1. Introduction

Non-invasive optical methods for analyzing biological tissues are important and useful for diagnosis and therapy [1, 2]. It is assumed that the absorption and scattering characteristics of tissue change according to the physiological state [3], therefore optical methods can recognize the changes with high sensitivity.

Photoplethysmography (PPG) is non-invasive, cheap, and very useful in biological and medical fields for optically detecting physiological tissue state such as oxygen saturation, blood perfusion and blood pressure. PPG is used to detect the variations in blood volume or blood flow in fingertips and toes that change during respiration by measuring changes in light absorption, regardless of the light scattering. Most PPG methods focus on the light reflection from a semi-infinite medium, while very few use the light transmission. A known and useful application is the pulse oximetry technique [4, 5] that determines blood oxygen saturation by computing the differential light absorption in the arterial blood from PPG signals in two wavelengths (red and infrared). But the current technique requires calibration [6], moreover other methods that use PPG signals require signal processing [7].

We suggest investigating the light scattering change from the whole tissue, with attention to changes in blood vessel diameters. Blood vessels are one of the absorbing elements in the tissue [8]; they vary in size during respiration with respect to the oxygen volume in the blood, and in accordance with shielding effect they change the effective reduced scattering coefficient of the whole tissue. We propose a new optical method to characterize a cylindrical tissue, such as a fingertip joint, ear lobe, or pinched tissue, by using the full profile of light scattering, which mean the angular distribution of the emitted light. In this work we present the experimental set-up for measuring the full light scattering profile from a cylindrical tissue and show results of phantom experiments.

We previously presented a full scattering profile simulation of a homogeneous cylindrical tissue [9–11], meaning reflection as well as transmission. In this work we present our unique set-up for noninvasive encircled measurements, and the cylindrical tissue-like phantoms that we prepared with different reduced scattering coefficients to mimic different physiological states. We use only one low power continuous wave (CW) laser as a light source and use the visible range, which does not put the patient at risk of tissue heating that causes damage to the skin, and a simple photodetector for a perimeter measurement. In addition, the influence of different cylindrical phantom diameters on the angular distribution is an interesting measurement and interpretation, since the diameter varies along one human tissue and between different patients. Moreover, the whole tissue is investigated using our noninvasive method as one unit, and since there is a change in the optical properties when blood vessel diameters change during respiration, it is essential to investigate the optical properties effect of the angular distribution for different reduced scattering coefficient (µ_s') values. We investigated the influence of the tissue diameter and the reduced scattering coefficient on the emitted light intensity by full scattering light profile exploration.

We are interested in the comparison between the different profiles, because of the isobaric point that we found in our previous work by simulation [10]. Finding that point experimentally will produce a reference point. This point gives us a basis for different measurements without the need for calibration between different sources and measuring equipment.

2. Materials and methods

2.1 Simulations

We built a simulation that describes the full scattering profile, meaning the angular distribution of scattered light from a circular tissue in each possible exit angle. The propagation of light in the tissue was calculated using a Monte-Carlo method [12]. This method predicts the average behavior of a complex system by numerical calculations of random events. We simulated a cylindrical tissue and calculated the light propagation according to this geometry, unlike the regular use of Monte-Carlo multi-layer (MCML) model that assumed different layers in a semi-infinite medium [13].

The probability of a photon to absorb is described by the following equation based on the Beer–Lambert Law [14]:

We present in this simulation different reduced scattering coefficients of our modal, which represent different physiological states that influence the optical properties. For example, high oxygen concentration in blood changes the scattering profile [6, 14]. The reduced scattering coefficient is defined by the equation:

We chose to work with several reduced scattering coefficients which are in the range of the human tissue values. Furthermore, the simulation was held for several different diameters to investigate the influence of cylindrical phantom diameters on the angular distribution.

2.2 The experimental set-up

The set-up includes a He-Ne gas laser (Melles Griot, California, USA) with an excitation wavelength of λ = 632.8 nm and maximum power of 5mW. The laser beam diameter is ω₀ = 0.59 mm. We use a portable fixed gain silicon detector as a photo detector. The detector has an active area of 0.8 (mm²) and it is placed on a rotation stage in order to enable the full scattering profile measurements .The stage can be rotated around a tube with an accuracy of one degree. The tube contains a liquid phantom which is described in section 2.3. The detector is fixed in constant optimal distance from the phantom surface. In order to avoid ambient light from entering the detection system and potential light loss, the detector is placed close to the phantom but not too close to block the light source. The voltage is measured every 5 degrees from θ = 0 to 145°, as shown in Fig. 1. The scattered light between 145° and 180° cannot be measured due to the photodetector's size, which blocks the light source.

