Oxygen diffusion in ellipsoidal tumor spheroids

Abstract

Oxygen plays a central role in cellular metabolism, in both healthy and tumour tissue. The presence and concentration of molecular oxygen in tumours has a substantial effect on both radiotherapy response and tumour evolution, and as a result the oxygen micro-environment is an area of intense research interest. Multicellular tumour spheroids closely mimic real avascular tumours, and in particular they exhibit physiologically relevant heterogeneous oxygen distribution. This property has made them a vital part of in vitro experimentation. For ideal spheroids, their heterogeneous oxygen distributions can be predicted from theory, allowing determination of cellular oxygen consumption rate (OCR) and anoxic extent. However, experimental tumour spheroids often depart markedly from perfect sphericity. There has been little consideration of this reality. To date, the question of how far an ellipsoid can diverge from perfect sphericity before spherical assumptions breakdown remains unanswered. In this work we derive equations governing oxygen distribution (and more generally, nutrient and drug distribution) in both prolate and oblate tumour ellipsoids, and quantify the theoretical limits of the assumption that the spheroid is a perfect sphere. Results of this analysis yield new methods for quantifying OCR in ellipsoidal spheroids, and how this can be applied to markedly increase experimental throughput and quality.\n\nAuthor summaryMulticellular tumour spheroids (MCTS) are an increasingly important tool in cancer research, exhibiting non-homogeneous oxygen distributions and central necrosis. These are more similar to in situ avascular tumours than conventional 2D biology, rendering them exceptionally useful experimental models. Analysis of spheroids can yield vital information about cellular oxygen consumption rates, and the heterogeneous oxygen contribution. However, such analysis pivots on the assumption of perfect sphericity, when in reality spheroids often depart from such an ideal. In this work, we construct a theoretical oxygen diffusion model for ellipsoidal tumour spheroids in both prolate and oblate geometries. With these models established, we quantify the limits of the spherical assumption, and illustrate the effect of this assumption breaking down. Methods of circumventing this breakdown are also presented, and the analysis here suggests new methods for expanding experimental throughput to also include ellipsoidal data.