Load Cases

This module contains the load cases used in the bone models. The load cases are used to implement e.g. disease states or different loading conditions for a certain time interval.

Lemaire Load Cases

This module contains the load cases for the bone cell population model by Lemaire et al. (2004). The load cases are used to define disease conditions phenomenologically using external injections of respective concentrations to either increase or decrease these concentrations.

class bone_models.bone_cell_population_models.load_cases.lemaire_load_cases.Lemaire_Load_Case_1[source]

Bases: object

Load case 1 for the Lemaire model: injection of active osteoblasts in a specific time interval.

Parameters:

OBp_injection (float) – external injection of precursor osteoblasts
OBa_injection (float) – external injection of active osteoblasts
OCa_injection (float) – external injection of active osteoclasts
PTH_injection (float) – external injection of parathyroid hormone
OPG_injection (float) – external injection of osteoprotegerin
RANKL_injection (float) – external injection of receptor activator of nuclear factor kappa-B ligand
start_time (float) – start time of the external injections
end_time (float) – end time of the external injections

Constructor method

class bone_models.bone_cell_population_models.load_cases.lemaire_load_cases.Lemaire_Load_Case_2[source]

Bases: object

Load case 2 for the Lemaire model: retraction of active osteoblasts in a specific time interval.

Parameters:

OBp_injection (float) – external injection of precursor osteoblasts
OBa_injection (float) – external injection of active osteoblasts
OCa_injection (float) – external injection of active osteoclasts
PTH_injection (float) – external injection of parathyroid hormone
OPG_injection (float) – external injection of osteoprotegerin
RANKL_injection (float) – external injection of receptor activator of nuclear factor kappa-B ligand
start_time (float) – start time of the external injections
end_time (float) – end time of the external injections

Constructor method

class bone_models.bone_cell_population_models.load_cases.lemaire_load_cases.Lemaire_Load_Case_3[source]

Bases: object

Load case 3 for the Lemaire model: injection of parathyroid hormone in a specific time interval.

Parameters:

OBp_injection (float) – external injection of precursor osteoblasts
OBa_injection (float) – external injection of active osteoblasts
OCa_injection (float) – external injection of active osteoclasts
PTH_injection (float) – external injection of parathyroid hormone
OPG_injection (float) – external injection of osteoprotegerin
RANKL_injection (float) – external injection of receptor activator of nuclear factor kappa-B ligand
start_time (float) – start time of the external injections
end_time (float) – end time of the external injections

Constructor method

class bone_models.bone_cell_population_models.load_cases.lemaire_load_cases.Lemaire_Load_Case_4[source]

Bases: object

Load case 4 for the Lemaire model: injection of active osteoclasts in a specific time interval.

Parameters:

OBp_injection (float) – external injection of precursor osteoblasts
OBa_injection (float) – external injection of active osteoblasts
OCa_injection (float) – external injection of active osteoclasts
PTH_injection (float) – external injection of parathyroid hormone
OPG_injection (float) – external injection of osteoprotegerin
RANKL_injection (float) – external injection of receptor activator of nuclear factor kappa-B ligand
start_time (float) – start time of the external injections
end_time (float) – end time of the external injections

Constructor method

class bone_models.bone_cell_population_models.load_cases.lemaire_load_cases.Lemaire_Load_Case_5[source]

Bases: object

Load case 5 for the Lemaire model: retraction of active osteoclasts in a specific time interval.

Parameters:

OBp_injection (float) – external injection of precursor osteoblasts
OBa_injection (float) – external injection of active osteoblasts
OCa_injection (float) – external injection of active osteoclasts
PTH_injection (float) – external injection of parathyroid hormone
OPG_injection (float) – external injection of osteoprotegerin
RANKL_injection (float) – external injection of receptor activator of nuclear factor kappa-B ligand
start_time (float) – start time of the external injections
end_time (float) – end time of the external injections

Constructor method

class bone_models.bone_cell_population_models.load_cases.lemaire_load_cases.Lemaire_Load_Case_6[source]

Bases: object

Load case 6 for the Lemaire model: injection of osteoprotegerin in a specific time interval.

