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Fractional transit compartment model for describing drug delayed response to tumors using Mittag-Leffler distribution on age-structured PKPD model

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  • Jong Hyuk Byun
  • Yunil Roh
  • In-Soo Yoon
  • Kwang Su Kim
  • Il Hyo Jung

Abstract

The response of a cell population is often delayed relative to drug injection, and individual cells in a population of cells have a specific age distribution. The application of transit compartment models (TCMs) is a common approach for describing this delay. In this paper, we propose a TCM in which damaged cells caused by a drug are given by a single fractional derivative equation. This model describes the delay as a single equation composed of fractional and ordinary derivatives, instead of a system of ODEs expressed in multiple compartments, applicable to the use of the PK concentration in the model. This model tunes the number of compartments in the existing model and expresses the delay in detail by estimating an appropriate fractional order. We perform model robustness, sensitivity analysis, and change of parameters based on the amount of data. Additionally, we resolve the difficulty in parameter estimation and model simulation using a semigroup property, consisting of a system with a mixture of fractional and ordinary derivatives. This model provides an alternative way to express the delays by estimating an appropriate fractional order without determining the pre-specified number of compartments.

Suggested Citation

  • Jong Hyuk Byun & Yunil Roh & In-Soo Yoon & Kwang Su Kim & Il Hyo Jung, 2022. "Fractional transit compartment model for describing drug delayed response to tumors using Mittag-Leffler distribution on age-structured PKPD model," PLOS ONE, Public Library of Science, vol. 17(11), pages 1-17, November.
    • Handle: RePEc:plo:pone00:0276654
    DOI: 10.1371/journal.pone.0276654
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    References listed on IDEAS

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    1. Roberto Garrappa, 2018. "Numerical Solution of Fractional Differential Equations: A Survey and a Software Tutorial," Mathematics, MDPI, vol. 6(2), pages 1-23, January.
    2. Francisco J. Ariza-Hernandez & Martin P. Arciga-Alejandre & Jorge Sanchez-Ortiz & Alberto Fleitas-Imbert, 2020. "Bayesian Derivative Order Estimation for a Fractional Logistic Model," Mathematics, MDPI, vol. 8(1), pages 1-9, January.
    3. David S. Glass & Xiaofan Jin & Ingmar H. Riedel-Kruse, 2021. "Nonlinear delay differential equations and their application to modeling biological network motifs," Nature Communications, Nature, vol. 12(1), pages 1-19, December.
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