We have used a simple experimental model to evaluate the size dependence of AMF-mediated hyperthermia and its associated cytotoxicity using prostate cancer cells containing intracellular ferromagnetic nanoparticles. We observe that the maximum measured temperature increase at the surface of cell pellets is a function of both pellet size and particle concentration as would be expected from diffusive heat transfer. Finally we observe that the cytotoxicity associated with AMF treatment scales with this temperature increase and becomes negligible in small pellets as the achieved increase in cell-pellet temperature diminishes.
The relationship between cell-pellet size, intracellular particle concentration and cell-pellet surface temperature increase is well described by the solution for the heat diffusion equation as it is applied to the steady-state (as t
> ∞) surface temperature increase of a uniformly and constantly heated spherical object existing in an infinite heat sink (Equation 4
). Here, the uniform heating rate is treated simply as the product of the particle concentration and particle SLP (Equation 6
). This agreement is remarkable considering the experimental system deviates significantly from the approximations used to derive Equation 4
in a number of ways. Significant deviations include: the intracellular particle distribution is not homogeneous, but is localized to vesicles as large as 500 nm in diameter (); the cell pellets are not spherical and possess significant asymmetry; cell membranes exist and separate the collections of nanoparticles; the peak change at the pellet surface temperature measured is assumed to be indicative of the change in temperature at t
= ∞, although it is measured at a finite time (30 min) after initiating heating and the heat sink is not infinite but is comprised of 0.5 ml of medium, the vessel and the circulating water jacket within the solenoid.
Our interpretation of the above results is that both the thermal and associated cytotoxic effects of hyperthermia mediated by intracellular nanoparticles behave according to heat diffusion theory and are subject to the same overarching scaling effect as other forms of hyperthermia. In other words, macroscopic heat diffusion dominates even on the relevant length scales for cells. Namely, the smaller a system that is heated from within (at a given rate of energy deposition per unit volume), the smaller the temperature increase incurred by that system and consequently the smaller the cytotoxic effect of such heating. Thus, it is presently impossible to therapeutically heat a single cell by magnetically perturbing intracellular nanoparticles. In fact, in this study, the smallest cell pellet in which significant hyperthermia-mediated cytotoxicity was observed comprised 2.5 × 105 cells (containing Fe at a concentration of 200 pg Fe/cell). The correlation of cytotoxicity with measured temperature change indicates that hyperthermia contributes in a dominant fashion to cell toxicity in this experiment.
A number of experimental studies evaluating cytotoxicity mediated by AMF-treated intracellular particles in pellets of cells have been reported [3
]. However, they fail to provide an explicit evaluation of the relationship between cytotoxicity and cell ensemble size. In aggregate these studies leave an unclear description of the relationship between intracellular and extracellular hyperthermia.
Kalambur and coworkers demonstrated a decrease in cell viability in prostate cancer cells loaded with iron oxide nanoparticles and heated while in pellet form by AMF and interpreted the cytotoxicity incurred as being due to a combination of effects from intracellular and extracellular nanoparticles [9
]. While they provide a theoretical scaling analysis of heat-ability as a function of cell ensemble size based on a simple heat diffusion model, they do not experimentally address variations in either heatability or cytotoxicity with cell-pellet size.
Wilhelm and coworkers evaluated the relative cytotoxicity of iron oxide nanoparticle-loaded and -unloaded cells coexisting in a large (20 million cells) loose pellet and exposed to AMF [22
]. They employed a single time point, flow cytometric measurement of propidium iodide to demonstrate equivalent relative propidium iodide uptake in nanoparticle-loaded and nanoparticle-empty cell populations. This result indicates that cytotoxic hyperthermia is a function of total iron particle content in the pellet, a finding consistent with the observations described here. These results also imply that a therapeutically significant temperature differential is not achieved between the cellular environments of transfected and untransfected cells. In short, their work supports the equivalency of intracellular and extracellular hyperthermia in terms of cytotoxic effect.
Jordan and coworkers attempted to compare intracellular and extracellular hyperthermia by comparing the clonogenic survival of nanoparticle-loaded cells treated in pellets by AMF with equivalent cell pellets treated by external water bath [3
]. They attempted to apply equivalent thermal schedules by modulating the intensity of AMF to maintain the temperature of the pellet (as measured at a single location within the pellet) at a value equivalent to the temperature of the water bath. Their results indicated preferential cytotoxicity for intracellular heating when attempting to maintain treatment temperature at 43°C. However, they fail to account for temperature variation expected across the cell pellet, which is evident in the theoretical treatment provided here (Equation 3
It is our position that a temperature measurement at a single location within an internally heated cell pellet is inadequate to assign thermal dose. We have also attempted to make this comparison by assigning a thermal isoeffective dose [23
], based on the well known Arrhenius relationship, to both our AMF-treated cell pellets and equivalent pellets treated by water bath (data not shown). We employed the commonly used cumulative equivalent minutes at 43°C (CEM 43). However, this assignment was based on our temperature measurement at a single location on the pellet surface and did not adequately account for either the expected temperature gradient across the pellet or the dynamic nature of this gradient. We therefore feel that using this approach to compare the cytotoxicity of hyperthermia mediated by intracellular particles to externally applied heat is misleading. These limitations may explain the discrepancy in cytotoxicity observed by Jordan et al.
In this work, we measure only the effects of intracellular hyperthermia, and we explore the size dependence of intracellular heating in terms of both thermal and cytotoxic effect. We have determined that this size dependence is remarkably well described by a simple model that ignores intercellular thermal barriers. We also confirm that the cytotoxicity associated with intracellular AMF-mediated heating becomes negligible in small collections of cells. We explicitly demonstrate the minimum number of cells within a pellet required for cytotoxic hyperthermia to be achieved for a given concentration of particles having a specific SLP. It is noteworthy to mention that we do not address the convective heat transfer that would be present in vascularized tumors in vivo
. We would expect a larger minimum size of tumor to be effectively heated in this setting. Further work is needed to compare these results with both external (interstitial) nanoparticle hyperthermia and with molecular-targeted (antibody) surface-bound nanoparticle hyperthermia. The latter case is particularly interesting in light of recently reported results [24