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The biokinetic models for various radionuclides have been published by ICRP, based on their chemical and physical form. The mathematical solution for such models is required for estimating intake and committed effective dose due to internal contamination. ICRP publishes retained fractions, excretion rates and dose coefficients based on default biokinetic parameters. There is a need for estimation of time dependent biological compartmental values for such cases where ICRP values are unavailable. This paper describes the solution of biokinetic compartment models for various radionuclides and for different intake scenarios. The mathematical solution developed for solving biokinetic model was verified for {sup 239}Pu class S inhalation intake based on ICRP default values. The retained fractions at different times after the intake for {sup 177}Lu class S inhalation are estimated and presented in this paper. The estimated retained fractions and excretion rates for {sup 131}I, {sup 137}Cs, {sup 60}Co, {sup 238}U, {sup 239}Pu and {sup 232}Th were in good agreement with the reported values given in ICRP/IMBA for inhalation, ingestion and injection. Estimated lung retained fraction for class S {sup 239}Pu in the case of inhalation intake and ICRP/IMBA. The whole body retained fractions for {sup 177}Lu class S at various times after inhalation intake which were not available in ICRP/IMBA. This method can be utilized for calculation of number of transformation over 50 years and dose conversion coefficient. The solution of biokinetic data can also be useful in the overexposure cases where non default values can be utilized in such models. The paper …