scholarly journals Co-dimension two bifurcations analysis of a delayed tumor model with Allee effect

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Qinrui Dai
Keyword(s):  
Growth Rate ◽  
Hopf Bifurcation ◽  
Tumor Growth ◽  
Allee Effect ◽  
Immune Cell ◽  
Functional Differential Equations ◽  
Tumor Model ◽  
Point Of View ◽  
Tumor Growth Rate ◽  
Tumor Models

AbstractThe mathematical model has become an important means to study tumor treatment and has developed with the discovery of medical phenomena. In this paper, we establish a delayed tumor model, in which the Allee effect is considered. Different from the previous similar tumor models, this model is mainly studied from the point of view of stability and co-dimension two bifurcations, and some nontrivial phenomena and conclusions are obtained. By calculation, there are at most two positive equilibria in the system, and their stability is investigated. Based on these, we find that the system undergoes Bautin bifurcation, zero-Hopf bifurcation, and Hopf–Hopf bifurcation with time delay and tumor growth rate as bifurcation parameters. The interesting thing is that there is a Zero-Hopf bifurcation, which is not common in tumor models, making abundant dynamic phenomena appear in the system. By using the bifurcation theory of functional differential equations, we calculate the normal form of these Co-dimension two bifurcations. Finally, with the aid of MATLAB package DDE-BIFTOOL, some numerical simulations have been performed to support our theoretical results. In particular, we obtain the bifurcation diagram of the system in the two parameter plane and divide its regions according to the bifurcation curves. Meanwhile, the phenomena of multistability and periodic coexistence of some regions can be also demonstrated. Combined with the simulation results, we can know that when the tumor growth rate and the delay of immune cell apoptosis are small, the tumor may tend to be stable, and vice versa.

scholarly journals Tumor growth characteristics of the Walker 256 AR tumor, a regressive variant of the rat Walker 256 A tumor

2010 ◽  
Vol 53 (5) ◽  
pp. 1101-1108 ◽  
Author(s):  
Fernando Guimarães ◽  
Alessandra Soares Schanoski ◽  
Tereza Cristina Samico Cavalcanti ◽  
Priscila Bianchi Juliano ◽  
Ana Neuza Viera-Matos ◽  
...  
Keyword(s):  
Growth Rate ◽  
Tumor Growth ◽  
Wistar Rats ◽  
Tumor Regression ◽  
Growth Characteristics ◽  
Tumor Growth Rate ◽  
Continuous Growth ◽  
Tumor Bearing ◽  
Walker 256 ◽  
Complete Tumor

The present study aimed at characterizing the subcutaneous development of the Walker 256 (W256) AR tumor, a regressive variant of the rat W256 A tumor. Wistar rats were injected subcutaneously with 4x10(6) W256 A or W256 AR tumor cells. The development of tumors was evaluated daily by percutaneous measurements. None of the W256 A tumors (n=20) regressed, but 62% of the W256 AR tumor-bearing rats (n=21) underwent complete tumor regression within 35 days. Continuous growth of AR tumors was characterized by an increase of the tumor growth rate from day 12, which reached values above 1.0 g/day, and were significantly higher (p<0.05) than those of the regressive AR tumors. Immunosuppression by irradiation before subcutaneous injection of AR cells completely abrogated tumor regression and was associated with severe metastatic dissemination. Daily evaluation of the tumor growth rate enabled the discrimination, in advance, between continuously growing tumors and those that regressed later on.

Targeted Treatment of Experimental Spinal Cord Glioma With Dual Gene-Engineered Human Neural Stem Cells

Neurosurgery ◽  
2015 ◽  
Vol 79 (3) ◽  
pp. 481-491 ◽  
Author(s):  
Alexander E. Ropper ◽  
Xiang Zeng ◽  
Hariprakash Haragopal ◽  
Jamie E. Anderson ◽  
Zaid Aljuboori ◽  
...  
Keyword(s):  
Spinal Cord ◽  
Stem Cells ◽  
Growth Rate ◽  
Neural Stem Cells ◽  
Tumor Growth ◽  
Rat Model ◽  
Weight Bearing ◽  
Tumor Growth Rate ◽  
Intramedullary Spinal Cord ◽  
Human Neural Stem Cells

Abstract BACKGROUND There are currently no satisfactory treatments or experimental models showing autonomic dysfunction for intramedullary spinal cord gliomas (ISCG). OBJECTIVE To develop a rat model of ISCG and investigate whether genetically engineered human neural stem cells (F3.hNSCs) could be developed into effective therapies for ISCG. METHODS Immunodeficient/Rowett Nude rats received C6 implantation of G55 human glioblastoma cells (10K/each). F3.hNSCs engineered to express either cytosine deaminase gene only (i.e., F3.CD) or dual genes of CD and thymidine kinase (i.e., F3.CD-TK) converted benign 5-fluorocytosine and ganciclovir into oncolytic 5-fluorouracil and ganciclovir-triphosphate, respectively. ISCG rats received injection of F3.CD-TK, F3.CD, or F3.CD-TK debris near the tumor epicenter 7 days after G55 seeding, followed with 5-FC (500 mg/kg/5 mL) and ganciclovir administrations (25 mg/kg/1 mL/day × 5/each repeat, intraperitoneal injection). Per humane standards for animals, loss of weight-bearing stepping in the hindlimb was used to determine post-tumor survival. Also evaluated were autonomic functions and tumor growth rate in vivo. RESULTS ISCG rats with F3.CD-TK treatment survived significantly longer (37.5 ± 4.78 days) than those receiving F3.CD (21.5 ± 1.75 days) or F3.CD-TK debris (19.3 ± 0.85 days; n = 4/group; P &lt;.05, median rank test), with significantly improved autonomic function and reduced tumor growth rate. F3.DC-TK cells migrated diffusively into ISCG clusters to mediate oncolytic effect. CONCLUSION Dual gene-engineered human neural stem cell regimen markedly prolonged survival in a rat model that emulates somatomotor and autonomic dysfunctions of human cervical ISCG. F3.CD-TK may provide a novel approach to treating clinical ISCG.

