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Determination of the Number of Tissue Groups of Kinetically Distinct Transit Time in Whole-Body Physiologically Based Pharmacokinetic (PBPK) Models II: Practical Application of Tissue Lumping Theories for Pharmacokinetics of Various Compounds

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Abstract

In our companion paper, we described the theoretical basis for tissue lumping in whole-body physiologically based pharmacokinetic (WB-PBPK) models and found that Kdet, a coefficient for determining the number of tissue groups of distinct transit time in WB-PBPK models, was related to the fractional change in the terminal slope (FCT) when tissues were progressively lumped from the longest transit time to shorter ones. This study was conducted to identify the practical threshold of Kdet by applying the lumping theory to plasma/blood concentration-time relationships of 113 model compounds collected from the literature. We found that drugs having Kdet < 0.3 were associated with FCT < 0.1 even when all peripheral tissues were lumped, resulting in comparable plasma concentration-time profiles between one-tissue minimal PBPK (mPBPK) and WB-PBPK models. For drugs with Kdet ≥ 1, WB-PBPK profiles appeared similar with two-tissue mPBPK models by applying the rule of FCT < 0.1 for lumping slowly equilibrating tissues. The two-tissue mPBPK model also appeared appropriate in terms of concentration-time profiles for drugs with 0.3 ≤ Kdet < 1, although, some compounds (15.9% of the total cases), but not all, in this range showed a slight (maximum of 18.9% of the total AUC) deviation from WB-PBPK models, indicating that the two-tissue model, with caution, could still be used for those cases. Comparison of kinetic parameters between traditional (model-fitting) and current (theoretical calculation) mPBPK analyses revealed their significant correlations. Collectively, these observations suggest that the number of tissue groups could be determined based on the Kdet/FCT criteria, and plasma concentration-time profiles from WB-PBPK could be calculated using equations significantly less complex.

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Funding

This study was supported by the Korea Environment Industry & Technology Institute (KEITI) through the project for BioMarkers TRANSLation of consumer chemicals/ft.life-stage PBPK modeling (BioTranSL/PBPK) (NO. 2022002970003).

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Authors and Affiliations

  1. College of Pharmacy and Research Institute of Pharmaceutical Sciences, Seoul National University, 1 Gwanak-ro, Gwanak-gu, Seoul, 08826, Republic of Korea

    Yoo-Seong Jeong, Min-Soo Kim & Suk-Jae Chung

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  1. Yoo-Seong Jeong
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  2. Min-Soo Kim
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  3. Suk-Jae Chung
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Contributions

Yoo-Seong Jeong: Conceptualization, methodology, formal analysis, investigation, data curation, writing-original draft, writing-review & editing, visualization

Min-Soo Kim: Methodology, software, formal analysis, data curation, writing-review & editing, visualization

Suk-Jae Chung: Conceptualization, methodology, formal analysis, writing-original draft, writing-review & editing, supervision, project administration, funding acquisition

Corresponding author

Correspondence to Suk-Jae Chung.

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Appendix

Appendix

By applying Gauss elimination of the system matrix A of PBPK Model C [10], 10 eigenvalues were readily determined using Eq. 11:

$$\frac{\frac{Q_1{f}_{d1}}{MT{T}_1}}{\lambda -\frac{1}{MT{T}_1}}+\frac{\frac{Q_2{f}_{d2}}{MT{T}_2}}{\lambda -\frac{1}{MT{T}_2}}+\dots +\frac{\frac{Q_9{f}_{d9}}{MT{T}_9}}{\lambda -\frac{1}{MT{T}_9}}={V}_B\left(\lambda -\frac{1}{MT{T}_c}\right)$$
(11)

When the two-tissue mPBPK model (Model D) is applicable, the eigenvalues (in terms of λ′; the roots corresponded to λα, λβ, and λγ) after tissue lumping could be determined by Eq. 12:

$$\frac{\frac{Q_{SEG}{f}_{d, SEG}}{{ MT T}_{SEG}}}{\lambda^{\prime }-\frac{1}{{ MT T}_{SEG}}}+\frac{\frac{Q_{REG}{f}_{d, REG}}{{ MT T}_{REG}}}{\lambda^{\prime }-\frac{1}{{ MT T}_{REG}}}\kern0.75em =\kern0.75em {V}_B\left({\lambda}^{\prime }-\frac{1}{MT{T}_c}\right)$$
(12)

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Jeong, YS., Kim, MS. & Chung, SJ. Determination of the Number of Tissue Groups of Kinetically Distinct Transit Time in Whole-Body Physiologically Based Pharmacokinetic (PBPK) Models II: Practical Application of Tissue Lumping Theories for Pharmacokinetics of Various Compounds. AAPS J 24, 91 (2022). https://doi.org/10.1208/s12248-022-00733-x

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