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J Neurol Surg B Skull Base 2019; 80(01): 072-078
DOI: 10.1055/s-0038-1667148
Original Article
Georg Thieme Verlag KG Stuttgart · New York

Mathematical Models for Tumor Growth and the Reduction of Overtreatment

Berdine L. Heesterman
1   Department of Otorhinolaryngology, Leiden University Medical Center, Leiden, The Netherlands
,
John-Melle Bokhorst
1   Department of Otorhinolaryngology, Leiden University Medical Center, Leiden, The Netherlands
,
Lisa M. H. de Pont
1   Department of Otorhinolaryngology, Leiden University Medical Center, Leiden, The Netherlands
,
Berit M. Verbist
2   Department of Radiology, Leiden University Medical Center, Leiden, The Netherlands
,
Jean-Pierre Bayley
3   Department of Human Genetics, Leiden University Medical Center, Leiden, The Netherlands
,
Andel G. L. van der Mey
1   Department of Otorhinolaryngology, Leiden University Medical Center, Leiden, The Netherlands
,
Eleonora P. M. Corssmit
4   Department of Endocrinology, Leiden University Medical Center, Leiden, The Netherlands
,
Frederik J. Hes
5   Department of Clinical Genetics, Leiden University Medical Center, Leiden, The Netherlands
,
Peter Paul G. van Benthem
1   Department of Otorhinolaryngology, Leiden University Medical Center, Leiden, The Netherlands
,
Jeroen C. Jansen
1   Department of Otorhinolaryngology, Leiden University Medical Center, Leiden, The Netherlands
› Author Affiliations
Further Information

Publication History

10 December 2017

13 June 2018

Publication Date:
23 July 2018 (online)

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Abstract

Background To improve our understanding of the natural course of head and neck paragangliomas (HNPGL) and ultimately differentiate between cases that benefit from early treatment and those that are best left untreated, we studied the growth dynamics of 77 HNPGL managed with primary observation.

Methods Using digitally available magnetic resonance images, tumor volume was estimated at three time points. Subsequently, nonlinear least squares regression was used to fit seven mathematical models to the observed growth data. Goodness of fit was assessed with the coefficient of determination (R 2) and root-mean-squared error. The models were compared with Kruskal–Wallis one-way analysis of variance and subsequent post-hoc tests. In addition, the credibility of predictions (age at onset of neoplastic growth and estimated volume at age 90) was evaluated.

Results Equations generating sigmoidal-shaped growth curves (Gompertz, logistic, Spratt and Bertalanffy) provided a good fit (median R 2: 0.996–1.00) and better described the observed data compared with the linear, exponential, and Mendelsohn equations (p < 0.001). Although there was no statistically significant difference between the sigmoidal-shaped growth curves regarding the goodness of fit, a realistic age at onset and estimated volume at age 90 were most often predicted by the Bertalanffy model.

Conclusions Growth of HNPGL is best described by decelerating tumor growth laws, with a preference for the Bertalanffy model. To the best of our knowledge, this is the first time that this often-neglected model has been successfully fitted to clinically obtained growth data.

Keywords

paragangliomas - growth - carotid body tumors - vagal body - mathematics - models
 

