A predictive 2D Zener model for laser-induced pressure waves in photoacoustic imaging of human tissue

Laser-induced pressure waves form the foundation of photoacoustic imaging (PAI), where accurate prediction of thermo-mechanical interactions is critical for improving resolution and safety in biomedical applications. This study develops a novel two-dimensional Zener-type thermo-viscoelastic model that advances conventional frameworks by incorporating three essential features: (i) non-Fourier heat conduction with finite thermal propagation speed, (ii) viscoelastic stress relaxation with time delay, and (iii) fully coupled radial–axial displacements. The governing equations are derived in cylindrical coordinates and solved using a reduced-order Galerkin approach, providing computationally efficient approximations to the coupled thermo-mechanical dynamics. The model predicts that longer laser pulses enhance thermal confinement and generate higher-amplitude pressure waves, while tissues with finite relaxation times exhibit greater persistence of waveforms compared with Fourier-based predictions. Analytical and numerical results further reveal that radial vibrations decay significantly faster than depth-wise displacements, offering a mechanistic basis for observed imaging artifacts. Validation against reported ex vivo data confirms the accuracy of the proposed framework. Overall, the model establishes a predictive mathematical foundation for optimizing laser parameters in PAI and contributes to the broader class of coupled bio-thermomechanical systems governed by non-Fourier heat conduction and viscoelasticity.