Too Big, Too Small, Too $O_2$: The Pandoro Effect from Oxygen Gradients in Tomographic Volumetric Additive Manufacturing

Abstract: Tomographic Volumetric Additive Manufacturing (TVAM) enables rapid, layerless biofabrication; however, its application to thermoreversible hydrogels is often compromised by complex chemical kinetics. In this study, we identify and characterize a recurrent printing artifact - termed the Pandoro effect - manifesting as a truncated-cone distortion caused by premature polymerization at the vial bottom and inhibition at the top. We demonstrate that this phenomenon originates from a vertical oxygen gradient driven by the thermal hysteresis of resin preparation: heating depletes dissolved oxygen, while subsequent cooling induces diffusion-limited re-oxygenation from the air-resin interface. To mitigate this, we present a multi-tiered strategy. First, we introduce a coupled ray-optical and photochemical optimization model that rigorously accounts for spatially heterogeneous inhibitor concentrations. Unlike conventional threshold-based approaches, this differentiable framework explicitly simulates the spatiotemporal reaction-diffusion dynamics of oxygen depletion, allowing the inverse solver to predictively compensate for local inhibition gradients. Complementing this algorithmic correction, we validate two process-based interventions: the elimination of the air-resin interface and the control of headspace atmosphere. We demonstrate that these strategies effectively suppress the Pandoro effect, and are compatible with cell-laden resins. This work establishes guidelines for reproducible volumetric bioprinting and expands our open-source Dr.TVAM platform with advanced polymerization modeling capabilities.