JP2012052819A - Calculation method for determination of ionized calcium - Google Patents

Abstract

PROBLEM TO BE SOLVED: To provide a method for calculating an ionized calcium level in human blood from each measured level of total calcium, albumin, total protein and inorganic phosphorus in serum and each normal level of citric acid, lactic acid and hydrogen carbonate ion.SOLUTION: A method for calculating an ionized calcium level comprises: a step for using six parameters to promote accuracy of calculation; a step for obtaining an amount of free ligand by means of acid dissociation balance system in order to eliminate an influence of pH; a step for obtaining each amount of calcium complexes from a complex balance system between the free ligand and calcium; a step for obtaining a final amount of calcium complex by a method of repeating calcium equilibrium calculation although the calcium complexes are competitive around the calcium; and a step for subtracting the final amount of calcium complex from a total calcium level.

Description

The present invention relates to a calculation method for obtaining a blood ionized calcium value.

Calcium in the blood is said to be about 43 to 47% protein-binding, 5 to 10% non-dissociated salt, and 48 to 52% ionic (Yasutaka Takagi, et al .: Clinical Pathology, 28, 1089, 1980). The protein binding type is a complex of albumin, globulin and calcium, and the non-dissociated salt type is a complex of calcium, phosphate, bicarbonate ion, citric acid, lactic acid and the like. The ionic form refers to unbound free ionized calcium.
Calcium is important for life such as bone formation, metabolism, blood coagulation, and maintenance of cardiac rhythm. In particular, ionized calcium plays an important role in physiological functions and is said to be essential for elucidation of disease states and diagnosis of diseases. In general laboratory tests, total calcium is widely measured. However, measurement of ionized calcium is not widely used as a daily clinical test, although it is said that it is more effective for diagnosis than total calcium. This is thought to be because it is difficult to measure ionized calcium and it is difficult to handle the sample.

For the conventional measurement of ionized calcium, (a) a colorimetric method described in Non-Patent Document 1 or Patent Document 1 using a murexide dye, (b) an electrode method described in Non-Patent Document 2 using a calcium electrode, (c) There are calculation methods described in Non-Patent Document 3 and Non-Patent Document 4 that are obtained by calculation from the measured values of serum total calcium value and protein without actually measuring ionized calcium.
The murexide dye method (a) is very troublesome because the sample needs to be dialyzed. The method described in Patent Document 1 has no proof of accuracy with respect to the measured value. The calcium electrode method (b) is currently the most accurate measurement method. As soon as the blood is exposed to air, it decarboxylates, increasing the blood pH, resulting in a significant decrease in ionized calcium. Therefore, it is necessary to handle the sample anaerobically, and immediately after blood collection, ionized calcium and pH are measured and corrected to pH 7.4. Therefore, it is difficult to measure a large amount of samples quickly. (C) The calculation method described in Non-Patent Document 3 is to calculate the ionized calcium value by multiplying the total calcium value or albumin value by a coefficient. There is. The calculation method described in Non-Patent Document 4 is a theoretical formula for calculating an ionized calcium value using an equilibrium equation because calcium is coordinated to serum total protein and exhibits a complex equilibrium. However, it is not calculated by dividing the protein into albumin and globulin, and low molecular ligands other than protein are ignored, and pH correction is not easy and lacks accuracy.

    The total amount of calcium in the body (in vivo) is biologically controlled by parathyroid hormone and vitamin D through absorption from the intestines and bones and excretion from the kidney. In contrast, total calcium collected and removed (in vitro) no longer increases or decreases. Among blood calcium, the protein-binding type is a complex in which calcium and albumin or globulin are coordinated, and the non-dissociated salt type is calcium and a ligand (ligand) such as citric acid, phosphoric acid, lactic acid, or bicarbonate ion. Is considered to be a coordination bond. The reaction of these calcium complexes is a very fast reversible reaction, and if the composition ratio of calcium is determined by the chemical equilibrium based on the law of mass action, the amount of multiple calcium complexes can be calculated from the equilibrium equation. It is considered that the final ionized calcium can be calculated by subtracting the complex amount from the total calcium value. To date, there have been reports on the idea of applying an equilibrium formula to all the ligands of proteins, inorganic substances, and organic substances in the same dimension, further adjusting the pH by incorporating an acid dissociation equilibrium formula, and then calculating ionized calcium. I can't find it.

