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ABSTRACT: The effects of vascular-disrupting treatments on normalization of tumor microvasculature and its microenvironmental flow were investigated, by mathematical modeling and numerical simulation of tumor vascular-disrupting and tumor haemodynamics. Four disrupting approaches were designed according to the abnormal characteristics of tumor microvasculature compared with the normal one. The results predict that the vascular-disrupting therapies could improve tumor microenvironment, eliminate drug barrier and inhibit metastasis of tumor cells to some extent. Disrupting certain types of vessels may get better effects. In this study, the flow condition on the networks with "vascular-disrupting according to flowrate" is the best comparing with the other three groups, and disrupting vessels of lower maturity could effectively enhance fluid transport across vasculature into interstitial space.
Molecular & cellular biomechanics: MCB 06/2012; 9(2):95-125.
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ABSTRACT: To investigate the influence of anti-angiogenesis drug Endostatin on solid tumor angiogenesis, a mathematical model of tumor
angiogenesis was developed with combined influences of local extra-cellular matrix mechanical environment, and the inhibiting
effects of Angiostatin and Endostatin. Simulation results show that Angiostatin and Endostatin can effectively inhibit the
process of tumor angiogenesis, and decrease the number of blood vessels in the tumor. The present model could be used as a
valid theoretical method in the investigation of anti-angiogenic therapy of tumors.
Applied Mathematics and Mechanics 04/2012; 30(10):1247-1254. · 0.56 Impact Factor
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ABSTRACT: The effects of anti-angiogenesis treatment by angiostatin and endostatin on normalization of tumor microvasculature and microenvironment
are investigated, based on mathematical modeling and numerical simulation of tumor anti-angiogenesis and tumor haemodynamics.
The results show that after anti-angiogenesis treatment: (i) the proliferation, growth, and branching of neo-vessels are effectively
inhibited, and the extent of vascularization in tumors is accordingly reduced. (ii) the overall blood perfusion inside of
tumor is declined, the plateau of tumor interstitial fluid pressure (IFP) is relieved, the interstitial fluid oozing out from
the tumor periphery into the surrounding normal tissue is reduced, the reduction of overall extravasation across vasculature
to tumor interstium is much less than the decreased overall blood perfusion, due to the decline of IFP, the intravasations
is remarkablely effected by the change, in some cases there are no intravasation flow appear.
Key wordssolid tumor–microenvironment normalization–numerical simulation–anti-angiogenesis
Applied Mathematics and Mechanics 04/2012; 32(4):437-448. · 0.56 Impact Factor
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ABSTRACT: To investigate the inhibiting effects of the anti-angiogenic factor andostatin and the anti-angiogenic drug endostatin on
tumour angiogenesis and tumour cells, a coupled mathematical model of tumor angiogenesis with tumour growth and blood perfusion
is developed. Simulation results show that angiostatin and endostatin can improve the abnormal microenvironment inside the
tumour tissue by effectively inhibiting the process of tumor angiogenesis and decreasing tumour cells. The present model can
be used as a valid theoretical method in the investigation of the tumour anti-angiogenic therapy.
Key wordstumour angiogenesis–tumour growth–anti-angiogenic therapy–coupled mathematical model
Applied Mathematics and Mechanics 04/2012; 32(10):1287-1296. · 0.56 Impact Factor
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ABSTRACT: We propose a mathematical modelling system to investigate the dynamic process of tumour cell proliferation, death and tumour angiogenesis by fully coupling the vessel growth, tumour growth and blood perfusion. Tumour growth and angiogenesis are coupled by the chemical microenvironment and the cell-matrix interaction. The haemodynamic calculation is carried out on the updated vasculature. The domains of intravascular, transcapillary and interstitial fluid flow were coupled in the model to provide a comprehensive solution of blood perfusion variables. An estimation of vessel collapse is made according to the wall shear stress criterion to provide feedback on vasculature remodelling. The simulation can show the process of tumour angiogenesis and the spatial distribution of tumour cells for periods of up to 24 days. It can show the major features of tumour and tumour microvasculature during the period such as the formation of a large necrotic core in the tumour centre with few functional vessels passing through, and a well circulated tumour periphery regions in which the microvascular density is high and associated with more aggressive proliferating cells of the growing tumour which are all consistent with physiological observations. The study also demonstrated that the simulation results are not dependent on the initial tumour and networks, which further confirms the application of the coupled model feedback mechanisms. The model enables us to examine the interactions between angiogenesis and tumour growth, and to study the dynamic response of a solid tumour to the changes in the microenvironment. This simulation framework can be a foundation for further applications such as drug delivery and anti-angiogenic therapies.
