Treatment of endometrial cancer from 2000 to 2020 in Germany: a retrospective population based cohort study.

PURPOSE: Endometrial cancer (EC) is one of the most common malignancies among women in western countries. This study aimed to assess data on patient treatment in Germany throughout two decades to evaluate the development and effect of surgery, radiation, and chemotherapy. METHODS: This retrospective registry study included 34,349 EC patients diagnosed between 2000 and 2020. Patients were classified into five risk groups. Overall survival was analyzed by Kaplan-Meier method as well as univariable and multivariable Cox regression to evaluate risk factors and treatment options. RESULTS: Over the study period, minimal invasive surgery was used more often compared to open surgery and was associated with better overall survival. Patients with advanced EC were more likely to receive multimodal therapy. Patients with intermediate risk EC had a good prognosis upon surgery, which further improved when radiotherapy was added. High-risk patients showed poorer prognosis but clearly benefited from additional radiotherapy. Survival of elderly high-risk patients with a non-endometrioid histology was improved when chemotherapy was added to surgery and radiotherapy. CONCLUSION: Our study includes a large analysis of data from German clinical cancer registries on the care of endometrial cancer during two decades. We observed an increase of minimal invasive surgery. There is evidence that minimal invasive surgery is not inferior to open surgery. Adjuvant radio- and chemotherapy further improves survival depending on risk group and age.

Some aspects of the anemia of chronic disorders modeled and analyzed by petri net based approach.

Anemia of chronic disorders is a very important phenomenon and iron is a crucial factor of this complex process. To better understand this process and its influence on some other factors we have built a mathematical model of the human body iron homeostasis, which possibly most exactly would reflect the metabolism of iron in the case of anemia and inflammation. The model has been formulated in the language of Petri net theory, which allows for its simulation and precise analysis. The obtained results of the analysis of the model's behavior, concerning the influence of anemia and inflammation on the transferrin receptors, and hepcidin concentration changes are the valuable complements to the knowledge following from clinical research. This analysis is one of the first attempts to investigate properties and behavior of a not fully understood biological system on a basis of its Petri net based model.

Modularization of biochemical networks based on classification of Petri net t-invariants.

BACKGROUND: Structural analysis of biochemical networks is a growing field in bioinformatics and systems biology. The availability of an increasing amount of biological data from molecular biological networks promises a deeper understanding but confronts researchers with the problem of combinatorial explosion. The amount of qualitative network data is growing much faster than the amount of quantitative data, such as enzyme kinetics. In many cases it is even impossible to measure quantitative data because of limitations of experimental methods, or for ethical reasons. Thus, a huge amount of qualitative data, such as interaction data, is available, but it was not sufficiently used for modeling purposes, until now. New approaches have been developed, but the complexity of data often limits the application of many of the methods. Biochemical Petri nets make it possible to explore static and dynamic qualitative system properties. One Petri net approach is model validation based on the computation of the system's invariant properties, focusing on t-invariants. T-invariants correspond to subnetworks, which describe the basic system behavior.With increasing system complexity, the basic behavior can only be expressed by a huge number of t-invariants. According to our validation criteria for biochemical Petri nets, the necessary verification of the biological meaning, by interpreting each subnetwork (t-invariant) manually, is not possible anymore. Thus, an automated, biologically meaningful classification would be helpful in analyzing t-invariants, and supporting the understanding of the basic behavior of the considered biological system. METHODS: Here, we introduce a new approach to automatically classify t-invariants to cope with network complexity. We apply clustering techniques such as UPGMA, Complete Linkage, Single Linkage, and Neighbor Joining in combination with different distance measures to get biologically meaningful clusters (t-clusters), which can be interpreted as modules. To find the optimal number of t-clusters to consider for interpretation, the cluster validity measure, Silhouette Width, is applied. RESULTS: We considered two different case studies as examples: a small signal transduction pathway (pheromone response pathway in Saccharomyces cerevisiae) and a medium-sized gene regulatory network (gene regulation of Duchenne muscular dystrophy). We automatically classified the t-invariants into functionally distinct t-clusters, which could be interpreted biologically as functional modules in the network. We found differences in the suitability of the various distance measures as well as the clustering methods. In terms of a biologically meaningful classification of t-invariants, the best results are obtained using the Tanimoto distance measure. Considering clustering methods, the obtained results suggest that UPGMA and Complete Linkage are suitable for clustering t-invariants with respect to the biological interpretability. CONCLUSION: We propose a new approach for the biological classification of Petri net t-invariants based on cluster analysis. Due to the biologically meaningful data reduction and structuring of network processes, large sets of t-invariants can be evaluated, allowing for model validation of qualitative biochemical Petri nets. This approach can also be applied to elementary mode analysis.

