273
Clinica Chimica Acta, 81 (1977) 273-276 @ Elsevier/North-Holland Biomedical Press
CCA 8917
A SIMPLE SLIDE-RULE METHOD FOR THE ASSESSMENT TUBULAR REABSORPTION OF PHOSPHATE IN MAN
R.J. WALTON
a-* and O.L.M.
BIJVOET
OF RENAL
b
a Department of Chemical Pathology and Human Metabolism, University of Southampton, Southampton (U.K.) and b Department of Endocrinology and Metabolism, University Hospital, Leiden (The Netherlands) (Received
May 12th,
1977)
Summary
The activity of renal tubular reabsorption of phosphate in man is best expressed as the ratio of the maximum rate of reabsorption to the glomerular filtration rate (TmP/GFR). A slide-rule method based on existing data is described for the derivation of TmP/GFR from values of phosphate and creatinine concentrations in single samples of plasma and urine. This is a simple method which is suitable both for research and for clinical purposes. _ Introduction
In most individuals, excluding patients with renal glomerular failure but including those with parathyroid disorders, plasma inorganic phosphate concentration is determined mainly by renal tubular reabsorptive activity, the setting of which is best expressed as the ratio of the maximum rate of renal tubular reabsorption of phosphate to glomerular filtration rate (TmP/GFR) [ 11. TmP/ GFR, otherwise known as the theoretical renal phosphate threshold [2] or the renal threshold phosphate concentration [ 31, is preferred to other indices of renal tubular reabsorption of phosphate since it is independent of the filtered load of phosphate [ 41, and is expressed in units of plasma concentration. Estimation of TmP/GFR is of value in the diagnosis of parathyroid disorders and for research into the renal handling of phosphate. This can be done directly by phosphate infusion techniques [ 1,5], but these are not suitable for routine clinical purposes or for sequential studies. Bijvoet and Morgan [ 41 showed that when the fractional tubular reabsorption of phosphate (TRP) was plotted against the ratio of TmP/GFR to plasma phosphate, the values from 100 phos* Correspondence ton
General
to: Hospital,
Dr.
R.J.
Walton.
Southampton.
South SO9
Laboratory
4XY.
U.K.
and
Pathology
Block,
Level
D,
Southamp-
274
phate infusion experiments performed both in normal subjects and in patients with abnormal parathyroid and thyroid function [l] were closely distributed about a curve which could be used as a nomogram for the derivation of TmP/ GFR. A simplified version of this nomogram has recently been devised [ 31. The present communication describes an even simpler indirect method for the derivation of TmP/GFR using a slide rule. This method is based on the same data [4] as the nomograms and on the same principles, namely that the form of the relationship between plasma phosphate and urine phosphate excretion is approximately the same in different individuals and that for any given value of TRP the ratio of TmP/GFR to plasma phosphate is constant. Method The subject is fasted overnight, the bladder emptied by voluntary voiding and the urine discarded. Urine and plasma samples are then collected one to two hours later (exact timing and urine volume meausrement are not necessary unless it is also wished to measure urinary excretion rates). Inorganic phosphate
Fig. 1. The slide-rule set for three different plasma phosphate concentrations. The values of TmP/GFR at various levels of TRP are shown in Table I. Scales as shown here, printed on self adhesive paper for adapting a standard 25 cm slide-rule, are available from R.J.W.
275 TABLE
I
VALVES The
arrow
lated
value
FOR
TmP/GFR
is placed of TRP
Plasma
AT
against (see
Fig.
VARIOUS the
observed
LEVELS plasma
OF
PLASMA
phosphate,
PHOSPHATE and
TmP/GFR
AND then
TRP
read
against
the
calcu-
1).
