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Anesth Analg 2006;102:991-997 © 2006 International Anesthesia Research Society doi: 10.1213/01.ane.0000198700.41026.2e
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Abstract |
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 Top Abstract IntroductionMethodsResultsDiscussionAppendix 1: Linear Approximation...References |
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During acute normovolemic hemodilution (ANH), autologous whole blood is collected in a series of collection bags containing anticoagulant. The effect of hemodilution on the actual hematological constituents of this sequestered whole blood product has never been examined. We developed a mathematical model that predicts how whole blood bag constituents change during ANH to elucidate the theoretical basis for ANH efficacy. Formulas were derived to calculate the effect of ANH on [X], the blood constituent of interest. An exponential envelope was defined so that the projected impact of ANH on each constituent could be computed while initial blood volume and whole blood bag volume (WBANH) were manipulated. Equivalency of autologous whole blood hemoglobin, platelets, and fibrinogen were determined by comparison with standard allogeneic blood products. We determined that the concentration of blood constituent X in a particular unit of collected blood ([X]n) is provided as a fraction of the initial concentration ([X]0). As WBANH increases relative to estimated blood volume, the decrement in [X]n increases in successive blood collection bags. Irrespective of initial blood volume, the equivalence of a 450-mL autologous whole blood bag to 1 U of packed red cells and 1 U of whole blood-derived platelet concentrate is 13.3 g/dL and 123 x 103/µL, respectively. The impact of ANH on autologous whole blood constituents may be accurately predicted using this model. Conversion of WBANH into equivalent allogeneic blood products could provide a useful method of comparing outcome in various ANH studies. The exponential envelope may be used to assess the actual ANH technique performed by the anesthesiologist, which in turn may impact quality assurance standards.
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Introduction |
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TopAbstractIntroductionMethodsResultsDiscussionAppendix 1: Linear Approximation...References |
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Perioperative blood conservation modalities impact the transfusion of allogeneic blood in patients undergoing surgery by reducing postoperative surgical hemorrhage, augmenting patient coagulation function, and preserving the autologous blood reservoir (1). One modality uses the principle of "hemospasia" and "sequestration," in which manipulation of a patient’s intravascular compartment with colloid or crystalloid produces hemodilution (2). Also termed "intraoperative autologous donation," whole blood is collected in blood bags containing an anticoagulant in the operating room, usually postanesthetic induction and before commencement of surgery (3). Simultaneously, as whole blood is collected, to maintain euvolemia and optimal hemodynamics, colloid or crystalloid is infused. This latter maneuver has coined various physiologic terms, including "acute normovolemic hemodilution" (ANH), "isovolemic hemodilution," "isovolumic hemodilution," or "anemia" (4). The putative effects of ANH are related to preservation of red cell mass because surgical hemorrhage after hemodilution is associated with a smaller quotient of lost red blood cells (5,6). In addition, the intraoperative provision of fresh whole blood containing platelets and coagulation factors theoretically augments coagulation and reduces surgical blood loss (7).
Examination of the hematological properties of autologous whole blood collected with ANH has been largely overlooked in published mathematical models or previous clinical studies. Heretofore, most studies have focused on surrogates of clinical efficacy of ANH, such as avoidance of allogeneic blood, potential savings of red blood cells, and so on, without correlating the qualities of the autologous blood product with any specific outcome variable. Because progressive hemodilution occurs during ANH, the constituents of whole blood collected after the initiation of ANH versus later during the maneuver could differ appreciably. In addition, it is unknown what impact ANH has on whole blood collected from a patient with a relatively low platelet count (PLC) or fibrinogen level ([FIB]). Intuitively, augmentation of blood coagulation after re-transfusion might be negligible because this autologous whole blood product would contain an even lower PLC or [FIB]. However, performing laboratory analyses of autologous ANH whole blood routinely during surgery is impractical and costly. Therefore, in this report, a mathematical model that focuses on the actual sequestered autologous whole blood product was developed to predict its hematological variables in quantifiable terms and examine specific variables. An additional goal was to develop a practical tool for researchers and clinicians to apply when examining the ANH technique and its efficacy in various studies and reports.
