arxiv: 2604.06313 · v1 · submitted 2026-04-07 · ⚛️ physics.optics

Recognition: 2 theorem links

· Lean Theorem

Too Big, Too Small, Too O₂: The Pandoro Effect from Oxygen Gradients in Tomographic Volumetric Additive Manufacturing

Riccardo Rizzo , Felix Wechsler , Qianyi Zhang , Christophe Moser

Authors on Pith no claims yet

Pith reviewed 2026-05-10 18:32 UTC · model grok-4.3

classification ⚛️ physics.optics

keywords Pandoro effectoxygen gradientvolumetric additive manufacturingTVAMthermoreversible hydrogelsbioprintingreaction-diffusion dynamicsinhibitor concentration

0 comments

The pith

Vertical oxygen gradients from resin heating and cooling cause truncated-cone distortions in tomographic volumetric additive manufacturing.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper identifies a recurring artifact called the Pandoro effect in tomographic volumetric additive manufacturing of thermoreversible hydrogels. This manifests as a truncated-cone shape because heating the resin depletes dissolved oxygen while cooling allows diffusion-limited re-oxygenation only from the air-resin interface at the top. A sympathetic reader would care because the effect limits uniform polymerization and therefore reliable cell-laden bioprinting. The authors trace the cause to this vertical oxygen gradient and show it can be addressed through a new optimization model plus simple changes to resin handling.

Core claim

The Pandoro effect, a truncated-cone distortion, 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. This produces premature polymerization at the vial bottom and inhibition at the top. The authors introduce a coupled ray-optical and photochemical optimization model that simulates the spatiotemporal reaction-diffusion dynamics of oxygen depletion, allowing predictive compensation for local inhibition gradients, and they validate process interventions that eliminate the air-resin interface and control headspace.

What carries the argument

The coupled ray-optical and photochemical optimization model that explicitly simulates spatiotemporal reaction-diffusion dynamics of oxygen depletion to compensate for spatially heterogeneous inhibitor concentrations.

Load-bearing premise

The observed truncated-cone distortion is caused primarily by the vertical oxygen gradient rather than by unaccounted variations in light dose, temperature during printing, or resin viscosity changes.

What would settle it

Directly measure dissolved oxygen concentration versus height in the prepared resin vial after cooling; if no vertical gradient exists yet the truncated-cone distortion still appears in prints, or if the gradient exists but the distortion pattern does not match the model's oxygen-inhibition prediction, the causal claim is falsified.

Figures

Figures reproduced from arXiv: 2604.06313 by Christophe Moser, Felix Wechsler, Qianyi Zhang, Riccardo Rizzo.

**Figure 1.** Figure 1: A) Schematic of tomographic volumetric additive manufacturing (TVAM) process. B) Schematic showing the formation of oxygen gradient following vial preparation with thermoreversible gelatin-based resin, and appearance of the Pandoro-like defects upon printing. Given the well-established inhibitory role of oxygen in free-radical photopolymerization - through scavenging of initiating and propagating radical s… view at source ↗

**Figure 2.** Figure 2: A-i) Representative prints and corresponding measured heights (n = 3) of the target model obtained 5, 30, 60, and 120 min after vial preparation, illustrating the progressive development of the Pandoro effect and ii) prints and measured heights at equilibrium (24 h) are shown without dose correction and after light-dose adjustment. B) Numerical simulation of the time-dependent oxygen gradient i) reveals di… view at source ↗

**Figure 3.** Figure 3: A) Comparison between patterns i) without and ii) with correction compensating for oxygen gradients and related diffusion. The close-up highlights higher intensities delivered to regions with higher oxygen concentrations. B) Defect-free i) simulated, and ii) experimental prints with iii) correspinding measured heights (n = 3) at 60 and 120 min using gradient-aware patterns. Unlike standard thresholding mod… view at source ↗

**Figure 4.** Figure 4: A) Schematic of vial preparation for air-interface removal showing use of standard caps (left) requiring high resin volume or custom caps (right) limiting resin consumption. B) Representative prints (i) and corresponding measured heights (n = 3) (ii) of the target model obtained at 5, 30, 60, 120 min and 24 h after vial preparation, illustrating the absence of the Pandoro effect. 2.5 Controlled atmosphere-… view at source ↗

**Figure 5.** Figure 5: A) Schematic of vial preparation for controlled atmosphere-based approach. B) Representative defect-free prints (i) and corresponding measured heights (n = 3) (ii) of the target model obtained at 5, 30, and 60 min afer vial preparation. The prints illustrate the absence of the Pandoro effect within the first 60 min, while a reverse Pandoro effect (iii) and overpolymerization issues arise after 120 min and … view at source ↗

**Figure 6.** Figure 6: A) Experimental prints (i) and measured heights (n = 3) (ii) of the target model obtained with cell-laden formulation (2 × 106 cells/mL) at 5 and 30 min afer vial preparation. The prints show no evidence of the Pandoro effect under any condition at 5 min. In contrast, the non-mitigated prints fail after 30 min, whereas all three proposed mitigation strategies result in defect-free prints. B) Representative… view at source ↗

read the original 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.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Desk Editor's Note private letter to a colleague

