Patrick J. La Riviere

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.

Penalized-likelihood sinogram smoothing for low-dose CT

We have developed a sinogram smoothing approach for low-dose computed tomography (CT) that seeks to estimate the line integrals needed for reconstruction from the noisy measurements by maximizing a penalized-likelihood objective function. The maximization is performed by an algorithm derived by use of the separable paraboloidal surrogates framework. The approach overcomes some of the computational limitations of a previously proposed spline-based penalized-likelihood sinogram smoothing approach, and it is found to yield better resolution-variance tradeoffs than this spline-based approach as well an existing adaptive filtering approach. Such sinogram smoothing approaches could be valuable when applied to the low-dose data acquired in CT screening exams, such as those being considered for lung-nodule detection.We have developed a sinogram smoothing approach for low-dose computed tomography (CT) that seeks to estimate the line integrals needed for reconstruction from the noisy measurements by maximizing a penalized-likelihood objective function. The maximization is performed by an algorithm derived by use of the separable paraboloidal surrogates framework. The approach overcomes some of the computational limitations of a previously proposed spline-based penalized-likelihood sinogram smoothing approach, and it is found to yield better resolution-variance tradeoffs than this spline-based approach as well an existing adaptive filtering approach. Such sinogram smoothing approaches could be valuable when applied to the low-dose data acquired in CT screening exams, such as those being considered for lung-nodule detection.

Image reconstruction in optoacoustic tomography for dispersive acoustic media

Conventional image reconstruction methods for optoacoustic tomography (OAT) assume an idealized, non-dispersive acoustic medium. However, the linear attenuation coefficient and the phase velocity of acoustic waves propagating in soft tissue depend on temporal frequency and satisfy a known dispersion law. These frequency-dependent effects are incorporated into an optoacoustic wave equation, and a corresponding reconstruction method for OAT is developed. The improvement in image fidelity that can be achieved over conventional reconstruction methods is demonstrated by use of computer-simulation studies.

Whole-animal Imaging, Gene Function, and the Zebrafish Phenome Project

Imaging can potentially make a major contribution to the Zebrafish Phenome Project, which will probe the functions of vertebrate genes through the generation and phenotyping of mutants. Imaging of whole animals at different developmental stages through adulthood will be used to infer biological function. Cell resolutions will be required to identify cellular mechanism and to detect a full range of organ effects. Light-based imaging of live zebrafish embryos is practical only up to ∼2 days of development, owing to increasing pigmentation and diminishing tissue lucency with age. The small size of the zebrafish makes possible whole-animal imaging at cell resolutions by histology and micron-scale tomography (microCT). The histological study of larvae is facilitated by the use of arrays, and histologys standard use in the study of human disease enhances its translational value. Synchrotron microCT with X-rays of moderate energy (10-25 keV) is unimpeded by pigmentation or the tissue thicknesses encountered in zebrafish of larval stages and beyond, and is well-suited to detecting phenotypes that may require 3D modeling. The throughput required for this project will require robotic sample preparation and loading, increases in the dimensions and sensitivity of scintillator and CCD chips, increases in computer power, and the development of new approaches to image processing, segmentation, and quantification.

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) based on a generalized radon transform (GRT) model assumes first-order geometrical acoustics (GA) approximation. In the GRT model, the pressure is related to the optical absorption, in an acoustically inhomogeneous medium, through integration over nonspherical isochronous surfaces. Previous research based on the GRT 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 GA expression that 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 2-D 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.

Approximate analytic reconstruction in x-ray fluorescence computed tomography.

X-ray fluorescence computed tomography (XFCT) is an emerging imaging modality that allows for the reconstruction of the distribution of nonradioactive elements within a sample from measurements of fluorescence x-rays produced by irradiation of the sample with monochromatic synchrotron radiation. XFCT is not a transmission tomography modality, but rather a stimulated emission tomography modality and thus correction for attenuation of the incident and fluorescence photons is essential if accurate images are to be obtained. In this work, we develop and characterize an approximate analytic approach to image reconstruction with attenuation correction in XFCT that is applicable when the incident beam attenuation is uniform and when a factor involving fluorescence attenuation and solid angle effects satisfies a certain approximation. When these conditions hold, we demonstrate that the XFCT imaging equation reduces to the exponential Radon transform, which can be readily inverted. The necessary approximation worsens as the total fluorescence attenuation in the sample grows, but the approach is found to be relatively robust as the approximation breaks down. In a long-axis, small solid angle geometry the proposed approach performs comparably to a previously proposed, more computationally expensive approximate method across a range of attenuation levels. In a short-axis, large solid angle geometry, the proposed approach is found to outperform this previous method.

Penalized-likelihood image reconstruction for x-ray fluorescence computed tomography

In this paper, we derive a monotonic penalized-likelihood algorithm for image reconstruction in X-ray fluorescence computed tomography (XFCT) when the attenuation maps at the energies of the fluorescence X-rays are unknown. In XFCT, a sample is irradiated with pencil beams of monochromatic synchrotron radiation that stimulate the emission of fluorescence X-rays from atoms of elements whose K- or L-edges lie below the energy of the stimulating beam. Scanning and rotating the object through the beam allows for acquisition of a tomographic dataset that can be used to reconstruct images of the distribution of the elements in question. XFCT is a stimulated emission tomography modality, and it is thus necessary to correct for attenuation of the incident and fluorescence photons. The attenuation map is, however, generally known only at the stimulating beam energy and not at the energies of the various fluorescence X-rays of interest. We have developed a penalized-likelihood image reconstruction strategy for this problem. The approach alternates between updating the distribution of a given element and updating the attenuation map for that elements fluorescence X-rays. The approach is guaranteed to increase the penalized likelihood at each iteration. Because the joint objective function is not necessarily concave, the approach may drive the solution to a local maximum. To encourage the algorithm to seek out a reasonable local maximum, we include in the objective function a prior that encourages a relationship, based on physical considerations, between the fluorescence attenuation map and the distribution of the element being reconstructed

Comparison of intensity-modulated continuous-wave lasers with a chirped modulation frequency to pulsed lasers for photoacoustic imaging applications.

