Welcome to Bone Models documentation!

This documentation provides an in-depth guide to the Bone Cell Population Models used for simulating bone remodeling and disease progression. The models implemented here are based on established theoretical frameworks from the literature and aim to describe the complex interactions between osteoblasts, osteoclasts, and biochemical signaling pathways under various physiological and pathological conditions.

This documentation is continuously updated as new models and features are integrated. If you have any questions or suggestions, feel free to contribute!

Contents:

• Bone Cell Population Models
  • Models
  • Legacy Models
  • Parameters
  • Load Cases
  • Utils
  • Examples
• Bone Mineralisation Models
  • Models
  • Parameters
  • Load Cases
  • Utils
  • Examples
• Bone Spatial Models
  • Models
  • Parameters
  • Load Cases
  • Examples

What’s included?

This repository includes multiple computational models, each extending previous work to incorporate additional biological mechanisms. The repository includes three categories of models according to their focus and operating scale:

1. Bone Cell Population Models: These models simulate the dynamics of bone cell populations, including osteoblasts and osteoclasts, under various conditions.

2. Bone Mineralisation Models: These models focus on the mineralization process of bone tissue, capturing the kinetics of mineral deposition and resorption.

3. Bone Spatial Models: These models incorporate spatial aspects of bone remodeling in 2D and 3D, allowing for the study of bone architecture and its changes over time.

Bone Cell Population Models include:

• Base Model (Base Model): A general framework for bone cell population dynamics.

• Lemaire Model (Lemaire Model): Implements the model by Lemaire et al. (2004), describing fundamental osteoblast-osteoclast interactions.

• Pivonka Model (Pivonka Model): Extends the Lemaire Model with intracellular signaling based on Pivonka et al. (2008).

• Scheiner Model (Scheiner Model): Further expands the Pivonka Model to include mechanical loading effects (Scheiner et al., 2013).

• Martinez-Reina Model (Martinez-Reina Model): Expands the Scheiner Model to account for trabecular bone disuse, overuse, PMO and denosumab treatment scenarios (Martinez-Reina et al., 2019).

• Martonova Model (Martonova Model): Computes cellular activity constants based on pulsatile PTH (Martonova et al., 2023).

• Modiz Model (Modiz Model): Introduces receptor dynamics and pulsatile PTH effects (Modiz et al., 2025), building upon the Lemaire Model and the Martonova Model.

• Lerebours Model (Lerebours Model): Integrates bone volume fraction and mechanical feedback into the Scheiner Model (Lerebours et al., 2015).

Bone Mineralisation Models include:

• Ruffoni Model (Ruffoni Model): Implements the model by Ruffoni et al. (2008,2009) describing Bone Mineral Density Distribution (BMDD) using a PDE.

• Modiz Model (Modiz Model): Implements the model by Modiz et al. (2026), analysing mineralisation kinetics depending on porosity.

Bone_Spatial Models include: - Lerebours Spatial Model (Lerebours Model): A spatial extension of the Lerebours Cell Population Model to simulate bone remodeling and loading on a 2D femoral cross section.

Each model is accompanied by a set of load cases that define specific disease states or disuse/ overuse scenarios by altering the model parameters. The model parameters are named in a consistent manner across all models, allowing for easy comparison and calibration. In the corresponding parameter files, the parameters are matched with the nomenclature used in the original publications. On a separate page, examples are provided to demonstrate how to use the models and load cases to simulate different scenarios and analyze the results.

Getting Started

To start using the models, install the required dependencies and follow the setup instructions. You can also find example scripts to help you implement simulations and analyze results.

To install the package, simply use pip:

pip install bone_models

Once installed, you can import the available models, load cases, and run simulations. Each bone cell population model is implemented as a class that automatically initializes the required parameters. If needed, the parameter files can be accessed and modified. The models can be imported and instantiated with a specific load case as shown below for the Lemaire and Pivonka models:

# Import models
from bone_models.bone_cell_population_models.models import Lemaire_Model, Pivonka_Model

# Optional: if needed, parameters can be imported via the following
from bone_models.bone_cell_population_models.parameters.lemaire_parameters import Lemaire_Parameters

# Import load cases (for some models there is more than one load case available)
from bone_models.bone_cell_population_models.load_cases.lemaire_load_cases import Lemaire_Load_Case_3
from bone_models.bone_cell_population_models.load_cases.pivonka_load_cases import Pivonka_Load_Case_2

# Initialize a model instance with a load case
lemaire_model = Lemaire_Model(Lemaire_Load_Case_3)
pivonka_model = Pivonka_Model(Pivonka_Load_Case_2)

All bone cell population models are solved using the solve_bone_cell_population_model function. This function requires a time span (tspan), which specifies the simulation duration.

# Define time span for simulation
tspan = [0, 1000]  # Start at time 0, end at time 1000 days

# Solve the model
lemaire_solution = lemaire_model.solve_bone_cell_population_model(tspan)
pivonka_solution = pivonka_model.solve_bone_cell_population_model(tspan)

After solving, the model contains the simulation results, including the evolution of cell populations over time. More detailed examples, including plots and analysis of the simulation results, can be found on the pages Examples, Examples or Examples page.