RU2501522C2 - Method of determining hemoglobin concentration in biological tissues - Google Patents

Abstract

FIELD: medicine.

SUBSTANCE: invention relates to field of laboratory medical analysis, analytical instrument making and can be used for determination of total hemoglobin concentration in biological tissues. Transmission of radiation on tissue into one or more points is performed at wavelengths λ equal 524, 578 and 662 nm or 524, 578 and 773 nm. Signals of diffuse reflection P(L_n,λ) at three or more distances L_n (n=1, 2, 3 …) between points of transmission and registration of radiation are measured. Standard signals r_n(λ)=P(L_n,λ)/P(L₁,λ) and their main components are determined, and total hemoglobin concentration is calculated on the basis of multiple regression equation, connecting it with main components of r_n(λ).

EFFECT: increased accuracy of determination of total hemoglobin concentration in biological tissues due to taking into account presence of oxyhemoglobin, deoxyhemoglobin, methemoglobin and carboxyhemoglobin in them, exclusion of impact of variations of thin upper tissue layer parameters (for instance, skin epidermis) and its diffusing properties, elimination of calibration measurements, as well as reduction of method cost.

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Description

The invention relates to the field of laboratory medical analysis, analytical instrumentation.

The hemoglobin content in the blood determines the vital activity of the entire human body, therefore monitoring of hemoglobin is a necessary clinical procedure for a reliable assessment of the patient’s current condition and subsequent prediction of the development of critical conditions in anesthesiology, resuscitation and intensive care. The procedure currently used to determine the level of hemoglobin in the blood includes taking a blood sample, processing it in a transforming solution to destroy red blood cells, and direct photometry of the resulting sample. This procedure does not have efficiency, they require strict implementation of lengthy operations and highly qualified medical staff. Moreover, in anesthesiology and surgery it is often necessary to continuously monitor the level of hemoglobin in the blood, in particular during hemorrhage and blood transfusion during surgical operations. Such monitoring provides continuous information on the dynamics of blood changes, which helps to avoid unnecessary transfusions and related complications, such as postoperative infection, increased likelihood of metastases and impaired lung function. The need for non-invasive and rapid determination of hemoglobin in the surface layers of biological tissues (skin, mucous membranes of organs) also exists in oncology [1, 2].

A known method for determining hemoglobin and dyshemoglobin fractions, based on measuring the passage of light through pulsating vessels in the spectral regions of 600, 625, 660, 760, 800, 940 and 1300 nm. For measurements, the photometric sensor is mounted on the finger or earlobe. Strict attachment of the method to the anatomical part of the body and cardiac rhythm in blood perfusion excludes the possibility of its use for determining the hemoglobin content in the surface layers of the skin and mucous membranes of organs, as well as in cases where the cardiac rhythm is absent, for example, when performing heart operations.

Closest to the proposed invention is a method [4], in which the diffuse reflection coefficients R (λ) of biological tissue are measured at two isobestic wavelengths of oxy-HbO ₂ and deoxyhemoglobin Hb, and the concentration of total hemoglobin in the tissue is determined based on its correlation with the ratio of the coefficients R (λ) for isobestic wavelengths. To preliminarily establish this correlation, R (λ) measurements are used for many samples of biological tissue or phantoms modeling it with a known hemoglobin content. The disadvantages of this method include the effect on the measurement accuracy of variations in the scattering properties of the tissue and its pigmentation, the lack of consideration for such forms of hemoglobin as carboxyhemoglobin and methemoglobin. In addition, a device that implements this method requires calibration before each measurement, which complicates its use in wide clinical practice.

The present invention is aimed at solving the problem of improving the accuracy of determining the concentration of total hemoglobin in biological tissues by taking into account the presence of oxyhemoglobin, deoxyhemoglobin, methemoglobin and carboxyhemoglobin molecules in it, eliminating the influence of variations in the parameters of the thin upper layer of the tissue (for example, the epidermis of the skin) and its scattering properties, eliminating calibration measurements, as well as reducing the cost of the method.

