Primary tumor growth.

<p>Comparison of the fit of the model and the data from <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0084249#pone.0084249-Huang1" target="_blank">[56]</a>. Data are mean standard error.</p

<i>In silico</i> simulation of the experiment from [56].

<p>A. Time development of the metastatic burden. B. Colonies size distribution at the end time T = 32 days (log-scale on the x-axis).</p

Large time simulation for large inhibitor production (<i>p</i> = 2.5×10⁻⁴ mg^.mm^−3.day⁻¹, <i>d</i> = 2.16 mm⁻²day⁻¹).

<p>The model predicts stabilization of the metastatic burden to a situation where the whole metastatic population is in a global dormancy state.</p

Values, units and meaning of the model parameters.

<p>PT = Primary Tumor. Met = metastases. I = global amount of angiogenic inhibitor in the blood. H = heuristic derivation.</p

Metastatic outputs.

<p>Comparison of the fit of the model and the data from <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0084249#pone.0084249-Huang1" target="_blank">[56]</a>. For the number of metastases, the reported model value is the number of tumors above a minimal visible size that we took to be 10 cells (tumors were counted using a dissecting microscope in <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0084249#pone.0084249-Huang1" target="_blank">[56]</a>). Mean size was given as diameter in <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0084249#pone.0084249-Huang1" target="_blank">[56]</a> and was converted here into volume using .</p

Schematic representation of the model for systemic inhibition of angiogenesis.

<p><b><i>m</i></b>, <b><i>α</i></b>: metastatic spreading parameters. <b><i>p</i></b>: production rate of angiogenesis inhibitor. <b><i>e</i></b>: efficacy parameter of inhibitor. <b><i>k</i></b>: elimination rate of the inhibitor.</p

Predictive power: Lung data.

<p>Models are presented in descending order of overall mean success (defined in (18)). , defined in (17), is the success score for prediction when using <i>n</i> data points and predicting at future depth <i>d</i>, i.e. time (see <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1003800#s2" target="_blank">Materials and Methods</a>). For relative errors (20), mean value among animals is reported with ranges in parenthesis. and stand for the success rates and relative errors for predictions of the late phase (see text for details). Reported in brackets in the column are the percent increase between and .</p><p>Predictive power: Lung data.</p

Predictive power: Breast data.

<p>Models are presented in descending order of overall mean success (defined in (18)). , defined in (17), is the success score for prediction when using <i>n</i> data points and predicting at future depth <i>d</i>, i.e. time (see <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1003800#s2" target="_blank">Materials and Methods</a>). For relative errors (20), mean value among animals is reported with ranges in parenthesis. and stand for the success rates and relative errors for predictions of the late phase (see text for details). Reported in brackets in the column are the percent increase between and .</p><p>Predictive power: Breast data.</p

Examples of predictive power.

<p>Representative examples of the forecast performances of the models for the lung data set (mouse number 2). Five data points were used to estimate the animal parameters and predict future growth. Prediction success of the models are reported for the next day data point (OK₁) or global future curve (OK_glob), based on the criterion of a normalized error smaller than 3 (meaning that the model prediction is within 3 standard deviations of the measurement error) for OK₁ and the median of this metric over the future curve for OK_glob (see <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1003800#s2" target="_blank">Materials and Methods</a> for details).</p

<i>A priori</i> information and improvement of prediction success rates.

<p>Predictions were considered when randomly dividing the animals between two equal groups, one used for learning the parameters distribution and the other for prediction, using <i>n</i> = 3 data points. Success rates are reported as mean ± standard deviation over 100 random partitions into two groups. A. Prediction of global future curve, quantified by the score (see <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1003800#s2" target="_blank">Materials and Methods</a>, Models predictions methods for its definition). B. Benefit of the method for prediction of the next day, using three data points (score ). C. Prediction improvement at various prediction depths, using the power law model (lung data) or the exponential-linear model (breast data). Due to lack of animals to be predicted for some of the random assignments, results of depths 2, 4, 6 and 9 for the breast data were not considered significant and were not reported (see <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1003800#s2" target="_blank">Materials and Methods</a>). * = <i>p</i><0.05, ** = <i>p</i><0.001, Student's t-test.</p