Analytical Solution of the Compartment Model for Respiratory Tract Clearance Used in the New ICRP Lung Model

Abstract

A new ICRP human respiratory tract model, Publication 66, consists of a larger number of clearance compartments than the former lung model in Publication 30. The number of the differential equations which express the retention of inhaled materials in the compartments increases from 10 to 27 in the new model. It needs long calculation time to solve numerically the differential equations with a conventional personal computer, because the integral time sometimes reaches 50 years. In the present paper, analytical solutions of the differential equations under instantaneous intake of unit activity are presented so as to calculate rapidly the retention of the deposited activity.

KEYWORDS:

• ICRP
• respiratory tract model
• clearance compartments
• retention
• inhaled materials
• analytical solutions
• differential equations
• numerical solution