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Methods |
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TopAbstractIntroductionMethodsResultsDiscussionAppendix 1: Linear Approximation...References |
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To calculate how the constituents of sequential whole blood units change during ANH, mathematical formulae were derived to describe the changes in concentration for each unit of blood removed. The model assumed that for each milliliter of whole blood withdrawn, an equal and exact volume of asanguinous fluid was infused to maintain normovolemia.
A general formula for the concentration of a given unit of sequestered blood was derived. Let [X] be the in vivo concentration of a particular blood constituent. During ANH, when a volume of blood (VL) is removed, [X] is given by the following well-known exponential formula (6):
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where [X]0 and V0 are the pre-ANH, or baseline, in vivo concentrations of X and blood volume, respectively.
As blood is removed, the in vivo mass of the blood constituent X decreases. The loss of mass when VL changes from VLu (the collected volume of blood before a given unit of blood is sequestered) to VLu + Vu, where Vu is the volume of the unit of blood, is given by the following integral:
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By conservation of mass, the concentration in the unit of removed blood ([X]u) is given by the following formula:
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Evaluating the integral using Equation 1 and solving for [X]u gives the following formula:
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Using Equation 2, a formula for the concentration of the nth unit of blood was then derived.
For the nth unit of blood, VLu = (n – 1)Vu, where n = 1, 2, 3, etc. Substituting this into Equation 2 and defining 
= Vu/V0, the concentration of the nth unit [X]n is the following equation:
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Equation 3 can be rewritten in terms of [X]1 as follows: Because [X]1/[X]0 = (1/)(1 – e–), then [X]2 = [X]1 e–, [X]3 = [X]1 e–2, etc. (A linear approximation to Equation 3 is provided in Appendix 1.)
A final step in these calculations requires definition of an "exponential envelope" in which the substitution of Z for n in the function provides the value of [X]n, the concentration in the nth unit of blood:
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A Microsoft Excel® macro was developed to enable input of the volume of the blood collection bag (Vu), pre-ANH patient concentration of X ([X]o), and pre-ANH patient blood volume (V0) to calculate [X] in the nth unit ([X]n) of collected whole blood. A plot was generated to demonstrate how [X]n changes in relation to Vu/V0. Using a whole blood collection bag volume of 450 mL, V0 was reduced from 8000 to 4000 mL in 500-mL decrements, and Equation 3 was used to calculate [X]n/[X]0 at each decremented point for four sequential whole blood collection bags. The sequential autologous whole blood units (WBANH) were noted in order of collection as 1WBANH, 2WBANH, 3WBANH, and 4WBANH. Applying [X]n/[X]0, hemoglobin concentration ([Hb]), PLC, and [FIB] were then calculated for each WBANH, and [Hb] decreased from 16 to 10 g/dL in 1-g/dL decrements, PLC decreased from 300,000 to 150,000/µL in 50,000/µL decrements, and [FIB] decreased from 400 to 200 mg/dL in 50-mg/dL decrements. Calculations for each hematological variable in sequential WBANH units were repeated as V0 and were reduced from 8000 to 4000 mL in 500-mL decrements. To compare the contents of each WBANH with commercial allogeneic blood products, the actual quantities of Hb, PLC, and FIB were then calculated in sequential WBANH measures, and each constituent and V0 were manipulated. For example, a 450-mL unit of autologous WBANH with a [Hb] of 15 g/dL, PLC of 300,000/µL, and [FIB] of 350 mg/dL would contain 67.5 g of Hb, 1.35 x 1011 of platelets, and 1.02 g of FIB. Four-hundred-fifty milliliters was selected as the standard volume of autologous whole blood units because this reflects the current practice of ANH (3–5); however, the calculations derived above enable designation of any volume of blood collection bag. The following variables for determining equivalency of allogeneic blood products were then applied: packed red blood cells (pRBCs) contain approximately 60 g of Hb, one single unit of whole blood-derived platelet concentrate contains at least 5.5 x 1010 platelets (8), whereas one unit of cryoprecipitate contains at least 250 mg of FIB (9). For platelet equivalency, a single unit of whole blood-derived platelet concentrate was selected instead of apheresis single-donor platelet concentrate because the PLC of the latter can be variable (3- to 6 x 1011) and is influenced by local blood bank collection practices (10).
