Learned spectral decoloring enables photoacoustic oximetry

Abstract

The ability of photoacoustic imaging to measure functional tissue properties, such as blood oxygenation sO[Formula: see text], enables a wide variety of possible applications. sO[Formula: see text] can be computed from the ratio of oxyhemoglobin HbO[Formula: see text] and deoxyhemoglobin Hb, which can be distuinguished by multispectral photoacoustic imaging due to their distinct wavelength-dependent absorption. However, current methods for estimating sO[Formula: see text] yield inaccurate results in realistic settings, due to the unknown and wavelength-dependent influence of the light fluence on the signal. In this work, we propose learned spectral decoloring to enable blood oxygenation measurements to be inferred from multispectral photoacoustic imaging. The method computes sO[Formula: see text] pixel-wise, directly from initial pressure spectra [Formula: see text], which represent initial pressure values at a fixed spatial location [Formula: see text] over all recorded wavelengths [Formula: see text]. The method is compared to linear unmixing approaches, as well as pO[Formula: see text] and blood gas analysis reference measurements. Experimental results suggest that the proposed method is able to obtain sO[Formula: see text] estimates from multispectral photoacoustic measurements in silico, in vitro, and in vivo.

Figure 1

Overview of the methodology: first, numerous p${}_0$ spectra are extracted from optical forward simulations (a). These pixel-wise spectra are retrieved from the multi-wavelength simulation by evaluating the p${}_0$ intensity at a fixed pixel location as a function of wavelength (b). The data is then used to train a deep learning algorithm (c), which afterwards is able to estimate sO${}_2$ values on data that comprises the same wavelengths (d).

Figure 2

Schematic representation of the three in silico data sets. (a) shows the generic data set, (b) depicts the in silico flow phantom data set, and (c) visualizes the structures of the forearm data set. The vascular structures are simulated as tubes. The dark blue structures specifically correspond to veins.(a, c) were simulated with a digital twin of a custom PAI device based on the DiPhAs imaging system (Gröhl et al.), whereas (b) was simulated with a pencil beam as the illumination source.

Figure 3

Visualization of the network architecture used for this work. The hidden layer has a size of twice the input layer. The blue color represents a layer of the network, the black arrows correspond to a fully connected transition, where every neuron of the previous layer is connected to the next. Red and green represent leaky rectified linear units and dropout layers, respectively.

Figure 4

Stylized summary of the key findings of the experiments. The in silico experiments demonstrated the general feasibility of the LSD method, the in vitro experiments revealed the large dynamic range of the LSD estimates, and the in vivo experiments showed that the method yields more plausible estimates than LU even in complex situations.

Figure 5

In silico estimation results for the generic data set (a), the flow phantom data set (b), and the forearm data set (c). The scatter plot is colored with the ground truth oxygenation value. The violin plots show the estimated sO${}_2$ for the ground truth sO${}_2$ intervals in increments of 10%. As such, in addition to the scatter plot, there is one violin plot for all ground truth sO${}_2$ values in equidistant steps of 10%.

Figure 6

The mean oxygenation estimation results from three different measurement methods, shown over time on three different blood samples: (1) LSD in blue, (2) LU in red, and (3) pO${}_2$ reference measurement in green. The standard deviation of the estimations within the ROI for LU and LSD unmixing is shown around the mean estimate in the corresponding color. The graphs are shown for human blood samples (a) and (b) and for a rat blood sample (c).

Figure 7

Visualization of a cross-sectional view through the flow phantom rat blood data. The left plot (a) shows the spatial distribution of sO${}_2$ estimates in the beginning of the experiment (t = 0 min) and the right plot (b) towards the end of the experiment (t = 33.3 min). The rim-core differences in the sO${}_2$ estimates are more pronounced in LU when compared to LSD.

Figure 8

The results of LSD in vivo on an open porcine brain with a deep learning model trained on the generic tissue data set. The LSD results are compared to the LU results. The red rectangle shows an ROI which the LSD (blue) and LU (orange) results were computed on. The green crosses mark the time points and values of reference arterial blood gas analysis (BGA) measurements.

Figure 9

The results of LSD in vivo on the forearms of two healthy human volunteers. The LSD model was trained on the in silico forearm data set. The results were compared to the results for data analyzed with LU. The top row shows the PA signal at 800 nm, the second row shows the segmentation masks of the imaged vessels, the third row compares the LU and the LSD sO${}_2$ estimates, and the last row shows the mean MSOT signal spectrum for each of these vessels.