и их главные компоненты, а концентрацию общего гемоглобина вычисляют на основе уравнения множественной регрессии, связывающего ее с главными компонентами r_n(λ).To solve this problem, in a method for measuring the concentration of hemoglobin in biological tissues by sending optical radiation to a tissue and measuring its diffuse reflection from the tissue, radiation is sent to the tissue at one or more points at wavelengths λ equal to 524, 578 and 662 nm, or 524, 578 and 773 nm, the diffuse reflection signals P (L _n , λ,) are measured at three or more distances L _n (n = 1, 2, 3 ...) between the points of sending and recording radiation, normalized signals are determined

and their main components, and the concentration of total hemoglobin is calculated based on the multiple regression equation connecting it with the main components r _n (λ).

The essence of the present invention is illustrated using figure 1, 2. Figure 1 presents a diagram of an experimental installation that implements the proposed method. An optical fiber probe 5 for measuring diffuse reflection coefficients (BWC) of biological tissues contains two transmitting fibers (excitation channels) 4 between which receiving fibers (recording channels) are placed 7. The radiation from the laser diodes 1 through beam splitting plates 2 is sequentially fed into the excitation channels 4 The radiation scattered by the fabric 6 into the back half-space enters the receiving fibers 7, through which it enters the photodetectors or is focused by a micro-lens 8 on the CCD line 9. So m, the radiation is detected simultaneously in all spatial channels registration. Comparison of the scattered radiation profiles from symmetrically located excitation channels makes it possible to assess the degree of heterogeneity of the illuminated volume and thereby choose the optimal skin area for measurements. As an alternative, such a configuration of optical fibers can be used in which a sending channel is located in the center of the probe 5, and registration channels are placed symmetrically in several directions from it. Such a scheme also makes it possible to detect heterogeneity of the studied tissue site and, in addition, allows to increase the level of the useful signal against the background of noise due to the greater total collective ability of the receiving fibers.

The recorded signals P (L, λ) in the considered optical fiber scheme depend on the spectral-spatial profile of the BWW - R (L, λ), as well as on the hardware constants and the radiation power of the laser diodes P ₀ (λ):

,

,

(n≤N_L - количество каналов регистрации), совпадающем с отношением

.where L is the distance between the centers of the sending and receiving fibers, λ is the radiation wavelength, S (λ) is the spectral sensitivity of the receiver, τ (λ) is the transmission function of the optical system. The coefficients R (L, λ) depend on the optical parameters of the medium and the collective ability of the optical fibers. To eliminate the need for calibration of measurements, P (L, λ) will operate with the signal ratio for spatially spaced recording channels

(n≤N _L is the number of registration channels) coinciding with the ratio

.

It should be noted that in addition to excluding calibration measurements, the use of diffuse reflection signals for spatially spaced points on the surface of biological tissue to solve the inverse problem also makes it possible to exclude the influence of its thin upper (e.g., epidermis of the skin) on the accuracy of restoration of the parameters of the lower layer (e.g., dermis skin). This is due to the fact that the optical paths traveled by light in a thin upper layer are approximately the same for adjacent recording channels and are subtracted by dividing the corresponding signals P (L, λ).

It is known that measurements of diffuse scattering at several distances from the point of illumination make it possible to separate the contributions of scattering and absorption to the recorded signals. If normalized diffuse scattering signals r _n (λ) are used to solve the inverse problem, then for the simultaneous determination of volume absorption coefficients k (λ) and scattering μ _s (λ) of biological tissue, it is necessary to measure its scattering at least three distances from the emitting fiber . As noted above, r _n ratio (λ) does not depend on the parameters of a thin upper layer of tissue, such as its pigmentation, and thus determined based on their spectra k (λ) characterize the component composition of the lower layer only. Its basis is a weakly absorbing, bloodless tissue in which vessels filled with blood pass. The absorption coefficient of blood is determined by the concentration of total hemoglobin and its chemical composition. Under normal conditions, hemoglobin is 96-98% composed of oxyhemoglobin HbO ₂ . The content of hemoglobin derivatives that are not able to carry oxygen is usually not large (1-4%), but in pathological conditions it can increase significantly. Clinically significant derivatives of hemoglobin are deoxyhemoglobin Hb, carboxyhemoglobin COHb and methemoglobin MetHb.

