Accurate estimation of the relative concentrations of chromophores in a spectroscopic photoacoustic (sPA) image can reveal immense structural, functional, and molecular information about physiological processes. However, due to nonlinearities and ill-posedness inherent to sPA imaging, concentration estimation is intractable. The Spectroscopic Photoacoustic Optical Inversion Autoencoder (SPOI-AE) aims to address the sPA optical inversion and spectral unmixing problems without assuming linearity. Herein, SPOI-AE was trained and tested on \textit{in vivo} mouse lymph node sPA images with unknown ground truth chromophore concentrations. SPOI-AE better reconstructs input sPA pixels than conventional algorithms while providing biologically coherent estimates for optical parameters, chromophore concentrations, and the percent oxygen saturation of tissue. SPOI-AE's unmixing accuracy was validated using a simulated mouse lymph node phantom ground truth.
Spectroscopic Photoacoustic (sPA) imaging is a powerful medical imaging modality capable of revealing physiological information at centimeter depth with high spatial resolution [1]- [3]. The contrast in a sPA image is derived from the presence of absorbing species, which can be either endogenous to the tissue or exogenous [4]. Quantifying the relative concentrations of endogenous or exogenous chromophores allows for clinical insights to be gleaned [5]. By determining the relative concentrations of oxygenated hemoglobin (HbO2) and deoxygenated hemoglobin (HHb), a spatial map of oxygen saturation (SO2) in tissue can be found. Computing such an SO2 map can, for example, track hypoxia in vasculature to identify malignant tumors [6], visualize the functional parameters of traumatic brain injuries, and study neuronal activities [7].
To calculate an SO2 map correctly, it is vital that the relative concentrations of HbO2 and HHb are estimated accurately. Oxygen saturation estimates must be accurate since even small errors can confound diagnoses [8]. In the case of identifying malignant tumors based on the oxygen saturation of vasculature, the difference between normal and abnormal SO2 values can be as little as 10 percent [9], [10]. Moreover, the difference between normoxia and hyperoxia in rat cerebral vasculature can be as little as nine percent [7]. Improved SO2 estimation can allow for more effective imaging of skin [11], [12], breast tissue, and the brain [13].
Based on these considerations, it is paramount that the relative chromophore concentration estimation algorithm-also known as the spectral unmixing algorithm-yields accurate results. The approaches discussed herein can be separated into two categories: linear and nonlinear. Linear spectral unmixing algorithms assume that a sPA image is a linear combination of chromophore concentrations [14]. Conversely, nonlinear algorithms try to compensate for wavelength-dependant fluence attenuation and optical scattering [15].
The linear unmixing algorithms explored herein are nonnegative-least-squares (NLS) and nonnegative-matrixfactorization (NMF). NLS spectral unmixing uses pure chromophore absorption spectra taken from literature to estimate relative absorption concentrations and is widely used thanks to its straightforward implementation [16]. NMF spectral unmixing, unlike NLS, leverages a data-driven mechanism to better describe sPA data [17]. There are other data-driven linear spectral unmixing algorithms available, notably principal-component-analysis and independentcomponent-analysis [18]. However, it was shown in [19] that NMF outperforms the alternative data-driven methods when unmixing sPA images, especially in tissues with high background absorption.
There are many nonlinear spectral unmixing approaches designed to better estimate relative chromophore concentrations. Some nonlinear approaches leverage simplifying assumptions to estimate the optical fluence of tissue. One notable example of such an algorithm is eigenspectra-multispectraloptoacoustic-tomography (eMSOT) [20]. The eMSOT method assumes that optical fluence can be estimated by a linear combination of so-called eigenspectra extracted using a principalcomponent analysis of simulated fluence spectra.
However, most nonlinear spectral unmixing approaches opt to leverage machine learning and neural networks. Several approaches estimate SO2 directly rather than spectrally unmixing first. The learned-spectral-decoloring (LSD) method and convolutional-encoder-decoder-with-skip-connections (EDS) both accurately estimate the oxygen saturation of in silico sPA images [21], [22]. The EDS method also uses 3Dconvolutional-neural-networks (3D-CNNs) to incorporate spatial relationships into the estimation mechanism.
Another approach using CNNs is the quantitativeoptoacoustic-tomography-network (QOAT-Net) [23]. QOAT-Net uses parallel U-Nets to estimate the optical fluence and absorption coefficients of a photoacoustic (PA) image. Similarly to the aforementioned machine learning unmixing methods, QOAT-Net was trained using in silico PA images with known fluence and absorption. However, the QOAT-Net project made use of a generative-adverserial-network (GAN) to modify in silico images so that those images were indiscriminable from in vivo ones. This allowed for QOAT-Net to be trained fullysupervised while better fitting in vivo sPA images.
It is also possible to design a machine-learning based spectral unmixing method trained on labeled phantom images. In [24], a U-Net (called “DL-Exp”) was used to estimate absorption coefficients from spectroscopic photoacoustic images. DL-Exp was trained on sPA images of well-characterized mineral oil phantoms with varied nigrosin concentrations to set absorption properties and titanium oxide concentrations to set scattering properties. By carefully measuring the optical properties of the phantoms used for training, DL-Exp can estimate the absorption coefficients as well
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