Liquid phantoms for near-infrared and diffuse correlation spectroscopies with tunable optical and dynamic properties

: We present the recipe and characterization for preparing liquid phantoms that are suitable for both near-infrared spectroscopy and diﬀuse correlation spectroscopy. The phantoms have well-deﬁned and tunable optical and dynamic properties, and consist of a solution of water and glycerol with fat emulsion as the scattering element. The recipe takes into account the eﬀect of bulk refractive index changes due to the addition of glycerol, which is commonly used to alter the sample viscosity.


Introduction
The combination of diffuse correlation spectroscopy (DCS) with near-infrared diffuse optical spectroscopy (NIRS) provides important and complementary information about the composition, structure and hemodynamics of the tissue under investigation [1]. Therefore, recently this combination has gained popularity as an emerging non-invasive biomedical modality. NIRS methods like time-resolved spectroscopy (TRS), frequency-domain or continuous wave optical spectroscopy allow the quantification of the wavelength dependent optical absorption and scattering coefficients of the probed tissue which, in turn, permit the estimation of the concentration of chromophores like oxy-and deoxy-haemoglobin, water, lipids, collagen, and give information on cell structure [2,3]. Near-infrared diffuse correlation spectroscopy (DCS), on the other hand, exploits the decay of the diffuse intensity auto-correlation function due to altered speckle statistics coming from diffuse light by moving particles (primarily red blood cells) in order to measure the microvascular blood flow in the tissue [1,4,5]. By combining the information retrieved by NIRS and DCS, it is possible to enhance the sensitivity to the hemodynamic biomarkers in order to discriminate between healthy and different pathological conditions such as brain injury, malignancy and others. Furthermore, the combination of NIRS and DCS increases the precision in retrieving the blood flow index by fixing parameters such as the reduced scattering coefficient and the absorption coefficient in DCS fitting procedure [1,6].
In order to validate and standardize NIRS and DCS measurements for clinical applications, it is important to develop reference standard phantoms, i.e. systems that mimic and reproduce the optical and dynamic properties of the tissue. Phantoms with calibrated properties are used to develop the system at the laboratory level, to measure the system performances against standardized protocols, to allow daily quality checks in clinical studies and to calibrate instruments for absolute measurements. All these measures go in the direction of increasing the reliability, and reproducibility of clinical studies and also to set the floor for standardization activities in the field [7,8].
The design of phantoms for NIRS allows their preparation with well-controllable optical properties. Essentially, the ideal bulk medium is non-diffusive and transparent in the whole optical spectrum of interest with the possibility to add the scattering centers and the absorbing centers in the proper ratio so as to obtain the desired wavelength (λ) dependent absorption coefficient (µ a (λ)) and reduced scattering coefficient (µ s (λ)). In literature we find several examples of liquid phantoms made of suspension of small fat droplets in water (lipid emulsions such as Intralipid20% -Fresenius Kaby, Germany -, Lipofundin20% -B. Braun Melsungen AG, Germany, and many others) and ink [9][10][11][12][13], and, solid phantoms made of epoxy resin or silicon rubber and titanium dioxide particles as scatterers [7,8,14].
The requirements of a phantom for DCS are basically the same as those of NIRS but with some additional constraints. The main difference is that DCS is based on the measurement of the temporal auto-correlation of laser speckles in the turbid medium which depends on the motion of the scattering centers. We note that it has been observed that the decay of the temporal autocorrelation curves of diffuse photons emerging from tissue is well fitted using an effective particle Brownian motion model [1,15]. Therefore, DCS phantoms often use the Brownian motion of the scattering centers as a contrast factor. Most common DCS phantoms are liquid phantoms made of water and Intralipid20% or Lipofundin20%. Previous attempts in changing the particle Brownian motion coefficient (D b ) varied from changing the viscosity of the medium to changing the temperature or inducing forced motion by pumps [16][17][18][19][20][21][22][23][24]. However, all these methods present different challenges that, to date, have not been addressed thoroughly. Viscosity is often altered by mixing glycerol or methyl-cellulose which alter also the index of refraction of the bulk medium hence altering light scattering properties [25]. Temperature also changes the viscosity of the bulk medium (often water) and may alter the composition of the fat droplets. Finally, forced motion induced by pumps through pipes or porous materials may lead to unpredictable dynamics.
Here, we demonstrate a recipe to fabricate a liquid phantom for near infrared spectroscopy and diffuse correlation spectroscopy with well-defined optical (absorption and scattering) and dynamic (Brownian diffusion coefficient) properties considering solutions of water and glycerol with Lipofundin20% (B. Braun Melsungen AG, DE) as the scattering element while accounting for the bulk refractive index changes. The dynamic and scattering properties of the phantoms can be tuned considering that the motion of the scatterers depends on the relative concentration of glycerol in water, which alters the viscosity of the solution, and that the reduced scattering coefficient of the system depends both on the concentration of scatterers and glycerol in the solution [25]. In the next sections we present the outcomes of independent TRS characterization experiments and of DCS experiments to develop this recipe.