Journal of Theoretical Biology 03/2011; 279(1):90-101. · 2.21 Impact Factor
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ABSTRACT: The coupling of intravascular and interstitial flow is a distinct feature of tumor microcirculation, due to high vessel permeability, low osmotic pressure gradient and absence of functional lymphatic system inside tumors. We have previously studied the tumor microcirculation by using a 2D coupled model. In this paper, we extend it to a 3D case with some new considerations, to investigate tumor blood perfusion on a more realist microvasculature, and the effects of vascular normalization by anti-angiogenic therapy on tumor microenvironment. The model predict the abnormal tumor microcirculation and the resultant hostile microenvironment: (1) in the intra-tumoral vessels, blood flows slowly with almost constant pressure values, haematocrit is much lower which contributes to hypoxia and necrosis formation of the tumor centre; (2) the total transvascular flux is at the same order of magnitude as intravascular flux, the intravasation appears inside of the tumor, the ratio of the total amount of intravasation flux to extravasation flux is about 16% for the present model; (3) the interstitial pressure is uniformly high throughout the tumor and drops precipitously at the periphery, which leads to an extremely slow interstitial flow inside the tumor, and a rapidly rising convective flow oozing out from the tumor margin into the surrounding normal tissue. The investigation of the sensitivity of flows to changes in transport properties of vessels and interstitium as well as the vascular density of the vasculature, gains an insight into how normalization of tumor microenvironment by anti-angiogenic therapies influences the blood perfusion.
Journal of biomechanics 05/2009; 42(6):712-21. · 2.66 Impact Factor
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ABSTRACT: The coupling of intravascular and interstitial flow is a distinct feature of tumor microcirculation, due to the high vessel permeability, the low osmotic pressure gradient as well as the absence of functional lymphatic system inside tumors. In this paper, a coupled mathematical model of tumor microcirculation is developed, which provides the link between microvasculature and interstitial space perfusion through the matrices determining a neighbor point belonging to either connected vessel (matrix B) or interstitial space (matrix A), and combines the intravascular and interstitial flow by vascular leaky terms. In addition, the compliance of tumor vessels, blood rheology with hematocritic distribution at branches is also considered. The microvascular network, on which the microcirculation calculation is carried out, is generated from our two-dimensional 9-point (2D9P) model of tumor angiogenesis, improved from the previous 2D5P one. A specific coupling procedure is developed in the study to couple the intravascular and interstitial flow. It is based on the iteratively numerical simulation techniques, including local iterations at individual parameter level and one global loop to provide coupling and simulation convergence. The simulation results not only present the basic features and characteristics of tumor microcirculation, which agree with the corresponding experimental observations reported, but also predict an intimate relationship between the tumor intravascular and interstitial flow quantitatively. Among the parameters, the vascular leakiness is a key to govern the systemic flowing pattern, influence the tumor internal environment and contribute to the metastasis of tumor cells, which could not be presented by the previous uncoupled models.
Journal of Biomechanics 02/2008; 41(5):996-1004. · 2.43 Impact Factor
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ABSTRACT: A coupled intravascular–transvascular–interstitial fluid flow model is developed to study the distributions of blood flow
and interstitial fluid pressure in solid tumor microcirculation based on a tumor-induced microvascular network. This is generated
from a 2D nine-point discrete mathematical model of tumor angiogenesis and contains two parent vessels. Blood flow through
the microvascular network and interstitial fluid flow in tumor tissues are performed by the extended Poiseuille’s law and
Darcy’s law, respectively, transvascular flow is described by Starling’s law; effects of the vascular permeability and the
interstitial hydraulic conductivity are also considered. The simulation results predict the heterogeneous blood supply, interstitial
hypertension and low convection on the inside of the tumor, which are consistent with physiological observed facts. These
results may provide beneficial information for anti-angiogenesis treatment of tumor and further clinical research.
Acta Mechanica Sinica 09/2007; 23(5):477-483. · 0.86 Impact Factor
