Physiological and pathological population dynamics of circulating human red blood cells

Abstract

The systems controlling the number, size, and hemoglobin concentrations of populations of human red blood cells (RBCs), and their dysregulation in anemia, are poorly understood. After release from the bone marrow, RBCs undergo reduction in both volume and total hemoglobin content by an unknown mechanism [Lew VL, et al. (1995) Blood 86:334-341; Waugh RE, et al. (1992) Blood 79:1351-1358]; after ∼120 d, responding to an unknown trigger, they are removed. We used theory from statistical physics and data from the hospital clinical laboratory [d'Onofrio G, et al. (1995) Blood 85:818-823] to develop a master equation model for RBC maturation and clearance. The model accurately identifies patients with anemia and distinguishes thalassemia-trait anemia from iron-deficiency anemia. Strikingly, it also identifies many pre-anemic patients several weeks before anemia becomes clinically detectable. More generally we illustrate how clinical laboratory data can be used to develop and to test a dynamic model of human pathophysiology with potential clinical utility.

Fig. 1.

Empirical measurement (A) and dynamic model (B) of coregulation of volume and hemoglobin of an average RBC in the peripheral circulation. The reticulocyte distribution is shown as blue iso-probability density contours and the population of all RBCs as red. The diagonal line projecting to the origin in A and B represents the average intracellular hemoglobin concentration (MCHC) in the population. An RBC located anywhere on this line will have an intracellular hemoglobin concentration equal to the MCHC. Fast dynamics (β) first reduce volume and hemoglobin for the typical large immature reticulocytes shown in the upper right of A and B. Slow dynamics (α) then reduce volume and hemoglobin along the MCHC line. Because biological processes are inherently noisy, we suggest that small random variations during the events required for reduction of volume and hemoglobin cause individual cellular hemoglobin concentrations to drift about the MCHC line, fluctuating with magnitude (D) around the MCHC line as shown in the Inset in B until reaching a critical volume (v_c in B) when cells are removed.

Fig. 2.

Boxplots of model parameters for 20 healthy individuals and patients with three forms of mild anemia: 11 with anemia of chronic disease (ACD), 33 with thalassemia trait (TT), and 27 with iron deficiency anemia (IDA). The upper and lower edges of each box are located at the 75th and 25th percentiles. The median is indicated by a horizontal red line. Vertical lines extend to data points whose distance from the box is <1.5 times the interquartile distance. More extreme data points are shown as red plus (+) symbols. The fast dynamics are characterized by β, the slow by α, random fluctuations by D, and the clearance threshold by .

Fig. 3.

Contour plots (A–C) of CBCs for a patient developing IDA after 4 mo. Each plot shows contours enclosing 35, 60, 75, and 85% of the probability density. The dashed line from the origin represents the MCHC. The short solid line perpendicular to the dashed line marks the position along the line corresponding to 85% of the mean projected cell. The circle shows the mean projection. A shows a normal CBC measured 116 d before the patient's presentation with iron deficiency anemia. The calculated P_0.85 (red area) is normal. B shows the normal CBC measured 65 d later and 51 d before detection of iron deficiency anemia. P_0.85 is abnormal even though the CBC is normal. C shows the CBC at the time IDA was diagnosed. D shows boxplots of P_0.85 for 20 normal CBCs from patients with a second normal CBC within 90 d and 20 normal CBCs from patients who were diagnosed with IDA up to 90 d later. P_0.85 successfully predicts IDA up to 90 d earlier than is currently possible with a sensitivity of 75% and a specificity of 100%. See main text and Predicting Iron Deficiency Anemia in Materials and Methods for more detail.

Fig. 4.

Differentiating TT and IDA as causes of microcytic anemia. This boxplot shows the distributions of D_h for 5 training cases with TT, 5 training cases with IDA, 28 test cases with TT, and 22 test cases with IDA.

Fig. 5.

Schematic of the projected distance (Δ) used to calculate the probability of clearance as described in Eq. 3. The cell is projected onto the MCHC line, and the probability of clearance is a function of the distance from the projected point to a threshold () along this line.

Fig. 6.

Comparison of fitted (red) and empirical (blue) steady-state joint volume–hemoglobin content probability distributions for a healthy individual. (Upper) The view projected on a vertical plane through the MCHC line (Fig. 1). (Lower) Ninety degree rotated view looking toward the origin.

Fig. 7.

Histograms of optimized parameter values from >200 separate simulations and the goodness of fit as determined by a sum of squared residuals objective function. Smaller values of the objective function signify a better fit. All parameters have well-defined optimal neighborhoods. See Eq. 5 for objective function.

Fig. 8.

Identifying a threshold for latent IDA. This boxplot shows the distributions of P_0.85 for the steady-state healthy and IDA patients shown in Fig. 2. On the basis of these results, we picked a threshold value for P_0.85 of 0.121 to use in a test of an independent set of patients shown in Fig. 3.