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In photoacoustic tomography (PAT) the image contrast is due to optical absorption, and because of this PAT images are sensitive to changes in blood oxygen saturation ( s O 2 ). However, this is not a linear relationship due to the presence of a non-uniform light fluence distribution. In this paper we systematically evaluate the conditions in which an approximate linear inversion scheme–which assumes the internal fluence distribution is unchanged when the absorption coefficient changes–can give accurate estimates of s O 2 . A numerical phantom of highly vascularised tissue is used to test this assumption. It is shown that using multiple wavelengths over a broad range of the near-infrared spectrum yields inaccurate estimates of oxygenation, while a careful selection of wavelengths in the 620-920nm range is likely to yield more accurate oxygenation values. We demonstrate that a 1D fluence correction obtained by fitting a linear function to the average decay rate in the image can further improve the estimates. However, opting to use these longer wavelengths involves sacrificing signal-to-noise ratio in the image, as the absorption of blood is low in this range. This results in an inherent trade-off between error in the s O 2 estimates due to fluence variation and error due to noise. This study shows that the depth to which s O 2 can be estimated accurately using a linear approximation is limited in vivo, even with idealised measurements, to at most 3mm. In practice, there will be even greater uncertainties affecting the estimates, e.g., due to bandlimited or partial-view acoustic detection.

A system for dynamic mapping of broadband ultrasound fields has been designed, with high frame rate photoacoustic imaging in mind. A Fabry-Perot interferometric ultrasound sensor was interrogated using a coherent light single-pixel camera. Scrambled Hadamard measurement patterns were used to sample the acoustic field at the sensor, and either a fast Hadamard transform or a compressed sensing reconstruction algorithm were used to recover the acoustic pressure data. Frame rates of 80 Hz were achieved for 32x32 images even though no specialist hardware was used for the on-thefly reconstructions. The ability of the system to obtain photocacoustic images with data compressions as low as 10% was also demonstrated.

In quantitative photoacoustic imaging, the aim is to recover physiologically relevant tissue parameters such as chromophore concentrations or oxygen saturation. Obtaining accurate estimates is challenging due to the non-linear relationship between the concentrations and the photoacoustic images. Nonlinear least squares inversions designed to tackle this problem require a model of light transport, the most accurate of which is the radiative transfer equation. This paper presents a highly scalable Monte Carlo model of light transport that computes the radiance in 2D using a Fourier basis to discretise in angle. The model was validated against a 2D finite element model of the radiative transfer equation, and was used to compute gradients of an error functional with respect to the absorption and scattering coefficient. It was found that adjoint-based gradient calculations were much more robust to inherent Monte Carlo noise than a finite difference approach. Furthermore, the Fourier angular discretisation allowed very efficient gradient calculations as sums of Fourier coefficients. These advantages, along with the high parallelisability of Monte Carlo models, makes this approach an attractive candidate as a light model for quantitative inversion in photoacoustic imaging.

Spectral methods have made linear acoustics simulations highly computationally efficient, but they currently lose their efficiency when modelling nonlinear waves with regular grids. Moving mesh methods can address this by distributing mesh nodes to minimise the number of nodes needed to represent a waveform. In this paper, a monitor function is presented which is designed specifically for spectral moving mesh methods. In comparison with past monitor functions, this new monitor function significantly improves the convergence rate of the spectral moving mesh method when applied to Burgers’ equation.

An optical ultrasound sensing method based upon the detection of acoustically- induced changes in the optical thickness of a Fabry Perot (FP) polymer film sensing interferometer has been developed as an alternative to piezoelectric based detection methods for ultrasound measurement applications. The technique provides an inherently broadband (~30MHz) response and excellent detection sensitivities (

Complex diffraction limited acoustic fields can be generated from a single element transducer using inexpensive 3-D printable acoustic kinoforms. This is extremely promising for a number of applications. However, the lack of ability to vary the field limits the potential use of this technology. In this work, this limitation is circumvented using multi-frequency acoustic kinoforms for which different acoustic fields are encoded onto different driving frequencies. An optimisation approach based on random downhill binary search is introduced for the design of the multi-frequency kinoforms. This is applied to two test cases to demonstrate the technique: a kinoform designed to generate the numerals “1,” “2,” and “3” in the same plane but at different driving frequencies, and a kinoform designed to generate 3 sets of eight foci lying on a circle with a driving-frequency-dependent radius. Field measurements from these samples confirmed that multi-frequency acoustic kinoforms can be designed that switch between d...

