2.1.

MC Simulations

The tMCimg MC code²⁵ was run for simplified tissue geometries where the bile duct was assumed to be an infinite cylinder, of $4\mathrm{mm}$ diam, running parallel to the tissue surface. Simulations were performed for bile-duct depths ranging from $3\text{to}15\mathrm{mm}$ between the tissue surface and the vessel center. The optical properties of tissues, namely, the absorption coefficient ${\mu }_a$ and the transport scattering coefficient ${\mu }_s^{\prime }$ , used to generate MC-simulated reflectance data, were collected from the literature.^{26, 27, 28, 29, 30, 31} We verified that except for very early time gates, not relevant to this work, the MC data were identical for a typical tissue-scattering anisotropy³² of 0.9 versus isotropic scattering. The latter was therefore adopted, which decreased MC computation times substantially. Figure 1 shows the MC-simulation geometry. A $100\times 100\times 20\mathrm{mm}$ volume was assigned adipose tissue optical properties ( ${\mu }_a=1.75\times {10}^{-3}{\mathrm{mm}}^{-1}$ , ${\mu }_s^{\prime }=1.10{\mathrm{mm}}^{-1}$ ), and the bile duct was assigned the optical properties of human bile ( ${\mu }_a=2.90\times {10}^{-1}{\mathrm{mm}}^{-1}$ , ${\mu }_s^{\prime }=5.40\times {10}^{-1}{\mathrm{mm}}^{-1}$ ) for a near-infrared wavelength of $820\mathrm{nm}$ . A $31\times 31\mathrm{mm}$ array of $1\times 1\mathrm{mm}$ detector pixels defined the simulated detector field of view (FOV).

Fig. 1

Three-dimensional view of tissue geometry implemented for MC simulations.

Simulations were performed for transmission as well as reflectance mode using 150 million photons for every simulation case, which took $\sim 16\mathrm{h}$ to run on a $3\text{-}\mathrm{GHz}$ PC. The illumination profile was simulated as a $6\text{-}\mathrm{cm}$ FWHM Gaussian beam to match the one used in experiments. For the MC studies comparing reflectance to transmission data in the same tissue geometry, the Gaussian beam illumination was set vertical to the tissue surface. In reflectance experiments, the illumination angle was at $30\mathrm{deg}$ to the surface normal so that the ICCD camera would not intersect the illumination path. In order to perform direct comparison to experiments, MC simulations were also run at a $30\text{-}\mathrm{deg}$ illumination angle. All simulations were run for 15 contiguous time gates of $0.3\text{-}\mathrm{ns}$ width, each thus recording data up to a $4.5\text{-}\mathrm{ns}$ delay, which was more than adequate for capturing the full time-resolved reflectance curves at all virtual detector pixel locations within the FOV. The instrument response function (IRF) of the ICCD setup was not simulated.

2.2.

Time-Gated Measurements with an ICCD Camera

Figure 2 shows the block diagram of the ICCD time-resolved optical imaging system (LaVision GmbH, Gottingen, Germany) employed for the phantom study. A picosecond pulsed laser (SC-450, Fianium Inc., Eugene, Oregon) provided trigger pluses to a constant fraction discriminator that, in turn, triggered a high-rate imager (HRI) picosecond control unit (Kentech Instruments Limited, Oxfordshire, England) through a personal computer (PC) interface, adding adjustable time delays to the signal. The HRI control unit triggered ICCD image acquisition. The HRI gain was set to $400\mathrm{V}$ , and 50 overlapping time gates of $0.3\text{-}\mathrm{ns}$ width were acquired with $0.05\text{-}\mathrm{ns}$ step size, which resulted in a $2.5\text{-}\mathrm{ns}$ scanned temporal range and a $320\text{-}\mathrm{ms}$ integration time for each experiment. The ICCD camera unit consisted of a Cooke SensiCamQE CCD coupled to a gated image intensifier (PicoStar HR, LaVision). The picosecond laser emitted $450–1800\mathrm{nm}$ broadband pulses that passed through a $1064\text{-}\mathrm{nm}$ short pass and an $820\pm 10\mathrm{nm}$ filter (provided by LaVision) before reaching the tissue phantom surface. The laser pulse width was $5\mathrm{ps}$ and was operated at a pulse rate of $20\mathrm{MHz}$ (one every $50\mathrm{ns}$ ). ICCD camera-specific software (Davis 7.0, LaVision) was used to control the image acquisition process. All measurements were taken in a dark room and saved on a PC. Before performing measurements on tissue phantoms, the system IRF was measured by reflecting the incident light beam onto a mirror rather than letting it propagate through the tissue phantom. The IRF was measured to be $300\mathrm{ps}$ at FWHM, which matched the system specifications.

