AbdomenGen: Sequential Volume-Conditioned Diffusion Framework for Abdominal Anatomy Generation

1. Problem Statement

Computational anatomical phantoms are essential for virtual imaging trials, radiation dosimetry, and surgical simulation. However, current methods face three critical limitations:

• Lack of Fidelity & Diversity: Existing models often fail to generate realistic, spatially coherent organs with sufficient morphological diversity, particularly for rare or pathological anatomies.
• Uncalibrated Control: While some generative models exist, they lack habitus-aware, organ-wise controllability. Specifically, conditioning directly on raw organ volume creates contradictory signals because organ size is naturally coupled to body habitus (body size).
• Sequential Consistency: Jointly generating multiple organs often struggles to maintain spatial consistency and global anatomical coherence.

The authors aim to solve the problem of generating controllable, multi-organ abdominal phantoms where organ sizes can be independently modulated without breaking anatomical relationships or re-encoding body habitus information.

2. Methodology: AbdomenGen

The proposed framework is a sequential, volume-conditioned diffusion model designed to synthesize 11 abdominal organs one by one.

A. Core Architecture

• Representation: Organs are represented as Signed Distance Fields (SDFs) on a fixed grid, providing smooth geometric signals suitable for diffusion modeling.
• Sequential Generation Strategy:
  • Organs are generated in a predefined order (from large, spatially defining structures to smaller, dependent ones).
  • For each organ $o_i$, the model conditions on:
    1. The Body Mask SDF ($B$).
    2. The Context SDF ($S^i_{ctx}$): An aggregation of all previously generated organs (computed as the max of prior SDFs).
    3. The Volume Control Scalar ($v_o$).
  • This autoregressive approach ensures that each new organ respects the spatial constraints of the body and previously placed organs.

B. Volume Control Scalar (VCS)

To address the coupling between organ size and body habitus, the authors introduce the Volume Control Scalar (VCS):

• Decoupling Mechanism: Instead of using raw volume, the model predicts the expected organ volume ($\hat{V}_o$) as a linear function of the body volume ($V_B$).
• Residual Calculation: The control variable is the standardized residual of the actual volume relative to the predicted volume based on body size:
  $$v_i = \frac{(V^{ref}_i - \hat{V}_i(V_B)) - \mu_i}{\sigma_i}$$
• Benefit: This creates an interpretable control axis that modulates organ size independently of the body habitus, preventing the model from requesting impossible body-organ volume pairs.

C. Diffusion Model & Training

• Network: A 3D denoising diffusion U-Net with FiLM (Feature-wise Linear Modulation) conditioning to inject the VCS scalar into intermediate network features.
• Inputs: Noisy organ SDF, Body SDF, Context SDF, and VCS.
• Loss Function:
  • $L_{SDF}$: $\ell_1$ reconstruction loss for the SDF.
  • $L_{BCE}$: Binary cross-entropy for the occupancy mask.
  • $L_{ov}$: Differentiable reverse Dice penalty to prevent organ overlap.
  • $L_{vcs}$: A calibration loss (activated after initial epochs) that forces the predicted volume's standardized residual to match the target VCS.

3. Key Contributions

1. AbdomenGen Framework: A scalable diffusion system generating 11 abdominal organs sequentially, achieving spatial coherence and independent organ-wise control.
2. Volume Control Scalar (VCS): A novel conditioning variable that decouples organ size from body habitus, resolving the "contradictory signal" problem of raw volume conditioning and providing a calibrated control axis.
3. Distribution-Level Controllability: The ability to match target patient populations (e.g., pathological cohorts) by selecting specific VCS distributions, demonstrated by a 73.6% reduction in distributional distance to a hepatomegaly cohort without retraining.

4. Experimental Results

The model was trained on 556 abdominal CT scans (314 train, 200 test) and evaluated against reference masks and external cohorts.

• Geometric Fidelity:
  • Achieved strong Dice scores, particularly for the liver (0.83 ± 0.05).
  • Lower scores for smaller/variable organs (e.g., Kidneys: 0.60) were attributed to surface deviations rather than volumetric failure.
  • Manifold Realism: Generated samples remained on the empirical anatomical manifold (distance to nearest training neighbor matched reference masks), proving the model did not simply memorize training data.
• Controllability:
  • Single-Organ: Sweeping VCS from -3 to +3 produced consistent, interpretable volume changes (e.g., linear scaling for liver/kidneys).
  • Multi-Organ Independence: Joint conditioning on liver and spleen showed minimal cross-coupling; changing one organ's VCS shifted the distribution primarily along the intended axis.
• Clinical Utility (Hepatomegaly):
  • By selecting an optimal VCS ($VCS = 4.9$), the framework reduced the Wasserstein-1 distance between generated liver volumes and a real-world hepatomegaly (enlarged liver) cohort by 73.6% (from 899.5 mL to 237.0 mL).
• Diversity: Compared to the MAISI model, AbdomenGen produced higher inter-sample variability (lower pairwise Dice, higher Chamfer distance), indicating a broader range of plausible anatomies.

5. Significance and Conclusion

AbdomenGen represents a significant advancement in computational phantom generation by bridging the gap between deep learning flexibility and clinical interpretability.

• Clinical Relevance: It enables the on-demand creation of "stress-test" populations for rare pathologies (like hepatomegaly) without requiring new data collection or complex post-hoc registration.
• Methodological Innovation: The VCS approach offers a robust solution for controlling geometric attributes in generative models where attributes are naturally correlated (size vs. habitus).
• Future Impact: The framework supports virtual imaging trials and segmentation stress-testing. While current limitations include error accumulation in sequential synthesis and difficulty with tubular structures (colon), the work establishes a foundation for statistically grounded, controllable anatomical modeling.