2.1.

Oxygen Saturation

Due to the critical nature of tissue oxygen consumption in the body, oxygen saturation, the amount of hemoglobin bound to oxygen compared with the amount of unbound hemoglobin, is an essential element of patient care; thus it is currently considered to be the fifth vital sign.¹⁰

Blood oxygenation can be evaluated by monitoring oxygenated hemoglobin (${\mathrm{HbO}}_2$) and deoxygenated or reduced hemoglobin (Hb) concentration parameters, which are also used to calculate the ${\mathrm{SO}}_2$ oxygen saturation parameter as

Kyriacou et al.¹¹ present the molar extinction coefficients or specific absorption constants of ${\mathrm{HbO}}_2$ and Hb as a function of wavelength, in the visible and near-infrared wavelength regions, where a large difference between the extinction coefficients of ${\mathrm{HbO}}_2$ and Hb is clear for some wavelengths. Another important aspect is that ${\mathrm{HbO}}_2$ and Hb have a different absorption throughout the spectrum, except at 805 nm, which is called the isosbestic point. For shorter wavelengths, the absorption is mainly due to Hb, whereas for longer wavelengths, most of the absorption is due to ${\mathrm{HbO}}_2$.

To obtain the oxygen saturation value using Eq. (1), it is necessary to select at least two wavelengths considering three main criteria: first, the selected wavelengths (${\lambda }_1$ and ${\lambda }_2$) must be sensitive to each of the main blood absorbers, ${\mathrm{HbO}}_2$ and Hb (which are generally opposite the isosbestic point). Second, the absorption difference between ${\mathrm{HbO}}_2$ and Hb at the chosen wavelengths should be the largest. Finally, the absorption spectra in the region of the chosen wavelengths should be relatively flat, indicating their proximity in terms of absorption magnitude.¹¹

2.2.

Propagation of Optical Radiation in Human Skin

The interval of the electromagnetic spectrum in which the tissues have a significant level of light penetration to provide information on the state of the tissues, but without causing a harmful effect on health, is known as the therapeutic window and is located between the wavelengths of 600 and 1300 nm.¹²

The interactions of electromagnetic radiation with the skin are governed by its physiological, biochemical, and morphological characteristics.¹³ They are characterized by a strong optical scattering due to the high degree of inhomogeneity caused by the organelles that the cells contain, which have different sizes and compositions; likewise they present a different refractive index to that of the substance in which the fibers are immersed and connective tissue cells.¹⁴ Therefore, the skin can be considered to be an inhomogeneous turbid medium.

When electromagnetic radiation interacts with the skin, a part of the radiation is reflected due to the difference between the refractive indices of the skin and the air, and the remaining radiation that crosses the border can be absorbed internally or scattered multiple times by the middle. Radiation that has undergone multiple scattering events can be diffusely transmitted or reflected.¹⁵ To describe the propagation of electromagnetic radiation in the skin, the absorption coefficient (${\mu }_a$), scattering coefficient (${\mu }_s$), anisotropy factor ($g$), and refractive index ($n$) are used as the most important optical properties.¹⁶

Because human skin is a tissue made up of different layers that contain a diversity of non-homogeneous structures, the study of the interaction of electromagnetic radiation with this medium becomes difficult due to the diversity in the size, shape, density, and refractive index of these components. Therefore, simplifications are generally made for their study, and the structures are considered to be homogeneously distributed spherical particles.¹⁷

2.3.

Radiative Transport Theory

The radiative transport theory considers that the only interaction of light with the medium is of an elastic type, changing the energy distribution of the incident light as it passes through such a medium.^18–21 This theory does not include the effects of coherence, polarization, interference, and diffraction. Its fundamental equation is the radiative transfer equation (RTE), which is an integral–differential equation. The radiance or specific intensity is the unknown quantity in this equation and includes parameters such as the scattering and absorption coefficients and the phase function of the medium.

To solve the RTE, the main problem that arises is the evaluation of the diffuse radiance because the scattered photons do not follow a determined trajectory. For this reason, appropriate statistical approximations and approaches must be chosen, that is, whether absorption or scattering is the dominant attenuation process.

