Fig 4. Optimising spheroid properties.

Optimal model parameterisations (spheroid radius and height) are identified by calculating a combined error between model output and in vivo oxygen measurements (A). The minimum error (red circle) indicates the most in-vivo-like representation of the sinusoidal oxygen gradient. The blue contour represents parameter combinations that simulates pericentral oxygen values for the minimal spheroid concentration whereas the red contour indicates hypoxia (defined as 10 mmHg). A 1D plot is provided for the optimal model parameterisation indicating the oxygen profile along the central axis of symmetry through the well (B). The minimal value corresponds to the in vivo central vein value (black dashed line). The in vivo portal vein value (black solid line) and hypoxic threshold (red dashed line) are also indicated. The green dashed line indicates the centre of the spheroid while blue dashed lines indicate the spheroid boundary. The mean boundary concentration is represented by the red dot. The corresponding oxygen consumption rate, expressed as a percentage of the maximal rate (V_max), is also shown for this 1D cross-section (C).