JP-A-6-335400

Rose GA,: Determination of the ionized and ultrafilterable calcium of normal human plasma, Clin Chimca Acta: 2,227236, 1957. Moore ED: Ionized calcium in normal serum, ultrafiltrates, and whole blood determined by ion-exchange electrodes, J Clin Invest 49: 318-334, 1970. Barry Kirschbaum: Effect of high bicarbonate hemodialysis on ionized calcium and risk of metastatic calcification.Clinca Chimica Acta 343: 231-236, 2004. Harris EK, DeMets DL: Biological and analytic components of variation in long-term studies of serum constituents in normal subjects, Clinical chemistry: 17, 983-987, 1971. Pedersen KO.Binding of calcium to serum albumin I.stoichiometry and intrinsic association constant at physiological pH, ionic strength and temperature.Scand J Clin Lab Invest 28: 459-469,1971 Pedersen KO: Binding of calcium to serum albumin II.effect of pH via competitive hydrogen and calcium ion binding to the imidazole groups of albumin, Scand J Clin Lab Invest, 29: 75-83, 1972. Pedersen KO: Protein-bound calcium in human serum.Quantitative examina -tion of binding and its variables by a molecular binding model and clinical chemical implications for measurement of ionized calcium, Scand J Clin Lab Invest, 30: 321-329, 1972.

<1> Many conventional calculation formulas for obtaining ionized calcium calculate using protein as a parameter. Other ligands should be used in the calculation to increase the accuracy of the ionized calcium value.
<2> Omission of pH measurement and anaerobic handling of samples required for the electrode method is a problem.
<3> Conventional calculation formulas are limited in application to special specimens having abnormal values of protein and phosphate. Therefore, it is desirable that the theoretical formula is applicable to special specimens.
<4> It is desirable that a large amount of specimens can be processed quickly and easily

In the calculation method of the present invention, blood total calcium is first measured, the amount of calcium complex is calculated from six ligand values by a complex equilibrium equation, and the plurality of calcium complexes are narrowed down by convergence calculation, and pH correction and calcium complex calculation are performed. The acid dissociation calculation is taken in to calculate the basic numerical value of.
<1> In order to improve accuracy, the above calculation was applied to all six parameters of albumin, total protein, inorganic phosphorus, citric acid, lactic acid, and bicarbonate ion.
<2> First, acid dissociation calculation will be described. Each ligand is coordinated with calcium, but also coordinated with a hydrogen ion as shown in (Chemical Formula 1), resulting in a reversible equilibrium state. Therefore, the amount of the hydrogen ligand complex is calculated first, and then the equilibrium amount of the complex between the remaining ligand and calcium is calculated. In general, the equilibrium between hydrogen ion and ligand is called acid dissociation equilibrium (Equation 1) and has a constant acid dissociation constant based on the law of mass action as shown in the acid dissociation equation A. In other words, if two of the three variables are determined, the remaining one is obtained. The total ligand amount is the sum of [Ligand] and [HLigand] as shown in (Equation 2), and if this is substituted into (Equation 1) acid dissociation equilibrium equation A, (Equation 3) acid dissociation equation B is obtained. It is done. Furthermore, when formulating Hligand, the formula for the hydrogen bond ligand of (Equation 4) is derived. (Unit: mol / L, charge omitted)

(Chemical formula 1) Acid dissociation reaction HLigand ⇔ Ligand + H
(Equation 1) Acid dissociation A Ka = [H] [Ligand] / [HLigand]
(Equation 2) tLigand = HLigand + Ligand
(Equation 3) Acid dissociation B Ka = [H] [tLigand-HLigand] / [HLigand]
(Equation 4) Formula for hydrogen bonding ligand HLigand = H x tLigand / (Ka + H)

