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


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.


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



area under curve


maximal cellular binding capacity of paclitaxel


total drug concentration in peritoneal fluid


maximal drug concentration in tumor


total drug concentration in plasma


concentration of cell-associated drug in tumor


total drug concentration in tumor


concentration of unbound drug in tumor


diffusivity in water


effective tumor diffusivity


diffusion coefficient in tumor interstitial space




interstitial drug flux


transvascular drug flux per unit volume


transvascular fluid flux per unit volume


tissue hydraulic conductivity


rate constant of paclitaxel association with cells


paclitaxel binding constant


rate constant of paclitaxel dissociation from cells


pharmacokinetic rate constant for systemic absorption


hydraulic conductivity of vessel wall


permeability of vessel wall to paclitaxel


Peclet number


interstitial fluid pressure


peritoneal pressure




microvascular pressure


radial position in tumor


radius of spherical tumor


vessel surface area per unit tissue volume


time at which Cmax is reached

tumor spatiokinetics

time-dependent and spatial-dependent drug concentrations in tumors


interstitial fluid velocity


volume of peritoneal fluid


half width


osmotic pressure of interstitial proteins


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


cellular volume fraction


interstitial volume fraction


vascular volume fraction


osmotic pressure of plasma proteins


reflection coefficient of vessels for plasma proteins


reflection coefficient of vessels for paclitaxel



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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