TY - JOUR
T1 - Fractional Order Nonlinear Bone Remodeling Dynamics Using the Supervised Neural Network
AU - Yotha, Narongsak
AU - Hiader, Qusain
AU - Sabir, Zulqurnain
AU - Raja, Muhammad Asif Zahoor
AU - Said, Salem Ben
AU - Al-Mdallal, Qasem
AU - Botmart, Thongchai
AU - Weera, Wajaree
N1 - Funding Information:
Funding Statement: This research project is supported by Thailand Science Research and Innovation (TSRI). Contract No. FRB650059/NMA/10. The eighth author is supported by the NSRF via the Program Management Unit for Human Resources & Institutional Development, Research and Innovation (grant number B05F640092).
Publisher Copyright:
© 2023 Tech Science Press. All rights reserved.
PY - 2023
Y1 - 2023
N2 - This study aims to solve the nonlinear fractional-order mathematical model (FOMM) by using the normal and dysregulated bone remodeling of the myeloma bone disease (MBD). For the more precise performance of the model, fractional-order derivatives have been used to solve the disease model numerically. The FOMM is preliminarily designed to focus on the critical interactions between bone resorption or osteoclasts (OC) and bone formation or osteoblasts (OB). The connections of OC and OB are represented by a nonlinear differential system based on the cellular components, which depict stable fluctuation in the usual bone case and unstable fluctuation through the MBD. Untreated myeloma causes by increasing the OC and reducing the osteoblasts, resulting in net bone waste the tumor growth. The solutions of the FOMM will be provided by using the stochastic framework based on the Levenberg-Marquardt backpropagation (LVMBP) neural networks (NN), i.e., LVMBPNN. The mathematical performances of three variations of the fractional-order derivative based on the nonlinear disease model using the LVMPNN. The static structural performances are 82% for investigation and 9% for both learning and certification. The performances of the LVMBPNN are authenticated by using the results of the Adams-Bashforth-Moulton mechanism. To accomplish the capability, steadiness, accuracy, and ability of the LVMBPNN, the performances of the error histograms (EHs), mean square error (MSE), recurrence, and state transitions (STs) will be provided.
AB - This study aims to solve the nonlinear fractional-order mathematical model (FOMM) by using the normal and dysregulated bone remodeling of the myeloma bone disease (MBD). For the more precise performance of the model, fractional-order derivatives have been used to solve the disease model numerically. The FOMM is preliminarily designed to focus on the critical interactions between bone resorption or osteoclasts (OC) and bone formation or osteoblasts (OB). The connections of OC and OB are represented by a nonlinear differential system based on the cellular components, which depict stable fluctuation in the usual bone case and unstable fluctuation through the MBD. Untreated myeloma causes by increasing the OC and reducing the osteoblasts, resulting in net bone waste the tumor growth. The solutions of the FOMM will be provided by using the stochastic framework based on the Levenberg-Marquardt backpropagation (LVMBP) neural networks (NN), i.e., LVMBPNN. The mathematical performances of three variations of the fractional-order derivative based on the nonlinear disease model using the LVMPNN. The static structural performances are 82% for investigation and 9% for both learning and certification. The performances of the LVMBPNN are authenticated by using the results of the Adams-Bashforth-Moulton mechanism. To accomplish the capability, steadiness, accuracy, and ability of the LVMBPNN, the performances of the error histograms (EHs), mean square error (MSE), recurrence, and state transitions (STs) will be provided.
KW - Bone remodeling
KW - artificial neural networks
KW - fractional-order
KW - levenberg-marquardt backpropagation
KW - myeloma disease
KW - population cell dynamics
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U2 - 10.32604/cmc.2023.031352
DO - 10.32604/cmc.2023.031352
M3 - Article
AN - SCOPUS:85141891614
SN - 1546-2218
VL - 74
SP - 2415
EP - 2430
JO - Computers, Materials and Continua
JF - Computers, Materials and Continua
IS - 2
ER -