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Mathematical modelling of bone remodelling at the cellular level and the interaction between myeloma cells and the bone microenvironment

Ji, Bing (Engineer)


Bing (Engineer) Ji


M. J. (Michael J.), 1957 Fagan


After an initial phase of growth and development, bone undergoes a continuous cycle of repair, renewal and optimization, by a process termed remodelling. Bone remodelling is the coordinated processes of resorption by osteoclasts and formation by osteoblasts, where old bone is replaced by new bone. Disorder of bone remodelling cycle can result in metabolic bone diseases, such as postmenopausal osteoporosis, hypothyroidism and primary hyperparathyroidism. Due to the large number of bone cell types, stages of differentiation, and the numerous growth factors and cell to cell interactions involved, our current understanding of bone remodelling and the coupling between osteoblasts and osteoclasts is still fragmentary.

In the first part of this research, a novel predator-prey based mathematical model is developed to simulate bone remodelling cycles in trabecular bone at the basic multicelluar unit level, through integrating bone removal by osteoclasts and formation by osteoblasts. The model is able to replicate the curves of bone remodelling cycles obtained from standard bone histomorphometric analysis. The application of the model is firstly demonstrated by using experimental data recorded for normal (healthy) bone remodelling, to simulate the temporal variation in the number of osteoblasts and osteoclasts, and resultant effect on bone thickness. The reconstructed histomorphometric data and remodelling cycle characteristics compared well with the specified input data. Two sample pathological conditions, hypothyroidism and primary hyperparathyroidism, were then examined to demonstrate how the model could be applied more broadly. The model was validated by comparing model predictions (maximum populations of osteoclasts and osteoblasts) in the normal condition with experimental data. Further data is required to fully validate the model’s predictive capability.

A second mathematical model is then developed to simulate how the interaction between multiple myeloma (MM) cells and the bone microenvironment leads to a ‘vicious cycle’ between tumour development and bone destruction. The model includes the roles of inhibited osteoblast activity and stimulated osteoclast activity, and is able to mimic the temporal variation of bone cell concentrations and resultant bone volume after invasion and then removal of the tumour cells. The model explains why MM-induced bone lesions rarely heal even after the complete removal of MM cells. The model’s predictions agree with published experimental and clinical observations. The model is also used to simulate therapies for MM-induced bone disease, including bisphosphonates, bortezomib and the inhibition of TGF-β. The simulation confirms that treatments with bisphosphonates and bortezomib can reduce the tumour burden and bone destruction, which is consistent with clinical observations. However, the inhibition of TGF-β does not appear to suppress bone destruction, although it does decrease the MM cell concentration.


Ji, B. (. (2012). Mathematical modelling of bone remodelling at the cellular level and the interaction between myeloma cells and the bone microenvironment. (Thesis). University of Hull. Retrieved from

Thesis Type Thesis
Deposit Date Dec 18, 2012
Publicly Available Date Feb 22, 2023
Keywords Engineering
Public URL
Additional Information Department of Engineering, The University of Hull
Award Date Jul 1, 2012


Thesis (2.3 Mb)

Copyright Statement
© 2012 Ji, Bing (Engineer). All rights reserved. No part of this publication may be reproduced without the written permission of the copyright holder.

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