Computational model of silica nanoparticle penetration into tumor spheroids: Effects of methoxy and carboxy PEG surface functionalization and hyperthermia

Drug delivery to tumors suffers from poor solubility, specificity, diffusion through the tumor micro‐environment and nonoptimal interactions with components of the extracellular matrix and cell surface receptors. Nanoparticles and drug–polymer complexes address many of these problems. However, large size exasperates the problem of slow diffusion through the tumor. Three‐dimensional tumor spheroids are good models to evaluate approaches to mitigate these difficulties and aid in design strategies to improve the delivery of drugs to treat cancer effectively. Diffusion of drug carriers is highly dependent on cell uptake rate parameters (association/dissociation) and temperature. Hyperthermia increases molecular transport and is known to act synergistically with chemotherapy to improve treatment. This study presents a new inverse estimation approach based on Bayesian probability for estimating nanoparticle cell uptake rates from experiments. The parameters were combined with a finite element computational model of nanoparticle transport under hyperthermia conditions to explore its effect on tumor porosity, diffusion and particle binding (association and dissociation) at cell surfaces. Carboxy‐PEG‐silane (cPEGSi) nanoparticles showed higher cell uptake compared to methoxy‐PEG‐silane (mPEGSi) nanoparticles. Simulations were consistent with experimental results from Skov‐3 ovarian cancer spheroids. Amorphous silica (cPEGSi) nanoparticles (58 nm) concentrated at the periphery of the tumor spheroids at 37°C but mild hyperthermia (43°C) increased nanoparticle penetration. Thus, hyperthermia may enhance cancer treatment by improving blood delivery to tumors, enhancing extravasation and penetration into tumors, trigger release of drug from the carrier at the tumor site and possibly lead to synergistic anti‐cancer activity with the drug. Carboxy‐PEG‐silane functionalized silica nanoparticle transport through Skov‐3 ovarian tumor spheroids under normal temperature and hyperthermia conditions was modeled by (i) solving Fick's equation with reaction terms, (ii) modeling heat generation and thermal damage to cells, (iii) calculating changes in porosity of the spheroid and membrane rate constants, and (iv) iterating until the stopping criteria is reached. The model accurately predicted the experimentally observed increase in nanoparticle tumor penetration at 43°C compared to 37°C.