TABLE 4.

Methods adopted to incorporate osteoporosis, PDB, PC, and MM in mathematical models.

Disease	Cause	Changed parameters	Method	References
Osteoporosis	Menopause	Minimal rate of OPG production	Decreasing the value until COCa/COBa, in the steady state, reaches 5 (reflecting the osteoporotic bone)	Lemaire et al., 2004
	1.25(OH)2D3 deficiency	PTH production rate	Increasing the value until it reaches 3,765 pM/day
	Glucocorticoid excess	Differentiation rates of osteoblast progenitors	Reduced to reach 1.7 × 10–4 pM/day in order to simulate the biological dysregulation
	-	PTH concentration	Increasing its value as PTH perturbs the homeostatic steady state of bone cells by inducing RANKL/OPG ratio rise	Pivonka et al., 2013
PDB	-	Autocrine parameters—normalized activity of resorption and formation	- Increasing the formation rates of bone cells - Increasing the value of the autocrine parameters - Increasing bone resorption activity parameter and reducing the formation one.	Komarova et al., 2003
Malignant bone	Prostate cancer	- Activation function of preosteoblast differentiation - TGFβ concentration - OPG concentration - PTH concentration	- Adding the effect of Wnt as stimulator of preosteoblast differentiation - Wnt production by PC cells is repressed by DKK-1 - Adding an activation function of TGFβ activation mediated by PSA binding to its receptor - Considering PTHrP concentration in the calculation of repression function controlling OPG production	Farhat et al., 2017
	Multiple myeloma	- Autocrine and paracrine parameters	- Autocrine and paracrine parameters depend on the tumor evolution; while tumor’s density increases, they increase for osteoclasts’ case and decrease for osteoblasts’ case	Ayati et al., 2010
		- RANKL concentration	- Effective carrying capacity on preosteoblast equation, which enters into RANKL concentration calculation, depends on the activation function mediated by PTH and IL-6 binding to their receptors. - IL-6 production by uncommitted osteoblasts is controlled by the activation function mediated by VLA4 and TGFβ binding to their receptors.	Wang et al., 2011
		- Differentiation from preosteoblasts to active osteoblast term - Apoptosis of active osteoblasts term -RANKL concentration	- Adding a repression function of preosteoblast differentiation mediated by VCAM1 binding to its receptor. - Adding an activation function of preosteoblasts differentiation mediated to VCAM1 binding to its receptor. - Effective RANKL concentration controlled by IL-6 activation function. - IL-6 production by uncommitted osteoblasts is controlled by the activation function mediated by VLA4 and TGFβ binding to their receptors. - VLA4 production depends on MM cell concentration. - MM cell proliferation is repressed by the repression function mediated by SLRP binding to its receptor.	Ji et al., 2014