Sub-mm resolution tomographic imaging in turbid media by an ultra-high density multichannel approach

Abstract

We demonstrate an ultra-high-density source-detector (SD) diffuse optical tomography system scalable to thousands of combinatorial SD pairs per cm³ of total voxel volume. We demonstrate the imaging of dynamic targets (including phantom arteries) with 100 um resolution at over 10 Hz frame rate within turbid media (> 60 MFP). Further, as a step toward a wearable mobile imager, we introduce monolithic mm-size dense semiconductor laser array chips as sources for potential unobtrusive epidermal tomographic use.

1. Introduction

Non-invasive, label-free neuroimaging of the brain and other anatomical targets of diagnostic structural and metabolic importance by all-optical methods has a rich history and continues to be an active field of biomedical optics. Many approaches and different near infrared (NIR) techniques are being engineered toward the goal to build clinically relevant systems while searching for means to reduce the fundamental barriers to spatial resolution due to light scattering. Except for the eye, photon propagation in other parts of the human anatomy involves penetration into complex and dense turbid media, such as the optical path through the scalp, the skull, and grey matter in brain neuroimaging [1,2]. To achieve both higher spatial resolution (on a sub-mm scale) as well as time resolution of relevance e.g. for dynamical events in the cortex (to ∼100 msec and below) is particularly challenging in infrared tomography. Yet such performance is needed for optical approaches to compete with large-scale machinery such as fMRI in exploiting hemodynamic markers so as to unveil underlying cortical activity from neurovascular coupling, for example. The optical problem scales (literally) exponentially in difficulty with increasing tissue thickness so that the penetration depths to reach the surface of the cortex in a primate may approach the equivalent of 100 photon mean free paths (MFP) in the dense diffusive photonic regime. Yet, for finding a way to build low-cost, wearable and mobile optical tomography devices which can compete with fMRI, PET and other large scale high-cost medical equipment could have a major impact on human health care, especially if designed for ambulatory diagnostic use in the office as well as for 24/7 monitoring in home environment.

To date, most existing diffusive optical tomography (DOT) systems are limited by (1) low spatial resolution, typically at centimeter level, especially when used for functional imaging; (2) trade-off between capture time and SNR that limits the quality of dynamic imaging; (3) relatively slow image reconstruction by algorithms aspiring for high resolution that use (large scale) models which generally make real-time DOT imaging challenging [3]. We have visited these challenges by considering an ultra-high-density approach (UHD-DOT) in designing a system concept where closely packed source-detector pairs on sub-mm scale (here total of up to 25600 channel pairs/cm³) focus on a given region of anatomical interest to achieve imaging potentially down to 100µm level of spatial resolution [11]. A proof-of-concept system is tested in a thick benchtop phantom model with optical pathlength exceeding 60 photon mean free paths (MFP). An intralipid model phantom embeds objects of simple geometries including a fluidic tube serving as a vasculature proxy in which the time-dependent oxy-deoxy ration of hemoglobin is mimicked by dynamical modulation of the optical density of an ink-based fluid in the tube. A particular feature of the system is that frame rates of 12 Hz and higher have been achieved with 250 µm spatial resolution of the dynamic proxy blood vessel, with efficient computational algorithms for image construction (fast post-processing, explained in section 2).

We note that a number of other groups have earlier used a range of source-detector hardware for what is generally called ‘high density’ DOT in the literature [1,2]. In high-density DOT, one increases the number of independent source-detector (SD) measurements to build a data base which consists of a large number of spatially overlapping measurements for a range of different SD pair distances to achieve higher image reconstruction quality. A high-density DOT method can be broadly defined by the nearest source detector pair being approximately below 15 mm. For instance, in the review by Wheelock on HD-DOT [2], the minimal source detector separation distance is cited as 13 mm. The main advantage of HD-DOT is that it enables improvement in spatial resolution for functional imaging. And multiple regions of the brain can be imaged by a wide spatial spread of sources and detectors, like a ‘helmet’ construct in multichannel, multiarea EEG systems. By contrast, we focus here on an ‘ultrahigh-density’ regime in which the multichannel strategy involves individual source element and detector element separation as small as 100 microns. Further, the aperture of the impinging semiconductor laser source and the corresponding pixel size in a detector camera may be as small as 10 microns. In terms or earlier work, we note pioneering research by Hillman [4,5] and later work by other groups [6] on so-called laminar optical tomography (‘LOT’) upon which has informed part of our work. In effect, the ‘LOT’ regime is a microscope version of diffusive tomography and can provide higher spatial resolution up to hundred microns level but has been so far limited only to shallow (2-3 mm) imaging depths in tissue. In our work we designate the term ‘UHD-DOT’ to denote an approach not only bridges the gap between traditional high density and lateral tomography regimes to achieve high spatial resolution (to 100 µm) but also allows for deep penetration into tissue.

