RU2607494C1 - Non-invasive method for determining blood glucose concentration - Google Patents

Abstract

FIELD: medicine.

SUBSTANCE: invention relates to medicine, and namely to endocrinology, and can be used for non-invasive determination of blood glucose concentration. For this purpose a thermistors is applied above the surface vein of the head of the test and is measured a temperature and blood glucose concentration. At the same time, blood glucose concentration is determined by two calibration characteristics: glukogramm and thermogramm, parameters of which a priori identified with upper and lower boundaries of the adaptive range of two known patients with standard parameters. Calculation is carried out by certain mathematic formulas.

EFFECT: method provides higher accuracy and metrological efficiency of non-invasive determination of concentration of glucose due to elimination of systematic and dynamic errors for automation of computer analyzers of glucose in the adaptive range of rated measures with higher efficiency.

1 cl, 8 dwg, 4 tbl

Description

The invention relates to medicine, in particular to endocrinology, and can be used to monitor the concentration of glucose in the blood.

A known method of non-invasive determination of glucose concentration in the blood [see Patent No. 2198586 (RF), АВВ 5/022, No. 2000123186 / Elbaev A.D .; Akayev S.A .; Kurdanov H.A. - 2003], in which systolic and diastolic blood pressure is measured on an empty stomach and after a meal. Calculate the blood glucose in mmol / l on an empty stomach (P) and after a meal (P1) according to the formulas: P = 0.37 ^⋅ 1.65 ^{⋅ K} , where E is a constant, E = 2.71828, P1 = 0 , 65⋅E ^{l, 5⋅K1} , where E is a constant, E = 2.71828, K and K1 are correlation coefficients, which are defined as the ratio of the arithmetic mean of systolic blood pressure to the arithmetic mean of diastolic blood pressure measured on both fasting patient’s hands (K) and after eating (K1).

Disadvantage: the method does not allow to achieve the desired accuracy and does not allow continuous monitoring of the concentration of glucose in the blood.

A known method for non-invasive determination of glucose in parts of the human body [see Patent 5795305 (US), 60/549 / Ok-Kyung Cho, Birgit Holzgreve, 08/18/98]. Use high-precision measurements of the temperature of the body area, infrared radiation of this area and the thermal conductivity of the skin in this area to determine the glucose concentration. The analysis is based on mathematical methods of extrapolation and does not take into account the influence of external factors on changes in body temperature.

The disadvantage of this method is the lack of a mathematical model of carbohydrate metabolism. The algorithm connects only the current concentration of glucose in the blood with the current temperature, which means that the method is not intended for long-term monitoring, and also does not take into account the influence of individual factors on temperature changes.

For the prototype adopted a method of non-invasive control of blood glucose [see patent 2180514 (RF), АВВ 5/01 No. 200111121/14 / Shmelev V.M., Bobylev V.M. - March 20, 2002], which determines the concentration of glucose in the blood using a measuring device, while continuously monitoring the concentration of glucose in the blood by measuring the heat flux in the surface veins of the head with a sensor of the measuring device, and the glucose concentration (X _g *) is determined by formula X _g * = X ₁ * + X ₂ *, where X ₁ * = W _mn (s) X _T *, X ₂ * = К _П W _mn (s) X _П *, where Х _Т * - dimensionless temperature deviation from the steady-state value, Х _П * - dimensionless deviation of the heat flux from the steady-state value, W _mn (s) = 1 / (T _TP s + 1) - transfer I is a function of the concentration of glucose in the blood by temperature and heat flux, T _TP - experimentally determined time constant of the transition process, K _P - experimentally determined dimensionless coefficient, s = d / dt - differentiation operator.

The disadvantage of the prototype is the low metrological efficiency due to the high error in a wide range of informative measurement parameters due to a fixed statistical calibration characteristic.

The technical objective of the method is to increase metrological efficiency by eliminating methodological and dynamic errors for the automation of computer glucose analyzers in the adaptive range of standardized measures.

The technical problem is achieved by a non-invasive determination of the concentration of blood glucose from a gluogram calibrated within the normalized boundaries of the adaptive range by the optimal maximum temperatures of the thermograms of known patients.

