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J Appl Physiol 98: 62-71, 2005; doi:10.1152/japplphysiol.00292.2004
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Prediction of dilutional acidosis based on the revised classical dilution concept for bicarbonate

Werner Lang and Rolf Zander

Institut für Physiologie und Pathophysiologie, Johannes Gutenberg-Universität Mainz, Mainz, Germany

Submitted 18 March 2004 ; accepted in final form 5 August 2004


   ABSTRACT
TOP
 ABSTRACT
Glossary
 MATERIALS AND METHODS
 RESULTS
 DISCUSSION
 APPENDIX
 REFERENCES
 
Due to the controversy surrounding the term dilutional acidosis, the classical dilution concept for bicarbonate has been rigorously revised for the prediction of pH, actual bicarbonate concentration, and base excess. In the algorithms derived for buffer solutions, blood, and whole body (1-, 2-, and 3-fluid compartment), only bicarbonate is considered. On dilution at constant PCO2, the final concentration of bicarbonate is the sum in terms of pH, due to the following processes: dilution, formation from chemical reaction with the nonbicarbonate buffers phosphate, hemoglobin, and plasma proteins, and transfer from erythrocytes and interstitial fluid to plasma. At constant PCO2, the level of carbonic acid is held constant, whereas those of the buffer bases are reduced by dilution, resulting in acidosis. In mixed bicarbonate/phosphate buffer, the final concentration of HCO3– exceeds the diluted value due to additional buffering of H2CO3 by HPO42–. For whole blood in vitro, pH, and actual bicarbonate concentration are predicted from dilution with 0.9% saline from initial Hb (100%) to infinite dilution (pure saline). The acidosis from dilution of plasma bicarbonate is mitigated by contributions from plasma proteins (<1 mmol/l) and from the erythrocytes (~5 mmol/l). Similarly, for whole body, the main contributions to combat primary dilutional acidosis in the range of hemodilution (relative Hb: 100–50%) are from the erythrocytes (1.2–2.2 mmol/l) and from the interstitial fluid (3.3–7.2 mmol/l). Perioperatively measured nonrespiratory acidosis is predictable if caused by hemodilution with fluids containing neither bicarbonate nor its precursors, irrespective of other electrolytes.

volume expansion; volume replacement; acute normovolemic hemodilution; infusion solutions

EFFECTS FROM LARGE AMOUNTS of crystalloid or colloid infusions into patients are manifold: decreased total protein ([Pr]) and hemoglobin ([Hb]) levels in blood and plasma, and changes in acid-base and electrolyte status. Many of the acid-base variables, pH, PCO2, and PO2, as well as many of the electrolytes, sodium, potassium, ionized calcium, chloride, and lactate, can be easily obtained by use of modern analyzing technique. Traditionally, the decrease in pH and the negative base excess (BE), e.g., from infusion of 0.9% saline, is called dilutional acidosis. In the clinical setting, however, it had generally been ignored, due to the widespread opinion that the decrease in plasma bicarbonate concentration ([HCO3–]) is only small (2–3 mmol/l), compared with the large extracellular fluid (ECF) expansion (30%) (15, 17). It was not until the nineties when the subject was rediscovered and soon became a matter of controversial discussions, both in view of the modern Stewart approach of acid-base and, conventionally, according to Henderson-Hasselbalch (HH) and Siggaard-Andersen (5, 9, 10).

The new contribution of the Stewart approach (3, 19) is the distinction between independent variables, PCO2, the strong ion difference (SID), and the total concentration of nonvolatile acid ([A]tot) in the plasma, and dependent variables, pH, [HCO3–], and others. The latter are completely determined by the independent variables and can only change if these are altered. For example, nonrespiratory acidosis from dilution with 0.9% saline is explained by a decrease in [A]tot, causing metabolic alkalosis, and a decrease in the SID, causing metabolic acidosis, which is prevailing (2). In this case, dilutional acidosis is characterized by high-chloride concentration (hyperchloremia) and low [HCO3–] (hypobicarbonatemia) in the plasma, called hyperchloremic metabolic acidosis. It is also clear that, for prediction of plasma pH or actual [HCO3–] after hemodilution at constant PCO2, prior predictions of the independent variables, [A]tot and SID, are necessary. For the SID, however, this comprises several ions (e.g., sodium, potassium, calcium, chloride, lactate) of which the concentrations may be decreased or increased by dilution, depending on the composition of the diluent and urinary excretion, and from movements between different compartments (plasma and erythrocytes; plasma and interstitial and intracellular fluid). Because those predictions are complex without extended measurements, HCO3– is preferred as a key ion, even though it is a dependent variable.