Phantoms
The phantoms considered for this study are solutions of ultrapure (Milli-Q, Milipore, USA) water and glycerol (Sigma-Aldrich Co. LLC. U.S., cod. 49770, ≥ 99.5%) with Lipofundin20% (B. Braun Melsungen AG, DE) [26] as the scattering element. We have mixed phantoms with different concentrations of glycerol in water ranging from 0% to 30% of the solution. For each concentration of glycerol, we have changed the concentration of scatterers ranging from 0.1% to approximately 4.0% of the solution by sequentially adding Lipofundin20% (mixed with glycerol, in order to preserve the ratio between water and glycerol). In this study, we have decided to not change the absorption of the phantoms, since, as shown in several works and as reported in the following sections, the absorption coefficient can be tuned independently from the scattering and dynamic properties by adding ink or other absorbers to the solution [27]. The experiments on every single phantom have been performed during one single day of measurements. For this reason, based on previous studies [10] and our experience, the optical and dynamic properties of the phantoms used can be considered stable over the duration of the experiments.
Experiments were conducted at two sites -Politecnico di Milano (POLIMI, Milan, Italy) and ICFO-the Institute of Photonic Sciences (ICFO, Barcelona, Spain). For the experiments performed at POLIMI, we have prepared solutions of 0%, 5%, 10%, 15%, 20%, 25%, 30% of glycerol in Milli-Q water. For each different solution of water and glycerol, the scatterer concentration is varied between 0.1% and 1.2% of the whole solution in ten equally spaced steps. The liquid solutions have been placed in a black PVC phantom box. The frontal wall of the phantom box has small transparent windows, allowing the laser light to enter the diffusive medium, and the re-emitted photons to be collected outside the box. The top of the phantom box is exposed to the air and the whole set is covered by a dark, light-proof curtain during the experiments. More details about the phantom box can be found in Ref. [28].
For the two independent experiments performed at ICFO, we have prepared solutions of 0%, 20% and 30% of glycerol in Milli-Q water. In order to obtain roughly similar scattering coefficient (considering that higher concentrations of glycerol reduces the scattering strength), we have added different concentrations of scatterers in the three phantoms with different glycerol concentration; for the phantom with 0% of glycerol, we have considered 0.75%, 1.5% and 2.3% concentrations of scatterers, for the phantom with 20% of glycerol, we have considered 0.89%, 1.8% and 2.7% concentrations of scatterers, and finally, for the phantom with 30% of glycerol, we have considered 1.3%, 2.6% and 4.0% concentrations of scatterers. The solutions that were placed in a black phantom box with a size of 20 cm × 20 cm × 20 cm which allow the access of the optical fibers used for the experiments from the top side of the box. The top of the phantom box is exposed to the air and the whole set is covered by a dark, light-proof curtain during the experiments.

