Application of diffusion approximation in quantitative photoacoustic tomography in the presence of low-scattering regions

Hänninen, Niko; Pulkkinen, Aki; Leino, Aleksi A.; Tarvainen, Tanja

doi:10.1016/j.jqsrt.2020.107065

Cited by 7 publications

(5 citation statements)

References 63 publications

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“…The credibility intervals of the scattering estimates are wider compared to the absorption estimates, which is most likely caused by that estimating the scattering coefficient is more ill-posed problem. This has also been observed in previous studies [45,32,31]. In the A-SGN, S-SGN 2 , S-SGN 3 , and A-SGN GN estimates, the true scattering values lie withing the credibility intervals in the whole cross section.…”

Section: Approach P Isupporting

confidence: 88%

“…In a highly scattering medium relatively far from a light source, light transport can be approximated by the diffusion approximation (DA) [33]. The DA has been utilized in QPAT for example in [56,24,23,5,53,6,67,68,57,32,31,49,18,46,45,1,35,19]. However, in typical size of imaged targets in QPAT, the approximations of the DA are not fully met, which can lead to errors in the solution of the inverse problem [56,66].…”

mentioning

confidence: 99%

“…However, in all of these studies, the scattering coefficient was assumed to be known. Estimating both scattering and absorption simultaneously in QPAT is an ill-posed problem, and scattering estimates typically suffer more from reconstruction artefacts and poor resolution [56,29,50,47,31,37]. Utilizing MC in estimation of both absorption and scattering has previously been considered in [37], where the convergence of the minimization problem was guaranteed using a large number of photon packets.…”

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confidence: 99%

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Estimating absorption and scattering in quantitative photoacoustic tomography with an adaptive Monte Carlo method for light transport

Hänninen,

Pulkkinen,

Arridge

et al. 2024

IPI

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In this work, the optical inverse problem of quantitative photoacoustic tomography is studied. Maximum a posteriori estimates for absorption and scattering are computed from absorbed energy density, and the reliability of the estimates is evaluated utilizing the Laplace's approximation. The forward operator and evaluation of the search direction in the minimization algorithm are based on the Monte Carlo method for light transport. Monte Carlo is a stochastic method where the solution of a light transport model is approximated by simulating paths of photon packets as they undergo absorption and scattering events in a scattering medium. This makes evaluation of the search direction also stochastic. In this work, we study an adaptive approach where the number of simulated photon packets on each iteration is determined by utilizing a so-called norm test. In the norm test, the variance of the gradient of the objective function is assessed and used to control the number of photon packets. The approach is studied with numerical simulations. The results show that the adaptive approach can be used to control the number of photon packets during an iterative solution of the inverse problem of quantitative photoacoustic tomography. Further, the adaptive approach can reduce the computational cost compared to a conventional approach where the number of photon packets is fixed.

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Section: Approach P Isupporting

confidence: 88%

mentioning

confidence: 99%

mentioning

confidence: 99%

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Estimating absorption and scattering in quantitative photoacoustic tomography with an adaptive Monte Carlo method for light transport

Hänninen,

Pulkkinen,

Arridge

et al. 2024

IPI

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“…The approximation naturally creates an approximation error that we have to account for. Modeling errors can be efficiently corrected with the established approximation error method (AEM) [2,14] and has been successfully applied in a wide area of inverse problems [6,11,24,29,35]. It is a linear correction that assumes that the approximation error has a Gaussian distribution.…”

mentioning

confidence: 99%

Sequential model correction for nonlinear inverse problems

Arjas¹,

Sillanpää²,

Hauptmann³

2023

Preprint

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Inverse problems are in many cases solved with optimization techniques. When the underlying model is linear, first-order gradient methods are usually sufficient. With nonlinear models, due to nonconvexity, one must often resort to second-order methods that are computationally more expensive. In this work we aim to approximate a nonlinear model with a linear one and correct the resulting approximation error. We develop a sequential method that iteratively solves a linear inverse problem and updates the approximation error by evaluating it at the new solution. We separately consider cases where the approximation is fixed over iterations and where the approximation is adaptive. In the fixed case we show theoretically under what assumptions the sequence converges. In the adaptive case, particularly considering the special case of approximation by first-order Taylor expansion, we show that the sequence converges to a neighborhood of a local minimizer of the objective function with respect to the exact model. Furthermore, we show that with quadratic objective functions the sequence corresponds to the Gauss-Newton method. Finally, we showcase numerical results superior to the conventional model correction method. We also show, that a fixed approximation can provide competitive results with considerable computational speed-up.

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“…[21][22][23] Spatial fluence modeling is commonly used in photoacoustic simulations to provide an accurate ground truth for experimental validation, 20,22 and this is usually accomplished via a Monte Carlo simulation of the radiative transfer equation (RTE). It is also often necessary in quantitative photoacoustic tomography to fully model the fluence such that the optical parameters of the tissue can be recovered absolutely, for example, in the recent work of Hänninen et al 24 In motivating their work, the authors highlight that a significant shortcoming of the standard Monte Carlo method is the necessary computation time, which can be prohibitive for large tomographic problems such as ours. This is further compounded in the case of non-stationary illumination since the fluence must be computed separately for each tomographic acquisition angle.…”

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confidence: 99%

Integrating photoacoustic tomography into a multimodal automated breast ultrasound scanner

2020

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Significance: Photoacoustic tomography (PAT) is a promising emergent modality for the screening and staging of breast cancer. To minimize barriers to clinical translation, it is common to develop PAT systems based upon existing ultrasound hardware, which can entail significant design challenges in terms of light delivery. This often results in inherently non-uniform fluence within the tissue and should be accounted for during image reconstruction. Aim: We aim to integrate PAT into an automated breast ultrasound scanner with minimal change to the existing system. Approach: We designed and implemented an illuminator that directs spatially non-uniform light to the tissue near the acquisition plane of the imaging array. We developed a graphics processing unit-accelerated reconstruction method, which accounts for this illumination geometry by modeling the structure of the light in the sample. We quantified the performance of this system using a custom, modular photoacoustic phantom and graphite rods embedded in chicken breast tissue. Results: Our illuminator provides a fluence of 2.5 mJ cm −2 at the tissue surface, which was sufficient to attain a signal-to-noise ratio (SNR) of 8 dB at 2 cm in chicken breast tissue and image 0.25-mm features at depths of up to 3 cm in a medium with moderate optical scattering. Our reconstruction scheme is 200× faster than a CPU implementation; it provides a 25% increase in SNR at 2 cm in chicken breast tissue and lowers image error by an average of 31% at imaging depths >1.5 cm compared with a method that does not account for the inhomogeneity of the illumination or the transducer directivity. Conclusions: A fan-shaped illumination geometry is feasible for PAT; however, it is important to account for non-uniform fluence in illumination scenarios such as this. Future work will focus on increasing fluence and further optimizing the ultrasound hardware to improve SNR and overall image quality.

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Application of diffusion approximation in quantitative photoacoustic tomography in the presence of low-scattering regions

Cited by 7 publications

References 63 publications

Estimating absorption and scattering in quantitative photoacoustic tomography with an adaptive Monte Carlo method for light transport

Estimating absorption and scattering in quantitative photoacoustic tomography with an adaptive Monte Carlo method for light transport

Sequential model correction for nonlinear inverse problems

Integrating photoacoustic tomography into a multimodal automated breast ultrasound scanner

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