In the calculation when CaLigand is generated, since CaLigand is an out-of-system substance in acid dissociation equilibrium, the value obtained by subtracting CaLigand from tLigand is calculated as the total ligand amount in acid dissociation equilibrium. That is, the formula for calculating the hydrogen bonding ligand is HLigand = H × (tLigand-CaLigand) / (Ka + [H]).
Formula for calculating the amount of hydrogen bonding ligand.
(Expression 5) HAlbsite = H × (tAlbsite-CaAlbsite) / (Ka1 + H)
(Equation 6) HGlbsite = H × (tGlbsite-CaGlbsite) / (Ka2 + H)
(Expression 7) H ₂ PO ₄ = H × (tPi-CaHPO ₄ ) / (Ka3 + H)
(Equation 8) HCitrate = H x (tCitrate-CaCitrate) / (Ka4 + H)
(Equation 9) HLact = H × (tLact-CaLact) / (Ka5 + H)
Since the normal value of hydrogen carbonate ion is the concentration after acid dissociation equilibrium, calculation by the acid dissociation equation is not necessary.

Explanation of terms in the above formula 1:
Ligand: free ligand (ligand), HLigand: hydrogen bond ligand, [H]: hydrogen ion concentration (mol / L), Ka: acid dissociation constant, tLigand: total ligand
HAlbsite: hydrogen-bonded albumin, tAlbsite: total number of albumin sites, CaAlbsite: number of calcium albumin complexes, HGlbsite: hydrogen-bonded globulin, tGlbsite: total number of globulin sites, CaGlbsite: number of calcium globulin complexes, and site definition in the next section <3> explain. tGlbsite concentration is calculated by subtracting serum albumin (g / L) from serum total protein (g / L) and multiplying the amount of globulin (g / L) by the maximum number of calcium bindings per gram of globulin (mol / g). The final unit is mol / L. The maximum number of bonds was calculated from the values described in Non-Patent Document 7. tPi: Serum inorganic phosphorus measurements, H2 PO4: dihydrogen phosphate ions, CaHPO _4: calcium hydrogen phosphate complexes, TCitrate: Serum Citrate normal mean value, HCitrate: citrate monosodium hydrogen ion, CaCitrate: calcium complex citrate, tLact: normal serum lactic acid average value, HLact: lactate monohydrogen ion, CaLact: calcium lactate complex
Ka1, Ka2, Ka3, Ka4, Ka5: acid dissociation constants of albumin site, globulin site, phosphoric acid, citric acid, and lactic acid.

    <3-1> Next, the calculation method for obtaining the amount of calcium complex will be described in terms of albumin. According to (Non-Patent Document 5), one albumin molecule can bind to a maximum of 12 molecules of calcium. In the same way as the Scatchard model (Koichiro Aoki et al. “Serum albumin” page 82 Kodansha Scientific), the 12 calcium binding sites are (A) independent of each other and do not affect other binding sites. (B) Each site Assuming that the binding of these is the same, the total number of albumin sites (several 10) is 12 times the molar concentration of albumin. This complex reaction of the albumin site and free calcium (Chemical Formula 2) is a reversible reaction, and a dynamic equilibrium as shown in the complex equilibrium formula A of (Equation 11) is established. (Unit: mol / L, charge omitted)

(Equation 10) Total number of albumin sites tAlbsite = tAlb × 12 (mol / L)
(Chemical formula 2) Calcium complex reaction fCa + fAlbsite ⇔CaAlbsite
(Equation 11) Complex equilibrium formula A Ka1 = [CaAlbsite] / ([fCa] [fAlbsite])
(Equation 12) Quantity relations in the complex equilibrium equation
fAlbsite + CaAlbsite = t'Albsite
fCa + CaAlbsite = t'Ca

The breakdown of total albumin sites is shown in (Equation 13). The total number of albumin sites (t'Albsite) in this complex equilibrium formula A (Equation 11) is the sum of (fAlbsite) and (CaAlbsite) (Equation 12). The total number of albumin sites (tAlbsite) is subtracted from the number of hydrogen-bonded albumin sites (Formula 5) not involved in the complex equilibrium equation (Formula 14).
The breakdown of total calcium is shown in (Equation 15). The total calcium (t'Ca) in this complex equilibrium equation A (Equation 11) is the sum of [fCa] and [CaAlbsite] (Equation 12). And the amount of calcium (Equation 16) obtained by subtracting the amount of calcium complex of each ligand falling outside the system of this equilibrium reaction from the total measured value of calcium (tCa).