Parameters:

OBp_injection (float) – external injection of precursor osteoblasts
OBa_injection (float) – external injection of active osteoblasts
OCa_injection (float) – external injection of active osteoclasts
PTH_injection (float) – external injection of parathyroid hormone
OPG_injection (float) – external injection of osteoprotegerin
RANKL_injection (float) – external injection of receptor activator of nuclear factor kappa-B ligand
start_time (float) – start time of the external injections
end_time (float) – end time of the external injections

Constructor method

class bone_models.bone_cell_population_models.load_cases.lemaire_load_cases.Lemaire_Load_Case_7[source]

Bases: object

Load case 7 for the Lemaire model: injection of precursor osteoblasts in a specific time interval.

Parameters:

OBp_injection (float) – external injection of precursor osteoblasts
OBa_injection (float) – external injection of active osteoblasts
OCa_injection (float) – external injection of active osteoclasts
PTH_injection (float) – external injection of parathyroid hormone
OPG_injection (float) – external injection of osteoprotegerin
RANKL_injection (float) – external injection of receptor activator of nuclear factor kappa-B ligand
start_time (float) – start time of the external injections
end_time (float) – end time of the external injections

Constructor method

class bone_models.bone_cell_population_models.load_cases.lemaire_load_cases.Lemaire_Load_Case_8[source]

Bases: object

Load case 8 for the Lemaire model: retraction of precursor osteoblasts in a specific time interval.

Parameters:

OBp_injection (float) – external injection of precursor osteoblasts
OBa_injection (float) – external injection of active osteoblasts
OCa_injection (float) – external injection of active osteoclasts
PTH_injection (float) – external injection of parathyroid hormone
OPG_injection (float) – external injection of osteoprotegerin
RANKL_injection (float) – external injection of receptor activator of nuclear factor kappa-B ligand
start_time (float) – start time of the external injections
end_time (float) – end time of the external injections

Constructor method

class bone_models.bone_cell_population_models.load_cases.lemaire_load_cases.Lemaire_Load_Case_9[source]

Bases: object

Load case 9 for the Lemaire model: injection of receptor activator of nuclear factor kappa-B ligand in a specific time interval.

Parameters:

OBp_injection (float) – external injection of precursor osteoblasts
OBa_injection (float) – external injection of active osteoblasts
OCa_injection (float) – external injection of active osteoclasts
PTH_injection (float) – external injection of parathyroid hormone
OPG_injection (float) – external injection of osteoprotegerin
RANKL_injection (float) – external injection of receptor activator of nuclear factor kappa-B ligand
start_time (float) – start time of the external injections
end_time (float) – end time of the external injections

Constructor method

Martonova Load Cases

This module contains the load cases for the two-state receptor model by Martonova et al. (2023). The load cases are used to define disease conditions based on changed pulsatile characteristics with or without drug administration.

class bone_models.bone_cell_population_models.load_cases.martonova_load_cases.Basal_PTH_pulse[source]

Bases: object

This class contains the basal PTH pulse parameters of the two-state receptor model by Martonova et al.

The following table provides a mapping between the model parameters and their original names from the publication:

Parameter Name	Symbol	Units
min	gamma_off	[nM]
max	gamma_on	[nM]
off_duration	tau_off	[min]
on_duration	tau_on	[min]
period	T	[min]

Parameters:

min (float) – concentration of non-pulsatile share of PTH pulse
max (float) – concentration of pulsatile share of PTH pulse
off_duration (float) – duration of non-pulsatile share of PTH pulse
on_duration (float) – duration of pulsatile share of PTH pulse
period (float) – duration of the PTH pulse period (pulse + non-pulse)

class bone_models.bone_cell_population_models.load_cases.martonova_load_cases.Martonova_Glucocorticoid_Induced_Osteoporosis[source]

Bases: object

This class contains the parameters for the glucocorticoid-induced osteoporosis state without injection of the two-state receptor model by Martonova et al.