и в тоже время является изобестической точкой Hb и COHb (k_Hb(λ₂)=k_COHb(λ₂)=0.14 г/литр). Причем, даже при низком содержании HbO₂ в крови, равном 60%, его поглощение в 2.3 раза превосходит суммарное поглощение Hb и COHb. Вклад MetHb в общее поглощение на этой длине волны не значителен (k_MetHb(λ₂)=0.06 г/литр). Таким образом, измерение k(λ₂) позволяет оценить концентрацию HbO₂. Длина волны λ₃=662 нм является изобестической точкой Hb и MetHb и характеризуется низким поглощением HbO₂ и COHb, что обуславливает высокую чувствительность k(λ₃) к суммарной концентрации Hb и MetHb. Альтернативной длиной волны является λ₃=773 нм - также изобестическая точка Hb и MetHb. Коэффициенты поглощения HbO₂, Hb и MetHb на этой длине волны сравнимы по величине, а поглощение COHb практически отсутствует. Следовательно, при известной концентрации HbO₂ из измерения k(λ₃) можно определить суммарную концентрацию Hb и MetHb. И наконец, установив суммарную концентрацию HbO₂, Hb и MetHb, можно по измерению коэффициента поглощения на их изобестической длине волны λ₁ оценить концентрацию COHb, а значит и F_tHb.Based on the analysis of the absorption spectra of Hb, HbO₂, COHb and MetHb [5] to determine the concentration of total hemoglobin F_tHb selected wavelengths λ_one= 524 nm, λ₂= 578 nm, λ₃= 662 nm (or λ₃= 773 nm). Wavelength λ₂ corresponds to the maximum absorption of HbO₂

 and in time is an isobestic point of Hb and COHb (k_Hb(λ₂) = k_COHb(λ₂) = 0.14 g / liter). Moreover, even with a low content of HbO₂ in blood, equal to 60%, its absorption is 2.3 times higher than the total absorption of Hb and COHb. The contribution of MetHb to the total absorption at this wavelength is not significant (k_Methb(λ₂) = 0.06 g / liter). Thus, the measurement of k (λ₂) allows you to estimate the concentration of HbO₂. Wavelength λ₃= 662 nm is an isobestic point of Hb and MetHb and is characterized by low absorption of HbO₂ and COHb, which leads to high sensitivity k (λ₃) to the total concentration of Hb and MetHb. An alternative wavelength is λ₃= 773 nm is also an isobestic point of Hb and MetHb. HbO absorption coefficients₂, Hb and MetHb at this wavelength are comparable in magnitude, and the absorption of COHb is practically absent. Therefore, at a known concentration of HbO₂ from the dimension k (λ₃) can determine the total concentration of Hb and MetHb. Finally, by setting the total concentration of HbO₂, Hb and MetHb, it is possible to measure the absorption coefficient at their isobestic wavelength λ_one estimate the concentration of COHb, and hence F_tHb.

Based on the foregoing, to determine the concentration of total hemoglobin in biological tissue, it is necessary to measure its diffuse reflection at wavelengths λ ₁ , λ ₂ and λ ₃ at least three distances from the point of illumination. Moreover, based on the accuracy of determination of F _tHb , it is more preferable to restore this parameter directly from the measured signals r _n (λ) than from the coefficients k (λ). However, the signals r _n (λ) contain both the spectral and spatial components of the information and do not allow a simple one-dimensional interpretation. For the convenience of their analysis, it is necessary to obtain a more uniform data structure. The values ln r _n (λ) can be considered as components of the random vector r. We expand the vector r in terms of the system of eigenvectors v _{k of} its covariance matrix forming an orthogonal basis [6]. The expansion coefficients ξ _k (main components) of any implementation of the vector r are found by the formula:

- средний вектор; k=1, …, N_PC; N_PC - количество главных компонент. В связи с быстрой сходимостью рассматриваемого разложения на первые собственные векторы приходится большая часть изменчивости вектора r, а соответствующие им главные компоненты ξ_k содержат в себе практически столько же информации, сколько ее и было в исходных данных. Следовательно, для восстановления F_tHb можно использовать не сам вектор измерений, а его главные компоненты.Where

is the average vector; k = 1, ..., N _PC ; N _PC is the number of major components. In connection with the fast convergence of the considered expansion into first eigenvectors, a large part of the variability of the vector r is accounted for, and the main components ξ _k corresponding to them contain almost as much information as there was in the original data. Therefore, to restore F _tHb, it is possible to use not the measurement vector itself, but its main components.

