Miika Suhonen, Aki Pulkkinen, and Tanja Tarvainen, "Single-stage approach for estimating optical parameters in spectral quantitative photoacoustic tomography," J. Opt. Soc. Am. A 41, 527-542 (2024)
In quantitative photoacoustic tomography, the optical parameters of a target, most importantly the concentrations of chromophores such as deoxygenated and oxygenated hemoglobin, are estimated from photoacoustic data measured on the boundary of the target. In this work, a numerical approximation of a forward model for spectral quantitative photoacoustic tomography is constructed by utilizing the diffusion approximation for light propagation, the acoustic wave equation for ultrasound propagation, and spectral models of optical absorption and scattering to describe the wavelength dependence of the optical parameters. The related inverse problem is approached in the framework of Bayesian inverse problems. Concentrations of four chromophores (deoxygenated and oxygenated hemoglobin, water, and lipid), two scattering parameters (reference scattering and scattering power), and the Grüneisen parameter are estimated in a single-stage from photoacoustic data. The methodology is evaluated using numerical simulations in different full-view and limited-view imaging settings. The results show that, utilizing spectral data and models, the spectral optical parameters and the Grüneisen parameter can be simultaneously estimated. Furthermore, the approach can also be utilized in limited-view imaging situations.
Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.
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Parameters of the Prior Model for Concentrations of Four Chromophores, Two Scattering Parameters, and the Grüneisen Parametera
Mean Standard Deviation
Deoxygenated Hemoglobin
Oxygenated Hemoglobin
Water
Lipid
Reference Scattering
Scattering Power
Grüneisen Parameter
Soft tissue
4.0
12.0
0.15
0.55
1.673
1.058
0.496
3.406
4.258
0.078
0.104
0.773
0.758
0.304
Vascular target
122.2
244.3
0.30
0.33
1.675
1.050
0.425
122.2
244.3
0.10
0.33
0.336
0.259
0.180
Used in the solution of the inverse problem in simulations mimicking soft biological tissue and in simulations with a vascular target.
Table 3.
Relative Errors of the Estimated Concentrations of Four Chromophores, Reference Scattering, Scattering Power, and the Grüneisen Parameter in Full-View Imaging Geometries with a Soft Tissue Mimicking Targeta
Deoxygenated Hemoglobin
7.5
6.8
44.4
Oxygenated Hemoglobin
6.3
5.2
45.6
Water
6.9
5.1
48.0
Lipid
5.5
5.0
48.1
Reference Scattering
31.5
31.1
32.8
Scattering Power
58.4
63.0
60.2
Grüneisen Parameter
5.9
The columns for the different scenarios: the relative errors when all parameters were estimated ${\rm RE} (\%)$, the relative errors when the Grüneisen parameter $\gamma$ was assumed to be known ${{\rm RE}_{{\rm ref,1}}} (\%)$, and relative errors when Grüneisen parameter $\gamma$ was assumed to be a constant ${{\rm RE}_{{\rm ref,2}}} (\%)$. In the reference situations, notation ${(^*})$ refers to an error between the true parameter and the parameter used in the reconstructions.
Table 4.
Relative Errors of the Estimated Concentrations of Four Chromophores, Reference Scattering, Scattering Power, and the Grüneisen Parameter in Limited-View Imaging Geometriesa
Relative Errors of the Estimated Concentrations of Four Chromophores, Reference Scattering, Scattering Power, and the Grüneisen Parameter with a Vascular Target
Full-View
Limited-View
Deoxygenated Hemoglobin
32.6
50.0
Oxygenated Hemoglobin
35.0
54.0
Water
22.2
27.2
Lipid
17.1
28.6
Reference Scattering
21.5
20.9
Scattering Power
29.0
28.4
Grüneisen Parameter
20.0
26.5
Tables (5)
Table 1.
Absorption Spectra of Four Chromophores at Various Wavelengths
Parameters of the Prior Model for Concentrations of Four Chromophores, Two Scattering Parameters, and the Grüneisen Parametera
Mean Standard Deviation
Deoxygenated Hemoglobin
Oxygenated Hemoglobin
Water
Lipid
Reference Scattering
Scattering Power
Grüneisen Parameter
Soft tissue
4.0
12.0
0.15
0.55
1.673
1.058
0.496
3.406
4.258
0.078
0.104
0.773
0.758
0.304
Vascular target
122.2
244.3
0.30
0.33
1.675
1.050
0.425
122.2
244.3
0.10
0.33
0.336
0.259
0.180
Used in the solution of the inverse problem in simulations mimicking soft biological tissue and in simulations with a vascular target.
Table 3.
Relative Errors of the Estimated Concentrations of Four Chromophores, Reference Scattering, Scattering Power, and the Grüneisen Parameter in Full-View Imaging Geometries with a Soft Tissue Mimicking Targeta
Deoxygenated Hemoglobin
7.5
6.8
44.4
Oxygenated Hemoglobin
6.3
5.2
45.6
Water
6.9
5.1
48.0
Lipid
5.5
5.0
48.1
Reference Scattering
31.5
31.1
32.8
Scattering Power
58.4
63.0
60.2
Grüneisen Parameter
5.9
The columns for the different scenarios: the relative errors when all parameters were estimated ${\rm RE} (\%)$, the relative errors when the Grüneisen parameter $\gamma$ was assumed to be known ${{\rm RE}_{{\rm ref,1}}} (\%)$, and relative errors when Grüneisen parameter $\gamma$ was assumed to be a constant ${{\rm RE}_{{\rm ref,2}}} (\%)$. In the reference situations, notation ${(^*})$ refers to an error between the true parameter and the parameter used in the reconstructions.
Table 4.
Relative Errors of the Estimated Concentrations of Four Chromophores, Reference Scattering, Scattering Power, and the Grüneisen Parameter in Limited-View Imaging Geometriesa
Relative Errors of the Estimated Concentrations of Four Chromophores, Reference Scattering, Scattering Power, and the Grüneisen Parameter with a Vascular Target
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