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Results |
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TopAbstractIntroductionMethodsResultsDiscussionAppendix 1: Linear Approximation...References |
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Figure 1 is a plot of the derived envelope, showing how the concentration of subsequent units decreases exponentially. In Figure 2, a plot of the [X]n/[X]0 versus sequential unit number is shown for varying
. The concentration of blood constituent X in a particular unit of collected blood, [X]n, is provided as a fraction of the initial [X]o. For example, for a Vu of 1000 mL and V0 of 5000 mL, the [X] of the fourth whole blood unit is 50% of the initial [X] ( = 1000/5000 = 0.2). As WBANH increases relative to V0, the decrement in [X]n increases in successive WBANH. For example, in examining sequential WBANH units, theoretically, hemodilution associated with a Vu/V0 of 0.05 produces a 2% and 24% decrease in [X]n for 1WBANH and 6WBANH, respectively. In contrast, for a Vu/V0 of 0.2, the decrease is 9% and 67%, respectively. Similarly, as Vu decreases relative to V0, also increases. For a 450-mL WBANH collection bag, as V0 decreases from 8000 to 4000 mL, the calculated [X]n/[X]o for four sequential WBANH is shown in Figure 3, demonstrating progressive hemodilution as V0 decreases.
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The [Hb] may be derived for a baseline or pre-ANH [Hb] of 16, 14, and 12 g/dL for an estimated blood volume (EBV) of 8000, 6000, and 4000 mL and WBANH of 450 mL as follows. As pre-ANH [Hb] or V0 decrease, the resultant [Hb] and total Hb content of respective WBANH decrease proportionally. Irrespective of V0, the threshold for pRBC equivalence for a 450-mL WBANH unit is a [Hb] of 13.3 g/dL. When total Hb content of individual WBANH is summated (1WBANH + 2WBANH + 3WBANH + 4WBANH), the equivalence of the total WBANH (TWBANH) volume (1800 mL) may be calculated. For example, in a patient with a pre-ANH [Hb] of 16 g/dL and V0 of 6000 mL, TWBANH Hb content is 248.4 g (equivalence –4.14 U pRBC). In contrast, when pre-ANH [Hb] is 12 g/dL, TWBANH Hb content is 186.3 g (equivalence –3.1 U of pRBC).
PLC may be derived for a pre-ANH PLC of 300, 250, 200, 150 x 103/µL for VO of 8000, 6000, and 4000 mL and WBANH of 450 mL as follows. Despite a lowest pre-ANH PLC of 150 x 103/µL, post-ANH PLC never decreases <100 x 103/µL in any WBANH units. Irrespective of V0, the threshold for PLC equivalence for a 450 mL WBANH unit is 123 x 103/µL. The decrement in PLC in sequential WBANH units increase as V0 is reduced, suggesting that equivalency of WBANH to allogeneic platelets is better preserved in patients with larger V0. Summation of total PLC in sequential WBANH provides additional insight into the autologous WBANH. When pre-ANH PLC is 300 x 103/µL and V0 is 8000 mL, TWBANH platelet quantity is 4.8 x 1011 (equivalence of 8.79 U of whole blood-derived platelet concentrate). Reducing baseline pre-ANH PLC to 150 x 103/µL and V0 to 4000 mL produces a TWBANH platelet quantity of 2.18 x 1011 and equivalence of 3.96 U of whole blood-derived platelet concentrate.
