Acoustics Modeling

PhysAI can use the power of COMSOL Multiphysics for advanced acoustics simulations, from biomedical and flow sensors applications to room acoustics and electromagnetic transducers.

Focused Ultrasound for Precision Targeting

Focused ultrasound (FUS) uses converging acoustic waves to target tumors or kidney stones noninvasively. COMSOL simulates the pressure field and heat deposition, solving the Helmholtz equation for wave propagation:

\[ \nabla^2 p + k^2 p = 0 \]

where \( k = \omega / c_0 \) is the wavenumber, and \( \omega \) is the angular frequency. By optimizing transducer design and focusing parameters, FUS achieves pinpoint accuracy, minimizing damage to surrounding tissues.

Unfocused ultrasound powers diagnostic imaging by emitting broad acoustic waves and interpreting reflected signals. COMSOL models wave scattering and attenuation, enabling rapid simulation of imaging scenarios. Integrating artificial intelligence (AI) enhances this process, accelerating image reconstruction through machine learning algorithms trained on simulated datasets.

Focused Ultrasound: The nanometer level surface displacement at the base of the applicator at 1.5MHz creates a pressure amplitude of around 0.3MPa at a target. The target experiences both mechanical forces and thermal dissipation. Depending on the application, both can be wanted or unwanted. One big challenge is to obtain the correct target depth, particularly when the environment between the source and target is not well characterized.

Shockwave Therapy in Biomedical Engineering

Shockwave therapy leverages high-energy acoustic waves to treat conditions like musculoskeletal disorders. The steep pressure front of a shockwave arises due to nonlinear effects, characterized by a high B/A nonlinearity coefficient in the governing equations. COMSOL Multiphysics models these phenomena using the nonlinear acoustics module, solving:

\[ \frac{\partial^2 p}{\partial t^2} - c_0^2 \nabla^2 p = -\frac{B/A}{2 \rho_0 c_0^2} \frac{\partial}{\partial t} \left( \left( \frac{\partial p}{\partial t} \right)^2 \right) \]

Here, \( p \) is the acoustic pressure, \( c_0 \) is the speed of sound, \( \rho_0 \) is the medium density, and \( B/A \) quantifies nonlinearity. This steep front enhances therapeutic efficacy by delivering concentrated energy to targeted tissues.

Room Acoustics Optimization

COMSOL Multiphysics excels in simulating room acoustics, addressing both external noise ingress and internal sound quality. Below, we explore key aspects of noise propagation and suppression.

External Noise Propagation into a Room

External noise enters rooms through multiple pathways, each modeled in COMSOL:

(a) Direct Transmission: Sound waves pass through walls or windows, governed by the transmission loss equation:
\[ T_L = 10 \log_{10} \left( \frac{I_i}{I_t} \right) \]
where \( I_i \) and \( I_t \) are incident and transmitted intensities.
(b) Structure-Borne Noise: Vibrations from external sources (e.g., traffic) travel through building structures, modeled via coupled structural-acoustic simulations.
(c) Flanking Noise and Paths: Sound bypasses barriers via indirect routes (e.g., ceilings or ducts), requiring detailed geometric modeling in COMSOL.

Internal Noise Suppression Methods

Internal noise perception arises from direct sound and subsequent reflections, including flutter echoes. The sound pressure level at a point is:

\[ L_p = 10 \log_{10} \left( \frac{p_{\text{rms}}^2}{p_{\text{ref}}^2} \right) \]

where \( p_{\text{rms}} \) is the root-mean-square pressure, and \( p_{\text{ref}} = 20 \, \mu\text{Pa} \). Reflections amplify perceived loudness, but COMSOL helps design suppression strategies:

Low Frequencies (20-200 Hz): Use thick, porous absorbers (e.g., bass traps) to dampen standing waves.
Mid Frequencies (200-2000 Hz): Install diffusers or mid-range absorbers to scatter and absorb speech-range noise.
High Frequencies (>2000 Hz): Apply thin, reflective surfaces or lightweight absorbers to reduce sharpness and flutter echoes.

By simulating direct and reflected paths, COMSOL optimizes room layouts and materials for a balanced acoustic environment.

Bedroom Acoustics: The streamline directions indicate the local energy flux and the color represents the sound pressure level as ambient noise from the outside enters through a window.