THREE TYPES OF SIMPLE DDE'S DESCRIBING TUMOR GROWTH

2007 ◽  
Vol 15 (04) ◽  
pp. 453-471 ◽  
Author(s):  
MAREK BODNAR ◽  
URSZULA FORYŚ
Keyword(s):  
Experimental Data ◽  
Dynamical Systems ◽  
Differential Equations ◽  
Tumor Growth ◽  
Delay Differential Equations ◽  
Ehrlich Ascites Tumor ◽  
Ascites Tumor ◽  
Ehrlich Ascites ◽  
Delay Differential

In this paper, we compare three types of dynamical systems used to describe tumor growth. These systems are defined as solutions to three delay differential equations: the logistic, the Gompertz and the Greenspan types. We present analysis of these systems and compare with experimental data for Ehrlich Ascites tumor in mice.

Die Beeinflussung des Wachstums des Ehrlich-Ascites-Tumors der Maus durch native und mit ultraviolettem Licht bestrahlte heterologe Desoxyribonucleinsäure

1963 ◽  
Vol 18 (7) ◽  
pp. 523-525 ◽  
Author(s):  
Rudolf K. Zahn ◽  
Ekkehard Tiesler
Keyword(s):  
Tumor Growth ◽  
Uv Irradiation ◽  
Deoxyribonucleic Acid ◽  
Tumor Development ◽  
Ehrlich Ascites Tumor ◽  
Ascites Tumor ◽  
Ehrlich Ascites ◽  
Ascites Tumors ◽  
Deoxyribonuclease Activity

1. Deoxyribonuclease activity has been determined by viscosimetry in the serum of the Ehrlich Ascites in the mouse to be equivalent to 2,3 ± 0,7·10-6 g/ml of crystalline beef pancreas DNase.2. Injections of heterologous deoxyribonucleic acid into the Ehrlich Ascites tumor under specified conditions does not alter tumor development.3. The same DNA however becomes strongly inhibitory for tumor growth after UV irradiation.4. Possible implications are discussed.

scholarly journals Cytokine profile of Ehrlich ascites tumor treated withBothrops jararacavenom

2002 ◽  
Vol 11 (4) ◽  
pp. 197-201 ◽  
Author(s):  
Reinaldo J. da Silva ◽  
Márcia G. da Silva ◽  
Lízia C. Vilela ◽  
Denise Fecchio
Keyword(s):  
Tumor Growth ◽  
Antitumor Effect ◽  
Cytokine Profile ◽  
Ehrlich Ascites Tumor ◽  
Enzyme Linked Immunosorbent Assay ◽  
Ascites Tumor ◽  
Ehrlich Ascites ◽  
Tnf Α ◽  
Cytokine Levels ◽  
Eat Cells

We previously demonstrated thatBothrops jararacavenom (BjV) has an antitumor effect on Ehrlich ascites tumor (EAT) cells and induces an increase of polymorphonuclear leukocytes in early stages of tumor growth. It has been reported that this venom presents an important inflammatory effect when inoculated in animal models and in human snakebites, and that cytokine levels have been detected in these cases. To evaluate whether the cytokines can be involved with the suppression of the tumoral growth, we evaluate the cytokine profile in the peritoneal cavity of mice inoculated with EAT cells and treated withBjV. Swiss mice were inoculated with EAT cells by the intraperitoneal route and treated withBjV venom (0.4 mg/kg, intraperitoneally), on the 1st, 4th, 7th, 10th, and 13th day. Mice were evaluated for cytokine levels on the 2nd, 5th, 8th, 11th and 14th day. Analysis was performed using an enzyme-linked immunosorbent assay for interleukin (IL)-1α, IL-2, IL-4, IL-6, IL-10, IL-13, and tumor necrosis factor-α (TNF-α) levels in the peritoneal washing supernatant. Results were analyzed statistically by the Kruskal-Wallis and Dunn's tests at the 5% level of significance. We observed that EAT implantation induces IL-6 production on the 11th and 14th days of tumor growth, IL-10 on the 11th day and TNF-α on the 14th day. The treatment withBjV suppresses production of these cytokines. In addition, IL-13 was produced by animals that were inoculated only with venom on the 11th and 14th days, and by the group inoculated with EAT cells and treated with venom on the 2nd and 14th days. Furthermore, we suggest that the IL-6 detected in the present study is produced by the EAT cells and the suppression of its production could be associated with the antitumor effect ofBjV.

Search for Periodic Orbits in Delay Differential Equations

2014 ◽  
Vol 24 (06) ◽  
pp. 1450084 ◽  
Author(s):  
Romina Cobiaga ◽  
Walter Reartes
Keyword(s):  
Dynamical Systems ◽  
Differential Equations ◽  
Periodic Orbits ◽  
Heuristic Search ◽  
Delay Differential Equations ◽  
Anharmonic Oscillator ◽  
Analysis Method ◽  
Van Der Pol ◽  
Homotopy Analysis ◽  
Delay Differential

In a previous paper, we developed a new way to apply the Homotopy Analysis Method (HAM) in the search for periodic orbits in dynamical systems modeled by ordinary differential equations. This method differs from the original in the heuristic search of the frequencies of the cycles. In this paper, we show that the method can be extended to the search for periodic orbits in delay differential equations. Herein, this methodology is applied twice, firstly in an equation of van der Pol type and secondly in an anharmonic oscillator, both systems with a delayed feedback.

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