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Review Article

Predicting Plasma Free Hemoglobin Levels in Patients Due to Medical Device–Related Hemolysis

Saylor, David M.*; Buehler, Paul W.; Brown, Ronald P.*; Malinauskas, Richard A.*

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doi: 10.1097/MAT.0000000000000801
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Damage to red blood cells (RBCs) can occur during blood passage through medical devices. Red blood cell damage results in intravascular hemolysis leading to increased levels of plasma free hemoglobin (pfH) and the depletion of plasma haptoglobin (Hpt), the putative pfH binding, and clearance protein.1 Intracellular hemoglobin has a tetrameric configuration, but pfH readily dimerizes and interacts with Hpt to form a stabile complex that is cleared from circulation after binding to CD163 receptors on the surface of liver and spleen resident macrophages.2 After binding to the cells, pfH is internalized and degraded within macrophage lysosomes, where heme is converted to bilirubin, carbon monoxide, and iron by the heme oxygenase system; iron is then stored in complex with ferritin until it is required for erythropoiesis.3,4 Critical to the overall system is that pfH (normally at a concentration <5 mg/dl) does not exceed the normal range of Hpt (30–200 mg/dl) found in human plasma.5 However, when the net balance of pfH exceeds Hpt, either adverse events or worsening of existing disease can occur.6,7 The pathophysiology induced by unbound pfH involves direct effects on the vascular endothelium causing a depletion of nitric oxide and subsequent vasoconstriction, extravasation into tissue sites causing localized cellular injury, and clearance through the glomerular filtration systems of the kidneys leading to both glomerular and renal tubule injury associated with hemoglobinuria.8,9

Medical devices associated with the risk of hemolysis include mechanical heart valves and ventricular assist devices (VADs), as well as those used in cardiopulmonary bypass (CPB), extracorporeal membrane oxygenation (ECMO), and continuous renal replacement therapy (CRRT).10–12 Each can cause differing levels of pfH in patients over time depending on the exposure of circulating RBCs to fluid shearing forces and artificial surfaces, and duration of device use. Understanding the extent of RBC damage caused by new devices is one important determinant in assessing safety before clinical use. This includes the evaluation of the hemolytic potential of blood contacting devices by dynamic benchtop testing, followed by animal and clinical studies for critical life-sustaining devices.13,14 Benchtop testing is usually performed under worst-case simulated clinical use conditions using animal blood to compare RBC damage caused by new devices to previously approved or cleared predicate devices with acceptable clinical performance profiles. However, in vitro testing is limited to making relative device comparisons because varying blood conditions and test parameters (e.g., differences in RBC fragility between animals and humans, variability between blood donors, blood age, hematocrit and blood volume, plasma protein and lipid levels, pH, and glucose levels15) could affect the resulting absolute levels of hemolysis. Thus, it would be extremely beneficial to establish methods to extrapolate in vitro hemolysis device test results, and their experimental uncertainties, to patients so that insight into their clinical safety could be elucidated.

Development of a biokinetic model to complement benchtop hemolysis test results could provide safety information over the course of device use by estimating the clinical balance between pfH generation and Hpt availability, and relating the results to adverse patient events. To this end, we have formulated a biokinetic model for pfH in patients experiencing device-related hemolysis. Clinical data on pfH generation and Hpt depletion/repletion rates occurring during and after CPB were used to establish and test the model parameters before applying them to the evaluation of short-term (72 hour duration) RBC damage caused by circulatory assist device systems. The model was then used to examine three proposed acceptance threshold rates of hemolysis (or pfH values) that appear in the medical literature for VAD blood pumps.16–18 As predictions of pfH levels are directly dependent on individual patient parameters (i.e., pump flow rate and plasma volume [PV]), a scaling analysis was applied to the model predictions to provide insight into the hemolysis levels that could occur in VAD patients over the weight range of 5 kg (neonates) to 110 kg (adults).

Materials and Methods

Biokinetic Model Formulation

To develop the biokinetic model, we start by considering not only the amount of pfH present in plasma but also the presence of Hpt and the binding reaction to form the pfH–Hpt complex. To simplify the notation for the model derivation, we refer to pfH and Hpt as compounds A and B, respectively, and provide a List of Defined Model Symbols in the Appendix. To account for normal physiologic kinetics of the two compounds in the absence of device-related hemolysis, the model assumes zero order generation () and first order elimination ( and for pfH and Hpt, respectively, as well as first order elimination of the pfH–Hpt complex (). To model the binding reaction, we first note that the Hpt protein can be present in different oligomeric configurations19 and at different concentrations across the general population (Hpt 1-1, 2-1, and 2-2). Similar to hemoglobin, Hpt is a tetramer composed of two alpha and two beta components. Irrespective of the Hpt phenotype, each Hpt beta globin chain contains one site that binds with one pfH dimer after dissociation of the pfH tetramer. For simplicity, we consider that tetrameric pfH (64.5 kDa) binds on a 1:1 molar basis with Hpt (phenotype 1-1), which has a characteristic molecular mass (86 kDa). This implies that, on a mass basis, the binding ratio between pfH and Hpt, , is about 0.75, based on the weight of the respective molecules. We assume that this binding ratio remains relatively constant for the larger oligomeric Hpt structures (phenotypes 2-1 and 2-2) with a proportional increase in the number of beta globin chains, and therefore binding sites for the pfH dimers, with molecular weight. Hence, although the model was parameterized based on Hpt 1-1, it should also be valid for Hpt 2-1 and 2-2, based on molar concentration. These considerations lead to the one-compartment model as shown schematically in Figure 1. To account for blood damage caused by a medical device, we represent device hemolysis with a zero order pfH generation rate, , which is also shown in Figure 1.

