Computer Simulations Show Coexisting Spheroids Alter Local Oxygen Uptake Rates

Biomedical researchers evaluating drug candidates and tissue models in multi-construct cellular systems often assume that individual organoids or spheroids behave as isolated replicates, yet computational simulations and physical experiments demonstrate that proximity profoundly alters their metabolic activity. In an exploratory investigation published in Frontiers in Bioengineering and Biotechnology, researchers from the University of Pisa utilized finite element models alongside physical culture platforms to quantify how the oxygen consumption rate of cell-laden spheroids shifts as a direct consequence of community abundance, construct size, and spatial spacing. The investigation reveals that when multiple cellular aggregates share an identical culture volume, the resulting competition for dissolved oxygen establishes localized concentration gradients that force individual constructs to down-regulate their metabolic uptake. These findings offer an empirical and theoretical framework indicating that phenotypic observations derived from densely seeded in vitro assays may reflect microenvironmental resource competition rather than pure pharmacological or toxicological responses.

To investigate the governing physics of cellular coexistence without introducing unintended geometric asymmetries, the research team designed an idealized in silico environment inside COMSOL Multiphysics software. Within this numerical platform, spherical constructs were arranged symmetrically within an aqueous-filled toroidal geometry that was entirely surrounded by an oxygen-saturated external boundary. Spheroid centers were mapped directly to the vertices of regular polygons inscribed along a concentric circumference of radius defined by the average of the internal and external toroidal boundaries. By scaling this average radius proportionally to the spheroid radius through an adjustable multiplier parameter and holding the distance between the construct surface and outer boundary fixed at three millimeters, the simulation decoupled construct volume increases from boundary proximity. This precise configuration guaranteed that every construct across the parametric sweep was exposed to identical boundary conditions and diffusive path lengths, allowing the researchers to isolate the specific impact of aggregate abundance and inter-construct spacing.

The mathematical formulation underlying the finite element simulations solved the steady-state diffusion-reaction equation across the toroidal domain and inside the cellular aggregates. In the cell-free aqueous culture medium, oxygen transport was governed purely by stationary diffusion, while inside the spheroids, oxygen uptake followed a modified formulation of Michaelis-Menten kinetics incorporating a switching function that accounts for local hypoxia and necrotic core formation. Transport parameters were assigned using established physiological values, including a diffusion coefficient of three times ten to the negative ninth square meters per second, an ambient oxygen saturation concentration of zero point two moles per cubic meter, and an in vivo-like cell density of five times ten to the fourteenth cells per cubic meter. Individual cellular consumption was parameterized with a maximum uptake rate of two point seventy-five times ten to the negative seventeenth moles per cell per second and a Michaelis-Menten constant of zero point two zero one moles per cubic meter, reproducing values established for human-derived organoids.

The numerical parametric sweep explored spheroid populations ranging from single controls up to communities of twenty constructs, testing log-spaced radii from thirty-one to five thousand micrometers and spatial distribution multipliers ranging from one to thirty-two. By integrating the stationary oxygen flux over the external surface of each construct, the investigators calculated the individual metabolic rate for every simulated configuration. For modest populations of three constructs, individual oxygen consumption remained essentially constant across varying distances, regardless of the construct radius. However, as the population abundance climbed to twenty spheroids, large constructs with radii equal to or exceeding four hundred sixty-six point twelve micrometers exhibited a significant positive correlation between individual metabolic rate and inter-spheroid spacing, yielding a non-parametric Spearman correlation coefficient of one with a p-value of zero point zero zero two eight. Under these crowded conditions, neighboring constructs drew from a shared oxygen pool, depleting local resources and depressing their metabolic uptake.

Beyond absolute uptake rates, the simulations systematically evaluated whether coexistence deviates the fundamental power-law scaling that relates metabolic rate to aggregate volume. Stepwise linear regression on log-log transformations of construct size and metabolic rate identified three distinct operational domains across all parametric combinations: an initial isometric regime in small aggregates, an intermediate non-isometric allometric regime where scaling exponents deviated significantly from unity, and a diffusion-limited geometric regime in large spheroids. For widely spaced aggregates with a spatial multiplier of thirty-two, non-isometric scaling exponents clustered tightly around three-quarters, mirroring classical biological allometry. Crucially, the transition radius from isometric to allometric behavior exhibited a strong positive correlation with spacing multiplier values, displaying a Spearman coefficient of zero point eight four five two with a p-value of zero point zero four six seven, proving that dense cellular packing forces constructs into diffusion-limited allometric regimes at substantially smaller physical sizes.