The paper names a truncated-cone distortion in TVAM bioprinting the Pandoro effect, traces it to oxygen gradients from resin heating and cooling, and adds a differentiable photochemical model plus two process fixes, though the causal evidence stays indirect.

read the letter

The main point is that they observed a consistent shape error in printed thermoreversible hydrogels and linked it to how dissolved oxygen redistributes during the heating and cooling steps before printing. Heating drives oxygen out, cooling lets it diffuse back in from the top surface, creating a vertical inhibitor gradient that slows polymerization at the top and speeds it at the bottom. They built a ray-tracing plus reaction-diffusion model that tracks this in space and time, made it differentiable so it can feed an inverse solver, and tested two practical changes: removing the air interface and controlling the headspace atmosphere. Both appear to reduce the distortion and work with cell-laden resins. The open-source update to their Dr.TVAM platform is a concrete deliverable for others in the field.

Referee Report

3 major / 1 minor

Summary. The manuscript identifies a recurrent printing artifact in tomographic volumetric additive manufacturing (TVAM) of thermoreversible hydrogels, termed the Pandoro effect, which manifests as truncated-cone distortion due to premature polymerization at the vial bottom and inhibition at the top. It attributes this to a vertical oxygen gradient arising from thermal hysteresis during resin preparation (heating depletes dissolved O2; cooling induces diffusion-limited re-oxygenation from the air-resin interface). The authors present a coupled ray-optical and photochemical optimization model that simulates spatiotemporal reaction-diffusion dynamics of oxygen to predictively compensate for heterogeneous inhibition, and they validate two process interventions (elimination of the air-resin interface and headspace atmosphere control) that suppress the effect while remaining compatible with cell-laden resins. The work also extends the open-source Dr.TVAM platform with advanced polymerization modeling.

Significance. If the central attribution and interventions hold, the work would be significant for enabling reproducible volumetric bioprinting of thermoreversible hydrogels, a key challenge in biofabrication. The differentiable modeling framework that explicitly handles spatially varying inhibitor concentrations advances beyond conventional threshold-based methods, and the open-source extension of Dr.TVAM provides a concrete community resource for handling complex oxygen dynamics in TVAM.

major comments (3)

[Results and Discussion] The central claim that the truncated-cone distortion originates specifically from the vertical oxygen gradient (driven by thermal hysteresis) is not supported by direct evidence such as spatially resolved dissolved-oxygen profiles before/after the thermal cycle or control prints that isolate O2 uniformity while matching light dose, temperature history, and viscosity. Without these, alternative explanations (vertical light attenuation or temperature-dependent flow) cannot be ruled out.
[Model Description] The optimization model is described as predictive and differentiable for compensating inhibition gradients, yet the manuscript provides no information on whether model parameters (e.g., diffusion coefficients or reaction rates) were fitted to the observed distortion data; this raises the risk that validation is circular rather than independent.
[Experimental Validation] The validation of the two process interventions lacks quantitative before-after metrics, error bars, statistical tests, or sample sizes demonstrating suppression of the Pandoro effect; the abstract states effectiveness but supplies no data to assess the magnitude or reproducibility of the improvement.

minor comments (1)

[Abstract] The abstract introduces the term 'Pandoro effect' without a brief etymology or reference to its visual resemblance, which would aid readers unfamiliar with the shape.

Simulated Author's Rebuttal

3 responses · 0 unresolved

We thank the referee for their thorough and constructive review of our manuscript. We have addressed each major comment in detail below, providing clarifications, additional discussion, and revisions where supported by our data and analysis. We believe these changes strengthen the attribution of the Pandoro effect and the validation of our interventions and model.

read point-by-point responses

Referee: [Results and Discussion] The central claim that the truncated-cone distortion originates specifically from the vertical oxygen gradient (driven by thermal hysteresis) is not supported by direct evidence such as spatially resolved dissolved-oxygen profiles before/after the thermal cycle or control prints that isolate O2 uniformity while matching light dose, temperature history, and viscosity. Without these, alternative explanations (vertical light attenuation or temperature-dependent flow) cannot be ruled out.

Authors: We acknowledge that direct, spatially resolved dissolved-oxygen profiles would constitute stronger evidence. Such measurements proved technically challenging in our viscous, thermoreversible hydrogel system during the thermal cycle and were not performed. However, we provide multiple lines of indirect but convergent evidence: the strict temporal correlation between the thermal hysteresis protocol and the appearance of the distortion; the ray-optical model, which already incorporates measured vertical light attenuation yet still requires the oxygen gradient term to reproduce the observed truncated-cone geometry; and the fact that the two interventions (air-resin interface removal and headspace atmosphere control) eliminate the distortion while light dose, temperature history, and viscosity remain unchanged. We have expanded the Results and Discussion sections to explicitly rule out vertical light attenuation (already accounted for in the model) and temperature-dependent flow (inconsistent with the observed top-to-bottom polymerization asymmetry and the success of oxygen-specific interventions). A new paragraph discusses the practical limitations of in-situ O2 profiling in this resin. revision: partial
Referee: [Model Description] The optimization model is described as predictive and differentiable for compensating inhibition gradients, yet the manuscript provides no information on whether model parameters (e.g., diffusion coefficients or reaction rates) were fitted to the observed distortion data; this raises the risk that validation is circular rather than independent.

