Hyperspectral wide-field time domain single-pixel diffuse optical tomography platform

: We present the design and comprehensive instrumental characterization of a time domain diffuse optical tomography (TD-DOT) platform based on wide-field illumination and wide-field hyperspectral time-resolved single-pixel detection for functional and molecular imaging in turbid media. The proposed platform combines two digital micro-mirror devices (DMDs) to generate structured light and a spectrally resolved multi-anode photomultiplier tube (PMT) detector in time domain for hyperspectral data acquisition over 16 wavelength channels based on the time-correlated single-photon counting (TCSPC) technique. The design of the proposed platform is described in detail and its characteristics in spatial, temporal and spectral dimensions are calibrated and presented. The performance of the system is further validated through a phantom study where two absorbers in glass tubes with spectral contrast are mapped in a turbid medium of ~20 mm thickness. The method presented here offers the potential of accelerating the imaging process and improving reconstruction results in TD-DOT and thus facilitates its wide spread use in preclinical and clinical in vivo imaging scenarios.


Introduction
Optical imaging is a powerful non-invasive tool to retrieve the distributions of exogenous fluorophores and/or endogenous chromophores in biological tissues. Especially, diffuse optical tomography (DOT) has found applications in numerous biomedical clinical and preclinical scenarios like breast cancer detection [1][2][3], functional brain imaging [4,5] and small animal imaging [6,7]. In addition, hybrid imaging systems that fuse DOT with other traditional medical imaging modalities [8][9][10] lead to complementary investigations of structural and functional information simultaneously or measurement cross-validations between different imaging modalities. However, the inherent ill-conditioned nature of DOT poses a great challenge to the performances of 3D reconstruction and renders it susceptible to noise and other modeling/instrumental uncertainties. Temporal modulation of light intensity, especially launching ultrashort mode-locking pulses in TD-DOT has proven to be a key factor to improve its performance. The abundant temporal information offered by time-resolved systems enables differentiating tissue absorption and scattering with minimal cross-talk [11,12] and sparse sampling of fluorescence contrast with improved accuracy [13] compared to its continuous wave (CW) counterparts. In addition, TD-DOT not only offers fluorescence lifetime as a robust and quantitative contrast for molecular unmixing but also presents improved resolution and reduced cross-talk in the 3D reconstruction of molecular information due to the combination of early-arriving photons and late-arriving highly diffused photons [14,15]. However, when there is need to acquire dense spatial, temporal and spectral hypercubes for optimal DOT performances, long data acquisition times are a limiting factor. [16,17] Fig. 7(c)). In addition, placing the D4110 NIR module on the detection side helps to make full use of its high transmission efficiency. The spectral resolution of the detector is independently characterized with a supercontinuum laser (WL-SC400-4, Fianium Inc, United Kingdom). An acousto-optic tunable filter (AOTF) (AOTF-V1-N2-DD, Fianium Inc, United Kingdom) is implemented to achieve an input spectrum of <2 nm FWHM. The spectrum at 700 nm is injected into the system and detected by the multi-anode detector. The output spectrum of the 16 spectral channels is interpolated and its FWHM is calculated to estimate the spectral resolution. The 1200 lines/mm grating in the spectrophotometer results in ~5.3 nm center wavelength distance between adjacent channels. The spectral resolution, in terms of FWHM, is estimated to be ~10 nm (see Fig. 7(d)). This spectral resolution is mainly determined by the blazed grating, slit width of the spectrograph and pixel size of the multi-anode PMT.

