Reliability assessment for blood oxygen saturation levels measured with optoacoustic imaging.

SIGNIFICANCE
Quantitative optoacoustic (OA) imaging has the potential to provide blood oxygen saturation (SO2) estimates due to the proportionality between the measured signal and the blood's absorption coefficient. However, due to the wavelength-dependent attenuation of light in tissue, a spectral correction of the OA signals is required, and a prime challenge is the validation of both the optical characterization of the tissue and the SO2.


AIM
We propose to assess the reliability of SO2 levels retrieved from spectral fitting by measuring the similarity of OA spectra to the fitted blood absorption spectra.


APPROACH
We introduce a metric that quantifies the trends of blood spectra by assigning a pair of spectral slopes to each spectrum. The applicability of the metric is illustrated with in vivo measurements on a human forearm.


RESULTS
We show that physiologically sound SO2 values do not necessarily imply a successful spectral correction and demonstrate how the metric can be used to distinguish SO2 values that are trustworthy from unreliable ones.


CONCLUSIONS
The metric is independent of the methods used for the OA data acquisition, image reconstruction, and spectral correction, thus it can be readily combined with existing approaches, in order to monitor the accuracy of quantitative OA imaging.

Here, z is the depth of the detection point r and d is the distance between the detection point and the illumination source.
For the MIS analysis in this study, the detection point r can be identified with the position (x c ij , z c ij ) of the vessel, see Sec. 2.2 of the main text. Following this nomenclature, the depth equals z c ij , for irradiation position x i and wavelength λ j , and the distance between detection point and illumination source is d ij = (x c ij − x i ) 2 + (y 0 ) 2 + (z c ij ) 2 . For our analysis, we neglected variations in the vessel position within a data set acquired at the same wavelength (i.e., assumed the position of the vessel center to be (x c 1j , z c 1j ) for all irradiation positions), since they were observed to be much smaller than variations in position between different wavelengths.
For every irradiation position x i and wavelength λ j , we determined the mean amplitude S ij of the vessel's OA signal by averaging the pixel values in the OA image S ij (r) over the respective support. In case of a homogeneous medium, it would be sufficient to perform a single fit of the analytical fluence model (Eq. (1)) to the amplitudes S ij determined for different d ij in order to retrieve µ eff (see Ref. 24). However, the envisaged purpose of the semi-empirical model was, as described in Ref. 23, the optical characterization of tissue in situations where the analytical diffusion approximation for a semi-infinite medium fails at accurately modeling the fluence. In particular, the model was designed to account for the fact that the diffusion approximation is expected to break down when the light propagation is influenced by boundaries or optical heterogeneities/by shadowing due to absorbing structures. Therefore, instead of simply fitting Eq. (1) to all S ij , a different procedure was carried out: The slope m ijk of log( S ij d 3 ij ) was determined for every d ij , by fitting a first-order polynomial to the data points around d ij , taking into account k points in total. This procedure was repeated for different k ranging from 2 to N , the total number of irradiation positions. Illustrations of the segmented OA signal and the fitting procedure are shown in Fig. 1 (a) and (b), respectively. For each slope m ijk , µ eff,ijk was calculated by inverting the first-order term m of the Taylor expansion of the diffusion approximation 1 and setting m to m ijk , and d to the center of the d ij of the k data points taken into account for the respective fit. We then performed a statistical analysis of µ eff,ijk realizations, assuming that the most frequently occurring effective attenuation coefficient optically characterizes a quasihomogeneous tissue segment. For each wavelength λ j , we histogrammed all µ eff,ijk values and determined µ eff,j of the tissue segment as the peak position of a Gaussian fitted to the histogrammed µ eff,ijk (see inset in Fig. 1 (b)). The standard deviation of the Gaussian was taken as a measure for the uncertainty of µ eff,j . In comparison to the method described in Ref. 23, the analysis has been extended by an additional step: we identified the set of irradiation positions corresponding to a tissue segment for which the diffusion approximation is valid. An irradiation position x i was considered to belong to this set if the absolute difference between µ eff,j and the µ eff,ijk was smaller than the uncertainty of µ eff,j for all wavelengths λ j . Spectral correction was performed only for these irradiation positions. With µ eff,j , we analytically calculated the fluences Φ ij (r) for all λ j and the identified x i , based on the diffusion approximation for semi-infinite media (Eq. (1)), with the pixel resolution of the OA images, and performed a spectral correction by pixelwise dividing the OA image S ij (r) by the corresponding fluence Φ ij (r).

Results
Figure 2 (a) and (b) display histograms of realizations of µ eff,ijk for all d ij and window sizes k, together with the best fits of Gaussian distributions to the data, for both the artery and the vein. It was observed that the influence of the choice of bin size for the histograms on the peak positions of the Gaussians is negligible compared to their widths. The spectra of the effective attenuation coefficient µ eff,j are given in Fig. 2 (c), for the tissue segments between the irradiation positions on the forearm surface and the artery and the vein, respectively. It can be seen that both the absolute   Fig. 1 (b)), together with the Gaussian fit (black line), for the artery and the vein, respectively. The peak position of the Gaussian determines µ eff,j . (c) µ eff spectra estimated for the tissue segments between the forearm surface and the artery (red) and the vein (blue), error bars represent the standard deviations of the Gaussian distributions fitted to the histograms. A video showing the figure parts (a) and (b) for all λ j is available (Video S1 MPEG, 5.3 MB).
ij as a function of the source-detector distance d ij (black circles), together with Φ ij d 3 ij (red line), shown in a logarithmic plot, for the artery (left) and the vein (right). For better visual comparison, S ij d 3 ij and Φ ij d 3 ij were normalized to their respective mean value. Note that, for the vein, we observed a lower signal-to-noise ratio than for the artery and thus discarded data points for i ≥ 18. The gray band corresponds to the set of irradiation positions for which the absolute difference between µ eff,j and the µ eff,ijk was smaller than the uncertainty of µ eff,j for the respective wavelength. The overlap of the sets identified for all wavelengths, defining the optically quasihomogeneous tissue region, is indicated in blue. A video showing the figure for all λ j is available (Video S2, MPEG, 5.6 MB).
values of µ eff,j as well as the trends of the spectra differ between the two vessels. These differences could possibly be explained by the fact that the tissue segment probed when analyzing signals stemming from the artery has different optical properties than that probed in the case of the vein. Figure 3 illustrates the data points S ij d 3 ij together with Φ ij d 3 ij (where Φ ij denotes the fluence at the position of the vessel) and visualizes the range of source-detector distances d ij defining the optically quasihomogeneous tissue region where the light propagation can be described based on Eq. (1), for both the artery and the vein. For the artery, the measured OA data and the fluence model agree very well for the identified region, whereas the agreement is lower for the vein, presumably, as mentioned in the main text, due to a stronger influence of the boundary (skin surface) and the stronger inhomogeneity of the probed tissue segment. The very good agreement for the artery confirms our h ypothesis: despite the presence of heterogeneities in the forearm, there exist tissue regions for which the simple analytical diffusion approximation can be used to model the light propagation.