Limits...
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.

Show MeSH

Related in: MedlinePlus

Fraction of the injected NPs adhering firmly at the blood vessel walls per tumor area (mm−2) as a function of the tumor development stage (days post tumor inception) for a range of magnitudes of the parameters α and β.Top: Fixed α = 1010 m−2 with β varying with values of 10−5 m−2s (solid black line), 10−4 m−2s (dashed black line), and 10−3 m−2s (solid/dotted gray line). Bottom: Fixed β = 10−4 m−2s with α varying with values of 108 m−2 (solid black line), 1010 m−2 (dashed black line), and 1012 m−2 (solid/dotted gray line).
© Copyright Policy
Related In: Results  -  Collection


getmorefigures.php?uid=PMC3585411&req=5

pone-0056876-g006: Fraction of the injected NPs adhering firmly at the blood vessel walls per tumor area (mm−2) as a function of the tumor development stage (days post tumor inception) for a range of magnitudes of the parameters α and β.Top: Fixed α = 1010 m−2 with β varying with values of 10−5 m−2s (solid black line), 10−4 m−2s (dashed black line), and 10−3 m−2s (solid/dotted gray line). Bottom: Fixed β = 10−4 m−2s with α varying with values of 108 m−2 (solid black line), 1010 m−2 (dashed black line), and 1012 m−2 (solid/dotted gray line).

Mentions: Figure 6 provides the fraction of NPs compared to the injected dose adhering per unit surface at the tumor vasculature as a function of the particle diameter d, parameters α and β, and stage of tumor development. For a fixed α = 1010 m−2 (Figure 6– top row), the number of NPs accumulating in the tumor vasculature grows with time rapidly over the first 10 days and then levels out for longer time points. This is consistent with the behavior of the average flow rate and shear rate in the neovasculature (Figure 3) showing a rapid increase within the first 10 days post tumor inception. The same plot shows that an increase in β leads to a reduction of the number of particles accumulating within the tumor vasculature, and the opposite behavior is depicted for the NP size d. This can be interpreted by considering that as β increases the contribution of the dislodging hydrodynamic forces increases, whereas, for these specific conditions, an increase in d is accompanied by an overall increase in adhesive strength. Note that non-specific accumulation in the pre-existing vasculature is negligibly small due to the lower affinity (100 times) and higher average shear rate (2–4 times).


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 per tumor area (mm−2) as a function of the tumor development stage (days post tumor inception) for a range of magnitudes of the parameters α and β.Top: Fixed α = 1010 m−2 with β varying with values of 10−5 m−2s (solid black line), 10−4 m−2s (dashed black line), and 10−3 m−2s (solid/dotted gray line). Bottom: Fixed β = 10−4 m−2s with α varying with values of 108 m−2 (solid black line), 1010 m−2 (dashed black line), and 1012 m−2 (solid/dotted gray line).
© Copyright Policy
Related In: Results  -  Collection

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

pone-0056876-g006: Fraction of the injected NPs adhering firmly at the blood vessel walls per tumor area (mm−2) as a function of the tumor development stage (days post tumor inception) for a range of magnitudes of the parameters α and β.Top: Fixed α = 1010 m−2 with β varying with values of 10−5 m−2s (solid black line), 10−4 m−2s (dashed black line), and 10−3 m−2s (solid/dotted gray line). Bottom: Fixed β = 10−4 m−2s with α varying with values of 108 m−2 (solid black line), 1010 m−2 (dashed black line), and 1012 m−2 (solid/dotted gray line).
Mentions: Figure 6 provides the fraction of NPs compared to the injected dose adhering per unit surface at the tumor vasculature as a function of the particle diameter d, parameters α and β, and stage of tumor development. For a fixed α = 1010 m−2 (Figure 6– top row), the number of NPs accumulating in the tumor vasculature grows with time rapidly over the first 10 days and then levels out for longer time points. This is consistent with the behavior of the average flow rate and shear rate in the neovasculature (Figure 3) showing a rapid increase within the first 10 days post tumor inception. The same plot shows that an increase in β leads to a reduction of the number of particles accumulating within the tumor vasculature, and the opposite behavior is depicted for the NP size d. This can be interpreted by considering that as β increases the contribution of the dislodging hydrodynamic forces increases, whereas, for these specific conditions, an increase in d is accompanied by an overall increase in adhesive strength. Note that non-specific accumulation in the pre-existing vasculature is negligibly small due to the lower affinity (100 times) and higher average shear rate (2–4 times).

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