Fig 1.
Hypoxia sources in tumours and diffusion range of substances.
Illustration of selected hypoxia sources and a hypoxic tumour micro-region in tumour tissue. Hypoxic micro-regions will usually form a characteristic tiled pattern throughout a tumour. For in vitro examples of patterning in tumour xenografts see Fig 2 in reference [13].
Fig 2.
Regulation of the cell cycle and radiation reaction.
(a) Overview of the cell cycle regulation, cell responses to environmental factors and radiation. (b) Survival curves for cells in specific cycle phases and with increased radioresistance due to quiescence, as described with the linear-quadratic model Eq 5. (c) Dependency of the oxygen enhancement ratio on the local oxygen concentration employed in order to alter the radiation response for hypoxic cells according to Eq 6, calculated according to equation 8 from [59].
Table 1.
Listing of parameters used in the model.
Further parameters and sources for cell interaction, nutrient diffusion and consumption can be found in [52] and [56].
Fig 3.
Distribution of nutrients in the spheroid and de-oxygenation during growth.
(a) Central cut-section through an in silico EMT6 tumour spheroid after 12 days of growth. Normoxic cells (pO2 > 2.5%) in blue, cells below 2.5% pO2 in purple, below 0.5% in red and necrotic cells in grey. Slice thickness is 40 μm. Compare to the in vitro immunodetection of pimonidazole in hypoxic cells in the peri-necrotic regions of a tumour spheroids (T47D after 10–14 days of growth) in Fig 3a in [80] (bar size in both images 50 μm). (b) Lateral concentration profiles of glucose and oxygen. The higher reach of survival-promoting glucose will lead to the formation of an anoxic region (between grey and brown dashed line). Hypoxic cells will be found in low-oxygen regions (between red and grey dashed line) and normoxic cells beyond the red dashed line. Compare also reference [1]. (c) Central cut-section of 40 μm thickness through an in silico EMT6 tumour with oxygen-dependent staining after 2, 6.5, 8.3, 9.5 and 10.2 days of growth. Cell staining corresponds to the line color in graph (d) (green cells are above 7.8%pO2). (d) Development of cell populations below defined oxygen concentrations in the spheroid as visualised in (c).
Fig 4.
Reoxygenation of the spheroid in response to a single radiation dose.
Irradiation has been performed with a dose of 4 Gy at day 14, either with normal oxygen enhancement (Omax = 2.9, left column) or with suppressed oxygen enhancement (Omax = 1, right column). (a-b) Pre- (left) and post-radiation (right) cutsection with oxygenation staining of cells as in Fig 3(c) and 3(d). (c-d) Fraction of cells which are subjected to different oxygen levels during growth and irradiation. Dot marker shows treatment-induced increase in hypoxic cells and star marker the regrowth-induced increase (refer to main text for details). (e-f) Lateral concentration profile of oxygen in the tumour spheroid at different time points during growth and treatment.
Fig 5.
Changes in oxygenation and diffusivity in response to irradiation and integral oxygen concentration as PET-equivalent.
(a-d) Change in the oxygen concentration (left column, difference in mM) and the density-dependent oxygen diffusion coefficient (right column, difference in μm2/s) between a pre- and post-radiated tumour state. Visualisation shows the difference in a central cutslice of the diffusion system (x and y denote grid nodes over 1000 μm, z and the color palette illustrate the difference in the according units). (a-b) show the rise in local oxygen concentration and the increase in the diffusivity as difference between a pre-radiated state and 12 hours after irradiation with 4 Gy and Omax = 2.9, (c-d) for 4 Gy and Omax = 1 with 24 hours difference. The dissolution and permeabilisation of dead cells will lead to a significant rise of oxygen diffusion into the tumour bulk. This influx is in parts due to a lower local consumption but also due to local increase in tissue diffusivity.
(e) Integral oxygen P(t) in the tumour spheroid in response to a single irradiation dose of 4 Gy x-rays at day 14 with full or suppressed oxygen enhancement in effect. The integral signal can be quantitatively compared to PET signals.
Fig 6.
Reoxygenation during repeated radiation delivery.
Persistence and stability of the reoxygenation response during multiple fractions and in prolonged irradiation regimes. Tumours where either irradiated with doses of 2 Gy per 24h (left column) or 4 Gy per 48h (right column). While a stable reoxygenation response can be observed, full reoxygenation is only possible if oxygen enhancement effects are suppressed via Omax = 1 as shown in the bottom row.