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cara/docs/full_diameter_dependence.rst
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@ -8,38 +8,41 @@ Context
The :mod:`cara.apps.calculator.model_generator` module is responsible to bind all the inputs defined in the user interface into the respective model variables.
The :py:mod:`cara.apps.calculator.report_generator` module is responsible to bind the results from the model calculations into the respective output variables presented in the CARA report.
The :mod:`cara.models` module itself implements the core CARA methods. A useful feature of the implementation is that we can benefit from vectorization, which allows runnning multiple parameterizations of the model at the same time.
The :mod:`cara.models` module itself implements the core CARA methods. A useful feature of the implementation is that we can benefit from vectorization, which allows running multiple parameterization of the model at the same time.
Unlike other similar models, some of the CARA varibles are considered for a given aerosol diameter **D**,
as the behaviour of the virus-laden particles in the room environment and inside the succeptible host (once inhaled) are diameter-dependent.
Unlike other similar models, some of the CARA variables are considered for a given aerosol diameter **D**,
as the behavior of the virus-laden particles in the room environment and inside the susceptible host (once inhaled) are diameter-dependent.
These variables are identified by **(D)** in the variable name, such as the **emission rate** -- **vR(D)**, **removal rate** -- **vRR(D)**, and **concentration** -- **C(t, D)**.
Despite the outcome of the CARA results include the entire range of diameters, throughout the model,
most of the variables and parameters are kept in their diameter-dependent form for any possible detailed analysis of intermidiate results.
Only the final quantities shown in output, such as the concentration and the dose, are integrated over the diameter distribuion.
most of the variables and parameters are kept in their diameter-dependent form for any possible detailed analysis of intermediate results.
Only the final quantities shown in output, such as the concentration and the dose, are integrated over the diameter distribution.
This is performed thanks to a Monte-Carlo integration at the level of the dose (**vD\ :sup:`total`\**) which is computed over a distribution of particle diameters,
from which the average value is then calculated -- this is equivalent to an analytical integral over diameters
provided the sample size is large enough.
It is important to distinguish between 1) Monte-Carlo random variables (which are vectorized independently on its diameter-dependence) and 2) numerical Monte-Carlo integration for the diameter-dependence
Since the integral of the diameter-dependent variables are solved when computing the dose -- **vD\ :sup:`total`\**, while performing some of the intermediate calculations,
It is important to distinguish between 1) Monte-Carlo random variables (which are vectorised independently on its diameter-dependence) and 2) numerical Monte-Carlo integration for the diameter-dependence
Since the integral of the diameter-dependent variables are solved when computing the dose -- **vD:math:'^{total}'**, while performing some of the intermediate calculations,
we normalize the results by *dividing* by the Monte-Carlo variables that are diameter-independent, so that they are not considered in the Monte-Carlo integration (e.g. :meth:`cara.models.ConcentrationModel.normed_integrated_concentration`).
Expiration
==========
One of the properties of the Expiration class is the :attr:`cara.models.Expiration.particle`, that represents the aerosol with a vectorised parameter, the diameter.
For a given diameter of aerosol, one :class:`cara.models.Expiration` object provides the aerosol **volume - Vp(D)**, weighted by the **mask outward efficiency - ηout(D)** when applicable.
In the **Expiration** class (representing the expiration of aerosols by an infected person) has , as one of its properties `Particle`, :attr:`cara.models.Expiration.particle`,
which represents the virus-laden aerosol with a vectorised parameter: the particle `diameter` (assuming a perfect sphere).
For a given aerosol diameter, one :class:`cara.models.Expiration` object provides the aerosol **volume - Vp(D)**, multiplied by the **mask outward efficiency - ηout(D)** to include the filteration capacity, when applicable.
The BLO model represents the distribution of diameters used in the model. It is a sum of three lognormal distributions, weighted by the **B**, **L** and **O** modes.
The aerosol diameters distribution is given by the :meth:`cara.monte_carlo.data.BLOmodel.distribution` method.
The BLO model represents the distribution of diameters used in the model. It corresponds to the sum of three lognormal distributions, weighted by the **B**, **L** and **O** modes.
The aerosol diameter distributions are given by the :meth:`cara.monte_carlo.data.BLOmodel.distribution` method.
The :class:`cara.monte_carlo.data.BLOmodel` class itself contains the method to return the raw value of the probability distribution for a given diameter (in microns), as well as the method to return the integral between the **min** and **max** diameters of the probability distribution.
The BLO model is only used to provide the distribution followed by the aerosol diameters, and to compute the total number of particles per mode B, L and O, **cn**. In other words, **cn** is the total concentration of aerosols per unit volume of expired air, integrated over all aerosol diameters. In the model it is used as a scaling factor.
The :class:`cara.monte_carlo.data.BLOmodel` class itself contains the method to return the mathematical values of the probability distribution for a given diameter (in microns),
as well as the method to return the limits of integration between the **min** and **max** diameters.
The BLO model is used to provide the probability density function (PDF) of the aerosol diameters for a given **Expiration** type defined in :meth:`cara.monte_carlo.data.expiration_distribution`.
To compute the total number concentration of particles per mode (B, L and O), **cn** in particles/cm:math:'^3', in other words, the total concentration of aerosols per unit volume of expired air,
an integration of the lognormal distributions is performed over all aerosol diameters. In the code it is used as a scaling factor in the :class:`cara.models.Expiration` class.
Under the :mod:`cara.apps.calculator.model_generator`, when it comes to generate the Expiration, the diameters property is sampled through the BLO :meth:`cara.monte_carlo.data.BLOmodel.distribution` method, while the value for the **cn** is given by the :meth:`cara.monte_carlo.data.BLOmodel.integrate` method.
To sum up, the expiration contains the distribution of the diameters as a vectorised float. Depending on different expiratory types, the contributions from each mode will be different, therefore the result in the distribution is different.
The cn is considered a scaling factor that results from the integration between the diameter limits -- it represents the total concentration of aerosols per unit volume of expired air (integrated over all aerosol diameters).
Under the :mod:`cara.apps.calculator.model_generator`, when it comes to generate the Expiration model, the `diameter` property is sampled through the BLO :meth:`cara.monte_carlo.data.BLOmodel.distribution` method, while the value for the **cn** is given by the :meth:`cara.monte_carlo.data.BLOmodel.integrate` method.
To summarize, the Expiration contains the distribution of the diameters as a vectorised float. Depending on different expiratory types, the contributions from each mode will be different, therefore the result in the distribution also differs from model to model.
Emission Rate - vR(D)
=====================