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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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Blood flow rate and adhering particle fraction. The simulated blood flow rate mapped directly over the tumor and pre-existing vascular network (top).The color map is scaled by the maximum flow rate reached in the pre-existing vessels inside the tumor (10−5 m3/s). The fraction of injected 1,000 nm NPs (×10−3) adhering firmly at the blood vessel walls is also shown at ∼100 min after systemic injection (bottom). The images correspond to the tumor stages depicted in Figure 2. Red arrows indicate the points of injection for the NPs, located upstream with respect to the tumor mass. The parameter α is 1012 m−2 in the tumor neovasculature and 1010 m−2 in the pre-existing vessels. The parameter β is fixed and equals 10−3 m−2 s. Note that under these conditions, the NPs accumulate mostly at the periphery of the tumor immediately downstream of the injection sites.
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pone-0056876-g004: Blood flow rate and adhering particle fraction. The simulated blood flow rate mapped directly over the tumor and pre-existing vascular network (top).The color map is scaled by the maximum flow rate reached in the pre-existing vessels inside the tumor (10−5 m3/s). The fraction of injected 1,000 nm NPs (×10−3) adhering firmly at the blood vessel walls is also shown at ∼100 min after systemic injection (bottom). The images correspond to the tumor stages depicted in Figure 2. Red arrows indicate the points of injection for the NPs, located upstream with respect to the tumor mass. The parameter α is 1012 m−2 in the tumor neovasculature and 1010 m−2 in the pre-existing vessels. The parameter β is fixed and equals 10−3 m−2 s. Note that under these conditions, the NPs accumulate mostly at the periphery of the tumor immediately downstream of the injection sites.

Mentions: Based on these model outputs, it is reasonable to argue that the accumulation of systemically injected NPs within the tumor vasculature would vary with the development stage of the tumor. Referring to the four timepoints considered so far, the distribution of the flow rate and the accumulation of 1,000 nm particles within the tumor vasculature are shown in Figure 4. The timescale for nanoparticle binding (assuming instantaneous attachment) is the flow time scale (sec−1). The flow rate appears to be relatively constant over time, with a slight increase towards the later stages, and mostly uniform within the malignant mass. As the tumor grows larger beyond the timespan simulated here, this uniformity is expected to be less pronounced. The flow rates are scaled by the flow rate in the pre-existing vessels inside the tumor, as shown by the color map. The NPs are injected upstream of the malignant mass (Figure 4b - red arrows), transported by the blood flow and adhere firmly to the vessel walls depending on the local hydrodynamic and biophysical conditions. In particular, for the simulations presented in Figure 4b, the parameters α and β are kept constant and equal to α = 1012 m−2 in tumor-induced vessels and α = 1010 m−2 in the pre-existing vessels, while β = 10−3 m−2 s. The difference in the value of α between the pre-existing vessels and the neovasculature reflects the over-expression of specific receptor molecules on the tumor endothelium. Under these hydrodynamic and biophysical conditions, the NPs preferentially deposit at the periphery of the tumor, closer to the injection sites (tumor inlet). Indeed, the NP distribution appears to be less uniform as the size of the tumor, and corresponding vasculature, increases. Also moving from the sites of injection towards the center of the malignant mass, the fraction of accumulating particles decreases progressively (from red to blue as indicated by the color map). Although the particles that adhere tend to preferentially bind closer to the injection sites, many particles still pass through the tumor without adhering as can be measured from the fraction of injected particles (Figure 4, bottom row). This implies that under these conditions, the majority of the injected NPs that adhere avidly bind to the neovasculature at the tumor inlet and only very few NPs actually adhere deeper into the malignant mass. This computational test demonstrates that high vascular affinity would impair the uniform accumulation of particles within the tumor vasculature. In this initial implementation, we make the simplifying assumption to neglect the effects of recirculation, which may not be negligible.


A computational model for predicting nanoparticle accumulation in tumor vasculature.

