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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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Fraction of the injected NPs adhering firmly at the blood vessel walls at about 100 min after injection on day 18, upstream of the tumor mass as indicated by the red arrows inFigure 4.The colors on the right provide a measure of the particle fraction adhering mainly to the neovasculature (irregular lines). The columns are related to three different NP sizes, namely 100, 600 and 1,000 nm; whereas the three rows are related to three different values for the parameter α (α = 1012 m−2 top row; α = 1010 m−2 middle row and α = 108 m−2 bottom row). For all cases, β = 10−4 m−2 s while α for the pre-existing vessels is 100 times smaller than for the corresponding tumor-induced neovessels. Tumor colors are as in Figure 2.
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pone-0056876-g005: Fraction of the injected NPs adhering firmly at the blood vessel walls at about 100 min after injection on day 18, upstream of the tumor mass as indicated by the red arrows inFigure 4.The colors on the right provide a measure of the particle fraction adhering mainly to the neovasculature (irregular lines). The columns are related to three different NP sizes, namely 100, 600 and 1,000 nm; whereas the three rows are related to three different values for the parameter α (α = 1012 m−2 top row; α = 1010 m−2 middle row and α = 108 m−2 bottom row). For all cases, β = 10−4 m−2 s while α for the pre-existing vessels is 100 times smaller than for the corresponding tumor-induced neovessels. Tumor colors are as in Figure 2.

Mentions: The importance of the NP vascular affinity is more clearly shown in Figure 5. Here, NPs with three different sizes, namely 100 nm (left column), 600 nm (middle column) and 1,000 nm (right column), are injected at day 18 in tumors exhibiting different levels of vascular receptor expressions in the neovasculature, namely α = 1012, 1010 and 108 m−2. In the pre-existing vessels, α is 100 times smaller than in the corresponding neovasculature. For the 100 nm particles, vascular accumulation occurs quite uniformly over the whole neovasculature but it lowers significantly as α decreases. For the larger 600 and 1,000 nm particles, the vascular accumulation is quite uniform only for the lower values of the parameter α, namely 1010 and 108 m−2. Differently, at α = 1012 m−2, the larger particles distribute not uniformly with a higher accumulation at the periphery of the malignant mass near the injection site, as seen in Figure 4. This computational analysis demonstrates that NP accumulation occurs uniformly throughout the tumor only for moderate vascular affinities.


A computational model for predicting nanoparticle accumulation in tumor vasculature.

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

Fraction of the injected NPs adhering firmly at the blood vessel walls at about 100 min after injection on day 18, upstream of the tumor mass as indicated by the red arrows inFigure 4.The colors on the right provide a measure of the particle fraction adhering mainly to the neovasculature (irregular lines). The columns are related to three different NP sizes, namely 100, 600 and 1,000 nm; whereas the three rows are related to three different values for the parameter α (α = 1012 m−2 top row; α = 1010 m−2 middle row and α = 108 m−2 bottom row). For all cases, β = 10−4 m−2 s while α for the pre-existing vessels is 100 times smaller than for the corresponding tumor-induced neovessels. Tumor colors are as in Figure 2.
© Copyright Policy
Related In: Results  -  Collection

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

pone-0056876-g005: Fraction of the injected NPs adhering firmly at the blood vessel walls at about 100 min after injection on day 18, upstream of the tumor mass as indicated by the red arrows inFigure 4.The colors on the right provide a measure of the particle fraction adhering mainly to the neovasculature (irregular lines). The columns are related to three different NP sizes, namely 100, 600 and 1,000 nm; whereas the three rows are related to three different values for the parameter α (α = 1012 m−2 top row; α = 1010 m−2 middle row and α = 108 m−2 bottom row). For all cases, β = 10−4 m−2 s while α for the pre-existing vessels is 100 times smaller than for the corresponding tumor-induced neovessels. Tumor colors are as in Figure 2.
Mentions: The importance of the NP vascular affinity is more clearly shown in Figure 5. Here, NPs with three different sizes, namely 100 nm (left column), 600 nm (middle column) and 1,000 nm (right column), are injected at day 18 in tumors exhibiting different levels of vascular receptor expressions in the neovasculature, namely α = 1012, 1010 and 108 m−2. In the pre-existing vessels, α is 100 times smaller than in the corresponding neovasculature. For the 100 nm particles, vascular accumulation occurs quite uniformly over the whole neovasculature but it lowers significantly as α decreases. For the larger 600 and 1,000 nm particles, the vascular accumulation is quite uniform only for the lower values of the parameter α, namely 1010 and 108 m−2. Differently, at α = 1012 m−2, the larger particles distribute not uniformly with a higher accumulation at the periphery of the malignant mass near the injection site, as seen in Figure 4. This computational analysis demonstrates that NP accumulation occurs uniformly throughout the tumor only for moderate vascular affinities.

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