Fig. 2

(a) Block diagram of the ICCD imaging system and phantom illumination geometry. Examples of (b) time-resolved and (c) CW reflectance images of a capillary at $4\text{-}\mathrm{mm}$ depth.

The tissue-simulating phantom consisted of a tub filled with 1% Intralipid (Baxter Inc.), emulating the optical properties of adipose tissue in the semi-infinite medium geometry. Additionally, we performed some reflectance experiments using a porcine adipose tissue phantom to simulate somewhat more closely the clinical setting. The optical properties of the 1% Intralipid ( ${\mu }_a=3.40\times {10}^{-3}{\mathrm{mm}}^{-1}$ , ${\mu }_s^{\prime }=0.92{\mathrm{mm}}^{-1}$ ) and porcine adipose tissue ( ${\mu }_a=1.80\times {10}^{-3}{\mathrm{mm}}^{-1}$ , ${\mu }_s^{\prime }=1.00{\mathrm{mm}}^{-1}$ ) phantoms were determined at $830\mathrm{nm}$ by a frequency domain dual-channel oximeter (model no. 96208, ISS, Champaign, Illinois). For all phantom experiments, the bile duct was approximated by a $3\text{-}\mathrm{mm}$ external diameter ink-filled capillary tube wrapped with black tape to augment its external diameter to $4\mathrm{mm}$ . The depth of the capillary tube inside the phantom was controlled by a vernier scale, to which one of the capillary ends was attached. The tissue phantom surface was illuminated by a Gaussian profile beam of $6\mathrm{cm}$ FWHM, created by expanding the diameter of a $3.3\text{-}\mathrm{mm}$ Gaussian laser beam into a cone and illuminating from a distance of $\sim 1\mathrm{m}$ at a $30\text{-}\mathrm{deg}$ angle [Fig. 2]. In order to get the best possible focus, the ICCD camera was kept $25\mathrm{cm}$ above the surface of the intralipid phantom and was focused on its surface. The resulting FOV size was $38\times 50\mathrm{mm}$ that was captured as a $1040\times 1376\text{pixel}$ image. To avoid camera saturation, the tissue phantom illumination power was increased gradually during time-gated acquisition until the cumulative photon count reached a value of $\sim 3500$ at the time gate, having the maximum counts (maximum of 4096 counts for this $12\text{-bit}$ camera; $320\text{-}\mathrm{ms}$ image capture time per time gate). To meet this requirement, illumination powers of $250–375\mathrm{mW}$ were used for time-resolved illumination, with higher powers being used for the larger capillary depths. To maintain the same image capture time during CW illumination the power was adjusted in the $150–200\mathrm{mW}$ range. The corresponding average illumination power densities across the detector FOV were $\sim 25$ and $\sim 14\mathrm{mW}∕{\mathrm{cm}}^2$ for time-resolved and CW illumination, respectively. Consequently, $\sim 1.8$ times higher power was used for time-gated imaging relative to CW imaging.

In this setting, time-gated reflectance images were acquired for capillary depths of $2–8\mathrm{mm}$ in steps of $1\mathrm{mm}$ [e.g., Fig. 2]. Images at depths $>8\mathrm{mm}$ were not acquired because the shadow of the capillary on the phantom surface was no longer detectable. Subsequently, a CW image was captured in dc mode [e.g., Fig. 2] down to a maximum detection depth of $7\mathrm{mm}$ . Comparison of Figs. 2 and 2 demonstrates how the capillary is less discernible in CW reflectance images than in time-resolved ones under Gaussian illumination. In order to make the reflectance profile across the detector FOV flatter and thus improve visibility of the capillary in reflectance images, we also performed control experiments with identical data acquisition settings, but in the absence of the capillary. The reflectance images in the presence and absence of the capillary were then divided, and the C/B and FWHM values were quantified for all time gates by the processing algorithm described in Section 2.3. Subsequently, the single time gate having the highest C/B and the one with the smallest FWHM were identified as the optimal ones for each metric, respectively. It is these latter values that were quantified in this work as a function of capillary depth to assess the ICCD system’s vessel localization capacity.