In terms of implementing an UHD-DOT imaging device for wearable, mobile use, chip scale semiconductor photonic components are desired. High density detectors with small pixel sizes are readily available in state-of-the-art CMOS cameras, for silicon imaging chips that are based of ordinary photodiodes [8,9] or time-gated single photon avalanche detectors (SPADs) [10], for example. For UHD-DOT use, however, such detector arrays need to be engineered for source-synchronized and independent readout of each pixel element. On the other hand, finding suitable chip scale, monolithic ultrahigh-density semiconductor laser sources has been problematic, to serve as a compact replacement of e.g. the raster scanned large frame benchtop lasers (the latter typically used in ‘LOT’ and related micro/macroscope optical setups) which are generally unsuitable for wearable use. We illustrate one solution below by introducing a new device class for high resolution tomography, namely dense arrays of programmable vertical cavity surface emitting lasers (VCSEL). Although we do not address the additional benefits of time-of-flight techniques (ToF) in this paper, usually implemented by using ultrashort-pulse tabletop bulk lasers, we note that modern VCSEL technology is capable of reaching multi-GHz speeds [18,19].

To orient the reader to the workflow in this paper, Fig. 1 summarizes the system-level approach to constructing an UHD-DOT scheme in our laboratory. Figure 1(a) shows a block diagram of the process flow and associated data flow which integrate experiments and simulations for 3D image reconstruction, tested here using our benchtop brain phantom in transmission geometry. The role of computation via the relevant biophysical models (both Monte Carlo simulations and image reconstruction algorithms) is indicated. The actual geometry of the source-detector array arrangement is shown in Fig. 1(b). In dissecting Fig. 1 below, we first summarize the approach to modeling and photon propagation models in dense turbid media applicable to the UHD-DOT regime, followed by benchtop experiments using a continuous-wave raster scanned tabletop laser in structural and then dynamical imaging of proxy vasculature in a phantom, near the hemoglobin marker wavelength of 850 nm. This is followed by a demonstration whereby the bulky tabletop laser source is replaced by a millimeter-size monolithic laser chip, composed of a high density VCSEL array with time-programmed electronic access to each individual device. The introduction of this advanced piece of photonics technology offers the prospect of engineering compact epidermal wearable UHD-DOT sensor systems in the future.

Fig. 1.

(a) Testbench for joint simulation-experimental pipeline for image reconstruction in a multichannel UHD-DOT scheme. (b) Geometry of the experimental and simulation arrangement. A square array of high-density laser point sources (bottom, red) and the CMOS detector camera chip (top, blue) are separated by 12 mm thickness (equivalent of 60 photon mean free paths) turbid media. A target object of interest (a 1mm diameter sphere in this illustration) is immersed in the middle of the densely scattering medium.

2. Baseline theoretical analysis and Monte Carlo simulations

The many approaches to simulating dense turbid media and consequent 3D image reconstruction in diffusive optical tomography have been extensively discussed and reviewed in the literature [1–3,7,12,15]. We have selectively adapted some of these techniques for in silico studies of the UHD-DOT regime. We focused on asking the practical device question regarding the optimal number of source-detector pairs suitable for a compact, monolithic, and eventually mobile multichannel scheme, capable of spatial resolution down to 100 micrometer range and tissue penetration depth at least on the order of 60 MFPs. A converse question is the limitation of the overall spatial coverage (field of view) when operating the experimental system in a mode which is effectively a kind of DOT microscope. (One additional motivation of ours is to eventually pursue the engineering of a wearable epidermal patch to probe a specific cortical functional region for non-invasive brain-machine interfaces).

