The AAPS Journal

, Volume 16, Issue 3, pp 424–439 | Cite as

Multiscale Tumor Spatiokinetic Model for Intraperitoneal Therapy

  • Jessie L.-S. Au
  • Peng Guo
  • Yue Gao
  • Ze Lu
  • Michael G. Wientjes
  • Max Tsai
  • M. Guillaume Wientjes
Research Article

Abstract

This study established a multiscale computational model for intraperitoneal (IP) chemotherapy, to depict the time-dependent and spatial-dependent drug concentrations in peritoneal tumors as functions of drug properties (size, binding, diffusivity, permeability), transport mechanisms (diffusion, convection), spatial-dependent tumor heterogeneities (vessel density, cell density, pressure gradient), and physiological properties (peritoneal pressure, peritoneal fluid volume). Equations linked drug transport and clearance on three scales (tumor, IP cavity, whole organism). Paclitaxel was the test compound. The required model parameters (tumor diffusivity, tumor hydraulic conductivity, vessel permeability and surface area, microvascular hydrostatic pressure, drug association with cells) were obtained from literature reports, calculation, and/or experimental measurements. Drug concentration-time profiles in peritoneal fluid and plasma were the boundary conditions for tumor domain and blood vessels, respectively. The finite element method was used to numerically solve the nonlinear partial differential equations for fluid and solute transport. The resulting multiscale model accounted for intratumoral spatial heterogeneity, depicted diffusive and convective drug transport in tumor interstitium and across blood vessels, and provided drug flux and concentration as a function of time and spatial position in the tumor. Comparison of model-predicted tumor spatiokinetics with experimental results (autoradiographic data of 3H-paclitaxel in IP ovarian tumors in mice, 6 h posttreatment) showed good agreement (1% deviation for area under curve and 23% deviations for individual data points, which were several-fold lower compared to the experimental intertumor variations). The computational multiscale model provides a tool to quantify the effects of drug-, tumor-, and host-dependent variables on the concentrations and residence time of IP therapeutics in tumors.

KEY WORDS

convective and diffusive transport multiscale models solid tumors spatiokinetics target site pharmacokinetics 

Abbreviations

AUC

area under curve

Bmax

maximal cellular binding capacity of paclitaxel

Cip,total

total drug concentration in peritoneal fluid

Cmax

maximal drug concentration in tumor

Cplasma,total

total drug concentration in plasma

Ctumor,bound

concentration of cell-associated drug in tumor

Ctumor,total

total drug concentration in tumor

Ctumor,unbound

concentration of unbound drug in tumor

Daqueous

diffusivity in water

D

effective tumor diffusivity

Dint

diffusion coefficient in tumor interstitial space

IP

intraperitoneal

Js,interstitial

interstitial drug flux

Js,transvascular

transvascular drug flux per unit volume

Jv

transvascular fluid flux per unit volume

K

tissue hydraulic conductivity

kassoc

rate constant of paclitaxel association with cells

kd

paclitaxel binding constant

kdissoc

rate constant of paclitaxel dissociation from cells

kp

pharmacokinetic rate constant for systemic absorption

Lp

hydraulic conductivity of vessel wall

Pd

permeability of vessel wall to paclitaxel

Pev

Peclet number

Pi

interstitial fluid pressure

Pip

peritoneal pressure

PK

pharmacokinetics

Pv

microvascular pressure

r

radial position in tumor

R

radius of spherical tumor

Sv/V

vessel surface area per unit tissue volume

Tmax

time at which Cmax is reached

tumor spatiokinetics

time-dependent and spatial-dependent drug concentrations in tumors

ui

interstitial fluid velocity

Vip

volume of peritoneal fluid

W1/2

half width

πi

osmotic pressure of interstitial proteins

αip

αp, βip, βp, PK rate constants for IP fluid and plasma

ϕc

cellular volume fraction

ϕi

interstitial volume fraction

ϕv

vascular volume fraction

πv

osmotic pressure of plasma proteins

σv

reflection coefficient of vessels for plasma proteins

σp

reflection coefficient of vessels for paclitaxel

Notes

Acknowledgments

This work was supported in part by research grants R01GM100487 from the National Institute of General Medical Sciences and R01EB015253 from the National Institute of Biomedical Imaging and Bioengineering, NIH, DHHS.

Conflict of Interest

The authors disclose no potential conflicts of interest.

Supplementary material

12248_2014_9574_MOESM1_ESM.docx (28 kb)
ESM 1(DOCX 28 kb)

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Copyright information

© American Association of Pharmaceutical Scientists 2014

Authors and Affiliations

  • Jessie L.-S. Au
    • 1
    • 2
  • Peng Guo
    • 2
  • Yue Gao
    • 1
  • Ze Lu
    • 2
  • Michael G. Wientjes
    • 2
  • Max Tsai
    • 1
  • M. Guillaume Wientjes
    • 1
    • 2
  1. 1.College of PharmacyThe Ohio State UniversityColumbusUSA
  2. 2.Optimum Therapeutics, LLCSan DiegoUSA

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