Mathematical modeling of the metastatic process

Mathematical modeling in cancer has been growing in popularity and impact since its inception in 1932. The first theoretical mathematical modeling in cancer research was focused on understanding tumor growth laws and has grown to include the competition between healthy and normal tissue, carcinogenesis, therapy and metastasis. It is the latter topic, metastasis, on which we will focus this short review, specifically discussing various computational and mathematical models of different portions of the metastatic process, including: the emergence of the metastatic phenotype, the timing and size distribution of metastases, the factors that influence the dormancy of micrometastases and patterns of spread from a given primary tumor.Comment: 24 pages, 6 figures, Revie

Einfluss von Chemotherapie auf das Tumorwachstum und die metastatische Progression im Computermodell

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

Mathematical modeling of tumor therapy with oncolytic viruses: Effects of parametric heterogeneity on cell dynamics

One of the mechanisms that ensure cancer robustness is tumor heterogeneity, and its effects on tumor cells dynamics have to be taken into account when studying cancer progression. There is no unifying theoretical framework in mathematical modeling of carcinogenesis that would account for parametric heterogeneity. Here we formulate a modeling approach that naturally takes stock of inherent cancer cell heterogeneity and illustrate it with a model of interaction between a tumor and an oncolytic virus. We show that several phenomena that are absent in homogeneous models, such as cancer recurrence, tumor dormancy, an others, appear in heterogeneous setting. We also demonstrate that, within the applied modeling framework, to overcome the adverse effect of tumor cell heterogeneity on cancer progression, a heterogeneous population of an oncolytic virus must be used. Heterogeneity in parameters of the model, such as tumor cell susceptibility to virus infection and virus replication rate, can lead to complex, time-dependent behaviors of the tumor. Thus, irregular, quasi-chaotic behavior of the tumor-virus system can be caused not only by random perturbations but also by the heterogeneity of the tumor and the virus. The modeling approach described here reveals the importance of tumor cell and virus heterogeneity for the outcome of cancer therapy. It should be straightforward to apply these techniques to mathematical modeling of other types of anticancer therapy.Comment: 45 pages, 6 figures; submitted to Biology Direc

Aspects of chemotherapy and photon and proton radiotherapy in patients with gastric cancer

Gastric cancer remains a major health problem worldwide. The addition of chemotherapy alone or in combination with radiotherapy to surgery in local gastric cancer improves outcome. In more advanced stages, the optimal palliative chemotherapy remains unknown, as well as the effect of different regimens on the patients’ quality of life. The aim of this thesis was to explore a new concept in chemotherapy, i.e. the sequential approach, and a new modality in radiotherapy, i.e. proton therapy, in the treatment of patients with gastric cancer. Quality of life (QoL) in patients treated with chemotherapy, and target delineation in radiotherapy of gastric cancer, were also studied. In Paper I, we evaluated the efficacy of sequential chemotherapy in patients with locally advanced and/or metastatic gastric cancer, with alternating irinotecan and docetaxel in combination with infusion 5-Fu. Eighty-one patients were randomized. No differences favoring either arm were found with respect to response rate, overall survival (OS), or toxicity. The median OS of 11 months indicated that the sequential approach was effective and similar to triple combinations, with potentially less toxicity. In Paper II, we evaluated the effect of sequential chemotherapy on the QoL in the same cohort. It was measured before, during, and after treatment. There were no statistically significant differences in QoL scores between the two treatment arms and no changes in mean scores during treatment. During the last 8 weeks of treatment, a significantly larger portion of patients with radiological response reported sustained or better QoL scores than those with no radiological response. In Paper III, we investigated the effect of inter physician variation on the delineation of target volumes in gastric cancer patients treated with perioperative chemoradiotherapy (CRT). Despite the use of a delineation atlas, we found a large variation in CTV and PTV volumes. There was only a small variation in target coverage and doses to organs at risk (OARs) in the corresponding plans. In Paper IV, we compared proton therapy to modern photon radiotherapy with respect to doses to OARs in gastric cancer patients treated with perioperative CRT. Protons offered significantly lower doses to the left kidney, liver, and spinal cord, and statistically lower risks for all types and malignant secondary neoplasms compared to photons. In Paper V, we evaluated the importance of daily anatomical variations, i.e. intestinal gas filling, on the dose distribution of proton beam therapy. The effect of intestinal gas variations on the PTV/CTV coverage was large. The sparing effect of protons was, however, sustained or the dose to the OARs did not significantly exceed the dose delivered with photons. In conclusion, sequential chemotherapy and proton radiotherapy are attractive alternatives in the treatment of gastric cancer. Standardization of target definitions in CRT, e.g. by reducing the inter physician variation, is important and should also be further investigated