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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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Simulated tumor and vasculature growth presented as a function of the number of days post tumor inception.(A) Tumor radius; (B) blood area fraction, defined as ratio of the vasculature to the tumor area, (C) average vascular flow rate; and (D) average wall shear rate. In (C) and (D), bars denote SEM (standard error of the mean) values estimated over the number of vessel segments in the tumor area (e.g., on day 24, the numbers were 6677 new vessel and 917 pre-existing vessel segments).
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pone-0056876-g003: Simulated tumor and vasculature growth presented as a function of the number of days post tumor inception.(A) Tumor radius; (B) blood area fraction, defined as ratio of the vasculature to the tumor area, (C) average vascular flow rate; and (D) average wall shear rate. In (C) and (D), bars denote SEM (standard error of the mean) values estimated over the number of vessel segments in the tumor area (e.g., on day 24, the numbers were 6677 new vessel and 917 pre-existing vessel segments).

Mentions: The variation of the tumor average radius with time is shown in Figure 3a up to 24 days post inception. The tumor shows overall a ∼30 fold increase in radius from ∼0.08 to 0.62 mm. The blood area fraction is introduced as the ratio between the total area covered by the vessel network and the tumor area in a cross section. The variation of such a fraction over time can be readily estimated processing the data of Figure 2. This is shown in Figure 3 for both the pre-existing and neovasculature. Interestingly, for the new vascular network originating with the tumor, the blood area fraction grows with time reaching a value close to 0.6 at 24 days, implying that more than 50% of the tumor cross section is covered by blood vessels. On the other hand, the blood area fraction for the pre-existing vasculature steadily decreases over time being always smaller than 10%. This curve starting at day 6 and rising through day 9 also shows that it takes almost 10 days for the nascent tumor to co-opt the existing vessels that surround it. The average flow rate and wall shear rate within the pre-existing vessels and the neovasculature are shown in Figure 3c and 3d, respectively. For the pre-existing vessels, a minor variation is observed over the 24 days which is contained within 10–20% of the corresponding mean values, 2.5×10−5 m3/s and 23 s−1. Differently, these two hydrodynamic parameters change dramatically for the neovasculature starting from zero during the avascular phase of the tumor, growing rapidly over the first 10 days, and reaching 0.8×10−5 m3/s and 10 s−1, respectively, at 24 days. Note that these values are comparable with those observed for the pre-existing vasculature, implying that after 10 days the tumor neovasculature is fully functional.


A computational model for predicting nanoparticle accumulation in tumor vasculature.

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

Simulated tumor and vasculature growth presented as a function of the number of days post tumor inception.(A) Tumor radius; (B) blood area fraction, defined as ratio of the vasculature to the tumor area, (C) average vascular flow rate; and (D) average wall shear rate. In (C) and (D), bars denote SEM (standard error of the mean) values estimated over the number of vessel segments in the tumor area (e.g., on day 24, the numbers were 6677 new vessel and 917 pre-existing vessel segments).
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Related In: Results  -  Collection

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getmorefigures.php?uid=PMC3585411&req=5

pone-0056876-g003: Simulated tumor and vasculature growth presented as a function of the number of days post tumor inception.(A) Tumor radius; (B) blood area fraction, defined as ratio of the vasculature to the tumor area, (C) average vascular flow rate; and (D) average wall shear rate. In (C) and (D), bars denote SEM (standard error of the mean) values estimated over the number of vessel segments in the tumor area (e.g., on day 24, the numbers were 6677 new vessel and 917 pre-existing vessel segments).
Mentions: The variation of the tumor average radius with time is shown in Figure 3a up to 24 days post inception. The tumor shows overall a ∼30 fold increase in radius from ∼0.08 to 0.62 mm. The blood area fraction is introduced as the ratio between the total area covered by the vessel network and the tumor area in a cross section. The variation of such a fraction over time can be readily estimated processing the data of Figure 2. This is shown in Figure 3 for both the pre-existing and neovasculature. Interestingly, for the new vascular network originating with the tumor, the blood area fraction grows with time reaching a value close to 0.6 at 24 days, implying that more than 50% of the tumor cross section is covered by blood vessels. On the other hand, the blood area fraction for the pre-existing vasculature steadily decreases over time being always smaller than 10%. This curve starting at day 6 and rising through day 9 also shows that it takes almost 10 days for the nascent tumor to co-opt the existing vessels that surround it. The average flow rate and wall shear rate within the pre-existing vessels and the neovasculature are shown in Figure 3c and 3d, respectively. For the pre-existing vessels, a minor variation is observed over the 24 days which is contained within 10–20% of the corresponding mean values, 2.5×10−5 m3/s and 23 s−1. Differently, these two hydrodynamic parameters change dramatically for the neovasculature starting from zero during the avascular phase of the tumor, growing rapidly over the first 10 days, and reaching 0.8×10−5 m3/s and 10 s−1, respectively, at 24 days. Note that these values are comparable with those observed for the pre-existing vasculature, implying that after 10 days the tumor neovasculature is fully functional.

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