The methods used are generally the Kubelka–Munk theory, the diffusion approximation, the Monte Carlo method, or the adding–doubling method. Each method is based on certain approximations that facilitate the RTE solution. In general, the complexity of any of the approaches is closely related to its precision, as well as to the computation time required to give a solution.

The inverse adding–doubling (IAD) method provides a tool for the fast and accurate solution of the inverse scattering problem. Adding–doubling is based on the general method for the solution of the RTE for flat and parallel layers, suggested by Van de Hulst and introduced to the optics of biological tissues by Prahl et al.²²

An important advantage of the IAD method when applied to biological tissue optics is the possibility of rapidly obtaining iterative solutions. Furthermore, it is flexible enough to consider scattering anisotropy and internal reflection from sample boundaries.

2.4.

Experimental Set-Up

To obtain tissue oxygen saturation, it is necessary to obtain the concentrations corresponding to oxygenated (${\mathrm{HbO}}_2$) and deoxygenated (Hb) hemoglobin. Those concentrations can be determined from the absorption coefficients of the tissue to be analyzed. The absorption coefficients are recovered by IAD from diffuse reflectance measurements made with an integrating sphere experimental set-up (see Fig. 1). The experimental set-up was used to measure the reflected light by the sample; then it is normalized and used as input parameter together with the scattering coefficient and the anisotropy factor.²³

Fig. 1

Experimental set-up for diffuse reflectance measurement. Inset: integrating sphere used to measure diffuse reflectance of the volunteer hand.

The experimental set-up consists of a tungsten lamp (HL-2000; Ocean Optics) that emits radiation in the visible spectrum (even though the spectrum is specified from 360 to 1700 nm) coupled to an optical fiber that carries light from the lamp to the input port of an integrating sphere (819C-SF-6; Newport) passing through a collimating lens (fiber optics do not penetrate the integrating sphere). The collimated light reaches the sample, which is placed in the opposite port to the entrance of the light source and is reflected in a specular and diffusive way. An optical fiber connected to the top port of the integrating sphere carries the diffusively reflected light from the sample to a spectrometer (USB4000; Ocean Optics, with a detection range between 200 and 1100 nm). A continuous wave collimating laser (BWF-975-450E) with a central wavelength of 975 nm and a maximum output power of 450 mW was used as the light source. For the experiments, only 1.0 mW was used in an area of $2.27{\mathrm{mm}}^2$, which is harmless for human skin.

The reflectance measurement was performed by placing the palm of the hand on the outlet port of the integrating sphere, as shown in Fig. 1. The light reflected by the tissue is collected and guided to the spectrometer by means of an optical fiber, and the spectrometer separates the reflected light at different wavelengths and provides a spectrum of the intensity.

The reflection measurements are normalized with respect to the incident light. Applying Eq. (2), a value of the total diffuse reflectance is obtained as

Fig. 2

Schematic representations of the measurement of $R_0$, $R_1$, and $R_R$ for calculation the of $M_R$.

The experimental tests were performed on healthy volunteers; for this reason, it was necessary to induce ischemia to simulate the reduction in blood flow that occurs in diabetic patients with peripheral vascular disease. A vascular occlusion test was performed using a sphygmomanometer; the blood pressure cuff was placed around the upper left arm and inflated to stop the flow of blood in the arteries/veins up to a certain pressure value indicated on the manometer. The vascular occlusion test has been used in various studies such as those carried out by Wang et al.,²⁴ who applied the occlusion test to healthy volunteers to evaluate their hybrid diffuse optical device in stroke diagnosis. Donati et al.²⁵ used the occlusion test in 27 healthy volunteers to detect alterations in tissue oxygenation and microvascular reactivity with the aim of predicting adverse outcome in critically ill patients. Bezemer et al.²⁶ applied the test to eight healthy volunteers to assess potential metabolic and microcirculatory alterations that patients may suffer during sepsis or shock.