Scattering properties
The optical properties of a liquid phantom are strongly dependent on several parameters such as the concentration of the scatterers, the refractive index contrast between the scattering elements and the environment and the wavelength of the light. In the independent scattering regime (low concentration of scatterers, each scattering event can be considered independent from the previous events), for a fixed wavelength λ, the bulk reduced scattering coefficient µ s of the phantoms is directly linked to the concentration of the scattering elements and to the scattering properties of a single scatterer through the relation [29] where σ s is the scattering cross section, g is the anisotropy factor and ρ s is the concentration of the scatterers. For a fixed solution of glycerol and water, the reduced scattering coefficient of the system linearly increases with the concentration of scatterers. For practical purposes, in order to interpret the experimental results, equation 1 is commonly reduced to the relation where s is the 'intrinsic' reduced scattering coefficient of the scattering element and C is a coefficient accounting for the fact that diffusion theory does not work properly for low concentration of scatterers [29-31]. Moreover, the reduced scattering coefficient depends on the refractive index contrast between scatterers and the bulk medium. For this reason, considering scatterers with higher refractive index than the bulk medium, it is expected that the reduced scattering coefficient decreases when the glycerol concentration in water increases. Adding glycerol (refractive index n = 1.47) to water (n = 1.33), indeed, reduces the refracting index contrast between scatterers and environment which affect the scattering cross section σ s and the anisotropy factor g in equation 1. As described by the Mie theory of light scattering, the decrease of the reduced scattering coefficient for increasing glycerol concentration ρ glyc is expected to be linear, given by where s is the 'intrinsic' scattering coefficient of the scattering element, glyc is the proportional coefficient depending on the optical properties of glycerol, and 0 s is the intrinsic reduced scattering coefficient of Lipofundin in water (0% of glycerol).
The optical properties of a liquid phantom are strongly dependent on the wavelength (λ) of the light. For tissue simulating phantoms in the near-infrared region, the dependence of the intrinsic reduced scattering coefficient, s , on the wavelength, λ, is well described by the power law derived from Mie scattering theory [8, 12, 13, 32-34] where A and b are related mainly to the density and refractive index contrast, and size of the scattering centers respectively, while λ 0 is a reference wavelength.

Dynamic properties
The dynamic properties of a liquid phantom can be controlled by changing the viscosity of the solution in which the scatterers are suspended. The Brownian diffusion coefficient D b of a particle undergoing Brownian motion in a fluid depends indeed on the viscosity η of the solution, following the Einstein relation [35] where K B is the Boltzmann's constant, T is the temperature and r is the radius of the particle. This relation states that, in the same environmental conditions, the ratio between the D b related to particles in two solutions with different viscosity is equal to the inverse of the ratio of the viscosity of the solutions A pellin broca prism couples the selected wavelength into a 50 µm fiber. Depending on the selected wavelength, the power at the tip of source fiber varies between 0.5 to 6 mW. Detection is achieved by a multi-mode step index fiber (1 mm core, length 50 cm, NA 0.39) connected to a photomultiplier tube (double channel microchannel plate). A time correlated single photon counting card (SPC-130, Becker & Hickl GmbH, Germany) was utilized for the acquisition of temporal curves. In this study, the measurements were performed in reflectance geometry at two source detector separations 20 and 30 mm, and, at six wavelengths 600, 700, 785, 900, 1000 and 1100 nm. The reduced scattering coefficients at the wavelengths of 600, 700 and 785 nm were retrieved by exploiting a linear method comparing the distribution of time of flights of photons at two different source-detector separations as described in ref. [38]. The linear method gives reliable results for the reduced scattering only in the diffusive regime and, therefore, it was not applied at measurements performed at wavelengths 900, 1000 and 1100 nm where the values of the reduced scattering coefficient were too low. The absorption coefficients have, on the other hand, been retrieved for all the wavelengths by a non-linear fit of the solution of the diffusion equation for a homogeneous medium, convoluted with the instrument response function as described in the following Section. The measurements have been performed at a room temperature of (25 ± 2)°C.