Parameters:

basal_PTH_pulse (Basal_PTH_pulse) – basal PTH pulse parameters
drug_dose (float) – dose of the drug
injection_frequency (float) – frequency of the drug injection (e.g. 24h)
injected_PTH_pulse (injected_PTH_pulse) – injected PTH pulse parameters

class bone_models.bone_cell_population_models.load_cases.martonova_load_cases.Martonova_Healthy[source]

Bases: object

This class contains the parameters for the healthy state without injection of the two-state receptor model by Martonova et al.

Parameters:

basal_PTH_pulse (Basal_PTH_pulse) – basal PTH pulse parameters
drug_dose (float) – dose of the drug
injection_frequency (float) – frequency of the drug injection (e.g. 24h)
injected_PTH_pulse (injected_PTH_pulse) – injected PTH pulse parameters

class bone_models.bone_cell_population_models.load_cases.martonova_load_cases.Martonova_Hypercalcemia[source]

Bases: object

This class contains the parameters for the hypercalcemia state without injection of the two-state receptor model by Martonova et al.

Parameters:

basal_PTH_pulse (Basal_PTH_pulse) – basal PTH pulse parameters
drug_dose (float) – dose of the drug
injection_frequency (float) – frequency of the drug injection (e.g. 24h)
injected_PTH_pulse (injected_PTH_pulse) – injected PTH pulse parameters

class bone_models.bone_cell_population_models.load_cases.martonova_load_cases.Martonova_Hyperparathyroidism[source]

Bases: object

This class contains the parameters for the hyperparathyroidism state without injection of the two-state receptor model by Martonova et al.

Parameters:

basal_PTH_pulse (Basal_PTH_pulse) – basal PTH pulse parameters
drug_dose (float) – dose of the drug
injection_frequency (float) – frequency of the drug injection (e.g. 24h)
injected_PTH_pulse (injected_PTH_pulse) – injected PTH pulse parameters

class bone_models.bone_cell_population_models.load_cases.martonova_load_cases.Martonova_Hyperparathyroidism_With_Drug[source]

Bases: object

This class contains the parameters for the hyperparathyroidism state with injection of the two-state receptor model by Martonova et al.

Parameters:

basal_PTH_pulse (Basal_PTH_pulse) – basal PTH pulse parameters
drug_dose (float) – dose of the drug in micrograms
injection_frequency (float) – frequency of the drug injection (e.g. 24h)
injected_PTH_pulse (injected_PTH_pulse) – injected PTH pulse parameters

class bone_models.bone_cell_population_models.load_cases.martonova_load_cases.Martonova_Hypocalcemia[source]

Bases: object

This class contains the parameters for the hypocalcemia state without injection of the two-state receptor model by Martonova et al.

Parameters:

basal_PTH_pulse (Basal_PTH_pulse) – basal PTH pulse parameters
drug_dose (float) – dose of the drug
injection_frequency (float) – frequency of the drug injection (e.g. 24h)
injected_PTH_pulse (injected_PTH_pulse) – injected PTH pulse parameters

class bone_models.bone_cell_population_models.load_cases.martonova_load_cases.Martonova_Osteoporosis[source]

Bases: object

This class contains the parameters for the osteoporosis state without injection of the two-state receptor model by Martonova et al.

Parameters:

basal_PTH_pulse (Basal_PTH_pulse) – basal PTH pulse parameters
drug_dose (float) – dose of the drug
injection_frequency (float) – frequency of the drug injection (e.g. 24h)
injected_PTH_pulse (injected_PTH_pulse) – injected PTH pulse parameters

class bone_models.bone_cell_population_models.load_cases.martonova_load_cases.Martonova_Postmenopausal_Osteoporosis[source]

Bases: object

This class contains the parameters for the postmenopausal osteoporosis state without injection of the two-state receptor model by Martonova et al.

Parameters:

basal_PTH_pulse (Basal_PTH_pulse) – basal PTH pulse parameters
drug_dose (float) – dose of the drug
injection_frequency (float) – frequency of the drug injection (e.g. 24h)
injected_PTH_pulse (injected_PTH_pulse) – injected_PTH_pulse parameters

class bone_models.bone_cell_population_models.load_cases.martonova_load_cases.injected_PTH_pulse[source]

Bases: object

This class contains the injected PTH pulse parameters of the two-state receptor model by Martonova et al.