In the conventional approach of dilutional acidosis (1, 15, 16), [HCO3–] in the plasma is the basic quantity, which is decreased from dilution at constant PCO2. Thus, in the HH equation, the normal acid-base ratio is changed, and pH decreases. However, quantitative prediction of the pH from simple dilution fails, and the effects from saline administration in vivo, as well as from in vitro dilution of blood, plasma, and buffer solutions, were described only empirically (4). In clinical practice, the pH, BE, and also many other variables measured in the course of hemodilution are unspecific and may include additional effects from acid-base disorders (renal, intestinal, or metabolic). This makes diagnosis often difficult and prevents critical examination of the benefits in outcome of the used resuscitation fluids.

Therefore, the classical dilution concept for HCO3– was reexamined and rigorously revised to allow quantitative predictions of pH, actual [HCO3–], and also BE from dilution with HCO3–-free fluids at constant PCO2. In the revised dilution concept, HCO3– is the central and the only ion that is consequently treated as a subject of dilution, HCO3– formation from buffering, and redistribution by transfer between the different fluid compartments. This was demonstrated by theoretical calculations for the following systems with increasing degree of complexity (1-, 2-, and 3-fluid compartment): 1) buffer solutions, containing HCO3–/carbonic acid; 2) blood in vitro; and 3) whole body. For whole blood and whole body, the fluid compartments are red cell volume (RCV), plasma volume (PV), and interstitial fluid (ISF) volume (ISV), respectively. The large intracellular volume, other than erythrocytes, is not included and is treated only as a source of carbon dioxide for equilibration of the surrounding fluids. Both the formation of HCO3– from chemical reaction at constant PCO2 in buffer solution (phosphate), plasma (protein), and erythrocytes (Hb), as well as the distribution of HCO3– between erythrocytes and plasma (rC), are derived in terms of pH from known empirical equations (17, 20), whereas the Gibbs-Donnan factor (D–) for the distribution of HCO3– between ISF and plasma is assumed to be constant. For prediction of dilutional acidosis in whole body, the following input variables are needed: measured values (pH, PCO2, [Pr], and [Hb] before and after hemodilution) and estimated values (from body weight: blood, plasma, interstitial and extracellular volume), as well as infused and exchanged volume, blood loss, and urinary volume. Concentrations of plasma electrolytes other than HCO3– are not necessary, even though they were useful in calculating the independent variables in the Stewart approach for comparison. It was argued that, if nonrespiratory acidosis is in agreement between predicted and reported, it must be of dilutional origin. This was tested by comparison with available literature data for whole blood in vitro and from appropriate recent clinical studies chosen according to the following criteria: 1) pure volume expansion (hypervolemia), i.e., only infusion, no blood loss, no surgery [Waters and Bernstein (21)]; 2) combined volume expansion + blood loss, i.e., surgery [Scheingraber et al. (14)]; and 3) acute normovolemic hemodilution (ANH), i.e., blood exchange, blood loss, surgery [Singbartl et al. (18) and Rehm et al. (12)].


   Glossary
TOP
 ABSTRACT
 Glossary
MATERIALS AND METHODS
 RESULTS
 DISCUSSION
 APPENDIX
 REFERENCES
 

ANH
Acute normovolemic hemodilution

[A]tot
Total plasma concentration of nonvolatile acid (mmol/l)

BE
Whole blood base excess (mmol/l)

BV, BVo
Final and initial blood volume (liters), respectively

BVout
Lost blood volume (liters)

{Delta}CE
Change in bicarbonate concentration in erythrocytes (mmol/l)

{Delta}CISF
Change in bicarbonate concentration in interstitial fluid (mmol/l)

D–
Concentrational Gibbs-Donnan factor for bicarbonate (plasma/interstitial fluid)