Integration of data from several adjacent time gates did not offer any advantage in further improving the optimal C/B and FWHM values. More specifically, for capillary depths of $<10\mathrm{mm}$ , sufficient photons were detected per time gate and, therefore, averaging could not offer any significant improvement in photon statistics. For capillary depths beyond $10\mathrm{mm}$ , the illumination laser power could not be further increased so that more photon counts per time gate could be collected and averaging of the optimal time gates with neighboring, nonoptimal, ones did not yield any substantial improvement in C/B and FWHM values. We also investigated whether these two image-derived parameters could be further optimized by deconvolving the system IRF. We found that deconvolving the latter did not have a significant effect on the optimal C/B and FWHM values. Possible reasons for that were the small IRF width relative to the temporal extent of reflectance curves and the fact that all data analyzed in this work were a ratio between two measurements—one with and one without the capillary inside the tissue phantom.

2.3.

Data Processing Algorithm

The ratio images were fitted by a nonlinear least-squares algorithm (fit.m, Matlab) to a Lorentzian curve shown below

Fig. 3

(a) Schematic showing fitted parameters for a Lorentzian. Example of fits to a Lorentzian profile at (b) early and (c) late ( $210\mathrm{ps}$ and $1.47\mathrm{ns}$ , respectively) time-gated reflectance images for a capillary at $5\text{-}\mathrm{mm}$ depth.

3.1.

MC Simulations

The MC-simulated images for all time gates were fit to Eq. 1 for all bile-duct depths. Figures 3 and 3 demonstrate sample fits of time-gated reflectance profiles to the Lorentzian curve. It is seen that at later time gates, contrast decreases and FWHM increases. Early time gates had low contrast values because photons had primarily traveled above the absorber; thus, there was only a weak signature of the absorber in the reflectance data. Therefore, we investigated the question of which time gates offered optimal C/B and FWHM values and how much better these values were compared to the ones obtained by CW imaging.

The overall pattern observed was that contrast was initially low, then increased at later time gates, and then decreased again at later times. However, as discussed further later in Fig. 7, in the comparison with experimental data, C/B grew from a low value to its maximum and then stayed relatively constant for later time gates. The reason was that background was decreasing along with contrast at the same rate, so that their ratio remained constant at a plateau value at all later time gates. We have selected the C/B value attained at the earliest time gate for which that plateau was reached as the optimal parameter choice for vessel detection sensitivity. The reason for selecting the earliest plateau time gate was that fewer photons were detected at subsequent time gates. As a result, later time gates had inferior photon statistics and therefore had higher uncertainty in C/B values, as seen later in Fig. 7. Figure 4 shows the resulting plots when comparing maximum C/B values as a function of bile-duct depth for reflectance versus transmission mode. It is seen that the two illumination modes are almost equivalent down to a depth of $10\mathrm{mm}$ , but the performance of transmission mode at greater depths is superior. This is because more photons travel through the bile duct and therefore cast a greater absorption signature at the detectors, when this vessel is located closer to the transilluminating light source at the bottom of the $2\text{-}\mathrm{cm}$ -thick adipose tissue slab. Therefore, the transmission time-gated mode appears to be the preferable illumination geometry for attaining good contrast for all bile-duct depths, even though the time-gated reflectance mode may have a marginal advantage at superficial depths. The advantage of transmission mode is far superior for CW illumination as can be seen in Fig. 4. In this case the early photons, which travel only superficially and above the bile duct, are the main contribution to the reflectance signal, which dramatically reduces the C/B ratio.

Fig. 4

Maximum C/B values attained as a function of bile-duct depth in (a) time-gated reflectance versus transmission mode, (b) CW reflectance versus transmission mode, (c) time-gated versus CW reflectance mode, and (d) time-gated versus CW transmission mode.

Fig. 7

(a) C/B as a function of time gate for a $4\text{-}\mathrm{mm}$ -diam bile duct (simulations) and a $4\text{-}\mathrm{mm}$ -diam capillary (experiments), both located at a depth of $4\mathrm{mm}$ . (b) Comparison of diffuse reflectance profiles between simulation and experiment for a vessel depth of $5\mathrm{mm}$ .

