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Theoretical evaluation of enhanced gold nanoparticle delivery to PC3 tumors due to increased hydraulic conductivity or recovered lymphatic function after mild whole body hyperthermia

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Abstract

The objective of this study is to investigate the effect of hyperthermia-induced improvement of hydraulic conductivity and lymphatic function on both tumoral IFP reduction and nanoparticle delivery to PC3 tumors. We developed a theoretical model for nanoparticle transport in a tumor incorporating Starling’s law, Darcy’s law, transient convection, and diffusion of chemical species in porous media, and nanoparticle accumulation in tumors. Results have shown that both mechanisms were effective to decrease the IFP at the tumor center from 1600 Pa in the control without heating to 800 Pa in tumors with whole body heating. IFP reductions not only elevate the nanoparticle concentration in the tumor, but also result in a more uniform nanoparticle concentration in the tumor than that in the control without heating. Due to the IFP reductions at the tumor center and/or local blood perfusion increases, the final amount of accumulated nanoparticles in the tumor increased by more than 35–95% when compared to the control without heating. We conclude that increases in the hydraulic conductivity and recovery of lymphatic functions are possible mechanisms that lead to IFP reductions and enhancement in nanoparticle deposition in PC3 tumors observed in our in vivo experimental studies.

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Abbreviations

D eff :

Diffusion coefficient of nanoparticles in the porous tumor, m2/s

C :

Concentration of nanoparticles in the porous tumor, mol/m3

C p :

Concentration of nanoparticles in the capillaries of tumors, mol/m3

p :

Interstitial fluid pressure in the tumor, Pa

p blood :

Blood pressure in capillary, Pa

V f,r :

Interstitial fluid velocity in the radial direction, m/s

K t :

Hydraulic conductivity of the porous tumor, m2/Pa s

S/V :

Surface area of capillaries per unit volume of the tumor, 1/m

S LY/V :

Surface area of lymphatic vessels per unit volume of the tumor, 1/m

L p :

Hydraulic permeability of the capillary wall, m/Pa s

L LY :

Hydraulic permeability of the lymphatic vessel wall, m/Pa s

\( {\dot{M}}_{\mathrm{acc}} \) :

Accumulation rate of nanoparticles in the entire tumor, mol/s

M acc :

Amount of nanoparticle deposition in the tumor, mol

k f :

Deposition rate coefficient of nanoparticles attached to tumor cells, 1/s

p LY :

Lymphatic hydrostatic pressure, Pa

r :

Coordinate in the radial direction in spherical coordinates, m

R :

Radius of the tumor, m

t :

Time, s

ε :

Porosity of the tumor

ϕ :

Fluid source or sink term in Darcy’s law,1/s

\( \dot{C} \) :

Source or sink term of nanoparticles in porous media, mol/m3·s

σ t :

Osmotic reflection coefficient for plasma proteins for tumors

σ f :

Filtration reflection coefficient through either the capillary or lymphatic vessel walls

π :

Osmotic pressure in the interstitial space of tumors, Pa

πblood :

Osmotic pressure in the capillaries of tumors, Pa

τ :

Time constant, s

blood:

Blood

LY:

Lymphatic

acc:

Accumulation

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Acknowledgments

The research was performed in partial fulfilment of the requirements for the PhD degree in Mechanical Engineering by Manpreet Singh from the University of Maryland Baltimore County, Baltimore, Maryland, USA.

Funding

This research was supported by a National Science Foundation research grant CBET-1705538.

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  1. Department of Mechanical Engineering, University of Maryland Baltimore County, 1000 Hilltop Circle, Baltimore, MD, 21250, USA

    Manpreet Singh, Ronghui Ma & Liang Zhu

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Correspondence to Liang Zhu.

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Singh, M., Ma, R. & Zhu, L. Theoretical evaluation of enhanced gold nanoparticle delivery to PC3 tumors due to increased hydraulic conductivity or recovered lymphatic function after mild whole body hyperthermia. Med Biol Eng Comput 59, 301–313 (2021). https://doi.org/10.1007/s11517-020-02308-4

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