Table 1.
Model parameters.
Fig 1.
Cell count over time for tumour spheroids.
In silico data, based on 10 simulations runs, are represented in terms of the mean value (black line) and standard deviation (grey ribbon). In vitro data (red error bars) are extracted from plots produced by Voissiere et al. [35] using a Java program (DataThief III [39]).
Fig 2.
The G1DF is incorporated in the model to achieve oxygen-dependent G1 arrest. The G1DF (dark line) is extrapolated from data (red crosses) from a previous mathematical study by Alarcon et al. [41].
Fig 3.
Proliferative and slow-cycling or non-proliferative cells.
Top: Images from in vitro experiments performed by Voissiere et al. [35], in which cell nuclei are stained blue and proliferative cells are stained green by the proliferation marker Ki-67. Bottom: Images from in silico experiments performed in this study, where proliferative (cycling) cells are coloured green and inner (slow-cycling or non-proliferative) cells are coloured blue.
Fig 4.
Top: Images from in vitro experiments performed by Voissiere et al. [35], in which hypoxic cells are stained green by pimonidazole and normoxic cells are stained blue. Bottom: Images from in silico experiments performed in this study, where hypoxic cells (pO2 ≤ 10 mmHg) are coloured green and normoxic cells (pO2> 10 mmHg) are coloured blue.
Fig 5.
The BRF expresses the fraction of HAP compound that reduces to AHAP compound within one hour as a function of oxygenation (in mmHg).
Fig 6.
The probability that a cell, in the mathematical model, exposed to a radiotherapy dose of 2 Gy survives.
The survival probability S(x, t) is function of a cell’s current cell-cycle phase and oxygenation value, as well as the applied radiotherapy dose. Cells are the most likely to survive radiotherapy when hypoxic.
Fig 7.
The oxygen enhancement ratio (OER) and the oxygen modification factor (OMF).
The OER and the OMF are incorporated in the mathematical model to quantify the influence of oxygen on radiotherapy responses. Cells are the least radiosensitive for low pO2 values. The OER and OMF curves have steep gradients between the oxygen values 0 and 10 mmHg, after which they respectively asymptote to the values 3 and 1 for higher oxygen values.
Fig 8.
The ‘Small’ (20 day old) MCTS and the ‘Large’ (30 day old) MCTS.
These two MCTSs are used to allow for comparisons in treatment responses between tumours with different oxygenation levels. Top: Simulation snapshots of the MCTSs at the time point T0 when treatments commence (A1: Small MCTS, B1: Large MCTS). Hypoxic cells (pO2≤ 10 mmHg) are green whilst normoxic cells are blue. Middle: Oxygen histograms at time T0, in which hypoxic cell counts are shown in green and normoxic cell counts are shown in blue (A2: Small MCTS, B2: Large MCTS). Bottom: Cell-cycle phase histograms at time T0 (A3: Small MCTS, B3: Large MCTS). The slow/non-proliferative, inner cancer cells are labeled S/N-P.
Fig 9.
Monotherapy results: Cell count.
Treatment responses for HAP (left) and IR (right) monotherapies for the ‘Small’ (top) and ‘Large’ (bottom) MCTS. The monotherapy is given at T0 = 0 hours. Graphs demonstrate cell-cycle specific cell count (i.e. number of viable, undamaged cells) over time. The slow/non-proliferative, inner cancer cells are labeled S/N-P. Solid lines show mean values, and the height of ‘+’ markers show standard deviations for 10 in silico runs.
Fig 10.
Monotherapy results: Cell cycle phase composition.
Treatment responses for HAP (left) and IR (right) monotherapies for the ‘Small’ (top) and ‘Large’ (bottom) MCTS. The monotherapy is given at T0 = 0 hours. Graphs demonstrate cell-cycle specific composition (of viable, undamaged cells) over time. The slow/non-proliferative, inner cancer cells are labeled S/N-P. Solid lines show mean values for 10 in silico runs (standard deviations are negligible hence not shown).
Fig 11.
Monotherapy results: Oxygen histograms.
Treatment responses for HAP (left) and IR (right) monotherapies for the ‘Small’ (top) and ‘Large’ (bottom) MCTS. Histograms over cellular oxygenation levels at time T0 (monotherapy administration time) and 4 hours later are shown. Results are based on mean values from 10 in silico runs.
Fig 12.
Combination treatment results: Scheduling.
Treatment responses (in terms of cell count) for HAP-IR combination therapies in the ‘Small’ MCTS (left) and the ‘Large’ MCTS (right). One dose of HAPs and one dose of IR are administered at various schedules. Solid and dashed lines show mean values, and the height of the ‘+’ markers show standard deviations for 10 in silico runs.
Fig 13.
Combination treatment results: HAPs as IR-treatment intensifiers.
Treatment responses of radiotherapy in various MCTSs when either (1) an IR monotherapy dose is administered at T0+ 48 hours or (2) IR is given at T0+48 hours following a prior HAP dose at time T0. Note that only explicit IR responses (not HAP responses) are shown. The oxygen-levels of the ‘Small’ (left) and ‘Large’ (right) tumours are scaled by a factor of 1 (least hypoxic), 1/2 or 1/4 (most hypoxic). The value calibrated from in vitro experiments [35] correspond to a scaling with factor 1. Orange + blue bars show number of viable cells (instantaneously) before IR administration, blue bars show the number of viable cells (instantaneously) post IR. Red bars show how many cells (as a fraction) survived the IR attack.
Fig 14.
Multicellular tumour spheroids (MCTSs) A and B prior to treatment commencing.
The MCTSs are visualised in both opaque and transparent formats. Hypoxic activator cells are shown in green and normoxic bystander cells are shown in blue. Activator and bystander cells are manually set so that MCTSs A and B contain the same number of activator and bystander cells before treatment commences.
Fig 15.
Treatment responses in multi-cellular tumour spheroid (MCTS) A and MCTS B when HAPs are administered at T0 = 0 hours.
The number of viable (undamaged) cells are plotted over time for MCTS A and MCTS B. Cell counts for activator cells (pO2 = 1 mmHg) are shown in dashed lines and bystander cell counts (pO2 = 100 mmHg) are shown in solid lines. Results demonstrate mean values for 10 in silico runs.