Original Article

European Journal of Clinical Nutrition (2012) 66, 481–487; doi:10.1038/ejcn.2011.169; published online 5 October 2011

Minerals, trace elements, vitamin D and bone health

A mathematical model for the hemoglobin response to iron intake, based on iron absorption measurements from habitually consumed Indian meals

P Thankachan1, S Kalasuramath1, A L Hill2, T Thomas1, K Bhat1 and A V Kurpad1

  1. 1Division of Nutrition, St John's Research Institute, St John's National Academy of Health Sciences, Bangalore, India
  2. 2Program in Biophysics and Harvard-MIT Division of Health Sciences and Technology, Harvard University, Cambridge, MA, USA

Correspondence: Dr P Thankachan, Division of Nutrition, St John's Research Institute, St John's National Academy of Health Sciences, Bangalore, Karnataka 560034, India. E-mail: prashanth@sjri.res.in

Received 18 February 2011; Revised 26 August 2011; Accepted 29 August 2011
Advance online publication 5 October 2011





The prevalence of iron deficiency (ID) and iron deficiency anemia (IDA) is high in India and appear unchanging over decades. To understand the persistence of these disorders, it is critical to measure iron (Fe) absorption from cereal-based Indian meals, its modulation by ID and the time-course of the response of hemoglobin (Hb) to Fe intake.



Fe absorption from rice-based meals was measured by the erythrocyte incorporation of the stable isotope label at 14 days in IDA (N=15) and Fe replete (IR) women (N=15). Hb level was used as surrogate for Fe status, and a response curve for Fe absorption versus the Hb level for a rice-based meal was constructed from measured data. This relationship was used as input for a mathematical model that examined the Hb response to different Fe intakes in normal and anemic women.



The mean fractional Fe absorption from a rice-based meal in IR and IDA women was 2.7% and 8.3%, respectively. The model predicted that Fe intakes between 20 and 55mg/day in low-bioavailability diets would result in stable, non-anemic levels of Hb in women over a 1-year period.



This mathematical model suggests that with a Fe intake of 20–30mg/day and a dietary bioavailability of 3–5%, Hb concentration would hover around 12g/dl with a variability of 0.5g/dl in pre-menopausal adult women.


anemia; iron deficiency; iron absorption; bioavailability; mathematical modeling; hemoglobin response



The high prevalence of iron deficiency anemia (IDA) in the Indian women has been resistant to change for decades (International Institute for Population Sciences 2006) despite programs to improve iron (Fe) intake. Multiple factors, including the continuing inadequate intake or low bioavailability of dietary Fe (Thankachan et al., 2007) and the presence of concurrent micronutrient deficiencies (Ahmed et al., 2005) and intestinal parasitic infections (Boccio, 2003), have been implicated in the continuing high prevalence of iron deficiency (ID) and IDA. Additional reasons may be poor compliance to long-term supplementation programs, along with logistic problems with the continuous supply of supplements.

Fe absorption is tightly regulated (Cook et al., 1974; Bezwoda et al., 1979; Taylor et al., 1988; Ganz 2005; Nemeth and Ganz 2006; Roe et al., 2009) by the Fe regulatory hormone hepcidin, which is feedback regulated by the plasma and liver Fe concentrations, and by the erythropoietic demand for Fe (Ganz 2005, 2011; Ganz and Nemeth 2006). Therefore, Fe absorption from the diet is dynamic, with several regulatory inputs. In India, diets are predominantly plant based with high phytic acid levels, which inhibit Fe absorption (Bothwell et al., 1989; Torre et al., 1991; FairweatherTait and Hurrell 1996). Even though acute studies show that Fe absorption increases about threefold in a Fe-depleted state (Thankachan et al., 2008), this may be temporary, as Fe absorption may be modulated downward in the long term, because of the different variables referred above. Therefore, although there have been many long-term studies of the effect of Fe fortification or supplementation, the impact on hemoglobin (Hb) levels cannot be predicted by simply considering the amount of Fe delivered into the intestine.

The dynamic nature of Fe absorption and erythropoiesis in response to Fe levels suggests that a mathematical model could give insight into Fe regulation. Because the measurement of Hb concentration is commonly used to assess the outcome following an intervention program in field settings, it is important to model the Hb response to a wide range of dietary Fe intakes. The hypothesis of this study was that as a result of the downregulation of Fe absorption at higher Hb levels, the modeled Hb concentration would take a long time to stabilize and would do so at potentially lower levels than anticipated. This is particularly important in the context of an inhibitory diet matrix. Further, the plateau value of Hb concentration with a range of dietary intakes is important from a public health viewpoint. If for example, for a range of normal dietary intakes, the modeled output plateaued near a Hb concentration of 12g/dl, then the assessment of anemia prevalence might become overly dependent on the analytical precision of the measurement of the Hb concentration.