Figure 1.
Figure 1.:
Schematic of the biokinetic model for plasma free hemoglobin generated by hemolysis due to a medical device. The model considers the presence of plasma free hemoglobin (A), haptoglobin (B), and the binding reaction to form the AB complex. Zero order rates (, , and ) are postulated for the intrinsic and device related synthesis of A and B, whereas the elimination rates (, , ) of all three species are assumed to be first order. , first order elimination rate of plasma free hemoglobin; , first order elimination rate of plasma haptoglobin; , first order elimination rate of plasma free hemoglobin–plasma haptoglobin complex; , zero order generation rate of plasma free hemoglobin; , zero order generation rate of plasma haptoglobin; and , zero order hemolysis rate due to a medical device.

As posed, the model depicted in Figure 1 results in three independent equations describing the time dependence of pfH, Hpt, and the pfH–Hpt complex. However, we can simplify the model dramatically by recognizing that the binding reaction is fast relative to the other rates in the model. The pfH–Hpt complex is considered to be one of the strongest molecular interactions in nature, with an equilibrium constant of M,20 and studies have shown that the reaction occurs at a timescale on the order of seconds.21 Thus, binding will be effectively instantaneous compared to the timescales of interest and completely consume the minority species. By assuming the binding reaction is at all times in equilibrium, the number of independent governing equations is reduced to two. To be consistent with quantities that are typically measured and reported in patients, we have elected to express these two remaining equations in terms of the total plasma mass concentration of pfH, , and Hpt, , where and and denote the mass concentrations and molecular weight of the individual chemical species, respectively. Next, we recognize that the vanishingly small equilibrium constant implies that if , then , , and . Under this condition, the governing equations can therefore be written as follows:

where . If we impose the initial conditions and , the system can be solved analytically, which yields

The governing equations in Equations 3 and 4 can be applied to situations where hemolysis is not substantial enough for the amount of pfH to exceed Hpt. However, if pfH exceeds Hpt on a molar basis (), then , , and , which leads to

If we again impose the same initial conditions, the resulting solution is of the form:

With Equations 3, 4, 7, and 8, we have relationships between the model parameters and and as a function of time. By solving these sets of equations in a piecewise manner, one can predict the evolution of the levels of pfH and Hpt in plasma both during and after cessation of hemolysis.

Biokinetic Parameters

To establish the model parameters, we first recognize that, in the absence of device-related hemolysis, the steady-state solutions to Equations 1 and 2 provide two relations between the five biokinetic model rate parameters and baseline values of pfH, , and Hpt, . Thus, we can reduce the number of unknown, independent biokinetic parameters by specifying these baseline values. Here, we have elected to express the zero order synthesis rates in terms of the three elimination parameters and the baseline values, i.e., and . Thus, by specifying and values, which are readily measurable quantities, only three unknown biokinetic parameters (i.e., kA, kB, kAB) remain. Throughout this manuscript, we assume constant elimination rate values () for all patients. This implies that any difference in baseline values among patients is solely because of changes in pfH and Hpt generation, and not elimination. The validity of this assumption is addressed later in the Discussion section. Further, unless otherwise noted, we assume mg/dl and mg/dl, the median values of the reported reference ranges of pfH and Hpt for adults, which have been identified as 1–4 mg/dl22 and 30–200 mg/dl,5 respectively.

To specify the remaining three biokinetic model parameters, , where indicates A, B, or the AB complex, we focus on two separate studies that have characterized the evolution of pfH and Hpt in humans after the introduction of excess free hemoglobin into plasma either after open heart surgery with extracorporeal circulation23 or by direct infusion,24 respectively. It should be noted that pfH values reported clinically are measurements of the sum of the unbound and Hpt-bound amounts of plasma hemoglobin. In Andersen et al.,23 the decay in pfH after CPB surgery was reported for two groups of patients. In the first group (identified as group I), the pfH levels did not exceed the binding capacity of Hpt, i.e., . These data, which represent the average of 18 patients, are indicated by red circles in Figure 2A. In the second group of nine patients (group II), pfH levels exceeding the binding capacity of Hpt were reported. These data are shown as blue circles in Figure 2A. Finally, Noyes and Garby24 reported Hpt levels up to 240 hours after direct infusion of pfH in six subjects. The data, representing the average of the six subjects, are shown as blue circles in Figure 2B. Because only normalized Hpt values were provided, we have scaled the reported values such that the observed asymptote after Hpt has replenished for hours corresponds to the baseline value . To solve for the unknown biokinetic model parameters, , we regressed the model in Equations 3, 4, 7, and 8 to all three of these data sets simultaneously. For the patients in group I of the Andersen et al.23 study, pfH was at all times less than Hpt and the observations were made after the patients were removed from extracorporeal circulation; thus, the biokinetic model would predict that the evolution of pfH should follow Equation 3 with . Initially for group II, , however as time progresses the pfH levels decay toward baseline, . Therefore, in this case, we solve Equations 3 and 7 in a piecewise manner, again with . Moreover, to establish when the transition occurs (i.e., ), is computed simultaneously. This requires both and to be specified. While is given by the data, Hpt levels for these postsurgical patients were not reported. However, in other studies of patients undergoing CPB surgery with comparable pfH values, Hpt levels decreased by approximately 50% at the end of the procedure.8,25 Thus, we make the approximation . For the Noyes and Garby24 patients, again , and the same piecewise approach is adopted, except in this case the initial values were provided (). Using this approach, we find optimal values of , , and 1/h. The best-fit curves are provided in Figure 2 for reference. We note that while we assumed for the group II patients, the fit values are quite insensitive to this parameter, remaining unchanged within the uncertainty of the fit for . This is not surprising because the model regression determined that the elimination rates of the pfH–Hpt complex and unbound pfH were similar (), which makes Equations 3 and 7 virtually identical and independent of all Hpt-specific quantities (, , , and ). However, it is important to note that although the model and fit parameters imply that total pfH ( is not substantively impacted by the amount of Hpt () present, Hpt will still have a significant impact on the amount of unbound pfH (), which is the critical quantity when considering the propensity for adverse effects. At this point, all model parameters are specified, with the exception of , which will depend on the specific procedure and devices used. Further, the apparent agreement between the best-fit model equations and the data from these studies suggest that the model is adequately capturing the primary mechanisms of pfH and Hpt introduction and removal from plasma in these patients.

