- Email: [email protected]
Radioisotope studies of calcium metabolism and their interpretation
Radioisotope Studies of Calcium Metabolism and their Interpretation J. REEVE N. VEALL
Prior to the availability of isotopic tracers for clinical use, quantitative information on calcium metabolism was restricted to the data provided by balance studies. In principle, it is possible to measure the net loss or gain of calcium from the bod y over the period of the study, and since some 99 per cent of the calcium in the bod y is in the skeleton, it is possible to attribute any net gain or loss to changes in the skeletal calcium content without invoking any abstruse theoretical concepts. When a number of isotopic tracers became available for clinical use, particularly 47Ca, it was not unreasonably hoped that it would be possible to gain further insight into disorders of calcium metabolism by using tracer techniques to quantitate such important factors as intestinal absorption, endogenous faecal loss, and skeletal accretion and resorption rates. Valid methods for the first two of these are now available, but there remains a certain amount of controversy over the skeletal measurements. This is mainly concerned with the methods which should be used to calculate the required parameters from the observational data. INTESTINAL ABSORPTION AND ENDOGENOUS SECRETION Intestinal absorption The simplest method in theory, though not necessarily in practice, is to give an oral dose of radiocalcium and to measure the recovered activity in the faeces over a period of six or seven days to allow the unabsorbed tracer to pass through the gut. It is then assumed that what is not recovered represents the absorbed fraction of the dose. This is reasonably valid ifit can be assumed that no faecal specimens have been lost. For the many workers who cannot feel justifiably confident on this point, it is best to use a non-absorbable marker to permit correction for faecal losses. One of the few instances of serendipity in a field which is bedevilled by difficulties is the fact that 47Ca decays to radioactive 47Sc, which is not absorbed by the gut. Thus, since this isotope has its own built-in inert marker, an absorption test can be carried out on a
185
186
J.
REEVE AND
N.
VEALL
single radioactive stool specimen (Ogg, Pearson and Veall, 1968). The faecal recovery method gives a slight underestimate owing to resecretion of absorbed tracer into the gut, but this error is usually small. The converse procedure is to measure the body retention directly by using a whole body counter (Rinsler, Dyche and Trott, 1960). The avoidance of faecal collections is an advantage, though it is still necessary to correct for urinary excretion. Also, whole body activity measurements (though simple in principle) are not free from technical problems (I.A.E.A., 1971).
Endogenous faecal calcium This may be calculated from the conventional balance data if the absorbed fraction has been determined as indicated above, since it is given by the difference between the unabsorbed fraction of the dietary intake and the total faecal excretion. Alternatively, it may be measured by giving a tracer intravenously and measuring the appearance of the isotope in the stools. Then Endogenous faecal Activity in stools (IlCi/day) Plasma Ca = Activity of plasma (IlCi/litre) X (mmol/litre) calcium (mmol/day) This is analogous to the conventional clearance formula UV/P used in renal studies. Note, however, that allowance has to be made for the delay in the gut, which is variable, so that the calculations should not be based on the rapidly changing part of the plasma activity curve, and a suitable marker needs to be used to estimate the gut transit time. It is, of course, possible to measure both absorption and endogenous faecal calcium by using 47Ca and 4SCa simultaneously, one given orally and the other intravenously. However, under these circumstances, it is better to use the plasma activity levels rather than faecal data. The double isotope technique (plasma samples) Figure 1(a) shows the plasma activity curve following the administration of a single intravenous injection of radiocalcium, i(t), together with the corresponding curve for the second tracer given orally, Q(t). The form of the latter function, Q(t), is determined by the form of the function h(t), which describes the transfer of radiocalcium from gut lumen to plasma, and at the same time by the rate of removal of the tracer from plasma by uptake in tissues and excretion by various routes, including secretion back into the gut as digestive juice calcium. Q(t) is a somewhat complex function, known as the convolution integral, which represents the interaction between the two functions i(t) and h(t). However, given that Q(t) and i(t) have been determined experimentally, h(t) can be derived by a process of mathematical deconvolution, with or without the aid of a computer. The integral of h(t), i.e. the area under the curve, gives the fraction of the absorbed dose. This technique was used originally by Scholer and Code (1954) for studying the transfer of water from the gut, and they gave a particularly lucid account of the mathematical procedures involved, including a simple explanation of the convolution integral and its application in the present context; but it was not till 1969 that an essentially similar method was used for calcium absorption studies by Birge et al (1969).
187
RADIOISOTOPE STUDIES OF CALCIUM METABOLISM
This technique is important in that its accuracy is limited only by the quantity and quality of the raw experimental data. It requires no assumptions, and it can give information on the pattern of absorption under different conditions (see Figure 1(b)) as well as the fraction of the oral dose which has been absorbed. There are numerous other tests based on plasma activity levels, but these represent simplifications of the technique described by Birge et al. In effect, one can use fewer samples (Nordin et ai, 1968). One can eliminate the second tracer and assume that the function i(t) is similar for most patients (Tothill, Dellipiani and Calvert, 1970) and use simpler calculations. Simplest of all is the use of a single plasma sample measured at two hours (Bhandarkar et aI, 1961) or a single measurement of 47Ca uptake in the forearm (Wills et aI, 1970) as a calcium absorption index. In short, the more limited the measurements and the more naive the method of calculation used, the cruder the estimate of calcium absorption.
10
c: c:
'E
s
0.014 0.012
~ 0.010
""~
0.008
25
0.006
!i:
11 Hyperparathyroid 21 Idiopathic Hypercalciuria 31 Normal < 100mg load 41 Normal> 100mg load 51 Hypoparathyroid 6) Nontropical Sprue
VI
~ 0.004
i!5 ~
<
0.002
oX
5
(a)
HOURS
10
(b)
0 -l""' .......= -=i-.....-.-.------.-----r=.::T="'i 0 20 40 60 80 100 120 140 160 180 MINUTES
Figure l(a). Plasma specific activity curves; i(t) is the time course of specific activity following the intravenous injection of one calcium isotope, Q(t) is' the curve resulting from oral administration of a second isotope at the same time. h(t) is obtained by mathematical deconvolution of i(t) from Q(t) and describes the rate of single passage transfer from gut to plasma. Figure l(b). Rates of transfer in different clinical disorders. The area under the curve gives the fraction of the tracer which is absorbed (after Birge et ai, 1969, reproduced by permission of the Editor, The Journal of Clinical Investigation).
Total digestive juicecalcium Given the balance data and the endogenous faecal excretion, the total amount of endogenous calcium entering the gut (total digestive juice calcium), and by the same token the total absorptive capacity of the gut, can only be calculated by making some assumption about the reabsorption, if any, of the endogenous calcium. It is usual to assume that this mixes with and is absorbed to the same extent as dietary calcium. This is not unreasonable, and this assumption does not appear to be seriously questioned.
J.
188
REEVE AND
N.