From the point of view of the efficiency of monitoring hemoglobin concentration, it is of interest to be able to calculate it on the basis of an analytical expression linking it with the main measurement components r _n (λ) for the above three λ. Such an expression can be obtained on the basis of measurements or numerical calculation of r _n (λ) for many samples of biological tissue or phantoms modeling it with known values of F _tHb and subsequent regression analysis of the ensemble of implementation of F _tHb and r _n (λ) [7]. In particular, polynomial regression can be used as such an expression.

и v_k, a также вышеотмеченного аналитического выражения они могут применяться для получения по измеряемым значениям r_n(λ) уже неизвестной заранее концентрации гемоглобина.where M = 6 is the degree of the polynomial. The numerical values of the coefficients a _{km are} determined by calculating by formula (1) the principal components ξ _k for all realizations r (each of which corresponds to a specific value F _tHb ) and using the least squares method to approximate the statistical relationship between ξ _k and F _tHb . After receiving the vectors

and v _k , as well as the aforementioned analytical expression, they can be used to obtain, by measured values of r _n (λ), the concentration of hemoglobin already unknown in advance.

, нахождение по формуле (1) их главных компонент и определение концентрации гемоглобина на основе множественной регрессии между ней и найденными главными компонентами.Thus, the method for determining the concentration of total hemoglobin in biological tissue involves measuring its diffuse scattering signals P (L, λ) at wavelengths λ ₁ = 524 nm, λ ₂ = 578 nm, λ ₃ = 662 nm or λ ₃ = 773 nm at three or more distances L between the excitation and registration channels, calculation of normalized signals

, finding according to formula (1) their main components and determining the concentration of hemoglobin based on multiple regression between it and the found main components.

, v_k и коэффициентов регрессии (2) на примере определения концентрации гемоглобина в тканях кожного покрова человека. Для получения ансамбля реализации F_tHb и r_n(λ) используется статистическая модель кожи, включающая спектры поглощения и рассеяния компонентов кожи и диапазоны вариаций ее структурных и биохимических параметров. Верхний слой кожи - эпидермис с толщиной L_epi=50-130 мкм, нижний - дерма, которая в оптическом плане считается бесконечно толстой. Показатель преломления слоев кожи относительно воздуха n_skin=1.4-1.5 считается одинаковым, поэтому френелевское отражение излучения имеет место только на границе раздела кожи с внешней средой. Объемные коэффициенты поглощения эпидермиса k_epi и дермы k_derm моделируются как линейная комбинация коэффициентов поглощения обескровленной ткани k_t, меланина k_mel и гемоглобина:Let us consider in more detail the process of obtaining

, v _k and regression coefficients (2) on the example of determining the concentration of hemoglobin in the tissues of the human skin. To obtain the ensemble of the implementation of F _tHb and r _n (λ), a statistical skin model is used, including the absorption and scattering spectra of the skin components and the ranges of variations in its structural and biochemical parameters. The upper layer of the skin is the epidermis with a thickness of L _epi = 50-130 microns, the lower layer is the dermis, which is optically considered to be infinitely thick. The refractive index of skin layers relative to air n _skin = 1.4-1.5 is considered the same, therefore, the Fresnel reflection of radiation takes place only at the interface between the skin and the environment. The volumetric absorption coefficients of the epidermis k _epi and dermis k _{derm are} modeled as a linear combination of the absorption coefficients of bloodless tissue k _t , melanin k _mel and hemoglobin:

,

,

,

,

, где λ₀=632 нм, A=(3-8)·10^-2 (мм^-1) и B=(6-8)·10^-3 Where

where λ ₀ = 632 nm, A = (3-8) · 10 ^-2 (mm ^-1 ) and B = (6-8) · 10 ^-3

(nm ^-1 ) - parameters characterizing the spectral dependence of k _t ; f _mel = 0.5-25% - volume concentration of melanin in the epidermis; M _Hb = 64500 g / mol - molar mass of hemoglobin; F _tHb = 0.2-14 g / liter - the concentration of total hemoglobin in the dermis; ε _HbO2 , ε _Hb , ε _COHb and ε _MetHb are the molar absorption coefficients of oxyhemoglobin, deoxyhemoglobin, carboxyhemoglobin and methemoglobin, respectively, in cm ^-1 / (mol / liter); f _HbO2 = 40-98%, f _Hb = 1-40%, f _COHb = 0.1-20%, f _MetHb = 0.1-20% - volumetric concentrations of hemoglobin derivatives; α (D _ν ) is a correction factor that takes into account the effect of localized absorption of light by blood vessels, D _ν = 5-30 μm is the average diameter of capillaries.

