Dual-ratio approach for detection of point fluorophores in biological tissue

Abstract

Significance: Diffuse in-vivo Flow Cytometry (DiFC) is an emerging fluorescence sensing method to non-invasively detect labeled circulating cells in-vivo. However, due to Signal-to-Noise Ratio (SNR) constraints largely attributed to background tissue autofluorescence, DiFC's measurement depth is limited. multiplies Aim: The Dual-Ratio (DR) / dual-slope is a new optical measurement method that aims to suppress noise and enhance SNR to deep tissue regions. We aim to investigate the combination of DR and Near-InfraRed (NIR) DiFC to improve circulating cells' maximum detectable depth and SNR.

Approach: Phantom experiments were used to estimate the key parameters in a diffuse fluorescence excitation and emission model. This model and parameters were implemented in Monte-Carlo to simulate DR DiFC while varying noise and autofluorescence parameters to identify the advantages and limitations of the proposed technique.

Results: Two key factors must be true to give DR DiFC an advantage over traditional DiFC; first, the fraction of noise that DR methods cannot cancel cannot be above the order of 10% for acceptable SNR. Second, DR DiFC has an advantage, in terms of SNR, if the distribution of tissue autofluorescence contributors is surface-weighted.

Conclusions: DR cancelable noise may be designed for (e.g. through the use of source multiplexing), and indications point to the autofluorescence contributors' distribution being truly surface-weighted in-vivo. Successful and worthwhile implementation of DR DiFC depends on these considerations, but results point to DR DiFC having possible advantages over traditional DiFC.

Fig 1

Conceptual application of Dual-Ratio (DR) Diffuse in-vivo Flow Cytometry (DiFC). In principle, source and detector pairs could be arranged (a) perpendicular, or (b) parallel to the underlying artery (in this case, the radial artery). (c) Use of two sources (1, 2) and two detectors (A, B) would permit four source and detector pairs separated by a source-detector distance $\left(\rho \right)$. (d) Photograph of Near-InfraRed (NIR) Diffuse in-vivo Flow Cytometry (DiFC) system on a diffusive flow phantom with fiber probes arranged perpendicular to the tubing direction. The dashed black line in (d) corresponds to the mid-plane shown in (c). The instrument permitted measurement with a single source and detector pair, in this case (2 & A). Background-subtracted sample DiFC data of fluorescent microspheres embedded (e) 0.75 mm deep and (f) 1.00 mm deep in a phantom with a flow channel.

Fig 2

Map of the Signal-to-Noise Ratio (SNR) to a fluorescent target at a particular position (in the $y=0\text{\hspace{0.17em}mm}$ plane) within a medium with surface-weighted ((a)-(d)) or homogeneous ((e)-(h)) AutoFluorescence (AF) contributors for four different measurement types with detectors represented by blue arrows and sources by red arrows. (a),(e) Single-Distance (SD) at a source-detector distance ($\rho$) of 0 mm. (b),(f) SD at a $\rho$ of 3 mm. (c),(g) SD at a $\rho$ of 4 mm. (d),(h) Dual-Ratio (DR) containing $\rho$s of 3 mm and 4 mm. Note: White regions represent SNR greater than the maximum color-bar scale (i.e., 11) and gray regions represent absolute SNR less than one. Parameters: Source = pencil, $\text{Detector}=0.5\text{NA}$ cone, $\text{voxel}=0.1\text{\hspace{0.17em}mm}\times 0.1\text{\hspace{0.17em}mm}\times 0.1\text{\hspace{0.17em}mm}$, absorption coefficient $\left({\mu }_a\right)=0.002{\text{ mm}}^{-1}$, scattering coefficient $\left({\mu }_s\right)=7{\text{ mm}}^{-1}$, anisotropy factor $\left(g\right)=0.9$, index of refraction $\left(n\right)=1.37$, for surface-weighted ((a)-(d)) AF fluorescence efficiency $\left(\eta \right)\propto e^{\text{ln} \left(0.5\right)z/0.1\text{\hspace{0.17em}mm}}$ for homogeneous ((e)-(h)) $\eta$ constant, & signal and noise parameters found in appendix Appendix C (in this simulation we assumed 5 % Non-Cancelable noise).

Fig 3

Traces of expected Signal-to-Noise Ratio (SNR) from a fluorescent target flowing at a particular depth (color) beneath the source-detector arrangement (same as Figure 1,2; $y=0\text{\hspace{0.17em}mm}$). These results are shown for surface-weighted and homogeneous AF contributors (line-type). (a),(e) Single-Distance (SD) at a source-detector distance ($\rho$) of 0 mm. (b),(f) SD at a $\rho$ of 3 mm. (c),(g) SD at a $\rho$ of 4 mm. (d),(h) Dual-Ratio (DR) containing $\rho$s of 3 mm and 4 mm. Note: Gray regions represent absolute SNR less than one. Parameters: The same as Figure 2 with assumed 5% Non-Cancelable noise.

Fig 4

Traces showing a comparison of experimental phantom data and expected results from the Monte-Carlo (MC) model. Single-Distance (SD) traces are normalized so that the mean peak maximum between panels (e) and (f) is one, meaning all sub-panels utilize the same normalization factors. (a) Schematic of perpendicular flow case. (b),(c) Comparison for perpendicular flow case. (d) Schematic of parallel flow case. (e),(f) Comparison for parallel flow case. Note: Shaded regions represent the noise level of the experimental data. Parameters: The same as Figure 2 with a known of 1.5 mm and assumed fluorescent target velocity of $25\text{\hspace{0.17em}mm}{\text{s}}^{-1}$.

Fig 5

Signal-to-Noise Ratio (SNR) from a fluorescent target below the centroid of the optodes used for each measurement type as a function of depth $\left(z\right)$. Colors show different measurement types, and line type shows the AutoFluorescence (AF) contributor distribution. Parameters: The same as Figure 2 with assumed 5 % Non-Cancelable noise.

Fig 6

The deepest fluorescent target that each data type can measure (Signal-to-Noise Ratio (SNR) greater than one) as a function of the fraction of non-cancelable (by Dual-Ratio (DR)) noise ($p_{NC}$). Colors show the data type, and line type shows the distribution of AutoFluorescence (AF) contributors. Note: For a definition of see Appendix B.2 or Equation 2. Parameters: The same as Figure 2.