Notation | Definition |

B_{2} | The transmission factor for radiation emanating from compartment 2 (thyroid) |

d_{1} | The distance (m) to a bystander from the patient’s skin at the extrathyroidal source |

d_{2} | The distance (m) to a bystander from the patient’s skin at the thyroid |

Δd_{1} | The depth in the patient (m) of the extrathyroidal line source |

Δd_{2} | 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 ^{131}I’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 ^{131}I) |

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 |