VEALL
SKELETAL ACCRETION AND RESORPTION RATES Single injection methods Most of the published methods for measuring the rate of incorporation of calcium into bone depend on the use of a single injection of a tracer such as 47Ca. At any given time t after the injection, a certain amount (which can be measured) will have been excreted in urine and faeces. The remainder is retained in the body. A fraction of this is incorporated into the skeleton; the rest may be thought of as being distributed in an indefinite number of illdefined 'pools' which exchange with the plasma calcium. Only the plasma pool is accessible for measurement of its specific activity. If the total amount of 47Ca in these various 'exchangeable' pools can be deduced from the plasma activity/time curve (Figure 2), then the uptake in the skeleton can be obtained by difference and the accretion rate calculated (the resorption rate is obtained by difference from the balance figure). To do this, it is necessary to postulate that at some time the calcium in all the pools classified as 'not bone' is in equilibrium with, and thus has the same specific activity as, the plasma calcium. With a falling plasma activity, this situation never occurs. Figure 3 shows an open system (i.e. plasma activity decreasing) with three compartments or pools exchanging with the plasma at different rates. Initially, the specific activity of every pool is less than that of the plasma calcium. Each pool achieves transient equilibrium with the plasma at a time which depends on its exchange rate. Thereafter the specific activity of the pool commences to decrease until its rate of decrease parallels that of the plasma curve. However, because of the time lag involved, the calcium specific activity in the pool is now higher than that of the plasma pool. The isotope
100 A ro U
E
C'l
L;:i Vl
o o ~ 10 IZ
D
LLJ
U 0::
LLJ
0..
1-+--------.--------.-------..,
o
5
10
15
DAYS
Figure 2. Plasma specific activity curve for the two-week period following a single injection of radiocalcium.
189
RADIOISOTOPE STUDIES OF CALCIUM METABOLISM
dilution formula for determining the size of the pool is valid for a single compartment system at any time after the rapid initial mixing, by definition (Brownell, Berman and Robertson, 1968). It is valid for an open two-compartment system at the moment of transient equilibrium. It cannot ever be formally valid for an open multicompartment system, since true equilibrium is never reached because each compartment has a different transient equilibrium time. However, it is possible to define a time when virtual equilibrium exists, at which point the sum of all the individual pool sizes multiplied by their individual specific activities divided by the total pool size (i.e. the weighted mean specific activity) is equal to that of the plasma calcium. It is not uncommon in other tracer studies to find that this state of virtual equilibrium may persist for an appreciable period, during which the compartments with falling specific activities approximately compensate those with rising specific activities and the system as a whole appears to be in equilibrium with the plasma. This is probably the situation over the region BC of the plasma activity curve (Figure 2), and it is on this part of the curve that many workers base their estimates of pool size and hence of bone accretion rate. Once the main assumption has been made that there exists a period (between 5 and 10 days after injection of the tracer) when there is virtual equilibrium between the various exchangeable calcium pools and the plasma calcium, then the way is open to apply a number of mathematical analyses to the data. For example, one can take two points on the plasma curve and solve the resulting pair of simultaneous equations to obtain the separate loss rates from the plasma due to excretion and bone accretion. Detailed protocols 100
I
C#
IA
plasma: I I
B# I I
50
~
,,
~ I I
I I
, I
?:'
-
... ... ...
: Plasma
.~
,,
u
, ,,
I
,:A I
I I I I
I
,
,. ...
I
I
,'B ,,, ,
,,
,,
,. ,.
,'c
I 10 +--r-....L,----,.-~...,......--r-__r---r-..--.....___,_---r
o
5
Time Figure 3. An open multicompartment mammillary system and curves showing the time course of specific activity in each compartment. At no time are the specific activities equal in all compartments. (Reproduced, with permission, from Veall, N. and Vetter, H., 1958, Radioisotope Techniques in Clinical Research and Diagnosis. Ch, II, p. 199. London: Butterworth.)
190
J.
REEVE AND
N.
VEALL
relating to clinical studies have been published by Bauer, Carlsson and Lindquist (1958) and Dymling (1971). Other workers prefer to obtain the pool turnover rate by conventional analysis of the plasma curve into three or more exponential functions (Aubert and Milhaud, 1960). The various methods based on compartmental analysis, their assumptions and errors, have been reviewed by several authors, in particular by Heaney (1963), and it is very difficult to improve on this comprehensive review. A more unconventional approach is based on the fact that curves which can be fitted by multiple exponentials can usually be equally well, sometimes better, fitted by a power law function, particularly where skeletal uptake of bone-seeking isotopes is concerned (Anderson, Tomlinson and Osborn, 1962). Plasma disappearance curves for tracers such as *Ca and *Sr can be fitted very well by a gamma function of the form plasma specific activity C(t) = At-a.e-~t where A, a and ~ are constants. For the first 15 hours or so the power law term is dominant, and is thought to reflect the progressive labelling 'of the skeleton by exchangeable processes. Thereafter the exponential term becomes more important and is thought to reflect the loss of label by excretion. Burkinshaw et al (1969) have developed a method which involves extrapolation of the power function obtained over the first 10 hours to seven days in order to estimate the fraction of the total pool depletion in the one-week period which can be attributed to skeletal uptake. All the various methods based on the analysis of plasma curves give essentially similar results. This is not surprising, since they are all based on the concept of an exchangeable pool in equilibrium with plasma. That the results obtained are consistent with previous knowledge and are not otherwise unreasonable is consistent with the suggestion that, although the exchangea ble pools cannot reach true equilibrium, there probably exists a period where there is virtual equilibrium. However, we have here a situation analogous to those which occur in other walks of life, where several groups hold differing views, all probably substantially correct but none capable of formal proof. This has provided the ideal milieu for a great deal of controversy and erudite discussion at conferences (Pearson and Joplin, 1964; LA.E.A., 1962, 1964), but for reasons outlined below we suggest that these differences of opinion are largely academic. For the purpose of bone accretion and resorption measurements, the only essential subdivision of the tracer is between 'bone' calcium and 'not bone' calcium, the latter being approximated by the 'exchangeable' calcium. However, even this boundary is a vague one, by reason of the existence of various exchange processes on bone surfaces with different rates, which do not represent permanent incorporation of the tracer into the bone structure. This uncertainty alone provides scope for a great deal of argument over what is primarily a semantic problem. It is partly for this reason that bone uptake measurements by external counting have little application to quantitative measurement, though they provide interesting qualitative data. Likewise, although it is possible to measure a 'rapidly exchanging pool' and a 'slowly exchanging pool' by using suitably timed plasma samples, these only bear a qualitative relationship to real physiological pools. The fact that numerous
*Anyone of several different available isotopes.
RADIOISOTOPE STUDIES OF CALCIUM METABOLISM
191
compartmental models, whose complexity is restricted only by the size of the available computer, can be constructed, and that they all yield plasma curves consistent with those observed, merely reflects the fact that it is impossible to characterise uniquely a complex system with insufficient experimental data. Continuous feeding of tracer I f the tracer is administered as multiple small doses over a sufficiently long period instead of as a single injection, the plasma *Ca level first rises rapidly and then asymptotically approaches a constant value. Provided sufficient time has elapsed, it is possible in principle to reach true equilibrium within the exchangeable pool complex. The rate of uptake of tracer by bone is then simply the difference between the rate of administration and the total excretion rate. This technique has been utilised by Nordin, Smith and Nisbet (1964), using a three-week equilibration period. This technique, which is analogous to the constant infusion techniques for measuring renal clearances, has the virtue of simplicity, it involves the minimum of assumptions, and the measured pool size as well as the accretion rates has real physical significance. The three-week equilibration period found' necessary by Nordin et al could probably be reduced by the initial injection of a priming dose of tracer. However, because of the time taken to reach equilibrium it is not possible to use 47Ca in conjunction with this method. It is necessary to assume that during the period of the study none of the tracer incorporated into the bone structure is resorbed and returned to the exchangeable pool. This is also a crucial assumption in the analyses of single injection methods discussed above. Recycling of accreted tracer If there is any return of the tracer from the 'bone' to the 'not bone' calcium pools, all the above methods break down. One school of thought believes that the change in slope of the plasma curve in the region CD (Figure 2) is due to return of tracer from the bone. This view is based largely on the results of double tracer studies with *Sr and *Ca (Heaney, 1963), where the ratio of the two isotopes in plasma is observed as a function of time. By reason of the discrimination in favour of Sr by the kidney, the ratio of *Srj*Ca in the plasma tends to decrease. It is observed, however, that the rate of fall of this ratio tends to decrease or become constant after IO days. This is interpreted as representing relative enrichment of the plasma *Sr pool by resorption from bone. Examination of the compartment model shown in Figure 3 suggests that this could equally well be interpreted as release of *Sr from any slowly exchanging pool or pools, and there may well be other possible explanations. The other school of thought, as represented by Nordin et al (I 964), attributes the change in slope of the *Ca plasma curve to the increasing influence of slowly exchanging pools with time. Again, there seems to be a semantic element in this controversy, since it can be argued that calcium which goes into the skeleton and comes out again in a few days should be more properly regarded as 'not bone' rather than 'bone'. Certainly, any bone
J.