TRP
TmPjGFR
phosphate _ 0.90
2.00
3.50
0.20
0.18
0.60
0.54
0.80
0.72
0.93
0.98
0.99
1.30
0.20
0.40
0.60
1.20
0.80
1.60
0.93
2.19
0.99
2.90
0.20
0.70
0.60
2.10
0.80
2.80
0.93
3.83
0.90
5.10
and creatinine concentrations are measured and TRP is calculated from the expression TRP=l-_-____urine phosphate urme creatinine
concentration concentration
in the plasma and urine samples,
X plasma creatinine X plasma phosphate
concentration concentration
(the units of measurement for these concentrations are irrelevant provided that they are consistent). The slide rule (Fig. 1) can then be used to derive TmP/GFR from the values of TRP and plasma phosphate as follows: 1. The sliding scale is moved so that the arrow on the “TRP” scale points to the observed plasma phosphate on the “cone” scale. 2. The value of TmP/GFR is read on the “cone” scale against the calculated value of TRP. Examples are given in Table I. Discussion This slide-rule method for the derivation of TmP/GFR is very simple and is suitable for use in outpatients and for sequential and population studies. The original phosphate infusion experiments on which the method is based were performed on fasting subjects in the morning. Under such conditions, the normal range for TmP/GFR in adults is 0.80-1.35 mmol/l (2.5-4.2 mg/lOO ml) [1,6]. Since TmP/GFR varies during the 24 h, it is important that these same conditions are used for the indirect slide-rule method if values are to be compared with this normal range. Values above the normal adult range are commonly found in growing children, and in patients with hypoparathyroidism, pseudohypoparathyroidism, acromegaly and thyrotoxicosis. Abnormally low
values occur particularly in patients with hyperparathyroidism, chronic renal failure, renal tubular syndromes and in some with idiopathic hypercalciuria [ 11. Estimation of TmP/GFR is therefore an addition to, rather than a substitute for, other clinical and laboratory tests of parathyroid function, particularly careful measurement of plasma calcium and immuno-reactive parathyroid hormone. Acknowledgement R.J.W. is grateful to the British Council for a travel grant. References 1
Bijvoet,
2
McSwiney.
3
Walton.
4
O.L.M.
(1969)
R.R. R.J.
and
and
Bijvoet,
Bijvoet.
O.L.M.
Normale
et Aspectes
5
Anderson,
6
Stamp.
and
J. (1955) T.C.B.
Clin.
and
Sci.
Prunty,
37,
F.T.G.
O.L.M.
Morgan,
23-36 (1961)
(1976) D.B.
(1971)
Physiopathologiques J. Physiol. Stacey,
T.E.
130, (1970)
Proc.
Lancet
Roy.
in Phosphate (Hioco,
Sm.
Med.
D.J.,
Sci.
639-641
et Mdtaholisme ed.).
268-277 Clin.
54,
ii, 309-310
39.
505-516
PP. 153-180,
Phosphocalcique. Sandoz.
Paris
RBgulation
Clinica Chimica Acta, 81 (1977) 273-276 @ Elsevier/North-Holland Biomedical Press
CCA 8917
A SIMPLE SLIDE-RULE METHOD FOR THE ASSESSMENT TUBULAR REABSORPTION OF PHOSPHATE IN MAN
R.J. WALTON
a-* and O.L.M.
BIJVOET
OF RENAL
b
a Department of Chemical Pathology and Human Metabolism, University of Southampton, Southampton (U.K.) and b Department of Endocrinology and Metabolism, University Hospital, Leiden (The Netherlands) (Received
May 12th,
1977)
Summary
The activity of renal tubular reabsorption of phosphate in man is best expressed as the ratio of the maximum rate of reabsorption to the glomerular filtration rate (TmP/GFR). A slide-rule method based on existing data is described for the derivation of TmP/GFR from values of phosphate and creatinine concentrations in single samples of plasma and urine. This is a simple method which is suitable both for research and for clinical purposes. _ Introduction
In most individuals, excluding patients with renal glomerular failure but including those with parathyroid disorders, plasma inorganic phosphate concentration is determined mainly by renal tubular reabsorptive activity, the setting of which is best expressed as the ratio of the maximum rate of renal tubular reabsorption of phosphate to glomerular filtration rate (TmP/GFR) [ 11. TmP/ GFR, otherwise known as the theoretical renal phosphate threshold [2] or the renal threshold phosphate concentration [ 31, is preferred to other indices of renal tubular reabsorption of phosphate since it is independent of the filtered load of phosphate [ 41, and is expressed in units of plasma concentration. Estimation of TmP/GFR is of value in the diagnosis of parathyroid disorders and for research into the renal handling of phosphate. This can be done directly by phosphate infusion techniques [ 1,5], but these are not suitable for routine clinical purposes or for sequential studies. Bijvoet and Morgan [ 41 showed that when the fractional tubular reabsorption of phosphate (TRP) was plotted against the ratio of TmP/GFR to plasma phosphate, the values from 100 phos* Correspondence ton
General
to: Hospital,
Dr.
R.J.
Walton.
Southampton.
South SO9
Laboratory
4XY.
