Time-domain Diffuse Optical Tomography Research Articles

An Integrated-Circuit Node for High-Spatiotemporal Resolution Time-Domain Near-Infrared Diffuse Optical Tomography Imaging Arrays

Next-generation brain–computer interfaces (BCIs) for healthy individuals are expected to largely rely on noninvasive functional imaging methods to record cortex-wide neural activity because of the risk associated with surgically implanted devices. In this work, we present a fully integrated 1.8 × 1.8 mm single chip that can be arrayed on a wearable patch to perform noninvasive, functional brain imaging over large cortical areas. This chip node contains two bonded vertical-cavity surface-emitting lasers (VCSELs), an 8 × 8 single-photon avalanche diode (SPAD) array with event-driven time-to-digital converters (TDCs) per row, and a digital back-end for on-chip histogramming and time-gating. We achieved 70-ps resolution for time-of-flight (ToF) imaging at the record-high 100-MHz laser repetition rate with 80-mW total power. We showed that time-gating improves the imaging contrast by as much as 36% using a brain-skull phantom. The fully integrated and compact node presented here is the key enabler for future high-spatiotemporal-resolution time-domain diffuse optical tomography (TD-DOT) imaging arrays.

High-Speed Time-Domain Diffuse Optical Tomography with a Sensitivity Equation-based Neural Network.

Steady progress in time-domain diffuse optical tomography (TD-DOT) technology is allowing for the first time the design of low-cost, compact, and high-performance systems, thus promising more widespread clinical TD-DOT use, such as for recording brain tissue hemodynamics. TD-DOT is known to provide more accurate values of optical properties and physiological parameters compared to its frequency-domain or steady-state counterparts. However, achieving high temporal resolution is still difficult, as solving the inverse problem is computationally demanding, leading to relatively long reconstruction times. The runtime is further compromised by processes that involve 'nontrivial' empirical tuning of reconstruction parameters, which increases complexity and inefficiency. To address these challenges, we present a new reconstruction algorithm that combines a deep-learning approach with our previously introduced sensitivity-equation-based, non-iterative sparse optical reconstruction (SENSOR) code. The new algorithm (called SENSOR-NET) unfolds the iterations of SENSOR into a deep neural network. In this way, we achieve high-resolution sparse reconstruction using only learned parameters, thus eliminating the need to tune parameters prior to reconstruction empirically. Furthermore, once trained, the reconstruction time is not dependent on the number of sources or wavelengths used. We validate our method with numerical and experimental data and show that accurate reconstructions with 1 mm spatial resolution can be obtained in under 20 milliseconds regardless of the number of sources used in the setup. This opens the door for real-time brain monitoring and other high-speed DOT applications.

Combined multi-scale mesh and full-matrix inversion for enhancing time-domain breast diffuse optical tomography.

Time-domain diffuse optical tomography can efficiently reconstruct both absorption and reduced scattering coefficients but is heavily limited by the ill-posedness in its inverse problem and low spatial resolution. To deal with these adversities, the truncated singular value decomposition (TSVD)-based whole-weighting-matrix inversion scheme can be a particularly suitable implementation. Unfortunately, TSVD is subject to a storage challenge for three-dimensional imaging of a bulk region, such as breast. In this paper, a multi-scale mesh strategy based on computed tomography (CT) anatomical geometry is adopted to solve the storage challenge, where a fine mesh is used in forward calculation to ensure accuracy, and a coarse mesh in the inversion process to enable TSVD-based inversion of the whole-weighting matrix. We validate the proposed strategy using simulated data for a single lesion model from clinical positron emission tomography images of a breast cancer patient, and further, for a complex model that is constructed by setting dual lesions at different separations in the CT breast geometry.

Evaluation of temporal moments and Fourier transformed data in time-domain diffuse optical tomography.

Time-domain diffuse optical tomography (TD-DOT) uses near-infrared pulsed lasers as light sources to measure time-varying exitance on the boundary of the target. These are used to estimate optical properties of the imaged target. Several integral-transform-based moments of the time-resolved data have been utilized in TD-DOT, the most common being the mean time of flight and variance. Recently, it has been shown that Fourier transforming the time-domain data to frequency domain enables utilization of these data at one or several frequencies, producing equally as good estimates as the whole time-domain data. In this work, we present a systematic comparison of the usage of the temporal moments and Fourier transformed data in TD-DOT. Both absolute and difference imaging are evaluated using numerical simulations. The simulations show that utilizing temporal moments and Fourier transformed data in TD-DOT provides good quality reconstructions with a good estimation accuracy. These estimates are improved if more than one data type is used. Furthermore, the simulations show that the frequency-domain computations enable computationally cheaper and straightforward implementation of the inverse solver when compared to the temporal moments.