The capacity of time-gated images for depth selectivity enables a substantial improvement of C/B (i.e., improved detection sensitivity) over CW, as is clearly seen in Fig. 4. However, the depth selectivity of time-gated imaging is reduced when imaging in reflectance mode for greater bile duct depths. This is because the photons that have traveled through the bile duct and make it back to the surface must have scattered many times, and due to the diffusive nature of this process, they could have visited a wide range of tissue depths. Therefore, in Fig. 4 it is seen that C/B values for time-gated imaging converge toward those of CW imaging for greater bile-duct depths. Interestingly, the detection sensitivity in CW transmission mode is only slightly inferior (i.e., by no more than $\sim 20\mathrm{\%}$ ) to the one for time-gated transmission imaging [Fig. 4]. This is because in transmission-mode photons can travel through the bile duct before reaching the detectors on the other side of the adipose tissue slab. We conclude that CW imaging in transmission mode may in fact be the simplest means of attaining good detection sensitivity of the bile duct, though time-gated imaging is superior in most cases.

The superiority of transmission relative to reflectance imaging was also confirmed by the improved spatial resolution, as quantified by the minimum FWHM values attained in the time-gated images. Figure 5 demonstrates that time-gated transmission attains better spatial resolution than time-gated reflectance as bile-duct depth increases, with FWHM improving by a factor of 2 at a depth of $15\mathrm{cm}$ . In reflectance mode, fewer photons reach the bile duct when it is located deeper in tissue. As a result the wide-field reflectance images become very noisy, which has increased the uncertainty of fitted FWHM values. Similarly, Fig. 5 demonstrates that transillumination also yields superior spatial resolution for the CW mode, especially at greater bile-duct depths. However, the spatial resolution of time-resolved illumination is not superior to CW illumination in reflectance mode but is only superior in transmission mode as demonstrated in Figs. 5 and 5, respectively. This is due to the weak depth selectivity that wide-field time-gated imaging can attain relative to the complete lack thereof in CW imaging.

Fig. 5

Minimum FWHM values attained as a function of bile duct depth in (a) time-gated reflectance versus transmission mode, (b) CW reflectance versus transmission mode, (c) time-gated versus CW reflectance mode, and (d) time-gated versus CW transmission mode.

Simulations for bile-duct depths of $>15\mathrm{mm}$ are not shown in Figs. 5 and 6 because the shadow of the bile-duct cast at the detectors was very shallow and therefore overwhelmed by MC stochastic noise. To improve the scoring statistics and remedy this problem, MC simulations would need to be run for substantially larger numbers of photon histories. Therefore, the plotted error bars that originated from the fitted parameter standard deviations could have been smaller magnitudes if longer MC runs were performed. However, the computational times involved would be impractical. This is particularly true for the time-resolved simulations, which spread the same amount of simulated photon histories over a large number of time gates. It is also important to mention that fewer photons would be scored at detectors closer to the edge of the Gaussian illumination profile, which could further reduce the maximum depth at which a vessel could be detected. In this work, the linear dimension of the detector array $\left(3.1\mathrm{cm}\right)$ was substantially smaller than the illumination profile’s FWHM $\left(6\mathrm{cm}\right)$ , which resulted in negligible variation of optimal C/B and FWHM values, and therefore, in depth detection sensitivity, across the FOV.

Fig. 6

Maximum C/B for a given vessel depth was attained at a time delay nearly equal to the time that incident light took to reach a mean visit tissue depth equal to the vessel’s center depth.

One final consideration for Figs. 4 and 5 was whether there was any relation between the time gates at which maximum C/B versus a minimum FWHM was attained. As the tMCimg²⁵ code can score the photon weights as a function of time gate and depth in tissue, we have computed the mean depth visited as a function of time delay. Figure 6 plots this latter quantity as well as the time delays at which maximum C/B was attained for a given vessel depth. It is seen that maximum C/B was attained when the mean visit depth was nearly equal to the depth of the vessel’s center. On the other hand, minimum FWHM was attained at the earliest possible time gate where the shadow of the tissue-embedded vessel could be seen in the reflectance profile, corresponding to tissue depths akin to the top side of the vessel (not shown in Fig. 6), and reliably fitted to Eq. 1.

3.2.