Authors: All kinetic and transport parameters (oxygen diffusion coefficient, reaction rate constants, etc.) were taken from peer-reviewed literature values for comparable photopolymerizable hydrogel systems and were not adjusted or fitted to the Pandoro-effect distortion data. The model was used in a forward predictive mode to compute the spatially varying light-dose compensation required by the oxygen gradient; the experimental validation of the interventions was performed independently of any parameter optimization. We have added a new subsection (Model Parameters and Validation Strategy) that lists the exact literature sources, states that no fitting to distortion observations occurred, and confirms the independence of the experimental tests. revision: yes
Referee: [Experimental Validation] The validation of the two process interventions lacks quantitative before-after metrics, error bars, statistical tests, or sample sizes demonstrating suppression of the Pandoro effect; the abstract states effectiveness but supplies no data to assess the magnitude or reproducibility of the improvement.

Authors: We agree that quantitative metrics are essential. In the revised manuscript we have added: (i) before-and-after measurements of the truncated-cone distortion angle (mean ± s.d., n = 6 independent prints per condition), (ii) error bars on all relevant figures, and (iii) statistical comparison (two-tailed Student’s t-test, p < 0.001) confirming significant suppression for both interventions. These data appear in the Results section, a new supplementary figure, and the abstract has been updated to reference the quantitative improvement. All experiments used cell-laden resins to demonstrate compatibility. revision: yes

Circularity Check

0 steps flagged

No significant circularity in derivation of Pandoro effect origin

full rationale

The paper's central claim attributes the truncated-cone distortion to a vertical oxygen gradient from thermal hysteresis (heating depletes O2; cooling allows diffusion-limited re-oxygenation from the air interface). This is supported by a coupled ray-optical/photochemical model that explicitly simulates spatiotemporal reaction-diffusion dynamics of oxygen depletion and by direct experimental interventions (eliminating the air-resin interface and controlling headspace atmosphere) that suppress the effect. The model is presented as a differentiable forward simulator enabling inverse compensation rather than a fit to the observed distortions themselves. No equations reduce the claimed cause to the target data by construction, no parameters are described as fitted to the Pandoro geometry and then called predictive, and no load-bearing self-citations or uniqueness theorems are invoked. The derivation chain remains self-contained via physical modeling and independent process controls.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

Central claim rests on standard photochemical knowledge that oxygen inhibits radical polymerization and on the physical process of diffusion-limited re-oxygenation; no new fundamental entities or fitted constants are introduced in the abstract.

axioms (1)

domain assumption Dissolved oxygen acts as a polymerization inhibitor in the resin
Invoked to explain inhibition at the top of the vial; this is standard in photochemistry for additive manufacturing

pith-pipeline@v0.9.0 · 5553 in / 1322 out tokens · 94149 ms · 2026-05-10T18:32:32.381537+00:00 · methodology

discussion (0)

Lean theorems connected to this paper

Citations machine-checked in the Pith Canon. Every link opens the source theorem in the public Lean library.

IndisputableMonolith/Cost/FunctionalEquation.lean washburn_uniqueness_aczel unclear

?

unclear
Relation between the paper passage and the cited Recognition theorem.

We solve Fick’s second law … ∂c/∂t = D ∂²c/∂h² … coupled ray-optical and photochemical optimization framework … c[O2] and c[P*] … loss with ReLU thresholds
IndisputableMonolith/Foundation/RealityFromDistinction.lean reality_from_one_distinction unclear

?

unclear
Relation between the paper passage and the cited Recognition theorem.

vertical oxygen gradient driven by thermal hysteresis … Henry’s law … diffusion-limited re-oxygenation

What do these tags mean?

matches: The paper's claim is directly supported by a theorem in the formal canon.
supports: The theorem supports part of the paper's argument, but the paper may add assumptions or extra steps.
extends: The paper goes beyond the formal theorem; the theorem is a base layer rather than the whole result.
uses: The paper appears to rely on the theorem as machinery.
contradicts: The paper's claim conflicts with a theorem or certificate in the canon.
unclear: Pith found a possible connection, but the passage is too broad, indirect, or ambiguous to say the theorem truly supports the claim.

Reference graph

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Dong C. Liu and Jorge Nocedal. “On the limited memory BFGS method for large scale opti- mization”. en. In:Mathematical Programming45.1 (Aug. 1989), pp. 503–528.doi:10.1007/ BF01589116. 13 The Pandoro effect in TVAM R. Rizzo, F. Wechsler, Q. Zhang, C. Moser Supplementary Information A Oxygen diffusion-related defects Our uncorrected prints display channels...

1989