Measurement of ionized calcium in biological fluids

CLINICA

CHIMICA

MEASUREMENT

ACTA

OF IONIZED

CALCIUM

11v BIOLOGICAL

Three methods are described for the determination of ionized ultrafiltrates and urine involving spectrophotometry, potentiometry calculation procedure. Good agreement between all three methods The percentage of ionized calcium in plasma ultrafiltrates is and 83(;b at 37’. In urine about 50:: of the total calcium is in the remainder being accounted sulphate and oxalate ions.

for in terms of soluble complexes

FLUIDS

calcium in plasma and a computer is demonstrated. about 8c)0Z, at 25’ ionized form, the

with citrate,

phosphate,

Since it was first demonstrated by McLean and Hastings’ that the free or ionized concentration of calcium was the physiologically active form of calcium, many attempts have been made to measure this constituent of biological fluids. These authors themselves developed a biological method for the determination of calcium ion concentrations in human serum and found that about 500,; was in the free form. Physico-chemical techniques which were developed at the same time using calcium amalgam2 and calcium fluoride3 electrodes were found to be unsuitable for measurements in biological fluids. Subsequently several chemical methods, based on the colour reaction of free calcium ions with the dye murexide, were developed for measuring ionized calcium in cerebrospinal fluid”, milk ultrafiltrates5, plasma ultrafiltrates”>’ and serum+‘“. Murexide, however, has the disadvantage of being pH dependentI and also forms a complex with plasma albumenlo. To overcome the problem of small pH differences in plasma ultrafiltrates the pH-independent dye, tetramethylmurexide, has been used 12. More recentlv i the advent of a specific calciumsensitive electrode (Orion Research Incorporated, Cambridge, Mass.) has enabled ionized calcium to be measured in plasma ultrafiltrates1Z31d. Most workers have found that about 50--55:~; of plasma calcium is in the ionized form. In urine it is the ionized form of calcium which is potentially dangerous for the precipitation and growth of calcium phosphate and calcium oxalate deposits. Measurcment of ionized calcium in urine is complicated, however, by the variability in pH, ionic strength and sodium concentration. Spectrophotometric methods using mur-

exide have been tried6,15,16 but \vere complicated b\r the pH dep~~~d~r~c~~ of tllc d\xx, ionic strengtli effects and interference from sodium ions. Methods ubing tlli, tclti-;Imethyl derivative htill required the mtaturement of ionic htrengtlr and an allo\\-ancxx for sodium interference’l,“,‘8. Iu general these mctllods have sllown tllat about jo”,, of urinary calcium is in the ionized foriil. It is possible to estimate ionized calcium c-oncentr;ltionr; in urine and plasn~a ultrafiltrates by a computer calculation tcchniclw from a Imowlt:dge of the pH, tlI(s

totnl concentrations

of calcium, magnesium, sodium, potassium, ammoniuni, pliohpliatc, osalate, citrate and sulpliate, and tlic stability cxnstant5 governing tllc> mutual interactions of tllese ions \vitlr one anotller to forln .solul)lc~ cvil~plr~sc~~ ancI ion-pairs. Tlr~ prcwnt paper tlescrilwb this tcclrniqur along \\itli a clirwt pttwtic,uietric technique for tlie measurement of ionized calcium iu urine usinK 3 calciuliisensiti\.cA electrode. Tlir~ results obtained win, CTthe nietliods :11x5c~mipni-~(1 \vitlr those froni convc~ntional sI)(,(~trc)I’llotoli~ctric. tcc~lrniqurs.

hers

The l~lootl samples used were taken from 10 malt and II female of staff. I’ltrafiltration of plasma was carried out h>r the method

and

Pe~‘cocli’ ‘L

staff

T11e urine sarnpl~~~ were two-hour collt~ctions taken from 38 male nwllllwrs of and I)atients wit11 ii0 history of renal disease. ~T\~,~nt~-four-liolnurines \v:‘rc~ also

taken

from

Total Xutohnalyzcr Ilrinarv

IIealtlr!. Ille~iiof Robertson

‘.

ho similar

and

iualc subjects.

ultrafiltrable

tecliniquc”‘. pH was measured

serum with

calcium

concentrations

a glass electrode

using

were

nicxurc~tl

a Kadiometcr

I)?- an

pH Meter

27; total calcium was measured by an :ZutoXnal!zer procedure2u; phosphate by tlw standard AutoAnalyzer technique; magnesium by atomic absorption flame photometry”’ ; sodiuln and potassium by flame emission photometr!~ using an Eppcntlorf flame pliotomctcr ; ammonia by the method of Chancy and Marbacl12* ; osalatt b!r tlic citrate t)!r the method of XIcArdle2’: ant1 method of Zarembski and HodgkinsonZ3; sulpllatc by tile metllocl of Rerglund and SorlxP.

