Published June 2000
Revised July 2004

Doubling Time
One cell divides into two, 2 to 4, 4 to 8, 8 to 16 etc. Exponential growth is found in many primary and metastatic malignancies. Use these calculators to determine doubling time.

Initial Film Date
 Enter dates as dd/mm/yyyy
Final Film Date
Days between studies
Initial Diameter (mm)
Final Diameter (mm)
Time between studies (days)
Doubling Time (days)
Model of Exponential Growth - click to play
Initial Volume (mm3)
Final Volume (mm3)
Time between studies (days)
Doubling Time (days)
Clinical Value of Growth Rate:
  • Differential diagnosis
  • Predictor of longevity
  • Planning screening programs
  • Evaluate therapy
  • Study natural history

Growth rate of malignant tumors generally between 30 and 500 days (median 100 days).

Error rate in measuring growth rate: 7%

Minimal difference observable by CT: 0.3 mm

Smallest nodules that can be reliably seen with CT: 2 mm

Diameter reliable? (from Revel)

  • Intrareader variability 1.32 to 1.7 mm
  • Interreader variability 1.73 mm
  • thus to state wind confidence that a nodule has truly increased in size when measurements are made by 2 radiologists requires that the size increase (or decrease) by 1.73 mm
  • In contrast volume (as determined by computer program) has much less variability

Natural History of Growth
Doublings
Cells
Diameter
0
1
10 um
microscopic
20
1 x 106
1 mm
microscopic
30
1 x 109
1 cm
Detectable CXR
35
1 x 1010.5
3 cm
Average Diagnosis
40
1 x 1012
10 cm
Death
Equation for Doubling time = Ti x log2 / 3 x log(Di/Do) or (ln2 x Ti)/(ln(Vi/Vo)
  • Ti = interval time
  • Di = initial diameter
  • Do = final diameter
  • Vi = initial volume
  • Vo = final volume
    • References:

    Collins VP, Loeffler RK, Tivey H. Observations on growth rates of human tumors. AJR 1957; 76:988-1000.

    Geddes DM. The natural history of lung cancer: a review based on rates of tumour growth. Br J Dis Chest 1979; 73:1-17.
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    Yankelevitz DF, Henschke CI. Does 2-year stability imply that pulmonary nodules are benign? AJR Am J Roentgenol 1997; 168:325-328.
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    Yankelevitz DF, Gupta R, Zhao B, Henschke CI. Small pulmonary nodules: evaluation with repeat CT--preliminary experience. Radiology 1999; 212:561-6.
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    M. Hasegawa, S. Sone, S. Takashima, F. Li, Z. G. Yang, Y. Maruyama and T. Watanabe. Growth rate of small lung cancers detected on mass CT screening. Br J Radiol 2000; 73:1252.
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    Winer-Muram HT, Jennings SG, Tarver RD, et al. Volumetric growth rate of stage I lung cancer prior to treatment: serial CT scanning. Radiology 2002; 223:798-805.
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    Revel MP, Bissery A, Bienvenu M, et al. Are two-dimensional CT measurements of small noncalcified pulmonary nodules reliable? Radiology 2004; 231:453-8.
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    Revel MP, Lefort C, Bissery A, et al. Pulmonary nodules: preliminary experience with three-dimensional evaluation. Radiology 2004; 231:459-66.
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    Kostis WJ, Yankelevitz DF, Reeves AP, Fluture SC, Henschke CI. Small pulmonary nodules: reproducibility of three-dimensional volumetric measurement and estimation of time to follow-up CT. Radiology 2004; 231:446-52.
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