Furthermore, when high construct abundance was coupled with minimal spatial separation, the scaling exponents within the non-isometric regime underwent pronounced downward deviations. For spatial multiplier values below or equal to eight, correlation analysis between the scaling exponent and community abundance yielded a Spearman coefficient of negative zero point nine four two nine, with a statistically significant p-value of zero point zero one six seven. As constructs were positioned in closer proximity, the intensified overlap of local depletion zones prevented internal cells from accessing ambient oxygen levels, accelerating the onset of hypoxic deceleration and lowering the effective power-law slope below the standard three-quarters baseline. These computational results demonstrate that cellular allometry in synthetic cultures is not an immutable intrinsic biological constant, but rather a dynamic physical property mediated by construct geometry, packing density, and local boundary constraints.

To obtain an initial experimental test of consistency for these computational predictions, the researchers adapted the multi-construct layout for benchtop validation using HepG2 liver hepatocellular cells. Highly spherical cellular constructs were fabricated using an automated, extrusion-based biofabrication system that dispensed a bioink suspension containing two point five million cells per milliliter within one percent alginic acid and zero point zero zero four percent type I collagen into a calcium chloride cross-linking bath through a one point six millimeter nozzle at eight microliters per second. To minimize metabolic variance arising from cell age, all experimental spheroids were derived from a narrow window of eight sequential cell passages spanning passage eleven to passage eighteen. The resulting spheroids were transferred to standard culture medium and stabilized overnight under controlled incubation at thirty-seven degrees Celsius, ninety-five percent relative humidity, and five percent carbon dioxide prior to metabolic testing.

The physical assay arranged three cell-laden spheroids at the vertices of an equilateral triangle within a culture dish filled with a fixed volume of nutrient medium, holding them in place using custom hemispherical niches cast into an oxygen-permeable agarose hydrogel base. Inter-spheroid surface-to-surface distances were set to zero millimeters across six replicates, two millimeters across fifteen replicates, and fourteen millimeters across ten replicates, while six isolated single-spheroid preparations served as baseline controls. The two-millimeter condition fell below a numerically determined threshold distance where oxygen concentration along the inter-construct axis drops below ten percent of its maximum, whereas the fourteen-millimeter spacing comfortably exceeded this threshold. Using a bare-fiber optical microsensor, researchers recorded stationary oxygen concentrations at the geometric center and outer boundary of individual spheroids until reading drifts stabilized within one percent of saturation over five minutes, calculating individual metabolic rates through steady-state spherical approximations.

The experimental measurements showed strong qualitative agreement with the trends predicted by the finite element simulations. A non-parametric Kruskal-Wallis test across the tested configurations revealed statistically significant differences among the median metabolic rates, yielding a p-value below zero point zero zero zero one. Post hoc Dunn multiple comparisons demonstrated that isolated spheroids exhibited significantly elevated oxygen metabolism compared to spheroids positioned in close physical proximity at zero and two millimeters of surface separation. While comparisons between isolated spheroids and those spaced at fourteen millimeters showed no statistically significant differences, the overall median metabolic rates displayed an upward trend with increasing separation distance. Although non-parametric correlation analysis yielded a Spearman coefficient of one with a p-value of zero point zero eight three three that did not reach the conventional significance threshold, the empirical data confirmed that physical coexistence depresses cellular oxygen uptake under crowded conditions.

The authors emphasized that these exploratory experiments serve as a preliminary proof of concept rather than a exhaustive quantitative validation, noting unavoidable discrepancies between idealized boundary conditions and benchtop culture dishes. In closed laboratory vessels, total medium volume, static liquid layers, and biofabrication cell density ceilings impose resource constraints that differ from continuous external boundary saturation. Furthermore, the present numerical model adopted stationary Michaelis-Menten kinetics and uniform cell distributions, whereas real biological tissues exhibit spatial heterogeneity, shifting cell-cycle phases, and dynamic adaptations. Despite these simplifications, the observed metabolic modulation matches documented responses in human hepatic cultures, where cell packing alters effective kinetic constants. Establishing predictive transport models provides an essential foundation to decouple neighbor-driven metabolic crosstalk from authentic drug efficacy, offering a quantifiable path to correct systematic screening biases and improve the translational reliability of preclinical organoid assays.

Subject of Research: Oxygen consumption dynamics and metabolic crosstalk in multi-spheroid cell cultures

Article Title: Finite element simulations drive the design of in vitro models of down-scaled crosstalk in oxygen metabolism

Article References: Mancini, P., Magliaro, C., & Botte, E. (2026). Finite element simulations drive the design of in vitro models of down-scaled crosstalk in oxygen metabolism. Frontiers in Bioengineering and Biotechnology, 14, Article 1975503. https://doi.org/10.3389/fbioe.2026.1975503

Image Credits: AI Generated

DOI: 10.3389/fbioe.2026.1975503

Keywords: finite element modeling, oxygen metabolism, cell spheroids, in vitro ecosystems, metabolic scaling, bioengineering, tissue models, diffusion kinetics, Finite, element, simulations, drive