192
REEVE AND
N.
VEALL
calcium which is laid down and then rapidly resorbed will not be included in the bone accretion rate measured by any of the above methods.
TOTAL BODY CALCIUM Since the first calcium balance studies were performed, it has been appreciated that the results of short-term studies are not likely to reveal a small abnormality in calcium metabolism which over a period of many years ultimately manifests itself as metabolic bone disease. Until recently, isotopic tracer studies could offer no additional help in this context, for such is the remarkable slowness of skeletal turnover in the normal adult (I· 5-8'0 per cent per annum according to Rivera, 1965) that the length of time required to study the reappearance of tracer following long-term skeletal labelling in the adul t has proved almost universally daunting. Probably the longest published calcium balance study to date is that of Munck (1964), which extended to nine months, and this is unlikely to be frequently repeated. The measurement of whole body 24Na was used initially as a measure of accidental neutron exposure (Hoffman and Hempelmann, 1957). Conversely, it has proved possible to measure whole body sodium following whole body neutron irradiation (Anderson et aI, 1964). More recently, total body calcium has been measured in the same way, as neutron activation gives = 8·9 min) from the stable isotope 48Ca rise to the short-lived 49Ca (Chamberlain et ai, 1968). Cohn, Dombrowski and Fairchild (1970) and Nelp et al (1970) have shown that the method can be made reproducible with a coefficient of variation of 1·7 per cent or better. It is therefore now possible to measure another absolute parameter, total body calcium, to add to the other data, and the first papers documenting the time course of total body calcium in pathological situations are now appearing (Chamberlain et ai, 1970). Clearly, serial measurements of total body calcium provide the best estimates of the net gain or loss of calcium by the skeleton over periods of months or years.
cr,
APPLICAnON OF TRACER STUDIES TO DIAGNOSIS AND ASSESSMENT OF TREATMENT Of the measurable parameters so far discussed, the last, total body calcium, appears to have far and away the greatest potential as a useful clinical measurement. This hope stems from the fact that there is a comparatively direct relationship between bone strength and the calcium content/unit volume of bone (Bell et aI, 1967), and the fact that 99 per cent of body calcium is contained in bone. The other measurements, calcium absorption and bone uptake and resorption rate of calcium, have proved of comparatively little clinical value when taken in isolation. They art: most likely to be of value when used in conjunction with measurements of other parameters of calcium metabolism to provide quantitative data for discriminant function analytical methods in differential diagnosis (Fraser et aI, 1971).
RADIOISOTOPE STUDIES OF CALCIUM METABOLISM
193
FUTURE DEVELOPMENTS In view of the evident sterility of the arguments surrounding the interpretation of steady-state plasma *Ca disappearance curves, it is not surprising that interest in this form of analysis should have waned somewhat in the last few years. However, it seems likely that there is still a considerable amount to be gained from kinetic analysis provided a less restricted approach is adopted. Mathematical techniques can be used in two fundamentally different ways when applied to biological problems. They can be used purely descriptively, in which case the resulting 'models' describe the biological system in a convenient shorthand without offering any more insight into its behaviour than was incorporated, a priori, by the model builder. A much more powerful type of model is one which can be used to make predictions about the behaviour of the system under a variety of different circumstances; this sort of model can then be used in the design of further experiments whose results can be incorporated in a more refined model. As a class, the steady-state models are approaching the end of their possibilities for development because they offer only very limited scope for the testing of the assumptions which are inherent in them. The considerable simplification made possible by the assumption that all pool sizes and exchange rates remain constant makes analysis of steady-state measurements attractive. On the other hand, disorders of calcium metabolism are nearly all disorders of homeostasis, and steady-state studies can provide little information on the nature of feedback control processes which, by definition, function to restore the steady state following a deviation from it. It follows that short-term studies are much more likely to help elucidate the long-term problems of calcium metabolism if they relate to non-steady-state conditions. Any model which can cope with the non-steady state must be very much more complex and will have to incorporate, inter alia, the investigator's assumptions on the nature of the calcium-magnesium-phosphate homeostatic control system. Such a model, if expressed in mathematical notation, would consist of a formidable array of differential equations; for this reason analogue computers have to be used to derive solutions. Crude analogue models of the calcium control system have been set up, based on the rather sketchy quantitative experimental data so far available. These models are capable of predicting the results of non-steady-state experiments such as calcium infusion tests and EDTA infusion tests. Furthermore, the investigator can induce his model to simulate tracer studies by adding the appropriate elements to his analogue model and making the usual assumption that the body cannot distinguish between the isotopes of calcium. In contrast to some simpler physiological systems, any even half-realistic model of calcium metabolism such as that shown in Figure 4 is bound to be complicated. Nevertheless it is not difficult to set up a model with this degree of complexity on a moderate sized analogue computer, or on a digital computer, using an analogue simulation programme. It is evident that it will take a considerable amount of time and effort to develop models which will make predictions that are on target for a wide range of different situations. But it is precisely this predictive power which is the underlying strength of this approach, since it enables the experimenter to compare the
J.
194 le.c.f. cal ?
5 -----+:
-------,
'u
I
c;
I
U
I
I
:
Complexed Ca
I
I
I
:
I
I
Complexed'
, I I
I I
,
N.
VEALL
(e. c. f. inorganic P0 1
1------I
REEVE AND
4
,, ,
- --{> ,-{>
PO
PTH
:
,....--+--"""'T--~~---i'
4
?
ii
'''---
a
t I
.8
'
C>.
Ionised P04
, , ,, ,, I I
I
I
-----,
-?
..,...
Uri ne Phosphate
Urine calcium
e ....