The following table provides a mapping between the model parameters and their original names from the publication:

Parameter Name	Symbol	Units
max	gamma_on	[nM]
off_duration	tau_off	[min]
on_duration	tau_on	[min]
period	T	[min]

Parameters:

max (float) – concentration of pulsatile share of injected PTH pulse
off_duration (float) – duration of non-pulsatile share of injected PTH pulse
on_duration (float) – duration of pulsatile share of injected PTH pulse
period (float) – duration of the injected PTH pulse period (pulse + non-pulse)

Modiz Load Cases

This module contains the load cases for the bone cell population model by Modiz et al. (2025). The load cases are used to define disease conditions based on changed pulsatile characteristics for the cellular activity constants. For the bone cell population model by Lemaire et al., (2004) used as a reference the load cases define disease states phenomenologically. In conclusion, the load cases contain both Lemaire and Martonova load cases.

class bone_models.bone_cell_population_models.load_cases.modiz_load_cases.Lemaire_Load_Case[source]

Bases: object

Load case for the reference class Lemaire model with external injections.

class bone_models.bone_cell_population_models.load_cases.modiz_load_cases.Modiz_Healthy_to_Glucocorticoid_Induced_Osteoporosis[source]

Bases: object

Load case for the subclass Modiz_Model for the transition from Healthy to Glucocorticoid-Induced Osteoporosis. It contains the load case class for the Lemaire model and the Martonova model. The latter is directly imported from the Martonova load cases.

Parameters:

lemaire (Lemaire_Load_Case) – Lemaire load case for reference model
martonova (bone_models.load_cases.martonova_load_cases.Martonova_Glucocorticoid_Induced_Osteoporosis) – Glucocorticoid-Induced Osteoporosis load case for Martonova model

class bone_models.bone_cell_population_models.load_cases.modiz_load_cases.Modiz_Healthy_to_Hypercalcemia[source]

Bases: object

Load case for the subclass Modiz_Model for the transition from Healthy to Hypercalcemia. It contains the load case class for the Lemaire model and the Martonova model. The latter is directly imported from the Martonova load cases.

Parameters:

lemaire (Lemaire_Load_Case) – Lemaire load case for reference model
martonova (bone_models.load_cases.martonova_load_cases.Martonova_Hypercalcemia) – Hypercalcemia load case for Martonova model

class bone_models.bone_cell_population_models.load_cases.modiz_load_cases.Modiz_Healthy_to_Hyperparathyroidism[source]

Bases: object

Load case for the subclass Modiz_Model for the transition from Healthy to Hyperparathyroidism. It contains the load case class for the Lemaire model and the Martonova model. The latter is directly imported from the Martonova load cases.

Parameters:

lemaire (Lemaire_Load_Case) – Lemaire load case for reference model
martonova (bone_models.load_cases.martonova_load_cases.Martonova_Hyperparathyroidism) – Hyperparathyroidism load case for Martonova model

class bone_models.bone_cell_population_models.load_cases.modiz_load_cases.Modiz_Healthy_to_Hypocalcemia[source]

Bases: object

Load case for the subclass Modiz_Model for the transition from Healthy to Hypocalcemia. It contains the load case class for the Lemaire model and the Martonova model. The latter is directly imported from the Martonova load cases.

Parameters:

lemaire (Lemaire_Load_Case) – Lemaire load case for reference model
martonova (bone_models.load_cases.martonova_load_cases.Martonova_Hypocalcemia) – Hypocalcemia load case for Martonova model

class bone_models.bone_cell_population_models.load_cases.modiz_load_cases.Modiz_Healthy_to_Osteoporosis[source]

Bases: object

Load case for the subclass Modiz_Model for the transition from Healthy to Osteoporosis. It contains the load case class for the Lemaire model and the Martonova model. The latter is directly imported from the Martonova load cases.

