2.1.

Upconverting Nanoparticles

In the last decade, there has been increased interest in using UCNPs for sensing, imaging, and/or as photoactivating fluorescent agents.^15–17 UCNPs are nanoscale particles that have the unique ability to absorb two or more incident photons of low energy and emit one with higher energy. Hence, UCNPs may potentially facilitate deep tissue applications since they can be excited in the infrared and emit in the visible or UV spectral bands. This upconversion process results in large Stokes shifts, multiple sharp emission bands, low autofluorescence, and very limited photobleaching. Herein, we selected a commercially available Lanthanide-doped UCNP for use.

Lanthanide-doped UCNPs are dilute guest host systems in which lanthanide ions function as guests in the lattice of the host.¹⁸ Selection of different lanthanide ions and synthesizing methods will make UCNPs emit different colors of light, from NIR to UV. One advantage of UCNPs is that the excitation of particles does not need high power or use of a pulsed laser, in contrast to multiphoton dyes.¹⁹ Briefly, the sensitizer ions, such as Ytterbium, will capture multiple incident low energy photons and transfer the energy to activators, such as thulium or erbium, which will emit high energy photons. In contrast to normal fluorescence dyes, the relationship between the emission intensities and the power of excitation is nonlinear and can be expressed as follows:

In Eq. (1), $I_{\mathrm{UCNP}}$ represents the intensity of emission light and $P$ is the power of incident light. $n$ is the power-dependent index of UCNPs, which will depend on the selection of ions, emission band, structure of UCNPs, etc.¹⁸ The mechanism of the upconversion process is complex and beyond the scope of this manuscript; the reader can refer to Refs. 2021.–22 for more details.

In our experiment, one UCNP (sodium yttrium fluoride, ytterbium and thulium doped, NaY0.77Yb0.20Tm0.03F4, Sigma-Aldrich, United States) was employed as an optical contrast agent. The UCNPs are a white powder with particle size less than $10\mu \mathrm{m}$ that can be easily and uniformly suspended in dental fillings or resin. To estimate the power-dependent index of UCNPs, a 975-nm laser diode (L975P1WJ, Thorlabs, United States) mounted to a TCLDM9 (Thorlabs), controlled by a current driver (LDC200C, Thorlabs) and temperature controller (TED200C, Thorlabs), was used as the excitation source. The laser output was collimated to form an illumination spot with a radius of 4 mm. The laser power was controlled to generate illumination power densities ranging from $50\mathrm{mW}/{\mathrm{cm}}^2$ up to $700\mathrm{mW}/{\mathrm{cm}}^2$ [see Fig. 4(a)]. A bandpass filter (FGB37M, Thorlabs) was employed to filter out the excitation light. The emission light of the UCNPs was coupled to an optical fiber that was connected to the spectrometer (USB 2000, Ocean Optics). The power of the excitation light was monitored by an optical power meter (S310C, Thorlabs). Double logarithm plots were employed to determine the power-dependent index, as shown in the following sections.

2.2.

Teeth Phantom Preparation

To mimic dental restoration after therapy, extracted teeth were acquired from local dentists with approval from Rensselaer Polytechnic Institute’s Institutional Biosafety Committee (IBC). Approximately three to four fiducial marks (shallow semispherical dents) were made in the apical part of mesiodistal root surface [see Fig. 1(a)]. The fiducial marks mainly have two functions: to perform rigorous registration between optical reconstructions and micro-CT images and to accurately pinpoint the irradiation point of excitation light. A simplified model in which a through hole with diameter 1.2 mm was drilled from the canal foramen to the pulp chamber was employed. A glass capillary with inner diameter 1.0 mm filled with optical contrast agents was then placed inside the cavity. The processed teeth were scanned by micro-CT (Medical Viva CT 40, Scanco, Switzerland) to obtain the anatomical structure [Fig. 1(b)]. In our experiments, micro-CT equipped with a microfocus cone beam X-ray source with tube voltage settings 70 kVp and current settings $160\mu \mathrm{A}$ was employed. The resolution of the micro-CT was set to $38\mu \mathrm{m}$ (voxel size $38\times 38\times 38\mu {\mathrm{m}}^3$), which was suitable for our purpose. The overall micro-CT scanning time for one tooth was around $\sim 20$ to 30 min. In total, around $\sim 300$ to 400 slices were acquired for each tooth. Furthermore, the micro-CT images were then processed by ImageJ or MATLAB for k-means segmentation or binarization [Fig. 1(c)]. Finally, a tetrahedron-based mesh was generated based on the binary images from micro-CT using the precompiled computational geometry algorithms library [Fig. 1(d)].

