shows the amplitude of emission light as a function of ICG concentration. are obtained from infinite and cylindrical geometries, respectively. Each set of measurement data is normalized to its maximum, which makes the data of different wavelengths comparable. In all wavelengths and both configurations, the emission strength increases quickly, reaches a maximum, and then decreases gradually. The dashed and the dotted lines in represent the fit to the corresponding data by using the diffusion model, which will be discussed in detail in Sec. 4.1. It can be seen that the emission properties are different for different source-detector separations (rsd) and different excitation wavelengths of 660 and 780 nm. At the excitation wavelength 780 nm, the positions of maxima are located at ~0.3 μM and ~0.4 μM for rsd=1.0 cm and rsd=1.6 cm, respectively. At 660 nm, a relative flat region of 1.7 to 2.7 μM appears in . For the cylindrical geometry, the concentration values of maximum emission are located between 4 to 6 μM for both wavelengths of 660 and 780 nm. These values are much higher than those of infinite geometry. The strength of excitation light collected by D2–D10 decreases with the increasing ICG concentration because the total absorption coefficient of the solution is increased. shows an example of the measured excitation strength at 4-cm source-detector separation as a function of the ICG concentration. Because the sources of different wavelength have different strengths, all data are normalized to their respective maxima. With the increasing ICG concentration, the normalized signals become weaker for all wavelengths. At the region of low concentration, 780 nm has the quickest decay rate, 830 nm is second, and 660 nm has the slowest decay rate. This result implies that the effect of ICG concentration on the absorption measurements of 780 and 830 nm in Intralipid solution is more dramatic than that of 660 nm. It is necessary to note that the emission photons excited by 660 and 780 nm in absorption measurement may increase the detected signal strength of excitation light at 660 and 780 nm. However, this increment is so weak that it can be neglected.
Fig. 3 Normalized emission amplitude of ICG in Intralipid solution as a function of ICG concentration. (a) Infinite geometry. The excitation wavelengths are 660 and 780 nm. The dashed and dotted lines are curves obtained from the diffusion model discussed in (more ...)
Normalized amplitude of excitation light as a function of ICG concentration measured at source-detector separation of rsc=4 cm.
The measurement results of absorption coefficient as a function of ICG concentration for three wavelengths are given in . correspond to measurements of 660, 780, and 830 nm, respectively. The dashed lines in are linear fit to the experimental data. For the concentration range of approximately 0 to 2.0 μM, the experimental data in can be fitted into a straight line, which has a slope of 0.041 and therefore the extinction coefficient ε=4.1 × 104 cm−1 M−1. Note that the absorption coefficient μa =ε[F], where ε is the molar extinction coefficient and [F] is the molarity of the solute. The last three points in can also be fitted into a straight line, which has a slope of 0.01365 and therefore the extinction coefficient ε=1.365 ×104 cm−1 M−1. We believe that the difference between the two slopes may originate from two possible reasons. One possibility is that the extinction coefficient of ICG in Intralipid solution decreases with the increasing ICG concentration. Another possibility is attributed to error in high concentration measurement due to weaker signal strength and lower signal-to-noise ratio (SNR). Nevertheless, we can select the extinction coefficient between the two values as 1.36×104<ε660 <4.1×104 cm−1 M−1. Similarly, results of 780 and 830 nm are shown in . The corresponding extinction coefficients are 3.43×105<ε780<5.73×105 cm−1 M−1 and 0.75×105<ε830<1.77×105 cm−1 M−1. It should be noted that in the accuracy of data is low for 780-nm excitation due to weaker signal and low SNR when the concentration of ICG is higher than 0.6 μM. Therefore, only the results with concentration less than 0.6 μM are given in .
Absorption coefficients of ICG solution in 0.6% Intralipid as a function of ICG concentration measured at (a) 660 nm, (b) 780 nm, and (c) 830 nm using a frequency domain multidistance photon migration method.
To validate that μs
′ can be approximated as a constant, we have used measured amplitude and phase and Eqs. (1)
to extract the real and the imaginary part of wave vector k
, and then compute μa
′ from Eq. (3)
. The results of μs
′ obtained from 660 nm are shown in . It can be seen that μs
′ is limited in a small range of 6.7 to 7.5 cm−1
with an average of 7.25 cm−1
when the ICG concentration is low. At higher concentration, μs
′ varies in a larger range due to fitting errors when Eq. (2)
is used to obtain the real part of the wave vector. However, the average value is about the same as the low concentration case. Thus, we have used an average μs
′ of 7.25 cm−1
and Eq. (4)
to extract absorption coefficient μa
shown in . The measured absorption coefficient and reduced scattering coefficient of background medium without ICG (0.6% Intralipid solution) were μa660
= 0.009 cm−1
= 0.018 cm−1
= 0.035 cm−1
= 7.25 cm−1
= 6.44 cm−1
, and μ′s830
= 6.04 cm−1
Measured reduced scattering coefficients at 660 nm vs. ICG concentration.