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Integrative models of vascular remodeling during tumor growth

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Malignant solid tumors recruit the blood vessel network of the host tissue for nutrient supply, continuous growth, and gain of metastatic potential. Angiogenesis (the formation of new blood vessels), vessel cooption (the integration of existing blood vessels into the tumor vasculature), and vessel regression remodel the healthy vascular network into a tumor‐specific vasculature that is in many respects different from the hierarchically organized arterio‐venous blood vessel network of the host tissues. Integrative models based on detailed experimental data and physical laws implement in silico the complex interplay of molecular pathways, cell proliferation, migration, and death, tissue microenvironment, mechanical and hydrodynamic forces, and the fine structure of the host tissue vasculature. With the help of computer simulations high‐precision information about blood flow patterns, interstitial fluid flow, drug distribution, oxygen and nutrient distribution can be obtained and a plethora of therapeutic protocols can be tested before clinical trials. In this review, we give an overview over the current status of integrative models describing tumor growth, vascular remodeling, blood and interstitial fluid flow, drug delivery, and concomitant transformations of the microenvironment. WIREs Syst Biol Med 2015, 7:113–129. doi: 10.1002/wsbm.1295 This article is categorized under: Analytical and Computational Methods > Computational Methods Models of Systems Properties and Processes > Mechanistic Models Models of Systems Properties and Processes > Organismal Models
Interstitial fluid flow, based on simulations of the model described in Ref , with a vascular network and tumor growth module as in Figure : (IFF) and interstitial fluid pressure (IFP) were computed for an artificially generated vascular network, incorporating a tumor vascular network in its center as a result of simulated tumor growth and vascular remodeling. Parameter settings were guided by experimental data for melanoma. The resulting network was taken as input for the IFF model. It was assumed that IFF behaves like flow through a porous medium following Darcy's law where flow velocity is proportional to the hydrostatic pressure gradient. Vessels can be sources or sinks of interstitial fluid, depending on the blood − IF pressure difference. The IFP coupling to tumor vessels was assumed to be particularly strong due to increased leakiness (permeability). A homogeneous background of lymphatics absorbs most of the flow coming from the tumor. These two plots depict a slices although the center of the tissue domain, displaying the fractional vascular volume (percentage occupied by vessels) in (a) and the IFP in (b). The location of the tumor is best inferred by the sharp drop in fBF, but it is also indicated by a thin white line. The IFP profile exhibits the expected plateaus near the center of the tumor and a steep gradient near the tumor edge. The simulation moreover predicts heterogeneities due to the particular vessel arrangement. It also shows that tumor vessels can reabsorb a significant amount of fluid if their blood pressure is much lower than neighboring vessels.
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Tumor oxygen distribution, based on simulations of the model described in Ref , with a vascular network and tumor growth module as in Figure , augmented by an oxygen concentration field computation as outlined in Section Oxygen Concentration: The distribution of intravascular and tissue oxygen was computed for an artificially generated vascular network. Tumor vascular remodeling was simulated, where the tumor size increases from a small nucleus to ca. 4 mm diamter, which is about half of the lateral size of the simulation box. Parameter settings were guided by experimental data from breast tumors. The result is a typical chaotic compartmentalized tumor network which is connected to an arterio‐venously structured vasculature of the host. This configuration was taken as input for a detailed computation of oxygen. Respective model couples advective oxygen transport by the blood stream via transvascular fluxes with diffusion within the tissue domain and seeks a self consistent solution. Advection in each vascular segment is approximated as one dimensional problem, neglecting radial concentration and velocity variations. These images depict slices through the simulation domain where the location of the tumor is indicated roughly by the circle. (a) depicts the vascular and tissue oxygen partial pressure (PO2). Vessels are shown as cylinders, but everything outside a central slab of 300 µm thickness has been cut away. The remaining vessels protrude up from the cutting plane showing the tissue oxygen distribution. (b) The vascular oxygen saturation where the slab thickness has been increased to 600 µm.
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Vascular network reconstruction: (a) A section of a cortical blood vessel network after reconstruction based on micro‐CT images. Vessels are color coded according to their radius. (Reprinted with permission from Ref . Copyright 2010 Nature Publishing Group). (b) Depth‐coded image obtained from confocal laser microscopy. This shows a section of human brain tissue (Reprinted with permission from Ref . Copyright 2006 Wiley‐Blackwell). (c) A coronary vascular network based on micro‐CT images. Various subnetworks are distinguished by random colors (Reprinted with permission from Ref . Copyright 2007 Elsevier Science).
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Tumor vascular network remodeling, based on simulations of the model described in Ref : An initial vascular network was synthetically generated. Then a simulation of tumor growth was performed using this network. The network edges are visualized as cylinders, color coded according to their associated blood pressure value. The viable tumor tissue is visualized as yellow mass. Hollow interior regions appear due to necrotic tissue which was once viable but has died from oxygen deprivation. The simulated area is a box of ca. 8 mm lateral size of which a quarter is cut away for display purposes. The cutting faces of vessels are colored light grey. (a) The initial state with a small tumor nucleus. (b) 200 h later angiogenesis has set in. Many tumor vessels have collapsed due to reduced blood flow. Surviving interior vessels are dilated due to switching from angiogenesis to circumferential growth. (c) After 400 h, the tumor network is thinned out sufficiently that tumor regions are located well outside the diffusion distance of oxygen, causing hypoxia and subsequent necrosis. (d) As the tumor continues to grow it pushes the region of angiogenic activity further into normal tissue and leaves a sparse network behind its rim. This state, as seen after 800 h simulated time, shows typical features of tumor vasculature: compartmentalization, highly vascularized rim, decreasing vascular density toward the center where the network is very sparse, vessel dilation, loss of hierarchical organization. The model parameter selection for this case was guided by experimental data for human melanoma.
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