Acoustic fields with multiple foci have many applications in physical acoustics ranging from particle manipulation to neural modulation. However, the generation of multiple foci at arbitrary locations in three-dimensional is challenging using conventional transducer technology. In this work, the optical generation of acoustic fields focused at multiple points using a single optical pulse is demonstrated. This is achieved using optically absorbing surface profiles designed to generate specific, user-defined, wavefields. An optimisation approach for the design of these tailored surface profiles is developed. This searches for a smoothly varying surface that will generate a high peak pressure at a set of target focal points. The designed surface profiles are then realised via a combination of additive manufacturing and absorber deposition techniques. Acoustic field measurements from a sample designed to generate the numeral “7” are used to demonstrate the design method.

The absorption of compressional and shear waves in many viscoelastic solids has been experimentally shown to follow a frequency power law. It is now well established that this type of loss behavior can be modeled using fractional derivatives. However, previous fractional constitutive equations for viscoelastic media are based on temporal fractional derivatives. These operators are non-local in time, which makes them difficult to compute in a memory efficient manner. Here, a fractional Kelvin-Voigt model is derived based on the fractional Laplacian. This is obtained by splitting the particle velocity into compressional and shear components using a dyadic wavenumber tensor. This allows the temporal fractional derivatives in the Kelvin-Voigt model to be replaced with spatial fractional derivatives using a lossless dispersion relation with the appropriate compressional or shear wave speed. The model is discretized using the Fourier collocation spectral method, which allows the fractional operators to be efficiently computed. The field splitting also allows the use of a k-space corrected finite difference scheme for time integration to minimize numerical dispersion. The absorption and dispersion behavior of the fractional Laplacian model is analyzed for both high and low loss materials. The accuracy and utility of the model is then demonstrated through several numerical experiments, including the transmission of focused ultrasound waves through the skull.

Planar sensor arrays have advantages when used for photoacoustic imaging: they do not require the imaging target to be enclosed, and they are easier to manufacture than curved arrays. However, planar arrays have a limited view of the acoustic field due to their finite size; therefore, not all of the acoustic waves emitted from a photoacoustic source can be recorded. This loss of data results in artifacts in the reconstructed photoacoustic image. A detection array configuration which combines a planar Fabry–Perot sensor with perpendicular acoustic reflectors is described and experimentally implemented. This retains the detection advantages of the planar sensor while increasing the effective detection aperture in order to improve the reconstructed photoacoustic image.

A new model for simulating elastic wave propagation using the open-source k-Wave MATLAB Toolbox is described. The model is based on two coupled first-order equations describing the stress and particle velocity within an isotropic medium. For absorbing media, the Kelvin-Voigt model of viscoelasticity is used. The equations are discretised in 2D and 3D using an efficient time-stepping pseudospectral scheme. This uses the Fourier collocation spectral method to compute spatial derivatives and a leapfrog finite-difference scheme to integrate forwards in time. A multi-axial perfectly matched layer (M-PML) is implemented to allow free-field simulations using a finite-sized computational grid. Acceleration using a graphics processing unit (GPU) is supported via the MATLAB Parallel Computing Toolbox. An overview of the simulation functions and their theoretical and numerical foundations is described.

To obtain high resolution ultrasound images, transducers able to operate at high frequencies are required. Optically generated ultrasound utilising the optoacoustic effect is a promising alternative to piezoelectric transducers to achieve this. To use optically generated ultrasound for imaging, a method to spatially steer and focus the acoustic pulses is desirable. In this paper, the use of binary amplitude holograms to focus broadband ultrasound pulses generated by a pulsed laser was investigated. This was done experimentally with patterned absorbers and in simulation. It was found that applying two or more laser pulses applied to a hologram at its design frequency was sufficient to form a focus. The position of this focus could be moved in 3-D by changing the hologram. Additional focal points to those designed for were also found in both the simulation and experimental data. These were generated by constructive interference of harmonics of the pulsing frequency. Simulations found that increasing hologram resolution and applying greater numbers of laser pulses to the hologram decreased the volume of the primary focal point, and that the volume of this focus decreased more rapidly with increasing laser pulse numbers at higher hologram resolutions.

Effective transcranial transmission of focused ultrasound is desirable for various therapeutic applications. Time-reversal (TR) focusing based on numerical simulations of ultrasound propagation can be used to correct for the aberrating skull layer. For weakly heterogeneous media, k-space and pseudospectral time domain (PSTD) methods have been shown to have increased accuracy and efficiency compared to the finite-difference time domain (FDTD) methods typically used in TR. However, their suitability for highly heterogeneous, transcranial simulations is less clear. Here, this is established in terms of spatial and temporal sampling requirements through numerical testing and comparison with FDTD schemes. PSTD schemes are shown to give equal or better accuracy compared to FDTD schemes for modelling propagation through tissue-realistic heterogeneities, which, combined with the reduction in numerical dispersion obtained with k-space correction, recommends them for use in simulated TR.

