SLD: Sum of Target Lesion Diameters

• SLD is a quantitative measure defined as the sum of the longest diameters of selected lesions, providing a standardized metric for tumor burden.
• The PDNet framework automates lesion segmentation via a two-stage process that integrates click-driven guidance with high-resolution keypoint regression.
• Clinical evaluations indicate that PDNet reduces inter-observer variability and delivers accurate RECIST measurements, supporting improved therapy response monitoring.

The Sum of Diameter of Target Lesions (SLD) is a quantitative metric defined by the Response Evaluation Criteria In Solid Tumors (RECIST) guideline for evaluating the aggregate size of selected target lesions on volumetric CT studies. SLD is determined as the sum of the longest diameters of a set of $N$ target lesions, each measured as the maximum linear span within the lesion on the axial slice showing the largest cross-section. SLD plays a critical role in monitoring disease progression and response to therapy in oncology, serving as a standardized endpoint for clinical assessment and trial response evaluation.

1. Principle and Formal Definition of SLD

SLD is computed by first identifying $N$ target lesions within a CT series. For each lesion, the long-axis diameter $D_i$ is measured as the greatest linear distance between two endpoints in the axial plane with the largest lesion section. The SLD is then formally defined as

$\mathrm{SLD} = \sum_{i=1}^N D_i$

where $D_i$ denotes the long-axis RECIST measurement for the $i$-th lesion. This operationalizes tumor burden as a single scalar, facilitating longitudinal comparison and therapy response tracking according to RECIST protocols (Tang et al., 2021).

2. Two-Stage PDNet Pipeline for SLD Computation

The PDNet framework enables fully automated lesion segmentation and RECIST diameter prediction from volumetric CT data with click-driven guidance. The process is organized as follows:

1. Stage 1 – Coarse Segmentation: A radiologist provides a single click $p = (x_0, y_0)$ on or near the lesion within the relevant axial slice. This input yields two prior channels:
   • A delta-image $\mathcal{C}(x, y)$, a one-pixel impulse at $(x_0, y_0)$.
   • A distance-transform channel $$\mathcal{D}(x, y) = \sqrt{(x - x_0)^2 + (y - y_0)^2}$$. Together with the CT intensity image, these form a 3-channel input to PDNet.
2. Stage 2 – High-Resolution Segmentation and Diameter Regression: The lesion of interest (LOI) is re-segmented at higher resolution. The network predicts four keypoint heat-maps ($N$0) corresponding to the endpoints of two RECIST axes. The spatial argmax of each heat-map yields keypoint coordinates $N$1, from which the long $N$2 and perpendicular short $N$3 axes are extracted using pixel spacing calibration.

The outputs for each lesion—specifically, the long-axis length—are accumulated across the $N$4 target lesions to yield the patient-level SLD (Tang et al., 2021).

3. PDNet Architecture and Loss Functions

The PDNet’s architecture consists of a ResNeSt-50 image encoder producing multi-scale feature maps $N$5, a parallel prior encoder generating attention maps $N$6, and a dual-path decoder that aggregates top-down (T2D) and bottom-up (B2U) features. The aggregation at each scale $N$7 is

$N$8

where $N$9 and $D_i$0 denote upsampled and downsampled features, respectively. A scale-aware channel attention block further refines $D_i$1.

Supervision is imposed through several losses:

• Segmentation Loss: At each decoder side-output,

$D_i$2

and an IoU-based loss

$D_i$3

yielding $D_i$4.

• RECIST Diameter (Keypoint) Loss: Applied to Gaussian heat-maps around endpoint keypoints,

$D_i$5

• Overall Loss:

$D_i$6

with $D_i$7 (Tang et al., 2021).

4. Extraction and Aggregation of RECIST Diameters

The extraction of RECIST diameters proceeds via heat-map regression:

• Endpoint coordinates $D_i$8 are obtained from the argmax of heat-maps $D_i$9.
• The long-axis diameter $\mathrm{SLD} = \sum_{i=1}^N D_i$0 is computed as the maximum of the two pairwise Euclidean distances:

$\mathrm{SLD} = \sum_{i=1}^N D_i$1

where $\mathrm{SLD} = \sum_{i=1}^N D_i$2.

• Per the RECIST guideline, SLD is the sum of $\mathrm{SLD} = \sum_{i=1}^N D_i$3 over all $\mathrm{SLD} = \sum_{i=1}^N D_i$4 selected targets.

This method ensures explicit and reproducible aggregation of tumor burden suitable for quantitative monitoring (Tang et al., 2021).

5. Performance Evaluation and Clinical Reliability

PDNet’s SLD measurements demonstrate high reliability on both the DeepLesion dataset (1,000 images) and an external multi-organ test set (1,350 lesions):

• Segmentation Dice: 0.924 ± 0.045 (DeepLesion), 0.885 ± 0.049 (external)
• Long-axis error: 1.733 ± 1.470 mm (DeepLesion), 2.174 ± 1.437 mm (external)
• Short-axis error: 1.524 ± 1.374 mm, 1.829 ± 1.339 mm

Compared to prior one-click approaches, PDNet reduces diameter bias by 0.01 to 0.4 mm and improves segmentation Dice by over 1%. Sub–2 mm endpoint error suggests that the automated SLD lies within clinically acceptable inter-reader variability for routine RECIST practice. This implies that PDNet-based SLD computation can serve as a reliable surrogate for manual expert measurement in clinical and research contexts (Tang et al., 2021).

6. Workflow Integration, Advantages, and Limitations

Clinical Workflow Integration

• Input: Radiologist loads the CT series and clicks once on each identified target lesion at its largest axial section.
• Processing: PDNet segments the lesion, regresses the four RECIST endpoints, computes both primary axes, and accumulates the SLD.
• Output: SLD serves as the primary quantitative measure for therapy response.

Advantages

• Significantly reduces manual tracing and measurement burden.
• Eliminates inter-observer variability in axis placement and orientation.
• Provides pixel-wise masks enabling subsequent volumetric analysis.

Limitations and Open Problems

• PDNet operates on a slice-by-slice basis; 3D/volumetric consistency remains an open research area.
• Extremely irregular, diffuse, or low-contrast lesions present ongoing challenges.
• Training uses pseudo-masks derived from RECIST ellipses and morphological snakes, suggesting that acquisition of accurate ground-truth masks could further improve robustness.
• Minimal user input is required; full automation would require reliable upstream lesion detection and tracking modules (Tang et al., 2021).

7. Summary and Implications

SLD, as operationalized through automated frameworks like PDNet, is a precise, scalable metric for quantitatively tracking solid tumor lesions by aggregating RECIST-defined diameters. The PDNet pipeline, utilizing click-driven attention and dual-path multi-scale aggregation, demonstrates clinically acceptable accuracy and can substantially streamline measurement workflows. Broader adoption is contingent on enhancements for volumetric consistency, more challenging lesion types, and eventual progression to fully automated lesion identification pipelines (Tang et al., 2021).