"
.~
c:
+--
II
It'ovement between pool s . . - - Positive nIl uences on movement /L . between pools or production '-r - Negative rates
."
le.c.f. Mjl
Figure 4. A simplified scheme of extracellular calcium, phosphate and magnesium homeostasis. Some of the more important extracellular pools of the three ions are shown together with their interactions. Where ignorance of the mechanism of or the quantitative importance of a pathway is particularly profound, a question mark is placed beside it. Many important interacting systems and regulatory influences have been omitted from the diagram to avoid visual confusion. Although complex, such a theoretical system can be modelled on an analogue computer with comparative ease.
model with both analytical and tracer experimental data over a wide range of non-steady-state situations and so progressively to refine the model. Because of the complexity of the subject, we are still at a very elementary stage in developing a realistic framework within which quantitative calcium data can be evaluated. An example of the gaps in our present knowledge is provided by the fact that it is not yet customary to distinguish between ionised and complexed calcium in metabolic tracer studies, notwithstanding the marked differences in their properties and metabolic behaviour (Veall
RADIOISOTOPE STUDIES OF CALCIUM METABOLISM
195
and Parsons, 1964). This is equivalent to trying to study iodine metabolism and thyroid physiology without distinguishing between protein-bound and inorganic radioiodine. In spite of these difficulties it seems likely that with the advent of neutron activation analysis for measuring whole body calcium and with the application of more sophisticated approaches to the analysis of short-term tracer studies, the use of the stable and radioactive isotopes of calcium will prove increasingly helpful in furthering our understanding of calcium metabolism, and the rational management of patients with disorders of calcium metabolism. SUMMARY It is now possible to measure the absorption of calcium from the gut and the rate of endogenous secretion with the aid of tracer techniques. Bone accretion and resorption rates can be measured provided it is assumed that there is no return of tracer from the bone once it has been incorporated and that there is a time after administration of the tracer when the plasma level of tracer reflects the size of the 'not bone' pool. It is suggested that there is little to choose between the various published compartmental models, since they all involve the same basic assumptions. The measurement of changes in total body calcium by neutron activation analysis is thought to be of considerable potential value for long-term studies. Short-term studies of skeletal metabolism under steady-state conditions have not provided much useful clinical information or further insight into calcium metabolism. Further progress depends on the development of more sophisticated models capable of analysing data obtained under non-steadystate conditions with a view to studying the homeostatic mechanisms involved. For this purpose the use of analogue computer techniques is recommended. REFERENCES Anderson, J. et al (1964) Neutron activation analysis in man in vivo-A new technique in medical investigation. Lancet, ii, 1201-1205. Anderson, J., Tomlinson, R. W. S. & Osborn, S. B. (1962) An interpretation ofradioisotope turnover data. Lancet, i, 949-950. Aubert, J.-P. & Milhaud, G. (1960) Methode de mesure des principales voies du metabolisme calcique chez I'homme. Biochimica et Biophysica Acta, 39, 122-139. Bauer, G. C. H., Carlsson, A. & Lindquist, B. (1958) Use of isotopes in clinical studies of skeletal metabolism. In Radioaktive Isotope in Klinik und Forschung, ed. Fellinger, K. & Vetter, H. Vol. 3, pp. 25-40. Munich & Berlin: Urban & Schwarzenberg. Bell, G. H. et al (1967) Variations in strength of vertebrae with age and their relation to osteoporosis. Calcified Tissue Research, 1, 75-86. Bhandarkar, S. D. et al (1961) An isotope test of calcium absorption. British Medical Journal, ii, 1539-1541. Birge, S. J. et al (1969) Study of calcium absorption in man: A kinetic analysis and physiologic model. The Journal of Clinical Investigation, 48, 1705-1713. Brownell, G. L., Berman, M. & Robertson, J. S. (1968) Nomenclature for tracer kinetics. International Journal of Applied Radiation & Isotopes, 19, 249-262. Burkinshaw, L. et al (1969) Bone turnover model based on a continuously expanding exchangeable calcium pool. Nature, 222, 146-148. Chamberlain, M. J. et al (1968) Total body calcium by whole body neutron activation: New technique for study of bone disease. British Medical Journal, ii, 581-583.
196
J.
REEVE AND
N.
VEALL
Chamberlain, M. J. et al (1970). The clinical use of whole body neutron activation analysis. In Radioaktive Isotope in Klinik und Forschung; ed. Fellinger, K. & Hofer, R. Vol. 9, pp. 27-35. Munich & Berlin: Urban & Schwarzenberg. Cohn, S. H., Dombrowski, C. S. & Fairchild, R. G. (1970) In-vivo neutron activation analysis of calcium in man. International Journal of Applied Radiation & Isotopes, 21, 127-137. Dymling, J-F. (1971) Studies of calcium absorption and metabolism. In Radioisotopes in Medical Diagnosis, ed. Belcher, E. H. & Vetter, H. Ch. 13. London: Butterworth. Fraser, P. et al (1971) Discriminant functions in differential diagnosis of hypercalcaemia. Lancet, i, 1314-1319. Heaney, R. P. (1963) Evaluation and interpretation of calcium kinetic data in man. Clinical Orthopaedics, 31, 153-183. Hoffman, J. G. & Hempelmann, L. R. (1957) Estimation of whole body radiation doses in accidental fission bursts. American Journal of Roentgenology, 77, 144-160. LA.E.A. (1962) Report on the Medical Uses of Calcium-47. Technical Reports Series No. 10. Vienna: International Atomic Energy Agency. LA.E.A. (1964) Report on the Medical Uses of Calcium-47. Technical Reports Series No. 32. Vienna: International Atomic Energy Agency. LA.E.A. (1971) Measurement of Radioactivity in Body Organs. Report of an I.A.E.A. Panel. International Journal of Applied Radiation & Isotopes, 22, 385-398. Munck, O. (1964) Osteoporosis due to malabsorption of calcium responding favourably to large doses of Vitamin D. Quarterly Journal of Medicine, 33, 209-221. Nelp, W. B. et al (1970) Measurement of total body calcium (bone mass) in vivo with the use of total body neutron activation analysis. Journal ofLaboratory & Clinical Medicine, 76, 151-162. Nordin, B. E. C., Smith, D. A. & Nisbet, J. (1964) Bone mineralisation and destruction rates determined by continuous feeding of radiocalcium. Clinical Science, 27, 111-122. Nordin, B. E. C. et a! (1968) Calculation of calcium absorption rate from plasma radioactivity. Clinical Science, 35, 177-182. Ogg, C. S., Pearson, J. D. & Veall, N. (1968) A method for measuring the gastrointestinal absorption of calcium-47 using scandium-47 as an inert marker. Clinical Science, 34, 327-332. Pearson, O. H. & Joplin, G. F. (eds.) (1964) Dynamic Studies of Metabolic Bone Disease. Oxford: Blackwell. Rinsler, M. G., Dyche, G. M. & Trott, N. G. (1960) Total body counting of calcium-47. In Radioaktive Isotope in Klinik und Forschung, ed. Fellinger, K. & Hofer, R. Vol. 4, pp. 19-28. Munich & Berlin: Urban & Schwarzenberg. Rivera, J. (1965) Human bone metabolism inferred from fall-out investigations. Nature, 207, 1330-1332. Scholer, J. F. & Code, C. F. (1954) Rate of absorption of water from stomach and small bowel of human beings. Gastroenterology, 27, 565-583. Tothill, P., Dellipiani, A. W. & Calvert, J. (1970) Plasma concentrations of radiocalcium after oral administration, and their relationship to absorption. Clinical Science, 38, 27-39. Veall, N. & Parsons, V. (1964) Complexed calcium and the evaluation of tracer kinetic studies: A revised compartmental model. In Medical Uses ofCalcium-47: Second Panel Report, pp. 12-17 (also refs on pp. 189-192). I.A.E.A. Technical Reports Series No. 32. Vienna: International Atomic Energy Agency. Wills, M. R. et al (1970). The measurement of intestinal calcium absorption by external radioisotope counting: Application to the study of nephrolithiasis. Clinical Science, 39,95-106.