U.K.
and
Pathology
Block,
Level
D,
Southamp-
274
phate infusion experiments performed both in normal subjects and in patients with abnormal parathyroid and thyroid function [l] were closely distributed about a curve which could be used as a nomogram for the derivation of TmP/ GFR. A simplified version of this nomogram has recently been devised [ 31. The present communication describes an even simpler indirect method for the derivation of TmP/GFR using a slide rule. This method is based on the same data [4] as the nomograms and on the same principles, namely that the form of the relationship between plasma phosphate and urine phosphate excretion is approximately the same in different individuals and that for any given value of TRP the ratio of TmP/GFR to plasma phosphate is constant. Method The subject is fasted overnight, the bladder emptied by voluntary voiding and the urine discarded. Urine and plasma samples are then collected one to two hours later (exact timing and urine volume meausrement are not necessary unless it is also wished to measure urinary excretion rates). Inorganic phosphate
Fig. 1. The slide-rule set for three different plasma phosphate concentrations. The values of TmP/GFR at various levels of TRP are shown in Table I. Scales as shown here, printed on self adhesive paper for adapting a standard 25 cm slide-rule, are available from R.J.W.
275 TABLE
I
VALVES The
arrow
lated
value
FOR
TmP/GFR
is placed of TRP
Plasma
AT
against (see
Fig.
VARIOUS the
observed
LEVELS plasma
OF
PLASMA
phosphate,
PHOSPHATE and
TmP/GFR
AND then
TRP
read
against
the
calcu-
1).
TRP
TmPjGFR
phosphate _ 0.90
2.00
3.50
0.20
0.18
0.60
0.54
0.80
0.72
0.93
0.98
0.99
1.30
0.20
0.40
0.60
1.20
0.80
1.60
0.93
2.19
0.99
2.90
0.20
0.70
0.60
2.10
0.80
2.80
0.93
3.83
0.90
5.10
and creatinine concentrations are measured and TRP is calculated from the expression TRP=l-_-____urine phosphate urme creatinine
concentration concentration
in the plasma and urine samples,
X plasma creatinine X plasma phosphate
concentration concentration
(the units of measurement for these concentrations are irrelevant provided that they are consistent). The slide rule (Fig. 1) can then be used to derive TmP/GFR from the values of TRP and plasma phosphate as follows: 1. The sliding scale is moved so that the arrow on the “TRP” scale points to the observed plasma phosphate on the “cone” scale. 2. The value of TmP/GFR is read on the “cone” scale against the calculated value of TRP. Examples are given in Table I. Discussion This slide-rule method for the derivation of TmP/GFR is very simple and is suitable for use in outpatients and for sequential and population studies. The original phosphate infusion experiments on which the method is based were performed on fasting subjects in the morning. Under such conditions, the normal range for TmP/GFR in adults is 0.80-1.35 mmol/l (2.5-4.2 mg/lOO ml) [1,6]. Since TmP/GFR varies during the 24 h, it is important that these same conditions are used for the indirect slide-rule method if values are to be compared with this normal range. Values above the normal adult range are commonly found in growing children, and in patients with hypoparathyroidism, pseudohypoparathyroidism, acromegaly and thyrotoxicosis. Abnormally low
values occur particularly in patients with hyperparathyroidism, chronic renal failure, renal tubular syndromes and in some with idiopathic hypercalciuria [ 11. Estimation of TmP/GFR is therefore an addition to, rather than a substitute for, other clinical and laboratory tests of parathyroid function, particularly careful measurement of plasma calcium and immuno-reactive parathyroid hormone. Acknowledgement R.J.W. is grateful to the British Council for a travel grant. References 1
Bijvoet,
2
McSwiney.
3
Walton.
4
O.L.M.
(1969)
R.R. R.J.
and
and
Bijvoet,
Bijvoet.
O.L.M.
Normale
et Aspectes
5
Anderson,
6
Stamp.
and
J. (1955) T.C.B.
Clin.
and
Sci.
Prunty,
37,
F.T.G.
O.L.M.
Morgan,
23-36 (1961)
(1976) D.B.
(1971)
Physiopathologiques J. Physiol. Stacey,
T.E.
130, (1970)
Proc.
Lancet
Roy.
in Phosphate (Hioco,
Sm.
Med.
D.J.,
Sci.
639-641
et Mdtaholisme ed.).
268-277 Clin.
54,
ii, 309-310
39.
505-516
PP. 153-180,
Phosphocalcique. Sandoz.
Paris
RBgulation