Because the absorption of Fe from typical Indian diet matrixes and its response to ID are not known, this study first aimed to measure Fe absorption from a habitually consumed (vegetarian) Indian meal in both IR and IDA young women. Second, the study aimed to mathematically model the time trend of the Hb response to a range of Fe intakes for an inhibitory vegetarian Indian diet matrix, to provide a predictive tool for Fe fortification programs.


Subjects and methods

Subjects and protocol

A screening program to identify IDA and IR women was conducted in garment factories and a total of 334 women were screened. From this group, 15 IDA and 15 IR women were selected based on their blood biochemistry. Hb was measured in whole blood, whereas silver-blackened fibers (SF), zinc protoporphyrin, soluble transferrin receptor and C-reactive protein were measured in plasma samples. All assays were carried out along with the quality control material that was provided by the manufacturer. The criteria for the IDA group were Hb <12.0g/dl, SF <15μg/l and zinc protoporphyrin >40μmol/mol of heme or soluble transferrin receptor >8.5mg/l. Fe absorption from a commonly consumed South Indian vegetarian rice-based meal was tested in women aged 18–35 years, coming from low socioeconomic status. Women with an elevated serum C-reactive protein >10mg/l were excluded. All were in good health, non-pregnant/lactating and none had donated blood for 6 months before the study. Vitamin/mineral supplements, if any, were discontinued 2 weeks before the study. Written informed consent was obtained from all the women and the protocol was approved by the Ethical Committee of St John's Medical College, Bangalore, India.

The subjects were divided into two groups (IDA: A, and IR: B) with N=15 in each group. Subjects reported to the laboratory in the morning in a fasted state and a baseline blood sample was obtained. The preparation of the isotopic label was similar to that earlier described (Walczyk et al., 1997) and 3mg of 57FeSO4 was dispensed onto the surface of the test meal before consumption. This dose was based on the estimated amount of circulating Fe in the subjects, the expected range of fractional Fe absorption and the attainable precision of the isotopic analysis. Complete consumption of the meal and the isotope label was ensured. No food or fluids were allowed until 3h post-test meal administration. A venous blood sample was drawn on day 15 to measure Fe absorption, which was based on erythrocyte incorporation of the 57Fe isotope label. A minimum of 10 subjects per study group was required to obtain 80% power to detect a significant difference of 50% in Fe absorption between the two groups. To account for any loss to follow-up we added an additional five subjects per group.

Biochemical measurements and isotopic analysis

The Fe concentration and isotopic composition of the dose were determined using atomic absorption spectrometry (ICE 3500, Thermo, Bremen, Germany) and negative thermal ionization mass spectrometry (Triton, Thermo). Hb isotopic analysis was carried out by TIMS (Thermo) with a multicollector system for simultaneous ion beam detection. The precision of the system for isotopic ratios of interest was 0.01%. The amount of circulating label was calculated as the product of the shift in the Fe isotopic ratio and the amount of circulating Fe in the blood (Walczyk et al., 1997). Circulating Fe was calculated from blood volume and Hb concentration (Kastenmayer et al., 1994). Blood volume calculations were made from height- and weight-based prediction equations (Brown et al., 1962). For calculations of fractional Fe absorption, it was assumed that there was an 80% incorporation of absorbed Fe into Hb within red blood cells (RBCs).

Hb in whole blood was determined (ABX Pentra 60 c+, Montpellier, France) with three-level quality controls (Liquichek, Bio-Rad, Hercules, CA, USA). Plasma SF was measured by an electro-chemiluminescence immunoassay (Roche, Mannheim, Germany), and plasma soluble transferrin receptor was determined by enzyme-linked immunosorbent assay (Roche). Assays were calibrated using the standards provided by the manufacturer (Roche for soluble transferrin receptor and SF, WHO quality control for SF). C-reactive protein was measured in serum samples by a particle-enhanced turbidometric immunoassay (Roche). Zinc protoporphyrin was measured in washed erythrocytes (Aviv Biomedical, Lakewood, NJ, USA) and three-level control material provided by the manufacturer.

Fe absorption values were logarithmically transformed for statistical analysis and are presented as geometric means (−s.d.; +s.d.). Means were compared using the Student's t-test.

Model construction and calibration

Our model for Fe metabolism only explicitly tracks two compartments of Fe (Figure 1): the Fe bound to Hb in RBC (variable y), and ‘other body iron’ (OBI, variable x). For simplicity, we combined Fe stored in hepatocytes, Fe from recently degraded RBCs transported in macrophages, Fe in RBC precursors in the bone marrow, both free and transferrin-bound Fe in the plasma and Fe in myoglobin and enzymes together as a single OBI compartment. The model assumes that Fe enters the OBI compartment from the diet. The amount that enters is the product of the dietary intake ‘I’ and the fractional Fe absorption from the diet (absp(y)), which is determined by the current Hb levels (y) (Thankachan et al., 2008). Although Fe absorption may depend on PO2, Fe stores or inflammation (Fleming and Bacon, 2005), the model only measures absorption as a function of Hb, because this dependence was explicitly measured in this study. The absorbed Fe is then used in erythropoiesis, at a rate (eryth(y) x) dependant on the Hb levels (y) and iron stores (OBI, x). It is necessary that this transfer depends on the OBI (x); otherwise a decrease in Fe levels would not result in lower Hb levels until Fe stores were completely depleted, which is unrealistic. Fe from the RBCs is recycled back to the OBI compartment through the death of RBCs (d) (Shemin and Rittenberg, 1946). A constant amount of Fe is excreted from the system each day from the Hb compartment (time-averaged menstrual losses, (e1) and a constant amount is lost from the OBI compartment (other losses from skin, hair and so on, e2), and this is termed as obligatory or basal Fe loss, which cannot be regulated. This model is a simplified, integrated version of previously published work (Mylrea and Abbrecht, 1971; Franzone et al., 1982; Lao and Kamei, 2006). The corresponding differential equations are as following:

Figure 1.
Figure 1 - Unfortunately we are unable to provide accessible alternative text for this. If you require assistance to access this image, please contact help@nature.com or the author

Schematic representation of compartmental model of Fe regulation. Fe in hemoglobin (y) and in the rest of the body (OBI, (x)).

Full figure and legend (59K)

dx/dt=I absp(y)+dy–eryth(y)x–e2


Table 1 gives values used for the parameters and their sources, with detailed explanations of calibrations given in the Supplementary Information. Briefly, we defined ‘healthy’ Hb levels as 13g/dl (the approximate mean observed in IR subjects in the absorption study), which for a 55kg woman corresponds to 1.62g of Fe in Hb and 0.7g in the OBI (Hallberg, 1982). Both absp(y) and eryth(y) were found to have a negative relationship with y, increasing as Hb levels fall and vice versa. Logistic curves were used to capture the dynamic aspect of the rates, because both rates are expected to plateau at both maximum and minimum values, and to have a strong dependence on Hb levels for intermediate values (see Supplementary Figure 1). We took values obtained experimentally in this study, for Fe absorbed from an Indian rice-based diet. For other diets the values of normal, minimum and maximum absorption should be changed appropriately based on the bioavailability of the diet. The model was further calibrated against the observed recovery time of Hb after a normal donation of 10% blood volume (Franzone et al., 1982) (see Supplementary Figure 2).

Mathematical modeling of Hb response to Fe intake

Fe stores (and Hb levels) are said to be at a steady state when input and excretion are exactly balanced. Because excretion of Fe is constant, for a given input, balance is achieved when excretion is the product of Fe absorption and intake. Because absorption is regulated dynamically, Fe balance can be achieved at any intake, as long as the intake is not too low for the maximum absorption or too high for the minimum absorption. This makes Fe different from other nutrients, because a single recommended dietary allowance value, at which balance is achieved, is difficult to propose. The rate of transfer of Fe between compartments may change the time-course or distribution between compartments, but it will not change the value of the steady state Fe level, which depends only on the rates of excretion and absorption. For the healthy Hb value of 13g/dl, a dietary Fe absorption of 3% was used (based on absorption studies, see Supplementary Information), and therefore balance is achieved with a daily intake of 55mg/day Fe, which we will call the ‘daily requirement’ for this inhibitory diet in healthy women.

We used the model to assess the theoretical effect of a range of intakes of Fe in an initially healthy individual, as well as the effect of intervention of a range of Fe intakes in a chronically anemic subject. In addition, the effect of variability in the daily dietary Fe intake on Hb concentration was assessed by generating a set of daily Fe intakes over a year in an individual, using dietary recall data as a template in similar study populations (unpublished data). Simulated Fe daily intakes following a log-normal distribution (median 13mg/day) were randomly generated using the Monte Carlo technique and used as input into the model, to assess variability in the Hb response. All simulations were done in Matlab (R2009b, The MathWorks, Natick, MA, USA) and statistical analyses were performed with SPSS statistical software (version 13; SPSS Inc., Chicago, IL, USA).



Subject characteristics Fe status and absorption

Subject anthropometric and Fe status measurements are summarized in Table 2. In the rice-based meal study that assessed both IDA and IR status subjects, all Fe status indicators were significantly different between the groups (P<0.001). The test meals contained ~2–3mg of native non-heme Fe (Table 3). Fe absorption from the rice-based meals was 2.7% in IR subjects and 8.3% in IDA subjects. Fe absorption was significantly upregulated and about threefold higher in the IDA group (P<0.001).

Modeled Hb response to Fe intake and interventions with pre-existing low OBI

We first used the model to assess the effect of various daily Fe intake levels on the expected Hb level. All simulations were started with Hb levels at the healthy value of 13g/dl, and assumed, that the starting Fe bioavailability in the food matrix was very low, at 3%. Figure 2 shows that for intakes of above 55mg of Fe per day, Hb levels rapidly stabilize only slightly above the normal value of 13g/dl. For Fe intakes between 30 and 55mg/day, Hb levels will eventually stabilize between 12 and 13g/dl. It is critical to emphasize the extreme inhibitory nature of the diet at healthy Hb levels; if the bioavailability increased to 5% at the same Hb levels, the same Hb response as above could be reached at an intake of 20mg. For a narrow range of Fe intake between 8 and 20mg/day, Hb levels will eventually reach an anemic level, though it may take years to stabilize. For example, with a steady intake of 10mg of Fe per day, a previously normal woman would become stably anemic in about 5 years, with a steady state Hb between 10 and 11g/dl.

Figure 2.
Figure 2 - Unfortunately we are unable to provide accessible alternative text for this. If you require assistance to access this image, please contact help@nature.com or the author

Time-course of (a) Hb levels and (b) Fe in the rest of the body (OBI), with varying daily Fe intakes. Simulated individuals start with healthy Hb levels of 13g/dl (corresponding to a bioavailability of 3%).

Full figure and legend (74K)

We also used the model to examine the expected effect of Fe interventions on low total body Fe levels (Hb and OBI levels), used to represent a chronically anemic state. Interventions were modeled by fixing intakes at specific values (Figure 3). Typically, the diet of Indian women contains about 10mg of Fe per day (Thankachan et al., 2007); therefore in this simulation, an intake of 20mg of Fe per day, for example, would mean an intervention that delivered an additional 10mg of Fe per day, assuming that the bioavailability of the Fe salt in the intervention was the same as that of the Fe in the diet. If this were different, a theoretical adjustment correcting for the different bioavailability of the fortifying salt to the amount of Fe intake would be required for the correct intake. The response to this level of intake in an individual with chronic anemia resulting in 20% Hb depletion (with starting Hb of 10.5g/dl) would be modest, at about 0.9g/dl at 1 year, and in 6 months would only be about 75% of this response (Figure 3).

Figure 3.
Figure 3 - Unfortunately we are unable to provide accessible alternative text for this. If you require assistance to access this image, please contact help@nature.com or the author

Time-course of (a) Hb levels and (b) Fe in the rest of the body (OBI), predicted by the model, after applying interventions to individuals with depleted Hb levels. Interventions consist of various fixed Fe intake levels (10, 20 or 50mg/day). Individuals begin with total body Fe losses resulting in either 20 or 50% depletions in Hb from an initial value of 13g/dl, and corresponding steady state depletions in OBI from an initial value of 0.7g.

Full figure and legend (90K)

The model tested the variation of the Hb response to a simulation of varying (coefficient of variation (CV)=60%) dietary intakes of Fe over 365 days (median Fe intake: 13mg/day); with this intake the mean Hb response at a steady state was 11g/dl with an s.d. of 0.2g/dl. The reason for this small effect was a buffering effect of the OBI on the response of Hb to the variability in Fe intake. We also examined the expected effect of varying Fe intakes on a range of initial Hb levels (ranging from 10 to 16g/dl). As expected, the initial Hb level did not significant influence on the variability of the outcome of Hb levels at a steady state. All simulations assumed that the starting Fe bioavailability in the food matrix was very low, at 3%.



The average Fe absorption from habitually consumed rice meal was 8. 3% in IDA and 2.7% in IR women. However, the Fe absorption was high in comparison to an earlier study on habitually consumed Indian diets carried out in IR men (Narasinga Rao et al., 1983), probably because of the lower Fe requirements in men. Fe absorption in this study was threefold higher in the IDA group similar to what we have shown before (Thankachan et al., 2008), despite the non-neutral nature of the test meals, which had higher levels of spices and phytic acid. Several studies have shown an inverse relation between the body Fe stores and Fe absorption: that is, more Fe is absorbed in an ID state and less Fe is absorbed in an IR state (Bezwoda et al., 1979; Taylor et al., 1988; Hunt, 2003). It is important to recognize that the model output demonstrates that for Fe, even within a single type of diet, a range of intakes exist at which an optimal Hb is achieved, due to changes in Fe absorption. The daily requirement is presently calculated from a static bioavailability figure that only seeks to replenish daily Fe loss, with no regard to the outcome (Hb level) or to the Fe stores, which dynamically change bioavailability. Therefore, in IR women, it appears that over the long term, any Fe intake between 30 and 55mg/day (from non-heme sources, in a very inhibitory matrix) would result in a Hb level between 12 and 13g/dl; if this Hb level were considered acceptable, then this would ideally be the range of recommended dietary allowance for Fe in women for such a diet. If a point values were required, it would be the lowest value in this range. The proposed requirement in this example is high because Fe absorption was assumed to be very low (3%); if this were increased (for example, by dietary variation) to about 5%, a non-anemic Hb concentration would be achieved with a daily Fe intake range of 20–40mg. In the case of very inhibitory millet-based diets with a low Fe content, measures to enhance dietary Fe bioavailability or Fe fortification need to be considered. In fortification programs applied to women with mild anemia (Hb >10g/dl), it is also evident that 6-month long studies would only show 75% of the near-plateau modest effect that would be seen after 1 year.

The use of the model to simulate the Hb response to daily variation in dietary Fe intake was also instructive. For these diets, with daily Fe intake of 13mg varying by about 60% a plateau of Hb response was about 11±0.2g/dl. On the one hand, if Fe intakes were supplemented with, for example, an additional daily 15mg Fe (the intrinsic variability in Fe intake would be the same), the Hb concentration would plateau at about 12±0.2g/dl. On the other hand, increasing the bioavailability of the diet, without fortification, to about 6–7% through modifications such as fruit inclusion or spacing of tea intake, would have a similar response. It would seem a particularly unfortunate coincidence that the plateau of the Hb response in a pre-menopausal woman, to a range of daily Fe intakes (from 20 to 30mg) and a range of bioavailability (from 5 to 3%) in an inhibitory, cereal-based vegetarian food matrix, would hover between 11.6 and 12.4g/dl, or around the current anemia cutoff of 12g/dl. Measurement of the prevalence of anemia in such women would be very vulnerable to analytical accuracy and precision. However, from a physiological perspective this cutoff value of 12g/dl is in itself imprecise and may not be universally applicable to all populations. It is also relevant to consider the appropriateness of this cutoff for women who are sedentary or very active in whom the need for oxygen delivery would be very different. This model is also based on a small number of data points and has not yet been validated in field setting. Although the model is specific for pre-menopausal women, other factors such as inter-individual variability in Fe losses, reproductive factors, chronic inflammation (effect of hepcidin), genetics and the micronutrient/vitamin status have not been considered, because while these would right-shift either the Hb–Fe absorption curve and/or the Hb-erythropoiesis curve in this model, a numeric quantification of this shift is not available. Additionally, the model focuses on Hb concentration alone and may not be sensitive enough to model the effect of interventions in individuals with Fe deficiency alone.

In summary, the bioavailability of Fe from a standard Indian rice-based diet is low in IR women, but upregulated considerably in IDA. The mathematical model based on these values suggests that there is a range of Fe intake, between 20 and 55mg/day that will result in stable and optimal levels of Hb in women eating Indian diets with bioavailability ranging from 3 to 5%. Interventions with Fe in IDA could take 1 year to show stable effects.


Conflict of interest

AVK is a member of the Kraft Health and Wellness Advisory Board; the other authors declare no conflict of interest.



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This study was supported by the Department of Biotechnology, Government of India. ALH was supported by the Harvard Nutrition and Global Health Program. We thank Shanthi Chellan, Charles Milton, Grace, Sunil, Stella, Leena Sebastian and Kiran Babu for their assistance in screening, biochemical analysis, sample preparation and TIMS measurements. We are most grateful to the management and employees of Sun & Ski Garment factory, Bangalore for their keen interest, participation and support during the study.

Supplementary Information accompanies the paper on European Journal of Clinical Nutrition website

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