JP5750601B2 - Calculation method for the determination of ionized calcium - Google Patents
Calculation method for the determination of ionized calcium Download PDFInfo
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本発明は血中イオン化カルシウム値を求めるための計算方法に関するものである。 The present invention relates to a calculation method for obtaining a blood ionized calcium value.
血中のカルシウムは蛋白結合型43〜47%、非解離塩型5〜10%、イオン型48〜52%程度(高木康,他:臨床病理,28,1089頁,1980)と言われる。蛋白結合型とはアルブミン、グロブリンとカルシウムとの錯体であり、非解離塩型とはリン酸、炭酸水素イオン、クエン酸、乳酸などとカルシウムとの錯体である。イオン型とは非結合の遊離イオン化カルシウムを指す。
カルシウムは骨の形成、代謝、血液の凝固、心筋の律動維持など生命にとって重要である。特にイオン化カルシウムは生理機能に重要な役割を演じており病態の解明、疾患の診断に必須であると言われる。通常臨床検査では総カルシウムが広く測定されている。しかしイオン化カルシウムの測定は総カルシウムより診断に有効的であると言われるにもかかわらず、日常の臨床検査として普及していない。これはイオン化カルシウムの測定が難しいことや試料の取り扱いが難しいためと考えられる。
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.
従来のイオン化カルシウムの測定には(a)ムレキシド色素を用いる非特許文献1や特許文献1に記載の比色法、(b)カルシウム電極を用いる非特許文献2に記載の電極法、(c) イオン化カルシウムを実測せずに、血清総カルシウム値と蛋白質等の測定値から計算によって求める非特許文献3及び非特許文献4に記載の計算法がある。
(a)のムレキシド色素法は試料を透析する必要があり大変面倒である。特許文献1に記載の方法は測定値に対する正確性の証明が無い。(b)のカルシウム電極法は現在最も正確な測定方法である。血液が空気に晒されると直ちに脱炭酸し、血液pHが上昇、その結果イオン化カルシウムは大きく低下する。そのため試料を嫌気的に取り扱うことが必要で、採血後直ちにイオン化カルシウムとpHを測定しpH7.4に補正して報告される。そのため多量検体を迅速に測定することが難しい。(c)非特許文献3に記載の計算法は、総カルシウム値やアルブミン値に係数を乗除し、イオン化カルシウム値を求めるもので、比較実験により係数を定めたいわば経験式で、適用検体に限界がある。また非特許文献4に記載の計算法はカルシウムが血清総蛋白に配位結合し錯体平衡を示すことから、平衡式を用いてイオン化カルシウム値を計算する理論式である。しかし蛋白をアルブミンとグロブリンに分けての計算でなく、さらに蛋白質以外の低分子リガンドを無視しており、pH補正も簡単ではなく正確性に欠ける。
For the conventional measurement of ionized calcium, (a) a colorimetric method described in Non-Patent
The murexide dye method (a) is very troublesome because the sample needs to be dialyzed. The method described in
生体内血中総カルシウム量(in vivo)は腸、骨からの吸収、腎臓からの排出等を通じて副甲状腺ホルモン、ビタミンDにより生物学的に制御されている。これに対し採血され対外に取り出された(in vitro)総カルシウムはもはや増減しない。血液カルシウムの内、蛋白結合型はカルシウムとアルブミンやグロブリンとが配位結合した錯体であり、非解離塩型はカルシウムとクエン酸、リン酸、乳酸、炭酸水素イオンといった配位子(リガンド)とが配位結合した錯体であると考えられる。これらカルシウム錯体の反応は非常に速い可逆反応で、そのカルシウムの構成比率は質量作用の法則に基づいた化学平衡によって決まると考えれば、平衡式から複数のカルシウム錯体量を計算することができ、この錯体量を総カルシウム値から差し引けば最終イオン化カルシウムが計算できると考えられる。これら蛋白質、無機物、有機物のすべてのリガンドに対し平衡式を同次元で適用させて、さらに酸解離平衡式を取り込むことでpH補正を行い、その後にイオン化カルシウムを計算するという発想の報告は今までに見当たらない。 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.