Planar sensor arrays have many advantages including ease of manufacture and low cost. However, when used for photoacoustic (PA) imaging, planar sensors have a limited view of the acoustic field, which means some of the waves from the PA source are not recorded. This results in artifacts in the reconstructed image of the PA source (the initial acoustic pressure distribution). In this paper, we describe novel sensor array configurations based on the Fabry Perot (FP) sensor and acoustic reflectors that retain its detection advantages while improving the visibility of the reconstructed PA image.

Five numerical phantoms were developed to investigate the accuracy of approximate inversion schemes in the reconstruction of oxygen saturation in photoacoustic imaging. In particular, two types of inversion are considered: Type I, an inversion that assumes fluence is unchanged between illumination wavelengths, and Type II, a method that assumes known background absorption and scattering coefficients to partially correct for the fluence. These approaches are tested in tomography (PAT) and acoustic-resolution microscopy mode (AR-PAM). They are found to produce accurate values of oxygen saturation in a blood vessel of interest at shallow depth - less than 3mm for PAT and less than 1mm for AR-PAM.

Photoacoustic tomography (PAT) has become a powerful tool for biomedical imaging, particularly pre-clinical small animal imaging. Several different measurement systems have been demonstrated, in particular, optically addressed Fabry-Perot interferometer (FPI) sensors have been shown to provide exquisite images when a planar geometry is suitable. However, in its current incarnation the measurements must be made at each point sequentially, so these devices therefore suffer from slow data acquisition time. An alternative to this point-by-point interrogation scheme, is to interrogate the whole sensor with a series of independent patterns, so each measurement is the spatial integral of the product of the pattern and the acoustic field (as in the single-pixel Rice camera). Such an interrogation scheme allows compressed sensing to be used. This enables the number of measurements to be reduced significantly, leading to much faster data acquisition. An experimental implementation will be described, which employs a wide NIR tunable laser beam to interrogate the FPI sensor. The reflected beam is patterned by a digital micro-mirror device, and then focused to a single photodiode. To demonstrate the idea of patterned and compressed sensing for ultrasound detection, a scrambled Hadamard operator is used in the experiments. Photoacoustic imaging experiments of phantoms shows good reconstructed results with 20% compression.

Key to the dynamics of the type of bubble collapse which is associated with such phenomena as sonoluminescence and the emission of strong rebound pressures into the liquid is the role of the liquid inertia. Following the initial formulation of the collapse of an empty spherical cavity, such collapses have been termed "Rayleigh-like." Today this type of cavitation is termed "inertial," reflecting the dominant role of the liquid inertia in the early stages of the collapse. While the inertia in models of spherical bubble collapses depends primarily on the liquid, experimental control of the liquid inertia has not readily been achievable without changing the liquid density and, consequently, changing other liquid properties. In this paper, novel experimental apparatus is described whereby the inertia at the early stages of the collapse of a conical bubble can easily be controlled. The collapse is capable of producing luminescence. The similarity between the collapses of spherical and conical bubbles is investigated analytically, and compared with experimental measurements of the gas pressures generated by the collapse, the bubble wall speeds, and the collapse times.

By infusing blood vessels with gas-filled microbubbles and using rapid ultrasound imaging to detect the bubbles, super-resolution imaging of an entire vessel system has been achieved in a rat brain. See Letter p.499 Conventional clinical ultrasound imaging offers a resolution of, at best, sub-millimetre scale due to fundamental limits of diffraction. Claudia Errico et al. demonstrate a new technique based on ultrasound imaging at ultrafast frame that has sufficiently high resolution at large depths to enable whole-organ mapping of microvasculature. The underlying technique is similar to that of optical localization super-resolution microscopy and is based on fast tracking of transient signals from a sub-wavelength contrast agent — here inert gas microbubbles that are intravenously injected into the blood system. The authors demonstrate the technique by reconstructing the brain microvasculature of a living rat.

The absorption of ultrasound waves in biological tissue has been experimentally shown to follow a frequency power law. This type of behaviour can be modelled using fractional derivative operators. However, previous elastic wave equations are based on fractional derivatives that are non-local in time. This makes them difficult to solve using standard numerical techniques in a memory efficient manner. Here, a fractional Kelvin-Voigt model is derived based on the fractional Laplacian. This is obtained by splitting the particle velocity into compressional and shear components using a dyadic wavenumber tensor. This allows the temporal derivatives to be replaced with spatial derivatives using the lossless dispersion relation with the appropriate compressional or shear wave speed. If the spatial gradients are computed using the Fourier collocation spectral method, this results in a computationally efficient elastic wave model that can account for arbitrary power law absorption of both compressional and shear waves.

