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A computational model for predicting nanoparticle accumulation in tumor vasculature.

Frieboes HB, Wu M, Lowengrub J, Decuzzi P, Cristini V - PLoS ONE (2013)

Bottom Line: It is shown that an optimal vascular affinity can be identified providing the proper balance between accumulation dose and uniform spatial distribution of the NPs.This balance depends on the stage of tumor development (vascularity and endothelial receptor expression) and the NP properties (size, ligand density and ligand-receptor molecular affinity).Also, it is demonstrated that for insufficiently developed vascular networks, NPs are transported preferentially through the healthy, pre-existing vessels, thus bypassing the tumor mass.

View Article: PubMed Central - PubMed

Affiliation: Department of Bioengineering, University of Louisville, Louisville, Kentucky, USA. hbfrie01@louisville.edu

ABSTRACT
Vascular targeting of malignant tissues with systemically injected nanoparticles (NPs) holds promise in molecular imaging and anti-angiogenic therapies. Here, a computational model is presented to predict the development of tumor neovasculature over time and the specific, vascular accumulation of blood-borne NPs. A multidimensional tumor-growth model is integrated with a mesoscale formulation for the NP adhesion to blood vessel walls. The fraction of injected NPs depositing within the diseased vasculature and their spatial distribution is computed as a function of tumor stage, from 0 to day 24 post-tumor inception. As the malignant mass grows in size, average blood flow and shear rates increase within the tumor neovasculature, reaching values comparable with those measured in healthy, pre-existing vessels already at 10 days. The NP vascular affinity, interpreted as the likelihood for a blood-borne NP to firmly adhere to the vessel walls, is a fundamental parameter in this analysis and depends on NP size and ligand density, and vascular receptor expression. For high vascular affinities, NPs tend to accumulate mostly at the inlet tumor vessels leaving the inner and outer vasculature depleted of NPs. For low vascular affinities, NPs distribute quite uniformly intra-tumorally but exhibit low accumulation doses. It is shown that an optimal vascular affinity can be identified providing the proper balance between accumulation dose and uniform spatial distribution of the NPs. This balance depends on the stage of tumor development (vascularity and endothelial receptor expression) and the NP properties (size, ligand density and ligand-receptor molecular affinity). Also, it is demonstrated that for insufficiently developed vascular networks, NPs are transported preferentially through the healthy, pre-existing vessels, thus bypassing the tumor mass. The computational tool described here can effectively select an optimal NP formulation presenting high accumulation doses and uniform spatial intra-tumor distributions as a function of the development stage of the malignancy.

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Model overview showing the main components, variables, and key system interactions.
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pone-0056876-g007: Model overview showing the main components, variables, and key system interactions.

Mentions: Figure 7 provides an overview of the main model components and Figure 8 summarizes the main equations. Since the spatiotemporal dynamics of solid tumor growth depend upon the balance of proliferation, apoptosis, necrosis, migration, and cell-cell and cell-ECM adhesion [27], [28], we express these dynamics in a mathematical model by physical conservation laws acting on the cells and tissue [19]–[20]. These laws represent conservation of mass (due to cell creation and destruction), conservation of momentum (due to tissue velocity as the tumor grows or shrinks), and physical transport (diffusion, advection, and convection of substances). Angiogenesis is incorporated by coupling models of vessel growth, branching, and anastomosis [29], together with blood flow [30]. The tumor vasculature acts as a source of oxygen and cell nutrients, as well as nanoparticles. This enables evaluation of the local effects of vascularization and blood flow on tumor cells and nanoparticle transport, and provides a better understanding of the micro-environment conditions such as hypoxia that lead to the development of intra-tumor heterogeneity.


A computational model for predicting nanoparticle accumulation in tumor vasculature.

Frieboes HB, Wu M, Lowengrub J, Decuzzi P, Cristini V - PLoS ONE (2013)

Model overview showing the main components, variables, and key system interactions.
© Copyright Policy
Related In: Results  -  Collection

Show All Figures
getmorefigures.php?uid=PMC3585411&req=5

pone-0056876-g007: Model overview showing the main components, variables, and key system interactions.
Mentions: Figure 7 provides an overview of the main model components and Figure 8 summarizes the main equations. Since the spatiotemporal dynamics of solid tumor growth depend upon the balance of proliferation, apoptosis, necrosis, migration, and cell-cell and cell-ECM adhesion [27], [28], we express these dynamics in a mathematical model by physical conservation laws acting on the cells and tissue [19]–[20]. These laws represent conservation of mass (due to cell creation and destruction), conservation of momentum (due to tissue velocity as the tumor grows or shrinks), and physical transport (diffusion, advection, and convection of substances). Angiogenesis is incorporated by coupling models of vessel growth, branching, and anastomosis [29], together with blood flow [30]. The tumor vasculature acts as a source of oxygen and cell nutrients, as well as nanoparticles. This enables evaluation of the local effects of vascularization and blood flow on tumor cells and nanoparticle transport, and provides a better understanding of the micro-environment conditions such as hypoxia that lead to the development of intra-tumor heterogeneity.

Bottom Line: It is shown that an optimal vascular affinity can be identified providing the proper balance between accumulation dose and uniform spatial distribution of the NPs.This balance depends on the stage of tumor development (vascularity and endothelial receptor expression) and the NP properties (size, ligand density and ligand-receptor molecular affinity).Also, it is demonstrated that for insufficiently developed vascular networks, NPs are transported preferentially through the healthy, pre-existing vessels, thus bypassing the tumor mass.

View Article: PubMed Central - PubMed

Affiliation: Department of Bioengineering, University of Louisville, Louisville, Kentucky, USA. hbfrie01@louisville.edu

ABSTRACT
Vascular targeting of malignant tissues with systemically injected nanoparticles (NPs) holds promise in molecular imaging and anti-angiogenic therapies. Here, a computational model is presented to predict the development of tumor neovasculature over time and the specific, vascular accumulation of blood-borne NPs. A multidimensional tumor-growth model is integrated with a mesoscale formulation for the NP adhesion to blood vessel walls. The fraction of injected NPs depositing within the diseased vasculature and their spatial distribution is computed as a function of tumor stage, from 0 to day 24 post-tumor inception. As the malignant mass grows in size, average blood flow and shear rates increase within the tumor neovasculature, reaching values comparable with those measured in healthy, pre-existing vessels already at 10 days. The NP vascular affinity, interpreted as the likelihood for a blood-borne NP to firmly adhere to the vessel walls, is a fundamental parameter in this analysis and depends on NP size and ligand density, and vascular receptor expression. For high vascular affinities, NPs tend to accumulate mostly at the inlet tumor vessels leaving the inner and outer vasculature depleted of NPs. For low vascular affinities, NPs distribute quite uniformly intra-tumorally but exhibit low accumulation doses. It is shown that an optimal vascular affinity can be identified providing the proper balance between accumulation dose and uniform spatial distribution of the NPs. This balance depends on the stage of tumor development (vascularity and endothelial receptor expression) and the NP properties (size, ligand density and ligand-receptor molecular affinity). Also, it is demonstrated that for insufficiently developed vascular networks, NPs are transported preferentially through the healthy, pre-existing vessels, thus bypassing the tumor mass. The computational tool described here can effectively select an optimal NP formulation presenting high accumulation doses and uniform spatial intra-tumor distributions as a function of the development stage of the malignancy.

Show MeSH
Related in: MedlinePlus