The Institute of Photonic Sciences experiments
Diffuse correlation spectroscopy and time-resolved spectroscopy experiments carried on at ICFO have been performed with a single hybrid diffuse optical device [37]. The DCS module of the hybrid device consists in single longitudinal mode laser (DL785-120-SO, CrystaLaser, Reno, NV, USA) as source. Light is injected in the phantom using a 200 µm core multimode fiber and the diffused reflectance is collected using a fiber bundle consisting of four 5.6 µm core single mode fibers. The detection part consists of four single photon counting avalanche photodiodes (SPCM-AQ4C, Excelitas, Québec, Canada), and the intensity temporal autocorrelation function of each channel is calculated in real time by a 8-channel digital correlator (correlator.com, New Jersey, USA). Source and detection fibers are placed in reflectance geometry at a distance of 2.5 cm. The acquired intensity temporal autocorrelation functions (g 2 ) are transformed into electric field temporal autocorrelation functions (g 1 ) which are fitted with the solution of the correlation diffusion equation for a semi-infinite medium (with extrapolated boundary conditions), as reported in ref. [1], in order to retrieve the scatterer Brownian diffusion coefficient (D b ). In the fitting procedure, we have considered the properly weighted index of refraction of solutions of water and glycerol, reported in literature [25]. Moreover, the absorption and reduced scattering coefficients (µ a and µ s ) are fixed parameters determined through the TRS measurements performed on the very same phantoms.
The TRS part used one pulsed laser (BHLP-700, Becker & Hickl GmbH, Germany) with a repetition rate of 50 M Hz and wavelength 785 nm. The laser light is sent to the phantom through a 62.5 µm core graded index fiber and the diffused reflectance is collected using a 54 fiber bundle of 62.5 µm core graded index fibers. The detection part consists of a hybrid photomultiplier detector (HPM-100-50, Becker & Hickl GmbH, Berlin, Germany) connected to a time correlated single photon counting card (SPC-130, Becker & Hickl GmbH, Berlin, Germany) and a detector control card (DCC-100, Becker & Hickl GmbH, Berlin, Germany).
We have acquired the distribution of time of flights of photons (DTOF) in reflectance geometry for a source-detector separation of 2.5 cm. The instrument response function (IRF) has been acquired by aligning the tips of source fiber with the detector bundle with a diffusing paper layer in between. After background subtraction, in order to retrieve the absorption and reduced scattering coefficients (µ a and µ s ), we have fitted the measured DTOF with the convolution of the solution of the diffusion equation for a semi-infinite medium (with extrapolated boundary conditions) with the IRF. The fitting interval ranges from approximately the 80% of the maximum of the curve on the rising edge to roughly the 0.1% of the maximum for the decaying tails. The measurements have been performed at a room temperature of (25 ± 2)°C.

Time-resolved spectroscopy results
As explained above, time-resolved spectroscopy measures the time-of-flight of short pulses through the sample. By fitting the measured curves by the use of the diffusion theory, it is possible to determine the optical properties of the phantoms reported in section 2.1. For each concentration of scatterers and glycerol, we have retrieved the reduced scattering coefficient µ s and the absorption coefficient µ a . As for the TRS, in the following we will report only results from the experiments performed at POLIMI, where a multi-wavelength analysis has been performed and where the linear method described in Ref.
[38] has been exploited for retrieving the reduced scattering coefficients. As a matter of fact, the use of this method ensures a better accuracy of the retrieved values. Figure 1(a) shows examples of the retrieved reduced scattering coefficients for varying scatterer concentration for solutions with different glycerol concentration (0%, 10%, 20% and 30%). As expected from theory and previous studies [9-11, 27], for a fixed glycerol concentration, the scattering coefficient increases linearly with the scatterer concentration. We also report fits performed with the equation 2. For the data fitting we have excluded the lowest concentrations of scatterers, since, as previously commented, at that concentrations the validity of diffusion approximation used to retrieve the optical properties is questionable. Detailed results of the fits are reported in Table 1, Section 3.3. Figure 1(a), furthermore, highlights that the scattering strength of the phantoms depends on the glycerol concentration. This effect is analyzed in Figure 1(b) where we show the fitted intrinsic scattering coefficient (see eq. 2) for the all concentrations of glycerol at three different wavelengths together with the linear fits performed using equation 3. The experimental data show a good agreement with the theory confirming that the scattering properties of the liquid phantoms are changed by adding glycerol to the solution. Detailed results of the linear fits are reported in Table 2, Section 3.3.
The experiments highlight the dependence of the scattering on the wavelength of light. In Figure 1 glycerol concentrations. The graph shows how the scattering coefficient of the phantom is smaller for longer wavelengths. The results of the fits performed with the empirical Mie relation (equation 4) [12,34] for different glycerol concentrations are reported in Table 3, Section 3.3. The TRS measurements allowed, furthermore, the determination of the absorption coefficient µ a of the system. An example of the absorption coefficient spectrum for different glycerol concentration and fixed scatterer concentration is reported in Figure 1(d) together with the absorption spectrum of the water. The measurements demonstrate that the absorption does not change significantly when the concentration of scatterers and glycerol in the solution changes. Moreover, Figure 1(d) highlights how the absorption coefficient of the solutions investigated reflects the water absorption. These results demonstrate that the absorption in liquid phantoms made of water/glycerol solutions with Lipofundin as the scattering element can be tuned independently from the scattering and dynamic properties by adding ink or other absorbers to the solution as described in several works [27].

