Oxygen (O₂) quantification is essential for assessing cell metabolism, and its consumption in cell culture is an important indicator of cell viability. Recent advances in microfluidics have made O₂ sensing a crucial feature for organ-on-chip (OOC) devices for various biomedical applications. OOC O₂ sensors can be categorized, based on their transducer type, into two main groups, optical and electrochemical. In this review, we provide an overview of on-chip O₂ sensors integrated with the OOC devices and evaluate their advantages and disadvantages. Recent innovations in optical O₂ sensors integrated with OOCs are discussed in four main categories: (i) basic luminescence-based sensors; (ii) microparticle-based sensors; (iii) nano-enabled sensors; and (iv) commercial probes and portable devices. Furthermore, we discuss recent advancements in electrochemical sensors in five main categories: (i) novel configurations in Clark-type sensors; (ii) novel materials (e.g., polymers, O₂ scavenging and passivation materials); (iii) nano-enabled electrochemical sensors; (iv) novel designs and fabrication techniques; and (v) commercial and portable electrochemical readouts. Together, this review provides a comprehensive overview of the current advances in the design, fabrication and application of optical and electrochemical O₂ sensors.

Mathematical modeling has significant potential for understanding of biological models of cancer and to accelerate the progress in cross-disciplinary approaches of cancer treatment. In mathematical biology, solid tumor spheroids are often studied as preliminary in vitro models of avascular tumors. The size of spheroids and their cell number are easy to track, making them a simple in vitro model to investigate tumor behavior, quantitatively. The growth of solid tumors is comprised of three main stages: transient formation, monotonic growth and a plateau phase. The last two stages are extensively studied. However, the initial transient formation phase is typically missing from the literature. This stage is important in the early dynamics of growth, formation of clonal sub-populations, etc. In the current work, this transient formation is modeled by a reaction–diffusion partial differential equation (PDE) for cell concentration, coupled with an ordinary differential equation (ODE) for the spheroid radius. Analytical and numerical solutions of the coupled equations were obtained for the change in the radius of tumor spheroids over time. Human glioblastoma (hGB) cancer cells (U251 and U87) were spheroid cultured to validate the model prediction. Results of this study provide insight into the mechanism of development of solid tumors at their early stage of formation.

Glioblastoma multiform (GBM) tumor progression has been recognized to be correlated with extracellular matrix (ECM) stiffness. Dynamic variation of tumor ECM is primarily regulated by a family of enzymes which induce remodeling and degradation. In this paper, we investigated the effect of matrix stiffness on the invasion pattern of human glioblastoma tumoroids. A 3D-printed tumor-on-a-chip platform was utilized to culture human glioblastoma tumoroids with the capability of evaluating the effect of stiffness on tumor progression. To induce variations in the stiffness of the collagen matrix, different concentrations of collagenase were added, thereby creating an inhomogeneous collagen concentration. To better understand the mechanisms involved in GBM invasion, an in silico hybrid mathematical model was used to predict the evolution of a tumor in an inhomogeneous environment, providing the ability to study multiple dynamic interacting variables. The model consists of a continuum reaction–diffusion model for the growth of tumoroids and a discrete model to capture the migration of single cells into the surrounding tissue. Results revealed that tumoroids exhibit two distinct patterns of invasion in response to the concentration of collagenase, namely ring-type and finger-type patterns. Moreover, higher concentrations of collagenase resulted in greater invasion lengths, confirming the strong dependency of tumor behavior on the stiffness of the surrounding matrix. The agreement between the experimental results and the model’s predictions demonstrates the advantages of this approach in investigating the impact of various extracellular matrix characteristics on tumor growth and invasion.

In this work, we studied the stability of radially symmetric growth in tumor spheroids using a reaction-diffusion model. In this model, nutrient concentration and internal pressure are local variables that implicitly relate the proliferation of cells to the growth of the tumor. The analytical solution of the governing model was presented in an orthonormal spherical harmonic basis. It was shown that the radially symmetric steady-state solution to the growth of tumor spheroids, under symmetric growth conditions, was unstable with respect to small asymmetric perturbations. Such perturbations excited the asymmetric modes of growth, which could grow in time and change the spherical configuration of the tumor. The number of such modes and their rates of growth depended on parameters such as surface tension, external energy and the rate of nutrient consumption. This analysis indicated that the spherical configuration of tumor spheroids, even under experimentally controlled symmetric growth conditions, were naturally unstable. This was confirmed by a comparison between the shapes of in vitro human glioblastoma (hGB) spheroids and the configuration of the first few asymmetric modes predicted by the model.

Chemoresistance poses a significant clinical challenge in managing glioblastoma (GBM), limiting the long‐term success of traditional treatments. Here, a 3D tumoroid model is used to investigate the metabolic sensitivity of temozolomide (TMZ)‐resistant GBM cells to iron chelation by deferoxamine (DFO) and deferiprone (DFP). This work shows that TMZ‐resistant GBM cells acquire stem‐like characteristics, higher intracellular iron levels, higher expression of aconitase, and elevated reliance on oxidative phosphorylation and proteins associated with iron metabolism. Using a microphysiological model of GBM‐on‐a‐chip consisting of extracellular matrix (ECM)‐incorporated tumoroids, this work demonstrates that the combination of iron chelators with TMZ induces a synergistic effect on an in vitro tumoroid model of newly diagnosed and recurrent chemo‐resistant patient‐derived GBM and reduced their size and invasion. Investigating downstream metabolic variations reveal reduced intracellular iron, increased reactive oxygen species (ROS), upregulated hypoxia‐inducible factor‐1α, reduced viability, increased autophagy, upregulated ribonucleotide reductase (RRM2), arrested proliferation, and induced cell death in normoxic TMZ‐resistant cells. Hypoxic cells, while showing similar results, display reduced responses to iron deficiency, less blebbing, and an induced autophagic flux, suggesting an adaptive mechanism associated with hypoxia. These findings show that co‐treatment with iron chelators and TMZ induces a synergistic effect, making this combination a promising GBM therapy.

The flow of non-spherical grains is strongly affected by the orientation of the grains, as observed in experiments and simulations. An existing model that predicts the orientation of grains as a function of the flow field and shape of the grains, is limited to homogenous orientational fields where the interaction of the grains with their surroundings is negligible. To address this limitation, we generalized the model to account for inhomogeneous orientational fields in the form of spatial non-convective orientational flux. The orientational flux accounts for the interactions of grains with their surroundings and the boundaries. The proposed model is used to study the influence of orientational diffusion and boundary conditions on the flow of dense granular material down an incline. It is shown that the boundary conditions can play a significant role in the orientation of grains in such flows.