East Asian mathematical journal

The Youngnam Mathematical Society (영남수학회)
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A FRACTIONAL-ORDER TUMOR GROWTH INHIBITION MODEL IN PKPD

  • Byun, Jong Hyuk (Department of Mathematics, Pusan National University) ;
  • Jung, Il Hyo (Department of Mathematics, Pusan National University)
  • Received : 2019.12.16
  • Accepted : 2020.01.20
  • Published : 2020.01.31
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Abstract

Many compartment models assume a kinetically homogeneous amount of materials that have well-stirred compartments. However, based on observations from such processes, they have been heuristically fitted by exponential or gamma distributions even though biological media are inhomogeneous in real environments. Fractional differential equations using a specific kernel in Pharmacokinetic/Pharmacodynamic (PKPD) model are recently introduced to account for abnormal drug disposition. We discuss a tumor growth inhibition (TGI) model using fractional-order derivative from it. This represents a tumor growth delay by cytotoxic agents and additionally show variations in the equilibrium points by the change of fractional order. The result indicates that the equilibrium depends on the tumor size as well as a change of the fractional order. We find that the smaller the fractional order, the smaller the equilibrium value. However, a difference of them is the number of concavities and this indicates that TGI over time profile for fitting or prediction should be determined properly either fractional order or tumor sizes according to the number of concavities shown in experimental data.

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References

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