Real-Time Dual-Wavelength Time-Resolved Diffuse Optical Tomography System for Functional Brain Imaging Based on Probe-Hosted Silicon Photomultipliers.

Near-infrared diffuse optical tomography is a non-invasive photonics-based imaging technology suited to functional brain imaging applications. Recent developments have proved that it is possible to build a compact time-domain diffuse optical tomography system based on silicon photomultipliers (SiPM) detectors. The system presented in this paper was equipped with the same eight SiPM probe-hosted detectors, but was upgraded with six injection fibers to shine the sample at several points. Moreover, an automatic switch was included enabling a complete measurement to be performed in less than one second. Further, the system was provided with a dual-wavelength (670 and 820 ) light source to quantify the oxy- and deoxy-hemoglobin concentration evolution in the tissue. This novel system was challenged against a solid phantom experiment, and two in-vivo tests, namely arm occlusion and motor cortex brain activation. The results show that the tomographic system makes it possible to follow the evolution of brain activation over time with a 1-resolution.

Time-domain diffuse optical tomography utilizing truncated Fourier series approximation.

Diffuse optical tomography (DOT) uses near infrared light for in vivo imaging of spatially varying optical parameters in biological tissues. It is known that time-resolved measurements provide the richest information on soft tissues, among other measurement types in DOT such as steady-state and intensity-modulated measurements. Therefore, several integral-transform-based moments of the time-resolved DOT measurements have been considered to estimate spatially distributed optical parameters. However, the use of such moments can result in low-contrast images and cross-talks between the reconstructed optical parameters, limiting their accuracy. In this work, we propose to utilize a truncated Fourier series approximation in time-resolved DOT. Using this approximation, we obtained optical parameter estimates with accuracy comparable to using whole time-resolved data that uses low computational time and resources. The truncated Fourier series approximation based estimates also displayed good contrast and minimal parameter cross-talk, and the estimates further improved in accuracy when multiple Fourier frequencies were used.

Multi Simulation Platform for Time Domain Diffuse Optical Tomography: An Application to a Compact Hand-Held Reflectance Probe

Time Domain Diffuse Optical Tomography (TD-DOT) enables a full 3D reconstruction of the optical properties of tissue, and could be used for non-invasive and cost-effective in-depth body exploration (e.g., thyroid and breast imaging). Performance quantification is crucial for comparing results coming from different implementations of this technique. A general-purpose simulation platform for TD-DOT clinical systems was developed with a focus on performance assessment through meaningful figures of merit. The platform was employed for assessing the feasibility and characterizing a compact hand-held probe for breast imaging and characterization in reflectance geometry. Important parameters such as hardware gating of the detector, photon count rate and inclusion position were investigated. Results indicate a reduced error (<10%) on the absorption coefficient quantification of a simulated inclusion up to 2-cm depth if a photon count rate ≥ 106 counts per second is used along with a good localization (error < 1 mm down to 25 mm-depth).

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.

Time-Domain Functional Diffuse Optical Tomography System Based on Fiber-Free Silicon Photomultipliers

Based on recent developments in both single-photon detectors and timing electronic circuits, we designed a compact and cost effective time-domain diffuse optical tomography system operated at 1 Hz acquisition rate, based on eight silicon photomultipliers and an 8-channel time-to-digital converter. The compact detectors are directly hosted on the probe in a circular arrangement around a single light injection fiber, so to maximize light harvesting. Tomography is achieved exploiting the depth sensitivity that is encoded in the arrival time of detected photons. The system performances were evaluated on simulations to assess possible the limitations arising from the use of a single injection point, and then on phantoms and in vivo to prove the eligibility of these technologies for diffuse optical tomography.

A Low-Cost Time-Correlated Single Photon Counting System for Multiview Time-Domain Diffuse Optical Tomography

Diffuse optical tomography resorting to time-domain measurements (TD-DOT) provides information-rich data that have not yet been fully exploited for image reconstruction, notably to increase imaging spatial resolution. Current TD-DOT scanners suffer from a very low sensitivity owing to their small number of detection channels. This leads to excessively long acquisition times for in vivo imaging. To obtain a higher number of detection channels, thus increasing detection density, a low-cost time-correlated single photon counting (TCSPC) system dedicated to TD-DOT was designed, resorting solely to off-the-shelf electronic components to reduce costs, in distinction to custom application-specific integrated circuit solutions. The system features four input channels, each of them including a leading-edge discriminator for direct interfacing with off-the-shelf photodetector modules and a programmable delay line to compensate for undesired propagation delays, thus also avoiding manual adjustment of cable lengths. The system supports a large number of TCSPC channels using a daisy-chain configuration through an onboard Ethernet switch. It also features a 13.02 ps bin width with a 12.5 ns dynamic range. Results show excellent linearity, with a $\sigma _{\mathrm{ DNL}}$ of 1.7% least significant bit (LSB), peak differential nonlinearity of 5% LSB, and peak integral nonlinearity of 10% LSB and an average accuracy of 19 ps full-width at half-maximum (FWHM) throughout two separate four-channel systems. The system was tested in a TD-DOT acquisition setup, and 37 ps FWHM instrument response functions were obtained using a single-photon avalanche diode (SPAD) detector. Diffuse intrinsic measurements were also acquired and compared with a reference TCSPC system showing similar results.