Figure 2.
Figure 2.:
Results of fitting the model equations to data reported by (A) Andersen et al. 23 and (B) Noyes and Garby24 to parameterize the biokinetic model. The data sets were fit simultaneously to determine , , and , assuming baseline mean values and mg/dl. Note that in A, patients had plasma free hemoglobin levels that did not exceed (group I) and did exceed (group II) the binding capacity of plasma haptoglobin. , baseline total plasma mass concentration of plasma free hemoglobin; , baseline total plasma mass concentration of plasma haptoglobin; , first order elimination rate of plasma free hemoglobin; , first order elimination rate of plasma haptoglobin; , first order elimination rate of plasma free hemoglobin–plasma haptoglobin complex.


Based on the calibration procedure provided above, all of the biokinetic parameters in the model were specified based on data in the absence of device-related hemolysis, i.e., . These baseline biokinetic parameters are summarized in Table 1. While these parameters serve as the basis for the analyses described in this section, and are, at times, varied to either account for observed differences in some patients or to probe the impact of the parameter. For clarity, the values of and used in each of the remaining figures in the manuscript are also provided in Table 1. Further, to relate the model device-related hemolysis rate to the commonly used normalized index of hemolysis (NIH) value, must be divided by a scaling parameter, the ratio of volumetric flow rate to PV. Therefore, we have also included the scaling ratio, which is a function of patient weight, and corresponding figure number in which it is used, in Table 1.

Table 1.
Table 1.:
Biokinetic and Scaling Parameters Used Throughout the Article

Hemolysis Rates

To further examine the validity of the model and to illustrate one of its potential applications, it was applied to predict hemolysis rates due to surgical procedures and medical devices in patients. The most detailed, simultaneous measurements of both pfH and Hpt levels available in the literature are two studies of patients undergoing CPB surgery8,25; thus, these studies will be the focus of our efforts here. In both studies, the concentrations of pfH and Hpt were determined at multiple time points during CPB and up to 48 hours after surgery. However, the postoperative time points of the measurements were not all explicitly provided. Therefore, for consistency with studies where these time points were identified, we have made the assumptions that blood sampling after arrival at the intensive care unit occurred 2 hours after cessation of CPB, and the postoperative day 1 and day 2 measurements were made 24 and 48 hours after the start of CPB.

In the study conducted by Billings et al.,25 60 patients primarily undergoing valvular surgery were divided evenly into two groups, in which one group received acetaminophen and the other a placebo drug. To avoid any impact of the effect of acetaminophen on the results, here we focus only on the 30 patients receiving the placebo (median CPB duration of 114 min). The mean values for pfH and Hpt are shown graphically as the blue points in Figure 3. Likewise, Windsant et al.8 evaluated 60 CPB patients comprised of two groups of 30 patients each. However, in this study, one group of patients underwent coronary artery bypass grafting (CABG, median CPB time of 68 min), whereas the other group had an additional complication of reconstruction or replacement of a valve (CABG + valve, median CPB time of 145 min). Hemodilution-corrected8 plasma concentrations of pfH and Hpt are shown as green (CABG + valve) and red (CABG) points in Figure 3, respectively. Note that the baseline values of both pfH and Hpt are markedly higher in both of these patient groups compared with median values of the normal adult reference ranges5,22 used to parameterize the model in the previous section. To accommodate for these deviations, we have set the baseline values for these two patient groups to the average of the presurgery observations, which yields mg/dl and mg/dl, and kept fixed at their previously specified values. Thus, the differences in baseline values between patient groups are assumed to be caused by changes in only basal pfH and Hpt generation, , and not elimination, . Again, the appropriateness of this assumption is addressed in the Discussion section.

Figure 3.
Figure 3.:
Results of applying the model to estimate hemolysis rates, , based on three distinct clinical data sets for patients undergoing cardiopulmonary bypass surgery.8,25 For each data set, the best fit value was determined by regressing the model equations to both (A) plasma free hemoglobin and (B) plasma haptoglobin levels when holding the previously specified biokinetic parameters fixed. Not only does the model exhibit consistency with the time dependence of both quantities in all three cases, but the fit procedure also illustrates the applicability of the model to estimate in vivo hemolysis rates from patient data. , zero order hemolysis rate due to a medical device.

For each of three patient groups described above, we determined a unique hemolysis rate, , during CPB. This was accomplished by determining the best-fit value based on regression of the data in each patient group to the governing equations. This approach resulted in best-fit values of , 54 ± 2, and mg/dl/h for the Billings, Windsant CABG + valve, and Windsant CABG data, respectively. Based on these values, we have plotted the model predicted pfH values in Figure 3A. The figure reveals that, during and after assumed CPB hemolysis generation, the data are well represented by the model, suggesting the assumption of constant is suitable for these studies. In addition to pfH levels, we can also compare the model predictions to the Hpt levels observed in these three studies, which are shown in Figure 3B. Inspection of the figure reveals that the model predictions are quantitatively consistent with the clinical Hpt measurements as well. While there are some discrepancies, these are not unreasonable given the variability in the clinical measurements (% coefficient of variation for the postoperative Hpt values exceeded 80% for the three clinical data sets8,25). It is interesting to note that the predicted hemolysis rates for the two patient groups in the Windsant et al.8 study are the same within the uncertainty of the fits. However, because the reported median CPB times for the CABG + valve patients (145 min) were more than two times longer than for the CABG patients (68 min), the maximum pfH levels scaled approximately in proportion to CPB time. Conversely, the hemolysis rate predicted for the Billings et al.25 patients was about 3.5 times the rates implied by the Windsant et al.8data, which resulted in significantly more hemolysis even though there was a comparable median CPB duration (114 min).