The study followed the tenets of the Declaration of Helsinki and the Mexican General Health Law on Research for Health, and the corresponding protocol was approved by the Ethics and Research Committee CONBIOETICA of the UASLP (registration number CEI-FE-046-023). The volunteers were informed in detail about the experimental procedure, and they provided written consent for their data to be used for research purposes. The group of participants consisted of 27 healthy volunteers, 13 men and 14 women, between 18 and 39 years old. For the experimental tests, volunteers were asked to sit comfortably in a chair and rest for 3 min. During this time, blood pressure, heart rate, and pulsatile oxygen saturation were measured. In addition, a diffuse reflection spectrum was taken from each volunteer to calculate their absorption spectrum (see Supplementary Material). The absorption coefficient at 632 nm was correlated with melanin content, according to a prior study²⁷ and classified into skin type on the Fitzpatrick scale,²⁸ with the volunteers being between skin types III and V. Subsequently, a sphygmomanometer around the left arm was placed to induce vascular occlusions, and the palm of their left hand was placed on the port of the integrating sphere, as shown in Fig. 3.

Fig. 3

Setting of a sphygmomanometer for measurements of ${\mathrm{StO}}_2$.

Four continuous measurements were made at 0, 60, 80, and 100 mmHg of the 27 adult volunteers. Each occlusion took $\sim 1\min$. At the end of the 100 mmHg measurement, the pressure in the cuff was released, and measurements were taken in the recovery period 1 and 2 min later. Volunteer characteristics such as age, blood pressure, heart rate, pulsatile oxygen saturation, and skin type were registered. The information of each volunteer was tagged using a consecutive number followed by their gender in parentheses.

2.5.

Algorithm for Obtaining Oxygen Saturation

The tissue absorption coefficient ${\mu }_a$ can be considered to be the sum of $n$ products of the molar extinction coefficients of the significant chromophores ${\epsilon }_i$ and their respective concentrations $C_i$, where $(\lambda )$ indicates a wavelength dependence, as calculated in Eq. (3):

From Eq. (2), concentrations of oxygenated hemoglobin ${\mathrm{HbO}}_2$ and deoxygenated or reduced hemoglobin $\mathrm{Hb}$ were obtained from the tissue absorption coefficients ${\mu }_a$ and molar extinction coefficients $\epsilon$ corresponding to each hemoglobin in two wavelengths ${\lambda }_1$ and ${\lambda }_2$, as indicated in Eqs. (4) and (5):

Due to the difference between ${\epsilon }_{{\mathrm{HbO}}_2}$ and ${\epsilon }_{\mathrm{Hb}}$ identified in the visible and near infrared region, these coefficients can be used for the evaluation of blood oxygenation.³⁰ The chosen wavelengths to obtain the ${\mathrm{StO}}_2$ in this work were 975 nm in the infrared region, as well as a wavelength in the visible region positioned at a similar distance from the isosbestic point as the infrared point and showing significant changes in the ${\mathrm{StO}}_2$.

The absorption coefficients ${\mu }_a^{\lambda 1}$ and ${\mu }_a^{\lambda 2}$ in Eqs. (3) and (4) were obtained from the in vivo measurements of diffuse reflectance with the integrating sphere experimental set-up and following the procedure described by Quistian-Vázquez et al.²³ to obtain the absorption coefficient ${\mu }_a$. The input parameters were the measurement of the diffuse reflectance $M_R$, the scattering coefficient ${\mu }_s$, and the anisotropy factor $g$ of the skin; these depend on the biochemical composition of the tissue and its cellular structure, as well as on the wavelength.

The values of ${\mu }_s^{\prime }$ as a function of wavelength were obtained from Jacques’ review.³¹ Equation (6) characterizes scattering in seven tissue groups: skin, brain, breast, bone, soft tissues, fibrous tissues, and fatty tissues. The values of $a$ and $b$ for skin are $a=46{\mathrm{cm}}^{-1}$ and $b=1.421$, respectively,

To define $g(\lambda )$ as a function of the wavelength, a sixth order polynomial was determined; it represents a polynomial fit of the values obtained by Ma et al.³² in a study carried out to determine the optical properties of the skin and that are presented in the Jacques review.³¹ Equation (7) shows the function obtained for $g(\lambda )$:

The scattering coefficient ${\mu }_s(\lambda )$ as a function of the wavelength was obtained from the relation ${\mu }_s^{\prime }={\mu }_s(1-g)$.

4.1.

