2.1.

Microfluidic Phantom Fabrication

The microfluidic flow phantom was cast using PDMS (Sylgard 184™, Dow Corning) with 1.8-mg titanium dioxide (${\mathrm{TiO}}_2$) added per gram of PDMS to generate a scattering background that mimics tissue optical properties at near infrared wavelengths (${{\mu }_s}^{\prime }=8{\mathrm{cm}}^{-1}$).^14,32 The PDMS-${\mathrm{TiO}}_2$ mixture was vigorously mixed for 15 min to ensure even distribution of the ${\mathrm{TiO}}_2$ in the phantom. Centrifugation (3000-g relative centrifugal force, 10 min) was then performed to de-gas the sample and remove any ${\mathrm{TiO}}_2$ clumps.

A machined aluminum mold was used to cast the microfluidic as shown in Fig. 1(a). The extrusion is $460\mu \mathrm{m}\times 460\mu \mathrm{m}\times 25\mathrm{mm}$, which formed three walls of the channel. The square cross-section (1:1 aspect ratio) approximates the circular cross-section of vascular geometries in vivo. The PDMS-${\mathrm{TiO}}_2$ mixture was carefully poured on top of the mold within a polystyrene petri dish and placed in a vacuum chamber to remove air bubbles introduced during pouring. The PDMS was then cured at 70°C for 1 hour, allowed to cool, and detached from the mold. The microchannel side of the phantom was then oxygen plasma bonded to a glass slide to seal the channel. Inlet and outlet ports were attached using 23 gauge blunt tip needles fitted partially inside the phantom, which were epoxied in place for an air-tight seal. Tygon^® microbore tubing (0.02″ inner diameter, Cole-Parmer Instrument Company, LLC) was connected to the blunt tip ports as inlet and outlet tubing. The inlet tubing was connected to the flow control system using fluidic fittings with FEP tubing (IDEX Health and Science, LLC). The outlet tubing drained into a vial, with the tubing end fully submerged in liquid (see S1 in the Supplementary Material). A photograph of the phantom is shown in Fig. 1(b), where the channel is visible inside the ${\mathrm{TiO}}_2$-doped PDMS with the glass slide sealing the surface.

Fig. 1

(a) Photograph of the machined aluminum mold with a $460\mu \mathrm{m}\times 460\mu \mathrm{m}\times 25\mathrm{mm}$ extrusion used to cast the PDMS during fabrication of the microfluidic flow phantom. (b) Photograph of the finished microfluidic flow phantom, showing PDMS bonded to a glass slide, with inlet and outlet ports secured using epoxy. Tubing was secured to the ports and connected with the rest of the system using fluidic fittings.

A colloidal mixture of suspended $1\mu \mathrm{m}$ diameter polystyrene microspheres (10% w/w, 5100A, Thermo Fisher Scientific, Inc.) in ultrafiltered deionized (UFDI) water was used as a blood-mimicking solution. Based on Ref. 33, the reduced scattering coefficient (${{\mu }_s}^{\prime }$) of whole blood with hematocrit of 0.5 is approximately $20{\mathrm{cm}}^{-1}$. Using a 7% by volume mixture of the microsphere solution and UFDI water (e.g., 10 mL of blood mimicking solution = 0.7 mL of the 5100A solution + 9.3-mL UFDI water), we were able to achieve a calculated ${{\mu }_s}^{\prime }$ of $19.8{\mathrm{cm}}^{-1}$. However, we note that the anisotropy of the microsphere solution is different than that of whole blood ($g=0.92$ versus $g=0.98$). The blood-mimicking solution was preferred for several reasons: cleaning and safety, ease of acquisition, and because the flow sensor was factory-calibrated for deionized water. Because the concentration of microspheres was very low (0.7% by weight in the final suspension), the water calibration of the flow sensor remained valid. The solution of microspheres was freshly mixed before each experiment to reduce particle aggregation. Once mixed, the solution was sonicated for 10 min to fully suspend the particles and then degassed under vacuum to eliminate air bubbles.

2.2.

