Parameters

This module defines the parameters used in the bone mineralisation models. Each model has a specific set of parameters governing its behavior, interaction dynamics, and biological processes. For the bone mineralisation models, the parameters are named consistently across models to facilitate comparison and understanding. In each parameter file, the parameter names are matched with the corresponding model nomenclature and units.

Ruffoni Parameters

This module contains the parameters for the bone mineralisation model of Ruffoni et al. In each parameter class, the parameter names are matched with the corresponding model nomenclature and units.

class bone_models.bone_mineralisation_models.parameters.ruffoni_parameters.Bone_Volume[source]

Bases: object

Class storing the bone volume parameters required for initializing the mineralization model.

Parameter (Type)	Description	Symbol in Paper
`initial_value` (float)	Initial bone volume used when initializing the model from a mineralization law in \(mm^3\)	BV

class bone_models.bone_mineralisation_models.parameters.ruffoni_parameters.Calcium[source]

Bases: object

Class to hold parameters for the calcium grid.

Parameter (Type)	Description	Symbol in Paper
`minimum_content` (float)	Minimum calcium content in % wt.	\(c_{0}\)
`maximum_content` (float)	Maximum calcium content in % wt.	\(c_{\max}\)

class bone_models.bone_mineralisation_models.parameters.ruffoni_parameters.Mineralization_Law[source]

Bases: object

Class representing the mineralization law parameters used in the mineralization model.

Parameter (Type)	Description	Symbol in Paper
`turnover_time` (float)	Turnover time of bone packets in years	\(t_{TO}\)
`primary_mineral_content` (float)	Primary mineral content in % wt.	\(c_{1}\)
`maximum_mineral_content` (float)	Secondary mineral content contribution in % wt	\(c_{2}\)
`primary_apposition_rate` (float)	Time constant of the primary mineralization process in years	\(\tau_{1}\)
`secondary_apposition_rate` (float)	Time constant of the secondary mineralization process years	\(\tau_{2}\)

class bone_models.bone_mineralisation_models.parameters.ruffoni_parameters.Rate[source]

Bases: object

Class to hold reference BMDD parameters for formation and resorption rates. The parameters are initialized here, but can be changed later depending on the initialized bone volume.

Parameter (Type)	Description	Symbol in Paper
`initial_formation` (float)	Initial formation rate in :math: mm^3/ year	\(\\j_{OB}\)
`final_formation` (float)	Final formation rate in :math: mm^3/ year	\(\\j_{OB}(t)\)
`initial_resorption` (float)	Initial resorption rate in 1/year	\(\omega_{OC}(c)\)
`final_resorption` (float)	Final resorption rate in 1/year	\(\omega_{OC}(c,t)\)

class bone_models.bone_mineralisation_models.parameters.ruffoni_parameters.Reference_BMDD[source]

Bases: object

Class to hold reference BMDD parameters for skewed Gaussian distribution if model is initialized with BMDD. The parameters were taken from the original paper and adjusted to fit a realistic BMDD. In real life, this should be initialized with a BMDD/ characteristics measured from an image.

Parameter (Type)	Description	Symbol in Paper
`standard_deviation_lower_percentile` (float)	Standard deviation of the lower percentiles of the BMDD in % wt.	\(\sigma_{1}\)
`standard_deviation_upper_percentile` (float)	Standard deviation of the upper percentiles of the BMDD in % wt.	\(\sigma_{2}\)
`peak` (float)	Peak position of the BMDD in % wt.	\(Ca_{peak}\)

class bone_models.bone_mineralisation_models.parameters.ruffoni_parameters.Ruffoni_Parameters[source]

Bases: object

Class to hold all parameters for the Ruffoni mineralization model.

Modiz Parameters

This module contains the parameters for the bone mineralisation model of Modiz et al. In each parameter class, the parameter names are matched with the corresponding model nomenclature and units.

class bone_models.bone_mineralisation_models.parameters.modiz_parameters.Modiz_Parameters[source]: Bases: object

class bone_models.bone_mineralisation_models.parameters.modiz_parameters.bone_volume[source]

Bases: object

This class defines the parameters relevant for bone volume.

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

Parameter Name	Symbol	Units
formation_rate	\(\mathrm{BFR}\)	1/day
resorption_rate	\(\mathrm{BRs.R}\)	1/day

Parameters:

formation_rate (float) – formation rate of bone volume
resorption_rate (float) – resorption rate of bone volume

class bone_models.bone_mineralisation_models.parameters.modiz_parameters.mineralisation[source]

Bases: object

This class defines the parameters relevant for mineralisation of the bone model.

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

Parameter Name	Symbol	Units
density_organic	\(\rho_{O}\)	g/cm³
density_mineral	\(\rho_{M}\)	g/cm³
volume_fraction_organic	\(f_O\)
lag_time	\(Mlt\)	days
primary_phase_duration	\(Mpt\)	days
primary_mineral_content	\(M_{prim}\)
maximum_mineral_content	\(M_{max}\)
length_of_queue	\(n\)
reference_apposition_rate	\(\mathrm{MAR}_{ref}\)
resorption_bias_age	\(t_{pref}\)

Parameters:

density_organic (float) – Density of organic material.
density_mineral (float) – Density of mineral material.
volume_fraction_organic (float) – Volume fraction of organic material.
lag_time (float) – Lag time before mineralisation begins.
primary_phase_duration (float) – Duration of the primary mineralisation phase.
primary_mineral_content (float) – Mineral content after the primary phase.
maximum_mineral_content (float) – Maximum achievable mineral content.
length_of_queue (int) – Length of the ageing queue.
reference_apposition_rate (float) – Reference mineral apposition rate.
resorption_bias_age (float) – Preferred age for resorption bias.