The spectrum of the reduced scattering coefficient µ _s (λ) of the epidermis and dermis is modeled as a superposition of scattering spectra corresponding to Mie and Rayleigh scatterers with dimensions d≥λ and d << λ, respectively:

,

,

where λ ₀ = 632 nm; C _s = 1-10 mm ^-1 ; ρ _Mie = 0.1-0.6 is the fraction of Mie scattering; x = 0.5-1.0 is the spectral dependence of the Mie scattering. The parameters C _s , ρ _Mie and x are structural parameters of the skin, since they characterize the volume content and size of its “effective” scatterers (connective tissue fibers). It should be noted that in order to take into account a possible increase in the volumetric coefficient of skin scattering due to the contact of the meter with it, the upper limit of the range of variations of the parameter C _{s is} chosen approximately three times higher than the maximum value of C _s for human skin.

To simulate the above-described experiment on the propagation of optical radiation in human skin, the Monte Carlo method [8] is used, based on tracking random walks of a large number of photons (3 · 10 ⁶ photons were specifically used) from the point of their entry into the medium until they are absorbed or released from the medium . After statistical modeling of the trajectories of all photons, the surface distribution function of the directional scattering coefficient was calculated:

,

,

where I is the intensity of the radiation emerging from the elementary site at a distance r from the origin in the solid angle ΔΩ = 2πµΔµ described around the direction µ = cosθ; F is the flux of radiation incident on the medium at the point r = 0 in the direction of the normal to its surface.

For a recording channel located at a distance L from the excitation channel, determined by the value of R (L, λ) is the ratio of the power of the recorded signal to the power of the probe light beam, which, taking into account the radial symmetry of the function S (r, μ), can be written as:

,

,

, A_c - числовая апертура оптического волокна; x и y - переменные интегрирования.where r ₀ and r are the radii of the transmitting and receiving fibers, respectively; l = Lx, L is the distance between the optical fibers;

, A _c is the numerical aperture of the optical fiber; x and y are integration variables.

The calculation of R (L, λ) is carried out according to the following scheme. The values of model parameters are _randomly selected from the above ranges, and μ _s (λ), k _epi (λ) and k _derm (λ) were _calculated . For each realization of the optical parameters of the skin, the Monte Carlo method calculates the coefficients R (L, λ) corresponding to the specific geometric parameters of the used fiber-optic diffuse scattering measurement scheme (fiber core diameter, distance between them and their numerical aperture).

сравнивается со значением F_tHb, соответствующем рассматриваемой реализации, и рассчитывается погрешность восстановления F_tHb. После перебора всех реализации вычисляется средняя погрешность восстановления F_tHb. Оптимальное значение N_PC находится по минимуму средней погрешности.The simulated implementation ensemble R (L, λ) and F _tHb , which forms the training data array, is used to calculate eigenvectors and obtain regression (2) between r _n (λ) and F _tHb . The optimal number of principal components N _PC in (2) is determined by a closed numerical experiment, which consists in the following. Initially, according to formula (1), the main components of all implementations of r _n (λ) are determined and regressions between N _PC main components and F _{tHb are established} . Then, all implementations of the model parameters are sorted and F _tHb is calculated for each implementation using (2) when random deviations are applied to r _n (λ) within δr (simulating measurement errors). The resulting value

is compared with the value of F _tHb corresponding to the implementation in question, and the reconstruction error F _{tHb is calculated} . After enumerating all the implementations, the average recovery error F _{tHb is calculated} . The optimal value of N _PC is at the minimum of the average error.

