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Lesion-Aware Adaptive Fourier Neural Operator for CT-to-PSMA PET Synthesis in Prostate Cancer

The paper introduces LAFNO, a lesion-aware adaptive Fourier neural operator that utilizes efficient CT-derived proxy channels for local density and texture to synthesize PSMA-PET images from CT scans, significantly improving tumor activity accuracy and radiomics reproducibility compared to standard global-loss models while maintaining high whole-volume image quality.

Original authors: Rashmi Bhaskara, Waleed M. Almutairi, Matthew Gopaulchan, Maram Musaad Alqurashi, Francis Asamoah, Alex Ocana, Clinton D. Bahler, Oluwaseyi M. Oderinde

Published 2026-08-12

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CC BY 4.0

Original authors: Rashmi Bhaskara, Waleed M. Almutairi, Matthew Gopaulchan, Maram Musaad Alqurashi, Francis Asamoah, Alex Ocana, Clinton D. Bahler, Oluwaseyi M. Oderinde

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

Imagine trying to find a tiny, glowing firefly hidden inside a massive, pitch-black warehouse. That's roughly what doctors face when they try to spot prostate cancer using modern imaging. They use a special scanner called a PET scan, which acts like a night-vision camera for cancer cells. These cells "eat" a radioactive tracer, making them light up like little stars against the dark background of healthy tissue. This is incredibly helpful for finding where the cancer has spread, but getting a PET scan is expensive, requires special radioactive materials that don't last long, and needs a machine that is in high demand.

To make things easier, scientists have been trying to teach computers to "imagine" what the PET scan would look like just by looking at a standard CT scan. A CT scan is like a detailed 3D X-ray that shows the shape and density of your bones and organs, but it's terrible at showing the soft, squishy details where cancer hides. It's like trying to guess the flavor of a cake just by looking at the box it came in. The challenge is that cancer spots are often tiny compared to the whole body, so when computers try to learn this trick, they often get distracted by the huge, boring background and miss the tiny, important fireflies. This paper introduces a new, clever way to teach the computer to stop ignoring those fireflies and start paying attention to the specific neighborhoods where they live.

The researchers behind this study, Rashmi Bhaskara and her team, have built a new AI model they call LAFNO (Lesion-Aware Adaptive Fourier Neural Operator). Think of LAFNO as a super-smart artist who is learning to paint a glowing picture of a tumor based only on a black-and-white sketch. In the past, these artists were trained to make the entire painting look as similar as possible to the real thing, pixel by pixel. The problem was that the "background" pixels (healthy tissue) made up 99% of the picture, so the artist would get an A+ for painting the background perfectly but still miss the tiny, glowing tumor in the corner.

To fix this, the team realized they needed to give the artist a special pair of "glasses" to help them see where the trouble spots might be, without needing to know exactly where the tumor is beforehand. They looked at thousands of real scans and noticed two simple patterns in the CT images around cancer:

The Contrast Proxy: Cancer spots often sit in a zone where the tissue density changes quickly, like a cliff edge. The model uses a mathematical trick to highlight these "cliffs."
The Disorder Proxy: The tissue right next to a tumor is often messy and chaotic, unlike the smooth, orderly healthy tissue. The model uses another trick to spot this "messiness."

Instead of feeding the computer a complex, pre-calculated map of the tumor (which takes too long and requires a human to draw it first), LAFNO uses these two simple "glasses" to condition its brain. It's like telling the artist, "Hey, pay extra attention to the cliffs and the messy patches; that's where the fireflies usually hang out."

But the team didn't stop there. They also changed the rules of the game. Instead of just grading the artist on how the whole painting looks, they added a special rule: "You must get the brightness of the fireflies exactly right." They created a new scoring system that specifically checks the total light coming from the tumor areas. If the artist paints the background perfectly but the tumor is too dim, they get a bad score. This forces the AI to care about the tiny, important details, not just the big picture.

When they tested this new system, the results were promising. The LAFNO model was just as good at painting the background as the other top models, with a structural similarity score (SSIM) of 0.960 for one type of tracer and 0.938 for another. But the real magic happened with the tumors. While other models often guessed the tumor's brightness with an error of around 60% to 70%, LAFNO brought that error down to 48.3% for one tracer and 64.0% for the other. It was also much better at recreating the tiny, intricate textures inside the tumor, which are crucial for doctors to understand how aggressive the cancer might be.

However, the authors are careful to note that this isn't a magic wand that solves everything yet. The model still struggles a bit with the "fuzzy" area right on the edge of the tumor, especially with one specific type of tracer called 68Ga-PSMA. They suggest this might be because that tracer creates a slightly blurrier image to begin with, making it harder for the AI to learn the exact boundaries. The study shows that by using these simple "cliff" and "messiness" clues, along with a stricter grading system for the tumor itself, we can get much closer to a perfect synthetic scan. It's a step forward that suggests we don't need to know exactly where the cancer is to teach a computer how to find it; we just need to teach it what the neighborhood looks like.

Technical Summary: Lesion-Aware Adaptive Fourier Neural Operator (LAFNO) for CT-to-PSMA PET Synthesis

Problem Statement
Deep learning models for synthesizing Positron Emission Tomography (PET) from Computed Tomography (CT) or Magnetic Resonance Imaging (MRI) aim to reduce patient radiation dose and scanner demand. However, existing models typically optimize for global image similarity using losses such as Mean Squared Error (MSE) or L1, treating all voxels equally. In whole-body Prostate-Specific Membrane Antigen (PSMA) PET, tumor voxels constitute a small fraction of the total volume but carry the clinically critical activity signal. Consequently, models optimized for global metrics (e.g., SSIM, PSNR) often achieve high structural similarity while underestimating lesion activity or failing to preserve tumor-specific structures. Furthermore, while radiomics offers biologically meaningful descriptors of tumor intensity and texture, direct conditioning on radiomics features is computationally expensive and requires time-consuming, operator-dependent lesion segmentation.