Calculations for FIB require consideration of another variable. The volume of distribution for FIB differs from RBC or platelets because it equals plasma volume and not whole blood volume. Therefore, [FIB]Plasma has to be first converted into [FIB]Blood by applying a correction factor (1 – hematocrit) (11). [FIB]Blood may be derived for a pre-ANH [FIB]Plasma of 400, 300, and 200 mg/dL for V0 of 8000, 6000, and 4000 mL and WBANH of 450 mL as follows. When pre-ANH [FIB]Plasma is 400 mg/dL, V0 is 8000 mL, and baseline hematocrit is 40%, four sequential WBANH units yield a TWBANH FIB content of 4.11 g (equivalence of 16.5 cryoprecipitate units). Reducing V0 to 4000 reduces TWBANH FIB content to 3.9 g (equivalence of 15.6 cryoprecipitate units). When pre-ANH [FIB]Plasma is reduced to 200 mg/dL and V0 is 8000 mL, TWBANH FIB content is 2.1 g (equivalence of 8.24 cryoprecipitate units). Reduction of V0 to 4000, in turn, reduces TWBANH FIB content to 1.9 g (equivalence of 7.8 cryoprecipitate units). In other words, a 50% reduction in V0 is associated with a 9.5% reduction in TWBANH FIB content. Because the volume of distribution of FIB increases during hemodilution as hematocrit decreases, when pre-ANH [FIB]Plasma is 400 mg/dL, V0 is 8000 mL, and baseline hematocrit is decreased to 35%, four sequential WBANH units reflect a slight increase in TWBANH FIB content, i.e., 4.4 g (equivalence of 17.7 cryoprecipitate units).
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Discussion |
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TopAbstractIntroductionMethodsResultsDiscussionAppendix 1: Linear Approximation...References |
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The exponential envelope [X]u (Z) demonstrated in Figure 1 represents a mathematical function that provides for [X] when evaluated at the desired end-point. The envelope was used to predict how progressive hemodilution in four sequential 450-mL WBANH units impacted [Hb], PLC, and [FIB]. As expected, the analysis reveals that 4WBANH and 1WBANH contain blood constituents that reflect maximal and minimum hemodilution, respectively. The magnitude of this hemodilution increases progressively in sequential WBANH as V0 decreases. After ANH, most anesthesiologists defer reinfusion of WBANH, using crystalloid or colloid to maintain euvolemia until the surgeon has completed that phase of the surgical procedure associated with maximal or near-maximal surgical hemorrhage. If reinfusion of WBANH is required during continuous surgical hemorrhage, volume replacement with the most hemodiluted WBANH unit is recommended (12). This model demonstrates that in patients with V0 >6000 mL, the sequence of re-infusing WBANH is probably irrelevant (e.g., 4WBANH contains 82% of pre-ANH hematological variables in a patient with an V0 of 8000 mL).
The conduct of ANH by an anesthesiologist requires that whole blood collection is simultaneously balanced by the infusion of an equivalent volume of asanguinous fluid. General clinical guidelines are that the sequestered whole blood is replaced with either colloid or crystalloid in a 1:1 or 1:3 volume ratio, respectively (7). Indeed, the mathematical functions described above assume that normovolemia is accurately maintained as whole blood is collected. Unfortunately, a commercial device that performs ANH and meticulously maintains these volumetric end-points is not currently available. Thus, anesthesiologists use clinical judgment, hemodynamic variables, and simple gadgets, such as a blood bag scale, to guide the ANH process, which, in turn, may be prone to some error. Because the predictive properties of the model described above are inexorably linked to a mathematical definition for ANH, if whole blood is collected more rapidly than asanguinous fluid is infused, i.e., a state of relative hypovolemia, the model will overestimate [Hb], PLC, and [FIB] in WBANH. In contrast, administration of asanguinous fluid in excess of blood collection produces hypervolemia; in turn, the model will underestimate these blood constituents in WBANH. A similar anomaly could occur if the IV site of blood collection is in proximity to the IV fluid replacement site, such as, for example, the proximal and distal ports of multilumen central venous catheters. These sites should be distinctly separate from each other so that the sequestered blood product is not inadvertently diluted by fluid infusing through a common central line or upper extremity. Notably, hemodynamic perturbations during the conduct of ANH, such as decreased systemic vascular resistance or increased cardiac output, do not, per se, affect the predictive properties of the model unless the euvolemic balance between blood collection and sanguinous fluid administration is affected. For example, if hypotension develops during ANH, the anesthesiologist may need to temporarily slow the speed of blood collection and administer more IV colloid.
Another important component of any mathematical model is whether it adequately interpolates the relationships between the measurement variables. Clinicians use simple formulas or nomograms to calculate V0, also known as estimated blood volume (EBV). However, accurate calculation of EBV is complex and influenced by multiple factors including the isotope tracer methodology, body habitus, sex, age, degree of obesity, and muscular development (13,14). Similarly, in calculating how various blood constituents are affected by hemodilution, an assumption that the constituent in question is strictly distributed to the whole blood compartment may not be strictly true. Platelets are normally sequestered within the spleen, but migrate from the spleen in the presence of epinephrine and increase PLC (15). Other coagulation factors are distributed across several compartments. For example, approximately 50% of blood Factor XIII resides in platelets, whereas tissue-based Factor XIII resides in monocytes and macrophages (16).
In predicting the constituents of WBANH, the analysis further reveals that calculation of the actual quantity of blood element, either in single WBANH or summated WBANH, as opposed to its concentration, provides a useful measure of blood conservation potential. In converting the quantity of blood constituents into equivalent allogeneic blood components, a dosage of specific blood element can be estimated. In turn, these calculations may be used to compare ANH technique in clinical trials and may provide a more accurate research tool to analyze ANH efficacy. More than 300 clinical studies using ANH in a variety of surgical settings and patient categories have been published since 1960. These studies are characterized by considerable divergence in patient selection, methodology, and results. Indeed, recent meta-analyses of ANH by Bryson et al. (17) and Segal et al. (18), using strict inclusion criteria, concluded that ANH was effective in reducing both the likelihood of exposure to allogeneic blood and the volume of blood transfused. However, the presence of substantial and unexplained heterogeneity suggested that the benefit was inconsistent, citing variability in the amount of WBANH as one of the contributory factors. An example of this variance can be seen by comparing three studies on ANH. Casati et al. (19) performed ANH in 103 patients undergoing cardiac surgery, concluding that ANH had no effect on allogeneic exposure or postoperative hemorrhage; WBANH was 500 mL. In contrast, Rosengart et al. (20) performed ANH in 50 Jehovah’s Witness patients in which none received allogeneic blood; WBANH was 1230 ± 510 mL. Finally, Matot et al. (21) performed ANH in 39 patients undergoing major hepatic surgery, concluding that ANH allowed a significant number of patients to avoid allogeneic blood transfusion; WBANH was 2020 ± 412 mL. Whereas baseline hematological variables and whole blood collection bag volumes were not consistently reported in these studies, application of our methodology suggests that there are huge differences with respect to the dose or equivalence of WBANH constituents across these studies, rendering interpretation or comparison of their findings impossible.
In calculating the dose of a particular blood constituent in WBANH, the therapeutic response after transfusion may be calculated as is demonstrated in the following examples. A patient with a baseline [Hb] of 16 g/dL and V0 of 6000 mL has a TWBANH Hb content of 248.4 g; after surgical hemorrhage, the patient’s [Hb] is reduced to 8 g/dL (total Hb content of 480 g). WBANH would increase the patient’s [Hb] to approximately 12.2 g/dL. A patient with a pre-ANH PLC of 300 x 103/µL and V0 of 8000 mL has a TWBANH platelet quantity of 4.8 x 1011 (four sequential WBANH); after surgical hemorrhage, PLC is reduced to 85 x 103/µL (total PLC of 6.8 x 1011). WBANH would increase the patient’s PLC to approximately 145 x 103/µL. Similarly, for FIB, when pre-ANH [FIB] is 400 mg/dL and V0 is 4000 mL, TWBANH FIB quantity is 3.9 g (four sequential WBANH); after surgical hemorrhage, if [FIB] is reduced to 100 mg/dL (total FIB quantity of 2.8 g), WBANH would increase a patient’s [FIB] to approximately 203 mg/dL. General guidelines are that 1 U of whole blood-derived platelet concentrate augments the PLC by 5- to 10 x 103/µL (8,22) and that 6 U of cryoprecipitate will increase [FIB] 45 mg/dL in a 70-kg patient (9). However, these projections are inherently less accurate than the derived exponential envelope. Allogeneic platelets are affected by storage age and are vulnerable to human leukocyte antigen and human platelet antigen alloimmunization, which influence the response to transfusion (23). In addition, only 75% of the actual FIB in cryoprecipitate is recovered after transfusion (9,24).