 

Fig. 1 Schema of the experimental system. (a) A laser beam irradiates a cylindrical phantom, and a photodetector is positioned on a rotation stage for measuring the light at every exit angle. (b) xz cross section of the experimental system, where $\theta$ is the detector's angle. (c) Photograph of the experimental system.

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2.3 Liquid phantoms

We prepared liquid phantoms with different reduced scattering coefficients in order to simulate tissues with different optical properties [2, 15, 16]. The phantoms were prepared using varying concentrations of Intralipid (IL, Lipofundin MCT/LCT 20%, B. Braun Melsungen AG, Germany), as a scattering component. The IL was diluted with water. The values of the reduced scattering coefficient for four different phantoms that we chose (µ_s' = 8, 10, 16, 26 cm⁻¹) represent the range of the human tissue values [1]. The concentration of IL is calculated according to the reduced scattering coefficients of each phantom and are presented in Table 1, based on Cubeddu [17]. The phantoms are placed in test tubes with different diameters.

Table 1. The concentration of IL in a phantom for each reduced scattering coefficient.

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3. Results

3.1 Simulation results

We simulated an irradiated cylindrical tissue in different diameters and we obtained the full scattering profiles of circular tissues with different reduced scattering coefficients. The angular distribution of scattered light is presented in Fig. 2, each curve in the graph represent a different reduced scattering coefficient. We found a common point to all of the curves, i.e. the isobaric point [10]. The intensity of the scattered light in this point is constant and does not depend on the optical tissue properties.

 

Fig. 2 Simulation results of the full scattering profile for a 10mm circular tissue. The curves represent simulations of different reduced scattering coefficients (diamond, square, triangle, x and circle in respect to 10, 12, 14, 16 and 18 cm ⁻¹).

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A simulation for higher diameters or higher reduced scattering coefficients of the circular tissue produced the full scattering profiles of multiple scattering in the medium. For example, 15mm tissue diameter graphs are present in Fig. 3. The scattered light which is measured after multiple scattering events has higher reflection, at 160° and above, than the reflection in single scattering range due to the higher reduced scattering coefficient and higher diameter, meaning longer optical path.

 

Fig. 3 Simulation results of the full scattering profile for multiple scattering in circular tissue. The curves represent simulations of 15mm tissue diameter with different reduced scattering coefficient (circle, square, triangle and x represent a reduced scattering coefficient of 18, 22, 26 and 30 cm⁻¹, respectively).

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3.2 Calibration and system sensitivity

The tissue-like phantoms that we measured were in different tubes because of the different diameters that we wanted to check. The thicknesses of the tubes that contained the liquid phantoms were not equal. The calibration of the system requires the comparison between the different tubes. The tolerance of the tube thickness is $\pm 0.07mm$.

In order to check the systems sensitivity we measured empty tubes and tubes with water, and collected the light that mostly transmits. The intensity of light for 0 to 10 degrees, for each case is shown in Fig. 4. We found that the scatter from the empty glass is expressed by a movement of one degree of the scattered light, compared to light propagation in free space (Fig. 4(a)), because there are no scattering elements in the light path except the glass tube. The scattered light from water is expressed by a movement of four degrees (Fig. 4(b)). Hence, we can conclude the system has a high sensitivity since it detects the low scattering coefficient of water.

 

Fig. 4 Calibration measurements of empty tube and water. (a) Scattering light profile from empty tubes in each angle between 0 to 10 degrees and (b) Scattering light profile from water in different tube diameters (diamond, square, triangle, x and asterisk in respect to 7, 10, 12, 13, and 16 mm).

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3.3 Phantom measurements

For each tissue-like phantom $({{\mu }^{\prime }}_s=8,10,16,26c{m}^{-1})$ we measured the full scattering profile. By using a photodetector we measured the scattered light from the phantoms in different angles (increments of 5°). Note that an angle of zero is the full transmission and 180 degrees is the full reflection. The highest angle that we measured is 145 degrees, since the scattered light in the rest of the angles is blocked by the photodetector.

We measured phantoms of several diameters (7, 10, 12, 13 and 16 mm). In the obtained profiles the transmitted light intensity is lower than the reflected light intensity due the scattering characteristics of the phantoms. The full scattering profiles for the different phantoms are presented in Fig. 5. We found the isobaric point for each diameter, for various optical properties. In Fig. 5, for exit angles higher than the isobaric point the intensity of the scattered light is higher as the reduced scattering coefficient increases. However, for the rest of the angels lower than the isobaric point, the order of the different reduced scattering coefficients is exactly opposite. This is the first time that experimental results confirmed our full scattering profile simulation and demonstrate the phenomenon of the isobaric point.