Parameters:

lemaire (Lemaire_Load_Case) – Lemaire load case for reference model
martonova (bone_models.load_cases.martonova_load_cases.Martonova_Osteoporosis) – Osteoporosis load case for Martonova model

class bone_models.bone_cell_population_models.load_cases.modiz_load_cases.Modiz_Healthy_to_Postmenopausal_Osteoporosis[source]

Bases: object

Load case for the subclass Modiz_Model for the transition from Healthy to Postmenopausal Osteoporosis. It contains the load case class for the Lemaire model and the Martonova model. The latter is directly imported from the Martonova load cases.

Parameters:

lemaire (Lemaire_Load_Case) – Lemaire load case for reference model
martonova (bone_models.load_cases.martonova_load_cases.Martonova_Postmenopausal_Osteoporosis) – Postmenopausal Osteoporosis load case for Martonova model

class bone_models.bone_cell_population_models.load_cases.modiz_load_cases.Modiz_Reference_Healthy_to_Glucocorticoid_Induced_Osteoporosis[source]

Bases: object

Load case for the subclass Reference_Lemaire_Model for the transition from Healthy to Glucocorticoid-Induced Osteoporosis. It contains a PTH_elevation factor, which is used to align disease states with the Modiz_Model to make them comparable. The PTH_elevation factor is calculated by the ratio of the maximum PTH values in bone_models.models.modiz_model.calculate_elevation_parameter().

Parameters:: PTH_elevation (float) – PTH_elevation factor to align the disease states

class bone_models.bone_cell_population_models.load_cases.modiz_load_cases.Modiz_Reference_Healthy_to_Hypercalcemia[source]

Bases: object

Load case for the subclass Reference_Lemaire_Model for the transition from Healthy to Hypercalcemia. It contains a PTH_elevation factor, which is used to align disease states with the Modiz_Model to make them comparable. The PTH_elevation factor is calculated by the ratio of the maximum PTH values in bone_models.models.modiz_model.calculate_elevation_parameter().

Parameters:: PTH_elevation (float) – PTH_elevation factor to align the disease states

class bone_models.bone_cell_population_models.load_cases.modiz_load_cases.Modiz_Reference_Healthy_to_Hyperparathyroidism[source]

Bases: object

Load case for the subclass Reference_Lemaire_Model for the transition from Healthy to Hyperparathyroidism. It contains a PTH_elevation factor, which is used to align disease states with the Modiz_Model to make them comparable. The PTH_elevation factor is calculated by the ratio of the maximum PTH values in bone_models.models.modiz_model.calculate_elevation_parameter().

Parameters:: PTH_elevation (float) – PTH_elevation factor to align the disease states

class bone_models.bone_cell_population_models.load_cases.modiz_load_cases.Modiz_Reference_Healthy_to_Hypocalcemia[source]

Bases: object

Load case for the subclass Reference_Lemaire_Model for the transition from Healthy to Hypocalcemia. It contains a PTH_elevation factor, which is used to align disease states with the Modiz_Model to make them comparable. The PTH_elevation factor is calculated by the ratio of the maximum PTH values in bone_models.models.modiz_model.calculate_elevation_parameter().

Parameters:: PTH_elevation (float) – PTH_elevation factor to align the disease states

class bone_models.bone_cell_population_models.load_cases.modiz_load_cases.Modiz_Reference_Healthy_to_Osteoporosis[source]

Bases: object

Load case for the subclass Reference_Lemaire_Model for the transition from Healthy to Osteoporosis. It contains a PTH_elevation factor, which is used to align disease states with the Modiz_Model to make them comparable. The PTH_elevation factor is calculated by the ratio of the maximum PTH values in bone_models.models.modiz_model.calculate_elevation_parameter().

Parameters:: PTH_elevation (float) – PTH_elevation factor to align the disease states

class bone_models.bone_cell_population_models.load_cases.modiz_load_cases.Modiz_Reference_Healthy_to_Postmenopausal_Osteoporosis[source]

Bases: object

Load case for the subclass Reference_Lemaire_Model for the transition from Healthy to Postmenopausal Osteoporosis. It contains a PTH_elevation factor, which is used to align disease states with the Modiz_Model to make them comparable. The PTH_elevation factor is calculated by the ratio of the maximum PTH values in bone_models.models.modiz_model.calculate_elevation_parameter().

