A Forward-Adjoint Operator Pair Based on the Elastic Wave Equation for Use in Transcranial Photoacoustic Computed Tomography

Photoacoustic computed tomography (PACT) is an emerging imaging modality that exploits optical contrast and ultrasonic detection principles to form images of the photoacoustically induced initial pressure distribution within tissue. The PACT reconstruction problem corresponds to an inverse source problem in which the initial pressure distribution is recovered from measurements of the radiated wavefield. A major challenge in transcranial PACT brain imaging is compensation for aberrations in the measured data due to the presence of the skull. Ultrasonic waves undergo absorption, scattering, and longitudinal-to-shear wave mode conversion as they propagate through the skull. To properly account for these effects, a wave-equation-based inversion method should be employed that can model the heterogeneous elastic properties of the skull. In this work, a forward model based on a finite-difference time-domain discretization of the three-dimensional elastic wave equation is established and a procedure for computing the corresponding adjoint of the forward operator is presented. Massively parallel implementations of these operators employing multiple graphics processing units are also developed. The developed numerical framework is validated and investigated in computer-simulation and experimental phantom studies whose designs are motivated by transcranial PACT applications

Image reconstruction in transcranial photoacoustic computed tomography of the brain

Photoacoustic computed tomography (PACT) holds great promise for transcranial brain imaging. However, the strong reflection, scattering, attenuation, and mode-conversion of photoacoustic waves in the skull pose serious challenges to establishing the method. The lack of an appropriate model of solid media in conventional PACT imaging models, which are based on the canonical scalar wave equation, causes a significant model mismatch in the presence of the skull and thus results in deteriorated reconstructed images. The goal of this study was to develop an image reconstruction algorithm that accurately models the skull and thereby ameliorates the quality of reconstructed images. The propagation of photoacoustic waves through the skull was modeled by a viscoelastic stress tensor wave equation, which was subsequently discretized by use of a staggered grid fourth-order finite-difference time-domain (FDTD) method. The matched adjoint of the FDTD-based wave propagation operator was derived for implementing a back-projection operator. Systematic computer simulations were conducted to demonstrate the effectiveness of the back-projection operator for reconstructing images in a realistic three-dimensional PACT brain imaging system. The results suggest that the proposed algorithm can successfully reconstruct images from transcranially-measured pressure data and readily be translated to clinical PACT brain imaging applications

Iterative image reconstruction in elastic inhomogenous media with application to transcranial photoacoustic tomography

Photoacoustic computed tomography (PACT) is an emerging computed imaging modality that exploits optical contrast and ultrasonic detection principles to form images of the photoacoustically induced initial pressure distribution within tissue. The PACT reconstruction problem corresponds to a time-domain inverse source problem, where the initial pressure distribution is recovered from the measurements recorded on an aperture outside the support of the source. A major challenge in transcranial PACT brain imaging is to compensate for aberrations in the measured data due to the propagation of the photoacoustic wavefields through the skull. To properly account for these effects, a wave equation-based inversion method should be employed that can model the heterogeneous elastic properties of the medium. In this study, an iterative image reconstruction method for 3D transcranial PACT is developed based on the elastic wave equation. To accomplish this, a forward model based on a finite-difference time-domain discretization of the elastic wave equation is established. Subsequently, gradient-based methods are employed for computing penalized least squares estimates of the initial source distribution that produced the measured photoacoustic data. The developed reconstruction algorithm is validated and investigated through computer-simulation studies

A continuous adjoint for photo-acoustic tomography of the brain

We present an optimization framework for photo-acoustic tomography of brain based on a system of coupled equations that describe the propagation of sound waves in linear isotropic inhomogeneous and lossy elastic media with the absorption and physical dispersion following a frequency power law using fractional Laplacian operators. The adjoint of the associated continuous forward operator is derived, and a numerical framework for computing this adjoint based on a k- space pseudospectral method is presented. We analytically show that the derived continuous adjoint matches the adjoint of an associated discretised operator. We include this adjoint in a first-order positivity constrained optimization algorithm that is regularized by total variation minimization, and show that the iterates monotonically converge to a minimizer of an objective function, even in the presence of some error in estimating the physical parameters of the medium.Comment: 28 pages, 24 figure (eps

A Forward-Adjoint Operator Pair Based on the Elastic Wave Equation for Use in Transcranial Photoacoustic Computed Tomography

Photoacoustic computed tomography (PACT) is an emerging imaging modality that exploits optical contrast and ultrasonic detection principles to form images of the photoacoustically induced initial pressure distribution within tissue. The PACT reconstruction problem corresponds to an inverse source problem in which the initial pressure distribution is recovered from measurements of the radiated wavefield. A major challenge in transcranial PACT brain imaging is compensation for aberrations in the measured data due to the presence of the skull. Ultrasonic waves undergo absorption, scattering, and longitudinal-to-shear wave mode conversion as they propagate through the skull. To properly account for these effects, a wave-equation-based inversion method should be employed that can model the heterogeneous elastic properties of the skull. In this work, a forward model based on a finite-difference time-domain discretization of the three-dimensional elastic wave equation is established and a procedure for computing the corresponding adjoint of the forward operator is presented. Massively parallel implementations of these operators employing multiple graphics processing units are also developed. The developed numerical framework is validated and investigated in computer-simulation and experimental phantom studies whose designs are motivated by transcranial PACT applications

Iterative image reconstruction in transcranial photoacoustic tomography based on the elastic wave equation

Photoacoustic computed tomography (PACT) is an emerging computed imaging modality that exploits optical contrast and ultrasonic detection principles to form images of the photoacoustically induced initial pressure distribution within tissue. The PACT reconstruction problem corresponds to a time-domain inverse source problem, where the initial pressure distribution is recovered from the measurements recorded on an aperture outside the support of the source. A major challenge in transcranial PACT of the brain is to compensate for aberrations and attenuation in the measured data due to the propagation of the photoacoustic wavefields through the skull. To properly account for these effects, a wave equation-based inversion method can be employed that can model the heterogeneous elastic properties of the medium. In this study, an optimization-based image reconstruction method for 3D transcranial PACT is developed based on the elastic wave equation. To accomplish this, a forward-adjoint operator pair based on a finite-difference time-domain discretization of the elastic wave equation is utilized to compute penalized least squares estimates of the initial pressure distribution. Computer-simulation and experimental studies are conducted to investigate the robustness of the reconstruction method to model mismatch and its ability to effectively resolve cortical and superficial brain structures