Estimation and uncertainty quantification of optical properties directly from the photoacoustic time series

Quantitative photoacoustic tomography seeks to estimate the optical parameters of a target given photoacoustic measurements as a data. Conventionally the problem is split into two steps: 1) the acoustical inverse problem of estimating the acoustic initial pressure distribution from the acoustical time series data; 2) the optical inverse problem of estimating the optical absorption and scattering from the initial pressure distributions. In this work, an approach for estimating the optical absorption and scattering directly from the acoustical time series is investigated with simulations. The work combines a homogeneous acoustical forward model, based on the Green's function solution of the wave equation, and a finite element method based diffusion approximation model of light propagation into a single forward model. This model maps the optical parameters of interest into a time domain signal. The model is used with a Bayesian approach to ill-posed inverse problems to form estimates of the posterior distributions for the parameters of interest. In addition to being able to provide point estimates of the parameters of interest, i.e. reconstruct the absorption and scattering distributions, the approach can be used to derive information on the uncertainty associated with the estimates

Quantitative photoacoustic tomography using illuminations from a single direction.

Quantitative photoacoustic tomography is an emerging imaging technique aimed at estimating optical parameters inside tissues from photoacoustic images, which are formed by combining optical information and ultrasonic propagation. This optical parameter estimation problem is ill-posed and needs to be approached within the framework of inverse problems. It has been shown that, in general, estimating the spatial distribution of more than one optical parameter is a nonunique problem unless more than one illumination pattern is used. Generally, this is overcome by illuminating the target from various directions. However, in some cases, for example when thick samples are investigated, illuminating the target from different directions may not be possible. In this work, the use of spatially modulated illumination patterns at one side of the target is investigated with simulations. The results show that the spatially modulated illumination patterns from a single direction could be used to provide multiple illuminations for quantitative photoacoustic tomography. Furthermore, the results show that the approach can be used to distinguish absorption and scattering inclusions located near the surface of the target. However, when compared to a full multidirection illumination setup, the approach cannot be used to image as deep inside tissues

Image reconstruction with noise and error modelling in quantitative photoacoustic tomography

Quantitative photoacoustic tomography is an emerging imaging technique aimed at estimating the optical parameters inside tissue from photoacoustic images. The method proceeds from photoacoustic tomography by taking the estimated initial pressure distributions as data and estimating the absolute values of the optical parameters. Therefore, both the data and the noise of the second (optical) inverse problem are affected by the method applied to solve the first (acoustic) inverse problem. In this work, the Bayesian approach for quantitative photoacoustic tomography is taken. Modelling of noise and errors and incorporating their statistics into the solution of the inverse problem are investigated

Bayesian parameter estimation in spectral quantitative photoacoustic tomography

Photoacoustic tomography (PAT) is an imaging technique combining strong contrast of optical imaging to high spatial resolution of ultrasound imaging. These strengths are achieved via photoacoustic e↵ect, where a spatial absorption of light pulse is converted into a measurable propagating ultrasound wave. The method is seen as a potential tool for small animal imaging, pre-clinical investigations, study of blood vessels and vasculature, as well as for cancer imaging. The goal in PAT is to form an image of the absorbed optical energy density field via acoustic inverse problem approaches from the measured ultrasound data. Quantitative PAT (QPAT) proceeds from these images and forms quantitative estimates of the optical properties of the target. This optical inverse problem of QPAT is illposed. To alleviate the issue, spectral QPAT (SQPAT) utilizes PAT data formed at multiple optical wavelengths simultaneously with optical parameter models of tissue to form quantitative estimates of the parameters of interest. In this work, the inverse problem of SQPAT is investigated. Light propagation is modelled using the di↵usion equation. Optical absorption is described with chromophore concentration weighted sum of known chromophore absorption spectra. Scattering is described by Mie scattering theory with an exponential power law. In the inverse problem, the spatially varying unknown parameters of interest are the chromophore concentrations, the Mie scattering parameters (power law factor and the exponent), and Gr¨uneisen parameter. The inverse problem is approached with a Bayesian method. It is numerically demonstrated, that estimation of all parameters of interest is possible with the approach

Direct Estimation of Optical Parameters From Photoacoustic Time Series in Quantitative Photoacoustic Tomography

