Tumor Growth Rate & Doubling Time Calculator
Calculate clinical kinetics based on volumetric measurements over time.
Specific Growth Rate (k):
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Doubling Time (DT):
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Daily Increase (%):
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Total Volume Change:
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How to Calculate Tumor Growth Rate
In clinical oncology and radiology, understanding how quickly a lesion is growing is vital for determining treatment efficacy and prognosis. The most common way to quantify this is through the Specific Growth Rate (SGR) and the Volume Doubling Time (VDT).
Tumor growth often follows an exponential model, especially in early stages. To calculate these values, you need two measurements of the tumor volume (V1 and V2) and the time interval between those measurements (T).
Formula for Growth Rate (k):
k = [ln(V2) – ln(V1)] / (t2 – t1)
Formula for Doubling Time (DT):
DT = ln(2) / k
k = [ln(V2) – ln(V1)] / (t2 – t1)
Formula for Doubling Time (DT):
DT = ln(2) / k
Understanding the Results
- Specific Growth Rate (k): This represents the speed of growth. A higher "k" value indicates a more aggressive, faster-growing tumor.
- Doubling Time (DT): This is the time required for the tumor to double in volume. In aggressive cancers, the DT might be only a few days, whereas in indolent (slow-growing) cancers, it could be hundreds of days.
- Percent Daily Increase: This converts the exponential growth rate into a simple daily percentage of new cell mass.
Practical Example
Imagine a patient has a lung nodule measured at 200 mm³ on January 1st. A follow-up scan on January 31st (30 days later) shows the nodule has grown to 450 mm³.
- Step 1: Calculate the natural logs: ln(450) ≈ 6.109, ln(200) ≈ 5.298.
- Step 2: Subtract: 6.109 – 5.298 = 0.811.
- Step 3: Divide by time: 0.811 / 30 days = 0.027 (Specific Growth Rate).
- Step 4: Doubling Time: ln(2) / 0.027 ≈ 25.6 days.
Why Volume is Better Than Diameter
While RECIST criteria often focus on the longest diameter, volume is a much more sensitive indicator of growth. A small increase in diameter (e.g., from 10mm to 13mm) actually represents a doubling in total volume. Calculating the volumetric growth rate provides a more accurate picture of the tumor burden change.