Fig. 1

Demonstrations of processing teeth. (a) Photograph of the teeth in which the red circle indicates the fiducial mark and the dashed blue box highlights the MFMT FoV; (b) one slice from a micro-CT image; (c) binary image of the same slice (b) with depiction of the illumination side and detection side (blue and green arrows, respectively; depiction not to size); and (d) mesh generated by the computational geometry algorithms library.

2.3.

Optical Settings

The system employed in the experiment was very similar to the MFMT system reported in Refs. 7 and 23, with two major modifications. First, transmission geometry was employed instead of the reflection geometry of MFMT, which means that the source and detectors were located at opposite sides of the object (see Fig. 2). This change in configuration was implemented because our previous MFMT configuration has limited detectable depth, typically between 3 and 5 mm.²⁴ However, for chairside applications, the teeth are embedded into the jaw, leading to potential total thicknesses of $\sim 1\mathrm{cm}$.²⁵ Second, an electron multiplying CCD (EM-CCD) camera was used instead of an avalanche photodiode array, leading to an increased number of measurements for improved resolution. A brief description of the whole system is provided below.

Fig. 2

Schematic of the system proposed in the manuscript. The red line represents excitation light (975 nm), whereas the blue line represents the upconverted emission light.

On the illumination side, a 975- or 658-nm excitation light (for use with UCNPs or linear dye) generated by the laser diode (L975P1WJ or L658P040, Thorlabs), controlled by the current controller (LDC200C, Thorlabs) and temperature controller (TED200C, Thorlabs), was fed into a 2-D galvoscanner system (GVS002, Thorlabs) and focused on the surface of the sample through an objective lens to yield a $\sim 1\mathrm{mm}$ diameter illumination spot. On the detection side, the emission light (upconverted blue and NIR, or fluorescence emission) was captured by the EM-CCD (iXonEM+ 885, Andor) after passing through specific filters (FGB37M, Thorlabs or FF01-800/12-25, Semrock) and lenses. The field-of-view (FoV) was set to $3\times 4{\mathrm{mm}}^2$ during the experiment. At each irradiation point, the galvoscanner would dwell 1 s before moving to the next position.

2.4.

Optical Reconstruction

In our experiment, tetrahedron-based Monte Carlo (MC) simulations²⁶ were employed to generate the Green’s function at each source and detector. The number of photons employed in the simulation was set to ${10}^6$ for each forward calculation. A forward-adjoint MC methodology was used to generate the sensitivity matrix.²⁷ The Born normalized formulation was used to cast the inverse problem:²⁸

In Eq. (2), $G^x$ and $G^m$ represent the Green’s functions at excitation (source) and emission (detector) wavelengths, respectively, and $\eta (r)$ represents the distribution of the optical contrast agent (UCNP or linear dye). $U_B$ is defined as $U_m/U_x$, in which $U_m$ and $U_x$ represent the acquired intensity data at emission (with optical contrast agent inside the object, irradiated by excitation light and with filter) and excitation (same conditions as emission except without the filter in place), respectively. Note that this formulation is very similar to the one used for classical NIR fluorophores (linear dyes) for which the power-dependent index $n$ is equal to 1 (for UCNP $n=2,3,4,\dots$ depending on the different components or synthesizing methods). Note also that no a-priori information on the location of the fluorescent heterogeneity, as could be derived from CT, was imparted in the inverse problem.²⁹

After direct discretization of Eq. (2), the following depth-dependent adaptive Tikhonov regularization equation was obtained:

2.5.

In silico and Ex-vivo Experiment Settings

To investigate the behavior of UCNPs, in silico experiments were first conducted. A real tooth model with anatomical structure obtained by micro-CT was employed as the phantom. A simulated cylinder filled with optical contrast agent was placed inside the tooth. To assess the effect of spatial sampling on the reconstruction quality, a series of simulations with a varied number of sources and/or detectors was performed. The detector sampling (associated with camera pixel selection) was set either to 70 or 105 [two sets of data—see Figs. 3(i) and 3(ii), left panel]. The distance between adjacent detectors was fixed to 0.5 mm, which means that 105 detectors would cover a larger area ($3\times 7{\mathrm{mm}}^2$) than 70 detectors ($3\times 4.5{\mathrm{mm}}^2$). For the source sampling (associated with galvo scanner settings), with a fixed number of detectors, we increased the spatial density of illumination points while keeping the illumination FoV constant ($3\times 4{\mathrm{mm}}^2$). The different number of sources was implemented by adjusting the distance between adjacent sources along two dimensions. The number of sources was set to 15, 20, 25, 27, 35, 36, 45, and 63 [see Figs. 3(a)–3(h), right panel].

