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update concentration chapter

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Andre Henriques 2022-06-23 15:49:25 -04:00
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cara/docs/full_diameter_dependence.rst
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@ -93,16 +93,13 @@ The long-range concentration, integrated over the exposure time (in piecewise co
In the :math:`C_{\mathrm{LR}}(t, D)` equation above, the **emission rate** :math:`\mathrm{vR}(D)` and **viral removal rate** :math:`\lambda_{\mathrm{vRR}}` (:meth: `infectious_virus_removal_rate`) are both diameter-dependent.
???? Hence, the concentration needs, equally, to be normalized by the diameter-dependent quantities: emission rate (AND VRR??).
???? Since the emission rate is, in turn, dependent on other diameter-independent variables (:math:`\mathrm{vl}_\mathrm{in}` and :math:`\mathrm{BR}_k``) (WHERE IS THIS?), those parameters shall also be excluded when calculating the integral,
the concentration method was written to be normalized by the emission rate.
In other words, we can split the concentration in two different formulations:
* Normalized concentration :meth:`cara.models.ConcentrationModel._normed_concentration` : :math:`\mathrm{C_\mathrm{LR, normed}}(t, D)` that cumputes the concentration without including the emission rate.
???? * Concentration :meth:`cara.models.ConcentrationModel.concentration` : :math:`C_{\mathrm{LR}}(t, D) = [\mathrm{C_\mathrm{LR, normed}}(t, D) \cdot \mathrm{vR}(D)] \cdot \mathrm{BR_k} \cdot \mathrm{vl_{in}}`, (WHERE IS THIS?)
where :math:`\mathrm{vR}(D)` that cumputes the full concentration, still as a function of the particle diameter,
* Concentration :meth:`cara.models.ConcentrationModel.concentration` : :math:`C_{\mathrm{LR}}(t, D) = \mathrm{C_\mathrm{LR, normed}}(t, D) \cdot \mathrm{vR}(D)`,
where \mathrm{vR}(D) is the result of the :meth:`cara.models._PopulationWithVirus.emission_rate_when_present` method.
Note that in order to get the total concentration value in this stage, the final result should be averaged by the particle diameters (i.e. Monte-Carlo integration over diameters, see above).
In the calculator app, the total concentration (MC integral over the diameter) :meth:??? is performed only when generating the concentration plot. Otherwise, the diameter-dependence continues until we cumpute the inhaled dose in :class:`cara.models.ExposureModel` class.