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On the correction for radioactive decay in pharmacokinetic modeling
L E Williams1, T L Odom-Maryon, A Liu
1Division of Radiology, City of Hope National Medical Center, Duarte, California 91010, USA.
Medical Physics
|October 1, 1995
Summary
Radioactive decay in biological modeling requires careful handling. Decay-corrected data is only valid for linear, homogeneous pharmacokinetic models; otherwise, physical decay must be included in all compartments.
Area of Science:
- Pharmacokinetics and Mathematical Modeling
- Radiochemistry and Nuclear Medicine
Background:
- Biological modeling often incorporates radioactive tracers, necessitating consideration of radioactive decay.
- Two approaches exist: using raw experimental data y(t) or decay-corrected data z(t).
- The validity of using decay-corrected data in purely pharmacokinetic models (without decay) is often assumed but requires scrutiny.
Purpose of the Study:
- To investigate the appropriate inclusion of radioactive decay in biological models analyzed with first-order differential equations.
- To determine the conditions under which decay-corrected data can be reliably used in pharmacokinetic modeling.
- To compare the outcomes of modeling using raw versus decay-corrected data.
Main Methods:
- Developed a general theorem to establish the limitations of using decay-corrected data.
- Analyzed a linear, homogeneous pharmacokinetic model for chimeric monoclonal antibody biodistribution.
- Examined an open, quadratic model to assess the impact of omitting decay.
- Investigated monoclonal antibody-antigen reactions to demonstrate discrepancies with decay-corrected data.
Main Results:
- A theorem was derived limiting the use of decay-corrected data to linear, homogeneous differential equation models.
- Statistically significant differences in model parameters were observed even in a linear, homogeneous model when comparing raw and decay-corrected data.
- Omitting decay in non-linear models can lead to maximized discrepancies when biological rates approach or exceed the decay constant.
- Discrepancies persisted in antibody-antigen reactions, even with competitive molecules present.
Conclusions:
- Decay-corrected data should only be used in modeling equations that are linear and homogeneous.
- For other model types, physical decay must be explicitly included in all relevant compartments.
- Incorrectly applying decay-corrected data can lead to inaccurate pharmacokinetic model parameters and biological interpretations.