Quantitative PA tomography of high resolution 3-D images: Experimental validation in a tissue phantom

Abstract

Quantitative photoacoustic tomography aims to recover the spatial distribution of absolute chromophore concentrations and their ratios from deep tissue, high-resolution images. In this study, a model-based inversion scheme based on a Monte-Carlo light transport model is experimentally validated on 3-D multispectral images of a tissue phantom acquired using an all-optical scanner with a planar detection geometry. A calibrated absorber allowed scaling of the measured data during the inversion, while an acoustic correction method was employed to compensate the effects of limited view detection. Chromophore- and fluence-dependent step sizes and Adam optimization were implemented to achieve rapid convergence. High resolution 3-D maps of absolute concentrations and their ratios were recovered with high accuracy. Potential applications of this method include quantitative functional and molecular photoacoustic tomography of deep tissue in preclinical and clinical studies.

Keywords: Blood oxygen saturation; Inverse problem; Model based inversion; Monte Carlo; Quantitative photoacoustic imaging; Spectral unmixing.

Fig. 1

Schematic of the experimental setup. Excitation pulses were generated by a wavelength-tunable OPO laser, the output of which was fiber-coupled to homogenize the beam. The output of the distal end of the fiber was collimated and directed through the FP sensor using a dichroic mirror.

Fig. 2

Absorption spectra of aqueous stock solutions of NiSO₄ (green) and CuSO₄ (blue) with concentrations of 1.54 and 0.28 M, respectively. Black crosses indicate the measured reduced scattering coefficient of diluted whole milk, the black line shows the exponential fit to the data.

Fig. 3

3-D rendered structure of the phantom obtained using manual image segmentation of the PA images. The color of the tubes indicates the relative concentrations, i.e. green indicates $c_{{\mathrm{NiSO}}_4}$, blue indicates $c_{{\mathrm{CuSO}}_4}$. The illumination beam profile of the excitation pulses is shown in the x–y-plane.

Fig. 4

Cross-sectional x–z-images (y = 8 mm) of the tissue phantom at an excitation wavelength of 721 nm. (A) Original image and (B) after applying the limited view correction (Section 2.3.1).

Fig. 5

Cross-sectional x–z-images (y = 8 mm) of the true and recovered chromophore concentrations. (A) and (D) True $c_{{\mathrm{NiSO}}_4}$ and $c_{{\mathrm{CuSO}}_4}$, respectively. (B) and (E) $c_{{\mathrm{NiSO}}_4}$ and $c_{{\mathrm{CuSO}}_4}$ recovered from uncorrected images. (C) and (F) $c_{{\mathrm{NiSO}}_4}$ and $c_{{\mathrm{CuSO}}_4}$ recovered from corrected images.

Fig. 6

Depth profile of the true and recovered 3-D maps of $c_{{\mathrm{NiSO}}_4}$ (A) and $c_{{\mathrm{CuSO}}_4}$ (B) along the dashed line indicated in the inset of (A). Inset of (A) x–z-slice of the true $c_{{\mathrm{CuSO}}_4}$ distribution (see Fig. 5D). (C) cross-sectional x–y-image of the initial pressure distribution at depth of z = 4.2 mm (λ = 726 nm). The initial pressure along the dashed line is shown in (D), which also shows the chromophore concentrations recovered from original and corrected image data sets. The solid, dotted and dashed lines indicate the true values, those recovered from original images, and those recovered from corrected images, respectively. $c_{{\mathrm{NiSO}}_4}$ is shown in green and $c_{{\mathrm{CuSO}}_4}$ in blue. The red solid line illustrates the initial pressure distribution (original image data set).

Fig. 7

Chromophore ratio R calculated from the recovered $c_{{\mathrm{NiSO}}_4}$ and $c_{{\mathrm{CuSO}}_4}$ maps. (A) Cross-sectional x–z-image of the recovered concentration ratio R, (B) recovered R, background subvolume is masked and rendered in gray, (C) true concentration ratios. Gray indicates areas where R is not defined, i.e. $c_{{\mathrm{NiSO}}_4}=c_{{\mathrm{CuSO}}_4}=0$ M. (D) Profiles of R (cross-sectional average) along the length of the nine tubes. True values are represented by dashed lines, recovered values by dotted lines.