Physics Models: P-ACOUSTICS

 Acoustics Solvers

The two full wave Acoustics Solvers (P-ACOUSTICS) encompass 1) a Graphics Processing Unit (GPU) and OpenMP accelerated non-linear FDTD method with an extended Westervelt-Lighthill equation applied to adaptive rectilinear meshes with inhomogeneous PML boundary conditions and 2) a fast near-field method combined with the hybrid angular spectrum approach (FNM-CHASM) to simulate complex wave propagation inside inhomogeneous tissue distributions and to rapidly calculate pressure distributions for applications such as focused ultrasound treatments. This is state-of-art in computational acoustics.

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

The novel ultrasound solvers account for pressure wave propagation, density variations and jumps, non-linearity, and diffusivity losses that occur in human tissue.

The FNM-CHASM solver offers near real-time simulations of acoustic propagation in inhomogeneous setups.

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)
  • Novel hybrid solver combining the fast near-field method (FNM) & the hybrid angular spectrum method (hASM) allowing for near real-time simulations of setups involving ultrasonic transducers with a principal propagation direction
  • Multi-core and GPU acceleration (fastest ultrasonic solver on the market)


  • 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
  • Capable of simulating entire therapeutic FUS setups involving large anatomical models in minutes
  • Tailored to the simulation of large ultrasonic arrays comprising hundreds to thousands of piezoelectric elements


  • Enables simulations with arbitrarily shaped transducers & arrays
  • Equipped with inhomogeneous PML modules, allowing for domain truncation through an inhomogeneous anatomy, thus restricting the domain size without the need for excessive padding
  • Coupled with automatic tools for beam-forming & focal steering based on analytical solutions, ray tracing, & time-reversal techniques
  • Built-in calculation of acoustically relevant quantities (intensity, radiation force, particle velocity, etc.)
  • Database of acoustic properties

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.