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Tumor Volume Distributions Based on Weibull Distributions of Maximum Tumor Diameters


Schneider, Uwe; Radonic, Stephan; Besserer, Jürgen (2023). Tumor Volume Distributions Based on Weibull Distributions of Maximum Tumor Diameters. Applied Sciences, 13(19):10925.

Abstract

(1) Background: The distribution of tumor volumes is important for various aspects of cancer research. Unfortunately, tumor volume is rarely documented in tumor registries; usually only maximum tumor diameter is. This paper presents a method to derive tumor volume distributions from tumor diameter distributions. (2) Methods: The hypothesis is made that tumor maximum diameters d are Weibull distributed, and tumor volume is proportional to dk, where k is a parameter from the Weibull distribution of d. The assumption is tested by using a test dataset of 176 segmented tumor volumes and comparing the k obtained by fitting the Weibull distribution of d and from a direct fit of the volumes. Finally, tumor volume distributions are calculated from the maximum diameters of the SEER database for breast, NSCLC and liver. (3) Results: For the test dataset, the k values obtained from the two separate methods were found to be k = 2.14 ± 0.36 (from Weibull distribution of d) and 2.21 ± 0.25 (from tumor volume). The tumor diameter data from the SEER database were fitted to a Weibull distribution, and the resulting parameters were used to calculate the corresponding exponential tumor volume distributions with an average volume obtained from the diameter fit. (4) Conclusions: The agreement of the fitted k using independent data supports the presented methodology to obtain tumor volume distributions. The method can be used to obtain tumor volume distributions when only maximum tumor diameters are available.

Abstract

(1) Background: The distribution of tumor volumes is important for various aspects of cancer research. Unfortunately, tumor volume is rarely documented in tumor registries; usually only maximum tumor diameter is. This paper presents a method to derive tumor volume distributions from tumor diameter distributions. (2) Methods: The hypothesis is made that tumor maximum diameters d are Weibull distributed, and tumor volume is proportional to dk, where k is a parameter from the Weibull distribution of d. The assumption is tested by using a test dataset of 176 segmented tumor volumes and comparing the k obtained by fitting the Weibull distribution of d and from a direct fit of the volumes. Finally, tumor volume distributions are calculated from the maximum diameters of the SEER database for breast, NSCLC and liver. (3) Results: For the test dataset, the k values obtained from the two separate methods were found to be k = 2.14 ± 0.36 (from Weibull distribution of d) and 2.21 ± 0.25 (from tumor volume). The tumor diameter data from the SEER database were fitted to a Weibull distribution, and the resulting parameters were used to calculate the corresponding exponential tumor volume distributions with an average volume obtained from the diameter fit. (4) Conclusions: The agreement of the fitted k using independent data supports the presented methodology to obtain tumor volume distributions. The method can be used to obtain tumor volume distributions when only maximum tumor diameters are available.

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Additional indexing

Item Type:Journal Article, refereed, original work
Communities & Collections:07 Faculty of Science > Physics Institute
Dewey Decimal Classification:530 Physics
Scopus Subject Areas:Physical Sciences > General Materials Science
Physical Sciences > Instrumentation
Physical Sciences > General Engineering
Physical Sciences > Process Chemistry and Technology
Physical Sciences > Computer Science Applications
Physical Sciences > Fluid Flow and Transfer Processes
Uncontrolled Keywords:Fluid Flow and Transfer Processes, Computer Science Applications, Process Chemistry and Technology, General Engineering, Instrumentation, General Materials Science
Language:English
Date:2 October 2023
Deposited On:15 Dec 2023 12:13
Last Modified:29 Jun 2024 01:40
Publisher:MDPI Publishing
ISSN:2076-3417
OA Status:Gold
Free access at:Publisher DOI. An embargo period may apply.
Publisher DOI:https://doi.org/10.3390/app131910925
  • Content: Published Version
  • Language: English
  • Licence: Creative Commons: Attribution 4.0 International (CC BY 4.0)