TABLE 1

Mathematic Notations and Definitions

Notation	Definition
B₂	The transmission factor for radiation emanating from compartment 2 (thyroid)
d₁	The distance (m) to a bystander from the patient’s skin at the extrathyroidal source
d₂	The distance (m) to a bystander from the patient’s skin at the thyroid
Δd₁	The depth in the patient (m) of the extrathyroidal line source
Δd₂	The depth in the patient (m) of the thyroidal point source
	The fraction of administered isotope initially partitioned into compartment 1
	The fraction of administered isotope initially partitioned into compartment 2
g_i	The perpendicular distance from the cylinder’s ith line source to the dose point
Δg_i	The perpendicular distance from the cylinder’s ith line source to the cylinder’s surface in the direction of the dose point
HVL	The broad-beam half-value layer in water (m) of ¹³¹I’s 364-keV photon (the value 0.1 m is used, reference (9))
	The air kerma rate at the position of a bystander resulting from patient emanations
	The total air kerma at the position of a bystander beginning at a start time t_s
l	Variable of integration, distance from midpoint of a line source to line source element dl
L	The length (m) of the line source
	The amount of isotope remaining in metabolic compartment 1 (extrathyroid) at time t
	The amount of isotope remaining in metabolic compartment 2 (thyroid) at time t
	The amount of isotope in the bladder at time t when the previous urination was at time T
	The amount of isotope remaining in the patient at time t (parallel model)
	The amount of isotope initially administered
	The effective half-life for the radioisotope leaving metabolic compartment 1
	The effective half-life for the radioisotope leaving metabolic compartment 2
T_oc	The occupancy factor, that is, the average fraction of time that a specific bystander is present at a specified location
t_s	The time that a family member or other bystander begins exposure to the patient’s radiation field
Γ	The air kerma rate constant (mGy/h/MBq at 1 m) for the radioisotope (the value 5.1613E−5 is used for ¹³¹I)
	The rate constant for the radioisotope leaving a metabolic compartment by nuclear decay
	The rate constant for the isotope leaving metabolic compartment 1 by biologic processes
	The rate constant for the isotope leaving metabolic compartment 2 by biologic processes
	The effective rate constant for the isotope leaving metabolic compartment 1
	The effective rate constant for the isotope leaving metabolic compartment 2
	The relationship between rate constant and half-life, where ln(2) is the natural log of 2