An analysis of the Petri net based model of the human body iron homeostasis process.

In the paper a Petri net based model of the human body iron homeostasis is presented and analyzed. The body iron homeostasis is an important but not fully understood complex process. The modeling of the process presented in the paper is expressed in the language of Petri net theory. An application of this theory to the description of biological processes allows for very precise analysis of the resulting models. Here, such an analysis of the body iron homeostasis model from a mathematical point of view is given.

Petri net based model of the body iron homeostasis.

The body iron homeostasis is a not fully understood complex process. Despite the fact that some components of this process have been described in the literature, the complete model of the whole process has not been proposed. In this paper a Petri net based model of the body iron homeostasis is presented. Recently, Petri nets have been used for describing and analyzing various biological processes since they allow modeling the system under consideration very precisely. The main result presented in the paper is twofold, i.e., an informal description of the main part of the whole iron homeostasis process is described, and then it is also formulated in the formal language of Petri net theory. This model allows for a possible simulation of the process, since Petri net theory provides a lot of established analysis techniques.

Application of Petri net based analysis techniques to signal transduction pathways.

BACKGROUND: Signal transduction pathways are usually modelled using classical quantitative methods, which are based on ordinary differential equations (ODEs). However, some difficulties are inherent in this approach. On the one hand, the kinetic parameters involved are often unknown and have to be estimated. With increasing size and complexity of signal transduction pathways, the estimation of missing kinetic data is not possible. On the other hand, ODEs based models do not support any explicit insights into possible (signal-) flows within the network. Moreover, a huge amount of qualitative data is available due to high-throughput techniques. In order to get information on the systems behaviour, qualitative analysis techniques have been developed. Applications of the known qualitative analysis methods concern mainly metabolic networks. Petri net theory provides a variety of established analysis techniques, which are also applicable to signal transduction models. In this context special properties have to be considered and new dedicated techniques have to be designed. METHODS: We apply Petri net theory to model and analyse signal transduction pathways first qualitatively before continuing with quantitative analyses. This paper demonstrates how to build systematically a discrete model, which reflects provably the qualitative biological behaviour without any knowledge of kinetic parameters. The mating pheromone response pathway in Saccharomyces cerevisiae serves as case study. RESULTS: We propose an approach for model validation of signal transduction pathways based on the network structure only. For this purpose, we introduce the new notion of feasible t-invariants, which represent minimal self-contained subnets being active under a given input situation. Each of these subnets stands for a signal flow in the system. We define maximal common transition sets (MCT-sets), which can be used for t-invariant examination and net decomposition into smallest biologically meaningful functional units. CONCLUSION: The paper demonstrates how Petri net analysis techniques can promote a deeper understanding of signal transduction pathways. The new concepts of feasible t-invariants and MCT-sets have been proven to be useful for model validation and the interpretation of the biological system behaviour. Whereas MCT-sets provide a decomposition of the net into disjunctive subnets, feasible t-invariants describe subnets, which generally overlap. This work contributes to qualitative modelling and to the analysis of large biological networks by their fully automatic decomposition into biologically meaningful modules.

New insights into the human body iron metabolism analyzed by a Petri net based approach.

Iron homeostasis is one of the most important biochemical processes in the human body. Despite this fact, the process is not fully understood and until recently only rough descriptions of parts of the process could be found in the literature. Here, an extension of the recently published formal model of the main part of the process is presented. This extension consists in including all known mechanisms of hepcidin regulation. Hepcidin is a hormone synthesized in the liver which is mainly responsible for an inhibition of iron absorption in the small intestine during an inflammatory process. The model is expressed in the language of Petri net theory which allows for its relatively easy analysis and simulation.