor in the axial plane. d), e), and f): Corresponding simulated slices generated at a detection level of 400 cells/. g), h), and i): Corresponding simulated slices generated at a detection level of 1 cell/. In simulations, white areas represent the tumor mass and black ones, tumor infiltration.
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 Figure 3 shows the predicted tumor-mass and infiltrative areas 40 days after diagnosis, over different slices from the axial plane, given a better overview of the 3D tumor evolution. At diagnosis time (270 days from tumor onset, figure 3), tumor mass affects 8.2% of the Brodmann area 41 and 12.6% of the Brodmann area 42 (references 2 and 3, respectively).
Case 1, predicted Talairach structures affected by the tumor mass during its development.. a) At diagnosis, b) 50 days after diagnosis, c) 100 days after diagnosis and d) 140 days after diagnosis (time of death). Tumor detection level at  cells/. Infiltrative areas have been omitted. Numbers indicate brain structures: 1: transverse gyrus, temporal lobe; 2: Brodmann area 41; 3: Brodmann area 42; 4: Brodmann areas 22; 5: Brodmann area 39; 6: superior gyrus, temporal lobe; 7: lateral ventricle; 8: Brodmann area 13; 9: Brodmann area 43; 10: precentral gyrus, frontal lobe; 11: insula; 12: lentiform nucleus; 13: thalamus.
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 Figure 4 superimposes the predicted tumor mass at different times upon the Talairach atlas, indicating the main brain structures that are being affected by tumor evolution. 50 days after diagnosis (320 days from tumor onset, figure 4(b)), the tumor mass invades great part of transverse and superior gyrus of the temporal lobe (references 1 and 6, respectively) and 10.9% of the Brodmann area 22 (reference 4). 100 days after diagnosis (370 days from tumor onset, figure 4(c)), the tumor has expanded to the pre-central gyrus of the frontal lobe (10) and up to the right lateral ventricle (7). Figure 4(d) predicts that, at the time of death (survival time of 140 days after diagnosis or 410 days from tumor onset), the tumor mass has extended through the insula (11), lentiform nucleus (12) and thalamus (13).
Case 1, predicted tumor evolution at death.. a) Simulated MRI images of central slices of the tumor generated at a detection level of 1 cell/. White areas represent the tumor mass and black ones, tumor infiltration. b) Simulated tumor mass near the area of the 'foramen magnum' evidenced by the Talairach atlas. Here, infiltrative areas have been omitted.
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 Figure 5 presents tumor status at the predicted time of death. Talairach atlas in figure 5(b). This means that herniation, and consequently death, could be imminent.
PMC3386273_02
Case 1 at diagnosis.. a) Coronal, b) Sagital and c) Axial view of T2 MRI real images of the tumor. d) and e) Corresponding simulated MRI images generated at a detection level of d) 400 cells/ and e) 1 cell/. In simulations, white areas represent the tumor mass and black ones, tumor infiltration.
pone.0039616.g001.jpg
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This figure should be compared with figure 1a and 1c from that shows the real MRI images from this patient. At diagnosis, real and simulated tumor mass radii are 8.9 and 8.7 mm; while tumor infiltration radii are 28.4 and 28.9 mm, respectively (compare figure 1a from with axial view from figure 6(a)). Eighteen days after diagnosis, real and simulated tumor mass radii are 11.4 and 10.6 mm; and tumor infiltration radii are 33.1 and 31.2 mm, respectively (compare figure 1c from with axial view from figure 6(c)). Real images show that tumor invasion through the corpus callosum is significantly augmented at that time (figures 1c and 1d from).
Case 2, comparison between models.. Simulated MRI images of central slices of the tumor generated at a detection level of 400 cells/. Left: simulations generated by the present model. Right: simulations generated by a previous model from bibliography. a) and b) at diagnosis. c) and d) 18 days after diagnosis e) and f) 100 days after diagnosis.
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File Case S2 video submitted as a supporting information file. Figure 6 compares simulations of this case at different times made with two distinct mathematical models: left column corresponds to simulations obtained with the present model, right column corresponds to simulations derived from our implementation of a model previously described in the literature (this model does not include differential migration based on topological brain structures). At diagnosis, real and simulated tumor mass radii are 8.9 and 8.7 mm; while tumor infiltration radii are 28.4 and 28.9 mm, respectively (compare figure 1a from with axial view from figure 6(a)). Eighteen days after diagnosis, real and simulated tumor mass radii are 11.4 and 10.6 mm; and tumor infiltration radii are 33.1 and 31.2 mm, respectively (compare figure 1c from with axial view from figure 6(c)). Simulations made with a previous model (figures 6(b) and 6(d)) also reach tumor dimensions similar to real ones. Although this kind of mathematical models do not include the mass-effect, this type of spreading through the corpus callosum can be observed in simulations made with our model (see axial view form figure 6(c)) but not in those derived from previous ones (axial view from figure 6(d)). This consideration is extremely important, as its consequences worsen with time: differences between both models become more evident 100 days after diagnosis, as it can be evidenced in figures 6(e) and 6(f).