Imaging methods applied to living organisms with emphasis on innovative approaches that use emerging technologies supported by rigorous physical and mathematical analysis and quantitative evaluation of performance. Membership in IEEE's technical societies provides access to top quality publications such as this one either as a member benefit or via discounted subscriptions. The lowest subscription prices for this title is available for members of the IEEE Engineering in Medicine and Biology Society, IEEE Signal Processing, IEEE Nuclear and Plasma Sciences Society, or the IEEE Ultrasonics, Ferroelectrics, and Frequency Control Society

Bayesian Modelling of Skull Conductivity Uncertainties in EEG Source Imaging

Knowing the correct skull conductivity is crucial for the accuracy of EEG source imaging, but unfortunately, its true value, which is inter- and intra-individually varying, is difficult to determine. In this paper, we propose a statistical method based on the Bayesian approximation error approach to compensate for source imaging errors related to erronous skull conductivity. We demonstrate the potential of the approach by simulating EEG data of focal source activity and using the dipole scan algorithm and a sparsity promoting prior to reconstruct the underlying sources. The results suggest that the greatest improvements with the proposed method can be achieved when the focal sources are close to the skull

Three dimensional photoacoustic tomography in Bayesian framework

The image reconstruction problem (or inverse problem) in photoacoustic tomography is to resolve the initial pressure distribution from detected ultrasound waves generated within an object due to an illumination by a short light pulse. Recently, a Bayesian approach to photoacoustic image reconstruction with uncertainty quantification was proposed and studied with two dimensional numerical simulations. In this paper, the approach is extended to three spatial dimensions and, in addition to numerical simulations, experimental data are considered. The solution of the inverse problem is obtained by computing point estimates, i.e., maximum a posteriori estimate and posterior covariance. These are computed iteratively in a matrix-free form using a biconjugate gradient stabilized method utilizing the adjoint of the acoustic forward operator. The results show that the Bayesian approach can produce accurate estimates of the initial pressure distribution in realistic measurement geometries and that the reliability of these estimates can be assessed

Thermal tomography utilizing truncated Fourier series approximation of the heat diffusion equation

In a thermal tomography measurement setup, a physical body is sequentially heated at different source locations and temperature evolutions are measured at several measurement locations on the surface of the body. Based on these transient measurements, the thermal conductivity, the volumetric heat capacity and the surface heat transfer coefficient of the body are estimated as spatially distributed parameters, typically by minimizing a modified data misfit functional between the measured data and the data computed with the estimated thermal parameters. In thermal tomography, heat transfer is modeled with the time-dependent heat diffusion equation for which direct time domain solving is computationally expensive. In this paper, the computations of thermal tomography are sped up by utilizing a truncated Fourier series approximation approach. In this approach, a frequency domain equivalent of the time domain heat diffusion equation is solved at multiple frequencies and the solutions are used to obtain a truncated Fourier series approximation for the solution and the Jacobian of the time domain heat transfer problem. The feasibility of the approximation is tested with simulated and experimental measurement data. When compared to a previously used time domain approach, it is shown to lead to a significant reduction of computation time in image reconstruction with no significant loss of reconstruction accuracy

Electrical impedance tomography system: an open access circuit design

BACKGROUND: This paper reports a simple 2-D system for electrical impedance tomography EIT, which works efficiently and is low cost. The system has been developed in the Sharif University of Technology Tehran-Iran (for the author's MSc Project). METHODS: The EIT system consists of a PC in which an I/O card is installed with an external current generator, a multiplexer, a power supply and a phantom with an array of electrodes. The measurement system provides 12-bit accuracy and hence, suitable data acquisition software has been prepared accordingly. The synchronous phase detection method has been implemented for voltage measurement. Different methods of image reconstruction have been used with this instrument to generate electrical conductivity images. RESULTS: The results of simulation and real measurement of the system are presented. The reconstruction programs were written in MATLAB and the data acquisition software in C++. The system has been tested with both static and dynamic mode in a 2-D domain. Better results have been produced in the dynamic mode of operation, due to the cancellation of errors. CONCLUSION: In the spirit of open access publication the design details of this simple EIT system are made available here