ANH efficacy is traditionally assessed by surrogate end-points, such as projected savings of autologous RBCs, impact on allogeneic blood transfusion rates, and volume of postoperative surgical blood loss. However, using the model developed in this study, another valuable end-point may be incorporated into the data analysis of clinical research studies. The calculated improvement in a patient’s hematological profile after WBANH transfusion may be compared with actual point-of-care measurements and coagulation studies. If actual patient [Hb], PLC, or [FIB] after WBANH infusion decrease to less than projected estimates, several factors may contribute to the discrepancy. These include continuing occult hemorrhage, consumptive coagulopathy, disseminated intravascular coagulopathy, hypervolemia (secondary to over-zealous asanguinous fluid administration), or calculation error.
The American Association of Blood Banks has recently described standards for perioperative autologous blood collection and administration, requiring that institutions seeking accreditation adhere to these guidelines (25). Whereas providing valuable new quality assurance directives to anesthesiology departments, particularly in the areas of duration of autologous blood storage, unfortunately, these standards do not address the actual ANH technique. Furthermore, other than simple clinical estimates of normovolemia, anesthesiologists currently do not have any objective tools that may be used perioperatively to assess whether ANH technique and the sequestered WBANH product actually achieved the desired hematological end-points. Because the exponential envelope predicts the concentration of WBANH constituents under ideal technical conditions, it may be used by anesthesiologists as a "gold standard" and incorporated into a perioperative quality improvement paradigm. Volumetric efficiency (VEff) of ANH, i.e., the ratio of actual versus predicted WBANH blood constituent concentration, could provide feedback to the anesthesiologist as to how accurate the blood collection and asanguinous fluid replacement maneuvers were counterbalanced. This could be conducted by measuring [Hb], PLC, or [FIB] in one randomly selected unit of WBANH and comparing the result with that predicted by the exponential envelope. A VEff <1.0 would suggest excessive asanguinous fluid replacement, whereas VEff of >1.0 would suggest excessive whole blood sequestration.
In conclusion, this is the first study to focus on the hematological constituents of WBANH and requires clinical validation in patients. Using the principles of WBANH equivalency or dosage, in which individual WBANH constituents are examined, future study designs should be standardized to include details about the hematological constituents of the actual autologous whole blood product. These data would then facilitate more detailed analyses of outcome and comparison of results among study centers, patient groups, individual patients, surgeons, and anesthesiologists. Because this methodology may be used to refine quality assurance standards, predict clinical response to perioperative autologous whole blood transfusion, and may impact empirical allogeneic blood transfusion practices, further research into simplifying this model for clinicians may be warranted. Finally, the effect of anticoagulant formulation and volume on this exponential model will require further analysis.
The authors thank the reviewer for suggesting the approximate formula given by Equation 4 in Appendix 1.
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Appendix 1: Linear Approximation to Equation 3 |
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TopAbstractIntroductionMethodsResultsDiscussionAppendix 1: Linear Approximation...References |
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Because Vu is typically small compared to V0, the exponential factor e-
may be approximated as (1 – ). This leads to the simpler (but approximate) formula when n > 1: |
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This formula will overestimate [X]n derived by the exponential factor by an amount approximately equal to (2/2) x [X] n – 1. Although insignificant when Vu is much smaller than V0, the approximation error increases with each unit of sequestered whole blood. In a similar approximation, when n = 1,
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Although these formulae may be easier to use than the exponential functions, the anesthesiologist should take appropriate care when applying them.
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Footnotes |
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Presented, in part, in March 2001 at the 75th IARS Clinical and Scientific Congress, Fort Lauderdale, FL.
Accepted for publication November 15, 2005.
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References |
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TopAbstractIntroductionMethodsResultsDiscussionAppendix 1: Linear Approximation...References |
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