Reconstructing images from measured time domain signals is an essential step in tomography-mode photoacoustic imaging. However, in practice, there are many complicating factors that make it difficult to obtain high-resolution images. These include incomplete or undersampled data, filtering effects, acoustic and optical attenuation, and uncertainties in the material parameters. Here, the processing and image reconstruction steps routinely used by the Photoacoustic Imaging Group at University College London are discussed. These include correction for acoustic and optical attenuation, spatial resampling, material parameter selection, image reconstruction, and log compression. The effect of each of these steps is demonstrated using a representative in vivo dataset. All of the algorithms discussed form part of the open-source k-Wave toolbox (available from http://www.k-wave.org).
Most reconstruction algorithms used in photoacoustic tomography do not account for the effects of acoustic attenuation on the recorded signals. For experimental measurements made in biological tissue, the frequency dependent acoustic attenuation causes high frequency components of the propagating photoacoustic waves to be significantly reduced. This signal loss manifests as a depth dependent magnitude error and blurring of features within the reconstructed image. Here, a general method for compensating for this attenuation using time-variant filtering is presented. The time-variant filter is constructed to correct for acoustic attenuation and dispersion following a frequency power law under the assumption the distribution of attenuation parameters is homogeneous. The filter is then applied directly to the recorded time-domain signals using a form of nonstationary convolution. Regularization is achieved using a time-variant window where the cutoff frequency is based on the local time-frequency distribution of the recorded signals. The approach is computationally efficient and can be used in combination with any detector geometry or reconstruction algorithm. Numerical and experimental examples are presented to illustrate the utility of the technique. Clear improvements in the magnitude and resolution of reconstructed photoacoustic images are seen when acoustic attenuation compensation is applied.
This paper investigates the application of the vessel filter proposed by Frangi et al., [MICCAI, LNCS vol. 1496, pp. 130-137, 1998] to photoacoustic images of the vasculature. The filter works by classifying the eigenvalue decomposition of the local Hessian matrix at each image voxel to find tubular structures in the image. A detailed analysis of the algorithm is provided, and the effect of the filters on photoacoustic images is studied using numerical and experimental phantoms. In particular, the impact of the filter on image resolution, feature preservation, and noise is discussed. The vessel filter is then applied to photoacoustic images of the vasculature in mice. The classical Hessian filter is shown to be highly effective at removing noise and highlighting vessels, at the expense of reducing the sharpness of vessel edges.
The use of a novel all-optical photoacoustic scanner for imaging the development of tumor vasculature and its response to a therapeutic vascular disrupting agent is described. The scanner employs a Fabry-Perot polymer film ultrasound sensor for mapping the photoacoustic waves and an image reconstruction algorithm based upon attenuation-compensated acoustic time reversal. The system was used to noninvasively image human colorectal tumor xenografts implanted subcutaneously in mice. Label-free three-dimensional in vivo images of whole tumors to depths of almost 10 mm with sub-100-micron spatial resolution were acquired in a longitudinal manner. This enabled the development of tumor-related vascular features, such as vessel tortuosity, feeding vessel recruitment, and necrosis to be visualized over time. The system was also used to study the temporal evolution of the response of the tumor vasculature following the administration of a therapeutic vascular disrupting agent (OXi4503). This revealed the well-known destruction and recovery phases associated with this agent. These studies illustrate the broader potential of this technology as an imaging tool for the preclinical and clinical study of tumors and other pathologies characterized by changes in the vasculature.
The ability to noninvasively image embryonic vascular anatomy in mouse models is an important requirement for characterizing the development of the normal cardiovascular system and malformations in the heart and vascular supply. Photoacoustic imaging, which can provide high resolution non invasive images of the vasculature based upon optical absorption by endogenous hemoglobin, is well suited to this application. In this study, photoacoustic images of mouse embryos were obtained ex vivo and in vivo. The images show intricate details of the embryonic vascular system to depths of up to 10 mm, which allowed whole embryos to be imaged in situ. To achieve this, an all-optical photoacoustic scanner and a novel time reversal image reconstruction algorithm, which provide deep tissue imaging capability while maintaining high spatial resolution and contrast were employed. This technology may find application as an imaging tool for preclinical embryo studies in developmental biology as well as more generally in preclinical and clinical medicine for studying pathologies characterized by changes in the vasculature.
Attenuation effects can be significant in photoacoustic tomography since the generated pressure signals are broadband, and ignoring them may lead to image artifacts and blurring. La Rivière et al. [Opt. Lett. 31(6), pp. 781-783, (2006)] had previously 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. We derive an integral operator relating the attenuated pressure signals to the absorbed optical energy for a planar measurement geometry. The matrix operator relating the two quantities is a function of the temporal frequency, attenuation coefficient and the two-dimensional spatial frequency. We perform singular-value decomposition (SVD) of this integral operator to study the problem further. 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 to characterize the ill-posedness of recovering the absorbed optical energy distribution at different depths in an attenuating medium. This integral equation can be inverted using standard SVD methods, and the initial pressure distribution can be recovered. We conduct simulations and derive an algorithm for image reconstruction using SVD for a planar measurement geometry. We also study the noise and resolution properties of this image-reconstruction method.