Reconstructing the targets inside the biological tissue in optical tomography presents the much-discussed classic inverse problem. The steps developed by earlier researchers typically include: (1) model for light propagation by using either analytical method (e.g. radiative transfer equation, diffusion equation [12]) or stochastic methods (e.g. Monte Carlo simulation [13–16]); (2) application of image reconstruction algorithms which include linearization approaches or nonlinear iterative approaches, to solve the inverse problem.

Monte Carlo simulation is considered as the gold standard for modeling photon propagation. However, it has been traditionally limited in speed when attempting simulation of large photon numbers (>10⁹). With the recent fast development of GPU technology has enabled significant acceleration in performing large scale Monte Carlo simulations. Here we used the ‘Monte Carlo Extreme’ toolkit (MCX) [13–16] to build our forward model with the benefit of its speed and accuracy when dealing with complex tissue media. To get the Jacobians rapidly, we used the “replay” function of MCX [16,21]. As for the choice of reconstruction algorithms, we first tested linearization approaches including the Born/Rytov approximations [21] and Tikhonov regularization [12]. The Born/Rytov approximations are here applied for inverse problem. This in reference to representation of measurement perturbation ΔΦ. It is formulated in terms of the unperturbed Φ₀ and perturbed measurements Φ, the Born approximation is when ΔΦ = Φ - Φ₀. In turn, the Rytov approximation is expressed as ΔΦ = (Φ - Φ₀)/ Φ₀.

It is generally accepted that for brain imaging studies (with hemodynamics mirroring cortical activity via neurovascular coupling) where activity related changes in the absorption coefficient µ_abs are sufficiently small, linear methods are adequate. We also used a nonlinear iterative approach: Fast Iterative Shrinkage Thresholding Algorithm (FISTA) [17] in comparing the relative enhancements of each approach for reconstruction quality. An example of our in silico reconstruction results applied to the UHD-DOT regime is shown in Fig. 2, where the number of source elements, arranged in a square grid, varies from 1 × 1 to 9 × 9 for the same total source area (4.2 × 4.2 mm²), while the number of detectors remains fixed (7 × 7 hemispherical detectors, with radius of 300 um). The proxy target (purple color), embedded in 18 mm thick model turbid media (µ_s= 8 mm^-1 mimicking average human head model [22]), was a simple thumbtack-shaped static object consisting of two cylinders (base cylinder: 1000 µm radius, 500 µm height; upward extruding cylinder: 300 µm radius, 2500 µm height). Our design rationale for this simple geometrical 3D target object was that its anisotropic shape could mimic tissue objects such as tumors and vessels; the thumbtack also had enough length along the z-axis to test the depth resolution in the simulated experiments. Both the background medium and the target had initially the same absorption coefficient µ_a= 0.01 mm^-1. Then the target’s µ_a was changed to 0.05 mm^-1 so as to create a thumbtack-induced ‘perturbation’ of Δµ=0.04 mm^-1. The anisotropy parameter and refractive index were set as 0.89 and 1.37, respectively, for both the background medium and the target object.

Fig. 2.

Examples of simulations for 3D image reconstruction of a mm-size ‘thumbtack’ immersed in the center of a model phantom (144 MFP thick; here in transmission geometry). The number of point sources is varied from 1 × 1 to 9 × 9 array in this investigation of the dependence of reconstruction quality on the number of source points in such an UHD-DOT illustration (here the detector size is fixed to 7 × 7 pixels).

