Number of metastases on the day of achieving a total tumour mass of 1 kg.

<p>The day of reaching a total tumour mass of 1 kg varies from day 1728 in scenario A to day 1852 in scenario D. By resecting the primary tumour this day can be shifted further into the future. In scenario A_R the lethal tumour mass is reached at day 1972 if the primary tumour is resected at day 680 or at day 2018 if the primary tumour is resected at day 620. In scenario B_R the tumour mass of 1 kg is no longer reached. The significant differences in the number of metastases between the scenarios where metastases are able to metastasize and the scenarios where they are not are particularly remarkable. The difference between scenario A and B is 3901 metastases and between the scenarios C and D 2093 metastases. In contrast, the day of reaching a total tumour mass of 1 kg was only shifted by 12 or 52 days, respectively, into the future.</p

The development of total tumour weight and number of metastases in time.

<p>To compare the different scenarios in terms of relevance for the patient the total tumour mass (blue line), including the primary tumour and all metastases, was computed. The value of the lethal tumour mass of 1 kg is marked with a dashed line. The number of metastases (red line) was also visualized in the graph. The tumour mass is mapped to the left y-axes and the number of metastases to the right y-axes. The day on which primary tumour and metastases reach the total mass of 1 kg is marked with a green dotted line. Again four different scenarios were simulated: A) Metastases are able to metastasize. B) Metastases are not able to metastasize. C) Primary tumour and metastases metastasize only until they reach a size of 10¹⁰ cells. Metastases are able to metastasize. D) Primary tumour and metastases metastasize only until they reach a size of 10¹⁰ cells. Metastases are not able to metastasize.</p

Case of a hepatocellular carcinoma with multiple metastases in the liver.

<p>The circles, squares and triangles represent the clinical data taken from the patient at the days 1110, 1237 and 1310 after the estimated origin of the primary tumour. The cumulative number of metastases according to the size of the metastases is shown. Four different scenarios were simulated (see <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0035689#pone-0035689-t001" target="_blank">Table 1</a> and <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0035689#pone-0035689-g004" target="_blank">Fig. 4</a>). The results for the scenarios A and B both fit well with the clinical data. The simulated data differs only in the range of very small metastases (see also <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0035689#pone.0035689.s003" target="_blank">Fig. S3</a>). Hence, on the basis of the available clinical data it is not decidable whether metastases metastasise or not. The simulation results of scenarios C and D clearly show a plateau, which arises from the fact that the primary tumour reached the plateau size of 10⁹ (dashed lines) or 10¹⁰ (solid lines) cells, respectably. All cells that are disseminated from the primary tumour from now on are no longer able to form a metastasis. In scenario D only the primary tumour is able to metastasise, so no further metastases are created. The number of metastases stays the same while the existing metastases keep on growing. In scenario C metastases are able to spread new metastases. As a consequence the number of metastases start rising again, as soon as the first metastases spread from the primary tumour are large enough to spread metastases themselves. A second plateau is discernible for the case that cells disseminated from tumours larger than 10⁹ cells lose the ability to form metastases (dashed lines). This second plateau indicates that the first metastasis reached the size of 10⁹ cells, too. Such a second plateau cannot be observed for the solid lines since up until day 1310 none of the metastases reached the critical size of 10¹⁰ cells. In addition to this figure the frequency distribution of the metastases sizes was plotted in <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0035689#pone.0035689.s007" target="_blank">Fig. S7</a>.</p

Scenarios considered for simulation.

<p>Six scenarios were considered for the computer simulations. In the scenarios A and B it is tested whether metastases do metastasize or not. In the scenarios C and D it is additionally investigated whether late disseminated tumour cells might be less capable to form metastases. To define the term “late” the size of the primary tumour/metastases is used as a benchmark. In the scenarios A_R and B_R the resection of the primary tumour is simulated. Again, once for the case that metastases are able to metastasise and once for the case that metastases are not able to metastasise.</p

Simulated resection of the primary tumour.

<p>The resection of the primary tumour was simulated for two different time points. The first time point is shortly after the initial diagnosis at day 680 (solid lines). The second time point is some time before the first diagnosis at day 620 (dotted lines) simulating early diagnosis e.g. as a result of tumour screening. The cumulative number of metastases according to the size of the metastases (graphs A_R1 and B_R1) and the development of the tumour mass and the number of metastases in time (graphs A_R2 and B_R2) are shown. After the resection no new metastases are founded for some time. In scenarios A_R the number of metastases starts rising again after some time. The time of death could be shifted to 244 days (resection at day 680) or 290 days (resection at day 620) into the future. In scenario B_R no new metastases are founded after the resection. The existing metastases keep growing, but never reach the benchmark value of 1 kg.</p

Compartment types.