Prior to the availability of isotopic tracers for clinical use, quantitative information on calcium metabolism was restricted to the data provided by balance studies. In principle, it is possible to measure the net loss or gain of calcium from the bod y over the period of the study, and since some 99 per cent of the calcium in the bod y is in the skeleton, it is possible to attribute any net gain or loss to changes in the skeletal calcium content without invoking any abstruse theoretical concepts. When a number of isotopic tracers became available for clinical use, particularly 47Ca, it was not unreasonably hoped that it would be possible to gain further insight into disorders of calcium metabolism by using tracer techniques to quantitate such important factors as intestinal absorption, endogenous faecal loss, and skeletal accretion and resorption rates. Valid methods for the first two of these are now available, but there remains a certain amount of controversy over the skeletal measurements. This is mainly concerned with the methods which should be used to calculate the required parameters from the observational data. INTESTINAL ABSORPTION AND ENDOGENOUS SECRETION Intestinal absorption The simplest method in theory, though not necessarily in practice, is to give an oral dose of radiocalcium and to measure the recovered activity in the faeces over a period of six or seven days to allow the unabsorbed tracer to pass through the gut. It is then assumed that what is not recovered represents the absorbed fraction of the dose. This is reasonably valid ifit can be assumed that no faecal specimens have been lost. For the many workers who cannot feel justifiably confident on this point, it is best to use a non-absorbable marker to permit correction for faecal losses. One of the few instances of serendipity in a field which is bedevilled by difficulties is the fact that 47Ca decays to radioactive 47Sc, which is not absorbed by the gut. Thus, since this isotope has its own built-in inert marker, an absorption test can be carried out on a
185
186
J.
REEVE AND
N.
VEALL
single radioactive stool specimen (Ogg, Pearson and Veall, 1968). The faecal recovery method gives a slight underestimate owing to resecretion of absorbed tracer into the gut, but this error is usually small. The converse procedure is to measure the body retention directly by using a whole body counter (Rinsler, Dyche and Trott, 1960). The avoidance of faecal collections is an advantage, though it is still necessary to correct for urinary excretion. Also, whole body activity measurements (though simple in principle) are not free from technical problems (I.A.E.A., 1971).
Endogenous faecal calcium This may be calculated from the conventional balance data if the absorbed fraction has been determined as indicated above, since it is given by the difference between the unabsorbed fraction of the dietary intake and the total faecal excretion. Alternatively, it may be measured by giving a tracer intravenously and measuring the appearance of the isotope in the stools. Then Endogenous faecal Activity in stools (IlCi/day) Plasma Ca = Activity of plasma (IlCi/litre) X (mmol/litre) calcium (mmol/day) This is analogous to the conventional clearance formula UV/P used in renal studies. Note, however, that allowance has to be made for the delay in the gut, which is variable, so that the calculations should not be based on the rapidly changing part of the plasma activity curve, and a suitable marker needs to be used to estimate the gut transit time. It is, of course, possible to measure both absorption and endogenous faecal calcium by using 47Ca and 4SCa simultaneously, one given orally and the other intravenously. However, under these circumstances, it is better to use the plasma activity levels rather than faecal data. The double isotope technique (plasma samples) Figure 1(a) shows the plasma activity curve following the administration of a single intravenous injection of radiocalcium, i(t), together with the corresponding curve for the second tracer given orally, Q(t). The form of the latter function, Q(t), is determined by the form of the function h(t), which describes the transfer of radiocalcium from gut lumen to plasma, and at the same time by the rate of removal of the tracer from plasma by uptake in tissues and excretion by various routes, including secretion back into the gut as digestive juice calcium. Q(t) is a somewhat complex function, known as the convolution integral, which represents the interaction between the two functions i(t) and h(t). However, given that Q(t) and i(t) have been determined experimentally, h(t) can be derived by a process of mathematical deconvolution, with or without the aid of a computer. The integral of h(t), i.e. the area under the curve, gives the fraction of the absorbed dose. This technique was used originally by Scholer and Code (1954) for studying the transfer of water from the gut, and they gave a particularly lucid account of the mathematical procedures involved, including a simple explanation of the convolution integral and its application in the present context; but it was not till 1969 that an essentially similar method was used for calcium absorption studies by Birge et al (1969).
187
RADIOISOTOPE STUDIES OF CALCIUM METABOLISM
This technique is important in that its accuracy is limited only by the quantity and quality of the raw experimental data. It requires no assumptions, and it can give information on the pattern of absorption under different conditions (see Figure 1(b)) as well as the fraction of the oral dose which has been absorbed. There are numerous other tests based on plasma activity levels, but these represent simplifications of the technique described by Birge et al. In effect, one can use fewer samples (Nordin et ai, 1968). One can eliminate the second tracer and assume that the function i(t) is similar for most patients (Tothill, Dellipiani and Calvert, 1970) and use simpler calculations. Simplest of all is the use of a single plasma sample measured at two hours (Bhandarkar et aI, 1961) or a single measurement of 47Ca uptake in the forearm (Wills et aI, 1970) as a calcium absorption index. In short, the more limited the measurements and the more naive the method of calculation used, the cruder the estimate of calcium absorption.
10
c: c:
'E
s
0.014 0.012
~ 0.010
""~
0.008
25
0.006
!i:
11 Hyperparathyroid 21 Idiopathic Hypercalciuria 31 Normal < 100mg load 41 Normal> 100mg load 51 Hypoparathyroid 6) Nontropical Sprue
VI
~ 0.004
i!5 ~
<
0.002
oX
5
(a)
HOURS
10
(b)
0 -l""' .......= -=i-.....-.-.------.-----r=.::T="'i 0 20 40 60 80 100 120 140 160 180 MINUTES
Figure l(a). Plasma specific activity curves; i(t) is the time course of specific activity following the intravenous injection of one calcium isotope, Q(t) is' the curve resulting from oral administration of a second isotope at the same time. h(t) is obtained by mathematical deconvolution of i(t) from Q(t) and describes the rate of single passage transfer from gut to plasma. Figure l(b). Rates of transfer in different clinical disorders. The area under the curve gives the fraction of the tracer which is absorbed (after Birge et ai, 1969, reproduced by permission of the Editor, The Journal of Clinical Investigation).
Total digestive juicecalcium Given the balance data and the endogenous faecal excretion, the total amount of endogenous calcium entering the gut (total digestive juice calcium), and by the same token the total absorptive capacity of the gut, can only be calculated by making some assumption about the reabsorption, if any, of the endogenous calcium. It is usual to assume that this mixes with and is absorbed to the same extent as dietary calcium. This is not unreasonable, and this assumption does not appear to be seriously questioned.
J.
188
REEVE AND
N.
