Extension of a Multiscale Model of Calcium Homeostasis and Bone Remodeling to Include the Progressive Effects of Estrogen Loss During Menopause Transition.

Purpose: Extend an existing multiscale model to describe the effect of naturally declining estrogen on calcium homeostasis and bone remodeling. Inclusion of this natural progression will enhance our understanding of the kinetic-dynamic mechanisms controlling these changes, as well as provide an accounting of these longitudinal changes in typical patients to be studied for related therapies (e.g., SERM, hormonal antagonism), combinations of therapies, or related disease states. Methods: The underlying multiscale model has been published and described previously. 1 For this extension of the model, data relating estrogen changes by age and menopause onset age 2, 3 were modeled to describe the natural longitudinal estrogen decline in women during the transition through menopause. Estrogen has been shown to decrease bone turnover, conversely leading to an increase in net bone resorption (loss) when natural estrogen levels decline. Longitudinal changes in bone markers following estrogen replacement therapy in postmenopausal women can be described by directly affecting TGF production and through intracellular changes affecting osteoblast apoptosis rates. 4 These same mechanisms were used to quantify the changes in bone makers during progression from peri- to post-menopause in women. In addition to these effects on bone turnover, estrogen inversely affects the renal excretion of calcium. 5, 6 To account for these changes within the existing model, an effect relating estrogen levels with the calcium renal tubular reabsorption maximum was investigated. The resulting model was used to simulate longitudinal effects for varying menopausal onset ages with and without subsequent estrogen replacement therapy. These results were compared to reported clinical observations, e.g., (Garnero et al., 1996; 7 Gallagher et al., 2002; 8 Greenspan et al., 2002; 9 Riggs et al., 2002 10 ). Results: Longitudinal changes (relative fraction) in endogenous estrogen (E) production were modeled using an ordinary differential equation with first-order elimination (E out , t 1=2 = 12 hours) and a zero-order endogenous production rate (E in ). The rate of production declined after 41 years of age with an additional fractional decline during menopause: E in = (E out )*(Age/41) 2:3 )*(1 - (0.64*(time meno ) 2:0 ) /((meno mid ) 2:0 + (time meno ) 2:0 ), where Age = contiguous patient age (years), time meno = time from the start of menopause, and meno mid = midpoint (0.83 years, total menopause duration = 1.66 years). Therefore, time meno was calculated based on menopause onset age, which itself was an adjustable parameter in the model. Power function models were used to describe the effect of estrogen on latent TGF production [k in;latent = k in;latentnorm ( 1 E 1 )], the conversion to active