(I) .S~cctvol?~zotol?zctvic. ‘l‘lic concentration of ioilized calcium in urine \vas lR of the method of iiaallaubl’ usiug tetrarlletll~ll~lure~i~l~~ measured b\r 3 modification as the indicator. Measurements were made at ~5~). (3) I’otcjztioMtc,tvic. (a) The
IOSIZED

stock

Ca

Ix

solutions

potassium

BIOLOGICAL

FLt~IIlS

of calcium

chloride

(1000

I.jl

chloride mequiv/l)

(IO mX),

sodium chloride

mequivil)

(1000

to mimic the urine in ionic strength

and

and sodium

concentration. The potential difference due to the calcium ion activity in urine \vas measured against a saturated calomel reference electrode at ~5” using the Orion Calciunl Electrode, and the calcium ion concentration read from the appropriate standard calibration curve. Only urine samples whose pH was greater than 5.3 could 1~ measured by this method. (3) 13~ cnlczrlntion. A computer program (run on the KDFq computer at Leeds Gniversit\-) was devised to perform the calculation of the concentration of ionized i Ca2-l, from the total concentrations of calcium ( Tc;,), magnesium ( Tai ,), calcium, sodium (Th-;,), potassium (TE;), ammonium (T~;H~~), phosphate ( TF), citrate (7‘vit) and sulphate (TsoJ, pH and the stability constants (at 25’) two complexes and ion-pairs produced between these ions. The clegree of each complex depends largely on the constitution of the urine or filtrate

oxalate (T,,,), of the twent!-= of importance plasma ultra-

under consideration. T11e complexes are: (i) in terms of the trivalent phosphate ion (1’O,3 -1:

~HPO,“-1,

iH,P04pe,

CaHPO,_,

the ion-pair

lCaPO,-!

IQHPO,‘,

SaHPO,~~,

KHPO,p:

and

(‘aH,PO,~;. Although

has been shown to exist in solutionZF it is 01

negligible importance at urinary pH levels. (ii) in terms of the osalate ion 10s2-] : I~HOx-1, 1CaOx[l and (~MgOx]. (iii) in terms of the citrate

1H Cite-l, 1I< Cit2-j.

IH, Citp],

CaHCit],

(iv) in terms of the sulpllate CaSO,_,

[MgSO,],

ion [ Citnp1 :

1NaSO,-]

\Ca (X-1,

‘lLrgHCit1, I MgCit-],

1Ka C&p!,

and

ion ~%0,2-~: and

KSO,-1.

The ionized calcium concentration is obtained by calculating the concentrations of all the calcium complexes and subtracting them from the total calcium concentration, i.c.

ICaZ +] = 7‘~:~~ jCaCit-j ~ CaH,PO,-I- 1.

~ LCaHCit] - [ CaHPO,i

- [CaOs] ~ ‘CaSO,] ~

The calculation is essentially an iterative process of successive approximations. Rough estimates of the values for ionized calcium, ICa2+], ionized magnesium, STg2i 1, ionized sodium, 1Na+l, ionized potassium, iK+; and ionic strength, 1, are used to start the calculation. At the end of tllc first cycle more correct estimates for these fret ion concentrations are obtained. These are fed into the beginning of the calculation again and the process continued until constant values are obtained from successive cycles. “Tl1c rough estimates for ionized calcium, magnesium, sodium and potassium are calculated from :

ROBERTSON

*52 :K+

11 =TK

(4)

jl refers to the first estimate of the concentration where 1 Hence the ionic strength is approximately. I, =- 1Na+;,+ [K’ IIf,

of the enclosed

NH,+]

(5)

Monovalent and divalent ion activity coefficients (fi and_fJ Davies2’ modification of the DebyeeHuckel equation. log (fi)l = 0.509 (2/11/(r+2j-l&o.2 log(f,), = 2.036 (~I,/(I+~/I~)~o.zxIJ

are calculated

(0) (7)

of the trivalent ion activity coefficient (J,) is taken of Bjerrum 28 for trivalent phosphate ions.

--log(f:,),

= -log

(f&+2.495

V11Y2.25

The first and second association calculated from Bjerrum’s data”“. fog(K,),

from the

XII)

An estimate pirical equation

ion.

constants

== 12.#+~2.495

~~,+2.25

=

\/‘11smI.04 1,

from the en-

11

(8) of the trivalent

phosphate

ion are

1,

(0)

and log

(K,),

where K, = and K, =

7.227-1.4()7

(I())

HPO,?p]/ PO1:‘p] x{H+), [H,PO,p]/~HPO,“-] x{H+].