<1>イオン化カルシウムを求める従来の計算式では蛋白質をパラメータとして計算するものが多い。イオン化カルシウム値の正確性を高めるためには他のリガンド(配位子)をも計算に用いるべきである。
<2>電極法で必要なpH測定と試料の嫌気的取り扱いの省略が課題である。
<3>従来の計算式は蛋白質やリン酸の異常値を持つ特殊な検体への適用に限界があった。よって特殊な検体にも適用できる理論式であることが望ましい。
<4>多量の検体を迅速に且つ容易に処理できることが望ましい
<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
本発明の計算方法は、まず血中総カルシウムを測定し、6個のリガンド値からカルシウム錯体量を錯体平衡式によって計算し、この複数のカルシウム錯体を収束計算で絞り込み、pH補正とカルシウム錯体計算の基礎数値算出のために酸解離計算を取り込んだものである。
<1>正確性を高めるため、アルブミン、総蛋白、無機リン、クエン酸、乳酸、炭酸水素イオンの6個のパラメータすべてに上記計算を当てはめた。
<2>まず酸解離計算について述べる。各リガンドはカルシウムと配位結合するが、また(化1)のように水素イオンとも配位結合し可逆平衡状態となる。そこでまず水素リガンド錯体量を計算し、しかる後に残存するリガンドとカルシウムとの間の錯体量を平衡計算する。一般に水素イオンとリガンドの平衡は酸解離平衡と呼ばれ(数1)酸解離式Aに示すように質量作用の法則に基づいた一定の酸解離定数を持つ。即ち変数が3個の内2個の数値が決まれば残り1個の変数が求まる。総リガンド量は(数2)に示すように[Ligand]や[HLigand]の合計値であり、これを(数1)酸解離平衡式Aに代入すれば(数3)酸解離式Bが得られる。さらにHligandについて整理すると(数4)の水素結合リガンドの計算式が導かれる。(単位はmol/L、電荷は省略)
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)
(化1)酸解離反応 HLigand ⇔ Ligand + H
(数1)酸解離A Ka = [H][Ligand] / [HLigand]
(数2) tLigand = HLigand + Ligand
(数3)酸解離B Ka = [H][tLigand- HLigand] / [HLigand]
(数4)水素結合リガンドの計算式 HLigand = H×tLigand / (Ka + H)
(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)
CaLigandが生成された場合の計算では、CaLigandが酸解離平衡の系外物質であるので、tLigandからCaLigandを差引いた値を酸解離平衡の総リガンド量として計算する。即ち水素結合リガンドの計算式はHLigand = H×(tLigand-CaLigand) / (Ka + [H])となる。
水素結合リガンド量の計算式。
(数5)HAlbsite = H×(tAlbsite - CaAlbsite) / (Ka1+H)
(数6)HGlbsite = H×(tGlbsite - CaGlbsite) / (Ka2+H)
(数7)H2PO4= H×(tPi - CaHPO4) / (Ka3+H)
(数8)HCitrate = H×(tCitrate - CaCitrate) / (Ka4+H)
(数9)HLact = H×(tLact - CaLact) / (Ka5+H)
炭酸水素イオンの正常値は酸解離平衡後の濃度であるため酸解離式による計算は不要である。
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.
上記式の用語説明1:
Ligand:遊離配位子(リガンド)、HLigand:水素結合配位子、[H]:水素イオン濃度(mol/L)、Ka:酸解離定数、tLigand:総リガンド
HAlbsite:水素結合アルブミン、tAlbsite:総アルブミンサイト数、 CaAlbsite:カルシウムアルブミン錯体数、HGlbsite:水素結合グロブリン、tGlbsite:グロブリンサイト総数、CaGlbsite:カルシウムグロブリン錯体数、サイトの定義については次項<3>にて説明する。tGlbsite濃度は血清総蛋白(g/L)から血清アルブミン(g/L)を差し引いて求めたグロブリン量(g/L)にグロブリン1g当たりのカルシウム最大結合数(mol/g)を乗じたもので、最終単位はmol/Lである。この最大結合数は非特許文献7の記載値から計算により求めた。tPi:血清無機リン測定値、H2PO4:リン酸二水素イオン、CaHPO4:リン酸一水素カルシウム錯体、tCitrate:血清クエン酸正常平均値、HCitrate:クエン酸一水素イオン、CaCitrate:クエン酸カルシウム錯体、tLact:血清乳酸正常平均値、HLact:乳酸一水素イオン、CaLact:乳酸カルシウム錯体
Ka1、Ka2、Ka3、Ka4、Ka5:アルブミンサイト、グロブリンサイト、リン酸、クエン酸、乳酸それぞれの酸解離定数。
