2013-06-05
Marek Bodnar (Uniwersytet Warszawski)
Traveling waves in reaction-diffusion equations with time delay
Abstract: I will talk about traveling waves in reaction diffusion systems with delay. On the basis on some simple equation I will show problems that arise when looking for traveling fronts in equation with delay. In fact, the system for the shape of wave front can be delay differential system and finding an appropriate solution is more difficult han is the case without delay and it is necessary to use Fixed Point Theorem or some interaction scheme.
2013-05-15
Urszula Ledzewicz (Southern Illinois University Edwardsville USA)
Coauthors: Heinz Shaettler, Washington University St. Louis USA
Timing and Dosage of Anti-Cancer Drug Therapies: An Optimal Control Approach
Abstract: A systematic study of cancer treatment requires that we take into account not only the cancerous cells and their growth, but also various aspects of the tumor microenvironment. Its elemets include various types of cancer cells, sensitive and resistant to the treatment, healthy cells, tumor vasculature, immune system and more. We shell discuss mathematical models that describe the dynamics of tumor growth in relation to its supproting vasculature under reciprocal angiogenic signaling. For such models, in addition to standard direct treatments that kill cancer cells, one can introduce the second indirect treatment by means of angiogenic inhibitors that target the tumor vasculature. A second indirect approach is to consider the interactions between the tumor and the immune system, inclusing tumor surveillance. Here a classical, minimally parametrized model of tumor-immune interactions will be discussed in connection with optimizing the treatment that combined traditional chemotherapy with a stimulatory effect of the immune system. We will also outline some future work on a more complex model wich encompasses more elements of the microenvironment and multi-target therapies. This will naturally lead to the topic of metronomic chemotherapy, a new direction in cancer treatment where the various aspects of the tumor microenvironment being targeted by one cytotoxic drug applied accord to a properly chosen "metronomic" protocol which involves between 20% and 80% MTD. It has been observed in experimental studies that such treatment has lower toxicity, lowe drug resistance and in addition exhibits anti-agiogenic and immune system stimulatory effects. The challenges concerning the modeling and mathematical analysis for metronomic chemotherapy will be addressed.
2013-04-17
Urszula Foryś (Uniwersytet Warszawski)
News from IMBM: modelling of prostate cancer immunotherapy
Abstract: During my visit in IMBM in January I have discussed the idea of new project with the team of Prof. Zvia Agur. We have decided to focus on the modelling of prostate cancer immunotherapy. I will present the model which was published in PlosOne recently. It is the system of several ODEs, however most of them are linear. It occurs that for one boost of immunotherapy this large system has simple, in fact one-dimensional dynamics. I will also present the analysis for impulsive treatment and give conditions sufficient to cure. At the end I will focus on the proposed changes in the model equations that are of our interest now.
2013-04-10
Michal Komorowski
The concept of information at the interface between statistics and systems biology
Abstract: The purpose of the talk is to discuss intricacies of quantifying information in some problems arising at the interface between statistic and biology. Behaviour generated by interacting molecules, cells or tissues is not random but focuses on sustaining life processes. Sustaining life, however, is to the large extend based on information storage, transmission and processing with examples ranging from the iconic DNA double-helix through signal transduction pathways to proteomic and metabolic networks. Understanding how information is processed in living cells and organism is therefore one of the crucial elements to understand how life is sustained.
The concept of information however is also inherent to statistics with Fisher and Shannon as most well known concepts. It has been originally associated with a precision parameters can be estimated in an experiment. Alternative approach by C. Shannon arose on the basic of communication theory and was later assimilated by statistical sciences. In the talk I will discuss relationships between such objects as posterior distribution, Shannon Information, Fisher Information and Jeffrey's prior. Using examples of experimental design techniques and signal transduction pathways I will demonstrate how statistical theory can be used to better understand biological systems at the cellular level.
English
Polski