Dosimetry

A dosimetry model is a group of functions used to calculate absorbed doses. Doses delivered by radon daughters to the lung depends on the aerosol involved and the morphology of the lung. The size of the particle, the size of the unattached fraction, and the equilibrium state all effect the aerosol portion. Several physiological factors combine to determine the rate of expulsion of particulate matter:

the depth of the target cells
the lung tidal volume
particle deposition fraction
thickness and effectiveness of the mucus

When we inhale...

the unattached fraction diffuses onto the walls of the respiratory tract according to the normal breathing rate of 750 liters per hour (for adults in light activity)
65% of the inhaled unattached fraction is removed by nasal breathing
the remainder is deposited in the upper portion of the airway.

The fraction attached to the aerosol is effected by diffusion, impaction, and sedimentation.

Diffusive deposition is the result of the random motion of small particles contacting the epithelium.
Impactive deposition is the result of inertia, preventing a particle from negotiating a change in the direction of an air streamline following a bifurcation in an airway so that it strikes an airway surface.
Sedimentation deposition< is the result of gravity.

The probability of deposition of attached atoms is a function of the size distribution of the atmospheric aerosol.

The rate of removal depends on several mechanisms:

Undesirable particles are transferred upward out of the airway by mucus and the cilia.
Following the dissolving/release of the radionuclides from the aerosol, they diffuse into the epithelium.
After diffusing, radionuclides either remain or are transferred into the bloodstream to be carried away.

The transfer of particulate matter by the mucus (known as the muco-ciliary escalator) carries deposited particles up to the throat, exposing each generation of airway to particles originally deposited deeper in the lung, however relative to the rate of radioactive decay, the rate of muco-ciliary escalation is fast. In the lung models used by the NEA experts group (1983) and the National Council on Radiation Protection and Measurements Task Group (1984), however, blood clearance takes a long time compared to radioactive decay time.

To write expressions describing radon dosage, the geometry of the respiratory system must be studied.

The uppermost portion consists of the nose, mouth throat, larynx and pharynx is known as the naso-pharyngeal (N-P) region. In this region, air flow is fastest and more likely to be turbulent.
The middle region begins with the trachea, which divides into two large airways. Divisions of the airways continue into smaller and smaller tubes, with each successive division along the "tree" known as a generation (thus the trachea is referred to as generation zero).
The tracheo-bronchial (T-B) region consists of the first sixteen generations, where the airspeed has slowed and laminar flow is observed.
Beyond generation sixteen, division of the airway continues, terminating in the alveoli.
Any portion of the respiratory system above generation sixteen is known as the pulmonary (P) region.

The cells at risk for alpha-particle induced cancer are the dividing basal cells of the epithelium of the airway walls. Lung cancer most commonly appears in the epithelium of the segmental bronchi of generation four, where the calculated dose is greatest. Following cell division, these cells become like the highly specialized, unciliated cells of the P region which do not undergo division. With time, these cells die and do not become cancerous, however the natural balance between cell death and reproduction may be altered. Dividing, irradiated cells may have a loss of regulatory control, leading to the formation of a tumor. The extent to which radiation effects the cells of the respiratory system depends on the thickness of the different layers along the respiratory tract, however these thicknesses vary among all individuals according to age and sex. Attempts to define the dosimetry of the lung even for a "standard male" requires complex mathematical modeling. measured epithelial dimensions of the lung using surgical specimens. Assuming that the length of the cilia approximates the thickness of the serous layer of the mucus and that the viscous mucus layer is of comparable thickness, then in the segmental bronchi Gastineau reports the following thickness ranges: 2.5-10 microns for the cilia and viscous mucus, 10-90 microns for the epithelium, and 5-10 microns for the basal layer.

Table of Penetration Distances for Radon progeny nuclei

The atmospheric aerosol typically forms small, ionized agglomerates with radon daughters and/or water vapor. The ions are one-thousandth of the size of the aerosol particles they combine with, and the size of the attached fraction can vary greatly with the aerosol.

In summary, to calculate the dose of alpha particles on the basal layer, several variables must be known:

the concentration of radon daughters in the air
the relationship between the muco-ciliary escalator and the rate of deposition
the actual energy delivered to the tissue.

Models of the Lung

The respiratory system is usually described in terms of the number of bifurcations of the airway following the trachea.

The Weibel "A" model, developed in 1963, treats the lung as a single unit with regular, symmetric bifurcations although it is known that in the right lung the first generation airway produces three second generation airways while the left lung only gives rise to two second generation airways.
The Yeh-Schum model either divides the lung into five lobes (each with its own subdivision pattern) or calculates an average value for the whole lung.

Each generation is given an index according to the number of bifurcations, with the trachea denoted as generation 0 in the Weibel "A" model and generation 1 in the Yeh-Schum model. Another difference between the two models is that the Yeh-Schum model ascribes slightly larger airway diameters, therefore changing the deposition probabilities. These two lung models led to the formation of the Jacobi-Eisfeld (J-E) model (1980), which uses the Weibel "A" model, and the James-Birchall (J-B) model (1980), which considers both whole-lung models. The J-E and J-B models are the most commonly used descriptions of the lung used today.

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