Spatio‐temporal modeling of nanoparticle delivery to multicellular tumor spheroids

Abstract

The inefficiency of nanoparticle penetration in tissues limits the therapeutic efficacy of such formulations for cancer applications. Recent work has indicated that modulation of tissue architecture with enzymes such as collagenase significantly increases macromolecule delivery. In this study we developed a mathematical model of nanoparticle penetration into multicellular spheroids that accounts for radially dependent changes in tumor architecture, as represented by the volume fraction of tissue accessible to nanoparticle diffusion. Parameters such as nanoparticle binding, internalization rate constants, and accessible volume fraction were determined experimentally. Unknown parameters of nanoparticle binding sites per cell in the spheroid and pore shape factor were determined by fitting to experimental data. The model was correlated with experimental studies of the penetration of 40 nm nanoparticles in SiHa multicellular spheroids with and without collagenase treatment and was able to accurately predict concentration profiles of nanoparticles within spheroids. The model was also used to investigate the effects of nanoparticle size. This model contributes toward the understanding of the role of tumor architecture on nanoparticle delivery efficiency.

Predictive Models of Diffusive Nanoparticle Transport in 3-Dimensional Tumor Cell Spheroids

“…A recent study describes a model that depicts the diffusional transport of negatively charged polystyrene beads in tumor cell spheroids (47). This earlier model used similar governing equations and similar, carboxylated polystyrene beads as in the current study (both used negatively charged, 20 nm diameter in the current study and 40 nm in the earlier study), but has significant differences with respect to experimental design and results, model parameters calculation, and, most importantly, model performance.…”

Drug delivery to solid tumors: the predictive value of the multicellular tumor spheroid model for nanomedicine screening

“…In this regard, 3D in vitro models and above all MCTS have been applied for evaluating the NP potential to accumulate and penetrate in depth the tumor tissue. 20,34,[56][57][58][59] Determination of free or drug-loaded NPs' distribution and concentration in spheroids can be performed by various techniques. The distribution of gold NPs in MCTS could be precisely assessed with transmission electronic microscopy (TEM), 60,61 while fluorescence microscopy was successfully applied for the detection of dye-labeled NPs.…”

Mathematical Modeling of Vesicle Drug Delivery Systems 2: Targeted Vesicle Interactions with Cells, Tumors, and the Body

“…At the center of the spheroid, r = 0, whereas at its outer rim, r = R. In most cases, D eff is assumed to be a constant throughout the spheroid. However, Goodman and coworkers 23 obtained D eff as a function of r considering the structural difference between the outer proliferating rim, the middle quiescent region, and the necrotic core region. The measurement of the effective diffusion coefficient will be discussed later.…”

“…Since Goodman and coworkers 23 mainly investigated the effect of the nanoparticle size and the tumor architecture, the effective diffusion coefficient was simulated in detail as a function of the porosity and pore size of spheroids, as well as the size of nanoparticles. Furthermore, the spheroid was divided into a center core region, a middle region, and an outer region.…”

“…However, verified in vitro design criteria may not apply to in vivo situations due (23) (24) (25) (26) (27) (28) to the geometric difference between a monolayer cell culture and a tumor tissue. Therefore, spheroids have been used to better mimic the geometry of tumor tissues.…”