General equations

DL Daan R. Löke RH Roxan F. C. P. A. Helderman NF Nicolaas A. P. Franken AO Arlene L. Oei PT Pieter J. Tanis JC Johannes Crezee HK H. Petra Kok

This protocol is extracted from research article:

Simulating drug penetration during hyperthermic intraperitoneal chemotherapy

**
Drug Deliv**,
Jan 11, 2021;
DOI:
10.1080/10717544.2020.1862364

Simulating drug penetration during hyperthermic intraperitoneal chemotherapy

Procedure

The equations governing the fluid dynamics are derived from the Navier–Stokes equation and can be described by the momentum and mass conservation equations:

where $U,\rho ,\mathit{\tau},p,g$ are the velocity [*m*/*s*], density [$kg/{m}^{3}$], shear-rate tensor [$kg/m/{s}^{2}$], pressure [*Pa*] and the gravitational vector [$m/{s}^{2}$], respectively. The energy equation is given by

where a heat flux is assumed, defined by $\overrightarrow{q}=-{\alpha}_{\mathit{eff}}\nabla e.$ The enthalpy [${m}^{2}/{s}^{2}$], *h* is defined as the sum of the internal energy, *e* [${m}^{2}/{s}^{2}$] and kinematic pressure $\frac{p}{\rho}:$

The third term in Equation (3) is the time derivative of the specific kinetic energy, which is given by $K=\left|{\overrightarrow{U}}^{2}\right|/2.$ The last term in Equation (3), *S _{therm}*, is the thermal sink.

The transport of cisplatin was modeled as a passive scalar, governed by

where *C* is the concentration of cisplatin [$\mathit{mol}/{m}^{3}$], *D* is the diffusion coefficient [${m}^{2}/s$] and *S _{c}* is the sink term for cisplatin [$\mathit{mol}/{m}^{3}/s$]. The use of these general equations to describe dynamics in the peritoneal cavity, healthy tissue, viable tumor and necrotic core is explained in more detail below.

This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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