Microfluidic Flow System Instrumentation

To assess the performance of the syringe pump and pressure-regulated flow systems, and to quantify the uncertainty of each system, it is necessary to know the true flow rate of the blood-mimicking solution through the microfluidic channel. A thermal mass flow sensor (FLU-L, $0\pm 1\mathrm{mL}/\min$, Fluigent, Inc.) was placed inline between the flow control system and the phantom inlet tubing, as shown in Fig. 2(a). This flow rate range corresponds to flow speeds of $0\pm 77.8\mathrm{mm}/\mathrm{s}$ in the microfluidic channel. The sensor output was relayed to a computer via an accompanying hub (Flowboard, FLB, Fluigent, Inc.) where the MAESFLO software (Fluigent, Inc.) was used to monitor and record the absolute flow rate. All flow sensor measurements were downsampled from 10 to 2 Hz using interpolation to match the timing of the optical measurements.

Fig. 2

(a) LSCI system schematic for microfluidic flow assessment (L = lens, F = filter). A commercial flow sensor was placed in series with the inlet tubing for the microfluidic flow phantom to obtain real-time absolute flow measurements. Flow was programmatically controlled using either a (b) syringe pump or (c) pressure-regulated flow system. The software for the pressure flow system used a feedback loop between the flow sensor readings and the pressure controller to regulate air pressure.

The syringe pump system (74905-04, Cole-Parmer Instrument Company, LLC) was connected to the flow sensor [Fig. 2(b)] and a 10-mL plastic syringe (#302149, BD) was filled with the blood-mimicking solution described in Sec. 2.1. The syringe pump was programmed to run a predefined flow profile, using the 14.5-mm inner diameter of the syringe to ensure a correct flow rate. It should be noted that a 3-mL syringe was also evaluated, however its performance was worse than the 10-mL syringe and could not hold sufficient volume for all trials without being refilled.

The pressure-regulated flow system used a pressure controller (MFCS-EZ with 69 mbar channel, Fluigent, Inc.) connected to a house air line regulated at 500 mbar, as shown in Fig. 2(c). This controller outputted regulated air flow (up to 69 mbar) to a 15-mL pressurized reservoir (Fluiwell-1C, Fluigent, Inc.) filled with the blood-mimicking solution. Prior to running a flow program, a calibration was performed that accounted for the resistance from the tubing, microfluidic channel, and hydrostatic pressure. The MAESFLO control software used feedback from the inline flow sensor to regulate the air pressure to achieve the desired flow rate.

2.3.

Microfluidic Flow System Assessment

Two separate stepped flow profile experiments were conducted to assess each flow system using the commercial flow sensor. First, a three-step flow profile was used to determine the uncertainty of each flow control system. The experiment lasted 240 s, beginning with 30 s of no flow ($0\mathrm{mm}/\mathrm{s}$) followed by one full minute at each flow speed (2.4, 3.6, and $4.8\mathrm{mm}/\mathrm{s}$) before concluding with an additional 30 s of no flow. The experiment was repeated three times on each system. The second flow profile experiment consisted of a 13-step flow profile. The flow speed was once again varied from 2.4 to $4.8\mathrm{mm}/\mathrm{s}$, however in smaller $0.2\mathrm{mm}/\mathrm{s}$ increments. As with the first experiment, the flow profile begins and ends with 30 s of no flow, with one full minute at each programmed flow speed (840 s total duration). The second experiment was also repeated three times on each flow control system.

To quantify and compare each flow system, we calculated the total combined uncertainty in accordance with National Institute of Standards and Technology guidelines.^34,35 Three main sources of uncertainty were identified for inclusion in the uncertainty budget: repeatability, reproducibility, and measurement bias. Standard uncertainties were calculated for each flow step using 55 s of data, allowing for 5 s of transition from the previous flow state. All values were expressed as percentages relative to their respective means.

The uncertainty in repeatability, which is a measure of within-run variance, was defined as

The uncertainty in reproducibility, which is a measure of between-run variance, was defined as

Finally, the uncertainty in measurement bias, an estimate of flow accuracy, was defined as

The total combined standard uncertainty ($u_c$) was then calculated using the root sum of squares of the individual uncertainty components and reported as the expanded uncertainty ($U=k{u}_c$) with a $k=2$ coverage factor corresponding to a level of confidence of $\sim 95\%$.

2.4.