ECV, ECVo
Final and initial extracellular volume (liters), respectively

FISF
Dilution factor for interstitial fluid

FP
Dilution factor for plasma

[Hb], [Hb]o
Final and initial total Hb concentration in blood (g/dl), respectively

[HCO3–(P)], [HCO3–(E)], [HCO3–(ISF)]
Final concentration of bicarbonate (mmol/l) in plasma (P), erythrocytes (E), or interstitial fluid (ISF), respectively

[HCO3–(P)]o, [HCO3–(E)]o, [HCO3–(ISF)]o
Initial concentration of bicarbonate (mmol/l) in plasma (P), erythrocytes (E), or interstitial fluid (ISF), respectively

Hct, Hcto
Final and initial hematocrit (dimensionless or %), respectively

Hctout
Hematocrit in lost blood

ISV, ISVo
Final and initial interstitial fluid volume (liters), respectively

MCHC
Mean cellular Hb concentration (g/l or mmol/l)

pK, pK1
Negative logarithm to base 10 of apparent dissociation constant of phosphate and bicarbonate buffer

[Pr–(P)]
Equivalent charges of total plasma protein (meq/l)

[Pr(P)], [Pr(P)]o
Final and initial concentration of total plasma protein (g/l), respectively

PV, PVo
Final and initial plasma volume (liters), respectively

PVout
Lost plasma volume (liters)

rC
Concentrational distribution ratio of bicarbonate ion (plasma/erythrocytes)

RCV, RCVo
Final and initial red cell volume (liters), respectively

RCVout
Lost red cell volume (liters)

sCO2
Solubility for carbon dioxide (mmol·l–1·Torr–1)

SID
Strong ion difference (meq/l)

UV
Urine volume (liters)

Vin, Vx
Infused or added volume (liters), respectively

x(E)
Concentration of formed bicarbonate in erythrocytes (mmol/l)

x(P)
Concentration of formed bicarbonate in plasma (mmol/l)


   MATERIALS AND METHODS
TOP
 ABSTRACT
 Glossary
 MATERIALS AND METHODS
RESULTS
 DISCUSSION
 APPENDIX
 REFERENCES
 
The study was approved by the Institut für Physiologie und Pathophysiologie der Universität Mainz.

For theoretical calculations of the pH and the [HCO3–] in the revised dilution concept, the following systems were considered.

The first system is hypothetical buffer solutions at the same total ionic strength (154 mmol/l): pure phosphate buffer (30 mmol/l)/NaCl (76 mmol/l), consisting of buffer base (Na2HPO4: 24 mmol/l), and buffer acid (NaH2PO4: 6 mmol/l); pure sodium bicarbonate (24 mmol/l)/NaCl (130 mmol/l); and combined buffer of sodium bicarbonate (24 mmol/l) and phosphate (30 mmol/l)/NaCl (52 mmol/l).

The second system is whole blood in vitro: normal blood with total [Hb] (15.2 g/dl), hematocrit (0.455), and zero BE. The [Pr] was assumed to be 70 g/l. Data for comparison were taken from Zander (23).

The third system is whole body. Data were taken from published recent clinical studies (12, 14, 18, 21).

In the revised dilution concept, the central quantity is the [HCO3–] in the solution and in the plasma for whole blood in vitro and for whole body. On dilution at constant PCO2, it is first decreased in accordance with the dilution factor (Fdil), followed by chemical interaction of the carbonic acid with available nonvolatile buffers in the solution or in the plasma and erythrocytes to form HCO3– and redistribution by transfer of HCO3– between erythrocytes and plasma and between ISF and plasma. This can be expressed in an equation. After dilution at final plasma pH, the final [HCO3–] in the plasma is the sum of the following terms:

(1)
As shown in detail in the APPENDIX, the right side of Eq. 1 can be presented as a function, depending only on pH and known quantities. Thus both the pH and the [HCO3–] at known PCO2 are determined, if, as a second equation, the familiar HH equation is used:

(2)
where pK1 is apparent pK of the carbonic acid/HCO3– buffer, sCO2 is the solubility factor for carbon dioxide (mmol·l–1·Torr–1) in the liquid phase, and the logarithm is to base 10. The method of calculation by use of Eqs. 1 and 2 is demonstrated in the following sections.

