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Optoacoustic inversion via convolution kernel reconstruction in the paraxial approximation and beyond.

ABSTRACT: In this article we address the numeric inversion of optoacoustic signals to initial stress profiles. Therefore we study a Volterra integral equation of the second kind that describes the shape transformation of propagating stress waves in the paraxial approximation of the underlying wave-equation. Expanding the optoacoustic convolution kernel in terms of a Fourier-series, a best fit to a pair of observed near-field and far-field signals allows to obtain a sequence of expansion coefficients that describe a given "apparative" setup. The resulting effective kernel is used to solve the optoacoustic source reconstruction problem using a Picard-Lindelöf correction scheme. We verify the validity of the proposed inversion protocol for synthetic input signals and explore the feasibility of our approach to also account for the shape transformation of signals beyond the paraxial approximation including the inversion of experimental data stemming from measurements on melanin doped PVA hydrogel tissue phantoms.

SUBMITTER: Melchert O

PROVIDER: S-EPMC6257913 | biostudies-literature | 2019 Mar

REPOSITORIES: biostudies-literature

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Optoacoustic inversion via convolution kernel reconstruction in the paraxial approximation and beyond.

Melchert O O Wollweber M M Roth B B

Photoacoustics 20181105

In this article we address the numeric inversion of optoacoustic signals to initial stress profiles. Therefore we study a Volterra integral equation of the second kind that describes the shape transformation of propagating stress waves in the paraxial approximation of the underlying wave-equation. Expanding the optoacoustic convolution kernel in terms of a Fourier-series, a best fit to a pair of observed near-field and far-field signals allows to obtain a sequence of expansion coefficients that ...[more]

PMID: 30510898

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Project description:Several simplifications used in clinical implementations of the convolution∕superposition (C∕S) method, specifically, density scaling of water kernels for heterogeneous media and use of a single polyenergetic kernel, lead to dose calculation inaccuracies. Although these weaknesses of the C∕S method are known, it is not well known which of these simplifications has the largest effect on dose calculation accuracy in clinical situations. The purpose of this study was to generate and characterize high-resolution, polyenergetic, and material-specific energy deposition kernels (EDKs), as well as to investigate the dosimetric impact of implementing spatially variant polyenergetic and material-specific kernels in a collapsed cone C∕S algorithm.High-resolution, monoenergetic water EDKs and various material-specific EDKs were simulated using the EGSnrc Monte Carlo code. Polyenergetic kernels, reflecting the primary spectrum of a clinical 6 MV photon beam at different locations in a water phantom, were calculated for different depths, field sizes, and off-axis distances. To investigate the dosimetric impact of implementing spatially variant polyenergetic kernels, depth dose curves in water were calculated using two different implementations of the collapsed cone C∕S method. The first method uses a single polyenergetic kernel, while the second method fully takes into account spectral changes in the convolution calculation. To investigate the dosimetric impact of implementing material-specific kernels, depth dose curves were calculated for a simplified titanium implant geometry using both a traditional C∕S implementation that performs density scaling of water kernels and a novel implementation using material-specific kernels.For our high-resolution kernels, we found good agreement with the Mackie et al. kernels, with some differences near the interaction site for low photon energies (<500 keV). For our spatially variant polyenergetic kernels, we found that depth was the most dominant factor affecting the pattern of energy deposition; however, the effects of field size and off-axis distance were not negligible. For the material-specific kernels, we found that as the density of the material increased, more energy was deposited laterally by charged particles, as opposed to in the forward direction. Thus, density scaling of water kernels becomes a worse approximation as the density and the effective atomic number of the material differ more from water. Implementation of spatially variant, polyenergetic kernels increased the percent depth dose value at 25 cm depth by 2.1%-5.8% depending on the field size, while implementation of titanium kernels gave 4.9% higher dose upstream of the metal cavity (i.e., higher backscatter dose) and 8.2% lower dose downstream of the cavity.Of the various kernel refinements investigated, inclusion of depth-dependent and metal-specific kernels into the C∕S method has the greatest potential to improve dose calculation accuracy. Implementation of spatially variant polyenergetic kernels resulted in a harder depth dose curve and thus has the potential to affect beam modeling parameters obtained in the commissioning process. For metal implants, the C∕S algorithms generally underestimate the dose upstream and overestimate the dose downstream of the implant. Implementation of a metal-specific kernel mitigated both of these errors.

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Optoacoustic inversion via convolution kernel reconstruction in the paraxial approximation and beyond.

Publications

Optoacoustic inversion via convolution kernel reconstruction in the paraxial approximation and beyond.

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