VEALL
SKELETAL ACCRETION AND RESORPTION RATES Single injection methods Most of the published methods for measuring the rate of incorporation of calcium into bone depend on the use of a single injection of a tracer such as 47Ca. At any given time t after the injection, a certain amount (which can be measured) will have been excreted in urine and faeces. The remainder is retained in the body. A fraction of this is incorporated into the skeleton; the rest may be thought of as being distributed in an indefinite number of illdefined 'pools' which exchange with the plasma calcium. Only the plasma pool is accessible for measurement of its specific activity. If the total amount of 47Ca in these various 'exchangeable' pools can be deduced from the plasma activity/time curve (Figure 2), then the uptake in the skeleton can be obtained by difference and the accretion rate calculated (the resorption rate is obtained by difference from the balance figure). To do this, it is necessary to postulate that at some time the calcium in all the pools classified as 'not bone' is in equilibrium with, and thus has the same specific activity as, the plasma calcium. With a falling plasma activity, this situation never occurs. Figure 3 shows an open system (i.e. plasma activity decreasing) with three compartments or pools exchanging with the plasma at different rates. Initially, the specific activity of every pool is less than that of the plasma calcium. Each pool achieves transient equilibrium with the plasma at a time which depends on its exchange rate. Thereafter the specific activity of the pool commences to decrease until its rate of decrease parallels that of the plasma curve. However, because of the time lag involved, the calcium specific activity in the pool is now higher than that of the plasma pool. The isotope
100 A ro U
E
C'l
L;:i Vl
o o ~ 10 IZ
D
LLJ
U 0::
LLJ
0..
1-+--------.--------.-------..,
o
5
10
15
DAYS
Figure 2. Plasma specific activity curve for the two-week period following a single injection of radiocalcium.
189
RADIOISOTOPE STUDIES OF CALCIUM METABOLISM
dilution formula for determining the size of the pool is valid for a single compartment system at any time after the rapid initial mixing, by definition (Brownell, Berman and Robertson, 1968). It is valid for an open two-compartment system at the moment of transient equilibrium. It cannot ever be formally valid for an open multicompartment system, since true equilibrium is never reached because each compartment has a different transient equilibrium time. However, it is possible to define a time when virtual equilibrium exists, at which point the sum of all the individual pool sizes multiplied by their individual specific activities divided by the total pool size (i.e. the weighted mean specific activity) is equal to that of the plasma calcium. It is not uncommon in other tracer studies to find that this state of virtual equilibrium may persist for an appreciable period, during which the compartments with falling specific activities approximately compensate those with rising specific activities and the system as a whole appears to be in equilibrium with the plasma. This is probably the situation over the region BC of the plasma activity curve (Figure 2), and it is on this part of the curve that many workers base their estimates of pool size and hence of bone accretion rate. Once the main assumption has been made that there exists a period (between 5 and 10 days after injection of the tracer) when there is virtual equilibrium between the various exchangeable calcium pools and the plasma calcium, then the way is open to apply a number of mathematical analyses to the data. For example, one can take two points on the plasma curve and solve the resulting pair of simultaneous equations to obtain the separate loss rates from the plasma due to excretion and bone accretion. Detailed protocols 100
I
C#
IA
plasma: I I
B# I I
50
~
,,
~ I I
I I
, I
?:'
-
... ... ...
: Plasma
.~
,,
u
, ,,
I
,:A I
I I I I
I
,
,. ...
I
I
,'B ,,, ,
,,
,,
,. ,.
,'c
I 10 +--r-....L,----,.-~...,......--r-__r---r-..--.....___,_---r
o
5
Time Figure 3. An open multicompartment mammillary system and curves showing the time course of specific activity in each compartment. At no time are the specific activities equal in all compartments. (Reproduced, with permission, from Veall, N. and Vetter, H., 1958, Radioisotope Techniques in Clinical Research and Diagnosis. Ch, II, p. 199. London: Butterworth.)
190
J.
REEVE AND
N.
VEALL
relating to clinical studies have been published by Bauer, Carlsson and Lindquist (1958) and Dymling (1971). Other workers prefer to obtain the pool turnover rate by conventional analysis of the plasma curve into three or more exponential functions (Aubert and Milhaud, 1960). The various methods based on compartmental analysis, their assumptions and errors, have been reviewed by several authors, in particular by Heaney (1963), and it is very difficult to improve on this comprehensive review. A more unconventional approach is based on the fact that curves which can be fitted by multiple exponentials can usually be equally well, sometimes better, fitted by a power law function, particularly where skeletal uptake of bone-seeking isotopes is concerned (Anderson, Tomlinson and Osborn, 1962). Plasma disappearance curves for tracers such as *Ca and *Sr can be fitted very well by a gamma function of the form plasma specific activity C(t) = At-a.e-~t where A, a and ~ are constants. For the first 15 hours or so the power law term is dominant, and is thought to reflect the progressive labelling 'of the skeleton by exchangeable processes. Thereafter the exponential term becomes more important and is thought to reflect the loss of label by excretion. Burkinshaw et al (1969) have developed a method which involves extrapolation of the power function obtained over the first 10 hours to seven days in order to estimate the fraction of the total pool depletion in the one-week period which can be attributed to skeletal uptake. All the various methods based on the analysis of plasma curves give essentially similar results. This is not surprising, since they are all based on the concept of an exchangeable pool in equilibrium with plasma. That the results obtained are consistent with previous knowledge and are not otherwise unreasonable is consistent with the suggestion that, although the exchangea ble pools cannot reach true equilibrium, there probably exists a period where there is virtual equilibrium. However, we have here a situation analogous to those which occur in other walks of life, where several groups hold differing views, all probably substantially correct but none capable of formal proof. This has provided the ideal milieu for a great deal of controversy and erudite discussion at conferences (Pearson and Joplin, 1964; LA.E.A., 1962, 1964), but for reasons outlined below we suggest that these differences of opinion are largely academic. For the purpose of bone accretion and resorption measurements, the only essential subdivision of the tracer is between 'bone' calcium and 'not bone' calcium, the latter being approximated by the 'exchangeable' calcium. However, even this boundary is a vague one, by reason of the existence of various exchange processes on bone surfaces with different rates, which do not represent permanent incorporation of the tracer into the bone structure. This uncertainty alone provides scope for a great deal of argument over what is primarily a semantic problem. It is partly for this reason that bone uptake measurements by external counting have little application to quantitative measurement, though they provide interesting qualitative data. Likewise, although it is possible to measure a 'rapidly exchanging pool' and a 'slowly exchanging pool' by using suitably timed plasma samples, these only bear a qualitative relationship to real physiological pools. The fact that numerous
*Anyone of several different available isotopes.
RADIOISOTOPE STUDIES OF CALCIUM METABOLISM
191
compartmental models, whose complexity is restricted only by the size of the available computer, can be constructed, and that they all yield plasma curves consistent with those observed, merely reflects the fact that it is impossible to characterise uniquely a complex system with insufficient experimental data. Continuous feeding of tracer I f the tracer is administered as multiple small doses over a sufficiently long period instead of as a single injection, the plasma *Ca level first rises rapidly and then asymptotically approaches a constant value. Provided sufficient time has elapsed, it is possible in principle to reach true equilibrium within the exchangeable pool complex. The rate of uptake of tracer by bone is then simply the difference between the rate of administration and the total excretion rate. This technique has been utilised by Nordin, Smith and Nisbet (1964), using a three-week equilibration period. This technique, which is analogous to the constant infusion techniques for measuring renal clearances, has the virtue of simplicity, it involves the minimum of assumptions, and the measured pool size as well as the accretion rates has real physical significance. The three-week equilibration period found' necessary by Nordin et al could probably be reduced by the initial injection of a priming dose of tracer. However, because of the time taken to reach equilibrium it is not possible to use 47Ca in conjunction with this method. It is necessary to assume that during the period of the study none of the tracer incorporated into the bone structure is resorbed and returned to the exchangeable pool. This is also a crucial assumption in the analyses of single injection methods discussed above. Recycling of accreted tracer If there is any return of the tracer from the 'bone' to the 'not bone' calcium pools, all the above methods break down. One school of thought believes that the change in slope of the plasma curve in the region CD (Figure 2) is due to return of tracer from the bone. This view is based largely on the results of double tracer studies with *Sr and *Ca (Heaney, 1963), where the ratio of the two isotopes in plasma is observed as a function of time. By reason of the discrimination in favour of Sr by the kidney, the ratio of *Srj*Ca in the plasma tends to decrease. It is observed, however, that the rate of fall of this ratio tends to decrease or become constant after IO days. This is interpreted as representing relative enrichment of the plasma *Sr pool by resorption from bone. Examination of the compartment model shown in Figure 3 suggests that this could equally well be interpreted as release of *Sr from any slowly exchanging pool or pools, and there may well be other possible explanations. The other school of thought, as represented by Nordin et al (I 964), attributes the change in slope of the *Ca plasma curve to the increasing influence of slowly exchanging pools with time. Again, there seems to be a semantic element in this controversy, since it can be argued that calcium which goes into the skeleton and comes out again in a few days should be more properly regarded as 'not bone' rather than 'bone'. Certainly, any bone
J.
