Numerical Simulation of the Inhibitory Effect of Angiostatin on Metastatic Tumor Angiogenesis and Microenvironment

Abstract

The present work formulates and analyzes the inhibitory effect of anti-angiogenic factor angiostatin excreted by the primary tumor on metastatic tumor angiogenesis, blood perfusion, and interstitial fluid flow in the tumor microenvironment by means of a numerical experiment. The simulation results demonstrate that angiostatin has an obvious impact on the morphology, growth rate, and the number of branches of microvascular network inside and outside the metastatic tumor, and angiostatin has the capacity to regulate and inhibit the formation of new blood vessels. Heterogeneous blood perfusion, widespread interstitial hypertension, and low convection within the metastatic tumor have obviously improved under the inhibitory effect of angiostatin, which are consistent with physiological observed facts. The simulation results may provide beneficial information and theoretical models for clinical research of anti-angiogenic therapy strategies.

3D Numerical Study of Metastatic Tumor Blood Perfusion and Interstitial Fluid Flow Based on Microvasculature Response to Inhibitory Effect of Angiostatin

“…3D mathematical model we present in this section originates from the previous 2D tumor antiangiogenesis mathematical model [5,21] describing how capillary networks form in a metastatic tumor in response to angiostatin released by a primary tumor. The conservation equation of endothelial cells (EC) indicates the migration of EC influenced mainly by four factors: random motility, inhibitory effect of angiostatin, chemotaxis, and haptotaxis.…”

“…The model provided a more realistic prediction of interstitial fluid flow pattern in solid tumor than the previous models. Some related works have been done on tumor-induced angiogenesis, blood perfusion, and interstitial fluid flow in the tumor microenvironment by using 2D mathematical methods [5,[21][22][23]. In spite of the valuable body of work performed in simulation of blood perfusion, interstitial fluid flow, and metastasis, previous studies have not examined blood perfusion and interstitial fluid pressure in the metastatic tumor microcirculation based on the 3D microvascular network response to the inhibitory effect of angiostatin which plays a significant role in suppressing tumor growth and metastasis.…”

Three-Dimensional Model of Metastatic Tumor Angiogenesis in Response to Anti-Angiogenic Factor Angiostatin

“…The 3D mathematical model developed in this study is based on previous 2D tumor anti-angiogenesis mathematical models 7,17 describing the formation of capillary networks inside and outside the metastatic tumor in response to anti-angiogenic factor angiostatin released by a primary tumor. The model assumes that the migration of ECs is influenced mainly by four factors 7,24 : inhibitory effect of angiostatin, chemotaxis, haptotaxis and random motility of ECs, to simulate metastatic tumor angiogenesis. All parameters and equations included in the present 3D model are expressed in dimensionless form.…”

“…where is an appropriate outward unit normal vector. According to previous mathematical models 7,24 and considering the 3D model, the initial concentration profiles of the angiogenic stimulators, angiostatin and fibronectin, respectively, can be expressed as…”

Computational systems biology approaches to anti-angiogenic cancer therapeutics

“…Earlier work by Sleeman and coworkers [38] investigated the effect of angiostatin, another endogenous inhibitor of angiogenesis. A recent study using a model that combined angiogenesis and hemodynamic simulations in metastatic tumors, predicted that treatment with angiostatin affects tumor vessels such that they more closely resemble normal vessels [39]. This process, called ‘vessel normalization’, results in reduced hypoxia and interstitial fluid pressure (IFP).…”