Given that the image reconstruction is fundamentally an ill-posed problem, the broad strategy behind designing an UHD-DOT system is that increasing S-D density will increase the number of overlapping SD photon channels within the volume of interest; i.e. that having significantly more independent equations will help in solving the inverse problem. The outcome from our simulation testbed, summarized in Fig. 2, helped us to (1) assess the benefit of increasing the number of SD pair combinations for a given tissue volume, and (2) to find the optimal/minimal number of SD pairs to achieve the most efficient image reconstruction for anticipated rough target size (i.e. extraction of structural information at high resolution vs. number of independent equations to be solved). The strategy is also important from a practical engineering point of view in future design of compact and wearable imaging sensors. Here, for the chosen geometry and given the fixed detector array choice, a reasonable reconstruction was obtained with 5 × 5 source array (100 µm interelement separation) whereas exceeding the source array beyond a 10 × 10 source array did not improve the performance. While not described here, we also found that using the singular value decomposition (SVD) method could help to find out the optimal number for the ‘most valuable’ SD channels (i.e. those that are most useful in adding further independent information).

In exploring different image reconstruction models, we also compared the Tikhonov regularization (L2 norm) with FISTA (L1 norm) in terms of reconstruction quality and speed. In the present multichannel high-density, source-detector configuration we found that when comparing to Tikhonov algorithm, the FISTA approach achieved better reconstruction for complex targets after a few (5-60) iteration steps. On the other hand, the Tikhonov regularization was computationally faster when FISTA needed more iterations (>10). Both algorithms could be run within 2s to achieve one reconstruction.

3. Benchtop UHD-DOT experiments: static and dynamic imaging in brain phantoms

For proof-of-concept experiments using benchtop phantoms, we created an array of closely packed near infrared laser source points by using a single-mode CW laser source at 850 nm (Toptica Photonics Inc.). Then a pair of programmable galvanometric mirrors were rapidly scanned to deliver bursts at a predetermined number of point sources, covering a selected target region in an intralipid liquid phantom in which an object was immersed. The optical properties of the experimental intralipid phantom are µ_a= 0.002 mm^-1, µ_s= 5 mm^-1, g = 0.89, thickness 12 mm, where µ_s­ is scattering coefficient, µ_a­ is absorption coefficient. MFP is defined by 1/ (µ_s­ +µ_a) [20]. So the total optical thickness is about 60 photon MFP (µ_a­ is negligible). The overall optical scheme, deployed here in transmission geometry of the UHD-DOT system is shown in Fig. 3(a) and was used for both structural static and dynamic imaging. As the photodetector, we used the Hamamatsu s14250 CMOS chip (Fig. 3(b3), 32 × 32 elements, 50µm pixel size) but redesigned the chip for a customized electronic readout, its interface being controlled by an FPGA whereby each camera pixel could be read out individually while time- synchronized with any given point source element. In this way, each camera pixel can be regarded as a single detector element. For example, for a closely packed square array of 5 × 5 laser source points (1 mm spacing), the combinatorial laser/detector optics yielded a total of 25600/cm³ (5 × 5 × 32 × 32) spatially closely packed SD pairs, with an overall field of view up to a cubic centimeter into the target intralipid volume. Figure 3(b4) shows the pixels of the CMOS camera. By grouping the adjacent pixels (e.g. 3 × 3 as 1), the detector size will be increased and the number of detectors can be reduced. In Fig. 3(b) we show elements of a future compact chip-scale system design where the multipoint optical source (e.g. a large frame laser) can be replaced by a single mm-size VCSEL array chip as described below.

Fig. 3.

(a) the benchtop imaging system, both schematic and a close-up photo of the optics surrounding the phantom. The mm-diameter tubes entering and exiting the intralipid dish feed proxy blood fluid into a 3D printed artery model (1mm diameter) submerged in the phantom; (b) photos of the FPC mounted CMOS camera chip (b.3,4) and a VCSEL array (b.1, latter discussed below); b.4 shows the pixels of the camera and the pixels can be regrouped to be a new larger detector; the cartoons (b.2) show the use of the proposed chip scale S-D arrays in transmission.

To experimentally demonstrate the high spatial resolution outcomes of UHD-DOT approach, first in structural imaging of static targets, a pair of black spheres (1 mm diameter) and a single-strand of black conducting wire (diameter ∼450 µm) (Fig. 4(a)), respectively, were submerged in the center of the intralipid phantom (Fig. 4(c)). The opacity of the intralipid rendered the targets invisible to a naked eye (Fig. 4(c)), even under bright ambient illumination. With the aid of Monte Carlo simulation and reconstruction algorithms, sub-mm levels details of the mini-spheres and the mini-wire embedded in the optically thick turbid could be readily imaged with spatial resolution reaching on the order of 100 µm (Fig. 4(b) and 4(d)).