<p>Compartments describe all parts that can contain malignant cells, such as primary tumour, blood stream or metastases and can be modelled in two different ways: In continuous compartments (A) all internal processes are represented by mathematical functions. The growth of the system is modelled via a growth function and the spread of metastases via a rate function. In a discrete compartment (B) all internal processes are modelled with the help of events. They describe what happens to a single cell at a specific time within the compartment. Events can be e.g. cell division, apoptosis, intravasation or the creation of a new metastasis and occur with an assigned probability in the compartment. Discrete compartments are used to simulate a compartment in detail. Continuous compartments are used to simulate bigger systems like the primary tumour or metastases.</p

The simulation configuration used for the simulations.

<p>The growth of the primary tumour and metastases are modelled via the mathematical function <i>x(t)</i> (see eq. 2). The blood stream is modelled via events. The intravasation events are created conforming to the colonization rate <i>β(x)</i> (see eq. 3). Executing the intravasation event, a cell is added to the blood stream and a new event describing what happens next to this cell is generated. In the simulated scenarios it is examined whether metastases are able to metastasize (dotted line) and whether particularly late disseminated tumour cells are capable to form metastases.</p

Time line of cancer progress and CT scans.

<p>The time line visualizes the progress of the cancer growth and the CT scans taken to detect metastases. The upper time dates were determined in reference to the diagnosis. In the second time line the dates were adapted in reference to the estimated origin of the primary tumour.</p

Radiotherapy and chemotherapy change vessel tree geometry and metastatic spread in a small cell lung cancer xenograft mouse tumor model

<div><p>Background</p><p>Tumor vasculature is critical for tumor growth, formation of distant metastases and efficiency of radio- and chemotherapy treatments. However, how the vasculature itself is affected during cancer treatment regarding to the metastatic behavior has not been thoroughly investigated. Therefore, the aim of this study was to analyze the influence of hypofractionated radiotherapy and cisplatin chemotherapy on vessel tree geometry and metastasis formation in a small cell lung cancer xenograft mouse tumor model to investigate the spread of malignant cells during different treatments modalities.</p><p>Methods</p><p>The biological data gained during these experiments were fed into our previously developed computer model “Cancer and Treatment Simulation Tool” (CaTSiT) to model the growth of the primary tumor, its metastatic deposit and also the influence on different therapies. Furthermore, we performed quantitative histology analyses to verify our predictions in xenograft mouse tumor model.</p><p>Results</p><p>According to the computer simulation the number of cells engrafting must vary considerably to explain the different weights of the primary tumor at the end of the experiment. Once a primary tumor is established, the fractal dimension of its vasculature correlates with the tumor size. Furthermore, the fractal dimension of the tumor vasculature changes during treatment, indicating that the therapy affects the blood vessels’ geometry. We corroborated these findings with a quantitative histological analysis showing that the blood vessel density is depleted during radiotherapy and cisplatin chemotherapy. The CaTSiT computer model reveals that chemotherapy influences the tumor’s therapeutic susceptibility and its metastatic spreading behavior.</p><p>Conclusion</p><p>Using a system biological approach in combination with xenograft models and computer simulations revealed that the usage of chemotherapy and radiation therapy determines the spreading behavior by changing the blood vessel geometry of the primary tumor.</p></div

Blood vessel densities in untreated tumors (control group) and tumors that have been treated by cisplatin (ChT) and hypofractionated radiotherapy (RT).

<p>The blood vessel densities are computed with respect to (A) the entire tumor, and (B) only to the viable and homogeneous tumor regions, i.e. excluding areas of necrosis. In both cases, the blood vessel counting was not restricted to certain fields of view but include the whole region under consideration (cf. section B in the <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0187144#pone.0187144.s001" target="_blank">S1 Text</a>). The margins of the tumors were excluded from the blood vessel counting due to unspecific staining this region. Each grey dot indicates the vessel density for a single tumor, which had been computed as the arithmetic mean over a number of histological sections (cf. section B of the <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0187144#pone.0187144.s001" target="_blank">S1 Text</a>). The arithmetic mean of the entire treatment group (Control, ChT, RT) is shown by a red line. Red boxes indicate one standard deviation of the vessel densities in the respective group. The blue boxes indicate the 95% confidence intervals of the arithmetic mean values. An asterisk represents a significance level of p<0.05, two asterisks denote a significance level of p<0.01.</p