Measurement of Absorption Coefficient Spectra In Vivo

Absorption spectra from diffuse reflectance measurements were obtained using the experimental set-up shown in Fig. 1 and applying the IAD technique. The graphs of Fig. 5 show the absorption coefficients spectra of 2 volunteers for each condition of applied pressure (0, 60, 80, and 100 mmHg) in which it is observed that the absorption coefficient increases with increasing pressure in the sphygmomanometer because of the increase in the concentration of deoxygenated hemoglobin (Hb). Figure 5(a) shows that, by increasing the applied pressure, the characteristic double peak pattern of oxygenated hemoglobin $({\mathrm{HbO}}_2)$ is replaced by the characteristic single peak pattern of deoxygenated hemoglobin (Hb). This behavior is better appreciated in Fig. 5(b) corresponding to a volunteer with a lower systolic pressure. In Fig. 5, the spectra also depend on the skin type because darker skin presents greater absorption.³⁶

Fig. 5

(a) and (b) Absorption coefficients of two volunteers for each condition of applied pressure.

There are several factors that can affect the measurements, which can be classified as anatomical or physiological; however, a statistical study of experimental data by principal component analysis (PCA) of the main skin chromophores (considering the absorption coefficients of melanin, deoxygenated hemoglobin, oxygenated hemoglobin, water, and fat), revealed that the chromophores that have the greatest effect on the total absorption coefficient are oxygenated and deoxygenated hemoglobin and melanin. PCA details can be found in the Supplementary Material.

4.2.

In Vivo Tissue Oxygen Saturation Measurement with OTOS Algorithm

The ${\mathrm{StO}}_2$ measurements were carried out with the developed computational algorithm. The skin type was classified according to three groups: I–fair skin, II–intermediate skin, and III–brown skin.

Subsequently, diffuse reflectance measurements and absorption coefficients were obtained for each pressure condition (0, 60, 80, and 100 mmHg). When obtaining the measurement of 0 mmHg (basal or resting condition), the slope of the absorption spectrum between 630 and 700 nm was calculated because that slope is directly related to the melanin content in the skin.³⁵ The slope obtained for each volunteer was used to discriminate the contribution of epidermal melanin to the absorption spectrum. From the value of the slope, the first wavelength necessary to perform the calculation of ${\mathrm{StO}}_2$, corresponding to the visible region of the electromagnetic spectrum, was chosen. The second wavelength corresponding to the near infrared region was 975 nm due to the availability of the infrared (IR) laser. The three groups specified for the skin type were related to the obtained slope value because the skin type is directly associated with the melanin content in the skin. Table 1 shows the classification group, as well as the interval of the corresponding slope value and selected wavelength for each group.

Table 1

Wavelength determination for StO2 calculation (considering the absolute value of the slope).

To assign a wavelength for each group of skin type, the behavior indicated by Ferguson-Pell and Hagisawa³⁷ was considered. It was observed that there was a change in wavelength in the calculation of the oxygenation index due to the influence of melanin. The obtained values of ${\mathrm{StO}}_2$ for each pressure condition during the occlusion test are shown in Figs. 6Fig. 7–8, where it can be seen that the value of ${\mathrm{StO}}_2$ tends to decrease as the applied pressure increases. Measurements were categorized in groups by gender, age, and corresponding systolic blood pressure measured before test. Figure 6(a) shows the results belonging to the group of women, and Fig. 6(b) corresponds to the men. Regarding gender, no correlation was found, so it can be concluded that it does not influence the measurement of tissue oxygen saturation.

Fig. 6

Graphs of ${\mathrm{StO}}_2$ values obtained for each pressure condition of occlusion test classified by gender: (a) female and (b) male.

Fig. 7

Graphs of ${\mathrm{StO}}_2$ for each pressure condition of occlusion test classified by age: (a) 18 to 20 years old, (b) 20 to 30 years old, and (c) 30 to 40 years old.

Fig. 8

Graphs of ${\mathrm{StO}}_2$ values obtained during the occlusion test: systolic blood pressure (a) 90 to 104 mmHg, (b) 105 to 114 mmHg, and (c) 115 to 130 mmHg.

