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CRITICALPOINT ANALYSIS FOR THREEVARIABLE CANCER ANGIOGENESIS MODELS
A computer algorithm describing the process of vessel formation and maturation, and its use for predicting the effects of antiangiogenic and antimaturation therapy on vascular tumor growth
Tumor Development under Angiogenic Signaling: A Dynamical Theory of Tumor Growth, Treatment Response, and Postvascular Dormancy1
The growth law of primary breast cancer as inferred from mammography screening trials data
ANGIOGENESIS MODEL WITH CARRYING CAPACITY DEPENDING ON VESSEL DENSITY
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HOPF POINT ANALYSIS FOR ANGIOGENESIS MODELS
HOPF POINT ANALYSIS FOR ANGIOGENESIS MODELS,Z. AGUR,L. ARAKELYAN,P. DAUGULIS,Y. GINOSAR
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HOPF POINT ANALYSIS FOR ANGIOGENESIS MODELS
(
Citations: 29
)
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Z. AGUR
,
L. ARAKELYAN
,
P. DAUGULIS
,
Y. GINOSAR
In this paper we present several ODE systems encoding the most essential observations and assumptions about the complex hierarchical inter active processes of tumor neovascularization (angiogenesis). From experi mental results we infer that a significant marker of tumor aggressiveness is the oscillatory behavior of tumor size, which is driven by its vascularization dynamics. To study the forces underlying these
oscillations
we perform a Hopf point analysis of the angiogenesis models. In the analyzed models Hopf points appear if and only if a nontrivial set of timedelays is introduced into the tu mor proliferation or the neovascularization process. We suggest to examine in laboratory experiments how to employ these results for containing cancer growth.
Published in 2004.
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Citation Context
(11)
...Rational and systematic planning of anticancer therapy may be directed by mathematical modeling and computeraided analysis, which provides a better understanding of the involved dynamics. Over the past 25 years, mathematical modeling strategies have been applied in oncologyfocused studies investigating tumor progression, angiogenesis and interactions with the immune system
...
Moran Elishmereni
,
et al.
An Integrated Disease/Pharmacokinetic/Pharmacodynamic Model Suggests I...
...For example, in [
33
], we have introduced and analysed several alternative general tumor angiogenesis models (with/without vascular maturation or with/without the effects of growth factors)...
...While it is recognized that timedelay will often elicit Hopf points, in [
33
], it was shown that the latter were to be found in any angiogenesis model with timedelay...
IJ Stamper
,
et al.
Oscillatory dynamics in a model of vascular tumour growth  implicatio...
..., tumorassociated angiogenesis
...
Natalie Kronik
,
et al.
Predicting Outcomes of Prostate Cancer Immunotherapy by Personalized M...
...The continuous models generally deflne three major processes: tumor growth, vascularization and protein proliferation which have been fully analyzed in [
1
,9].The dynamics of vessel compartments is assumed to be a superposition of four processes, some are contrasting some of the others: formation of immature vessels, regression of immature vessels, maturation of immature vessels, and destabilization of mature vessels into immature vessels...
...It was shown in [
1
,4,7] that for models without time delays, no Hopf points occur...
...The time dependent variables of angiogenesis models are the number of tumor cells or tumor size denoted N, the amount of growth factors like proteins P supplying the tumor, the volume of blood in mature and immature vessels feeding the tumor denoted V . A threedimensional model with no time delay is given by the following equations [
1
,2,4,9]...
...1 1+ek(x+s) [
1
,4] of MichaelsMenten type dx 2...
...This model is modifled in [
1
] by assuming that the protein is consumed by growing vessels...
...It was shown in [
1
,4] that there exist no Hopf points in these models and the oscillations observed in the experiments can not be detected in the models without time delays like (1)...
...After introducing time delays, the threedimensional model (1) becomes [
1
,4,7,9]...
...In order to make the models more realistic, more compartments are introduced for representing complex vascularity and protein efiects[
1
,9]...
...The protein denoted by P is replaced by two speciflc proteins, namely vascular endothelial growth factor(VGEF), denoted P1 and angiopoietin1(Ang1), denoted P2. It was assumed in [
1
,9] that VEGF is produced by the tumor at a rate sigmoidally dependent on the efiective vessel density and decays at a constant rate ‐1, and that Ang1 is produced by the tumor at a constant rate fi and decays at a constant rate ‐2. The extension of the three ...
... vascular endothelial growth factor(VGEF), denoted P1 and angiopoietin1(Ang1), denoted P2. It was assumed in [1,9] that VEGF is produced by the tumor at a rate sigmoidally dependent on the efiective vessel density and decays at a constant rate ‐1, and that Ang1 is produced by the tumor at a constant rate fi and decays at a constant rate ‐2. The extension of the three dimensional (5) to flve dimensional models with time delays in [
1
,9] are ...
...It was demonstrated in [
1
,9] that the ode systems (5) and (6) admit a Hopf bifurcation point if and only if at least one of the delays is nonzero...
...The basic assumptions taken from the literature to build our model are as follows [
1
,2]:...
...We flrst compared the our hybrid piecewise linear model(HDS) with the three variable delayed difierential equation(DDE) model in [
1
] for the tumor size...
...In Figure 2 we have the simulation results for the tumor size plotted, where dashed lines represents the numerical results for the DDE model in [
1
], the solid line the results according to our model HDS...
Bülent Karasözen
,
et al.
A model of angiogenesis by hybrid systems with delay on the piecewise ...
...Mathematical models for tumor progression (
46
), cancer therapy (710), and related...
...assumptions is described in detail elsewhere (
4
, 5, 24)...
Boris Gorelik
,
et al.
Efficacy of Weekly Docetaxel and Bevacizumab in Mesenchymal Chondrosar...
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Citations
(29)
An Integrated Disease/Pharmacokinetic/Pharmacodynamic Model Suggests Improved Interleukin21 Regimens Validated Prospectively for Mouse Solid Cancers
Moran Elishmereni
,
Yuri Kheifetz
,
Henrik Søndergaard
,
Rune Viig Overgaard
,
Zvia Agur
Journal:
PLOS Computational Biology  PLOS COMPUT BIOL
, vol. 7, no. 9, 2011
Towards microscopic ab initio calculations of astrophysical S factors
Thomas Neff
,
Hans Feldmeier
,
Karlheinz Langanke
Journal:
Progress in Particle and Nuclear Physics  PROG PART NUCL PHYS
, vol. 66, no. 2, pp. 341345, 2011
Oscillatory dynamics in a model of vascular tumour growth  implications for chemotherapy
(
Citations: 4
)
IJ Stamper
,
PK Maini
,
HM Byrne
Journal:
Biology Direct  BIOL DIRECT
, vol. 5, no. 1, pp. 2717, 2010
Predicting Outcomes of Prostate Cancer Immunotherapy by Personalized Mathematical Models
(
Citations: 1
)
Natalie Kronik
,
Yuri Kogan
,
Moran Elishmereni
,
Karin HaleviTobias
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Stanimir VukPavlovic
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Zvia Agur
,
Sven G. Meuth
Journal:
PLOS One
, vol. 5, no. 12, 2010
Chemotherapy of vascularised tumours: Role of vessel density and the effect of vascular “pruning”
(
Citations: 1
)
Alberto d’Onofrio
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Alberto Gandolfi
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Journal of Theoretical Biology  J THEOR BIOL
, vol. 264, no. 2, pp. 253265, 2010