TY - JOUR

T1 - Modeling of drug diffusion in a solid tumor leading to tumor cell death

AU - Rahman, Aminur

AU - Ghosh, Souparno

AU - Pal, Ranadip

N1 - Funding Information:
The authors express their gratitude to NIH (Grant No. 1R01GM122084) for supporting this work. Thanks are also due D. Pappas and A. Ibragimov for fruitful discussions. In addition, the authors are grateful for the detailed reviews, which have helped to greatly improve this article. A.R. and S.G. appreciate the support of the Department of Mathematics and Statistics at TTU, and R.P. appreciates the support of the Department of Electrical and Computer Engineering at TTU.
Publisher Copyright:
© 2018 American Physical Society.

PY - 2018/12/18

Y1 - 2018/12/18

N2 - It has been shown recently that changing the fluidic properties of a drug can improve its efficacy in ablating solid tumors. We develop a modeling framework for tumor ablation and present the simplest possible model for drug diffusion in a porous spherical tumor with leaky boundaries and assuming cell death eventually leads to ablation of that cell effectively making the two quantities numerically equivalent. The death of a cell after a given exposure time depends on both the concentration of the drug and the amount of oxygen available to the cell, which we assume is the same throughout the tumor for further simplicity. It can be assumed that a minimum concentration is required for a cell to die, effectively connecting diffusion with efficacy. The concentration threshold decreases as exposure time increases, which allows us to compute dose-response curves. Furthermore, these curves can be plotted at much finer time intervals compared to that of experiments, which may possibly be used to produce a dose-threshold-response surface giving an observer a complete picture of the drug's efficacy for an individual. In addition, since the diffusion, leak coefficients, and the availability of oxygen is different for different individuals and tumors, we produce artificial replication data through bootstrapping to simulate error. While the usual data-driven model with sigmoidal curves use 12 free parameters, our mechanistic model only has two free parameters, allowing it to be open to scrutiny rather than forcing agreement with data. Even so, the simplest model in our framework, derived here, shows close agreement with the bootstrapped curves and reproduces well-established relations, such as Haber's rule.

AB - It has been shown recently that changing the fluidic properties of a drug can improve its efficacy in ablating solid tumors. We develop a modeling framework for tumor ablation and present the simplest possible model for drug diffusion in a porous spherical tumor with leaky boundaries and assuming cell death eventually leads to ablation of that cell effectively making the two quantities numerically equivalent. The death of a cell after a given exposure time depends on both the concentration of the drug and the amount of oxygen available to the cell, which we assume is the same throughout the tumor for further simplicity. It can be assumed that a minimum concentration is required for a cell to die, effectively connecting diffusion with efficacy. The concentration threshold decreases as exposure time increases, which allows us to compute dose-response curves. Furthermore, these curves can be plotted at much finer time intervals compared to that of experiments, which may possibly be used to produce a dose-threshold-response surface giving an observer a complete picture of the drug's efficacy for an individual. In addition, since the diffusion, leak coefficients, and the availability of oxygen is different for different individuals and tumors, we produce artificial replication data through bootstrapping to simulate error. While the usual data-driven model with sigmoidal curves use 12 free parameters, our mechanistic model only has two free parameters, allowing it to be open to scrutiny rather than forcing agreement with data. Even so, the simplest model in our framework, derived here, shows close agreement with the bootstrapped curves and reproduces well-established relations, such as Haber's rule.

UR - http://www.scopus.com/inward/record.url?scp=85059392534&partnerID=8YFLogxK

U2 - 10.1103/PhysRevE.98.062408

DO - 10.1103/PhysRevE.98.062408

M3 - Article

AN - SCOPUS:85059392534

VL - 98

JO - Physical Review E

JF - Physical Review E

SN - 2470-0045

IS - 6

M1 - 062408

ER -