Methodology
The authors propose LAFNO (Lesion-Aware Adaptive Fourier Neural Operator), a framework designed to synthesize PSMA-PET from CT by integrating radiomics-motivated patterns without requiring explicit lesion segmentation during inference.

Radiomics Analysis and Proxy Derivation:
The authors first analyzed 10,209 PSMA-avid tumor regions in the TCIA PSMA-PET-CT-Lesions dataset. They observed two systematic CT signatures:
- Core-to-Periphery Attenuation: CT attenuation decreases monotonically from the tumor core to the peritumoral region.
- Texture Heterogeneity: CT texture heterogeneity increases when moving from the tumor core into the peritumoral region.
  To capture these signatures efficiently, they introduced two differentiable, CT-derived proxy channels that do not require ground-truth masks:
- Contrast Proxy: Computed via a Gaussian residual filter ( $C(x) = CT(x) - G_\sigma * CT(x)$ ) to approximate local density variation.
- Disorder Proxy: Computed via local variance over a sliding window ( $D(x) = CT_w^2(x) - (CT_w(x))^2$ ) to approximate local texture heterogeneity.
Architecture (LAFNO):
The model utilizes a 3D U-Net architecture with an Adaptive Fourier Neural Operator (AFNO) bottleneck. The two CT-derived proxy channels are injected into the bottleneck layer (after pooling) and concatenated with the latent features before passing through the AFNO blocks. This allows the model to condition the synthesis on tumor-relevant density and texture patterns.
Lesion-Aware Loss Function:
The training objective combines whole-volume reconstruction with specific lesion-level and peritumoral supervision:
- $\mathcal{L}_{L1}$ : Standard voxel-wise L1 loss for global reconstruction.
- $\mathcal{L}_{TLA}$ (Total Lesion Activity): A lesion-wise loss that supervises the summed activity of each connected component independently. It uses a logarithmic transform and normalization to prevent large lesions from dominating the gradient and to weight lesions by count rather than absolute magnitude.
- $\mathcal{L}_{c}$ (Tumor-Contrast): Applies the contrast operation to predicted and ground-truth PET volumes within the tumor mask to penalize mismatches in local uptake structure.
- $\mathcal{L}_{peri}$ (Peritumoral): An exponential distance-weighted L1 loss applied to the 0–10 mm ring outside the tumor mask, encouraging fidelity in the tumor-adjacent microenvironment.

Key Contributions

CT-Derived Proxy Conditioning: The introduction of computationally efficient contrast and disorder proxy channels that replace high-dimensional radiomics conditioning, enabling the model to learn tumor-core and peritumoral patterns without requiring segmentation during inference.
Lesion-Aware Objective: A composite loss function that explicitly supervises total lesion activity (TLA) and penalizes errors in the tumor-adjacent peritumoral region, moving beyond global similarity metrics.
Evaluation Framework: An evaluation strategy that assesses synthetic PET not only via whole-volume metrics (SSIM, PSNR) but also through lesion-level uptake metrics and tumor/peritumoral radiomics reproducibility (Intraclass Correlation Coefficient, ICC).

Results
The model was evaluated on the TCIA PSMA-PET-CT-Lesions dataset containing 18F-PSMA ( $N=335$ ) and 68Ga-PSMA ( $N=204$ ) patients, compared against four baselines: AFNO-L1, Pix2Pix, FlowLet, and cWDM.

Whole-Volume Quality: LAFNO achieved competitive global image quality, with SSIM scores of 0.960 (18F) and 0.938 (68Ga). While the baseline AFNO-L1 (without lesion-aware components) slightly outperformed LAFNO in global metrics, LAFNO prioritized lesion fidelity.
Lesion Activity Preservation: LAFNO significantly reduced per-patient TLA error compared to baselines. For 18F-PSMA, the mean absolute patient-level TLA error was reduced to 48.3% (vs. 58.7–69.0% for baselines). For 68Ga-PSMA, the error was 64.0%. LAFNO also achieved the highest fraction of lesions with TLA errors below 25%, 50%, and 75%.
Radiomics Reproducibility: LAFNO achieved the highest ICC across all feature classes (First-order, GLCM, GLRLM, GLSZM) in the tumor core for both tracers, indicating superior preservation of tumor texture and structure.
Peritumoral Fidelity: In the 0–10 mm peritumoral ring, LAFNO showed the highest ICC for 18F-PSMA across all feature classes. For 68Ga-PSMA, results were mixed, with other models performing better on certain feature classes. The authors note that peritumoral reproducibility remains challenging, particularly near the immediate tumor boundary.

Significance and Claims
The paper claims that LAFNO successfully addresses the bias of global reconstruction models toward healthy background tissue by incorporating radiomics-motivated, lesion-aware supervision. By using CT-derived proxies, the model captures biologically relevant tumor patterns (density gradients and texture heterogeneity) without the computational burden of real-time radiomics extraction or segmentation.

The authors emphasize that while LAFNO improves lesion-level accuracy and tumor-core radiomics reproducibility, peritumoral fidelity remains a significant challenge, particularly for 68Ga-PSMA. They attribute residual errors to tumor heterogeneity, the one-to-many nature of the CT-to-PET mapping, and variations in scanner parameters and tracer physics (e.g., positron range differences between 18F and 68Ga). The study concludes that synthetic PSMA-PET models must move beyond global image similarity to preserve clinically relevant tumor information, though biological fidelity in the tumor microenvironment requires further refinement.

Technical Summary: Lesion-Aware Adaptive Fourier Neural Operator (LAFNO) for CT-to-PSMA PET Synthesis

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