The reconstruction of images in photoacoustic tomography is reliant on specifying the speed of sound within the propagation medium. However, for in vivo imaging, this value is not normally accurately known. Here, an autofocus approach for automatically selecting the sound speed is proposed. This is based on maximizing the sharpness of the reconstructed image as quantified by a focus function. Several focus functions are investigated, and their performance is discussed. The method is demonstrated using phantom measurements made in a medium with a known sound speed and in vivo measurements of the vasculature in the flank of an adult mouse.
Photoacoustic tomography can provide high resolution 3D images of vascular networks, making it well suited to
characterising the development of tumour vasculature and its response to treatment. In this study, photoacoustic images
to depths of up to 9 mm were obtained using an all optical ultrasound detection scheme. Two type of colorectal tumours
(LS174T and SW1222) implanted subcutaneously in a mouse were studied. 3D photoacoustic images were obtained in
vivo revealing the different vascular architectures of each tumour type and their evolution over a period of several days.
The results suggest that photoacoustic imaging could play a role in providing essential pre-clinical information on
tumour pathophysiology and eliciting the biological mechanisms underlying anti-angiogenic therapies and other
The reconstruction algorithms commonly used in photoacoustic tomography do not account for the effects of
acoustic attenuation on the measured time-domain signals. For experimental measurements made in biological
tissue, acoustic attenuation causes the high frequency components of the generated ultrasound signals to be
significantly reduced. When this signal loss is neglected, it manifests as a depth dependent magnitude error and
blurring of features within the reconstructed photoacoustic image. Here, the approach described by Treeby
et al. [Inverse Problems 26(11), p. 115003, 2010] is applied to the reconstruction of high-resolution threedimensional
photoacoustic images of vascular networks around the abdomen of a pregnant female mouse. The
reconstruction is based on the idea of time reversal in which a numerical model of the acoustic forward problem
is run backwards in time. Compensation of acoustic attenuation in the inverse problem is achieved by using
a forward model that accurately accounts for the frequency dependent attenuation experimentally observed in
biological tissue. The regularisation of the inverse problem is discussed, and the methodology demonstrated
through the reconstruction of several images. Clear improvements in image magnitude and resolution are seen
when attenuation compensation is included.
A new, freely available third party MATLAB toolbox for the simulation and reconstruction of photoacoustic wave fields is described. The toolbox, named k-Wave, is designed to make realistic photoacoustic modeling simple and fast. The forward simulations are based on a k-space pseudo-spectral time domain solution to coupled first-order acoustic equations for homogeneous or heterogeneous media in one, two, and three dimensions. The simulation functions can additionally be used as a flexible time reversal image reconstruction algorithm for an arbitrarily shaped measurement surface. A one-step image reconstruction algorithm for a planar detector geometry based on the fast Fourier transform (FFT) is also included. The architecture and use of the toolbox are described, and several novel modeling examples are given. First, the use of data interpolation is shown to considerably improve time reversal reconstructions when the measurement surface has only a sparse array of detector points. Second, by comparison with one-step, FFT-based reconstruction, time reversal is shown to be sufficiently general that it can also be used for finite-sized planar measurement surfaces. Last, the optimization of computational speed is demonstrated through parallel execution using a graphics processing unit.
Most image reconstruction algorithms for biomedical photoacoustic tomography make the assumption that the
optically-generated ultrasonic waves are recorded by pressure detectors with an omni-directional response. In
other words, the detectors are assumed to sample the pressure field exactly at a point. In practice this is
rarely the case as real detectors have a finite size and often respond not purely to pressure changes but to some
combination of acoustic pressure and pressure gradient (or other derivatives). This can make them less sensitive
to pressure waves at some angles. The effect of this sensor directionality on photoacoustic tomography was
considered here for the case of time-reversal image reconstruction. The ultrasound simulation toolbox k-Wave
was used to perform the study.
Photoacoustic tomography is an emerging medical imaging modality based on the reconstruction of an initial internal
pressure distribution from surface measurements of photoacoustic wave pulses over time. Current methods used for this
image reconstruction assume that the propagation medium is acoustically non-attenuating. However, in soft biological
tissue, the frequency dependent ultrasonic attenuation is sufficient to cause considerable distortion to photoacoustic
waves, even over short propagation distances. This distortion introduces blurring artifacts into images reconstructed
under the assumption of a lossless medium. Here, a general lossy wave equation applicable to biological media is
developed for which an exact solution (formed in the wavenumber-frequency domain) is derived. Explicit consideration
is given to sound speed dispersion which is shown to have a negligible effect on photoacoustic imaging. Given an initial
pressure distribution, the developed model allows the complete pressure field within the domain to be computed at an
arbitrary time without iteration. The computation relies only on the Fourier transform and a decaying time propagator
dependent on the attenuation in the medium. This facilitates the fast calculation of pressure fields in two or three
dimensions over large domains. The model is demonstrated through the simulation and reconstruction of an example
pulse distribution in a lossy medium.