Diffuse correlation spectroscopy results
The Brownian motion of the scatterers in the phantoms is measured through diffuse correlation spectroscopy experiments performed at ICFO. We have measured phantoms with three different concentrations of glycerol while tuning the reduced scattering coefficient by adding Lipofundin to the initial solution. As explained in Section 2.1, we have tuned the concentration of scatterers in order to obtain approximately the same reduced scattering coefficients (0.5 mm −1 , 1 mm −1 and 1.5 mm −1 ) for phantoms with different glycerol concentrations. Table 4 Table 4, Section 3.3.

Tables of results and phantom recipe
In this section, we report for completeness a summary of the results obtained through TRS and DCS measurements in different experiments, performed at Politecnico di Milano and at ICFO together with a practical, explicit phantom recipe.
Tables below show detailed results from all the experiments. Table 1 reports the results of the fits of the reduced scattering coefficient (µ s ) for varying scatterer concentrations (ρ s ), using equation 2. Table 2 reports the results of the fits of the intrinsic scattering coefficient ( s ) for varying glycerol concentration (ρ glyc ). Please note that, differently from Figure 1 (a) and (b) where concentrations are reported in % (normalized to 100), here, for consistence with the literature, the results of the fits are reported considering concentrations in g/g (mass of the solid scatterers divided by the mass of the whole solution). Table 3 reports the results of the fits of the intrinsic reduced scattering coefficient ( s ) for varying wavelength using the empirical Mie relation (equation 4) at different glycerol concentrations. Table 4 reports the results of the DCS experiments performed, at different scatterer and glycerol concentrations, together with the expectations from theory (equation 6).
These results provide the basis for a recipe to produce phantoms with the desired optical and dynamic properties. The dynamic properties of the phantom are set considering equation 6 and the viscosity of water/glycerol solutions present in the literature [25]. The results reported in Table 1 can be directly used to set the optical properties of the phantom using equation 2. This provides us with a recipe limited to the glycerol concentrations (0%, 5%, 10%, 15%, 20%, 25%, 30%) and wavelengths (600, 700 and 785 nm) that were investigated in our experiments. The extension of the recipe to other glycerol concentrations in water is obtained combining equations 2 and 3, which results in: This equation allows the determination of the concentration of scatterers that have to be inserted in the solution of water and glycerol in order to obtain the desired reduced scattering coefficient for a given wavelength. We note here that, considering the common tissue scattering properties [39], the correction introduced by the coefficient C is negligible considering the experimental errors. A more general phantom recipe considering the wavelength dependence of the reduced scattering coefficient, can be obtained with a deeper analysis of the results reported in Table 3. As expected, the coefficient A scales linearly as the glycerol concentration in the solution increases as where m is the slope, ρ glyc is the concentration of glycerol, and A 0 is the intercept, i. e. the value of A for solution with no glycerol. Performing a linear fit we obtain A 0 = (82.1 ± 1.4) mm −1 g/g and m = (−136.4 ± 8.0) mm −1 . Furthermore, the exponent b that depends on the size of the scattering particles is shown to be independent of glycerol concentration. For the purpose of developing a recipe for phantoms we can consider the average of the values reported in Table 3, b = 1.39 ± 0.61. Finally, equations 2, 4 and 8 can be combined to obtain the most general form of the phantom recipe as where, as already mentioned, the correction introduced by the coefficient C is negligible considering the experimental errors, and C can be considered equal to zero for the purposes of developing tissue mimicking phantoms. Equation 9 is the most general formula for developing phantoms based on water/glycerol solutions and considers both the changes in the bulk refractive index due to the addition of glycerol as well as the wavelength dependence of the optical properties.

Conclusion
In conclusion, we have designed and prepared liquid phantoms consisting on solutions of water and glycerol with Lipofundin as the scattering element. The phantoms produced have well defined optical and dynamic properties and have been characterized through TRS and DCS measurements. The experiments allowed us to provide a practical recipe to prepare liquid phantoms. By tuning the glycerol concentration in water it is possible to control the viscosity of the solution, i. e. tuning the Brownian diffusion of the scatterers. Then, for fixed concentrations of glycerol, we have stated the recipe to obtain the desired scattering properties, adding Lipofundin to the solution.