Chromophore decomposition in multispectral time-resolved diffuse optical tomography.

Multicomponent phantom measurements are carried out to evaluate the ability of multispectral time domain diffuse optical tomography in reflectance geometry to quantify the position and the composition of small heterogeneities at depths of 1-1.5 cm in turbid media. Time-resolved data were analyzed with the Mellin-Laplace transform. Results show good localization and correct composition gradation of objects but still a lack of absolute material composition accuracy when no a priori geometry information is known.

Increasing the collection efficiency of time-correlated single-photon counting with single-photon avalanche diodes using immersion lenses.

Single-photon avalanche diodes (SPADs) achieving high timing resolution (≈20-50 ps) developed for time-correlated single-photon counting (TCSPC) generally have very small photosensitive areas (25-100 μm in diameter). This limits the achievable photon counting rate and signal-to-noise ratio and may lead to long counting times. This is detrimental in applications requiring several measurements, such as fluorescence lifetime imaging (FLIM) microscopy, which requires scanning, and time-domain diffuse optical tomography (TD-DOT). We show in this work that the use of an immersion lens directly affixed onto the photosensitive area of the SPAD helps alleviate this problem by allowing more light to be concentrated onto the detector. Following careful optical design and simulations, our experimental results show that it is actually possible to achieve the predicted theoretical increase in the photon counting rate (we achieve a factor of ≈4 here). This work is of high relevance in high timing resolution TCSPC with small photosensitive area detectors and should find widespread interest in FLIM and TD-DOT with SPADs.

Time-domain diffuse optical tomography using silicon photomultipliers: feasibility study.

Silicon photomultipliers (SiPMs) have been very recently introduced as the most promising detectors in the field of diffuse optics, in particular due to the inherent low cost and large active area. We also demonstrate the suitability of SiPMs for time-domain diffuse optical tomography (DOT). The study is based on both simulations and experimental measurements. Results clearly show excellent performances in terms of spatial localization of an absorbing perturbation, thus opening the way to the use of SiPMs for DOT, with the possibility to conceive a new generation of low-cost and reliable multichannel tomographic systems.

Quantification in time-domain diffuse optical tomography using Mellin-Laplace transforms.

Simulations and phantom measurements are used to evaluate the ability of time-domain diffuse optical tomography using Mellin-Laplace transforms to quantify the absorption perturbation of centimetric objects immersed at depth 1-2 cm in turbid media. We find that the estimated absorption coefficient varies almost linearly with the absorption change in the range of 0-0.15 cm-1 but is underestimated by a factor that depends on the inclusion depth (~2, 3 and 6 for depths of 1.0, 1.5 and 2.0 cm respectively). For larger absorption changes, the variation is sublinear with ~20% decrease for δμa = 0.37 cm-1. By contrast, constraining the absorption change to the actual volume of the inclusion may considerably improve the accuracy and linearity of the reconstructed absorption.

Improving the reconstruction image contrast of time-domain diffuse optical tomography using high accuracy Jacobian matrix

An algorithm for time-domain diffuse optical tomography using a high accuracy Jacobian matrix has been developed. The Jacobian matrix has been calculated using a new direct method that uses two finite element meshes of different sizes. A low density mesh has been used for the inverse calculations where the tissue optical properties are reconstructed at its nodes’ locations. The second mesh has a bigger size and is used to calculate the high accuracy light fluence rates and the Jacobian matrix. The high accuracy light fluence is interpolated to obtain its values at the nodes of the low density mesh and at the detectors’ locations. The high accuracy Jacobian matrix at the nodes of the low density mesh are obtained by integrating the Jacobian calculated using the high density mesh. The integration of the Jacobian using the proposed method does not require calculating the Jacobian explicitly at all nodes of the high density mesh which is inefficient in memory requirement and computation speed. The improvement of the Jacobian accuracy while using a low density mesh for the inverse calculations improves the reconstructed image contrast and the computation speed. The optical properties are reconstructed in a region of interest by solving iteratively a self-regularized minimization problem. The minimization problem uses the calculated Jacobian and the light fluence at precisely selected points on the temporal profile of each source-detector pair for the reconstruction. The algorithm has been applied to a three-dimensional model of a neonatal brain and to a three-dimensional model of the mouse for a small animal model. The reconstruction results by the proposed method have been compared with the results using a single mesh for the Jacobian calculations. The effect of using different sizes of the low density mesh for the inverse calculations on the image contrast has been reported.

