Quantitative photoacoustic imaging of two-photon absorption

Abstract

Photoacoustic tomography (PAT) is a hybrid imaging modality where we intend to reconstruct optical properties of heterogeneous media from measured ultrasound signals generated by the photoacoustic effect. In recent years, there have been considerable interests in using PAT to image two-photon absorption, in addition to the usual single-photon absorption, inside diffusive media. We present a mathematical model for quantitative image reconstruction in two-photon photoacoustic tomography (TP-PAT). We propose a computational strategy for the reconstruction of the optical absorption coefficients and provide some numerical evidences based on synthetic photoacoustic acoustic data to demonstrate the feasibility of quantitative reconstructions in TP-PAT.

Inverse transport and diffusion problems in photoacoustic imaging with nonlinear absorption

“…With the assumptions we have, the result in [5, Theorem 2.1] ensures the well-posedness of the linear transport equation (10) in the L ∞ dξ (Γ − ) → L ∞ (X) framework. This allows Theorem 2.6 of [6] to be reproduced in the Λ We now differentiate (9) twice with respect to ε, and obtain that v • ∇u (2)…”

“…Note that in Proposition A.2, for suitable chosen g ∈ L ∞ dξ (Γ − ), there exists a unique positive solution u (1) to (10) such that u (1) ≥ ε > 0 for some constant ε > 0 depending on g, Ω, σ a , σ s . We…”

A sparsity-based nonlinear reconstruction method for two-photon photoacoustic tomography

“…On the other hand, PACT gives a larger penetration depth beyond one centimeter, but at the expense of inferior spatial resolution. To overcome the limitation of PAM, non-linear mechanisms have been introduced such as two-photon absorption [6,21,35]. The phenomenon when an electron transfers to an excited state after simultaneously absorbing two photons can be defined as two-photon absorption.…”

“…The mathematical formulation of 2P-PAT was first introduced in [6,21], where the authors consider an optically absorbing and scattering medium Ω ⊂ R n (n ≥ 2). Denoting the density of photons at a point x ∈ Ω as u(x), it was shown that u(x) solves the following semi-linear diffusion equation −∇ • (D(x)∇u(x)) + σ(x)u(x) + µ(x)|u(x)|u(x) = 0, in Ω, u(x) = g(x), on ∂Ω,…”

Listening to tissues with new light: recent technological advances in photoacoustic imaging

“…Generally, PAM is often used for highresolution imaging within a depth of several millimeters, while PACT is mostly utilized for volumetric imaging with a larger penetration depth beyond one centimeter at the expense of inferior spatial resolution. One of the most recent advances in PAM is super-resolution imaging, enabled by non-linear mechanisms, such as two-photon absorption (8)(9)(10), absorption saturation (11)(12)(13)(14)(15), thermal relaxation (12,16,17), photothermal bleaching (18,19) and reversible photoswitching (6,20,21). Meanwhile, PACT has made significant progress in attaining three-dimensional (3D) (22)(23)(24), real-time (25,26), and whole-body small-animal imaging (27,28) performance.…”