Dilution of simple buffer solutions in a closed and in an open system.   For pure phosphate and pure HCO3– buffer without gas phase in a closed system, dilution with normal saline is trivial. It is also trivial for a solution of pure sodium bicarbonate in an open system at fixed PCO2. Because there is no formation of HCO3– and no transfer, the other two terms are zero, and, according to Eq. 1, the new [HCO3–] is:

(3)
where the concentration of diluted HCO3– is initial concentration ([HCO3–]o) x Fdil, and pH is obtained from Eq. 2. In a combined buffer, however, consisting of HCO3– ([HCO3–]o) and phosphate of total concentration (Co), HCO3– is formed from chemical reaction (x) between the diluted buffer base of phosphate and carbonic acid: HPO42– + H2CO3 = H2PO4– + HCO3–, and the second term is not zero:

(4)
Equation 4 can be given as a function of pH: [HCO3–] = f1(pH) (see Eq. A1), if the HH equation is applied to the phosphate buffer with apparent pK = 6.8,

(5)
and solved for x = [HCO3–]formed. The second function for [HCO3–] = f2(pH), is obtained from Eq. 2 with apparent pK = 6.1 and solubility factor = 0.03 assumed for the system:

(6)
Thus, for calculation of pH and [HCO3–], two equations exist, which can be solved from the condition that the difference, f1(pH) – f2(pH), must be zero. This is evaluated by numerical analysis as described in the APPENDIX.

Dilution of whole blood in vitro.   The dilution of whole blood in vitro by addition of 0.9% saline (Vx) to initial blood volume (BVo) at constant PCO2 is based on the assumption that only the initial PV (PVo) is diluted, whereas the initial RCV (RCVo) is not changed. Thus, in the first step of pure dilution (dil), all initial values (pHo, [Hb]o, [Pr]o) are changed in the plasma {PV = PVo + Vx, pHdil < pHo, [HCO3–(P)]dil, and [Pr(P)]dil} and in the blood (BV = BVo + Vx and [Hb]), but not in the erythrocytes {RCV = RCVo, pHo(E), [HCO3–(E)]o, and mean cellular [Hb] (MCHC) = total [Hb] in the erythrocytes}. The Fdil for plasma (FP) is obtained from known [Hb] and hematocrit in the blood before and after dilution:

(7)
In the next step, formation of HCO3– from chemical reaction takes place, both in the plasma [x(P), mmol/l]: Pr– + H2CO3 = HPr + HCO3–, and in the erythrocytes [x(E), mmol/l]: HbO+ H2CO3 = HHbO2 + HCO3–.

The concentration of formed HCO3– in the plasma after dilution is equal to the decrease in the proteinate concentration and is calculated according to Thomas (20):

(8)
Similarly, in the erythrocytes, it is equal to the decrease in the oxyhemoglobinate concentration, calculated according to the equation:

(9)
The last step consists of transfer of HCO3– between the erythrocytes (E) and the plasma (P), until the new distribution is in accordance with the Donnan equilibrium at final plasma pH: rC = [HCO3–(E)]/[HCO3–(P)]. For rC, the distribution ratio of HCO3– as a function of pH, a known empirical relationship is used (17): rC = 2.642 – 0.28 x pH. The final [HCO3–] in the erythrocytes (E) is:

(10)
where {Delta}CE is the difference between [HCO3–]o and final [HCO3–] in the erythrocytes if plasma pH changes from initial pHo to final pH, and in the plasma:

(11)
where the first term is the decreased [HCO3–] from pure plasma dilution, the second is the increment from chemical reaction with plasma proteins, and the third is the increase from transfer of HCO3– produced in the erythrocytes. From combination of Eqs. 10 and 11, and substituting for rC and rearranging, {Delta}CE is expressed as a function of only pH and known quantities. To calculate pH, however, a second relationship for {Delta}CE must be known. This is obtained from the HH equation for the HCO3–/carbonic acid system in the plasma:

(12)
if [HCO3–(P)] is substituted from Eq. 11. pH is then calculated from {Delta}CE by variation of pH, until {Delta}CE(1) – {Delta}CE(2) is equal to zero. The detailed equations are explicitly given in the APPENDIX.