Fig. 4.

(a) Photos of a segment of a black wire target (diameter ∼450um) and two dark mini-spheres (diameter ∼1mm) for static structural imaging, respectively; (c) close-up photo of the intralipid phantom and surrounding source-detector optics in transmission geometry; (b) and (d) results from reconstructing the object images by the UHD-DOT system for the wire and the pair of mini-spheres, demonstrating spatial resolution to 100 µm scale (1 voxel = 100 µm).

We then constructed a “dynamic phantom” as follows: A simple 3D-printed artery model composed of a single fluidic tube with a 1 mm outer diameter and with feature precision (tube uniformity) approximately 50 µm was immersed into the same intralipid-based liquid phantom (i.e. 60 MFP optical thickness). Two syringe pumps were programmed to inject pulses of absorbing and transparent fluid in a periodic temporal sequence to mimic optical modulation in a blood vessel from the pulsating blood flow and associated dynamical oxygen/dioxygen hemoglobin variation. The tube was immersed at 6 mm depth into the intralipid. Figure 5 shows results from the experiments where the optical density was changed at a 1 Hz frequency to mimic the case of a rhythmic heartbeat (the system’s speed is 13 Hz for reconstruction and it was limited to the particular camera chip’s frame rate). The simulation toolkit described above was used to compute in silico the corresponding model dynamics as a means of validating the experimental outcomes where MC simulations were applied to the fluidic tube geometry with time-varying optical contrast to simulate the corresponding dynamic (1 voxel = 250 um). These experiments are presently being extended to more complex dynamical vasculature models of anatomical relevance (bifurcated, coaxial and other microtube geometries).

Fig. 5.

Imaging a dynamic target, here a piece of a 1mm diameter proxy vessel with periodic optical density changes at 1 Hz frequency to mimic the heartbeat; (a) shows reconstructed absorption perturbation captured from a video over an eight second epoch (optical intensity variation measured from the central voxel of the reconstructed 3D vessel). Each red dot represents one reconstruction. The reconstructed video frame rate is 13 Hz. (b) reconstructed images of the vessel at different time captured from a video (for one period shown in the green rectangular box in (a)). The 2D images represent a view in the x-y plane at depth of z = 6 mm (the center of phantom). Scale: 1 voxel = 250 µm.

At current stage, all the reconstructions are running post-experiments. The speed of the imaging system (frame rate) itself depends on the combined speed of the electronic drivers for source array (VCSEL array) and detector array (CMOS camera). The forward Monte Carlo simulations are run once before the experiments to get the Jacobian matrix (typically needs 2-5 mins, depending on the source number and voxel size). Then the Jacobian matrix will be used with algorithms like Tikhonov Regularization or FISTA (Fast Iterative Shrinkage Thresholding Algorithm) to solve the inverse problem (typically take < 2 seconds for one reconstruction).

4. Surface emitting semiconductor laser array as a compact multipoint source in UHD-DOT

Next, the optics and the experimental configuration described above were compacted by replacing the benchtop laser with a custom-designed programmable VCSEL array chip as a multichannel point source (Fig. 6), operating at λ=850 nm. The individual device aperture of each microlaser element was 25 µm with an interelement pitch of 200 µm and output power from each device up to 5 mW. The laser chip was mounted in a chip carrier and wire-bonded by standard microelectronics packaging techniques. The VCSEL chip was electronically connected with the CMOS photodiode detector chip for time-synchronized serial readout of the individual source-detector pair matrix elements, i.e. S_i,j x D_k,l. We note that among compact NIR laser sources in the mW power regime, VCSELs have the highest electrical-to-optical conversion efficiencies (>50%) and have the benefit of a planar form factor, useful, for example for envisioning an epidermic “band-aid” type skin contact. While VCSEL arrays have recently emerged as now mass-manufactured sources of multipoint illumination for 3D imaging in the latest smartphone cameras (e.g. iPhone 13) as well as many LIDAR applications, these devices generally lack the property critical for our UHD-DOT application, namely direct electronic drive to each laser element which our devices were capable of.