Fig. 3

Source–detector configurations—left panel (blue): detector spatial location for (i) 70 and (ii) 105 sampling, respectively; right panel (green): source position for (a) 15, (b) 20, (c) 25, (d) 27, (e) 35, (f) 36, (g) 45, and (h) 63 total illumination points. The position of the source–detectors is overlaid on each external element of the tetrahedron-based mesh used for the forward and inverse calculations.

Reconstructions were performed for all the sampling settings described above and the fidelity of the inverse problem was assessed using two image-driven quantities. The first is the relative error between the volume of reconstruction and simulated volume within the FoV. The second metric is the absolute centroid error between the centroid of the reconstruction and the simulated object. The differences of centroid position along three dimensions were calculated first, and the largest one was employed as the absolute centroid error, namely $\max \{e_x,e_y,e_z\}$. In the in silico study, the power-dependent index was set to typical values, which were $n=3$ for blue emission and $n=2$ for NIR emission.

The average volume for the elements was set to $0.001{\mathrm{mm}}^3$, which sets the limit in resolution to around 0.1 mm. Overall, the imaging space was discretized into 32,242 nodes and 196,469 elements. The optical properties of the tooth were assumed to be homogenous over the sample and were set based on a literature review.^31,32 The absorption coefficient of dentin was set to ${\mu }_{\mathrm{a}}=0.3{\mathrm{mm}}^{-1}$ for all wavelengths. The scattering coefficient of dentin was set to ${\mu }_{\mathrm{s}}=14.2{\mathrm{mm}}^{-1}$ at 975 nm and ${\mu }_{\mathrm{s}}=17.1{\mathrm{mm}}^{-1}$ at around 800 nm.³² For the blue light, the scattering coefficient of dentin was set to ${\mu }_{\mathrm{s}}=40{\mathrm{mm}}^{-1}$.³¹ For all the simulations and experiments herein, the Henyey–Greenstein scattering function was employed and the anisotropy factor was set to $g=0.93$, as reported in Ref. 31.

Besides in silico experiments, ex vivo experiments were conducted with the same sample used to generate the synthetic phantom. Three optical contrast agent mixtures were tested: (1) pure UCNPs with blue and NIR emission, respectively (NaY0.77Yb0.20Tm0.03F4), (2) mixture of UCNPs and bisphenol A glycol dimethacrylate (Bis-GMA), 20% w.t. with blue emission and NIR emission, respectively, and (3) linear dye: $26\mu \mathrm{M}$ Alexa Fluor 660 (Succinimidyl ester, ThermoFisher) in water. The synthesis of Bis-GMA can be found in Ref. 33. After thoroughly mixing UCNPs with Bis-GMA, the mixture was cured with irradiation. For each optical contrast agent, the transmitted intensity fields at excitation and emission were recorded sequentially by the EM-CCD and the appropriate spectral filter sets. In the ex vivo experiments, the number of sources was set to 63 and the number of detectors was set to 105 following the findings of the in silico investigation (see Sec. 3.2). Due to our mesh-based MC methodology, the optical reconstructions were seamlessly registered with anatomical structure obtained from micro-CT via affine registration algorithms (Amira 5.4.5, FEI), leading to a rigorous comparison between the two imaging modalities. As in the in silico experiments, relative volume error and absolute centroid error were calculated to assess the accuracy of optical reconstruction compared with the ground-truth obtained from micro-CT.

3.1.

Determination of Power-Dependent Index for Upconversion Nanoparticles with Blue Emission

We experimentally established the power-dependent index of our UCNPs by comparing illumination power density versus the relative UCNP emission intensity. The spectral UCNP emission as reported via spectrophotometry and for various illumination power densities is provided in Fig. 4(a). The blue spectral emission was integrated to yield the overall blue-emitted intensity, as depicted in Fig. 4(b). The experimental power-dependent index was estimated via the linear relationship between illumination power density and emitted intensity and was found to be $n=1.78$. Hence, for all experimental reconstructions, a power-dependent index of $n=2$ was employed for the calculation of the forward model.

