Table 1.
Variable and parameter glossary.
Fig 1.
(A) ODM sketch. (B) ODM iteration block diagram. In each iteration, we calculate radius, oxygen profile and update the volume. Hypoxia and necrosis are then calculated heuristically as proportions of the total volume.
Fig 2.
(A) comparison between linear (top) and exponential spatial discretisation (bottom). (B) example of spatial discretisation of 1–5 shells with constant oxygen drop.
Fig 3.
(A) Results of the fit with data (extracted from paper by Ribba’s group [5]). The plot contains information for tumour volume, hypoxia and necrosis for colon carcinoma cell line HT29. (B) Model fit for a data set containing IHC information on HIF1α for hypoxia at end of study point for MCF7 tumours.
Table 2.
Parameter results (kP, , KH, KN) for the ODM model for Ribba et al. [5]. Data and MCF7 with hypoxic endpoint.
Fig 4.
Growth curve fit for 2 example xenografts.
Panels (A-B) show fits of the model for Calu6 and Colo205. The plots also include simulation of hypoxia and necrosis. (A) is a faster proliferating tumour model (Calu6) and (B) grows slightly slower (Colo205). (C-D) CD31 IHC staining in Calu6 and Colo205 respectively. (E) summary data of CD31 for both tumour models.
Table 3.
Parameter results (kp and ) for the ODM model in xenografts.
Confidence intervals for each parameter are specified as well as the rank of the FIM (as a measure of the number of identifiable parameters), the collinearity index (Identifiable if γ<10), the condition number (Indentifiable if κ<1000) and the normalised residual. Cell lines denoted by * are unidentifiable and cell lines denoted by # are arguably identifiable.
Fig 5.
Results of parameter estimates.
(A) Parameter space (kp-) for different tissue of origin lines. (B) Same as (A) but divided into Fast, Medium, Slow and Very Slow Growth Xenografts. (C) Parameter space for explant-like tumour models.
Fig 6.
Growth curve fit for explants.
(A) Growth curve fit for 4 explant models, 2 for squamous lung carcinoma and 2 for colorectal carcinoma. The xenografted cell line Calu3 shows very similar behaviour to explant models. (B) Comparison between Calu6 and Calu3 lung cell lines; a squamous lung cancer explant; and clinical tumour material analyses. The bar chart shows the proportions of microvessel density (MVD) in area (quantified from CD31), necrosis (quantified from Hematoxylin & Eosin staining) and stroma (alpha smooth muscle actin (αSMA) positive staining). (C) Images of the different tumour models stained for αSMA and counter-stained with hematoxylin.
Table 4.
Parameter results (kp and ) for the ODM model in explant-like tumours.
Fig 7.
(A) Sketch of the ODM model (oxygen dependent, left) as described here plus a single compartment (Stroma) (VS, oxygen independent, right). Where kS is the stroma recruitment constant and kG is the growth enhancement constant. (B) Example of cell line fit for Lung 1 explant model. Tumour volume over time and hypoxia at end of study are presented. Also a simulation of necrosis is presented.
Table 5.
Parameter results (kPG, , kS) for the ODM model for Lung 1 explant model data.