Fig 1.
Tumor volume over time of a single mouse from a control group which was inoculated with lung H1975 tumor cells.
The raw data (observations represented with points and joined with dashed lines) shows an apparent oscillatory profile in contrast with the predictions obtained from the commonly used tumor growth dynamics models (solid colored lines).
Fig 2.
Tumor volume raw data from multiple experiments including different tumor types (panels) and cell lines (different colors in each panel).
Points and colored lines represent the observed tumor volume observations for each individual.
Fig 3.
(A) Single case example of tumor volume observation (dots) fitted with the spline function (dashed line), and with a classical tumor growth dynamic model, in this case Gompertz equation (solid line). (B) Using the spline line of the case example as reference (dotted black line), the difference with the best classical model for each individual (Gompertz equation for this case example) is represented with a solid black line. Additionally, crossing with the zero-line (red points) and the local extrema (blue triangles) are marked in the graph.
Fig 4.
Schematic representation of the final model. Solid arrows indicate the proliferation/activation or the death processes, and the dashed arrows describe the different interactions between the three species. Parameters are defined in the text. Graphical elements are adapted from Servier medical art repository (https://smart.servier.com).
Fig 5.
(A) Boxplots of the half-periods for the different tumor types. (B) Estimated percentiles and p-value of Kolmogorov-Smirnov (KS) test for zero-crossing (blue) or extrema (red). The dashed blue lines correspond to the expected height of all the bins for the uniform distribution.
Fig 6.
Models results and a graphical evaluation of the final tumor growth model: (A) visual predictive check: the black dots show the tumor volume measure, black lines represent the 5th, 50th and 95th percentiles of the raw data, colored areas denote the 95th confidence interval of model-predicted median (orange areas), 5th and 95th percentiles (blue areas). (B) Weighted residuals versus time (right panel) and lag plot (where i represents each residual value in chronological order of observations) (left panel). (C) Tumor volume vs time observations (solid circles) and individual model predictions corresponding to the individual model parameters obtained from the selected (orange) and Simeoni (blue) models, for six different mice chosen at random.
Table 1.
Final model parameters of the tumor growth model.
Fig 7.
Numerical solution of the mean population parameters (red thick curve), together with 50 solutions (gray lines) obtained by perturbing the initial conditions by a Gaussian white noise vector (the variance for resources, angiogenesis and tumor volume being 0.1, 0.1 and 1, respectively).
The plot reflects the dynamics of the resources (au) (RES), angiogenesis (au) (ANG), and tumor volume (mm3) (TV).
Fig 8.
(A). Sensitivity analysis of the model when one parameter at a time is modified representing the percentage of change in tumor volume at 20 days after tumor inoculation. B. Deterministic model simulations of the tumor size, angiogenesis and resources over time for different values of kang, kres and kconsumption.
Fig 9.
Impact of virtual combination therapies.
Points represent the change in the area under the tumor size vs time curve (AUTC) for each combination of the kres, kang, and kconsumption parameters with respect to the one corresponding to the typical parameter estimates (Table 1). The circle in red corresponds to the reference AUTC value. AUTC was calculated from time 0 to 100 days. Additionally, a tumor volume profile over time for four different parameter combinations is shown on the right side of the figure.