Comparison between MC Simulations and ICCD Camera Experiments

We have also performed time-gated reflectance experiments on tissue-simulating phantoms, mimicking the MC-simulation geometry, with an ICCD camera as described in Section 2. Figure 7 shows that the time-gated C/B values for a $4\text{-}\mathrm{mm}$ -diam ink-filled capillary, mimicking the bile duct at $4\mathrm{mm}$ depth, agree rather well with simulation data. Both the ink and the bile-duct absorption coefficient assumed in the simulations²⁹ have very high values; thus, exact matching in their absorption values was not necessary. Similar agreement in C/B versus time delay was attained for greater vessel depths. However, acquisition of such C/B versus time-delay curves proved very challenging due to the limited dynamic range of our $12\text{-bit}$ ICCD camera system. More specifically, no such curve could be acquired across a time-delay range of a few nanoseconds with a single camera gain setting. In Fig. 7, the C/B value seems relatively flat for most time delays, but this is a result of contrast and background decreasing at the same rate with time delay so that their ratio remains constant. Therefore, from an experimental point of view, there were many fewer counts at later time gates, which resulted in a “floor” effect related to the detector’s limited dynamic range, and photon counts were underestimated. Therefore, the only way to acquire curves such as the one in Fig. 7 was to acquire data at different time-delay ranges, of a few hundred picoseconds’ width at a time, with progressively increasing gain for later time gates. While acquiring data in a given time-delay range, the detector was programmed to not be active at earlier time gates so that it would not saturate. C/B for different time-delay ranges were then normalized as a fraction of the average count rate at each camera gain setting and were stitched together to form curves like the one shown in Fig. 7. Though these experiments validated the MC-simulation results, they would be impractical to implement in a clinical setting due to the need for continual adjustment of gain, because later time gates have substantially fewer photons than earlier ones. A higher dynamic range system, such as the commercially available $16\text{-bit}$ version of the ICCD camera used in this work, could obviate the need for continual gain adjustment and therefore be more practical for use in the clinic.

Figure 7 shows the comparison of diffuse reflectance profiles along a line crossing through the center of the Gaussian illumination profile, across the camera FOV. The reflectance profiles were asymmetric because the illumination was incident at an angle of $30\mathrm{deg}$ to avoid the camera being in the way of the illumination path (Fig. 2). Good agreement was observed between the MC-simulated and experimentally acquired profiles for that geometry [Fig. 7, time delay $350\mathrm{ps}$ ]. Good agreement was also observed for the maximum C/B [Fig. 8 ] and minimum FWHM [Fig. 8] values found from fitting MC-simulated and experimental images to Eq. 1. As the profiles where asymmetric due to angled illumination, a linear correction for the slanted background was implemented before fitting to Eq. 1 for both experimental and corresponding MC data. However, the ICCD camera’s limited dynamic range affected the maximum depth at which the diffuse shadow of the capillary could be detected in the reflectance profile to $\sim 7\mathrm{mm}$ for CW and to $\sim 8\mathrm{mm}$ for time-gated illumination. Had the $16\text{-bit}$ version of the same commercial ICCD system been available to us, the aforementioned dynamic range problems discussed in the context of Figs. 7 and 8 would be less severe and may have enabled observation of the vessel at even greater depths.

Fig. 8

Comparison between MC simulations and experiments on Intralipid and adipose tissue phantoms for (a) maximum C/B and (b) minimum FWHM values as a function of capillary depth.

In addition to the measurements on Intralipid phantoms, reflectance measurements were also performed with the capillary embedded at different depths within porcine adipose tissue. The motivation for these latter measurements was that the heterogeneous texture of adipose tissue would emulate somewhat more closely the clinical setting compared to the uniform Intralipid fluid. Reflectance measurements from the Intralipid phantom were divided with corresponding adipose-embedded capillary reflectance measurements to flatten the illumination profile. It was found that the optimal C/B and FWHM values for adipose tissue measurements were not significantly different compared to the ones deduced from the Intralipid phantom experiments [Figs. 8 and 8]. The only difference was that the maximum depth at which the diffuse shadow of the capillary could be detected in the reflectance profile was now reduced to $\sim 6\mathrm{mm}$ for CW and to $\sim 7\mathrm{mm}$ for time-gated illumination. The reduction of maximum detection depth by $\sim 1\mathrm{mm}$ relative to the Intralipid case was found to be due to the heterogeneity of adipose tissue, which introduced small spatial heterogeneity in the reflectance signal. Once the vessel shadow depth became comparable in magnitude to the amplitude of spatial variations in reflectance, the vessel was no longer detectable. Therefore, in the adipose tissue case, the depth detection sensitivity was limited by spatial heterogeneity of the reflectance profile in the FOV and not by the ICCD dynamic range.