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>次にカルシウム錯体量を求める計算方法について、アルブミンで述べる。(非特許文献5)によるとアルブミン1分子は最大12分子のカルシウムと結合できる。Scatchardのモデル(青木幸一郎ほか「血清アルブミン」82ページ講談社サイエンティフィク)と同じ考え方で、12個のカルシウム結合サイトは(A)互いに独立し、他の結合サイトに影響しない、(B)各サイトの結合は同一性質であると仮定すると、総アルブミンサイト数(数10)はアルブミンモル濃度の12倍したものである。このアルブミンサイトと遊離カルシウムの錯体反応(化2)は可逆反応で(数11)の錯体平衡式Aに示すような動的平衡が成り立つ。(単位はmol/L、電荷は省略) <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)
(数10)総アルブミンサイト数 tAlbsite = tAlb×12 (mol/L)
(化2) カルシウム錯体反応 fCa + fAlbsite ⇔CaAlbsite
(数11)錯体平衡式A Ka1=[CaAlbsite] / ([fCa][fAlbsite])
(数12)錯体平衡式内の量関係
fAlbsite + CaAlbsite = t’Albsite
fCa + CaAlbsite = t’Ca
(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
総アルブミンサイトの内訳は(数13)に示すものであるが、この錯体平衡式A(数11)における合計アルブミンサイト数(t'Albsite)は(fAlbsite)と(CaAlbsite)の合計(数12)であり、且つ総アルブミンサイト数(tAlbsite)から本錯体平衡式に関与しない水素結合アルブミンサイト数(数5)を差引いたもの(数14)である。
また総カルシウムの内訳は(数15)に示すものであるが、この錯体平衡式A(数11)における合計カルシウム(t’Ca)は[fCa]と[CaAlbsite]の合計(数12)であり、且つ総カルシウム測定値(tCa)から本平衡反応の系外に当たる各リガンドのカルシウム錯体量を差し引いたカルシウム量(数16)である。
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).
(数13) tAlbsite=fAlbsite+HAlbsite+CaAlbsite
(数14) t’Albsite=tAlbsite-HAlbsite
(数15) tCa=fCa+CaAlbsite+CaGlbsite+CaHPO4+CaCitrate+CaLact +CaHCO3
(数16) t’Ca=tCa -CaGlbsite -CaHPO4 -CaCitrate -CaLact -CaHCO3
これらを(数11)錯体平衡式Aに代入すると(数17)錯体平衡式Bが求まる。この式をCaAlbsiteについて整理すると下記(数23)2次式が得られ、これを解くことにより CaAlbsite錯体量を算出することができる
(数17)錯体平衡式B Ks1=[CaAlbsite] / ([t’Ca-CaAlbsite][t’Albsite - CaAlbsite])
(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])
同様にして錯体平衡式に使用する合計リガンド量を以下に示す。
(数18) t’Glbsite = tGlbsite - HGlbsite
(数19) t’Pi = tPi - H2PO4
(数20) t’Citrate = tCitrate - HCitrate
(数21) t’Lact = tLact - HLact
(数22) t’HCO3 = 0.02mol/l
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
CaAlbsite錯体量の計算式と同様にした、CaGlbsite錯体量、CaHPO4錯体量、Citrate錯体量、CaLact錯体量、CaHCO3錯体量の計算式を示す。
(数23)
Ks1×CaAlbsite2- (Ks1×t’Ca +Ks1× t’Albsite +1)×CaAlbsite + Ks1×t’Ca×t’Albsite = 0
(数24)
Ks2×CaGlbsite2 - (Ks2×t’Ca + Ks2× t’Glbsite+ 1)×CaGlbsite + Ks2×t’Ca×t’Glbsite = 0
(数25)
Ks3×CaHPO4 2 - (Ks3×t’Ca +Ks3×t’Pi + 1)×CaHPO4 + Ks3×t’Ca×t’Pi = 0
(数26)
Ks4×CaCitrate2 - (Ks4×t’Ca +Ks4× t’Citrate + 1)×CaCitrate + Ks4×t’Ca× t’Citrate = 0
(数27)
Ks5×CaLact2 - (Ks5×t’Ca + Ks5×t’Lact +1)×CaLact + Ks5×t’Ca×t’Lcat = 0
(数28)
Ks6×CaHCO3 2 - (Ks6×t’Ca + Ks6× t’HCO3 + 1)× CaHCO3 + Ks6×t’Ca×t’HCO3 = 0
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