192
REEVE AND
N.
VEALL
calcium which is laid down and then rapidly resorbed will not be included in the bone accretion rate measured by any of the above methods.
TOTAL BODY CALCIUM Since the first calcium balance studies were performed, it has been appreciated that the results of short-term studies are not likely to reveal a small abnormality in calcium metabolism which over a period of many years ultimately manifests itself as metabolic bone disease. Until recently, isotopic tracer studies could offer no additional help in this context, for such is the remarkable slowness of skeletal turnover in the normal adult (I· 5-8'0 per cent per annum according to Rivera, 1965) that the length of time required to study the reappearance of tracer following long-term skeletal labelling in the adul t has proved almost universally daunting. Probably the longest published calcium balance study to date is that of Munck (1964), which extended to nine months, and this is unlikely to be frequently repeated. The measurement of whole body 24Na was used initially as a measure of accidental neutron exposure (Hoffman and Hempelmann, 1957). Conversely, it has proved possible to measure whole body sodium following whole body neutron irradiation (Anderson et aI, 1964). More recently, total body calcium has been measured in the same way, as neutron activation gives = 8·9 min) from the stable isotope 48Ca rise to the short-lived 49Ca (Chamberlain et ai, 1968). Cohn, Dombrowski and Fairchild (1970) and Nelp et al (1970) have shown that the method can be made reproducible with a coefficient of variation of 1·7 per cent or better. It is therefore now possible to measure another absolute parameter, total body calcium, to add to the other data, and the first papers documenting the time course of total body calcium in pathological situations are now appearing (Chamberlain et ai, 1970). Clearly, serial measurements of total body calcium provide the best estimates of the net gain or loss of calcium by the skeleton over periods of months or years.
cr,
APPLICAnON OF TRACER STUDIES TO DIAGNOSIS AND ASSESSMENT OF TREATMENT Of the measurable parameters so far discussed, the last, total body calcium, appears to have far and away the greatest potential as a useful clinical measurement. This hope stems from the fact that there is a comparatively direct relationship between bone strength and the calcium content/unit volume of bone (Bell et aI, 1967), and the fact that 99 per cent of body calcium is contained in bone. The other measurements, calcium absorption and bone uptake and resorption rate of calcium, have proved of comparatively little clinical value when taken in isolation. They art: most likely to be of value when used in conjunction with measurements of other parameters of calcium metabolism to provide quantitative data for discriminant function analytical methods in differential diagnosis (Fraser et aI, 1971).
RADIOISOTOPE STUDIES OF CALCIUM METABOLISM
193
FUTURE DEVELOPMENTS In view of the evident sterility of the arguments surrounding the interpretation of steady-state plasma *Ca disappearance curves, it is not surprising that interest in this form of analysis should have waned somewhat in the last few years. However, it seems likely that there is still a considerable amount to be gained from kinetic analysis provided a less restricted approach is adopted. Mathematical techniques can be used in two fundamentally different ways when applied to biological problems. They can be used purely descriptively, in which case the resulting 'models' describe the biological system in a convenient shorthand without offering any more insight into its behaviour than was incorporated, a priori, by the model builder. A much more powerful type of model is one which can be used to make predictions about the behaviour of the system under a variety of different circumstances; this sort of model can then be used in the design of further experiments whose results can be incorporated in a more refined model. As a class, the steady-state models are approaching the end of their possibilities for development because they offer only very limited scope for the testing of the assumptions which are inherent in them. The considerable simplification made possible by the assumption that all pool sizes and exchange rates remain constant makes analysis of steady-state measurements attractive. On the other hand, disorders of calcium metabolism are nearly all disorders of homeostasis, and steady-state studies can provide little information on the nature of feedback control processes which, by definition, function to restore the steady state following a deviation from it. It follows that short-term studies are much more likely to help elucidate the long-term problems of calcium metabolism if they relate to non-steady-state conditions. Any model which can cope with the non-steady state must be very much more complex and will have to incorporate, inter alia, the investigator's assumptions on the nature of the calcium-magnesium-phosphate homeostatic control system. Such a model, if expressed in mathematical notation, would consist of a formidable array of differential equations; for this reason analogue computers have to be used to derive solutions. Crude analogue models of the calcium control system have been set up, based on the rather sketchy quantitative experimental data so far available. These models are capable of predicting the results of non-steady-state experiments such as calcium infusion tests and EDTA infusion tests. Furthermore, the investigator can induce his model to simulate tracer studies by adding the appropriate elements to his analogue model and making the usual assumption that the body cannot distinguish between the isotopes of calcium. In contrast to some simpler physiological systems, any even half-realistic model of calcium metabolism such as that shown in Figure 4 is bound to be complicated. Nevertheless it is not difficult to set up a model with this degree of complexity on a moderate sized analogue computer, or on a digital computer, using an analogue simulation programme. It is evident that it will take a considerable amount of time and effort to develop models which will make predictions that are on target for a wide range of different situations. But it is precisely this predictive power which is the underlying strength of this approach, since it enables the experimenter to compare the
J.
194 le.c.f. cal ?
5 -----+:
-------,
'u
I
c;
I
U
I
I
:
Complexed Ca
I
I
I
:
I
I
Complexed'
, I I
I I
,
N.
VEALL
(e. c. f. inorganic P0 1
1------I
REEVE AND
4
,, ,
- --{> ,-{>
PO
PTH
:
,....--+--"""'T--~~---i'
4
?
ii
'''---
a
t I
.8
'
C>.
Ionised P04
, , ,, ,, I I
I
I
-----,
-?
..,...
Uri ne Phosphate
Urine calcium
e ....
