TY - CHAP
T1 - The Impact of Fractional Differentiation in Terms of Fitting for a Prostate Cancer Model Under Intermittent Androgen Suppression Therapy
AU - Mizrak, Ozlem Ozturk
AU - Mizrak, Cihan
AU - Kashkynbayev, Ardak
AU - Kuang, Yang
N1 - Funding Information:
Acknowledgements: O.O.M. is supported by the Scientific and Research Council of Turkey within the context of 2214-A-Ph.D. Research Fellowship Abroad and by the Scientific Research Unit of Ankara University with the grant number 17L0430006. We are also grateful to Nicholas Bruchovsky for the clinical data set.
PY - 2020
Y1 - 2020
N2 - Actually, the main motivation for the contents of this chapter is to introduce fractional calculus as a prospective mathematical tool for cancer dynamics, in particular prostate cancer modeling. In this context, firstly, our main problem on the controversial role of androgens for prostate cancer development is handled, and according to our hypothesis a new mathematical model consisting of conventional logistic growth phenomena is constructed versus another prospective model based on ecological phenomena, cell quota. Then, we compare these two models demonstrating the mean squared error (MSE) values for androgen and prostate-specific antigen (PSA) for the first 1.5 cycles of intermittent androgen suppression (IAS) therapy administered to 62 selected patients from Vancouver Prostate Center (Vancouver, BC, Canada). To reduce MSE values, we also generate the fractional version of the model and verify that fractional differentiation provides nearly better data fitting for mathematical modeling. Moreover, with a discussion part, which hints for future works should be taken into account are pointed out.
AB - Actually, the main motivation for the contents of this chapter is to introduce fractional calculus as a prospective mathematical tool for cancer dynamics, in particular prostate cancer modeling. In this context, firstly, our main problem on the controversial role of androgens for prostate cancer development is handled, and according to our hypothesis a new mathematical model consisting of conventional logistic growth phenomena is constructed versus another prospective model based on ecological phenomena, cell quota. Then, we compare these two models demonstrating the mean squared error (MSE) values for androgen and prostate-specific antigen (PSA) for the first 1.5 cycles of intermittent androgen suppression (IAS) therapy administered to 62 selected patients from Vancouver Prostate Center (Vancouver, BC, Canada). To reduce MSE values, we also generate the fractional version of the model and verify that fractional differentiation provides nearly better data fitting for mathematical modeling. Moreover, with a discussion part, which hints for future works should be taken into account are pointed out.
KW - Androgen
KW - Cell quota
KW - Data fitting
KW - Fractional calculus
KW - Intermittent androgen suppression therapy
KW - Logistic growth
KW - Mean squared error
KW - Prostate cancer modeling
KW - Prostate-specific antigen
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U2 - 10.1007/978-981-15-2286-4_5
DO - 10.1007/978-981-15-2286-4_5
M3 - Chapter
AN - SCOPUS:85080936775
T3 - Forum for Interdisciplinary Mathematics
SP - 151
EP - 197
BT - Forum for Interdisciplinary Mathematics
PB - Springer
ER -