Final Report Summary - ANGIODEL (Influence of delays on the models of angiogenesis process and immunotherapy of cancer)
Reintegration project "Influence of delays on the models of angiogenesis process and immunotherapy of cancer" was a 3 years project implemented by Dr. M. Piotrowska and Prof. U. Forys (project coordinator) at the Faculty of Mathematics, Informatics and Mechanics, University of Warsaw (UW), co-financed by European Commission.
Tumour growth, dynamics and interactions with an immune system are very important processes from medical point of view, and therefore it is also important to consider it as a topic of mathematical modelling and analysis. In the project we mainly focused on the models of tumour angiogenesis and immunotherapy of cancer known from the literature and studied the influence of time delays on their dynamics. It is known that the signalling pathways or interactions between the immune system and tumour cells can be modelled either by large systems of ordinary differential equations (ODEs) or one can reduce these systems by assuming that the loops present in the system can be expressed by the functions of other variables but with delays reflecting time lags in considered processes. Therefore, the considered models described by systems of ODEs where modified to the systems of delay differential equations. Such modification was considered e. g. in case of the Hahnfeldt et al. model of tumour angiogenesis which is one of the widely accepted models of this process. Additionally, the whole family of systems describing the vessel formation was considered. Moreover, the analytical and numerical analysis of the Gompertz equation, which is the basis of the Hahnfeldt type and a number of other models, with two delays was also done.
Mathematical modelling of such processes can bring some new knowledge of the disease dynamics and treatment, that is important especially in case of non-standard treatments as immunotherapy which is very expensive and may be not efficient. However, there are also promising experiments showing the effectiveness of such type of therapy for specific cancers. Kogan et al. (2010) showed that the effective immunotherapy can be used in case of very aggressive brain cancer GBM. Therefore, within the project different aspects of immunotherapy of MGs were studied, where the immune reactions were considered as delayed with respect to the stimuli.
The main part of the project was focused on the study of the time delays influence on the dynamics of solutions to systems of differential equations describing mentioned phenomena, especially on the models with at least two delays. From mathematical point of view the dynamics of systems with several delays was not as well-known as in case of one discrete delay and such analysis was a challenging problem and additionally it brought also some insight to the medical knowledge and the treatment of cancer.
Within project 6 papers in the high ranked international journals, 4 in the peer-reviewed conferences proceedings and 1 preprint were published. Additionally, 2 papers were submitted to the international journals and 4 manuscripts are in preparation. Dr. Piotrowska presented the obtained results on seminars, international and national scientific events. She co-organised the international and national workshops and conferences.
During the grant period Dr. Piotrowska has been awarded with: Monash University Visiting Grant, 1 year Research Scholar for the Best Young Doctor within Modern University, co-financed by the European Social Fund and by the Foundation for Polish Science with 1 year scholarship within the START Programme for young scientists.
Dr. Piotrowska filled the obligations arising from the grant contract including the teaching obligations. Hence, we affirm with certainty that the reintegration of Dr. Piotrowska has been successful and resulted in the hiring of Dr. Piotrowska at the UW as the full time assistant professor.
Contact:
Dr. Piotrowska: monika@mimuw. edu. pl
Prof. Forys: urszula@mimuw. edu. Pl
Tumour growth, dynamics and interactions with an immune system are very important processes from medical point of view, and therefore it is also important to consider it as a topic of mathematical modelling and analysis. In the project we mainly focused on the models of tumour angiogenesis and immunotherapy of cancer known from the literature and studied the influence of time delays on their dynamics. It is known that the signalling pathways or interactions between the immune system and tumour cells can be modelled either by large systems of ordinary differential equations (ODEs) or one can reduce these systems by assuming that the loops present in the system can be expressed by the functions of other variables but with delays reflecting time lags in considered processes. Therefore, the considered models described by systems of ODEs where modified to the systems of delay differential equations. Such modification was considered e. g. in case of the Hahnfeldt et al. model of tumour angiogenesis which is one of the widely accepted models of this process. Additionally, the whole family of systems describing the vessel formation was considered. Moreover, the analytical and numerical analysis of the Gompertz equation, which is the basis of the Hahnfeldt type and a number of other models, with two delays was also done.
Mathematical modelling of such processes can bring some new knowledge of the disease dynamics and treatment, that is important especially in case of non-standard treatments as immunotherapy which is very expensive and may be not efficient. However, there are also promising experiments showing the effectiveness of such type of therapy for specific cancers. Kogan et al. (2010) showed that the effective immunotherapy can be used in case of very aggressive brain cancer GBM. Therefore, within the project different aspects of immunotherapy of MGs were studied, where the immune reactions were considered as delayed with respect to the stimuli.
The main part of the project was focused on the study of the time delays influence on the dynamics of solutions to systems of differential equations describing mentioned phenomena, especially on the models with at least two delays. From mathematical point of view the dynamics of systems with several delays was not as well-known as in case of one discrete delay and such analysis was a challenging problem and additionally it brought also some insight to the medical knowledge and the treatment of cancer.
Within project 6 papers in the high ranked international journals, 4 in the peer-reviewed conferences proceedings and 1 preprint were published. Additionally, 2 papers were submitted to the international journals and 4 manuscripts are in preparation. Dr. Piotrowska presented the obtained results on seminars, international and national scientific events. She co-organised the international and national workshops and conferences.
During the grant period Dr. Piotrowska has been awarded with: Monash University Visiting Grant, 1 year Research Scholar for the Best Young Doctor within Modern University, co-financed by the European Social Fund and by the Foundation for Polish Science with 1 year scholarship within the START Programme for young scientists.
Dr. Piotrowska filled the obligations arising from the grant contract including the teaching obligations. Hence, we affirm with certainty that the reintegration of Dr. Piotrowska has been successful and resulted in the hiring of Dr. Piotrowska at the UW as the full time assistant professor.
Contact:
Dr. Piotrowska: monika@mimuw. edu. pl
Prof. Forys: urszula@mimuw. edu. Pl