Fig. 6.

(a) 80-channel high speed VCSEL driver capable of addressing individual laser elements at > kHz speed; (b-d) Photographs at increasing resolution of the individual addressable VCSEL array chip (85 elements) designed as a programmable point source array as one chip scale planar element in a compact, wearable epidermal UHD-DOT device.

Here we demonstrate for the first time (to our knowledge) the utility of this type of VCSEL array in optical tomography in general and in UHD-DOT in particular. We deployed a programmable InGaAs/GaAs quantum well (QW) VCSEL array (85 elements) in the 850 nm range in a series of experiments, using the scheme of Fig. 1 for both static and dynamical imaging of sub-mm sized targets in thick turbid media. A dedicated multichannel current-source driver was built to enable scanning the elements in the VCSEL array according to a pre-defined temporal-spatial sequence. Figure 7. shows an example of static (structural) imaging of a single 1mm size minisphere in a thick turbid medium using the VCSEL array as the light source and the Hamamatsu camera chip as the detector array.

Fig. 7.

(a) Image reconstruction result for a mini-sphere with 1mm diameter using a VCSEL array as the 850 nm multipoint light source; (b) photo of the experimental setup with VCSEL array chip on the left, the intralipid phantom in the middle and the CMOS camera chip on the right.

Unlike the VCSEL sources used in previous works [7,27,28], which are few, sparse and not integrated (acquired individually). We designed and packaged the ultrahigh density VCSEL source array chips so that each microlaser can be accessed independently by the external multichannel current driver. Additionally, each microlaser of our customized VCSEL array is also synchronized with each pixel at the CMOS camera detector. We note that the present devices and drivers are capable of injecting current pulses at sub-nsec speeds for possible future addition of time-of-flight (ToF) capability to the system. This exploration is presently under way.

Because of the very large number of photon channels which the combination of a multipoint source laser/camera array affords, our research shows a much improved spatial resolution and, based on simulations, also suggests a capability for deeper tissue penetration depth. The key point is that the work in our paper offers a photonics technology platform for many bioimaging applications. Given the dimension restrictions of the current UHD-DOT setup, it is currently best used in small sized imaging targets, such as brain imaging in small animals (noninvasive as well as invasive), as well as tissue and organ engineering applications. In these applications where the target medium is within < 2cm, in principle UHD-DOT can also be achieved through reflection geometry. For noninvasive brain imaging on small animals, previously we have performed in-depth studies in the modeling of photon migration in layer structures [23,24], and has published adaptive filtering based algorithm which use the measurements from the shortest (∼0-10 mm) separations mainly image the extracerebral tissue as the reference for the removal of superficial interferences [25,26].

5. Conclusion

While building on the many earlier pioneering accomplishment in near infrared tomography for label-free bioimaging, we have focused in this paper on the development of a multipoint source-detector strategy for ultrahigh resolution in both structural and dynamical imaging. In particular, an UHD-DOT multichannel prototype system has been built and tested on the benchtop for simple geometrical objects (mini-spheres and wires) as well as in a simple vasculature phantom in a dense turbid medium, and shown to be capable of spatial resolution on the 100 µm scale with a temporal resolution of about 100 msec, a time scale of neurovascular interest.

The introduction of an mm-size multipoint VCSEL light source to high-resolution optical tomography, in conjunction with CMOS-based camera chips, can be an important step for the development of wearable monolithic ‘skin patch’ metabolic monitoring devices for mobile subjects such as the brain cortex. Chip scale semiconductor photonic devices allow a new kind of design flexibility, e.g. in placing ultracompact probes directly atop the brain region of special interest. Given the GHz speeds of VCSELs used routinely in optical telecommunication, the UHD-DOT approach described here can be extended to the time-of-flight domain for gating/rejecting early-arriving photons from superficial tissue when combined with special purpose CMOS cameras in one monolithic epidermal sensor for tracking dynamics of local physiological circuits in general.

Disclosures

The authors declare no conflict of interests.

Data availability

Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.