Fig. 4

Blue emission band of UCNPs. (a) Blue emission intensity and wavelength between 440 and 510 nm at different laser power. (b) Relation of max emission intensity and laser power.

3.2.

In Silico Experiments

Examples of the sensitivity matrix as calculated by the adjoint mesh MC approach for the same source–detector pair but at different excitation and emission settings are provided in Fig. 5. A visual inspection of these profiles determines that the Jacobian associated with the blue emission of UCNPs [Fig. 5(a)] has the sharpest sensitivity profile despite being associated with the largest scattering coefficient. By contrast, the sensitivity profile of the linear dye [Fig. 5(c)] exhibits a more homogenous distribution and, hence, increased volume probed by the detected photons. However, when considering the full Jacobians and assessing their respective ill-posedness via their condition numbers and eigenvalue distribution [Fig. 5(d)], the linear dye outperforms the UCNPs and the NIR spectral band is better conditioned than the blue spectral band. Hence, it is expected that the UCNP inverse problem is more prone to artefacts and is harder to solve. This assessment is validated via an image-driven assessment of the reconstructions.

Fig. 5

Comparison of sensitivity profiles of different optical contrast agents. (a) UCNPs with blue emission (475 nm). (b) UCNPs with NIR emission (800 nm). (c) Linear dye with NIR emission. (d) Comparison of the eigenvalue of sensitivity matrices for different optical contrast agents. The position of the specific source–detector pair depicted in these sensitivity maps is provided by arrows.

Tables 1 and 2 summarize the reconstruction volume and corresponding error for the different optical contrast agents considered and for 70 and 105 detectors separately. First, as expected, we noticed that increasing the number of sources leads to a reduction in the relative error no matter if we use UCNP- or linear dye-based reconstructions. However, for identical optode settings, the UCNP-based reconstructions systematically exhibit larger relative volume errors compared to the linear dye-based reconstructions. Note that the error reported herein is calculated for reconstructions with individual optimal regularization parameters.

Table 1

Reconstruction volume with 70 detectors of different optical contrast agents.a

Table 2

Reconstruction volume with 105 detectors of different optical contrast agents.a

Similarly, the absolute centroid error is provided in Table 3. The same findings are observed when using this metric. The absolute centroid error for the linear dye is smallest ($<0.1\mathrm{mm}$) whereas for UCNPs, the error is around 0.5 mm for NIR emission and $\sim 1.0$ to 1.2 mm for blue emission. Note that the absolute centroid error does not reduce with an increasing number of sources under the same number of detectors. In all cases herein, the largest error always occurred along the $z$ direction [see Fig. 1(d)]. This depth-related volume enlargement is associated with the single projection configuration of our instrument design. Overall, the linear dye inverse problems provided more reliable reconstructions, followed by the UCNP NIR spectral band and then the UCNP blue spectral band.

Table 3

The absolute centroid error of different optical contrast agents.

3.3.

Ex Vivo Experiments

In all experiments, we were able to acquire optical signals with relatively good signal-to-noise ratio (SNR). The data were acquired both at excitation and emission over the three cases tested. The experimental data were postprocessed to yield the same formulation in the in silico investigation. Reconstructions were performed using the same inverse problem methodology. The optical reconstructions for the best regularization parameters and with micro-CT fusion are provided for two views in Figs. 6 and 7. The optical reconstructions are displayed with an isosurface set at 0.5.

Fig. 6

Merged image of micro-CT and optical reconstructions (front view). (a) UCNPs with blue emission, (b) Bis-GMA mixture with UCNPs (20% w.t.) blue emission, (c) UCNPs with NIR emission, and (d) Bis-GMA mixture with UCNPs (20% w.t.) NIR emission.

Fig. 7

Merged image (lateral view): (a) UCNPs with blue emission, (b) Bis-GMA mixture with UCNPs (20% w.t.) blue emission, (c) UCNPs with NIR emission, and (d) Bis-GMA mixture with UCNPs (20% w.t.) NIR emission.

The relative volume error and absolute centroid error were calculated as in the in silico experiments and are provided in Table 4. The real volume in the FoV is $3.14{\mathrm{mm}}^3$, and the centroid of the real cylinder was estimated as (4.5, 7.0, 4.2) mm from micro-CT images. From Table 4, the relative volume error of UCNP reconstructions is normally $<10\%$, while the absolute centroid error is around 1.0 mm from the bottom of sample. As in the in silico experiments, the linear dye outperforms the UCNPs.

Table 4

Relative volume error and absolute centroid error between optical reconstructions and real values.