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Supplementary information

Additional file 10: Figure S5. Box-plots of parameter estimation results based on different initial volume conditions (true initial tumor volume = 0.1 mm3). The initial volume V0 was fixed (x-axis) during the fitting procedure. Results are based on 20 synthetic data samples with different measuring frequencies (1, 2, 3 and 4 days between each time point).

Additional file 2: Table S2. Parameter estimation of Gompertzian growth based on different data availability and growth behavior (first measured tumor data point on day 14 with a size of about 150 mm3). Fitting were performed from day 14 to day 43, which corresponds to an initial tumor volume of about 150 mm3. Indicated are the mean values for each parameter. () = Minimum and maximum values for each parameter. {} = Parameter estimation bias (peb). [] = Coefficient of variation (CV). *Parameter V0 was set to 1 mm3 during the fitting procedure. True values: V0 = 1 mm3, a = 0.56 day− 1, β = 0.0719 day− 1.

Additional file 7: Figure S2. Effect of sample size on selection of most appropriate growth function for the underlying power law data based on the lowest RMSE value. Each sample size (number of animals) was generated 10 times (synthetic dataset number) to mimic a power growth behavior including caliper measurement errors. For each growth function, Gompertz (Gomp), exponential (Exp), power (Pow) and logistic (Log), the RMSE value was determined for each individual sample within each dataset (e.g. dataset 2 and sample size 10). The relative frequency denotes how often each of the growth functions had the lowest RMSE value for an individual fit in each sample size group.

Additional file 9: Figure S4. Box-plots of parameter estimation results based on different initial volume conditions (true initial tumor volume = 1 mm3). The initial volume V0 was fixed (x-axis) during the fitting procedure. Results are based on 20 synthetic data samples with different measuring frequencies (1, 2, 3 and 4 days between each time point).

Diese Arbeit konzentriert sich auf die Rolle der Blutgefäßgeometrie bei der Behandlung von Tumorerkrankungen. Zur Untersuchung wurde eine Kombination von mathematischen Modellen, Computersimulationen und experimentellen Daten verwendet. Die Anwendung einer Cisplatin-Chemotherapie reduziert signifikant die Blutgefäßdichte und beeinflusst somit das Ausbreitungsverhalten von Metastasen. Der Zeitpunkt einer Chemotherapie ist ein kritischer Faktor für den Behandlungserfolg, da sich der behandelbare Anteil aufgrund der begrenzten Verteilung von Chemotherapeutika mit der Zeit rapide verringert.

Additional file 6: Figure S1. Effect of sample size on selection of most appropriate growth function for the underlying exponential data based on the lowest RMSE value. Each sample size (number of animals) was generated 10 times (synthetic dataset number) to mimic an exponential growth behavior including caliper measurement errors. For each growth function, Gompertz (Gomp), exponential (Exp), power (Pow) and logistic (Log), the RMSE value was determined for each individual sample within each dataset (e.g. dataset 2 and sample size 10). The relative frequency denotes how often each of the growth functions had the lowest RMSE value for an individual fit in each sample size group.