Introduction of hypermatrix and operator notation into a discrete mathematics simulation model of malignant tumour response to therapeutic schemes in vivo. Some operator properties

Stamatakos, GS; Dionysiou, DD

dc.contributor.author	Stamatakos, GS	en
dc.contributor.author	Dionysiou, DD	en
dc.date.accessioned	2014-03-01T01:58:45Z
dc.date.available	2014-03-01T01:58:45Z
dc.date.issued	2009	en
dc.identifier.issn	11769351	en
dc.identifier.uri	https://dspace.lib.ntua.gr/xmlui/handle/123456789/28715
dc.relation.uri	http://www.scopus.com/inward/record.url?eid=2-s2.0-77649251042&partnerID=40&md5=9e63028ad400b7496bbb68e7044a82cf	en
dc.subject	Cancer multiscale modeling	en
dc.subject	Computer models	en
dc.subject	Hypermatrix	en
dc.subject	In silico oncology	en
dc.subject	Oncosimulator	en
dc.subject	Operator notation	en
dc.subject	Radiobiology	en
dc.subject	Tumour growth	en
dc.subject	Tumour response to treatment	en
dc.subject.other	algorithm	en
dc.subject.other	article	en
dc.subject.other	cancer radiotherapy	en
dc.subject.other	computer program	en
dc.subject.other	mathematical model	en
dc.subject.other	simulation	en
dc.subject.other	treatment response	en
dc.subject.other	tumor growth	en
dc.title	Introduction of hypermatrix and operator notation into a discrete mathematics simulation model of malignant tumour response to therapeutic schemes in vivo. Some operator properties	en
heal.type	journalArticle	en
heal.publicationDate	2009	en
heal.abstract	The tremendous rate of accumulation of experimental and clinical knowledge pertaining to cancer dictates the development of a theoretical framework for the meaningful integration of such knowledge at all levels of biocomplexity. In this context our research group has developed and partly validated a number of spatiotemporal simulation models of in vivo tumour growth and in particular tumour response to several therapeutic schemes. Most of the modeling modules have been based on discrete mathematics and therefore have been formulated in terms of rather complex algorithms (e.g. in pseudocode and actual computer code). However, such lengthy algorithmic descriptions, although sufficient from the mathematical point of view, may render it difficult for an interested reader to readily identify the sequence of the very basic simulation operations that lie at the heart of the entire model. In order to both alleviate this problem and at the same time provide a bridge to symbolic mathematics, we propose the introduction of the notion of hypermatrix in conjunction with that of a discrete operator into the already developed models. Using a radiotherapy response simulation example we demonstrate how the entire model can be considered as the sequential application of a number of discrete operators to a hypermatrix corresponding to the dynamics of the anatomic area of interest. Subsequently, we investigate the operators' commutativity and outline the ""summarize and jump"" strategy aiming at efficiently and realistically address multilevel biological problems such as cancer. In order to clarify the actual effect of the composite discrete operator we present further simulation results which are in agreement with the outcome of the clinical study RTOG 83-02, thus strengthening the reliability of the model developed. © the authors, licensee Libertas Academica Ltd.	en
heal.journalName	Cancer Informatics	en
dc.identifier.volume	7	en
dc.identifier.spage	239	en
dc.identifier.epage	251	en