Skip to main content

Theoretical Study of Exponential Best-Fit: Modeling hCG for Gestational Trophoblastic Disease

  • Conference paper
  • First Online:
Knowledge Science, Engineering and Management (KSEM 2021)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 12817))

  • 1913 Accesses

Abstract

With the removal of the hydatidiform mole it has been shown that the human chorionic gonadotropin (hCG) hormone levels drop exponentially in women diagnosed with Gestational Trophoblastic Disease (GTD). This papers aims to introduce a new method at forecasting the decrease of the hCG levels as this could reduce the number of weekly blood test that a patient would require throughout the one year of monitoring. The hCG levels are modeled as a vertically shifted exponential curve, and this paper proposes and demonstrates a mathematical solution to finding the best parameters for this model. The method is validated using synthetic data as well as real data, and the results show that it is reliable, with decent accuracy and speed.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 79.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 99.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  1. Almufti, R., et al.: A critical review of the analytical approaches for circulating tumor biomarker kinetics during treatment. Ann. Oncol. 25(1), 41–56 (2014)

    Article  Google Scholar 

  2. Ammar, G., Dayawansa, W., Martin, C.: Exponential interpolation: theory and numerical algorithms. Appl. Math. Comput. 41(3), 189–232 (1991)

    MathSciNet  MATH  Google Scholar 

  3. Costigan, C., Tabirca, S., Coulter, J.: Mathematically modelling hCG in women with gestational trophoblastic disease using logarithmic transformations. In: 2016 UKSim-AMSS 18th International Conference on Computer Modelling and Simulation (UKSim), pp. 55–59. IEEE (2016)

    Google Scholar 

  4. Ehiwario, J., Aghamie, S.: Comparative study of bisection, Newton-Raphson and secant methods of root-finding problems. IOSR J. Eng. 4(04), 01–07 (2014)

    Google Scholar 

  5. Enderling, H., Chaplain, M.A.J.: Mathematical modeling of tumor growth and treatment. Curr. Pharm. Des. 20(30), 4934–4940 (2014)

    Article  Google Scholar 

  6. Forsythe, G.E.: Computer methods for mathematical computations. Prentice-Hall Ser. Autom. Comput. 259 (1977)

    Google Scholar 

  7. Huang, S.J., Huang, C.L.: Control of an inverted pendulum using grey prediction model. IEEE Trans. Ind. Appl. 36(2), 452–458 (2000)

    Article  MathSciNet  Google Scholar 

  8. Kerestely, A., Costigan, C., Tabirca, S.: Vertically shifted exponential best-fit. In: Proceedings of the 35th International Business Information Management Association (IBIMA), Seville, Spain, pp. 13855–13868 (2020)

    Google Scholar 

  9. Phillips, G.M.: Interpolation and Approximation by Polynomials, vol. 14. Springer, Heidelberg (2003)

    Book  Google Scholar 

  10. Pisal, N., Tidy, J., Hancock, B.: Gestational trophoblastic disease: is intensive follow up essential in all women? BJOG: Int. J. Obstet. Gynaecol. 111(12), 1449–1451 (2004)

    Google Scholar 

  11. Schoeberl, M.R.: A model for the behavior of \(\beta \)-hCG after evacuation of hydatidiform moles. Gynecol. Oncol. 105(3), 776–779 (2007)

    Article  Google Scholar 

  12. Seckl, M.J., Sebire, N.J., Berkowitz, R.S.: Gestational trophoblastic disease. Lancet 376(9742), 717–729 (2010)

    Article  Google Scholar 

  13. Soper, J.T.: Gestational trophoblastic disease. Obstet. Gynecol. 108(1), 176–187 (2006)

    Article  Google Scholar 

  14. Szidarovszky, F., Yakowitz, S.J.: Principles and Procedures of Numerical Analysis, vol. 14. Springer, Heidelberg (2013)

    MATH  Google Scholar 

  15. Van Trommel, N., Massuger, L., Schijf, C., Sweep, C., Thomas, C., et al.: Early identification of persistent trophoblastic disease with serum hCG concentration ratios. Int. J. Gynecol. Cancer 18(2), 318–323 (2008)

    Article  Google Scholar 

  16. Xiao, X., White, E.P., Hooten, M.B., Durham, S.L.: On the use of log-transformation vs. nonlinear regression for analyzing biological power laws. Ecology 92(10), 1887–1894 (2011)

    Article  Google Scholar 

  17. You, B., et al.: Early prediction of treatment resistance in low-risk gestational trophoblastic neoplasia using population kinetic modelling of hCG measurements. Br. J. Cancer 108(9), 1810–1816 (2013)

    Article  Google Scholar 

  18. You, B., et al.: Predictive values of hCG clearance for risk of methotrexate resistance in low-risk gestational trophoblastic neoplasias. Ann. Oncol. 21(8), 1643–1650 (2010)

    Article  Google Scholar 

  19. Young, T., Coleman, R., Hancock, B., Drew, D., Wilson, P., Tidy, J., et al.: Predicting gestational trophoblastic neoplasia (GTN): is urine hCG the answer? Gynecol. Oncol. 122(3), 595–599 (2011)

    Article  Google Scholar 

  20. Zwietering, M., Jongenburger, I., Rombouts, F., Van’t Riet, K.: Modeling of the bacterial growth curve. Appl. Environ. Microbiol. 56(6), 1875–1881 (1990)

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Arpad Kerestely .

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2021 Springer Nature Switzerland AG

About this paper

Check for updates. Verify currency and authenticity via CrossMark

Cite this paper

Kerestely, A., Costigan, C., Holland, F., Tabirca, S. (2021). Theoretical Study of Exponential Best-Fit: Modeling hCG for Gestational Trophoblastic Disease. In: Qiu, H., Zhang, C., Fei, Z., Qiu, M., Kung, SY. (eds) Knowledge Science, Engineering and Management. KSEM 2021. Lecture Notes in Computer Science(), vol 12817. Springer, Cham. https://doi.org/10.1007/978-3-030-82153-1_35

Download citation

  • DOI: https://doi.org/10.1007/978-3-030-82153-1_35

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-82152-4

  • Online ISBN: 978-3-030-82153-1

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics