iron kinetics and erythropoiesis in fanconi's anaemia

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Scand J Haematol(l978) 21,29-39 Iron Kinetics and Erythropoiesis in Fanconi’s Anaemia G. BAROSI,~ M. CAZZOLA,~ A. MARC HI,^ S. MORANDI,’ V. PERANI,’ M. STEFANELLI~ & S. PERUGINI~ 1 Clinica Medica I ‘A. Ferrata’, 2 Istituto di Patologia Medica I, 3 Clinica Pediatrica and 4 lstituto di Elettronica, University of Pavia, Italy Ferrokinetic studies were carried out in 4 patients with Fanconi‘s anaemia (FA). Experimental data were analysed by means of a mathematical model of iron kinetics in order to obtain a quantitative assessment of effective and ineffective erythmpoietic activity, mean red cell lifespan, and nan-erythroid iron turnover. The major patho- genetic mechanism of the anaemia appeared to be relative marrow failure, i.e. a reduction in the proliferative capacity of the erythroid marrow. The role of in- effective erythropoiesis was of minor importance. On the basis of the results obtained both the pathogenesis and the natural course of the disease are discussed. Key words: aplastic anaemia - erythropoiesis - Fanconi’s anaemia - ferrokinetics - iron kinetics - mathematical models Accepted for publication March 16, 1978 Correspondence to: Dr. G. Barosi, Clinica Medica I ‘A. Ferrata’, Policlinico S. Matt-, 27100 Pavia, Italy Since the original description in 3 brothers by Fanconi (1927), about 300 cases of this constitutional pancytopenia associated with congenital abnormalities have been reported (Nilsson 1960, Gmyrek & Syllm-Rapoport 1964, Storti & Perugini 1969, Beard et a1 1973, Beard 1976). The most prominent characteristic of the disease seems to be wide variation in the haematological find- ings (Fanconi 1964, 1967). Undoubtedly, marrow hypoplasia is the most frequent feature and the anaemia is generally con- sidered to be of aregenerative type (Beard et a1 1973). On the other hand, isotope methods revealed various degrees of in- effective erythropoiesis (Debray & Najean 1959, Sjolin & Wranne 1962, Storti & Perugini 1969) and hyperhaemolysis (Ber- nard et a1 1958, Fanconi 1964, Vaccaro et a1 1966, Storti & Perugini 1969, Beard et a1 1973). In some cases, increased red cell breakdown was considered to be the major factor responsible for anaemia (Ber- nard et a1 1958, Vaccaro et a1 1966). The differences in erythrokinetic features have been attributed to the variability of the

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Page 1: Iron Kinetics and Erythropoiesis in Fanconi's Anaemia

Scand J Haematol(l978) 21,29-39

Iron Kinetics and Erythropoiesis in Fanconi’s Anaemia

G. BAROSI,~ M. CAZZOLA,~ A. MARC HI,^ S. MORANDI,’ V. PERANI,’

M. STEFANELLI~ & S. PERUGINI~

1 Clinica Medica I ‘A. Ferrata’, 2 Istituto di Patologia Medica I , 3 Clinica Pediatrica and

4 lstituto di Elettronica, University of Pavia, Italy

Ferrokinetic studies were carried out in 4 patients with Fanconi‘s anaemia (FA). Experimental data were analysed by means of a mathematical model of iron kinetics in order to obtain a quantitative assessment of effective and ineffective erythmpoietic activity, mean red cell lifespan, and nan-erythroid iron turnover. The major patho- genetic mechanism of the anaemia appeared to be relative marrow failure, i.e. a reduction in the proliferative capacity of the erythroid marrow. The role of in- effective erythropoiesis was of minor importance. On the basis of the results obtained both the pathogenesis and the natural course of the disease are discussed.

Key words: aplastic anaemia - erythropoiesis - Fanconi’s anaemia - ferrokinetics - iron kinetics - mathematical models

Accepted for publication March 16, 1978

Correspondence to: Dr. G. Barosi, Clinica Medica I ‘A. Ferrata’, Policlinico S. Matt-, 27100 Pavia, Italy

Since the original description in 3 brothers by Fanconi (1927), about 300 cases of this constitutional pancytopenia associated with congenital abnormalities have been reported (Nilsson 1960, Gmyrek & Syllm-Rapoport 1964, Storti & Perugini 1969, Beard et a1 1973, Beard 1976). The most prominent characteristic of the disease seems to be wide variation in the haematological find- ings (Fanconi 1964, 1967). Undoubtedly, marrow hypoplasia is the most frequent feature and the anaemia is generally con- sidered to be of aregenerative type (Beard

et a1 1973). On the other hand, isotope methods revealed various degrees of in- effective erythropoiesis (Debray & Najean 1959, Sjolin & Wranne 1962, Storti & Perugini 1969) and hyperhaemolysis (Ber- nard et a1 1958, Fanconi 1964, Vaccaro et a1 1966, Storti & Perugini 1969, Beard et a1 1973). In some cases, increased red cell breakdown was considered to be the major factor responsible for anaemia (Ber- nard et a1 1958, Vaccaro et a1 1966).

The differences in erythrokinetic features have been attributed to the variability of the

Page 2: Iron Kinetics and Erythropoiesis in Fanconi's Anaemia

30 BAROSI, CAZZOLA, MARCHI, MORANDI, PERANI et a1

a,, aa, - * . , 2 9

disease or to different stages (Fanconi 1967, Sjolin & Wranne 1962). At present, the erythropoietic defect in Fanconi's anaemia (FA) is not fully understood.

This paper reports ferrokinetic studies in 4 patients with FA. Experimental ferro- kinetic data were used for estimating the parameters of a mathematical model of iron kinetics (Barosi et a1 1976, 1978, Berzuini et a1 1978) which takes into account iron exchanges induced by cell death during maturation within the marrow and in cir- culating blood. In each case, effective and ineffective erythropoiesis, red cell lifespan and non-erythroid iron turnover were es- timated.

The results obtained allowed us to dis- cuss the pathogenesis of anaemia and its evolution in the natural cuurse of the dis- ease.

a- +

MATERIALS AND METHODS

Patients and controls

Our cases of FA are reported in chronological order, i.e. according to the dates when they were studied. Clinical and diagnostic information is

Nm-Erythroid Tiasues

summarized in Table 1. The diagnosis of FA was established on the basis of the criteria indicated by Fanconi (1964, 1967) and reviewed more re- cently by Beard (1976). Haematological data at the time of the ferrokinetic studies are reported in Table 2.

For a full assessment of the results obtained in the 4 patients with FA, we also present ferro- kinetic data for eight normal subjects and four patients with idiopathic acquired aplastic anae- mia. The normal subjects were medical students who presented a normal blood count and normal values for plasma iron and TIBC. They all gave their fully informed consent. The 4 patients with aplastic anaemia underwent clinical investigation. They had less than 25 % utilization of radioiron in the circulating red cells on the lOth-Uth d and could be considered therefore to be cases of severe marrow failure (Storti & Perugini 1969).

1 a ' a,,, -3

a% PI soma a72 - - 6 5 . a l l 1

Ferrokinetic studies

The ferrokinetic methodology employed has been described in detail in previous papers (Barosi et al 1W6,1978). Plasma and red cell radioactivity were determined by a method for liquid scintillation counting of 59Fe (Perugini et a1 1974). Samples were prepared using 1 ml of plasma and 0.2 ml of whole blood. The average background was 30 cpm and mean counting efficiency was about 85 % for plasma and 82 % for whole Mood sam- ples.

In 3 patients (Z.M., T.R., B.D.) the ferrokinetic

*

%a R BC

4

HCS

7 b

Figure 1. Iron kinetics model. RBC: red blood cell compartment. HCS: Hb catabolic system.

d(t; xsl -

Page 3: Iron Kinetics and Erythropoiesis in Fanconi's Anaemia

TABLE 1 Clinical features of the 4 patients with FA

Case 1. Z.M., M Case 3. T.R., F Case 4. B.D., M Case 2. C.E., M

Age at onset of

Age at diagnosis haematological symptoms

Diagnostic criteria 1. Type of cytopenia 2. Skin pigmentation 3. Associated defects

4. Stature 5. Familiarity 6. HbF 7. Chromatid breaks

Bone marrow at diagnosis

Age and clinical status at the time of the ferrokinetic study

Follow-up after diagnosis

5 yrs 5 yrs

pancytopenia increased not found

normal a sister with FA 6 %

29 %

increased cellularity, erythroid hyperplasia, megaloblastic features

7 yrs, during a phase of haematological improvement induced by testosterone

relapse at the age of 8 during androgen treatment; died of sepsis at the age of 10

7 Yrs 15 yrs

pancytopenia increased hypogenitalism

short absent 3.5 % 18 %

decreased cellularity

15 yrs, when the need for transfusions became great

died of cerebral haemor- rhage 3 months after the ferrokinetic test without any response to androgens

16 yrs 17 yrs

anaemia and neutropenia increased syndactily between the 2nd and 3rd toes

short a sister with FA 12 % 28 %

increased cellularity, erythroid hyperplasia, megaloblastic features

17 yrs, after two months of androgen treatment and no haematological improvement

no response to androgens; alive; at present, the need for transfusions is 4 units per month

7 yrs 7 yrs

pancytopenia increased hypoplasia of the first metacarpal bones short absent 10 % 19 76

increased cellularity, erythroid hyperplasia, megaloblastic features

7 yrs, at the time of diagnosis

good haematological improvement with testosterone; alive

Page 4: Iron Kinetics and Erythropoiesis in Fanconi's Anaemia

32

H b Wdl) Subjects

BAROSI, CAZZOLA, MARCHI, MORANDI, PERANI et a1

Un-

(pmoW

Retics Serum iron TIBC conjungate (109/1) (pmolfl) (LcmoW bilirubin

TABLE 2 Haematological data of the 4 patients with FA, of the patients with acquired aplastic

anaemia and of the 8 normal subjects

Mean value Range

15 56 20 62 9.9 14.2-15.6 44-71 14-25 55-69 8.4-12.0

* Transfused prior to study.

study was combined with the W r red cell sur- vival determination. Autologous red blood cells were labelled with 5lCr according t o the method A of the ICSH Panel (1971). The S9Fe and W r activities in blood were simultaneously measured using an original method based on liquid scintilla- tion counting (Cazzola et al 1976).

Ferrokinetic data were analysed according to the model of iron kinetics previously prmented by Barosi et a1 (1976, 1978). It consists of two main pathways, as shown in Figure 1: the ery- throid and the non-erythroid pathways. In the first pathway, iron enters the erythroblasts and either leaves the bone marrow in mature red cells or reaches the reticulo-endothelial system (RES) following the destruction of immature cells (in- effective erythropoiesis) .

Iron in circulating red blood cells (RBC) re- turns to the plasma as a result of haem catabolism in the RES. In the model shown in Figure 1, RES is represented as a distinct compartment referred to as the H b catabolic system (HCS). The non- erythroid pathway involves a storage compartment exchanging with the plasma through an inter- mediate one. This latter represents both the extra- vascular circulation and the tissue iron which exchanges rapidly with the plasma.

Some features of the model presented here deserve emphasis. Firstly, it is not assumed a

priori that iron leaving the marrow in mature red cells will not return to the plasma during the 14 d of the ferrokinetic study. Secondly, the dynamics of red blood cell production is de scribed by a two-compartment model with the aim of introducing a delay t o account for erythroid development. The subdivision of the erythroid compartment is merely functional. This lumped model of intramedullary matura- tion constitutes a first step towards the formula- tion of a distributed model, presented elsewhere (Colli Franzone et a1 1976), which seems to provide a more adequate description of the pro- cess. Finally, the dynamics of the HCS is de- scribed by a monocompartmental model under the assumption that reticuloendothelial cells in the marrow and in the spleen behave identically.

A mathematical analysis of the kinetic model shwon in Figure 1 is given in the Appendix. The parameters of the model were estimated by minimizing a suitable function of the difference between model prediction and experimental data. In the present approach, both plasma and red cell activity measurements were used. The numerical minimization procedure (Berzuini et al 1978) was implemented on a Honeywell 6030 computer.

From a clinical point of view, the behaviour of internal iron exchanges at the steady state is of great interest. Thus, assuming that the same

Page 5: Iron Kinetics and Erythropoiesis in Fanconi's Anaemia

ERYTHROPOIESIS IN FANCONI'S ANAEMIA 33

model is suited for describing both iron metab- olism and radioiron kinetics and that the frac- tional rate coefficients ai, (see Figure 1) have the same values for labelled and unlabelled iron, the size Xi of the i-th compartment can be evaluated (see Appendix).

Consequently, the following ferrokinetic para- meters useful for diagnostic purposes can be cal- d a t e d (Barosi et a1 1976):

Plasma iron turnover (PIT) =

(MIT) = X, JcrnoVd

= a,, X, JcmoVd

= 82, XI - a,, X, JcrnoVd

+ a51) x X, JcmoVd , M~~~~~ iron

Red cell iron turnover (RCIT)

Ineffective red cell iron turnover (IIT)

10

d

1

0.1

1001 X a x

0 5 10 146

C. E. 1 I 1 1 I I 1 1 1 I l l 1 1

0 5 10 14

x a P

1

d

1 T.R. I B.D.

\

Figure 2. Plasma 59Fe clearance and red cell utilization curves in the 4 patients with FA. Dots are the experimental data and lines

o.O1! , I I I I I I , I I , o.O1 I I I I , I I , represent model prediction. 14 Shaded areas are the normal 0 5 10 , l 4 0 5

ranges. Time in days

Scand J Haematol (1978) 21 3

Page 6: Iron Kinetics and Erythropoiesis in Fanconi's Anaemia

34 BAROSI, CAZZOLA, MARCHI, MORANDI, PERANI et a1

This quantity may be more conveniently expressed as a percentage of MIT

ZIT % = [l - (a4, X, / %, X,)] x 100 Daily haemoglobin synthesis (DHS) = a4, X, / 62 g/d given that 1 g of haemoglobin contains 62 pmol of iron.

'

Mean red cell lifespan (MRCL) = (RCV x MCHC x 62) / (aa3 X3) d where RCV is the red cell vol- ume in dl and MCHC is the mean corpuscular haemoglobin concentration in g/dl.

Non-erythroid tissue iron turnover (NEIT) = as, X, pmoVd.

In order to compare data from different subjects, PIT, MIT, RCIT, IIT and NEIT are expressed as pmoY1 b l d d , and DHS is expressed as g/l b l d d .

RESULTS

The estimates of the clinically useful para- meters concerning the four patients with FA are reported in Table 3. The same table includes the results obtained in the eight normal subjects and in the four patients with severe acquired aplastic anaemia. Experimental data and model prediction concerning in vitro curves of patients with FA are shown in Figure 2.

Patients with FA cleared 59Fe from plas- ma more slowly than normal subjects. The red cell utilization curves showed time courses which were significantly different from patient to patient. The fraction of injected 59Fe accumulated in red cells at the end of the test ranged from 25 % to 75 %. Also the estimates of the clinically useful parameters obtained in the four pa- tients with FA showed wide variation. Therefore it seemed more convenient to present each case separately.

Only the patient C.E. exhibited a ferro- kinetic pattern typical of hypoplastic anae- mia. Although PIT was slightly greater than

the normal value, MIT and RCIT were clearly below the basal level. However, the calculated erythropoietic activity did not appear so strongly reduced as in the four patients with acquired aplastic anae- mia (Table 3).

Data collected in the remaining patients indicated that anaemia was not due to an absolute decrease in erythropoietic activity. In patient D.B., the red cell radioactivity increased rapidly up to the 6th day and thereafter maintained a roughly constant value (Figure 2). This suggested the pres- ence of a significant peripheral haemolysis, as confirmed by the value of MRCL com- puted from both ferrokinetic and W r data. In this case PIT was increased, while MIT and RCIT were nearly normal. Thus, anae- mia was probably due to an uncompensated peripheral haemolysis.

The same pathogenetic mechanism was also suggested by the results obtained in the patient T.R.

A consistent peripheral red cell break- down was found also in the case Z.M. However, this patient exhibited the greatest degree of both total and effective erythro- poietic activity. In fact, red cell utilization was the highest, and both MIT and RCIT were significantly increased (Table 3).

Ineffective erythropoiesis, as indicated by IIT, was somewhat increased in all patients with FA. However, in no case could it be considered the major factor in the produc- tion of the anaemia. This is clearly demon- strated by the data reported in Figure 3, which provides both actual and potential haemoglobin concentration for each patient according to Samson et a1 (1976). The potential Hb concentration is that which would have been achieved if the percent- age ineffective erythropoiesis had been nor- mal, i.e. 6 %. Figure 3 shows that in no

Page 7: Iron Kinetics and Erythropoiesis in Fanconi's Anaemia

TABLE 3 Estimates of clinically useful parameters in the 4 patients with FA

Values refemng to 4 patients with severe acquired aplastic anaemia and to 8 normal subjects are also included for a comparison

'Iasma iron

Subjects

Non- erythroid

iron turnover (pmovl b l d d )

. Daily Hb Mean red cell lifespan (dl synthesis

(e/l blood/d) Marrow iron turnover

SD 16 7 10 11 3 4 0.17 13 Range 99-143 1842 78-105 73-100 1-12 1-14 1.21-1.64 88-124

(pmol/l b l d d )

PIT I NEIT

* Transfused prior to study.

m P

X 3 MIT I RCIT I IIT I IIT% DHS 59Fe 1 W r

Page 8: Iron Kinetics and Erythropoiesis in Fanconi's Anaemia

36 BAROSI, CAZZOLA, MARCHI, MORANDI, PERANI et a1

patient with FA was the potential Hb level within the normal limits.

As regard the identification of the sites of red cell destruction, in the first three patients there was no specific localization. Only in the patient B.D. did both ferro- kinetic and W r measurements indicate a predominant splenic uptake.

Finally, in all patients NEIT was marked- ly greater than the normal value.

DISCUSSION

The 4 patients included in the present study represent well documented cases of FA on the basis of currently accepted diagnostic criteria (Fanconi 1967, Beard 1976). As shown in Table 1, in all of them panmyelo- pathy was associated with congenital abnor- malities and typical lymphocyte chromo- somal changes. In two patients the disease was also present in another member of the

The results presented here seem the sug- gest firstly, that the degree of erythropoietic activity is related to the natural course of

family.

Z.M. d - C.E. d' 0-0

T. R. 9 co

B.D. d c-0

I l l l l l l l l l l l l l l 4 6 8 10 12 14 16 18

Hb ( g m

Figure 3. Evaluation of the role of ineffective ery- thropoiesis. The potential Hb is that which would be achieved if the percentage of ineffective ery- thropoiesis was normal, i.e. 6 %. Actual Hb (0); potential Hb (0); the shaded area represents the normal range of Hb conc. * Transfused prior to study.

the disease. As a matter of fact, in the pa- tient C.E. the ferrokinetic study was per- formed just before death, after the disease had lasted 8 years, and an absolute de- crease in erythropoiesis was found. In the other cases, anaemia had lasted from 5 to 24 months at the time of the study and erythropoiesis was found to be at or above the basal level. The above suggestion is confirmed by the time course of the mar- row picture in the first three patients. Ac- tually, at the onset of cytopenia, anaemia was mild and the bone marrow appeared hypercellular. Later anaemia became more severe and the bone marrow hypoplastic. It must be considered that in the patient Z.M. erythropoietic activity was also in- fluenced by androgen treatment, since the ferrokinetic study was carried out during a phase of haematological response.

As regards the pathogenesis of the anae- mia, previous erythrokinetic studies have given conflicting results (Bernard et a1 1958, Debray & Najean 1959, Sjolin & Wranne 1962, Vaccaro et a1 1966, Storti & Perugini 1969, Beard et a1 1973). A complex patho- genesis was suggested by Storti & Perugini (1969) and more recently by Najean (1976) who carried out ferrokinetic studies in about 20 patients with FA: a qualitative defect was always superimposed on the quanti- tative defect of the bone marrow.

In previous investigations, ferrokinetic data were analysed by means of the mono- compartmental model by Huff et a1 (1951). Effective and ineffective erythropoiesis were estimated only from plasma iron turnover and maximum red cell utilization of 59Fe. As clearly demonstrated by Ricketts et a1 (1977), such an approach does not permit one to obtain an adequate estimate of erythropoiesis and of its effectiveness, and offers a poor insight into the nature of a

Page 9: Iron Kinetics and Erythropoiesis in Fanconi's Anaemia

ERYTHROPOIESIS IN FANCONI’S ANAEMIA 37

patient’s haematological disease. The direct estimates of erythropoiesis ob-

tained in the present work indicate that the predominant erythrokinetic feature in the 4 patients with FA is ‘relative marrow failure’. This latter definition was introduced by Loeb et a1 (1953) and subsequently taken up by Finch et a1 (1970) to describe hypo- proliferative anaemia, i.e. a condition with a rate of erythropoiesis less than 2 times normal in the presence of a high plasma iron. The ferrokinetic parameters of the patients with FA reported in Table 3 il- lustrate clearly the concept of relative mar- row failure. In the 3 patients in steady state (Z.M., T.R., B.D.) MRCL was reduced to 40-60 % of the mean normal value. In order to compensate fully for such destruc- tion rates, red cell production would have to be increased to the same extent (Garby & Groth 1970). On the contrary, in the above patient MIT ranged from 1 to 1.8 times the mean normal value indicating a marked reduction in the proliferative capa- city of the erythroid marrow. In addition a slightly increased ineffective erythropoiesis contributed to the onset of the anaemia. The evolution of the disease seems to be a progressive worsening of the relative mar- row failure, marrow aplasia being the end- point. However, complete aplasia is un- common in FA, and the persistence of a residual erythropoietic activity even in the last phase of the disease seems to be a peculiar feature of FA (Najean 1976).

The pattern of relative marrow failure distinguishes FA from severe acquired aplastic anaemia which is characterized by an absolute marrow failure, documented by the data reported in Table 3. This considera- tion seems to indicate a difference in the pathogenesis in FA with respect to acquired aplastic anaemia; such a difference has been

suggested also by other investigations (Jal- bert et a1 1975). Erythroid and granulocyte colony data seem to suggest that in FA the defect is intrinsic to the haemopoietic stem cell (Iscove 1976). The ferrokinetic pattern of relative marrow failure is in agreement with a defect within the compartment of the proliferating cells. Besides defective proliferation there is also evidence of de- fective maturation. Whether these different features have a common genetic causation or whether they are a consequence of dif- ferent genetic defects is not clear. But in a disease like FA with mulitple chromosomal defects, an accumulation of errors is likely (Lajtha 1976).

APPENDIX

Non-steady state model: experimental stage

Let us denote by x,(t) the amount of radioiron in the i-th compartment at time t and by the fractional transfer coefficient between the j-th and i-th compartment. The flow d(t;x,) indicates the amount of radioiron fixed in the red cells taken up per unit time by the HCS.

Thus, according to the scheme shown in Fig- ure 1, the mathematical model of radioiron kinetics consists of the following system of integro-differential equations:

x1 = - (%1 + a5J x1 + a15x6 + alp7

xz = azlxl - (rsz + x3 = 832x2 - (a43 + a?,)

x4 = a43x3 - d(t;x,)

x2

(1)

x5 = a51x1 - (a15 + a65) x5 + a56x63

x,, = a85x5 - a56x6

x7 = a72x2 + a73x3 - a17x7 + d(t;x,)

The initial conditions representing the impulsive injection of radioiron into plasma at t = 0 are:

x1 (0) = 100, x, (0) = 0 i = 2, . . . . . , 7

Page 10: Iron Kinetics and Erythropoiesis in Fanconi's Anaemia

38 BAROSI, CAZZOLA, MARCHI, MORANDI, PERANI et a1

Moreover, since the flow of radioiron to the RBC compartment is given by a,,x, (t), d(t;x,) can be completely defined by introducing a red blood cell death probability function p(q) .

This function is such that &)dt gives the prob- ability that a red cell of age v will be taken up by HCS within the time interval dt. From p(a) one can derive the loss function g(a) which pro- vides the relative amount of red cells of age 7 entering HCS per unit of time. According to Bergner (1962) and Garby et a1 (1969), g(a) may be written:

g(v) = p(a) exp ( - iIp(Od6 1 hence: d(t;x,) = a,, !>, (t - a) g(v) da

In the present study, the function p(a) was de- fined as follows: p(q) = 0 for 0 < < 'lo and p(a ) = a for 11 > ao. The parameters yo and a were estimated from 5 1 C r survival data, as de- scribed in Berzuini et al (1978).

Steady state model: basal stage

The behaviour of internal iron exchanges in the steady state is defined by the algebric system which is obtained by setting the derivatives with respect to time xi (i = 2, 3, 5, 6, 7) equal to zero in (1).

Since plasma iron X, and RBC iron X, are directly measurable during the ferrokinetic study, the following relations provide an evaluation of the size of the remaining compartments:

Whenever a red cell death probability function p(q ) is known and assigned in the model, an es- timate of RBC iron is given by the following relation:

x, = ;a,&,

where = Vg(v) d s is the mean cell lifespan

derived from p(v ) (Bergner 1962). s,"

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