Modeling spheroid assembly dynamics and mechanical stress generation in magnetic-based biofabrication

Magnetic biofabrication enables rapid assembly of multicellular spheroids but still lacks a basis for predictive control over structure and mechanical environment. Here, we combine experiments and an individual spheroid-based model to study magnetic assembly of periosteum-derived spheroids. Spheroids are treated as discrete particles interacting through magnetic forces, contact mechanics, and interfacial friction, with parameters obtained from independent measurements. This model quantitatively captures assembly dynamics arising from magnetic force patterns and viscous drag with the well surface. The spatial distribution of magnetic forces, determined by magnet geometry and positioning, predicts the size and morphology of magnetic assembloids, including disk- and ring-like structures. Magnetic assembly further generates heterogeneous compressive stresses that depend on magnet geometry and spheroid number. Radial stresses arise collectively through inter-spheroid interactions, whereas vertical stresses are mainly determined by magnetic loading of individual spheroids. These results establish a minimal physical framework for magnetic biofabrication and provide a basis for predictive control of both tissue structure and mechanical microenvironment.