1. In a non-invasive method for determining the concentration of glucose in the blood, which consists in applying thermistors over the superficial vein of the head of the subject and measuring the temperature and concentration of glucose in the blood, in contrast to the prototype, the blood glucose concentration is determined by two calibration characteristics: glucose and thermogram, parameters which are a priori identified with the upper and lower boundaries of the adaptive range of two well-known patients with normalized parameters, thermogram parameters: time constant T and max mal E the temperature is found from the measured excess temperatures U _i for i = 1, 2 in the two instants t ₁ and binary t ₂ = 2t ₁ glyukogrammy parameters are: maximum temperature of E ₀ and the limiting concentration of glucose P ₀ blood, which is monitored by measured glucose concentrations P _j , where j = 1, 2 for two maximum temperatures E ₁ and a multiple of E ₂ = nE _{1 of the} thermogram U (t)

with identical parameters of the range: time constant T and maximum temperature E

2. In the method according to claim 1, in contrast to the prototype, the gluogram

reflects the physics of a full-scale experiment with parameters identical to the limits of the range: limiting temperature E ₀ and limiting glucose P ₀

The essence of the proposed method is illustrated in figures 1-8.

The proposed method before measuring includes 2 stages: 1 - calibration of the parameters of the thermogram and 2 - calibration of the parameters of the gluogram.

Stage 1

(фиг. 1, правая шкала) в начальный момент времени. Избыточные температуры (фиг. 1, левая шкала), с учетом начальной температуры

, определяются соотношением:a) When examining a patient on an empty stomach, apply thermistors above the superficial vein of the head and measure the temperature

(Fig. 1, right scale) at the initial time. Excessive temperatures (Fig. 1, left scale), taking into account the initial temperature

are determined by the ratio:

b) After the patient has taken glucose-containing food, a change in temperature U _{i is} recorded for i = 1, 2 over time t ₁ and binary t ₂ = 2t ₁ , according to which the limiting parameters of the thermogram are calculated (Fig. 1).

c) The limiting parameters are found a priori for known patients with normalized boundaries of the adaptive range of the calibration temperature characteristic U from time t (thermogram):

taking into account the parameters: E - maximum temperature and T - time constant.

The regularities of the parameters E and T are identical to the optimal equivalents (Fig. 1, lines 2, 3) of the thermogram (2), which integrate the variables of temperature U and time t:

what the ultimate solutions prove

The time constant T of the thermogram (2) is found from the system of equations:

We divide the second equation of system (3) into the first, given that t ₂ = 2t ₁ :

After reducing by the denominator and logarithm, we find the thermogram parameter T - time constant:

The maximum temperature E of the thermogram (1) is determined from the system of equations inverse with respect to (3):

After dividing the second equation of system (5) by the first

, получим логарифмическое уравнение:given binary intervals

, we obtain the logarithmic equation:

which corresponds after exponentiation to the quadratic equation:

Opening the brackets and reducing the units and the denominator E, we find the optimization algorithm for the second parameter of the calibration characteristic of the thermogram E - the maximum temperature:

The maximum temperatures (6) of the thermogram (2) at stage 2 serve as normalized boundaries of the adaptive range of the studied gluogram for its identification with the equivalent of a full-scale experiment by finding the optimal parameters of the reference gluogram.

2 stage

a) Determine the concentration P of blood glucose through the maximum temperature E according to the calibration characteristic of the gluogram, mmol / l:

taking into account informative parameters: P ₀ - limit blood glucose and E ₀ - limit temperature (see Fig. 2).

The patterns of parameters P ₀ (Fig. 2, line 2) and E ₀ (Fig. 2, line 3) are identical to the optimal equivalent of the gluogram (7):

what the ultimate solutions prove

b) The calibration characteristic (7) is introduced a priori for two well-known patients with normalized boundaries of the adaptive range of blood glucose concentrations P ₁ , P ₂ , for which the maximum temperatures E ₁ , E ₂ are determined at the first stage. From the two known glucose concentrations and the recorded maximum temperatures P ₁ , E ₁ and P ₂ , E ₂ find the limit glucose P ₀ blood and the limit temperature E ₀ (Fig. 2).

