Physics Models: P-ACOUSTICS

  Acoustics Solvers

Sim4Life offers a novel full-wave Acoustics Solver (P-ACOUSTICS) based on the linear pressure wave equation (LAPWE), extended and optimized for heterogeneous, lossy materials for the modeling of the propagation of pressure waves through highly inhomogeneous media like tissue and bone. All relevant phenomena like scattering, reflection, refraction, diffraction, interference, and absorption are captured by this method. The dissipated acoustics energy can be translated into a heat source for Sim4Life’s thermal solver (P-THERMAL) to capture the coupling of acoustic and thermal phenomena.

Precise ablation of a liver tumor located behind the ribs considering respiratory movements.

An adaptive rectilinear grid is used to discretize the computational domain with feature-specific granularity and inhomogeneous perfectly matched layers (PML) boundary conditions are used to close the problem. The numerical solver, which is based on a non-uniform finite difference time domain (FDTD) method, is substantially accelerated by either GPU or OpenMP processing.

The P-ACOUSTICS solvers have been extensively validated and the associated uncertainties have been quantified using analytical solutions, benchmarks, and robotic 3D-scan hydrophone measurements in complex setups. Comprehensive documentation is available for Sim4Life.



  Application Areas

  • Safety & Efficacy Assessment of Ultrasonic Devices for Therapeutic Purposes
  • Design & Optimization of Ultrasonic Devices for Therapeutic Purposes


  • FUS-Based Bbb Disruption for Increased Delivery of Neuro-Active Agents
  • FUS-Based Thrombolysis
  • FUS-Based Neural Stimulation


  • MRgFUS Neurosurgery Applications: Tumor Ablation, Neuropathic Pain Treatment, Movement Disorders
  • Sound Exposure (e.g., in MRI)

  Key Features

  • Linear & non-linear 3D full-wave solvers based on the Westervelt-Lighthill equation (expanded with density variation terms to account for the presence of bones & strongly reflecting material)
  • Database of acoustic properties
  • Tailored to the simulation of large ultrasonic arrays comprising hundreds to thousands of piezoelectric elements


  • Applicable to both audible acoustics and therapeutic ultrasound simulations
  • Coupled with the thermal solver to calculate temperature increases induced by deposited acoustic energy
  • Tailored to the simulation of entirely heterogeneous simulation domains
  • Multi-core and GPU acceleration (fastest ultrasonic solver on the market)


  • Capable of simulating entire therapeutic FUS setups involving large anatomical models in minutes
  • Enables simulations with arbitrarily shaped transducers & arrays
  • Equipped with inhomogeneous PML modules, allowing for domain truncation through inhomogeneous anatomy, thus restricting the domain size without the need for excessive padding

Optimized transcranial phase aberration correction for a large array FUS neurosurgery system.

Evaluation of fetal exposure to acoustic stimuli.

HIFU treatment planning for neck cancers.