Prospects on Time-Domain Diffuse Optical Tomography Based on Time-Correlated Single Photon Counting for Small Animal Imaging

This paper discusses instrumentation based on multiview parallel high temporal resolution (<50 ps) time-domain (TD) measurements for diffuse optical tomography (DOT) and a prospective view on the steps to undertake as regards such instrumentation to make TD-DOT a viable technology for small animal molecular imaging. TD measurements provide information-richest data, and we briefly review the interaction of light with biological tissues to provide an understanding of this. This data richness is yet to be exploited to its full potential to increase the spatial resolution of DOT imaging and to allow probing, via the fluorescence lifetime, tissue biochemical parameters, and processes that are otherwise not accessible in fluorescence DOT. TD data acquisition time is, however, the main factor that currently compromises the viability of TD-DOT. Current high temporal resolution TD-DOT scanners simply do not integrate sufficient detection channels. Based on our past experience in developing TD-DOT instrumentation, we review and discuss promising technologies to overcome this difficulty. These are single photon avalanche diode (SPAD) detectors and fully parallel highly integrated electronics for time-correlated single photon counting (TCSPC). We present experimental results obtained with such technologies demonstrating the feasibility of next-generation multiview TD-DOT therewith.

Time-domain diffuse optical tomography using recursive direct method of calculating Jacobian at selected temporal points

An algorithm for time-domain diffuse optical tomography based on the resolution of the time-domain diffusion equation using the finite element method has been developed. An efficient direct method including a recursive approach has been used to obtain the light fluence derivatives with respect to tissue optical properties at precise selected points on the temporal profile resulting in a considerable savings in computation time and memory. The algorithm reconstructs the tissue optical properties in a permissible region or a region-of-interest and the input data for reconstruction comprises selections of points on the temporal curve of the measured pulse. The optical properties have been reconstructed by solving an iterative normalized minimization problem. The algorithm has been applied to a three-dimensional simplified model of a new born baby head and to a three-dimensional model of the mouse (MOBY) for a small animal model. The computation speed and memory usage of the algorithm have been compared with that of other techniques based on continuous wave and frequency domain representations. The effects of using different sizes of time steps and number of time steps on the reconstruction accuracy and the computation time have been reported.

Calculation of the weighting functions for the reconstruction of absorbing inhomogeneities in tissue by time-resolved optical projections

We report a new method for determining the weighting functions to reconstruct absorbing inhomogeneities in tissue by perturbation time-domain diffuse optical tomography using the transmission geometry of a flat layer. The method is based on an analytical approach to the calculation of the weighting functions for a semi-infinite scattering medium and on the use of the original method of an equivalent inverse source in order to obtain weight distributions for the flat layer geometry. The correctness of the proposed method of the weighting function calculation is evaluated by a numerical experiment on the reconstruction of absorbing inhomogeneities. It is shown that the perturbation reconstruction model based on the proposed weighting function calculation method allows the inhomogeneities smaller than and , located respectively in the transverse and longitudinal directions to the probe light direction, to be resolved in the centre of an -thick object.

Theoretical limit of spatial resolution in diffuse optical tomography using a perturbation model

We have assessed the limit of spatial resolution of time-domain diffuse optical tomography (DOT) based on a perturbation reconstruction model. From the viewpoint of the structure reconstruction accuracy, three different approaches to solving the inverse DOT problem are compared. The first approach involves reconstruction of diffuse tomograms from straight lines, the second – from average curvilinear trajectories of photons and the third – from total banana-shaped distributions of photon trajectories. In order to obtain estimates of resolution, we have derived analytical expressions for the point spread function and modulation transfer function, as well as have performed a numerical experiment on reconstruction of rectangular scattering objects with circular absorbing inhomogeneities. It is shown that in passing from reconstruction from straight lines to reconstruction using distributions of photon trajectories we can improve resolution by almost an order of magnitude and exceed the accuracy of reconstruction of multi-step algorithms used in DOT.

Statistical characteristics of photon distributions in a semi-infinite turbid medium: Analytical expressions and their application to optical tomography

The paper focuses on the determination of statistical characteristics of photon distributions in a semi-infinite turbid medium, specifically the photon average trajectory and the root-mean-square deviation of photons from the average trajectory, with an approach based on the diffusion approximation to the radiative transfer equation. We show that the Dirichlet and Robin boundary conditions used for this purpose give close results. We derive exact analytical expressions for the case of the Dirichlet boundary condition. To demonstrate the practical value of our results we consider approximate solution of the inverse problem of time-domain diffuse optical tomography with the flat layer transmission geometry. The problem is solved with the method of photon average trajectories which are constructed with analytical expressions derived for a semi-infinite medium.