Quantitative photoacoustic tomography is an emerging imaging technique aiming at estimating the distribution of optical parameters inside tissue from photoacoustic image which is formed by combining optical information and ultrasound propagation. In this paper reconstruction of absorption and scattering distributions using the radiative transfer equation and the diffusion approximation as forward models for light propagation is investigated. Data is simulated using Monte Carlo method and different size target domains are considered. The results show that the radiative transfer equation can estimate both absorption and scattering distributions with good accuracy. Furthermore, in the simulated test cases, the diffusion approximation can produce as good estimates for absorption as the radiative transfer equation.

Quantitative photoacoustic tomography involves the construction of a photoacoustic image from surface measurements of photoacoustic wave pulses and the recovery of the optical properties of the imaged region. This is a nonlinear, ill-posed inverse problem, for which model-based inversion techniques have been proposed. Here, the radiative transfer equation is used to model the light propagation, and the acoustic propagation and image reconstruction are included. In other words, the full quantitative inversion is tackled. Since Newton-based minimisations are impractical when dealing with three-dimensional images, an adjoint-assisted gradient-based inversion was used as a practical alternative to determining the optical coefficients.

Almost all known photoacoustic image reconstruction algorithms are based on the assumption that the acoustic waves leave the object (the imaged region) after a finite time. This assumption is fulfilled if the measurements are made in free space and reflections from the detectors are negligible. However, when the object is surrounded by acoustically hard detectors arrays (and/or by additional acoustic mirrors), the acoustic waves will bounce around in such a reverberant cavity many times (in the absence of absorption, forever). This paper proposes fast reconstruction algorithms for the measurements made from the walls of a rectangular reverberant cavity. The algorithms are tested using numerical simulations.

Plane wave ultrasound imaging using a single short, broadband planar source pulse generated by photoacoustic excitation, was demonstrated.

Powdered maize starch thickeners are used to modify drink consistency in the clinical management of dysphagia. Amylase is a digestive enzyme found in saliva which breaks down starch. This action is dependent on pH, which varies in practice depending on the particular drink. This study measured the effects of human saliva on the viscosity of drinks thickened with a widely used starch-based thickener. Experiments simulated a possible clinical scenario whereby saliva enters a cup and contaminates a drink. Citric acid (E330) was added to water to produce a controlled range of pH from 3.0 to 7.0, and several commercially available drinks with naturally low pH were investigated. When saliva was added to thickened water, viscosity was reduced to less than 1% of its original value after 10–15 min. However, lowering pH systematically slowed the reduction in viscosity attributable to saliva. At pH 3.5 and below, saliva was found to have no significant effect on viscosity. The pH of drinks in this study ranged from 2.6 for Coca Cola to 6.2 for black coffee. Again, low pH slowed the effect of saliva. For many popular drinks, having pH of 3.6 or less, viscosity was not significantly affected by the addition of saliva.

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.

A numerical inversion scheme for recovering a map of the absolute conductivity from the absorbed power density map that is conventionally reconstructed in thermacoustic imaging is described. This offers the prospect of obtaining an image that is more closely related to the underlying tissue structure and physiology. The inversion scheme employs a full 3D full wave model of electromagnetic propagation in tissue which is iteratively fitted to the measured absorbed power density map using a simple recursive method. The reconstruction is demonstrated numerically using three examples of absorbers of varying geometries, tissue realistic complex permittivity values and noise. In these examples, the reconstruction is shown to rapidly converge to within good estimates of the true conductivity in less than 20 iterations.

3D photoacoustic images of the vasculature in mice were obtained in vivo using a photoacoustic scanner based on a Fabry Perot polymer film ultrasound sensor and an attenuation compensated acoustic time reversal image reconstruction method.

While photoacoustic methods offer significant promise for high-resolution optical contrast imaging, quantification has thus far proved challenging. In this paper, a noniterative reconstruction technique for producing quantitative photoacoustic images of both absorption and scattering perturbations is introduced for the case when the optical properties of the turbid background are known and multiple optical illumination locations are used. Through theoretical developments and computational examples, it is demonstrated that multiple-illumination photoacoustic tomography (MI-PAT) can alleviate ill-posedness due to absorption-scattering nonuniqueness and produce quantitative high-resolution reconstructions of optical absorption, scattering, and Gruneisen parameter distributions. While numerical challenges still exist, we show that the linearized MI-PAT framework that we propose has orders of magnitude improved condition number compared with CW diffuse optical tomography.