Now HP042p] /T, = HP0,2p] /(~HP0,2-] f [P045p] + j H,PO,- ]-t_ 1H,PO, I $ + [CaH,PO,+] i- 1CaHPO,] _t [MgHPO, + j NaHPO,p] C .KHPO,- 1). Since

LPO13-I and [ H,PO,!

are negligible

under urinary

conditions,

then

HP0,2- j = TIT/(I + !H,PO,p] / HPO,“-_ + CaHPO,] / i HP0,2pj + 1MgHPO, HP0,2p] + NaHPO,-: // HP0,2pI + / KHPO,p] /_HPO,Zpl + i CaH,PO,i- /

/

!HPO,“p]). Thus [HPO,“p],

= T~,/(I+(K,),x{H~}+I(c~HPo*x

[Mg2+], x (&“+ x(W1

x{H+}

KN~HPO~

x

l(:a”+],x(f~),2SKar,~,~,“4x

x LNa~-I, x (fi)l+K~~~~oI

x [K-‘-;, x (fz)lSK~~~~~~~~~y

ICa2+lI x (f2)J

(11)

where Kcanpoa ( = ~CaHPO,: /_Ca”+] . ,_HPO,Z-; .(_f.J’) etc. are the thermodynamic bility constants of the complexes concerned (Table I).

sta-

Hence ;H,PO,-], = {H-} x HP0,2-], x (K,), -CaHPO,], = I
11X (fi)r”

[MgHPO,j, = KNI~HPO~X [Mg2+]lx !HP0,2~l, X(fi)l' NaHPO,-J, =: KN~HPO~x [Nat:, x jHPOpP~~]lX (f2)1 ! KHPO,-] = KXHPO~ x [K+], x [HP0,2p], x (fi), LCaH,PO,-+], = Kcan2p04 x ! Ca++‘, x LH,PO,p], x (fi),

(12) (13) (14) (1s) (16) (17)

Similarly, ~Oxa-ll = To~/(I+KHo~x(H+} x ( %"+l~x(jA2)

Clwt. Chim.Acta, 24 (rsr:o) 1.~9~157

X(f2)l/(fi)l~K~m~X

[Ca’+], X (f~)~“+Knrsox>’

(IS)

IONIZED Ca IS BIOLOGICAL FLUIDS

I53

THE THERMO”YSAMIC STABILITY CONSTAh-TS OF THE MAJOR

SOLUBLE

G~?$dl-.~

Ii (25” C)

Referme

CaHPC), SIgHI’O~

5.0 s 102 3.16 x I+ 12.9 IO.0 IL.0 I.93 v 104 7.07 x 103 2.69 x 10~ 2.51 x 106 5.75 x 104 1.23 x 108 7.09 x 104 2.88 x 102 3.72 x 104 8.5 12.6 2.04 >: 102 I.78 x 102 5.2.5

Davies and Hoyles8 (;rccnwald Et aZ.3” from Smith and Alberty31 from Smith and i\lbertpl Davies and Hoyl@ \‘osburg and Beckman32 from &lles and Sala~na~~ Davies”l Muus and Lebc135 Muus and Lcbel= Uavics and Il0ylt2~~ Bjerrum and Ilnmack3’ from Li et ~1.~” from Li fzt nl.“” from \Valser39 from XValscr39 Hell and (;c0rgc4~ Nair and Yancollas”’ Jenkins and Monk42 Jenkins and 310111~~~

NaHPO,

KI-11’04C:aH,PO,+ HOT C‘a0X s1gox HCit?H,CitC‘aHCit CaC‘itMqHCit RIgCitNaCit2I<:Cit”(:a X), MgSO, saw), KS),-

g.II

COMPLEXES

IN URINE

Thus lCaO X]l = Kcaox x ,_Ca2+11x [Ox*-_I1x (fJ,* IMgOx], = K~gox x [IQ”+], x ‘!Ox2-1, x (fz)12

(19) (20)

Also LCiP], +Kcacit x (Jj)~i-

= Tcit/(I+Kwcit X [ca2+11 x &)I KarsHcit

x (/Jl/(fJ-kKNacit

x KHCit

X{H+j X (f&/(fA+K X ;&?+I,

X [Na+ll

X (_fJ)l/(fJ1+KHCit

X KII,cit

CaHCit X KHcit

x {H+}

X (fz), X (fz)dK~~gCit

X (fi)~ X (_frJ1/(.fz)1+KKCit

X{H+}‘X

X rca2+:1 X{H+}

X I K+l,

(j”3)l/(fi)l X (fi),

X ~Mg’+]l

X

X (&

X (_/;)I x (f2)1/

(f&)

(21)