上記式の用語説明2:
tAlb:アルブミン測定値(mol/L)、12:アルブミン1モルが結合できるカルシウムのブミンサイトモル数、fCa:遊離カルシウムモル数、t’Ca:錯体平衡式中の総カルシウム、Ks1:アルブミンとカルシウムの錯体平衡定数
Ks1,Ks2,Ks3,Ks4,Ks5,Ks6:アルブミンサイト、グロブリンサイト、リン酸、クエン酸、乳酸、炭酸水素イオンとカルシウムとの平衡定数。CaAlbsite, CaGlbsite, CaHPO4, CaCitrate, CaLact, CaHCO3:それぞれのリガンドのカルシウム錯体モル濃度
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>次に複数のカルシウムリガンド錯体間の多重平衡ついて述べる。1つのカルシウム錯体量の計算が終わると生成されたカルシウム錯体量の分だけ遊離カルシウム量が減少する。そのため他のリガンドの平衡が崩れる。よって減少した遊離カルシウムを用いて錯体の平衡計算を再度し直さなければならない。遊離カルシウム濃度の変化に応じて再計算を10回程度行えば一定した値に収束される。(図1)に繰り返し計算の概要を示す。 <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>イオン化カルシウム量は血清総カルシウム値から最終各リガンドのカルシウム錯体量を差し引いて求める。下記に(数29)にイオン化カルシウムを求める最終式を示す。
(数29)
イオン化カルシウム= tCa - CaAlbsite - CaGlbsite - CaHPO4 - CaCitrate - CaLact - CaHCO3
<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>パーソナルコンピュータの表計算ソフトに本計算のプログラムを付けることで、多数検体の迅速な計算を可能とした。 <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>計算のパラメータ数を増やすことで、従来式より正確性が増した。
<2>酸解離式を採用することでpH測定が不要となり、且つ検体の嫌気的取り扱いが不要となった。
<3>錯体平衡式に基づく化学量論的計算であるため検体の適用範囲が広がる。
<4>パーソナルコンピュータ用のプログラムを作成したことで、計算が迅速且つ容易となり、日常検査としての実施が可能となる。
<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.
試料として健常人から真空採血管にて嫌気的に採血し血清分離後直ちに測定した。イオン化カルシウムの測定にはSiemensの血液ガス分析機 RapidPoint405電極装置を使用した。総蛋白、アルブミン、総カルシウム、無機リンについては臨床検査用の生化学自動分析装置を使用した。測定結果は総蛋白7.6g/dl、アルブミン4.5g/dl、総カルシウム9.2mg/dl、無機リン4.1mg/dlであった(グロブリン量=総蛋白値−アルブミン値)。その他の項目値にはクエン酸=2.4mg/dl、乳酸=10mg/dl、炭酸水素イオン=20mMの各正常値相当を計算に使用した。 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.
各リガンドの酸解離定数には-log(Ka1)=7.55, -log(Ka2)=7.55, -log(Ka3)= 7.2, -log(Ka4)=4.76, -log(Ka5)=3.86を使用した。各リガンドの錯体平衡定数には log(Ks1)=2.38, log(Ks2)=2.55, log(Ks3)=2.66, log(Ks4)=3.16, log(Ks5)=1.42, log(Ks6)=1.0を使用した。(Ka及びKs値は非特許文献6非特許文献7及び化学便覧II日本化学会編丸善pp317-331, 1993等から引用する)
イオン化カルシウムの成績:計算結果1.10mmol/L、電極法測定結果1.16mmol/L
-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
カルシウム代謝異常を示した34試料を使用する。
イオン化カルシウム及びその他生化学項目の測定方法については実施例1と同じものを使用した。酸解離定数、平衡定数、クエン酸、乳酸、炭酸水素イオン含量は実施例1と同じ数値を使用した。
34試料の成績:電極法平均値1.24 計算平均値1.20、相関係数r=0.993 回帰直線 y=0.95x - 0.02、図2に個々のデータを相関図として示す。
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.
臨床診断及び経過観察として血中イオン化カルシウムの測定は大きな意義があり、要望がある。本計算法で容易にイオン化カルシウム値が得られるため実用的価値は大きい。 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.
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