Purpose This study aimed to determine a mathematical model for accurately calculating time-integrated activities (TIAs) of target tissue in 131I therapy for benign thyroid disease using the population-based model selection and non-linear mixed-effects (PBMS-NLME) method. Methods Biokinetic data of 131I in target tissue were collected from seventy-three patients at 2, 6, 24, 48, and 96 (N = 53) or 120 (N = 20) h after oral capsule administration with 1 MBq 131I. Based on the Akaike weight, the best sum-of-exponential function (SOEF) describing the biokinetic data was selected using PBMS-NLME modelling. Nine SOEF with three to six parameters (including the function from the European Association of Nuclear Medicine Standard Operational Procedure (EANM SOP)) were used. The fittings were repeated 1000 times with different starting values of the SOE parameters to find the optimal fit. Akaike weight was used to identify the performance of the best model from PBMS-NLME and the EANM SOP SOE function with individual fitting. Results Based on the PBMS-NLME analysis, the SOEF <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="40658_2025_735_Article_IEq1.gif" Format="GIF" Height="33" Rendition="HTML" Resolution="72" Type="Linedraw" Width="433" /> </InlineMediaObject> <EquationSource Format="TEX">$\frac{{\lambda_{1} }}{{\lambda_{2} + \lambda_{1} - \lambda_{3} }}\left( {e^{{ - \left( {\lambda_{3} + \lambda_{phys} } \right)t}} - e^{{ - \left( {\lambda_{1} + \lambda_{2} + \lambda_{phys} } \right)t}} } \right) + a_{1} e^{{ - \left( {\lambda_{1} + \lambda_{2} + \lambda_{phys} } \right)t}}$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mfrac> <msub> <mi>λ</mi> <mn>1</mn> </msub> <mrow> <msub> <mi>λ</mi> <mn>2</mn> </msub> <mo>+</mo> <msub> <mi>λ</mi> <mn>1</mn> </msub> <mo>-</mo> <msub> <mi>λ</mi> <mn>3</mn> </msub> </mrow> </mfrac> <mfenced close=")" open="("> <mrow> <msup> <mi>e</mi> <mrow> <mo>-</mo> <mfenced close=")" open="("> <mrow> <msub> <mi>λ</mi> <mn>3</mn> </msub> <mo>+</mo> <msub> <mi>λ</mi> <mrow> <mi mathvariant="italic">phys</mi> </mrow> </msub> </mrow> </mfenced> <mi>t</mi> </mrow> </msup> <mo>-</mo> <msup> <mi>e</mi> <mrow> <mo>-</mo> <mfenced close=")" open="("> <mrow> <msub> <mi>λ</mi> <mn>1</mn> </msub> <mo>+</mo> <msub> <mi>λ</mi> <mn>2</mn> </msub> <mo>+</mo> <msub> <mi>λ</mi> <mrow> <mi mathvariant="italic">phys</mi> </mrow> </msub> </mrow> </mfenced> <mi>t</mi> </mrow> </msup> </mrow> </mfenced> <mo>+</mo> <msub> <mi>a</mi> <mn>1</mn> </msub> <msup> <mi>e</mi> <mrow> <mo>-</mo> <mfenced close=")" open="("> <mrow> <msub> <mi>λ</mi> <mn>1</mn> </msub> <mo>+</mo> <msub> <mi>λ</mi> <mn>2</mn> </msub> <mo>+</mo> <msub> <mi>λ</mi> <mrow> <mi mathvariant="italic">phys</mi> </mrow> </msub> </mrow> </mfenced> <mi>t</mi> </mrow> </msup> </mrow> </math></EquationSource> </InlineEquation> was selected as the function most supported by the data. The Akaike weight of the best function was approximately 100%. The best SOEF from the PBMS-NLME approach shows a better performance in describing the biokinetic data of 131I in the thyroid gland than the function from the EANM SOP with individual fitting, based on the Akaike weight. Conclusions The best mathematical model from the PBMS-NLME approach has one more free parameter than the EANM SOP function, which could lead to more accurate TIAs.

Non-linear mixed-effects modelling and population-based model selection for ¹³¹I kinetics in benign thyroid disease

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2025年4月8日

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Deni Hardiansyah,
Ade Riana,
Heribert Hänscheid,
Ambros J. Beer,
Michael Lassmann,
Gerhard Glatting

摘要

Purpose

This study aimed to determine a mathematical model for accurately calculating time-integrated activities (TIAs) of target tissue in ¹³¹I therapy for benign thyroid disease using the population-based model selection and non-linear mixed-effects (PBMS-NLME) method.

Methods

Biokinetic data of ¹³¹I in target tissue were collected from seventy-three patients at 2, 6, 24, 48, and 96 (N = 53) or 120 (N = 20) h after oral capsule administration with 1 MBq ¹³¹I. Based on the Akaike weight, the best sum-of-exponential function (SOEF) describing the biokinetic data was selected using PBMS-NLME modelling. Nine SOEF with three to six parameters (including the function from the European Association of Nuclear Medicine Standard Operational Procedure (EANM SOP)) were used. The fittings were repeated 1000 times with different starting values of the SOE parameters to find the optimal fit. Akaike weight was used to identify the performance of the best model from PBMS-NLME and the EANM SOP SOE function with individual fitting.

Results

Based on the PBMS-NLME analysis, the SOEF $\frac{{\lambda_{1} }}{{\lambda_{2} + \lambda_{1} - \lambda_{3} }}\left( {e^{{ - \left( {\lambda_{3} + \lambda_{phys} } \right)t}} - e^{{ - \left( {\lambda_{1} + \lambda_{2} + \lambda_{phys} } \right)t}} } \right) + a_{1} e^{{ - \left( {\lambda_{1} + \lambda_{2} + \lambda_{phys} } \right)t}}$ $\frac{λ_{1}}{λ_{2} + λ_{1} - λ_{3}} (e^{- (λ_{3} + λ_{phys}) t} - e^{- (λ_{1} + λ_{2} + λ_{phys}) t}) + a_{1} e^{- (λ_{1} + λ_{2} + λ_{phys}) t}$ was selected as the function most supported by the data. The Akaike weight of the best function was approximately 100%. The best SOEF from the PBMS-NLME approach shows a better performance in describing the biokinetic data of ¹³¹I in the thyroid gland than the function from the EANM SOP with individual fitting, based on the Akaike weight.

Conclusions

The best mathematical model from the PBMS-NLME approach has one more free parameter than the EANM SOP function, which could lead to more accurate TIAs.

Non-linear mixed-effects modelling and population-based model selection for 131I kinetics in benign thyroid disease

摘要

Non-linear mixed-effects modelling and population-based model selection for ¹³¹I kinetics in benign thyroid disease