(Equation 13) tAlbsite = fAlbsite + HAlbsite + CaAlbsite
(Equation 14) t'Albsite = tAlbsite-HAlbsite
(Equation 15) tCa = fCa + CaAlbsite + CaGlbsite + CaHPO ₄ + CaCitrate + CaLact + CaHCO ₃
(Equation 16) t'Ca = tCa -CaGlbsite -CaHPO ₄ -CaCitrate -CaLact -CaHCO ₃
By substituting these into (equation 11) complex equilibrium equation A, (equation 17) complex equilibrium equation B is obtained. When this equation is arranged for CaAlbsite, the following (Equation 23) quadratic equation is obtained, and by solving this, the amount of CaAlbsite complex can be calculated. (Equation 17) Complex equilibrium equation B Ks1 = [CaAlbsite] / ([t 'Ca-CaAlbsite] [t'Albsite-CaAlbsite])

Similarly, the total amount of ligand used in the complex equilibrium formula is shown below.
(Equation 18) t'Glbsite = tGlbsite-HGlbsite
(Equation 19) t'Pi = tPi-H ₂ PO ₄
(Equation 20) t'Citrate = tCitrate-HCitrate
(Equation 21) t'Lact = tLact-HLact
(Equation 22) t'HCO ₃ = 0.02 mol / l

The calculation formulas for the CaGlbsite complex amount, the CaHPO ₄ complex amount, the Citrate complex amount, the CaLact complex amount, and the CaHCO ₃ complex amount are shown in the same manner as the calculation formula for the CaAlbsite complex amount.
(Equation 23)
Ks1 × CaAlbsite ^2- (Ks1 × t'Ca + Ks1 × t'Albsite +1) × CaAlbsite + Ks1 × t'Ca × t'Albsite = 0
(Equation 24)
Ks2 × CaGlbsite ^2- (Ks2 × t'Ca + Ks2 × t'Glbsite + 1) × CaGlbsite + Ks2 × t'Ca × t'Glbsite = 0
(Equation 25)
Ks3 × CaHPO ₄ ^2- (Ks3 × t'Ca + Ks3 × t'Pi + 1) × CaHPO ₄ + Ks3 × t'Ca × t'Pi = 0
(Equation 26)
Ks4 × CaCitrate ^2- (Ks4 × t'Ca + Ks4 × t'Citrate + 1) × CaCitrate + Ks4 × t'Ca × t'Citrate = 0
(Equation 27)
Ks5 × CaLact ^2- (Ks5 × t'Ca + Ks5 × t'Lact +1) × CaLact + Ks5 × t'Ca × t'Lcat = 0
(Equation 28)
Ks6 × CaHCO ₃ ^2- (Ks6 × t'Ca + Ks6 × t'HCO ₃ + 1) × CaHCO ₃ + Ks6 × t'Ca × t'HCO ₃ = 0

Explanation of terms in the above formula 2:
tAlb: Measured value of albumin (mol / L), 12: Number of moles of calcium bumine site to which 1 mole of albumin can bind, fCa: Number of moles of free calcium, t'Ca: Total calcium in the complex equilibrium formula, Ks1: Albumin and calcium Complex equilibrium constant of
Ks1, Ks2, Ks3, Ks4, Ks5, Ks6: Equilibrium constants of albumin site, globulin site, phosphate, citrate, lactic acid, bicarbonate ion and calcium. _{CaAlbsite, CaGlbsite, CaHPO 4, CaCitrate} , CaLact, CaHCO 3: calcium complex molar concentration of each ligand

    <3-2> Next, multiple equilibrium between a plurality of calcium ligand complexes will be described. When the calculation of the amount of one calcium complex is completed, the amount of free calcium is reduced by the amount of the calcium complex produced. Therefore, the equilibrium of other ligands is lost. Therefore, the complex equilibrium calculation must be re-executed using the reduced free calcium. If recalculation is performed about 10 times according to the change of the free calcium concentration, it is converged to a constant value. (Fig. 1) shows the outline of the repeated calculation.