Hemolysis Limits

Another potential application of the model is to provide insight into hemolysis rates that may give rise to adverse effects because of unbound hemoglobin. Therefore, we have employed the model to predict a critical hemolysis rate, , for various conditions. The most straightforward way to define is as the hemolysis rate below which there is an absence of unbound hemoglobin, i.e., . The values associated with this limiting condition as a function of time are shown as the blue line in Figure 4 for the baseline mean values and mg/dl. The curve shows an initially rapid decay in of 87 mg/dl/h at 1 hour exposure time. By 72 hours, the value has decreased by a factor of about 40 as it approaches the eventual asymptote of 2.1 mg/dl/h. This implies that significantly lower hemolysis rates, i.e., nearly two orders of magnitude, are necessary for chronic medical devices to avoid the potential for adverse effects compared with acute applications when considering exposure duration alone. Although the model was parameterized and tested based on averaged patient data with baseline Hpt levels, , at or near the midpoint of the anticipated range, it is instructive to explore model extrapolations to the extrema of this range. Thus, we have also included the time-dependent values given Hpt levels, , of 30 and 200 mg/dl as the green and red curves, respectively, in Figure 4. Inspection of the figure reveals that these curves all exhibit the same time-dependent behavior and roughly scale in proportion with baseline Hpt level. Thus, the model predicts that the propensity for unbound pfH scales approximately with baseline Hpt, at least throughout the normal plasma concentration range.

Figure 4.
Figure 4.:
Critical hemolysis rates, , defined by model predictions when the amount of plasma free hemoglobin exactly equals the amount of plasma haptoglobin, i.e., . The impact of baseline plasma haptoglobin level, , is also shown for fixed mg/dl. The corresponding NIH values, assuming an 80 kg man, are given on the secondary y axis, with the conversion calculation described in the text. For reference, three proposed critical threshold rates for chronic hemolysis for blood pumps from the literature are indicated by I,16 II,17 and III.18 , baseline total plasma mass concentration of plasma free hemoglobin; , baseline total plasma mass concentration of plasma haptoglobin; NIH, normalized index of hemolysis; , critical device hemolysis rate where total plasma free hemoglobin equals the binding capacity of plasma haptoglobin, i.e., .

For chronic blood pumps, a few criteria have been proposed as hemolysis threshold values in the medical literature. These are defined in terms of the NIH16,18 value or by in vivo pfH levels ().17 Historically, the NIH calculation was derived to compare hemolysis rates in devices during in vitro testing by normalizing for differences in flow rate, test circuit blood volume, hematocrit, and test duration.15 The NIH value, in units of g/100 L, represents the mass of hemoglobin released from damaged RBCs per 100 L of blood flowing through the device. To make a direct comparison between the model predictions and the suggested hemolysis limits from the literature, we have provided the NIH estimates for a typical 80 kg man that correspond to the values in Figure 4. To calculate an in vivo NIH value for patients, must be divided by the ratio of pump flow rate to PV. A relative PV of 46.6 ml/kg was derived, based on the reported relative blood volume (71.1 ml/kg) for adult males26 and assuming a hematocrit of 34.5%. The hematocrit was estimated from a median total hemoglobin value of 11.4 g/dl reported for a 3,894 patient cohort (more than 75% male with a median weight of 86 kg) from the Interagency Registry for Mechanically Assisted Circulatory Support (INTERMACS) database by Rossano et al.27 The flow rate for the pump was estimated by calculating the cardiac output (CO) for normal 80 kg adults (based on a weight-based CO of 65.9 ml/[min·kg]).28 Using these representative VAD patient values (i.e., 80 kg man with PV = 3.73 L and pump flow rate = 5.28 L/min), we can compare directly some of the proposed hemolysis criteria. Bernstein et al.16 suggested a biologic tolerance for pump-derived hemolysis in an adult male up to NIH = 0.1 g/100 L based on continuous infusions of free hemoglobin in dogs, whereas Nosé18 proposed NIH < 0.01 g/100 L as a design objective for chronic blood pumps when tested in vitro. These levels are shown as cases I and III, respectively, in Figure 4. To compare a limiting hemolysis value expressed in terms of pfH concentration, the INTERMACS17 threshold definition of hemolysis for circulatory assist devices, mg/dl after 72 hours postimplantation, was used in the model to compute a hemolysis rate, . The INTERMACS definition of hemolysis appears as case II in the figure and corresponds to a model-predicted value of NIH = 0.07 g/100 L for the 80 kg patient. We note that for a given , the choice of baseline Hpt level does not have a substantive impact on the total pfH, , at any time. Thus, the model predicts the hemolysis rate corresponding to the INTERMACS definition, which is based on the total pfH concentration (both bound and unbound pfH), will be insensitive to baseline Hpt level. However, the amount of unbound pfH, , will be strongly dependent on baseline Hpt.