scholarly journals Tumor Growth Rate Determines the Timing of Optimal Chronomodulated Treatment Schedules

2010 ◽  
Vol 6 (3) ◽  
pp. e1000712 ◽  
Author(s):  
Samuel Bernard ◽  
Branka Čajavec Bernard ◽  
Francis Lévi ◽  
Hanspeter Herzel
Keyword(s):  
Growth Rate ◽  
Tumor Growth ◽  
Tumor Growth Rate

Efficacy of KD033, an anti-human-PD-L1-IL-15 bispecific protein, in human-PD-L1 positive and negative murine tumor models.

2021 ◽  
Vol 39 (15_suppl) ◽  
pp. e14556-e14556
Author(s):  
Stella Martomo ◽  
Dan Lu ◽  
Zhanna Polonskaya ◽  
Xenia Luna ◽  
Zhikai Zhang ◽  
...  
Keyword(s):  
Fusion Protein ◽  
Tumor Growth ◽  
Nk Cells ◽  
Immune Cell ◽  
Clinical Stage ◽  
Tumor Models ◽  
T Cell Infiltration ◽  
Negative Tumor ◽  
Tumor Expression ◽  
The Impact

e14556 Background: KD033 is a clinical-stage bispecific fusion molecule consisting of a high-affinity anti-human-PD-L1 antibody and human IL-15. Preclinical studies have demonstrated that targeting IL-15 with anti-PD-L1 antibody resulted in increased efficacy, safety and maximal tolerated dose of the fusion protein compared to administration of free IL-15, as well as reduction of tumor growth in both PD-L1 positive and negative tumor models (1). The goal of the current study is to directly compare KD033 efficacy when PD-L1 is present or absent on the surface of the same tumor. Methods: KD033 was administered in the human-PD-L1/PD-1 transgenic C57/Bl6 mice subcutaneously transplanted with human-PD-L1 positive and negative MC38 colon carcinoma cells. This animal model allowed the evaluation of the impact of the presence or absence of human-PD-L1 expression on the tumor cell surface without altering human-PD-L1 expression on immune cells. Results: KD033 treatment resulted in significant tumor growth reduction in both human-PD-L1 positive and negative MC38 tumors. Analysis of peripheral immune cell populations showed similar increases of CD8 T and NK cells between human-PD-L1 positive and negative MC38- bearing mice after KD033 administration. Immunohistochemistry demonstrated a significant increase in CD8 T-cell infiltration into the human-PD-L1 positive MC38 tumors, whereas NK cells infiltration was more pronounced in the human-PD-L1 negative MC38 tumors. Analysis of tumor gene transcription after KD033 treatment highlighted differences in gene signatures between human-PD-L1 positive and negative MC38 tumors following KD033 treatment. Conclusions: These results showed that the efficacy of anti-PD-L1-IL-15 fusion protein is not limited to PD-L1 tumor expression as KD033 was efficacious in both PD-L1 positive and negative tumors. Mol Cancer Ther February 1 2021 (20) (2) 347-356; DOI: 10.1158/1535-7163.MCT-20-0457

A nanoemulsion of an anti-oxidant synergy formulation reduces tumor growth rate in neuroblastoma-bearing nude mice

2007 ◽  
Vol 66 (5) ◽  
pp. 428
Author(s):  
Fonghsu Kuo ◽  
Timothy Kotyla ◽  
Thomas Wilson ◽  
Lydia Kifle ◽  
Thomai Panagiotou ◽  
...  
Keyword(s):  
Growth Rate ◽  
Tumor Growth ◽  
Nude Mice ◽  
Tumor Growth Rate ◽  
Anti Oxidant

scholarly journals Performance of Low-dose CT Screening for Detecting Lung Cancer at the Early Stage and the Estimated Tumor Growth Rate According to the Smoking Status/Age

Haigan ◽  
2014 ◽  
Vol 54 (7) ◽  
pp. 937-946
Author(s):  
Shusuke Sone ◽  
Ryoichi Kondo ◽  
Keiko Ishii ◽  
Takayuki Honda ◽  
Kazuo Yoshida ◽  
...  
Keyword(s):  
Lung Cancer ◽  
Growth Rate ◽  
Tumor Growth ◽  
Low Dose ◽  
Early Stage ◽  
Smoking Status ◽  
Tumor Growth Rate ◽  
Ct Screening ◽  
Low Dose Ct

scholarly journals 68Gallium-DOTATATE PET in meningioma: A reliable predictor of tumor growth rate?

2016 ◽  
Vol 18 (7) ◽  
pp. 1021-1027 ◽  
Author(s):  
Michael Sommerauer ◽  
Jan-Karl Burkhardt ◽  
Karl Frontzek ◽  
Elisabeth Rushing ◽  
Alfred Buck ◽  
...  
Keyword(s):  
Growth Rate ◽  
Tumor Growth ◽  
Tumor Growth Rate ◽  
Reliable Predictor
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