A noninvasive, multimodal photoacoustic and optical coherence tomography (PAT/OCT) scanner for three-dimensional in vivo (3D) skin imaging is described. The system employs an integrated, all optical detection scheme for both modalities in backward mode utilizing a shared 2D optical scanner with a field-of-view of ~13 × 13 mm(2). The photoacoustic waves were detected using a Fabry Perot polymer film ultrasound sensor placed on the surface of the skin. The sensor is transparent in the spectral range 590-1200 nm. This permits the photoacoustic excitation beam (670-680 nm) and the OCT probe beam (1050 nm) to be transmitted through the sensor head and into the underlying tissue thus providing a backward mode imaging configuration. The respective OCT and PAT axial resolutions were 8 and 20 µm and the lateral resolutions were 18 and 50-100 µm. The system provides greater penetration depth than previous combined PA/OCT devices due to the longer wavelength of the OCT beam (1050 nm rather than 829-870 nm) and by operating in the tomographic rather than the optical resolution mode of photoacoustic imaging. Three-dimensional in vivo images of the vasculature and the surrounding tissue micro-morphology in murine and human skin were acquired. These studies demonstrated the complementary contrast and tissue information provided by each modality for high-resolution 3D imaging of vascular structures to depths of up to 5 mm. Potential applications include characterizing skin conditions such as tumors, vascular lesions, soft tissue damage such as burns and wounds, inflammatory conditions such as dermatitis and other superficial tissue abnormalities.

Photoacoustic imaging is a promising technique combining high ultrasonic resolution and high optical contrast. However, quantification has proved rather challenging. In this paper, we present a non-iterative reconstruction strategy with multiple-optical-sources for reconstruction of absorption, scattering perturbations as well as the spatially varying Grueneisen parameter from a known turbid background. We term this method the multiple-illumination photoacoustic tomography (MI-PAT). While numerical challenges still exist, we demonstrated that the linearized MI-PAT framework we propose has orders of magnitude improved condition number compared with Continuous-Wave Diffuse Optical Tomography (CW-DOT).

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 treatments.

A k-space pseudospectral model is developed for the fast full-wave simulation of nonlinear ultrasound propagation through heterogeneous media. The model uses a novel equation of state to account for nonlinearity in addition to power law absorption. The spectral calculation of the spatial gradients enables a significant reduction in the number of required grid nodes compared to finite difference methods. The model is parallelized using a graphical processing unit (GPU) which allows the simulation of individual ultrasound scan lines using a 256 × 256 × 128 voxel grid in less than five minutes. Several numerical examples are given, including the simulation of harmonic ultrasound images and beam patterns using a linear phased array transducer.

A model-based inversion scheme was used to determine absolute chromophore concentrations from multiwavelength photoacoustic images. The inversion scheme incorporated a forward model, which predicted 2D images of the initial pressure distribution as a function of the spatial distribution of the chromophore concentrations. It comprised a multiwavelength diffusion based model of the light transport, a model of acoustic propagation and detection, and an image reconstruction algorithm. The model was inverted by fitting its output to measured photoacoustic images to determine the chromophore concentrations. The scheme was validated using images acquired in a tissue phantom at wavelengths between 590 nm and 980 nm. The phantom comprised a scattering emulsion in which up to four tubes, filled with absorbing solutions of copper and nickel chloride at different concentration ratios, were submerged. Photoacoustic signals were detected along a line perpendicular to the tubes from which images of the initial pressure distribution were reconstructed. By varying the excitation wavelength, sets of multiwavelength photoacoustic images were obtained. The majority of the determined chromophore concentrations were within +/-15% of the true value, while the concentration ratios were determined with an average accuracy of -1.2%.

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.

In photoacoustic tomography, by using a contrast agent that absorbs only above or below a certain fluence threshold its concentration could be estimated using only singlewavelength images by varying the illumination intensity.

In recent years, some of the promised potential of biomedical photoacoustic imaging has begun to be realised. It has been used to produce good, three-dimensional, images of blood vasculature in mice and other small animals, and in human skin in vivo, to depths of several mm, while maintaining a spatial resolution of

In biomedical photoacoustic tomography (PAT), ultrasonic pulses generated by the absorption of near-infrared light are recorded over an array of detectors, and the measured pressure time series are used to recover an image of the initial acoustic pressure distribution within the tissue, which is related to the tissue optical coefficients and therefore to tissue physiology. For high resolution imaging, large-area detector arrays with a high density of sensitive, small elements are required. Such arrays can be expensive, so reverberant-field PAT has been suggested as a means of obtaining PAT images using arrays with a smaller number of detectors or even a single detector. We propose that by recording the reflections from a reverberant cavity in addition to the primary acoustic waves, sufficient information can be captured to allow a PAT image to be reconstructed, without the requirement for a large-area array. A pilot study using simple 2D simulations, backprojections and modal inversions was undertaken to assess the feasibility of this approach to PAT.