"
.~
c:
+--
II
It'ovement between pool s . . - - Positive nIl uences on movement /L . between pools or production '-r - Negative rates
."
le.c.f. Mjl
Figure 4. A simplified scheme of extracellular calcium, phosphate and magnesium homeostasis. Some of the more important extracellular pools of the three ions are shown together with their interactions. Where ignorance of the mechanism of or the quantitative importance of a pathway is particularly profound, a question mark is placed beside it. Many important interacting systems and regulatory influences have been omitted from the diagram to avoid visual confusion. Although complex, such a theoretical system can be modelled on an analogue computer with comparative ease.
model with both analytical and tracer experimental data over a wide range of non-steady-state situations and so progressively to refine the model. Because of the complexity of the subject, we are still at a very elementary stage in developing a realistic framework within which quantitative calcium data can be evaluated. An example of the gaps in our present knowledge is provided by the fact that it is not yet customary to distinguish between ionised and complexed calcium in metabolic tracer studies, notwithstanding the marked differences in their properties and metabolic behaviour (Veall
RADIOISOTOPE STUDIES OF CALCIUM METABOLISM
195
and Parsons, 1964). This is equivalent to trying to study iodine metabolism and thyroid physiology without distinguishing between protein-bound and inorganic radioiodine. In spite of these difficulties it seems likely that with the advent of neutron activation analysis for measuring whole body calcium and with the application of more sophisticated approaches to the analysis of short-term tracer studies, the use of the stable and radioactive isotopes of calcium will prove increasingly helpful in furthering our understanding of calcium metabolism, and the rational management of patients with disorders of calcium metabolism. SUMMARY It is now possible to measure the absorption of calcium from the gut and the rate of endogenous secretion with the aid of tracer techniques. Bone accretion and resorption rates can be measured provided it is assumed that there is no return of tracer from the bone once it has been incorporated and that there is a time after administration of the tracer when the plasma level of tracer reflects the size of the 'not bone' pool. It is suggested that there is little to choose between the various published compartmental models, since they all involve the same basic assumptions. The measurement of changes in total body calcium by neutron activation analysis is thought to be of considerable potential value for long-term studies. Short-term studies of skeletal metabolism under steady-state conditions have not provided much useful clinical information or further insight into calcium metabolism. Further progress depends on the development of more sophisticated models capable of analysing data obtained under non-steadystate conditions with a view to studying the homeostatic mechanisms involved. For this purpose the use of analogue computer techniques is recommended. REFERENCES Anderson, J. et al (1964) Neutron activation analysis in man in vivo-A new technique in medical investigation. Lancet, ii, 1201-1205. Anderson, J., Tomlinson, R. W. S. & Osborn, S. B. (1962) An interpretation ofradioisotope turnover data. Lancet, i, 949-950. Aubert, J.-P. & Milhaud, G. (1960) Methode de mesure des principales voies du metabolisme calcique chez I'homme. Biochimica et Biophysica Acta, 39, 122-139. Bauer, G. C. H., Carlsson, A. & Lindquist, B. (1958) Use of isotopes in clinical studies of skeletal metabolism. In Radioaktive Isotope in Klinik und Forschung, ed. Fellinger, K. & Vetter, H. Vol. 3, pp. 25-40. Munich & Berlin: Urban & Schwarzenberg. Bell, G. H. et al (1967) Variations in strength of vertebrae with age and their relation to osteoporosis. Calcified Tissue Research, 1, 75-86. Bhandarkar, S. D. et al (1961) An isotope test of calcium absorption. British Medical Journal, ii, 1539-1541. Birge, S. J. et al (1969) Study of calcium absorption in man: A kinetic analysis and physiologic model. The Journal of Clinical Investigation, 48, 1705-1713. Brownell, G. L., Berman, M. & Robertson, J. S. (1968) Nomenclature for tracer kinetics. International Journal of Applied Radiation & Isotopes, 19, 249-262. Burkinshaw, L. et al (1969) Bone turnover model based on a continuously expanding exchangeable calcium pool. Nature, 222, 146-148. Chamberlain, M. J. et al (1968) Total body calcium by whole body neutron activation: New technique for study of bone disease. British Medical Journal, ii, 581-583.
196
J.
REEVE AND
N.
VEALL
Chamberlain, M. J. et al (1970). The clinical use of whole body neutron activation analysis. In Radioaktive Isotope in Klinik und Forschung; ed. Fellinger, K. & Hofer, R. Vol. 9, pp. 27-35. Munich & Berlin: Urban & Schwarzenberg. Cohn, S. H., Dombrowski, C. S. & Fairchild, R. G. (1970) In-vivo neutron activation analysis of calcium in man. International Journal of Applied Radiation & Isotopes, 21, 127-137. Dymling, J-F. (1971) Studies of calcium absorption and metabolism. In Radioisotopes in Medical Diagnosis, ed. Belcher, E. H. & Vetter, H. Ch. 13. London: Butterworth. Fraser, P. et al (1971) Discriminant functions in differential diagnosis of hypercalcaemia. Lancet, i, 1314-1319. Heaney, R. P. (1963) Evaluation and interpretation of calcium kinetic data in man. Clinical Orthopaedics, 31, 153-183. Hoffman, J. G. & Hempelmann, L. R. (1957) Estimation of whole body radiation doses in accidental fission bursts. American Journal of Roentgenology, 77, 144-160. LA.E.A. (1962) Report on the Medical Uses of Calcium-47. Technical Reports Series No. 10. Vienna: International Atomic Energy Agency. LA.E.A. (1964) Report on the Medical Uses of Calcium-47. Technical Reports Series No. 32. Vienna: International Atomic Energy Agency. LA.E.A. (1971) Measurement of Radioactivity in Body Organs. Report of an I.A.E.A. Panel. International Journal of Applied Radiation & Isotopes, 22, 385-398. Munck, O. (1964) Osteoporosis due to malabsorption of calcium responding favourably to large doses of Vitamin D. Quarterly Journal of Medicine, 33, 209-221. Nelp, W. B. et al (1970) Measurement of total body calcium (bone mass) in vivo with the use of total body neutron activation analysis. Journal ofLaboratory & Clinical Medicine, 76, 151-162. Nordin, B. E. C., Smith, D. A. & Nisbet, J. (1964) Bone mineralisation and destruction rates determined by continuous feeding of radiocalcium. Clinical Science, 27, 111-122. Nordin, B. E. C. et a! (1968) Calculation of calcium absorption rate from plasma radioactivity. Clinical Science, 35, 177-182. Ogg, C. S., Pearson, J. D. & Veall, N. (1968) A method for measuring the gastrointestinal absorption of calcium-47 using scandium-47 as an inert marker. Clinical Science, 34, 327-332. Pearson, O. H. & Joplin, G. F. (eds.) (1964) Dynamic Studies of Metabolic Bone Disease. Oxford: Blackwell. Rinsler, M. G., Dyche, G. M. & Trott, N. G. (1960) Total body counting of calcium-47. In Radioaktive Isotope in Klinik und Forschung, ed. Fellinger, K. & Hofer, R. Vol. 4, pp. 19-28. Munich & Berlin: Urban & Schwarzenberg. Rivera, J. (1965) Human bone metabolism inferred from fall-out investigations. Nature, 207, 1330-1332. Scholer, J. F. & Code, C. F. (1954) Rate of absorption of water from stomach and small bowel of human beings. Gastroenterology, 27, 565-583. Tothill, P., Dellipiani, A. W. & Calvert, J. (1970) Plasma concentrations of radiocalcium after oral administration, and their relationship to absorption. Clinical Science, 38, 27-39. Veall, N. & Parsons, V. (1964) Complexed calcium and the evaluation of tracer kinetic studies: A revised compartmental model. In Medical Uses ofCalcium-47: Second Panel Report, pp. 12-17 (also refs on pp. 189-192). I.A.E.A. Technical Reports Series No. 32. Vienna: International Atomic Energy Agency. Wills, M. R. et al (1970). The measurement of intestinal calcium absorption by external radioisotope counting: Application to the study of nephrolithiasis. Clinical Science, 39,95-106.