How is this tool used in Oncology?

1. Measuring and Tracking Tumor Volumes

• Instant Geometric Conversion: The ruler allows clinicians to take a single radius or diameter measurement of a radiographic or clinical lesion and instantly find its estimated spherical volume and Volume Doubling Number ($n$).
• Tracking Disease Velocity: By looking at the change in the doubling number over time ($\Delta n$), oncologists can calculate the Volume Doubling Time (VDTime) for growing tumors. For responding tumors, it can calculate the Volume Halving Time (VHTime) or Regression Velocity (RV).
• Total Tumor Burden: Clinicians can sum the individual volumes of multiple parameter lesions to calculate a patient’s total body tumor burden and its corresponding total $n$ value.

2. Standardizing Treatment Response Criteria

Different oncological bodies use different geometric metrics to define whether a tumor is responding to treatment, progressing, or stable. The VADRuler allows investigators to easily compare these diverse criteria side-by-side:

• RECIST: Uses the sum of the longest diameters.
• WHO & Cheson Criteria: Use the sum of the products of perpendicular diameters (effectively measuring area).
• The ruler unifies these single-vector data points (diameter, area, and volume) so a clinician can evaluate a single lesion’s response across all three standards simultaneously.

3. Estimating Malignant Cell Density

• Baseline Cell Counts: The VADRuler normalizes a 1 cm³ tumor to $n_{30}$, utilizing the Collins model which suggests this volume can contain up to 1 billion cancer cells.
• Biopsy Adjustments: If a tumor biopsy indicates a lower cell density (e.g., only 100,000 cells/cc), the baseline formula can be adjusted using $n_{cc} = \frac{\log(10^y \text{ cells/cc})}{\log(2)}$ to give a more accurate representation of the actual malignant cell count. The document notes this principle could also be extended to track stem cell counts.

4. Specialized Oncology Scenarios

• Dermatology (Melanoma): Because the depth of cutaneous metastases or superficial spreading melanomas can be difficult to estimate, the Area Doubling Ruler (ADR) calculates the Area Doubling Number ($n_A$). If a superficial lesion eventually becomes nodular and 3D, the tool seamlessly accommodates the transition from 2D area tracking to 3D volume tracking.
• Gastrointestinal Stromal Tumors (GIST): In specific cases where tumors lose metabolic activity (seen on PET scans) without actually shrinking in physical diameter, the ruler helps quantify the response. Clinicians use the volumes and $n$ values to subtract the metabolically inactive tissue, allowing them to calculate the “truer smaller active cancer volume.”