Causality Analysis of Frequency Dependent Wave Attenuation

TL;DR

This paper derives and analyzes causal models for frequency-dependent wave attenuation, highlighting limitations of standard models and proposing more physically meaningful alternatives for biomedical imaging.

Contribution

It introduces causality-preserving equations for wave attenuation and critically evaluates existing models, demonstrating the need for causally consistent approaches in photoacoustic imaging.

Findings

Standard models lack causality in relevant parameter ranges

Numerical experiments show unphysical behavior of standard models

Proposed models exhibit realistic wave propagation behavior

Abstract

The work is inspired by thermo-and photoacoustic imaging, where recent efforts are devoted to take into account attenuation and varying wave speed parameters. In this paper we derive and analyze causal equations describing propagation of attenuated pressure waves. We also review standard models, like frequency power laws, and the thermo-viscous equation and show that they lack causality in the parameter range relevant for biological photoacoustic imaging. To discuss causality in mathematical rigor we use the results and concepts of linear system theory. We present some numerical experiments, which show the physically unmeaningful behavior of standard attenuation models, and the realistic behavior of the novel models.