LSCI Instrumentation

A schematic of the LSCI setup is shown in Fig. 2(a). Measurements were performed using a 660-nm laser diode (HL6545MG, Thorlabs Inc.) mounted in a temperature-controlled housing (LDM21, Thorlabs Inc.) and expanded using an aspheric lens to obliquely illuminate the microfluidic. The laser diode controller (LDC205C, Thorlabs, Inc.) was set to 200 mA ($\sim 120\mathrm{mW}$) while the temperature controller (TED200C, Thorlabs Inc.) was set to 10.5 kΩ (23.8°C). A pair of fixed focal length consumer camera lenses (AF Nikkor 50-mm $f/1.8\mathrm{D}$, Nikon Corp.) were placed in tandem with infinity focus for 1:1 imaging. The aperture of the lower lens was set to $f/11$ to properly sample the speckle pattern³⁶ while the upper lens was left at its maximum size of $f/1.8$. A longpass red filter (600 nm, R-60, Edmund Optics, Inc.) was placed between the two lenses to filter stray background light. The scattered light was imaged with a camera (piA640-210gm, $648\text{pixels}\times 488\text{pixels}$, Basler AG) controlled using custom software. The full sensor array was used, resulting in a field-of-view of $4.8\mathrm{mm}\times 3.6\mathrm{mm}$. The camera exposure time was set to 0.5 ms and allowed to run at full speed, resulting in an effective acquisition rate of $\sim 150$ frames-per-second (fps).

2.5.

LSCI Flow Measurements

To validate the flow sensor measurements, single-exposure LSCI was used to simultaneously image the microfluidic flow phantom during the 13-step flow experiments described in Sec. 2.3. Raw intensity images were converted to speckle contrast images using Eq. (4), where speckle contrast ($K$) is defined as the ratio of the standard deviation (${\sigma }_s$) to the mean intensity ($⟨I⟩$) in a sliding $7\times 7\text{-}\text{pixel}$ window centered at every pixel of the raw image

During post-processing, the average speckle contrast was extracted from each frame within a region centered in the microfluidic channel. This value was used to estimate the correlation time (${\tau }_c$) of the speckle autocorrelation function, which is considered a more quantitative measure of flow.³⁷ The averaged speckle contrast value at each timepoint was fitted for its corresponding ${\tau }_c$ using the following equation

Because ${\tau }_c$ is inversely related to the speed of moving scatterers in the sample,³⁹ the inverse correlation time ($ICT=1/{\tau }_c$) is commonly used for visualization. To compare the LSCI measurements with the flow sensor, the relative flow for each technique was calculated using the average value of the first step ($2.4\mathrm{mm}/\mathrm{s}$) as the baseline. Because the flow sensor software used a separate clock than the LSCI acquisition, the datasets were synchronized during post-processing using the initial rise of the first flow step.

2.6.

MESI Instrumentation

A schematic of the MESI setup is shown in Fig. 3. MESI was performed using a wavelength-stabilized 785-nm laser diode (LD785-SEV300, Thorlabs, Inc.) mounted in a temperature-controlled housing (TCLDM9, Thorlabs, Inc.) and collimated using an aspheric lens (C280TMD-B, Thorlabs, Inc.). The operating current on the laser diode controller (LDC205C, Thorlabs, Inc.) was fixed at 380 mA (300 mW) and the target temperature set to 25°C on the temperature controller (TED200C, Thorlabs, Inc.). The collimated laser light was passed through a free-space optical isolator (Electro-Optics Technology, Inc.) to minimize back reflections that interfere with single frequency performance. Because the external volume holographic grating of the stabilized laser diode produces a dark spot in the far field, the laser was coupled into a single-mode fiber optic patch cable (P3-780A-FC-2, Thorlabs, Inc.) to obtain a Gaussian beam. The fiber output was recollimated (F230APC-780, Thorlabs, Inc.), intensity modulated with an acousto-optic modulator (AOM, 3100-125; RF Driver 1110AF-AIFO-1.0, Gooch & Housego, Ltd.), and relayed to obliquely illuminate the microfluidic.

Fig. 3

System schematic for microfluidic flow assessment of MESI and LSCI measurements using only the pressure-regulated flow system (A = aperture, M = mirror, L = lens, F = filter).