Using a Green’s function solution to the photoacoustic wave equation, we compare intensity-modulated continuous-wave (CW) lasers with a chirped modulation frequency to pulsed lasers for photoacoustic imaging applications. Assuming the same transducer is used in both cases, we show that the axial resolution is identical and is determined by the transducer and material properties of the object. We derive a simple formula relating the signal-to-noise ratios (SNRs) of the two imaging systems that only depends on the fluence of each pulse and the time-bandwidth product of the chirp pulse. We also compare the SNR of the two systems assuming the fluence is limited by the American National Standards Institute (ANSI) laser safety guidelines for skin. We find that the SNR is about 20 dB to 30 dB larger for pulsed laser systems for reasonable values of the parameters. However, CW diode lasers have the advantage of being compact and relatively inexpensive, which may outweigh the lower SNR in many applications.

Simultaneous multiview capture and fusion improves spatial resolution in wide-field and light-sheet microscopy

Most fluorescence microscopes are inefficient, collecting only a small fraction of the emitted light at any instant. Besides wasting valuable signal, this inefficiency also reduces spatial resolution and causes imaging volumes to exhibit significant resolution anisotropy. We describe microscopic and computational techniques that address these problems by simultaneously capturing and subsequently fusing and deconvolving multiple specimen views. Unlike previous methods that serially capture multiple views, our approach improves spatial resolution without introducing any additional illumination dose or compromising temporal resolution relative to conventional imaging. When applying our methods to single-view wide-field or dual-view light-sheet microscopy, we achieve a twofold improvement in volumetric resolution (~235 nm × 235 nm × 340 nm) as demonstrated on a variety of samples including microtubules in Toxoplasma gondii, SpoVM in sporulating Bacillus subtilis, and multiple protein distributions and organelles in eukaryotic cells. In every case, spatial resolution is improved with no drawback by harnessing previously unused fluorescence.

Experimental demonstration of novel imaging geometries for x‐ray fluorescence computed tomography

PURPOSE X-ray fluorescence computed tomography (XFCT) is an emerging imaging modality that maps the three-dimensional distribution of elements, generally metals, in ex vivo specimens and potentially in living animals and humans. At present, it is generally performed at synchrotrons, taking advantage of the high flux of monochromatic x rays, but recent work has demonstrated the feasibility of using laboratory-based x-ray tube sources. In this paper, the authors report the development and experimental implementation of two novel imaging geometries for mapping of trace metals in biological samples with ∼50-500 μm spatial resolution. METHODS One of the new imaging approaches involves illuminating and scanning a single slice of the object and imaging each slices x-ray fluorescent emissions using a position-sensitive detector and a pinhole collimator. The other involves illuminating a single line through the object and imaging the emissions using a position-sensitive detector and a slit collimator. They have implemented both of these using synchrotron radiation at the Advanced Photon Source. RESULTS The authors show that it is possible to achieve 250 eV energy resolution using an electron multiplying CCD operating in a quasiphoton-counting mode. Doing so allowed them to generate elemental images using both of the novel geometries for imaging of phantoms and, for the second geometry, an osmium-stained zebrafish. CONCLUSIONS The authors have demonstrated the feasibility of these two novel approaches to XFCT imaging. While they use synchrotron radiation in this demonstration, the geometries could readily be translated to laboratory systems based on tube sources.PURPOSE X-ray fluorescence computed tomography (XFCT) is an emerging imaging modality that maps the three-dimensional distribution of elements, generally metals, inex vivo specimens and potentially in living animals and humans. At present, it is generally performed at synchrotrons, taking advantage of the high flux of monochromatic x rays, but recent work has demonstrated the feasibility of using laboratory-based x-ray tube sources. In this paper, the authors report the development and experimental implementation of two novel imaging geometries for mapping of trace metals in biological samples with ∼50-500 μm spatial resolution. METHODS One of the new imaging approaches involves illuminating and scanning a single slice of the object and imaging each slices x-ray fluorescent emissions using a position-sensitive detector and a pinhole collimator. The other involves illuminating a single line through the object and imaging the emissions using a position-sensitive detector and a slit collimator. They have implemented both of these using synchrotron radiation at the Advanced Photon Source. RESULTS The authors show that it is possible to achieve 250 eV energy resolution using an electron multiplying CCD operating in a quasiphoton-counting mode. Doing so allowed them to generate elemental images using both of the novel geometries for imaging of phantoms and, for the second geometry, an osmium-stained zebrafish. CONCLUSIONS The authors have demonstrated the feasibility of these two novel approaches to XFCT imaging. While they use synchrotron radiation in this demonstration, the geometries could readily be translated to laboratory systems based on tube sources.