Parameters:: PTH_elevation (float) – PTH_elevation factor to align the disease states

Pivonka Load Cases

This module contains the load cases for the bone cell population model by Pivonka et al. (2008). The load cases are used to define disease conditions phenomenologically using external injections of respective concentrations to either increase or decrease these concentrations.

class bone_models.bone_cell_population_models.load_cases.pivonka_load_cases.Pivonka_Load_Case_1[source]

Bases: object

Load case for Pivonka et al. 2008 model: injection of PTH during a specified time period. The same load cases as in Lemaire et al. 2004 are implemented.

Parameters:

OBp_injection (float) – Osteoblast precursor injection rate
OBa_injection (float) – Osteoblast injection rate
OCa_injection (float) – Osteoclast injection rate
PTH_injection (float) – Parathyroid hormone injection rate
OPG_injection (float) – Osteoprotegerin injection rate
RANKL_injection (float) – Receptor activator of nuclear factor kappa-B ligand injection rate
TGFb_injection (float) – Transforming growth factor beta injection rate
differentiation_rate_OCp_multiplier (float) – Osteoclast precursor differentiation rate multiplier
start_time (float) – Start time of the load case
end_time (float) – End time of the load case

Scheiner Load Cases

This module contains the load cases for the bone cell population model by Scheiner et al. (2013). The load cases are used to define disuse or overuse conditions during a certain time interval. The load cases from Lemaire et al. or Pivonka et al., can also be included.

class bone_models.bone_cell_population_models.load_cases.scheiner_load_cases.Scheiner_Load_Case[source]

Bases: object

Load cases of the Scheiner et al., 2013 model: disuse simulation in the time interval [50, 2050] days using a stress tensor with reduced unixial compressive stress (-25 vs. -30 MPa in habitual loading according to paper).

Parameters:

start_time (float) – start time of the load case
end_time (float) – end time of the load case
stress_tensor (numpy.ndarray) – applied stress tensor
OBp_injection (float) – injection of precursor osteoblasts
OBa_injection (float) – injection of active osteoblasts
OCa_injection (float) – injection of active osteoclasts
PTH_injection (float) – injection of parathyroid hormone
OPG_injection (float) – injection of osteoprotegerin
RANKL_injection (float) – injection of receptor activator of nuclear factor kappa-B ligand
TGFb_injection (float) – injection of transforming growth factor beta

Martinez-Reina Load Cases

This module contains the load cases for the bone cell population model by Martinez-Reina et al. (2019). The load cases are used to define disuse or overuse conditions, PMO and denosumab treatment during certain time intervals. The load cases from Lemaire et al. or Pivonka et al., can also be included.

class bone_models.bone_cell_population_models.load_cases.martinez_reina_load_cases.Martinez_Reina_Load_Case[source]

Bases: object

Load cases of the Martinez-Reina 2019 model. Mechanical loading is applied to the bone (compression with 5 MPa, same as habitual loading), external injections like the Lemaire et al., 2004 model can be given (but are zero in this case), and postmenopausal osteoporosis (from beginning to end) and denosumab treatment (from one year onwards with a treatment period of 183 days) are simulated.

Parameters:

start_time (float) – start time of the mechanical loading
end_time (float) – end time of the mechanical loading
stress_tensor (numpy.ndarray) – stress tensor applied to the bone
OBp_injection (float) – external injection of precursor osteoblasts
OBa_injection (float) – external injection of active osteoblasts
OCa_injection (float) – external injection of active osteoclasts
PTH_injection (float) – external injection of parathyroid hormone
OPG_injection (float) – external injection of osteoprotegerin
RANKL_injection (float) – external injection of receptor activator of nuclear factor kappa-B ligand
TGFb_injection (float) – external injection of transforming growth factor beta
start_postmenopausal_osteoporosis (float) – start time of postmenopausal osteoporosis
end_postmenopausal_osteoporosis (float) – end time of postmenopausal osteoporosis
start_denosumab_treatment (float) – start time of denosumab treatment
end_denosumab_treatment (float) – end time of denosumab treatment
treatment_period (float) – period of denosumab treatment
denosumab_dose (float) – dose of denosumab in ng/kg body weight