In relation to the proposed chronic hemolysis limits for assist devices (Figure 4), the model predicts that unbound pfH would be present chronically in plasma for at least some patients if any of the three hemolysis limits is considered (I–III). For cases I and II, unbound pfH would be predicted chronically for all patients within the typical range of baseline Hpt levels, whereas criteria III would protect against unbound pfH for all patients except those with the lowest initial Hpt concentration near 30 mg/dl. However, the presence of unbound pfH does not necessarily imply that adverse effects will occur. In fact, clinical observations suggest that finite levels of unbound pfH can be tolerated without symptoms, at least for acute hemolysis. For example, Andersen et al.23 did not observe the onset of hemoglobin in urine (hemoglobinuria) until unbound pfH exceeded 35 mg/dl on average, and hemoglobinuria disappeared while substantial amounts of unbound pfH remained in the plasma (35–85 mg/dl). Also note that these unbound clinical pfH levels were likely under-reported because they were computed as the difference of total pfH and Hpt by weight without accounting for binding on a molar basis. Similarly, postoperative acute kidney injury (AKI) was observed in some CPB patients in both studies described in the previous section.8,25 However, these patients exhibited high pfH levels (with mean values exceeding 150 mg/dl) that were substantially greater than the available Hpt at the same time points, suggesting that significant amounts of unbound pfH existed in these patients as well. Thus, it is important to examine the implications of the model on not only the presence but also the extent of unbound pfH associated with the three proposed hemolysis acceptance criteria described above for chronic blood pumps.

Figure 5 depicts the predicted time dependence of both the total and unbound amounts of pfH, and , respectively, for all three hemolysis criteria (I–III) and for different baseline Hpt levels, , in an 80 kg patient. Again, the total pfH level (i.e.) is insensitive to choice of in the normal range, so only a single curve is shown for each case. The plot shown in Figure 5 for case I, the least conservative criteria (NIH = 0.1 g/100 L), illustrates that the model predicts the steady state levels of pfH associated with this hemolysis rate are reached within a day or two and the amount of unbound pfH will typically fall in the range of 14–24 mg/dl chronically. Although clinical observations of adverse effects may not be encountered until the unbound pfH ≥ 35 mg/dl, these observations were made for acute CPB durations,23 and all three hemolysis criteria were proposed specifically for chronic exposure. In general, the extent and timeframe of exposure to unbound hemoglobin that will give rise to adverse effects is not well established. Thus, a more conservative limit than case I (NIH = 0.1 g/100 L) may be warranted for long-term pump hemolysis. In support of this, the difference between the INTERMACS definitions of minor and major hemolysis for assist devices (case II) is based on whether there are any associated clinical symptoms when the pfH level exceeds 20 mg/dl after 72 hours,17 which suggests that this level of pfH, corresponding to NIH ≥ 0.07 g/100 L in adults, may be associated with adverse effects in some cases. It is interesting to note that model results for criteria III (NIH = 0.01 g/100 L) suggest that the presence of unbound pfH will be effectively negligible at all times, when assuming an 80 kg patient. In fact, the model predicts the amount of unbound pfH will not exceed about 1 mg/dl, even for the lowest baseline Hpt level considered, i.e., mg/dl. Therefore, based on the model, one would not anticipate a substantive probability for adverse effects to manifest in the adult patient population at this in vivo rate of hemolysis.

Figure 5.
Figure 5.:
Predicted total () and unbound () plasma free hemoglobin levels as a function of time for three different prescribed constant hemolysis rates, . The impact of baseline plasma haptoglobin level, , is also shown. The hemolysis rates I–III correspond to normalized index of hemolysis values of 0.1, 0.07, and 0.01 g/100 L, respectively. These proposed critical threshold rates for chronic hemolysis were derived from the literature, specifically I,16 II,17 and III.18 Conversions from normalized index of hemolysis to the corresponding values were conducted assuming an 80 kg man and are described in detail within the text. , total plasma mass concentration of plasma free hemoglobin; , baseline total plasma mass concentration of plasma haptoglobin; , plasma mass concentration of unbound plasma free hemoglobin; , zero order hemolysis rate due to a medical device.

Scaling Analysis

The previous sections have focused on adult patients for which the model was parameterized and applied. Although the model appeared to adequately capture the evolution of both pfH and Hpt observed in the clinical studies of adult patients undergoing CPB, it is unclear whether the biokinetic parameters would change over longer timeframes or for different patient populations. It is currently not possible to assess rigorously the potential dependencies of the biokinetic parameters on these factors based on available data. However, the conditions under which the model might be parameterized and applied can be expanded to different patients as the necessary clinical data (patient-specific values for pfH and Hpt as a function of time during and after hemolysis occurs) become available. For example, the model may be applicable to assess new circulatory assist devices that are under development for use in patients as small as 2–25 kg.29 Although the pfH and Hpt values have been reported in a limited number of studies on pediatric patients,30–32 the reliability of these data is questionable because of confounding factors during surgery and inconsistencies within and between studies. For example, Simpson et al.30 noted that the Hpt levels they observed may have been artificially high because of steroid administration and plasma priming of the pumps impacting Hpt levels. Further, although the time frame of pfH elimination after pediatric CPB in both the Simpson et al.30 and Mamikonian et al.31 studies was consistent with the observations in adults, the results reported by Ricci et al.32 suggest a much slower elimination of pfH in pediatric patients.