  • References

  • 1 van Hulsteijn LT, Heesterman B, Jansen JC. , et al. No evidence for increased mortality in SDHD variant carriers compared with the general population. Eur J Hum Genet 2015; 23 (12) 1713-1716
    PubMedGoogle Scholar
  • 2 Boedeker CC. Paragangliomas and paraganglioma syndromes. GMS Curr Top Otorhinolaryngol Head Neck Surg 2011; 10: Doc03
    PubMedGoogle Scholar
  • 3 Weissman JL, Hirsch BE. Beyond the promontory: the multifocal origin of glomus tympanicum tumors. AJNR Am J Neuroradiol 1998; 19 (01) 119-122
    PubMedGoogle Scholar
  • 4 Boedeker CC, Hensen EF, Neumann HP. , et al. Genetics of hereditary head and neck paragangliomas. Head Neck 2014; 36 (06) 907-916
    CrossrefPubMedGoogle Scholar
  • 5 Taïeb D, Kaliski A, Boedeker CC. , et al. Current approaches and recent developments in the management of head and neck paragangliomas. Endocr Rev 2014; 35 (05) 795-819
    CrossrefPubMedGoogle Scholar
  • 6 Heesterman BL, Bayley JP, Tops CM. , et al. High prevalence of occult paragangliomas in asymptomatic carriers of SDHD and SDHB gene mutations. Eur J Hum Genet 2013; 21 (04) 469-470
    PubMedGoogle Scholar
  • 7 Suárez C, Rodrigo JP, Mendenhall WM. , et al. Carotid body paragangliomas: a systematic study on management with surgery and radiotherapy. Eur Arch Otorhinolaryngol 2014; 271 (01) 23-34
    CrossrefPubMedGoogle Scholar
  • 8 Hensen EF, Jansen JC, Siemers MD. , et al. The Dutch founder mutation SDHD.D92Y shows a reduced penetrance for the development of paragangliomas in a large multigenerational family. Eur J Hum Genet 2010; 18 (01) 62-66
    PubMedGoogle Scholar
  • 9 Heesterman BL, de Pont LMH, Verbist BM. , et al. Age and tumor volume predict growth of carotid and vagal body paragangliomas. J Neurol Surg B Skull Base 2017; 78 (06) 497-505
    Article in Thieme ConnectPubMedGoogle Scholar
  • 10 Carlson ML, Sweeney AD, Wanna GB, Netterville JL, Haynes DS. Natural history of glomus jugulare: a review of 16 tumors managed with primary observation. Otolaryngol Head Neck Surg 2015; 152 (01) 98-105
    CrossrefPubMedGoogle Scholar
  • 11 Gerlee P. The model muddle: in search of tumor growth laws. Cancer Res 2013; 73 (08) 2407-2411
    CrossrefPubMedGoogle Scholar
  • 12 Talkington A, Durrett R. Estimating tumor growth rates in vivo. Bull Math Biol 2015; 77 (10) 1934-1954
    CrossrefPubMedGoogle Scholar
  • 13 Benzekry S, Lamont C, Beheshti A. , et al. Classical mathematical models for description and prediction of experimental tumor growth. PLOS Comput Biol 2014; 10 (08) e1003800
    CrossrefPubMedGoogle Scholar
  • 14 Heesterman BL, Verbist BM, van der Mey AG. , et al. Measurement of head and neck paragangliomas: is volumetric analysis worth the effort? A method comparison study. Clin Otolaryngol 2016; 41 (05) 571-578
    CrossrefPubMedGoogle Scholar
  • 15 Collins VP, Loeffler RK, Tivey H. Observations on growth rates of human tumors. Am J Roentgenol Radium Ther Nucl Med 1956; 76 (05) 988-1000
    PubMedGoogle Scholar
  • 16 Laird AK. Dynamics of tumor growth. Br J Cancer 1964; 13: 490-502
    PubMedGoogle Scholar
  • 17 Spratt JA, von Fournier D, Spratt JS, Weber EE. Decelerating growth and human breast cancer. Cancer 1993; 71 (06) 2013-2019
    CrossrefPubMedGoogle Scholar
  • 18 Vaidya VG, Alexandro Jr FJ. Evaluation of some mathematical models for tumor growth. Int J Biomed Comput 1982; 13 (01) 19-36
    CrossrefPubMedGoogle Scholar
  • 19 Som PM, Curtin H. Chapter 38 parapharyngeal and masticator space lesions. In: Som PM, Curtin H. , eds. Head and Neck Imaging. St. Louis: Mosby; 2003: 1954-2003
    Google Scholar
  • 20 Knöfel WT, Otto U, Baisch H, Klöppel G. Stability of human renal cell carcinomas during long term serial transplantation into nude mice: histopathology, nuclear grade, mitotic rate, and DNA content in thirty tumors. Cancer Res 1987; 47 (01) 221-224
    PubMedGoogle Scholar
  • 21 Nakasu S, Nakasu Y, Fukami T, Jito J, Nozaki K. Growth curve analysis of asymptomatic and symptomatic meningiomas. J Neurooncol 2011; 102 (02) 303-310
    CrossrefPubMedGoogle Scholar
  • 22 An C, Choi YA, Choi D. , et al. Growth rate of early-stage hepatocellular carcinoma in patients with chronic liver disease. Clin Mol Hepatol 2015; 21 (03) 279-286
    CrossrefPubMedGoogle Scholar
  • 23 Park Y, Choi D, Lim HK. , et al. Growth rate of new hepatocellular carcinoma after percutaneous radiofrequency ablation: evaluation with multiphase CT. AJR Am J Roentgenol 2008; 191 (01) 215-220
    CrossrefPubMedGoogle Scholar
  • 24 Crispen PL, Soljic A, Stewart G, Kutikov A, Davenport D, Uzzo RG. Enhancing renal tumors in patients with prior normal abdominal imaging: further insight into the natural history of renal cell carcinoma. J Urol 2012; 188 (04) 1089-1093
    CrossrefPubMedGoogle Scholar
  • 25 Honegger J, Zimmermann S, Psaras T. , et al. Growth modelling of non-functioning pituitary adenomas in patients referred for surgery. Eur J Endocrinol 2008; 158 (03) 287-294
    CrossrefPubMedGoogle Scholar
  • 26 Jung M. Breast, prostate, and thyroid cancer screening tests and overdiagnosis. Curr Probl Cancer 2017; 41 (01) 71-79
    CrossrefPubMedGoogle Scholar
  • 27 Draisma G, Etzioni R, Tsodikov A. , et al. Lead time and overdiagnosis in prostate-specific antigen screening: importance of methods and context. J Natl Cancer Inst 2009; 101 (06) 374-383
    CrossrefPubMedGoogle Scholar
  • 28 Benson JR, Jatoi I, Toi M. Treatment of low-risk ductal carcinoma in situ: is nothing better than something?. Lancet Oncol 2016; 17 (10) e442-e451
    CrossrefPubMedGoogle Scholar
  • 29 Bokhorst LP, Valdagni R, Rannikko A. , et al; PRIAS study group. A decade of active surveillance in the PRIAS study: an update and evaluation of the criteria used to recommend a switch to active treatment. Eur Urol 2016; 70 (06) 954-960
    CrossrefPubMedGoogle Scholar
  • 30 Elshof LE, Tryfonidis K, Slaets L. , et al. Feasibility of a prospective, randomised, open-label, international multicentre, phase III, non-inferiority trial to assess the safety of active surveillance for low risk ductal carcinoma in situ - The LORD study. Eur J Cancer 2015; 51 (12) 1497-1510
    CrossrefPubMedGoogle Scholar
  • 31 Halliday J, Rutherford SA, McCabe MG, Evans DG. An update on the diagnosis and treatment of vestibular schwannoma. Expert Rev Neurother 2018; 18 (01) 29-39
    CrossrefPubMedGoogle Scholar
  • 32 Lee EJ, Park JH, Park ES, Kim JH. “Wait-and-See” strategies for newly diagnosed intracranial meningiomas based on the risk of future observation failure. World Neurosurg 2017; 107: 604-611
    CrossrefPubMedGoogle Scholar