In biomedical photoacoustic tomography of soft tissue, the initial acoustic pressure distribution following the absorption of a short excitation laser pulse, is recovered as a function of position. This initial pressure distribution is proportional to the absorbed optical energy density, and is thus related (albeit indirectly) to the tissue optical coefficients. When imaging soft tissue which contains several absorbing chromophores (such as oxy- and deoxy-haemoglobin, water, etc.), the primary quantity of interest is the concentrations of the chromophores at each point in the tissue, and not the absorbed optical energy density, which is nonlinearly related to the chromophore concentrations, and also depends on the distribution of scattering. Estimating the distribution of the concentration of a chromophore therefore requires the recovery of two unknown functions (chromophore concentration and scattering distributions) from measurements of one (absorbed energy density). For measurements made at a single optical wavelength, this problem suffers from nonuniqueness, and cannot be solved without additional information being incorporated. A simulated example is used here to demonstrate that, in principle, by using multi-wavelength data and incorporating the known wavelength dependence of the chromophore absorption and the scattering as prior information, a chromophore concentration and spatial dependence of the scattering can be recovered simultaneously. This step opens the way to physiological and molecular imaging using multispectral photoacoustic tomography.

Photoacoustic spectroscopy has been shown to be capable of making non-invasive, spatially resolved measurements of haemodynamic parameters, such as the concentrations of oxy- and deoxyhaemoglobin and blood oxygen saturation. The development of photoacoustic techniques for molecular imaging that go beyond the measurement of haemodynamic parameters has recently become an area of interest. These techniques are aimed at the detection and quantification of for example contrast agents targeted at pathologies such as tumours for diagnostic or therapeutic purposes. This study aimed to validate a model-based inversion scheme by recovering chromophore concentrations from 2D multiwavelength images obtained using a tissue phantom. The inversion scheme employed a complete photoacoustic forward model, which incorporates a model of light transport, a model of acoustic propagation and Fourier transform image reconstruction algorithm. Using the structural information from the measured images, the photoacoustic forward model was used to calculate theoretical multiwavelength photoacoustic images as a function of the concentrations of spatially distributed tissue chromophores and scatters. The chromophore concentrations were determined by fitting the model to the measured images. It was found that concentration ratios of reasonable accuracy were recovered while the absolute concentrations showed significant errors due to light-induced instabilities in the nearinfrared dyes used in the tissue phantom.© (2008) COPYRIGHT SPIE--The International Society for Optical Engineering. Downloading of the abstract is permitted for personal use only.

A model of the frequency-dependent directivity of a planar, optically-addressed, Fabry-Perot (FP), polymer film ultrasound sensor is described and validated against experimental directivity measurements made over a frequency range of 1 to 15 MHz and angles from normal incidence to 80 degrees. The model may be used, for example, as a predictive tool to improve sensor design, or to provide a noise-free response function that could be deconvolved from sound-field measurements in order to improve accuracy in high-frequency metrology and imaging applications. The specific question of whether effective element sizes as small as the optical-diffraction limit can be achieved was investigated. For a polymer film sensor with a FP cavity of thickness d, the minimum effective element radius was found to be about 0.9 d, and that an illumination spot radius of less than d/4 is required to achieve it.

The aim in quantitative photoacoustic imaging (QPI) is to recover the spatial distributions of the optical absorption and scattering coefficients from an absorbed energy density distribution (a conventional photoacoustic image). This paper proposes a gradient-based minimisation approach and demonstrates that functional gradients may be calculated efficiently by using a finite element model of light transport based on the diffusion approximation, in conjunction with a related adjoint model. The gradients calculated using this adjoint method are tested against finite-difference estimates, and inversions for the absorption or scattering coefficient distributions (from simulated data) are shown for the case where the other coefficient is known a priori. Simultaneous estimation for both absorption and scattering is ill-posed, and so multiwavelength inversion, in which the specific absorption spectra of the constituent chromophores and the wavelength-dependence of the scatter are known, is proposed as a means of ameliorating the ill-posedness. The unknown parameters are now the spatial variation of the chromphore concentrations and scattering coefficient. It is shown that the functional gradients for both of these can be obtained straightforwardly from the gradients for absorption and scatter and require no significant additional calculations. A simulated example is given in which the distributions of two chromophores with different spectra are recovered from absorbed energy images obtained at multiple wavelengths, when the scattering is assumed known.

