Dimple Modgil

Application of inverse source concepts to photoacoustic tomography

Photoacoustic tomography (PAT), also known as optoacoustic or thermoacoustic tomography, is a hybrid imaging technique that possesses great potential for a wide range of biomedical imaging applications. Image reconstruction in PAT is tantamount to solving an inverse source problem, where the source represents the optical energy absorption distribution in the object that is induced by an interrogating pulsed optical waveform. In this work, we re-examine the PAT image reconstruction problem from a Fourier domain perspective by use of established time-harmonic inverse source concepts. A mathematical relationship between the photoacoustic pressure wavefield data on an aperture that encloses the object and the three-dimensional Fourier transform of the optical absorption distribution evaluated on a collection of concentric spheres is investigated. In addition to providing a framework for deriving both exact and approximate analytic reconstruction formulae, we demonstrate that this mapping provides an intuitive means of understanding certain spatial resolution characteristics of PAT.

Photoacoustic image reconstruction in an attenuating medium using singular-value decomposition

Photoacoustic tomography (PAT) or optoacoustic tomography reconstructs an image of the optical absorption function of a medium using the ultrasound signals induced when it is exposed to pulsed electromagnetic radiation. These signals are generated due to the thermal expansion caused by localized heating from the absorption of pulsed electromagnetic radiation [1]. The majority of the image reconstruction algorithms in PAT so far have assumed a non-dispersive acoustic medium. The effect of frequency-dependent attenuation on acoustic waves can be significant since PAT uses broadband detection. Reconstructed images may exhibit distortion and artifacts if these effects are not taken into account. Previous work on dispersive acoustic media done by our group [2] focused on incorporating the frequency-dependent attenuation effects into the PAT model. In this paper, we will use an approach similar to that by Schotland et al. [3] [4], in optical diffusion tomography, to derive an inversion formula for the optical absorption function using singular-value decomposition (SVD). This formula is applicable in a planar geometry where the array of transducers lies in a plane. It provides an insight into the conditioning of the inverse problem and offers a promising method for image reconstruction in an attenuating medium.

Optimizing wavelength choice for quantitative optoacoustic imaging using the Cramer–Rao lower bound

Several papers have recently addressed the issue of estimating chromophore concentration in optoacoustic imaging (OAI) using multiple wavelengths. The choice of wavelengths obviously affects the accuracy and precision of the estimates. One might assume that the wavelengths that maximize the extinction coefficients of the chromophores would be the most suitable. However, this may not always be the case since the distribution of light intensity in the medium is also wavelength dependent. In this paper, we explore a method for optimizing the choice of wavelengths based on the Cramer-Rao lower bound (CRLB) on the variance of the chromophore concentration. This lower bound on variance can be evaluated numerically for different wavelengths using the variation of the extinction coefficients and scattering coefficients with wavelength. The wavelengths that give the smallest variance will be considered optimal for multi-wavelength OAI to estimate the chromophore concentrations. The expression for the CRLB has been derived analytically for estimating the concentration of multiple chromophores for several simple phantom models for the case when the optoacoustic signal is proportional to the product of the optical absorption and the illumination function. This approach could be easily extended to other geometries.

Image reconstruction in photoacoustic tomography with variable speed of sound using a higher-order geometrical acoustics approximation

Previous research correcting for variable speed of sound in photoacoustic tomography (PAT) has used a generalized radon transform (GRT) model . In this model, the pressure is related to the optical absorption, in an acoustically inhomogeneous medium, through integration over non-spherical isochronous surfaces. This model assumes that the path taken by acoustic rays is linear and neglects amplitude perturbations to the measured pressure. We have derived a higher-order geometrical acoustics (GA) expression, which takes into account the first-order effect in the amplitude of the measured signal and higher-order perturbation to the travel times. The higher-order perturbation to travel time incorporates the effect of ray bending. Incorrect travel times can lead to image distortion and blurring. These corrections are expected to impact image quality and quantitative PAT. We have previously shown that travel-time corrections in 2D suggest that perceivable differences in the isochronous surfaces can be seen when the second-order travel-time perturbations are taken into account with a 10% speed of sound variation. In this work, we develop iterative image reconstruction algorithms that incorporate this higher-order GA approximation assuming that the speed of sound map is known. We evaluate the effect of higher-order GA approximation on image quality and accuracy.

Photoacoustic image reconstruction in an attenuating medium using singular value decomposition

Attenuation effects can be significant in photoacoustic tomography (PAT) since the measured pressure signals are broadband and ignoring them may lead to image artifacts and blurring. Previous work by our group had derived a method for modeling the attenuation effect and correcting for it in the image reconstruction. This was done by relating the ideal, unattenuated pressure signals to the attenuated pressure signals via an integral operator. In this work, we explore singularvalue decomposition (SVD) of a previously derived 3D integral equation that relates the Fourier transform of the measured pressure with respect to time and two spatial components to the 2D spatial Fourier transform of the optical absorption function. We find that the smallest singular values correspond to wavelet-like eigenvectors in which most of the energy is concentrated at times corresponding to greater depths in tissue. This allows us characterize the ill posedness of recovering absorption information from depth in an attenuating medium. This integral equation can be inverted using standard SVD methods and the optical absorption function can be recovered. We will conduct simulations and derive algorithm for image reconstruction using SVD of this integral operator.

Material identification in x-ray microscopy and micro CT using multi-layer, multi-color scintillation detectors.