A pair of consumer camera lenses were used to image the scattered light (AF Nikkor 50 mm $f/1.8\mathrm{D}$ + AF Micro-Nikkor 105 mm $f/2.8\mathrm{D}$, Nikon Corp.) with $2.1\times$ magnification through a bandpass filter ($785\mathrm{nm}\pm 31\mathrm{nm}$, 87-773, Edmund Optics Inc.) to a camera (acA1920-155um, $1920\text{pixels}\times 1200\text{pixels}$, Basler AG). The aperture of the lower lens was set to $f/5.6$ while the upper lens was left at its maximum size of $f/2.8$. Only a subset of the overall sensor array was used ($1000\text{pixels}\times 750\text{pixels}$), resulting in a field-of-view of $2.9\mathrm{mm}\times 2.2\mathrm{mm}$. The camera exposures were temporally synchronized with the modulated laser pulses from the AOM. Fifteen different camera exposures ranging between $50\mu \mathrm{s}$ and 80 ms were recorded for each complete MESI frame, resulting in an effective acquisition rate of $\sim 2.5\mathrm{fps}$. The total amount of light used to capture each exposure was held constant with the AOM to minimize the effects of shot noise.¹⁴ The entire acquisition was controlled using custom software written in C++ integrated with a multifunction I/O device (USB-6363, National Instruments Corp.) for the generation of camera exposure trigger signals and AOM modulation voltages.

2.7.

MESI and LSCI Performance

A stepped flow profile experiment was conducted using the pressure-regulated flow system to assess the performance of both MESI and LSCI using the same optical hardware. The flow profile consisted of 19 steps spanning 1 to $10\mathrm{mm}/\mathrm{s}$ in $0.5\mathrm{mm}/\mathrm{s}$ increments. Each speed was maintained for two min with a total experiment duration of 40 min, including brief periods of no flow ($0\mathrm{mm}/\mathrm{s}$) at the beginning and end of the profile. MESI measurements were acquired continuously throughout the experiment at the maximum acquisition rate of the system ($\sim 2.5\mathrm{fps}$). Single-exposure (0.5 ms) LSCI frames were extracted from the MESI dataset post hoc. The initial rise of the first flow step was again used to synchronize the timing of the MESI/LSCI and flow sensor datasets. The experiment was repeated a total of four times across 2 days.

The raw intensity images were converted to speckle contrast images and the average value within the microfluidic channel extracted from each frame as described previously in Sec. 2.5. The average speckle contrast values from all fifteen exposure times were then fitted to the multi-exposure speckle visibility equation ¹⁴ to obtain an estimate of ${\tau }_c$

To directly compare the MESI and single-exposure LSCI measurements with the flow sensor, the relative flow was calculated using the average value of the first step ($1\mathrm{mm}/\mathrm{s}$) as the baseline. The average values for each flow step were calculated using 115 s of data, allowing for 5 s of transition from the previous step.

3.1.

Microfluidic Flow System Assessment

The comparison between the syringe pump and the pressure-regulated flow systems as measured with the inline flow sensor is shown in Fig. 4. These plots demonstrate that the pressure-regulated flow system outperforms the syringe pump by accurately and steadily matching the programmed flow speeds across both experiments. While both flow systems responded quickly to the desired flow changes during the large step size experiment [Fig. 4(a)], the syringe pump system suffered from accuracy and stability issues compared to the pressure-regulated flow system. Furthermore, the small step size experiment [Fig. 4(b)] demonstrated that the syringe pump system could not reliably reproduce the finer flow changes as evidenced by the loss of the stair-stepped flow pattern.

Fig. 4

Flow sensor measurements for the syringe pump (blue) and pressure-regulated (red) flow systems compared to the ideal programmed flow (black) for one run of the (a) 3-step and (b) 13-step experiments. The microfluidic flow speed varied between 2.4 and $4.8\mathrm{mm}/\mathrm{s}$ in 1.2 and $0.2\mathrm{mm}/\mathrm{s}$ steps for the 3- and 13-step experiments, respectively.

Table 1 shows a comparison of the standard uncertainties for repeatability ($u_{\text{repeat}}$), reproducibility ($u_{\text{reproduce}}$), and bias ($u_{\text{bias}}$) for each system at the flow speeds tested in the three-step experiments. These results quantify the observations from Fig. 4 that the pressure-regulated flow system is more stable, repeatable, and accurate at all the tested flow speeds. The combined and expanded uncertainties for both systems are presented in Table 2. These results provide evidence of the superiority of the pressure-regulated flow system, particularly when attempting to produce small flow changes. With the syringe pump system, it would be impossible to reliably separate 20% changes in relative flow from flow system noise at the $2.4\mathrm{mm}/\mathrm{s}$ flow speed. This magnitude of uncertainty in flow generation would make it difficult to assess an optical system’s ability to detect small changes in flow. This limitation is visually represented in Fig. 4(b), where the syringe pump fails to resolve the finer $0.2\mathrm{mm}/\mathrm{s}$ flow changes. Using the pressure-regulated flow system, experiments could be designed with relative flow changes of only 1.25% while remaining confident that the resulting optical system measurements were not caused by flow system noise. This level of certainty would also permit assessing improvements to optical system performance at this scale.