;CaHCit], = KCsHCit X KHCit X iCa2f;l X (H+} X [cit3p]1 X (fg)~ x (f& CaCit-1, = Kcacit x [Caz+!, x iCit3-ll x (f&X (f&/(f& [LMgHCit], = KbrgHCit X KHCit X [hfg’+], X{H+) X [Cittp]l X (_&)I X (.f:t)~ MgCitF], = KptgCit x I~Mg”+]l X I CitS-ll x (fJ, X (&/(,fi)l ‘NaCitzp], = KNaCit X [Na+ll X ICit3-_]1 X (fi)l X (_f&/(f& [KCit2-]l = Kl
(22)

Thus (23) (24)

(25) (26)

(27)

Also LSO,~~], =

Tso~/(I+Kc~so~

+KNasoqx

PJa+l,x (fi)l+K~~~~4~

x LCa2+l, x(~~)~~+K~I&so~x

LK+llx(f2)1)

~Mg2+11x(fJ12+

(28)

Thus [CaSO,], = Kcasor x [Ca2+], x [S0.,2-], x (fJ,” _MgSO,], = Karpsod x ‘Mg2+l, x ISQp]l x (fi),” NaSO,-1, = KNGO( x rNa+l, x YS04*p], x (f2), j KSO,p’, = Km04 x :K+ll x 1S0,‘-11 x (fi),

(29) (30) (31) (32)

ID

2.c

Measured concentration

3.0

4.0

5.0

6.0

ionized Coltlum (mM)

7.0 cl

2

8 Total

c”,lcium

cobncentration

i0 (mM)

156

I
human plasma ultrafiltrate. It can be seen that at pH =: 7.4 the calculated 89’: 0 at 2 j” is slightly higher than the measured one at 37’.

x-alue of

Fig. 2 shows the relationship between the calculated and s~c,ctrojlhotonzctvicall?’ determined values for urinary ionized calcium in 20 urine samples at 25’. This shows good agreement between the two procedures (Y =: o.#), the ,standard c‘rror of tlltl difference being 0.16 nm~oles/l. Fig. 3 shows the corresponding relationship between the calculated and @f~tiomzctricall~~ determined values for urinary ionized calcium in 18 urine samples at 25‘. This again shows good agreement between the two procedures (r ~~ o.qq), the standard error of the difference being o.q mmoles/l. Llrinary ionized calcium shows a marked dependence on the total calcium and forms a fairly constant proportion of it. Fig. 3 shows the relationship between ionizccl and total calcium in 24-11 urines from 60 normal male subjects. The mean percentafic ( !- I S.D.) of ionized calcium in the group is _cq.cI 8.j. The computer calculation procedure permits the calculation of the percentages of tile various soluble calcium complexes and Table II I shows the fractions of calciulll bound to citrate, phosphate and sulphatr: in these 60 normal urines.

Measurement of ionized calcium concentrations in serum, plasma ultrafiltrate and urine has produced a wide range of values depending on the method of analvsis is the casicst to anal\-sc, employed 1,6-18,a3Of thes:: three fluids plasma ultrafiltrate of pH, sodium concentration and since interfering factors, such as the variability protein effects, are kept to a minimum. Our measured values at 37” in plasma ultrafiltrates using a Calcium Xctivitv Elec-trode arc similar to those obtained 13~.workers employing the same conditions of temperature’:‘, I:‘, but arc slightly lowerb than tlrcs values obtained by sI’ectropliotometr?at room teiiipcraturc”,:~“~“‘. The latter \~tlue~ are confirmed by our computer calculation technique using stabilit!, constants tlerivcttl at 25”. This is in accord with tht findings of Gupta44. It is possible that the lowc~r ionized calcium values at 37’ arc a result of the greater stability of the calciuiiibinding complexes (CaHJ’O;1) and (CaHI’0,)26 at that tctmpcraturc than at 25’ Urine is difficult to analyse for ionized calcium since conditions of pH, sodium concentration and ionic strength 1x-y consideralA!-. WC have shown, however, tllat three procedures involving spectropllotometr~., potentiometry and a computational technique mutually correlate. The percentage of ionized calcium in urine, is about Our computer ca50% of the total, which agrees with most workers’ observations. culation technique also shows that the remaining jool, of urinarv calcium can lx, accounted for quantitatively in terms of the various soluble cwnplcxes formed hetnwn calcium and citrateSfi,:“, l~liosl~l~atezi~~!‘,sulpllatc ‘I’ and oxalaWX ions.

The author wishes to thank Dr. 13. E. C. Sordin for his support and advice and Dr. M. Peacock for his clinical assistance during this work. The author also xis1lc.s

IONIZED

Ca

IN BIOLOGICAL

to acknowledge Smith.

I57

FLUIDS

the technical

assistance

of Mrs. Margaret

Butler

and Mrs. Carolyn