<3-3> The amount of ionized calcium is obtained by subtracting the calcium complex amount of each final ligand from the serum total calcium value. The final formula for obtaining ionized calcium is shown in (Equation 29) below.
(Equation 29)
Ionized calcium = tCa-CaAlbsite-CaGlbsite-CaHPO ₄ -CaCitrate-CaLact-CaHCO ₃

    <4> By adding this calculation program to the spreadsheet software of a personal computer, it is possible to quickly calculate a large number of samples.

<1> By increasing the number of parameters for calculation, the accuracy has increased from the conventional method.
By adopting the <2> acid dissociation formula, pH measurement becomes unnecessary, and anaerobic handling of the specimen becomes unnecessary.
<3> Since the stoichiometric calculation is based on the complex equilibrium formula, the range of application of the specimen is expanded.
<4> By creating a program for a personal computer, calculation is quick and easy, and it can be implemented as a daily inspection.

Overview of ionized calcium calculation method Comparison of calculated values of ionized calcium and measured values of electrodes

    As a sample, blood was anaerobically collected from a healthy person using a vacuum blood collection tube, and measurement was performed immediately after serum separation. Siemens blood gas analyzer RapidPoint405 electrode device was used for the measurement of ionized calcium. For the total protein, albumin, total calcium, and inorganic phosphorus, an automatic biochemical analyzer for clinical tests was used. The measurement results were total protein 7.6 g / dl, albumin 4.5 g / dl, total calcium 9.2 mg / dl, inorganic phosphorus 4.1 mg / dl (globulin content = total protein value−albumin value). As other item values, citric acid = 2.4 mg / dl, lactic acid = 10 mg / dl, and bicarbonate ions = 20 mM corresponding to normal values were used in the calculation.

-Log (Ka1) = 7.55, -log (Ka2) = 7.55, -log (Ka3) = 7.2, -log (Ka4) = 4.76, -log (Ka5) = 3.86 were used for the acid dissociation constant of each ligand. . The complex equilibrium constant of each ligand is log (Ks1) = 2.38, log (Ks2) = 2.55, log (Ks3) = 2.66, log (Ks4) = 3.16, log (Ks5) = 1.42, log (Ks6) = 1.0 used. (Ka and Ks values are cited from Non-Patent Document 6, Non-Patent Document 7, and Chemical Handbook II edited by The Chemical Society of Japan, Maruzen pp317-331, 1993, etc.)
Results of ionized calcium: 1.10 mmol / L of calculation results, 1.16 mmol / L of electrode method measurement results

34 samples showing abnormal calcium metabolism are used.
About the measuring method of ionized calcium and another biochemical item, the same thing as Example 1 was used. The acid dissociation constant, equilibrium constant, citric acid, lactic acid, and bicarbonate ion content were the same as in Example 1.
Results of 34 samples: electrode method average value 1.24 calculated average value 1.20, correlation coefficient r = 0.993 regression line y = 0.95x−0.02, FIG. 2 shows individual data as a correlation diagram.

    Measurement of ionized calcium in blood has great significance as clinical diagnosis and follow-up, and there is a demand. Since the ionized calcium value can be easily obtained by this calculation method, the practical value is great.

Claims (1)

    (1) Using the six ligand-containing values of albumin, globulin, inorganic phosphorus, citric acid, lactic acid, and bicarbonate ions in serum, (2) Each release from the formula created using the acid dissociation formula of each ligand as a means The amount of ligand is obtained, (3) the amount of each calcium complex is obtained by means of a complex equilibrium formula consisting of each free ligand and ionized calcium, and (4) free calcium decreases when a calcium complex of one ligand is formed. When the free calcium decreases, the equilibrium of other ligands is lost, so it is necessary to redo the equilibrium calculation. By repeating this recalculation, the amount of final calcium complex that converges is obtained. A calculation method for calculating ionized calcium by subtracting the amount of ligand complex.

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