Legacy Models

Warning

This module contains legacy models kept for historical reference only. They are not recommended for new work. This documentation is linked from specific models where the legacy implementation is contextually relevant.

Lerebours Model V1 (Legacy)

class bone_models.bone_cell_population_models.models.legacy.lerebours_model_v1.Lerebours_Model_V1(load_case, porosity, specific_surface_multiplier=1)[source]

Bases: Scheiner_Model

Constructor for the Scheiner_Model class as subclass of the Pivonka_Model class.

Parameters:: load_case (object) – load case for the model

bone_cell_population_model(x, t=None)[source]

Calculates the system of ordinary differential equations for the bone cell population model, vascular pore volume fraction and bone volume fraction. This function is overwritten from the source model to add vascular pore volume fraction and bone volume fraction, that are necessary to solve in every time step.

Parameters:

x (list) – state variables of the model
t (float) – time variable

Returns:

rate of change of state variables

Return type:

list

calculate_MCSF_activation_OCu()[source]

calculate_OPG_concentration(OBp, OBa, t)[source]

Calculates the osteoprotegerin (OPG) concentration based on the osteoblasts’ production, PTH repression, maximum concentration, external injection and degradation rate. As described in the source publication, OPG can be produced by either precursor or active osteoblasts - determined by boolean variables.

Parameters:

OBp (float) – precursor osteoblast cell concentration
OBa (float) – active osteoblast cell concentration
t (float) – time variable

Returns:

OPG concentration

Return type:

float

calculate_PTH_concentration(t)[source]

Calculate the PTH concentration depending on intrinsic and external PTH and degradation rate.

Parameters:: t (float) – time variable
Returns:: PTH concentration
Return type:: float

calculate_RANKL_activation_OCp(OBp, OBa, t)[source]

Calculates the activation of precursor osteoclasts by RANKL based on the RANKL-RANK complex concentration and activation coefficient.

Parameters:

OBp (float) – precursor osteoblast cell concentration
OBa (float) – active osteoblast cell concentration
t (float) – time variable

Returns:

activation of precursor osteoclasts by RANKL

Return type:

float

calculate_RANKL_activation_OCu(OBp, OBa, t)[source]

calculate_RANKL_concentration(OBp, OBa, t)[source]

Calculates the RANKL concentration based on the effective carrying capacity, RANKL-RANK-OPG binding, degradation rate, intrinsic RANKL production and external injection of RANKL. An additional RANKL production is added due to mechanical effects.

Parameters:

OBp (float) – precursor osteoblast cell concentration
OBa (float) – active osteoblast cell concentration
t (float) – time variable

Returns:

RANKL concentration

Return type:

float

calculate_TGFb_concentration(OCa, t)[source]

Calculates the TGF-beta concentration based on the osteoclastic resorption, external injection and degradation rate. Note: the resorption rate in this formula is included in the original model, but not coded.

Parameters:

OCa (float) – active osteoclast cell concentration
t (float) – time variable

Returns:

TGF-beta concentration

Return type:

float

calculate_steady_state(porosity)[source]

Calculate the steady state of the bone cell population model using root finding of the ODE system.

Returns:: steady state values of the model
Return type:: numpy.ndarray

calculate_turnover(porosity)[source]

specific_surface(porosity)[source]: This function calculates the specific surface of bone based on the porosity.