In recent years, the capability of performing 3D full-wave nonlinear ultrasound simulations in tissue-realistic media has been demonstrated by a number of groups. These models have since underpinned a range of interesting studies into the interaction of ultrasound fields with the human body. However, simulations have thus far been limited to domain sizes on the order of 1 billion grid points. This limitation usually means either the spatial area or highest frequency of interest is truncated. Looking toward the exascale era, where supercomputers integrating over 1M cores are predicted to appear before 2020, there is a significant opportunity to use models to gain new insight into ultrasound-tissue interaction with unprecedented detail. The challenge is to develop suitable numerical methods that map to these massively parallel architectures, in particular, that minimize data movement, allow the exploitation of co-processors, and minimize the accumulation of numerical errors. Here, we show a novel domain decomposition approach for the Fourier collocation spectral method that allows ultrasound simulations to be distributed across up to 32k CPU cores or hundreds of accelerators with reasonable efficiency. Using this model, we demonstrate for the first time the possibility of ultrasound simulations exceeding 70 billion grid points.

Biomedical photoacoustic imaging produces a map of the initial acoustic pressure distribution, or absorbed energy density, in tissue following a short laser pulse. Quantitative photoacoustic imaging (QPI) takes the reconstruction process one stage further to produce a map of the tissue optical coefficients. This has two important advantages. Firstly, it removes the distorting effect of the internal light distribution on image contrast. Secondly, by obtaining images at multiple wavelengths, it enables standard spectroscopic techniques to be used to quantify the concentrations of specific chromophores, for instance, oxy and deoxy haemoglobin for the measurement of blood oxygenation - applying such techniques directly to "conventionally" reconstructed absorbed energy maps is problematic due to the spectroscopic 'spatial crosstalk' effects between different tissue chromophores. As well as naturally-occurring chromophores, dye-labelled molecular markers can be used to tag specific molecules, such as cell surface receptors, enzymes or pharmaceutical agents. In QPI, a diffusion-based finite element model of light transport in scattering media, with δ-Eddington scattering coefficients, is fitted to the absorbed energy distribution to estimate the optical coefficient maps. The approach described here uses a recursive algorithm and converges quickly on the absorption coefficient distribution, when the scattering is known. By adding an area of known absorption, an unknown constant scattering coefficient may also be recovered. With optical coefficient maps estimated in this way, QPI has the potential to be a powerful tool for quantifying the concentration of molecular markers in photoacoustic molecular imaging.

Photoacoustic signals are usually generated using bulky and expensive Q-switched Nd:YAG lasers, with limited scope for varying the pulse repetition frequency, wavelength and pulse width. An alternative would be to use laser diodes as excitation sources; these devices are compact, relatively inexpensive, and available in a wide variety of NIR wavelengths. Their pulse duration and repetition rates can also be varied arbitrarily enabling a wide range of time and frequency domain excitation methods to be employed. The main difficulty to overcome when using laser diodes for pulsed photoacoustic excitation is their low peak power compared to Q-switched lasers. However, the much higher repetition rate of laser diodes (~ kHz) compared to many Q-switched laser systems (~ tens of Hz) enables a correspondingly greater number of events to be acquired and signal averaged over a fixed time period. This offers the prospect of significantly increasing the signal-to-noise ratio (SNR) of the detected photoacoustic signal. Choosing the wavelength of the laser diode to be lower than that of the water absorption peak at 940nm, may also provide a significant advantage over a system lasing at 1064nm for measurements in tissue. If the output of a number of laser diodes is combined it then becomes possible, in principle, to obtain a SNR approaching that achievable with a Q-switched laser. It is also suggested that optimising the pulse duration of the laser diode may reduce the effects of frequency-dependent acoustic attenuation in tissue on the photoacoustic signal. To investigate this, a numerical model based on the Poisson solution to the wave equation was developed. To validate the model, a high peak power pulsed laser diode system was built. It was composed of a 905nm stacked array laser diode coupled to an optical fibre and driven by a high current laser diode driver. Measurements of the SNR of photoacoustic signals generated in a purely absorbing medium (ink) were made as a function of pulse duration. This preliminary study shows the potential for using laser diodes as excitation sources for photoacoustic applications in the biomedical field.

Photoacoustic imaging, which generates a map of the initial acoustic pressure distribution generated by a short laser pulse, has been demonstrated by several authors. Quantitative photoacoustic imaging takes this one stage further to produce a map of the distribution of an optical property of the tissue, in this case absorption, which can then be related to a physiological parameter. In this technique, the initial pressure distribution is assumed to be proportional to the absorbed laser energy density. A model of light transport in scattering media is then used to estimate the distribution of optical properties that would result in such a pattern of absorbed energy. The light model used a finite element implementation of the diffusion equation (with the delta-E(3) approximation included to improve the accuracy at short distances inside the scattering medium). An algorithm which applies this model iteratively and converges on a quantitative estimate of the optical absorption distribution is described. 2D examples using simulated data (initial pressure maps) with and without noise are shown to converge quickly and accurately.

