# Mathematical modeling of bone remodeling after surgical menopause

## TL;DR

This paper introduces a mathematical model to understand how bone loss changes after surgical menopause, focusing on the role of osteocytes in bone remodeling.

## Contribution

The novelty is a new model capturing increased bone loss and long-term rebound after surgical menopause, incorporating osteocyte dynamics.

## Key findings

- The model shows increased bone loss in the first 15 years after surgical menopause.
- A rebound in bone mineral density is predicted in the long-term post-surgery.
- Osteocyte regulation is identified as a key factor in bone remodeling after estrogen deficiency.

## Abstract

Osteoporosis is a skeletal pathology characterized by decreased bone mass and structural deterioration resulting from an imbalance in bone metabolic processes. Estrogen deficiency in postmenopausal women leads to an increased risk of osteoporosis, while women who have undergone complete oophorectomies display an even higher risk due to the sudden decrease in estrogen. Some evidence indicates that bone loss slows in the period beyond 15 years after surgery; however, there is substantial uncertainty in clinical data. To explore the effects of surgically induced menopausal transition, here we propose a mathematical model for the bone cell dynamical responses to sudden estrogen deficiency, which extends an existing model for osteoporosis due to aging and natural menopause. Using data on key effects observed in female mice and humans after bilateral oophorectomy, this new model considers the role of osteocytes embedded within the mineralized bone matrix in regulating bone remodeling, which results in net bone loss after surgical menopause. The model parameter values in natural and surgical menopause were estimated from aggregated human clinical data from existing longitudinal studies. The new model effectively captures the previously unmodeled increase in bone loss during the first 15 years post-surgical menopause and the rebound in bone mineral density in the long-term. With this model, effects of treatments on targeting osteocyte dynamics could be explored in the future.