With these caveats in mind, it is possible to explore the potential impact of patient weight on pfH levels and hemolysis rates in terms of the NIH index using only simple scaling arguments, assuming the biokinetic parameters, including baseline levels, remain unchanged. Specifically, for a given NIH value, the corresponding is obtained using the ratio of pump flow rate to PV for different patients (Table 1). The model can then be used to predict pfH levels over time based on . For adults, the assumed dependence of pump flow rate and PV on patient weight was described previously. For pediatric patients, we analogously estimate that pump flow rate is equivalent to CO as defined by a weight-based allometric relation for normal children and adolescents over the weight range of 10–25 kg (Table 1).28 Because of the paucity of data for subjects below 10 kg in weight,28 a direct estimate of CO per body weight (CO/BW = 240 ± 45 ml/[min·kg]) for a 5 kg patient was obtained by interpolating data from multiple studies.28,33–37 A relative PV of 51.4 ml/kg was assumed for pediatric subjects in the range of 5–25 kg, based on a reported relative blood volume of 78.5 ml/kg38 and the same 34.5% hematocrit level as used for adults. The latter is supported by similar baseline median total hemoglobin concentrations reported in pediatric (PediMACS) and adult (INTERMACS) patients (11.5 and 11.4 g/dl, respectively) for time-matched cohorts with continuous-flow VADs.27

Based on these patient parameters, we used the model to predict pfH levels at 72 hours after device implantation over a range of in vivo–based NIH values for select pediatric (5, 10, 25 kg) and adult (50, 80, 110 kg) patients (Figure 6). For adults, the pfH values increased linearly with NIH and were contained within a relatively narrow band over the twofold weight range. However, as the relative weight range was fivefold for the pediatric subjects, the predicted pfH concentrations for these patients covered a much wider range, and they were markedly greater than for the adults at the same NIH values. This was because of the significantly higher assumed pump flow rates for pediatric patients relative to their PVs, which resulted in a faster accumulation of free hemoglobin. For example, the ratios of pump output to PV (PO/PV) for a 10 and 80 kg patient are 261 and 85 (ml/h/[ml plasma]), respectively. This results in a nearly threefold predicted increase in pfH levels for 10 kg pediatric patients compared with 80 kg adults at the same NIH hemolysis values.

Figure 6.
Figure 6.:
Relationship between in vivo NIH rate of hemolysis and pfH levels after 72 hours of exposure inferred from simple scaling arguments for two different patient populations: pediatrics (red, 5–25 kg body weight) and adults (blue, 50–110 kg). The filled regions are bounded by patient weights corresponding to the estimated limiting values of the ratio of pump output (ml/h) to plasma volume (ml) in parentheses for each population. Further, characteristic values for 10 kg infants and 80 kg adults are provided and indicated by the solid lines. For reference, previous and current INTERMACS criteria for hemolysis are also shown on the plot. INTERMACS, Interagency Registry for Mechanically Assisted Circulatory Support; NIH, normalized index of hemolysis; pfH, plasma free hemoglobin.

To put the implications of this scaling into a clinical context, we have included two pfH hemolysis criteria that have been used in adverse patient event definitions for circulatory support devices in Figure 6 for reference. The first clinical hemolysis definition (pfH > 40 mg/dl) dates back to at least 1988,39 was referenced by the blood pump community as they began to formalize VAD clinical trial design in 1998,40 and is still used by some today.41 The INTERMACS device registry42 originated in 2005 and expanded on the definition to include pfH > 40 mg/dl in association with clinical signs related to hemolysis (e.g., drop in hematocrit, hyperbilirubinemia) occurring after the first 72 hours postimplant.12 Clinical studies from 2014 reported that continuous-flow rotary blood pump patients included in this INTERMACS hemolysis category had a significantly higher risk for death and pump thrombosis, and that the pfH > 40 mg/dl threshold was too high because it was not sufficiently sensitive to detect clinically important patient events at early time points.12,43 Subsequently, the INTERMACS and PediMACS adverse event definitions were revised and currently include a classification based on the plasma hemoglobin concentration (after 72 hours postimplant) for “minor hemolysis” (pfH > 20 mg/dl in the absence of clinical symptoms) and “major hemolysis” (pfH > 20 mg/dl associated with clinical symptoms, such as hemoglobinuria or anemia).17 The two defined pfH hemolysis thresholds, irrespective of whether clinical symptoms occur at these levels, are indicated in Figure 6. Inspection of the figure reveals that at in vivo NIH values less than 0.07 g/100 L, where the model predicts an 80 kg patient would not exceed either hemolysis threshold criteria, a 10 kg pediatric patient could have pfH levels up to 57 mg/dl under the assumed scaling, and exceed both hemolysis limits. Furthermore, the plot also illustrates that in vivo NIH values below 0.02 g/100 L may be necessary to prevent minor hemolysis using the current INTERMACS definition (pfH ≥ 20 mg/dl) in a 10 kg pediatric patient. Hence, the applied body weight scaling scheme suggests that NIH hemolysis limits for pediatric patients are weight dependent and should be about 2–4 times lower than for adults. However, the implications of the model for pediatric patients can only be more rigorously assessed when reliable data needed to parameterize and validate the model for this specific patient population become available.


As pfH can directly cause adverse patient events and act as a biomarker for damage to other blood elements (e.g., platelet activation and thrombosis), we have developed an in vivo biokinetic model for pfH and Hpt that accounts for not only the generation, elimination, and complexation of these biomolecules but also for medical device–related hemolysis. Because the complexation of pfH and Hpt is rapid with a negligible equilibrium constant, it was possible to reduce the complexity of governing equations, enabling relatively simple analytical solutions that quantitatively link hemolysis rates to pfH and Hpt levels. We found that the model was quantitatively consistent with both pfH and Hpt levels over time (0–50 hours) for all adult CPB patient groups considered in this manuscript, which suggests that the primary mechanisms of short-term generation and elimination of these molecules were adequately captured by the model. The goal of this article was not to establish definitive hemolysis thresholds for medical devices, but rather to develop a biokinetic model and demonstrate its utility by comparing NIH and pfH values that have been proposed in the medical literature to be acceptable limits for chronic blood pumps, and to assess how patient size could potentially impact device-related blood damage levels. While the NIH parameter may be useful for comparing hemolysis between blood pumps evaluated in vitro under different test conditions, it cannot predict time-varying pfH levels and clinical performance, especially when important patient parameters can be highly variable or unknown (e.g., flow rate, PV, hematocrit, haptoglobin level). As pfH is a key analyte for the clinical assessment of hemolysis, the usefulness of the model is that it can predict patient levels of pfH from NIH values, and vice versa. In what follows, we discuss the current limitations of the model, including the potential impact of assumptions made during model development, and future considerations for applications of the model.

