Physics Models: P-THERMAL

 Thermodynamics Solvers

The Thermodynamic Solvers (P-THERMAL) enable the modeling of heat transfer in living tissue using advanced perfusion and thermoregulation models. The two solvers adapted from SEMCAD X are based on 1) the finite-difference time-domain solver with conformal surface correction and 2) a steady-state finite volume solver to support adaptive rectilinear meshes and arbitrary active domain shapes.

Treatment planning for liver radiofrequency ablation (RFA) (specific absorption rate (SAR), CEM43 thermal tissue damage assessment).

The solvers allow for the coupled simulation of local vascular effects using discrete networks (1D trees) and, in the near future, CFD results.

Exclusive thermal damage and effect quantification models, e.g., T-CEM43, are included.

The P-THERMAL solvers have been extensively validated by comparison with analytically solvable cases, experimental measurements under controlled conditions, and in vivo measurements. Comprehensive documentation is available for Sim4Life.


  Application Areas

  • MRI Tx RF Coil Design w/ Gradient Interaction & Safety
  • Active & Passive Implants MRI Safety
  • RF Hyperthermia
  • Safety & Efficacy Assessment of Ultrasonic Devices for Therapeutic Purposes


  • RF/MW Tumor Ablation, RF Surgery
  • Design & Optimization of Ultrasonic Devices for Therapeutic Purposes
  • MRgFUS Neurosurgery Applications: Tumor Ablation, Neuropathic Pain Treatment, Movement Disorders


  • Hypothermia
  • Cryosurgery
  • Temperature Impact on Neuronal Dynamics
  • Flow in Eye (oxygenation, heating)
  • Local Cooling by Blood

  Key Features

  • T standalone solver
  • Coupled EM-T, extended Pennes Bioheat Equation for BioEM
  • Discrete vessel model for BioEM
  • Steady state T solver
  • Multiple EM sources (not bound to single simulation)
  • Correlated/uncorrelated superposition of fields, individual scaling


  • Pulsed excitation/time profile, on-off switch
  • T dependent tissues (electric conductivity, SAR, blood perfusion)
  • Time dependent specific heat generation rates
  • Tensorial heat diffusion
  • Spline-based vessels
  • Conformal subcell T solver


  • Flexible boundary-conditions (Neumann, Dirichlet, mixed, for every interface and every direction)
  • Extended T solver functionality (field optimization extended features)
  • Thermal ablation (tissue damage) measure
  • Convective flow term
  • LF solver results as T sources
  • Field statistics for T results

In vivo temperature evaluation of radiofrequency (RF)-safe pacemakers.

Optimization of liver tumor focused ultrasound (FUS) ablation considering
breathing motions.

Optimized positioning and steering of hyperthermia
applicator arrays.