A multimodal adjoint-state formulation of Quantitative Photoacoustic Tomography with external acoustic sources.

Quantitative Photoacoustic Tomography (QPAT) aims to recover spatially varying optical and acoustic tissue parameters by utilizing the photoacoustic effect. The associated inverse problem is highly ill-conditioned due to strong coupling between optical absorption, optical scattering, density, and speed of sound. To alleviate the ill-conditioned nature of this problem, an externally generated ultrasonic wavefield is incorporated in addition to photoacoustic sources, resulting in a multimodal formulation of QPAT. We present a fully coupled, one-step QPAT reconstruction method for the simultaneous recovery of optical absorption, density, and compressibility directly from measurement data, with speed of sound obtained as a derived property. Conventional QPAT and multimodal QPAT arise as special cases within the proposed method. The approach is formulated as a PDE-constrained optimization problem, and the Fréchet derivative of the complete forward model is derived using an optimize-then-discretize adjoint state method. Two-dimensional numerical simulations demonstrate accurate reconstruction of optical absorption, density, and compressibility.