Assumptions and Limitations

In addition to limiting the current scope of the model mainly to adult patients because of the lack of available pediatric data, we also assumed that variations in the baseline values of pfH and Hpt are accommodated due to changes in only basal pfH and Hpt generation, , and not on changes in the elimination rates, . We note that of the four studies explored in this article, only the data reported by Windsant et al.8 showed any substantive deviation from the midpoints of the reported reference ranges5,22 used to specify the baseline values of pfH and Hpt in the initial parameterization of the model. Although the relative agreement of the model with these data lends support to the validity of the assumption, there are insufficient data available to make any definitive conclusions regarding the constancy of as a function of baseline pfH and Hpt levels throughout the entire anticipated range. Nevertheless, this assumption was made in our analysis of the various proposed hemolysis acceptance criteria. However, this assumption can be considered worst-case with respect to the most susceptible patients in which Hpt was at its lowest value, i.e., mg/dl. If we instead assume that reduced is because of increased elimination and not decreased generation, both and also increase until they converge to the mean Hpt value of mg/dl at steady state. In fact, if changes in basal Hpt levels are due only to elimination and not generation, the steady-state values of both total and unbound pfH become independent of . Thus, the values in Figures 4 and 5 corresponding to mg/dl can be considered worst-case predictions for the patient population even in light of the uncertainty in the validity of the assumption on which they are based.

Our analysis of the model was also limited in that the intrinsic variability among patients was not addressed. In each of the six patient groups, from the four different clinical studies used to develop and evaluate the validity of the model, only the mean values of pfH and Hpt at each observation time point were considered. However, wide ranges of both of these quantities, which may have been impacted by the need to correct for changes in PV because of hemodilution or RBC administration in the CPB patients, were reported.8 Moreover, we did not account for the variation in weight-based estimates of PV and CO (as an estimate of pump flow rate), which are needed to link NIH values to pfH levels using the model. We estimate that CO per body weight (CO/BW) has a percent coefficient of variation of 14–23%. This variation range is based on CO/BW data for neonates weighing 1–5 kg,33–36 and on cardiac index (CO/body surface area) variability reported for normal adult males44 and 0–6 month postimplanted VAD patients.45 Variation in the relative PV (PV/BW), which is also needed to relate NIH values to the model parameter , is around 13%.26,38 In the future, it would be instructive to specifically account for the measured variability in patient data by applying probabilistic methods to assess the variation in the biokinetic model parameters. Furthermore, rather than relying on patient weight to interpret the pfH results in Figure 6, it may be useful to consider the PO/PV values from individual patients (examples of which are shown in parentheses on the plot) if those quantities are available.

Beyond determining the extent to which the biokinetic model parameters vary with patient size and baseline characteristics, the proposed model can also be improved on. For example, the current model does not explicitly consider the mechanisms of unbound pfH elimination. Although unbound pfH can be eliminated from plasma through migration to the kidney or into the vascular wall,46 the model does not consider these mechanisms independently, only through a single combined elimination parameter . It is, therefore, not currently possible to predict the extent of pfH present at a specific anatomic site (other than within plasma), which could enable the propensity for adverse effects to be linked to specific tissue levels. This refinement was not explored because of the lack of data on specific tissue levels during hemolysis. For instance, even if it is assumed that the removal of unbound pfH from plasma is due only to migration to the kidney, one would still need to include an additional kidney compartment and have detailed information on the levels of pfH in urine during hemolysis. This would enable the accumulation and clearance of pfH in the kidney to be predicted, which could then potentially be linked to the propensity for hemoglobinuria and associated glomerular and renal tubule injury to occur. However, data needed to parameterize these refinements to the model are virtually nonexistent in the literature.

Another relevant limitation to the model regarding removal of the pfH–Hpt complex from plasma via monocyte/macrophage internalization is that data do not exist for accurate parameterization of individual differences in key cellular pathways (i.e., CD163 receptor expression and heme oxygenase-1 availability and activity) that can vary in health and disease states. Additionally, it is important to acknowledge that certain drugs such as steroids down-regulate both Hpt and CD163 (estrogens), whereas others can increase Hpt and CD163 (glucocorticoids).47

Future Considerations

The implications of the model on the extent of total and unbound pfH as a function of hemolysis rate were explored and compared with three proposed acceptance threshold values in the literature for chronic blood pumps. For the least conservative proposed criterion of NIH = 0.1 g/100 L, the model predicts that total and unbound pfH will not exceed 27 and 24 mg/dl, respectively, in an 80 kg adult after 72 hours. Although these concentrations do exceed the adverse event hemolysis threshold defined by INTERMACS (pfH > 20 mg/dl after 72 hours postimplantation), they are below acute levels that have been associated with adverse effects after CPB surgery such as hemoglobinuria and AKI in the literature.8,23,25 While there are insufficient data available to extend the model to other patient populations, simple scaling arguments suggest that the same NIH hemolysis values would result in about a threefold increase in pfH levels for pediatric patients (10 kg) compared with adults (80 kg). This provisional result may be considered in the development of new VAD devices for pediatric patients. In comparison to the two proposed NIH hemolysis threshold values of 0.1 g/100 L16 and 0.01 g/100L,18 the results of the model indicate that in vivo NIH values corresponding to the pfH > 20 mg/dl level defined as hemolysis by INTERMACS were 0.07 and 0.02 g/100 L for an 80 and 10 kg patient, respectively (Figure 6). These latter NIH value predictions may be the most relevant for humans as the INTERMACS hemolysis criterion is based on commonly measured patient pfH values and supported somewhat by clinical data,12,43 as opposed to the other two suggested NIH thresholds (derived from infusion of hemoglobin in dogs16 or in vitro tests with animal blood18). As more patient-specific clinical data become available, the biokinetic model can be applied more rigorously to adult and pediatric subjects.