We demonstrate that a dual-layer, dual-color scintillator construct for microscopic CT, originally proposed to increase sensitivity in synchrotron imaging, can also be used to perform material quantification and classification when coupled with polychromatic illumination. We consider two different approaches to data handling: (1) a data-domain material decomposition whose estimation performance can be characterized by the Cramer-Rao lower bound formalism but which requires careful calibration and (2) an image-domain material classification approach that is more robust to calibration errors. The data-domain analysis indicates that useful levels of SNR (>5) could be achieved in one second or less at typical bending magnet fluxes for relatively large amounts of contrast (several mm path length, such as in a fluid flow experiment) and at typical undulator fluxes for small amount of contrast (tens of microns path length, such as an angiography experiment). The tools introduced could of course be used to study and optimize parameters for a wider range of potential applications. The image domain approach was analyzed in terms of its ability to distinguish different elemental stains by characterizing the angle between the lines traced out in a two-dimensional space of effective attenuation coefficient in the front and back layer images. This approach was implemented at a synchrotron and the results were consistent with simulation predictions.

Implementation and comparison of reconstruction algorithms for two-dimensional optoacoustic tomography using a linear array

Our goal is to compare and contrast various image reconstruction algorithms for optoacoustic tomography (OAT) assuming a finite linear aperture of the kind that arises when using a linear-array transducer. Because such transducers generally have tall, narrow elements, they are essentially insensitive to out-of-plane acoustic waves, and the usually 3-D OAT problem reduces to a 2-D problem. Algorithms developed for the 3-D problem may not perform optimally in 2-D. We have implemented and evaluated a number of previously described OAT algorithms, including an exact (in 3-D) Fourier-based algorithm and a synthetic-aperture-based algorithm. We have also implemented a 2-D algorithm developed by Norton for reflection mode tomography that has not, to the best of our knowledge, been applied to OAT before. Our simulation studies of resolution, contrast, noise properties, and signal detectability measures suggest that Nortons approach-based algorithm has the best contrast, resolution, and signal detectability.

Sinogram smoothing techniques for myocardial blood flow estimation from dose-reduced dynamic computed tomography

Abstract. Dynamic contrast-enhanced computed tomography (CT) could provide an accurate and widely available technique for myocardial blood flow (MBF) estimation to aid in the diagnosis and treatment of coronary artery disease. However, one of its primary limitations is the radiation dose imparted to the patient. We are exploring techniques to reduce the patient dose by either reducing the tube current or by reducing the number of temporal frames in the dynamic CT sequence. Both of these dose reduction techniques result in noisy data. In order to extract the MBF information from the noisy acquisitions, we have explored several data-domain smoothing techniques. In this work, we investigate two specific smoothing techniques: the sinogram restoration technique in both the spatial and temporal domains and the use of the Karhunen–Loeve (KL) transform to provide temporal smoothing in the sinogram domain. The KL transform smoothing technique has been previously applied to dynamic image sequences in positron emission tomography. We apply a quantitative two-compartment blood flow model to estimate MBF from the time-attenuation curves and determine which smoothing method provides the most accurate MBF estimates in a series of simulations of different dose levels, dynamic contrast-enhanced cardiac CT acquisitions. As measured by root mean square percentage error (% RMSE) in MBF estimates, sinogram smoothing generally provides the best MBF estimates except for the cases of the lowest simulated dose levels (tube current=25  mAs, 2 or 3 s temporal spacing), where the KL transform method provides the best MBF estimates. The KL transform technique provides improved MBF estimates compared to conventional processing only at very low doses (<7  mSv). Results suggest that the proposed smoothing techniques could provide high fidelity MBF information and allow for substantial radiation dose savings.

Implementation and comparison of reconstruction algorithms for 2D optoacoustic tomography using a linear array

The goal of this paper is to compare and contrast various image reconstruction algorithms for tomography (OAT) assuming a finite linear aperture of the kind that arises when using a linear-array transducer. Because such transducers generally have tall, narrow elements, they are essentially insensitive to out of plane acoustic waves, and the usually 3D OAT problem reduces to a 2D problem. Algorithms developed for the 3D problem may not perform optimally. We have implemented and evaluated a number of previously described OAT algorithms, including an exact (in 3D) Fourier-based algorithm and a synthetic aperture based algorithm. We have also implemented an exact 2D algorithm developed by Norton for reflection mode tomography that has not, to the best of our knowledge, been applied to OAT before. Our simulation studies of resolution, contrast, noise properties and signal detectability measures suggest that Nortons approach based algorithm has the best contrast, resolution and signal detectability.

Adaptive temporal smoothing of sinogram data using Karhunen-Loeve (KL) transform for myocardial blood flow estimation from dose-reduced dynamic CT

There is a strong need for an accurate and easily available technique for myocardial blood flow (MBF) estimation to aid in the diagnosis and treatment of coronary artery disease (CAD). Dynamic CT would provide a quick and widely available technique to do so. However, its biggest limitation is the dose imparted to the patient. We are exploring techniques to reduce the patient dose by either reducing the tube current or by reducing the number of temporal frames in the dynamic CT sequence. Both of these dose reduction techniques result in very noisy data. In order to extract the myocardial blood flow information from the noisy sinograms, we have been looking at several data-domain smoothing techniques. In our previous work,1 we explored the sinogram restoration technique in both the spatial and temporal domain. In this work, we explore the use of Karhunen-Loeve (KL) transform to provide temporal smoothing in the sinogram domain. This technique has been applied previously to dynamic image sequences in PET.2, 3 We find that the cluster-based KL transform method yields noticeable improvement in the smoothness of time attenuation curves (TAC). We make use of a quantitative blood flow model to estimate MBF from these TACs and determine which smoothing method provides the most accurate MBF estimates.