The classification by age is shown in Fig. 7. The results for the 10 to 20 years old group is observed in Fig. 7(a), for the 20 to 30 years old group in Fig. 7(b), and the 30 to 40 years old group is in Fig. 7(c). No special correlation between volunteers of a similar age was observed. Age influences some physiological characteristics such as hydration and the quantity/structure of collagen fibers present in the skin. However, the volunteers’ ages ranged between 18 and 39 years, which does not represent a considerable difference.

Figure 8(a) shows the results for the group that presented a systolic blood pressure between 90 and 104 mmHg, Fig. 8(b) corresponds to the group with a blood pressure of 105 to 114 mmHg, and Fig. 8(c) shows the group with a blood pressure of 115 to 130 mmHg.

Classifications by gender and age do not present a special pattern or behavior. However, in the classification by group of systolic blood pressure, it is observed that the group with the lowest blood pressure (90 to 104 mmHg) presents a pronounced drop in ${\mathrm{StO}}_2$, unlike the group with the highest blood pressure (115 to 130 mmHg). This is an expected behavior because the volunteers with lower systolic blood pressure practically reach a situation of zero blood flow in the highest applied pressure (100 mmHg); therefore they present a greater affectation. It is also expected that, in the absorption spectra of this group of volunteers, the characteristic double peak pattern of oxygenated hemoglobin gets lost faster, as is the case of volunteer V21(M) in Fig. 8(a) which corresponds to volunteer V7(M) in Fig. 5(b).

Figure 9 shows the graphs of ${\mathrm{StO}}_2$ versus time in minutes, where 1 measurement was taken each 1 min. These graphs also show the measurements corresponding to the ${\mathrm{StO}}_2$ recovery stage, that is, after evaluating 100 mmHg, the pressure applied by the sphygmomanometer cuff was immediately released and 2 consecutive measurements were taken.

Fig. 9

Graphs of ${\mathrm{StO}}_2$ values versus test time: volunteer’s initial systolic blood pressure (a) 90 to 104 mmHg, (b) 105 to 114 mmHg, and (c) 115 to 130 mmHg.

In Fig. 9, it can be seen that the ${\mathrm{StO}}_2$ tends to go up again in the recovery stage, and a heterogeneous behavior can be observed between the recovery stage of the different volunteers of each group. Based on observations made in various studies, this recovery stage is considered to be a reflection of the endothelial function and has been correlated with perfusion pressure; therefore, it can be derived from the interaction between perfusion pressure and endothelial integrity.³⁸ However, the obtained results indicate a much lower ischemic challenge than that study because the maximum applied pressure (100 mmHg) was not as high as the initial systolic blood pressure and therefore does not present a good degree of comparison. Despite this, in the volunteers V12(H) in Fig. 9(b) and V25(M) in Fig. 9(c) it was observed that, in the first measurement of the recovery stage, the ${\mathrm{StO}}_2$ temporarily went up above the initial values. This behavior may indicate the condition known as reactive hyperemia, mentioned in the literature, which represents post-ischemic vasodilation and capillary recruitment.^38,39 Although multiple comparisons were made to identify differences between subgroups of volunteers, no statistically significant differences between gender, age, or skin color were found.

The validation of the results obtained in comparison with values from the literature is difficult because there is not a defined standard and previous studies report different results regarding the measurement zones, the separation between the optical probes, and the algorithms used. However, our results showed agreement with those reported by Tseng et al.,⁴⁰ in which they performed diffuse reflectance measurements with visible and near-infrared light and determined two regions to obtain the ${\mathrm{StO}}_2$. The region between 500 and 600 nm provide saturation values between 60% and 70% because the depth of penetration is lower and the measurements correspond to the blood vessels of the upper dermis, whereas the region from 600 to 1000 nm provides values of saturation from 97% to 99% by covering a greater depth of measurement in the region of the lower dermis.

The proposed method gives saturation values between 97% and 99% for healthy people under normal conditions; therefore it satisfies the necessary characteristics to be considered a technique for obtaining ${\mathrm{StO}}_2$ because it can be applied in vivo and non-invasively, requires less evaluation time, and provides an objective and quantifiable evaluation.

As future work, the implementation of the portable device designed to apply the technique in clinical practice will be considered; it will work with LED illumination and photodiodes for detection. In addition, this device has the advantage of changing the size of the port and thus being able to measure smaller areas, allowing for the application of the technique to other possible conditions.