A Bayesian approach to the optical reconstruction problem associated with spectral quantitative photoacoustic tomography is presented. The approach is derived for commonly used spectral tissue models of optical absorption and scattering: the absorption is described as a weighted sum of absorption spectra of known chromophores (spatially dependent chromophore concentrations), while the scattering is described using Mie scattering theory, with the proportionality constant and spectral power law parameter both spatially-dependent. It is validated using two-dimensional test problems composed of three biologically relevant chromophores: fat, oxygenated blood and deoxygenated blood. Using this approach it is possible to estimate the Gr?neisen parameter, the absolute chromophore concentrations, and the Mie scattering parameters associated with spectral photoacoustic tomography problems. In addition, the direct estimation of the spectral parameters is compared to estimates obtained by fitting the spectral parameters to estimates of absorption, scattering and Gr?neisen parameter at the investigated wavelengths. It is shown with numerical examples that the direct estimation results in better accuracy of the estimated parameters.

Quantitative photoacoustic tomography (QPAT) offers the possibility of high-resolution molecular imaging by quantifying molecular concentrations in biological tissue. QPAT comprises two inverse problems: (1) the construction of a photoacoustic image from surface measurements of photoacoustic wave pulses over time, and (2) the determination of the optical properties of the imaged region. The first is a well-studied area for which a number of solution methods are available, while the second is, in general, a nonlinear, ill-posed inverse problem. Model-based inversion techniques to solve (2) are usually based on the diffusion approximation to the radiative transfer equation (RTE) and typically assume the acoustic inversion step has been solved exactly. Here, neither simplification is made: the full RTE is used to model the light propagation, and the acoustic propagation and image reconstruction are included in the simulations of measured data. Since Hessian- and Jacobian-based minimizations are computationally expensive for the large data sets typically encountered in QPAT, gradient-based minimization schemes provide a practical alternative. The acoustic pressure time series were simulated using a k-space, pseudo-spectral time domain model, and a time-reversal reconstruction algorithm was used to form a set of photoacoustic images corresponding to four illumination positions. A regularized, adjoint-assisted gradient inversion using a finite element model of the RTE was then used to determine the optical absorption and scattering coefficients.

Performing realistic simulations of the propagation of nonlinear ultrasound waves through biological tissue is a computationally difficult task. This is because the domain size of interest is often very large compared to the wavelengths of the high-frequency harmonics generated as the ultrasound waves progress. Recently, the k-space pseudospectral method has been applied to this problem to reduce the number of grid points required per wavelength compared to finite difference methods. However, the global nature of the spectral gradient calculations used in this method introduces new challenges for tackling large-scale problems. Here, we discuss three important issues for pseudospectral methods in the context of distributed computing. (1) Decomposing the domain to allow distribution across multiple nodes while still retaining the global accuracy of the spectral gradient calculations. (2) Using non-uniform grids to allow grid points to be clustered around highly nonlinear regions. (3) Avoiding aliasing error...

Quantitative photoacoustic tomography is a novel hybrid imaging technique aiming at estimating optical parameters inside tissues. The method combines (functional) optical information and accurate anatomical information obtained using ultrasound techniques. The optical inverse problem of quantitative photoacoustic tomography is to estimate the optical parameters within tissue when absorbed optical energy density is given. In this paper we consider reconstruction of absorption and scattering distributions in quantitative photoacoustic tomography. The radiative transport equation and diffusion approximation are used as light transport models and solutions in different size domains are investigated. The simulations show that scaling of the data, for example by using logarithmic data, can be expected to significantly improve the convergence of the minimization algorithm. Furthermore, both the radiative transport equation and diffusion approximation can give good estimates for absorption. However, depending on the optical properties and the size of the domain, the diffusion approximation may not produce as good estimates for scattering as the radiative transport equation.

Computational acoustics offers a powerful tool for investigating the interaction between ultrasound waves and the human body. However, in many common ultrasound settings, performing realistic simulations is computationally difficult due to the large size of the tissue volume compared to the size of the acoustic wavelength. This is particularly true in the case of high-intensity focused ultrasound where large diameter transducers are used to tightly focus ultrasound waves, often deep within the tissue. Here, an efficient model for large-scale ultrasound simulation is presented. The model is based on coupled first-order acoustic equations valid for nonlinear wave propagation in heterogeneous media with power law absorption. The equations are discretized using the k-space pseudospectral method and encoded using advanced programming techniques for parallel computer architectures. This allows the efficient simulation of nonlinear ultrasound propagation in three-dimensions over hundreds of wavelengths. Applicat...