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

Blood flow rate and adhering particle fraction. The simulated blood flow rate mapped directly over the tumor and pre-existing vascular network (top).The color map is scaled by the maximum flow rate reached in the pre-existing vessels inside the tumor (10−5 m3/s). The fraction of injected 1,000 nm NPs (×10−3) adhering firmly at the blood vessel walls is also shown at ∼100 min after systemic injection (bottom). The images correspond to the tumor stages depicted in Figure 2. Red arrows indicate the points of injection for the NPs, located upstream with respect to the tumor mass. The parameter α is 1012 m−2 in the tumor neovasculature and 1010 m−2 in the pre-existing vessels. The parameter β is fixed and equals 10−3 m−2 s. Note that under these conditions, the NPs accumulate mostly at the periphery of the tumor immediately downstream of the injection sites.
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Related In: Results  -  Collection

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getmorefigures.php?uid=PMC3585411&req=5

pone-0056876-g004: Blood flow rate and adhering particle fraction. The simulated blood flow rate mapped directly over the tumor and pre-existing vascular network (top).The color map is scaled by the maximum flow rate reached in the pre-existing vessels inside the tumor (10−5 m3/s). The fraction of injected 1,000 nm NPs (×10−3) adhering firmly at the blood vessel walls is also shown at ∼100 min after systemic injection (bottom). The images correspond to the tumor stages depicted in Figure 2. Red arrows indicate the points of injection for the NPs, located upstream with respect to the tumor mass. The parameter α is 1012 m−2 in the tumor neovasculature and 1010 m−2 in the pre-existing vessels. The parameter β is fixed and equals 10−3 m−2 s. Note that under these conditions, the NPs accumulate mostly at the periphery of the tumor immediately downstream of the injection sites.
Mentions: Based on these model outputs, it is reasonable to argue that the accumulation of systemically injected NPs within the tumor vasculature would vary with the development stage of the tumor. Referring to the four timepoints considered so far, the distribution of the flow rate and the accumulation of 1,000 nm particles within the tumor vasculature are shown in Figure 4. The timescale for nanoparticle binding (assuming instantaneous attachment) is the flow time scale (sec−1). The flow rate appears to be relatively constant over time, with a slight increase towards the later stages, and mostly uniform within the malignant mass. As the tumor grows larger beyond the timespan simulated here, this uniformity is expected to be less pronounced. The flow rates are scaled by the flow rate in the pre-existing vessels inside the tumor, as shown by the color map. The NPs are injected upstream of the malignant mass (Figure 4b - red arrows), transported by the blood flow and adhere firmly to the vessel walls depending on the local hydrodynamic and biophysical conditions. In particular, for the simulations presented in Figure 4b, the parameters α and β are kept constant and equal to α = 1012 m−2 in tumor-induced vessels and α = 1010 m−2 in the pre-existing vessels, while β = 10−3 m−2 s. The difference in the value of α between the pre-existing vessels and the neovasculature reflects the over-expression of specific receptor molecules on the tumor endothelium. Under these hydrodynamic and biophysical conditions, the NPs preferentially deposit at the periphery of the tumor, closer to the injection sites (tumor inlet). Indeed, the NP distribution appears to be less uniform as the size of the tumor, and corresponding vasculature, increases. Also moving from the sites of injection towards the center of the malignant mass, the fraction of accumulating particles decreases progressively (from red to blue as indicated by the color map). Although the particles that adhere tend to preferentially bind closer to the injection sites, many particles still pass through the tumor without adhering as can be measured from the fraction of injected particles (Figure 4, bottom row). This implies that under these conditions, the majority of the injected NPs that adhere avidly bind to the neovasculature at the tumor inlet and only very few NPs actually adhere deeper into the malignant mass. This computational test demonstrates that high vascular affinity would impair the uniform accumulation of particles within the tumor vasculature. In this initial implementation, we make the simplifying assumption to neglect the effects of recirculation, which may not be negligible.

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