характеризует чувствительность решения обратной задачи к погрешности оптических измерений, а также к вариациям биофизических параметров кожи. Видно, что рассматриваемый способ позволяет определять концентрацию гемоглобина во всем диапазоне ее возможных значений для кожи человека с погрешностью достаточной для решения задач онкологии и хирургии.Using the above algorithm, we estimate the errors in determining the concentration of hemoglobin in skin tissues from signals r _n (λ), measured on the basis of the diagram of fiber diffuse scattering measurements shown in Fig. 1 with the following parameters: λ ₁ = 524 nm, λ ₂ = 578 nm, λ ₃ = 773 nm; L ₁ = 0.43 mm, L ₂ = 1.06 mm, L ₃ = 1.69 mm; the core diameter of all fibers is 600 μm, the shell thickness is 15 μm, and the numerical aperture is A _c = 1.0. Table 1 shows the eigenvectors v _n , and Table 2 shows the regression coefficients (2) corresponding to this measurement scheme. The results of the numerical experiments described above allow us to conclude that, with an optical measurement error of δr≤5%, _{it is} optimal to use 4 main components of the initial data to restore F _tHb . Figure 2 shows the corresponding results of the restoration of F _tHb for the entire simulated ensemble of realizations F _tHb and r _n (λ) (n = 2, 3), as well as the ensemble average reconstruction errors F _tHb . The recovery of F _{tHb was} performed by applying random deviations δr = 0 and 5% to r _n (λ). The scatter of points in the figures is relatively straight

characterizes the sensitivity of solving the inverse problem to the error of optical measurements, as well as to variations in the biophysical parameters of the skin. It can be seen that the method under consideration allows us to determine the concentration of hemoglobin in the entire range of its possible values for human skin with an error sufficient to solve the problems of oncology and surgery.

Table 1.

и первые четыре собственных вектора v_n ковариационной матрицы rAverage measurement vector

and the first four eigenvectors v _{n of the} covariance matrix r λ, nm L _n mm

Custom vectors one 2 3 four 524 1.06 -3.9692 0.4305 -0.1994 -0.6361 0.4126 1.69 -7.2598 0.4218 -0.3044 -0.3510 -0.6125 578 1.06 -3.9336 0.4296 -0.2211 0.3662 0.5312 1.69 -7.3771 0.4194 -0.3217 0.5800 -0.2401 773 1.06 -1.8979 0.3674 0.6153 0.0194 0.1716 1.69 -3.3701 0.3759 0.5802 0,0378 -0.2922

Table 2. The regression coefficients a _km (2) for N _PC = 4 and M = 6. k m 0 one 2 3 four 5 6 0 0.9685 one 0.6414 0,0301 0.0040 0.0010 0.0001 0.0000 2 0.4750 -0.0642 0,0258 0,0003 -0.0025 0,0003 3 -0.7170 -0.9576 -0.7321 0.1167 0.3271 0,0853 four 2.0277 -0.4069 0.2567 -0.2753 0.1185 -0.0170

и концентрацией гемоглобина составляют основу простого и эффективного способа неинвазивного оперативного определения концентрации гемоглобина в биологической ткани, учитывающего присутствие в крови основных производных гемоглобина (оксигемоглобин, деоксигемоглобин, карбоксигемоглобин и метгемоглобин), исключающего влияние вариаций параметров тонкого верхнего слоя ткани (например, пигментации кожи) и ее рассеивающих свойств на результат измерений. Точность измерений также повышается и за счет исключения необходимости калибровочных измерений. При этом упрощается процедура измерений и повышается экономичность.Thus, measurements of diffuse light reflection signals from biological tissues P (L, λ) in the spectral regions λ = 524, 578 and 662 nm or λ = 524, 578 and 773 nm at three or more distances L _n (n = 1, 2 , 3 ...) between the points of sending and recording radiation and the multiple regression equation between the main components of normalized signals

and hemoglobin concentration form the basis of a simple and effective method for non-invasive rapid determination of hemoglobin concentration in biological tissue, taking into account the presence of the main hemoglobin derivatives (oxyhemoglobin, deoxyhemoglobin, carboxyhemoglobin and methemoglobin) in the blood, eliminating the influence of variations in the parameters of the thin upper layer of tissue (for example, skin pigmentation) its scattering properties on the measurement result. Measurement accuracy is also improved by eliminating the need for calibration measurements. This simplifies the measurement procedure and increases efficiency.

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Claims (1)

A method for determining the concentration of hemoglobin in biological tissues by sending radiation to the tissue and measuring its diffuse reflection from the tissue, characterized in that the radiation is sent to the tissue at one or more points at wavelengths λ equal to 524, 578 and 662 nm or 524, 578 and 773 nm, the diffuse reflection signals P (L _n , λ) are measured at three or more distances L _n , n = 1, 2, 3 ..., between the points of sending and recording radiation, normalized signals r _n (λ) = P ( _{L n / λ) / P (} L ₁ / λ), and their main ingredients, and the total hemoglobin concentration is calculated on the Snov multiple regression equation, binding with its main components r _n (λ).

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