A Mass Balance-Based Semiparametric Approach to Evaluate Neonatal Erythropoiesis

Abstract

Postnatal hemoglobin (Hb) production in anemic preterm infants is determined by several factors including the endogenous erythropoietin levels, allogeneic RBC transfusions administered to treat anemia, and developmental age. As a result, their postnatal Hb production rate can vary considerably. This work introduces a novel Hb mass balance-based semiparametric approach that utilizes infant blood concentrations of Hb from the first 30 postnatal days to estimate the amount of Hb produced and the erythropoiesis rate in newborn infants. The proposed method has the advantage of not relying on specific structural pharmacodynamic model assumptions to describe the Hb production, but instead utilizes simple mass balance principles and nonparametric regression analysis. The developed method was applied to the Hb data from 79 critically ill anemic very low birth weight preterm infants to evaluate the dynamic changes in erythropoiesis during the first month of life and to determine the inter-subject variability in Hb production. The estimated mean (±SD) cumulative amount of Hb produced by the infants over the first month of life was 6.6 ± 3.4 g (mean body weight, 0.768 kg), and the mean estimated body weight-scaled Hb production rate over the same period was 0.23 ± 0.12 g/day/kg. A significant positive correlation was observed between infant gestational age and the mean body weight-scaled Hb production rate over the first month of life (P < 0.05). We conclude that the proposed mathematical approach and its implementation provide a flexible framework to evaluate postnatal erythropoiesis in newborn infants.

Keywords: anemic preterm infants; neonatal erythropoiesis; pharmacodynamic; postnatal hemoglobin production; very low birth weight.

Fig. 1

Hb amount present in the circulation of a representative infant during the first month of life. The individual data shown (+) represent Hb _T(t), the total amount of Hb present in infant circulation at any time during the first month of life (Eq.1). The solid line represents Hb _B(t) + Hb _TR(t), the sum of transfused Hb and the Hb produced in utero prior to birth and remaining in the infant’s circulation following birth after accounting for phlebotomy loss. The solid line represents a prediction and is not a model fit. The difference between the solid line and the data points (+) represent Hb _P(t), the amount of Hb produced by the infant at that time before accounting for phlebotomy loss

Fig. 2

Iman Conover nonparametric regression fit and subsequent cubic spline fit to infant Hb data. The amount of Hb produced during the first month of life (Hb _P(t)) was estimated using Eq. 12. a These data were then fit with the Iman Conover nonparametric regression. The solid line represents the regression fit to the calculated Hb _P(t) data (+). b The final predicted cumulative Hb amounts (+) were then fit with a nonparametric cubic smoothing spline function (solid line)

Fig. 3

a–d Dynamic change in postnatal Hb production during the first month of life for four representative subjects. The solid line represents the cubic smoothing spline fit to the estimated cumulative Hb produced (+). The other solid line represents the dynamic changes in body weight-scaled Hb production rate during the first month of life

Fig. 4

Influence of GA on the postnatal Hb production. The individual data points represent the estimated body weight-scaled postnatal Hb production rate over the first week of life vs. the GA for the 79 VLBW and ELBW anemic preterm study infants