# Also in the Article

General equations
This protocol is extracted from research article:
Simulating drug penetration during hyperthermic intraperitoneal chemotherapy
Drug Deliv, Jan 11, 2021;

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 $U,ρ,τ,p,g$ are the velocity [m/s], density [$kg/m3$], shear-rate tensor [$kg/m/s2$], pressure [Pa] and the gravitational vector [$m/s2$], respectively. The energy equation is given by

where a heat flux is assumed, defined by $q→=−αeff∇e.$ The enthalpy [$m2/s2$], h is defined as the sum of the internal energy, e [$m2/s2$] and kinematic pressure $pρ:$

The third term in Equation (3) is the time derivative of the specific kinetic energy, which is given by $K=|U→2|/2.$ The last term in Equation (3), Stherm, is the thermal sink.

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

where C is the concentration of cisplatin [$mol/m3$], D is the diffusion coefficient [$m2/s$] and Sc is the sink term for cisplatin [$mol/m3/s$]. 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.

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