Table 1

Standard uncertainties for repeatability, reproducibility, and bias by flow speeds for the syringe pump and pressure-regulated flow systems.

Table 2

Combined and expanded uncertainties (with k=2 coverage) by flow speeds for the syringe pump and pressure-regulated flow systems.

3.2.

LSCI Flow Measurements

The comparison between the syringe pump and the pressure-regulated flow systems as measured with the inline flow sensor and single-exposure LSCI using the system described in Sec. 2.4 is shown in Fig. 5. The underlying data for both plots are the same as in Fig. 4(b) but are normalized against the first flow step to permit comparison. The relative flow changes measured by LSCI closely track those of the flow sensor and corroborate the accuracy and stability issues seen with the syringe pump system. These results demonstrate that LSCI is capable of detecting similar changes as the commercial flow sensor when measuring relative flow changes up to double the baseline.

Fig. 5

Relative flow measurements for the (a) syringe pump and (b) pressure-regulated flow systems as measured with the flow sensor (blue) and single-exposure LSCI (red). All measurements were normalized to the average of the first flow step ($2.4\mathrm{mm}/\mathrm{s}$) and compared to the ideal programmed flow (black).

3.3.

MESI and LSCI Performance

The flow measurement performance assessment using the pressure-regulated flow system is shown in Fig. 6. The relative flow measured by MESI and LSCI using the system described in Sec. 2.6 are plotted alongside the flow sensor measurements from a single trial in Fig. 6(a). All relative flows were calculated using the average of the first flow step ($1\mathrm{mm}/\mathrm{s}$) as the baseline. Data for each flow step were pooled and averaged across all four trials to assess the overall performance as seen in Fig. 6(b). The coefficients of determination ($R^2$) for this averaged MESI and LSCI data relative to the flow sensor were 0.988 and 0.839, respectively. The concordance correlation coefficients (${\rho }_c$), a metric designed to evaluate reproducibility,⁴¹ were 0.994 and 0.908, respectively. These results demonstrate both strong agreement between MESI and the flow sensor measurements and that MESI outperforms LSCI across large changes in relative flow. It should be noted that the apparent disparity in LSCI performance between Figs. 5(b) and 6 is primarily the result of different flow steps being used as the baseline in each set of experiments. While not an exact comparison, the LSCI measured flow at the $5\mathrm{mm}/\mathrm{s}$ step is $1.94\times$ the flow at the $2.5\mathrm{mm}/\mathrm{s}$ step in Fig. 6, approximately mirroring the $2\times$ change seen between the 2.4 and $4.8\mathrm{mm}/\mathrm{s}$ steps in Fig. 5(b).

Fig. 6

(a) Relative flow profiles for the flow sensor (black), LSCI (blue), and MESI (red) for one trial, all normalized to the average of the first flow step ($1\mathrm{mm}/\mathrm{s}$). (b) Performance of LSCI and MESI flow estimates compared to measured microfluidic flow speed aggregated across all four trials (mean ± sd). The dashed line denotes the line of equality indicative of a linear 1:1 relationship.

Figure 7 summarizes the accuracy of the MESI and LSCI measurements at each flow step aggregated across all four trials. The absolute error for MESI was below 5% except for flow speeds between 3.5 and $6\mathrm{mm}/\mathrm{s}$, where it increased to almost 9%. In contrast, the LSCI error was over 8.2% for all flow speeds, increasing to over 17% for flow speeds $>4\mathrm{mm}/\mathrm{s}$. Aggregated across all tested flow speeds, the average absolute error for MESI was $4.6\pm 2.6\%$ and LSCI was $15.7\pm 4.6\%$.

Fig. 7

Percent error for LSCI (blue) and MESI (red) measurements at each flow step relative to the corresponding flow sensor measurements. Data aggregated by flow step and averaged across all four trials.