Glucogram parameter (7), the limiting temperature E _{0 is} found from the system of equations

We divide the second equation of system (8) into the first

and after logarithm, we find the limit temperature E _{0 of the} gluogram:

Limit glucose P ₀ is determined from the system of equations inverse with respect to (8)

after dividing the second equation of system (10) by the first

, получим логарифмическое уравнениеTaking into account the multiplicity of the relation

we get the logarithmic equation

which corresponds after exponentiation to the power equation

After dividing by the denominator, the degree is reduced by one

and find the second parameter of the glucose P ₀ - limit glucose

The advantages of the proposed diagnostic method compared to the prototype include improving the accuracy of the method by eliminating methodological and dynamic errors by calibrating the gluogram in the normalized boundaries of the adaptive range with the optimal maximum temperatures of the thermograms of known patients.

Let us prove the metrological effectiveness of the proposed method relative to the prototype by the reliability of measurements in the adaptive range for the studied dependence.

1. Assessment of methodological error

a) Thermogram (Fig. 1 and Fig. 3, curves 1, 2)

,

(фиг. 1), с учетом начальной температуры

избыточные температуры U_i=0,422, 0,578 по алгоритмам (4) и (6) оптимальные параметры Е₁=0,668, Т=1800 термограммы (фиг. 3).For the first patient, we find the measured temperatures from the binary intervals t ₁ = 1800, t ₂ = 3600

,

(Fig. 1), taking into account the initial temperature

excess temperatures U _i = 0.422, 0.578 according to algorithms (4) and (6) optimal parameters E ₁ = 0.668, T = 1800 thermograms (Fig. 3).

According to the found parameters E ₁ and T for the first patient, we find from (2) the calibration characteristic U _j :

,

(фиг. 1) с учетом начальной температуры U_i=36° избыточные температуры U_i=0,495, 0,677 по алгоритмам (4) и (6) оптимальные параметры Е₂=0,783, Т=1800 термограммы.For the second patient, we find the measured temperatures at binary intervals t ₁ = 1800, t ₂ = 3600 and

,

(Fig. 1) taking into account the initial temperature U _i = 36 °, the excess temperatures U _i = 0.495, 0.677 according to algorithms (4) and (6) the optimal parameters are E ₂ = 0.783, T = 1800 of the thermogram.

According to the found parameters E ₂ and T for the second patient, we find (Fig. 3, curve 2) from (2) the calibration characteristic U _j :

Let us evaluate the reliability (Fig. 4) of the reference (experimental) U _e (Fig. 3 curve 1) with respect to the calibration characteristic U _i (Fig. 3 curve 2) with respect to the relative error ε _i :

We systematize the results in Table 1 for the analysis of the methodological error of the innovation thermogram (u) and prototype (n) by efficiency

Tab. 1 shows that the innovation parameters E _ju and T _ju uniquely determine thermograms with a minimum error of not more than 0.12% and 0.06% (Fig. 4), and the prototype E _jn and T _jn have a 5% error in determination. Then the efficiency (12a) of the calibrated thermogram of the proposed solution differs by 42-83 times, i.e. two orders of magnitude higher than the prototype, regulated by statistical analysis of the set of unnormalized variables by the rigid calibration characteristic of the average phantom.

b) Glucogram

We find for known values of P ₁ = 3.1, P ₂ = 4.7 and certain maximum temperature values E ₁ = 0.668, E ₂ = 0.783 according to algorithms (9) and (11) the optimal parameters E ₀ = 0.276 and P ₀ = 0.276 gluograms (Fig. 5, curve 1).

According to the found parameters E ₀ and P ₀ we find from (7) the calibration characteristic P _j (Fig. 5, curve 2):

We will evaluate the reliability (Fig. 6) of the reference (experimental) glucogram P _s (Fig. 5, curve 1) with respect to the calibration characteristic (Fig. 5, curve 2) and the prototype P (Fig. 5, curve 3) with respect to the relative error ε _j :

For glucose analysis, we systematize the data in the table. 2.

Tab. 2 shows that the parameters E ₀ and P ₀ uniquely determine the reference and calibrated gluograms with a minimum methodological error of not more than 0.035% (identical to Fig. 4), while the prototype has an error of 5% in the range (E ₁ -E ₂ ) of a healthy patient and 500% in risk groups (Fig. 6) due to statistical analysis with linear approximation (Fig. 5, graph 3).