A potential application of the proposed model is to complement comparative in vitro device testing by providing a framework to help establish in vitro to in vivo correlations for hemolysis. With sufficient data, it would be possible to compare hemolysis rates derived by the model based on measurements of pfH and Hpt in patients to hemolysis values measured during short-term in vitro tests that recirculate blood through the same devices under similar flow conditions. Validated in vitro to in vivo correlations could then be used to guide device design by providing a facile method to estimate absolute in vivo hemolysis and corresponding pfH levels for specific patients based on bench test data. However, the necessary in vitro and clinical testing results to establish such correlations are not widely available. In one limited example, the original Pierce-Donachy (PD) total artificial heart was compared with a modified (MOD) version.48,49 Significant hemolysis (pfH > 100 mg/dl) occurred in three of four patients with the MOD pump, whereas the average pfH was <10 mg/dl for the original PD pump in four patients. Similar to the discrepant hemolysis values encountered clinically, subsequent in vitro testing with human blood revealed NIH values of 0.200 ± 0.011 g/100 L (n = 8) for the MOD pump and 0.074 ± 0.024 g/100 L (n = 36) for the PD pump. While limited, these NIH values are generally consistent with our model results, which, for an 80 kg adult patient, would predict in vivo pfH levels of 54 and 21 mg/dl, for the MOD and PD pumps, respectively, based on the mean in vitro NIH values using human blood. Hence, the model predicts that pfH values for the MOD pump would exceed the higher outdated 40 mg/dl INTERMACS hemolysis threshold, whereas the PD pump would perform closer to the lower 20 mg/dl threshold. Clearly, more extensive data comparing in vitro, animal, and clinical studies are needed to rigorously establish correlations that could be used in the evaluation of new device designs. It is also important to recognize that many blood handling and variability issues can affect RBC mechanical fragility and need to be considered when extrapolating the results of in vitro hemolysis testing, which is typically conducted with animal blood from different species, to patients.13,15,50 For instance, in vitro levels of mechanical hemolysis have been reported to be 2–3 times greater for human blood compared with bovine blood.49,50 As such, the results of the in vivo biokinetic model illustrated in Figure 6 are only applicable within the bounds of the assumptions made for patients in terms of blood flow rates, PVs, prescribed hematocrit (and total hemoglobin concentration), and for human blood.

Finally, this article focused on the measurement of plasma hemoglobin concentration as an indicator of hemolysis because it is routinely measured during in vitro testing of devices and serves as a surrogate for mechanical damage to other blood components. It is also used in the definition of adverse patient events for both INTERMACS (pfH > 20 mg/dl) and ECMO (pfH > 50 mg/dl) applications,51 and it is clinically associated with increased renal injury and mortality.52 However, by virtue of its longer half-life in the body compared with pfH, lactate dehydrogenase (LDH) released from RBCs is also vital as an in vivo biomarker for hemolysis and has been shown to be a more sensitive predictor of clinical thrombotic events in VAD patients.43 Hence, INTERMACS also defines hemolysis as an adverse patient event based on LDH serum levels (LDH > 2.5× upper limit of normal range, approximately LDH ≥ 600 IU/L),12,17 although LDH is not exclusively contained within erythrocytes and can be released when other cell types are injured (e.g., cardiac, liver, brain, lung). It was recently reported that serum LDH in VAD patients was significantly associated with urine hemoglobin levels as assessed by dipstick urinalysis.53 Interestingly, trace to mild amounts of hemoglobinuria were present even when serum LDH levels were below the 600 IU/L hemolysis threshold, before and after excluding extraneous sources of LDH and urine hemoglobin. This suggests that urinalysis for hemoglobin may offer a sensitive, noninvasive, and less expensive method compared with serum analysis for assessing hemolysis in VAD patients. Moving forward, it may be useful to consider in vivo measures and a biokinetic model that includes pfH, LDH, and urine hemoglobin in future evaluations of device hemolysis.

In summary, we have described the development and parameterization of a unique biokinetic model for pfH generated from medical device–related mechanical hemolysis. Further, we have illustrated that when provided with pfH and Hpt levels in patients, the model can be used to estimate an in vivo hemolysis rate and may be useful to interpret biomonitoring data, as well as to provide insight to assess acceptance criteria, for a variety of device applications (e.g., CPB, VADs, ECMO, hemodialysis). At this time, more clinical data are needed to specify the model parameters for pediatric patients and to build a framework to extrapolate in vitro hemolysis test results to clinical measures. Additional data would also enable the model to be extended and refined to include considerations for other specific anatomical sites, intrinsic patient variability, and other biomarkers for hemolysis (e.g., LDH, urine hemoglobin).


At the FDA, the authors acknowledge Dr. Tina Morrison and Dr. Arielle Drummond for reviewing the manuscript. The authors also thank Martha Rumford and Kathy Osterholzer of MC3, Inc. for providing the two Weldner et al. references and clarifying information (by M.R.) concerning the device testing.


List of Defined Model Symbols


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plasma free hemoglobin; hemolysis; haptoglobin; compartment model; biomonitoring; medical devices

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