Optical inverse problem
In this work, a time-resolved mesh-based wide-field forward-adjoint Monte Carlo (aMC) method optimized for wide-field structured light strategies [22,23] is employed to compute the forward model and associated Jacobian matrix. We apply the Rytov approximation [24]  and Ω is the imaging volume. Suppose Ω is discretized into node N nodes and datasets are acquired with P source-detector pairs and T time gates. Then, the discretized distribution vector of k a λ δμ within Ω can be expressed as k λ x and retrieved by solving the inverse problem of the following equation:  and the inverse problem to retrieve the concentrations of L absorbers using measurements from P source-detector pairs, N wavelengths, and T time gates can be established as: denotes the weight matrix for the n th absorber at the k th wavelength and vector n Ω C is the absorber concentration over the whole volume. We adopted an optode calibration method [25] to suppress the artifacts induced by the fluctuations in source-detector coupling coefficients. In this method, coupling amplitude Thus Equation (6) can be updated as: where S W and D W represent the involvement of source and detector masks for each measurement using "1" (source or detector used for acquiring the measurements) and "0" (source or detector not used).
k k a λ λ μ x is the relative absorption perturbation to the background medium, so that the reconstructed vector becomes dimensionless and the dynamic range can be reduced. Vectors s and d are coupling coefficient vectors (independent of wavelength). Similarly, the forward problems described in Equation (8) and can be updated as: by stacking sensitivity matrices and updated measurements from different wavelengths. The measurements are updated based on Eq. (10) so that contributions from coupling coefficients to k λ b are removed and ˆk λ b only accounts for the contributions of absorbers. The 3D distributions of two absorbers are retrieved by inverting the forward problem described in Equation (11). In this study, L 1 -norm based regularization method [26] is implemented to solve the inverse problem. Information from both the early and late time gates are employed where reconstruction of early gate serves as the initial guess to the final reconstruction [13]. A liquid phantom study is conducted to validate the system performance for functional tomographic reconstruction in turbid media. Two water-soluble absorbers: India ink (Speedball Art Products, NC) and Epolight 2735 (Epolin Inc, NJ) are used to generate spectrally resolved absorption contrasts while intralipid (20% stock solution, Sigma-Aldrich, MO) is used to control the scattering property of the medium. An 80 × 50 × 22.5 mm 3 liquid phantom is prepared in a polycarbonate clear tank (see Fig. 8(a)). In the medium, the concentrations of India ink (volume concentration), Epolight 2735 (mass concentration), and Intralipid are set to 0.0024%, 0.0008%, and 0.8% respectively to generate optical properties of µ a = 0.15 cm −1 and µ s ' = 8.39 cm −1 at 740 nm. Two glass tubes (10.25 mm and 10.38 mm in diameter and 16 mm center-to-center distance) are suspended at 10 mm depth in the liquid medium. Intralipid concentration is set to 0.8% in both tubes to keep the scattering properties same as the medium. In the left tube, concentrations of Epolight 2735 and India ink are set to ~0.0034% and ~0.0024% to create 3.249 times of absorption perturbation from Epolight 2735. In the right tube, the concentration of Epolight 2735 and India ink are prepared as ~0.0008% and ~0.0092% to create 2.825 times of absorption perturbation from India ink. Figure 8(b) depicts the absorption coefficient trends of the absorber mixtures in the medium and the solutions added to the two tubes over the detection wavelength range. The extinction coefficients of the two absorbing materials are calibrated using Monte Carlo-based timeresolved spectroscopy [22]. Figure 8(c) shows the absorption coefficients of 0.0008% Epolight 2735 and 0.0024% India ink obtained from the calibration tests and a clear spectral contrast could be observed.  with the increase of spectral information in reconstruction. At the same time, the quantification accuracy of the reconstructed concentration ratio increases with spectral multiplexing. The estimation error of the relative concentration of the two absorbers reduces from 81.07% (using 2 wavelength channels for reconstruction) to 0.17% (using 12 wavelength channels for reconstruction).  Finally, the performance of the above method to retrieve absorber concentrations is compared with the method that performs linear decomposition at each node within the phantom volume. The results of using the reconstructed absorption maps at twelve wavelength channels with data of four time-gates to conduct linear decomposition is shown in Fig. 10(d). The result is highly compromised in terms of maximum crosstalk (51.78%) and relative quantification accuracy (reconstructed relative concentration ratio = 0.56 against ground truth = 0.38) compared to the result shown in Fig. 10(c). Linear decomposition at each node offers poor performance because it fails to exploit the correlations between nodes.

Discussion and conclusion
To sum up, we report on a detailed calibration of the proposed time-resolved DOT system based on wide-field structured illumination and hyperspectral single-pixel detection and validate the system performance with phantom studies. Spectral and spatial characteristics of two DMDs on illumination and detection sides show their abilities to project wide-field patterns over large area. By inputting patterns recorded during the calibration stage into our MC code, we are able to account for the non-uniformity during illumination and detection. The temporal calibration indicates that temporal resolution is not compromised by the widefield technique.
Using a supercontinuum fiber laser to perform hyperspectral excitation of the sample offers a spectral information boost within the same data acquisition time compared to monospectral excitation situations. Moreover, the hyperspectral wide-field single-pixel detection implementation facilitates fast collection and utilization of this abundant information. The benefits of the proposed method are also reflected by the reconstruction results where the maximum crosstalk and quantification accuracy of the relative concentration ratios retrieved through TD-DOT are improved with increasing the spectral information. Note that overall, the study reported herein is not optimized in terms of optical reconstructions strategies as well as acquisition speeds. The focus of this report is to provide a detailed characterization of the instrumental design and subcomponent of our hyperspectral dual-DMD setup which involves non-trivial elements. We opt to present the characterization of the system as usually done for time-resolved instruments with the addition of the spectral DMD characterization and validation in phantom experiments as typically done in the field. We expect overall that significant improvement in reconstructions can be achieved via more refined inverse problem methodologies, such as multimodal strategies. Similarly, we expect that significant reduction in acquisition speed can be achieved by optimizing the system or performing data postprocessing.
Indeed, the maximum photon counts allowed and data acquisition time of this study is limited by the 25 MHz repetition rate of the supercontinuum fiber laser to avoid pile-up effect during TCSPC data acquisition. Since supercontinuum fiber lasers with 80 MHz repetition rate are widely available in the market, the time needed to acquire these hyperspectral information-rich data sets could be significantly reduced to <20 min. Moreover, we have not investigated what is the required maximum photon counts in the acquired TPSF to allow for robust functional imaging. In the case of FMT, this photon counts can be reduced further, and hence, could lead to one order of magnitude in time of acquisition. Similarly, postprocessing methodologies such as gating could lead to improved photon counts without compromising the temporal information [27,28]. Moreover, the system is not fully optimized in the detection channel where we still have space for improving the transmission by replacing the inefficient components like fiber light guide and high f-number spectrograph. Furthermore, the optical masks we applied have proven to be robust and working well for in vivo imaging [29] but other sets of patterns can be considered [30,31]. For instance, we recently reported that a Hadamard base ranked by frequency provided the best results for 2D lifetime imaging when a single-pixel methodology was employed and in further studies, we will extend this work to tomographic imaging [32]. Last, one significant appeal of spatial light modulators is their ability to adaptively adjust illumination [21]. Such scheme is well suited to account for inhomogeneity inside biological tissue and complex geometries leading to large variation in dynamical range acquired when the animal is in a prone position as required for live preclinical studies.