 

Fig. 5 Influence of reduced scattering coefficient on the full scattering profile; Intensity of light at each angle between 0 to 145 degrees for different reduced scattering coefficients (diamond, square, triangle and x in respect to 8, 10, 16 and 26cm⁻¹). Phantom diameters were (a) 7mm, (b) 10mm, (c) 12mm, (d) 13mm and (e) 16mm.

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Furthermore, a linear dependence between the diameter and the isobaric point angle was found. We present in Fig. 6 the angle of each isobaric point that was extracted from Fig. 5(a)-5(e). The angels of the different isobaric points are presented as function of the phantom diameter.

 

Fig. 6 Influence of phantom diameter on the isobaric point angle. A linear dependence is presented between the central angle of the isobaric point and the phantom diameter.

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For clinical purposes one must consider the influence of tissue diameter on the full scattering profile, since this parameter varies between different patients. In Fig. 7 we present experimental results of the full scattering profile of a range of human finger diameters (7, 10, 12 and 13 mm) while keeping a constant reduced scattering coefficient (${{\mu }^{\prime }}_s=16c{m}^{-1}$). We can identify a crossover point (115°) between the curves of the different phantom diameters. This point is common for various diameters, which means in the experimental aspect that we can expect a constant value of light intensity in different patients at the same single angle, therefore only one measurement in the mentioned angle is necessary and not the full scattering profile.

 

Fig. 7 Full scattering profile of phantoms with different diameters, corresponding to different patients. In all phantoms the reduced scattering coefficient was kept constant (${{\mu }^{\prime }}_s=16c{m}^{-1}$) while the diameter changes (diamond, square, triangle, x and asterisk in respect to 7, 10, 12 and 13 mm).

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4. Discussion and conclusions

In this work we present experimental results of our unique set up, for noninvasive simple encircled optical measurements. Using one low power CW laser and a simple detector we measured the angular distributions of the emitted light from an irradiated phantom. We present the full scattering profile of cylindrical homogenous phantoms that mimic tissues, such as a fingertip joint, ear lobe, or pinched tissue. By using phantoms with various diameters and different ${{\mu }^{\prime }}_s$, we simulate different physiological states.

The comparison between the angular distributions of tissues with different optical properties reveals the isobaric point, that has no dependence on the optical properties of the phantom. These experimental results verify what we offered in the simulation modal of full scattering profiles and the isobaric point. Moreover, we present here the full scattering profile of different phantom diameters and we identify a crossover point between them.

Furthermore, we found more than one crossover point in a wide range of diameters. Two different crossover points are actually able to distinguish between the range of single scattering to the range of multiple scattering. Figure 8(a) shows measurement results of low reduced scattering coefficient phantoms with ${{\mu }^{\prime }}_s=8c{m}^{-1}$ in different diameters, compared to Fig. 8(b) that shows higher reduced scattering coefficient phantom with ${{\mu }^{\prime }}_s=16c{m}^{-1}$ in different diameters. In Fig. 8(a) one crossover point can be identified (110°) for the full scattering profiles of the four lowest diameters, while in Fig. 8(b) we can identify two crossover points (120°, 135°), one crossover point for the lower diameters (7mm, 10mm and 12mm) of single scattering, and the second crossover point for the higher diameters (13mm and 16mm) that belong to the multiple scattering range. The multiple scattering occurs in higher diameters, due to the new scattering events that occurred during prolonged advancement in the medium. The lower reduced scattering coefficients in lower diameters guarantee a single scattering behavior. However, the higher diameters guarantee a multiple scattering behavior for a wide region of reduced scattering coefficients.

 

Fig. 8 Comparison of full scattering profiles for different diameters. Full scattering profile for different diameters is shown (diamond, square, triangle, x and asterisk in respect to 7, 10, 12, 13, and 16 mm). Phantoms with different scattering coefficient are presented (a) ${{\mu }^{\prime }}_s=8c{m}^{-1}$ (b) ${{\mu }^{\prime }}_s=26c{m}^{-1}$

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These findings can be relevant to cylindrical tissues or any pinched tissue for detecting physiological state and implemented in near infrared spectroscopy, PPG experiments, and analyzing exact oxygen saturation values. Our distinction of the multiple scattering ranges can predict propagation of light in new researches. We focus in our experiment on homogenous phantoms that mimic tissue without absorbents that have different reduced scattering coefficients. Our future work will deal with the challenges of preparing nonhomogeneous cylindrical phantoms, with absorbents, that can mimic blood vessels.