2. The estimation of dynamic error

a) Thermogram

The dynamic error (Fig. 7) is determined by the non-linearity η _{1 of the} thermograms, regulated by the ratio of the time intervals of the variables t of the prototype and the normalized time constant of the proposed solution T (Figs. 1, 3):

The nonlinearity (14) of the proposed solution η _{1u is} identical to the unit equivalent (Fig. 7, curve 1), because

The prototype uses unnormalized variables of time t:

and the non-linearity of thermograms (Fig. 1) of the prototype change according to the logarithmic law

The reproducibility of the results of the thermogram (Fig. 3) is presented in table. 3.

From the table. Figure 3 shows that in the proposed innovation, the parameters E, T = const (Fig. 1) are normalized by the boundaries of the adaptive range of known patients. The nonlinearity of the proposed solution is regulated by a single equivalent (Fig. 7, line 1), in contrast to the variable non-linearity of the prototype, which varies according to the logarithmic law due to the set of unnormalized variable thermograms t _i , U _i (Fig. 7, curve 2).

b) Glucogram

The dynamic error is determined by the nonlinearity η _{2 of the} gluogram (Fig. 5), determined by the ratio of the glucose concentrations P of the prototype and the normalized limit glucose of the proposed solution P ₀ .

The nonlinearity (15) of the claimed solution η _{2u is} identical to the unit equivalent (Fig. 8, line 1), because

The prototype uses abnormal values of glucose concentrations P:

and the non-linearities of the prototype vary exponentially (Fig. 8, curve 2)

The reproducibility of the thermogram results is presented in Table 4.

From the table. 4 it follows that in the proposed innovation, the parameters E ₀ , P ₀ = const are normalized by the boundaries of the adaptive range of known patients. The nonlinearity of the proposed solution is regulated by a single equivalent (Fig. 8, line 1), in contrast to the variable nonlinearity of the prototype, which varies exponentially (Fig. 8, curve 2) due to the multitude of unnormalized variable thermograms E _i , P _i .

3. Estimation of the width of the range

The range efficiency η _D is the ratio of the range D _{u of the} proposed innovation to the range D _{n of the} prototype (see Fig. 5, charts 2, 3):

From the formula (16) shows that the efficiency in the range of the proposed innovation is at least 5 times higher than the efficiency in the range of the prototype.

4. Efficiency assessment

Increasing the efficiency of the proposed innovation proves the effectiveness of the measurement time t. In the proposed method, t≤T measurement does not exceed the time constant (Fig. 1), and for the prototype 3-5 times greater than t _n = (3-5) T to determine the maximum temperature with an error of 5-1%.

для погрешности (5-1)% следует, что оперативность предлагаемого способа в 3-5 раз выше известных способов.From time efficiency

for an error of (5-1)% it follows that the efficiency of the proposed method is 3-5 times higher than the known methods.

Thus, a non-invasive determination of blood glucose concentration from a glucogram calibrated at the normalized boundaries of the adaptive range by the optimal maximum temperatures of thermograms of known patients, in contrast to known solutions, reduces methodological and dynamic errors by several orders of magnitude with an increase in efficiency of at least 3 times, which ultimately increases the metrological efficiency of determining glucose concentration by temperature with a priori specified accuracy for automation of computer analysis factors in the adaptive range of standardized measures.

Claims (8)

A non-invasive method for determining the concentration of glucose in the blood, which consists in applying thermistors over the superficial vein of the head of the subject and measuring the temperature and concentration of glucose in the blood, characterized in that the blood glucose concentration is determined by two calibration characteristics: a gluogram and a thermogram, the parameters of which are a priori identified with upper and lower boundaries of the adaptive range of two well-known patients with normalized parameters, thermogram parameters: time constant T and maximum th E the temperature is found from the measured excess temperatures U _i for i = 1, 2 in the two instants t ₁ and binary t ₂ = 2t ₁ glyukogrammy parameters are: maximum temperature of E ₀ and the limiting concentration of glucose _P0 blood, which is monitored by measured glucose concentrations P _j , where j = 1, 2 for two maximum temperatures E ₁ and a multiple of E ₂ = nE _{1 of the} thermogram U (t)

, with identical parameters of the range: time constant T and maximum temperature E

,

, a glucogram

calibrated with parameters identical to the limits of the range: limit temperature E ₀ and limit glucose P ₀

,

where

.

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