Dilution in whole body.   For whole body, the two-fluid compartment for whole blood in vitro is extended to a three-fluid compartment by including the ISV. It is assumed to contain no other buffers except HCO3–/carbonic acid, and the distribution ratio of HCO3– between plasma (P) and ISF at end plasma pH is determined by the D–:

(13)
In good approximation: D– = 1 – 0.5 x [Pr–(P)]/{[Na+(P)] + [K+(P)]}. It is further assumed that only the ECF is diluted from volume infusion (Vx), i.e., the plasma (FP = PVo/PV) and the ISF (FISF = ISVo/ISV), but not the RCV. Hence, [HCO3–(ISF)] = FISF x [HCO3–(ISF)]o – {Delta}CISF, where {Delta}CISF is the change in ISF between diluted [HCO3–]o and final [HCO3–]. The mole number of HCO3–, transferred from the ISF to the plasma or vice versa and expressed as concentration in the plasma, must be added to Eq. 11:

(14)
In the same way as for whole blood in vitro, the final concentration of HCO3– in Eq. 14 at end-plasma pH must also fulfill both the Donnan distribution equilibrium between erythrocytes and plasma (Eq. 10) and the dissociation equilibrium for HCO3–/carbonic acid in the plasma according to HH (Eq. 12). Hence, if substituting for {Delta}CISF in Eq. 14, two equations are obtained for {Delta}CE in whole body as a function of pH: {Delta}CE(1) and {Delta}CE(2). As above, the pH is found by variation until the condition {Delta}CE(1) – {Delta}CE(2) = 0 is satisfied, and all of the other variables, such as BE or actual [HCO3–] in the plasma, in the erythrocytes, or in the ISF, can be predicted. For calculation of whole blood BE, the Van Slyke equation, according to Lang and Zander (6), is used.

ANH.   ANH is a procedure widely used in clinical practice in which blood is removed from a patient preoperatively and simultaneously replaced with an appropriate volume of crystalloids or colloids by infusion to maintain the initial intravascular volume (BVo). Compared with classical dilution from infusion without blood loss, initially decreased [HCO3–] in the plasma is not caused from hypervolemia of the blood (BV) and ISF (ISV), but from exchange of defined blood volume out (BVout) against infused volume in (Vin). Even though this exchange is a continuous process in interaction with the surrounding ISF and the erythrocytes, the final [HCO3–] at end-plasma pH is calculated in the same way as in whole body (Eqs. 13 and 14). It is assumed that the final state at the end of ANH is the same, irrespective of whether it is reached continuously or in one step, consisting of dilution of the [HCO3–]o in the plasma and in the ISF with additional formation and transfer of HCO3– from the erythrocytes and from the ISF to the plasma. Because decreased [Hb] is used as a measure for hemodilution ([Hb]), the FP is the same (Eq. 7).

In all calculations, using the algorithm for dilution in whole body, BVo was estimated from known body weight by an empirical formula (7). For men, BVo (ml) = 41.0 x body weight (kg) + 1,530, and, for women, BVo (ml) = 47.16 x body weight (kg) + 864. In both equations, the coefficient of variation is the same: ±8.9%.


   RESULTS
TOP
 ABSTRACT
 Glossary
 MATERIALS AND METHODS
 RESULTS
DISCUSSION
 APPENDIX
 REFERENCES
 
Buffer solutions.   In pure phosphate buffer (HPO42–: 24 mmol/l; H2PO4–: 6 mmol/l; total: 30 mmol/l) (Table 1) and also in pure HCO3– buffer (HCO3–: 24 mmol/l; CO2: 1.2 mmol/l; total: 25.2 mmol/l) in a closed system without gas phase, the initial pH at 7.4 is not changed after dilution (1:2) with 0.9% saline. All concentrations of the corresponding buffer pairs and also of total buffer are proportionately (1:2) decreased, and, therefore, their acid-base ratios do not change.


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  		Table 1. Hypothetical buffer solutions: pH and concentrations before and calculated after dilution with 0.9% saline and subsequent chemical reaction

 
However, in an open system at constant PCO2 = 40 Torr, the concentration of the gaseous carbonic acid component is held permanently constant (CO2: 1.2 mmol/l), whereas those of the nonvolatile buffer components are reduced, resulting in acidosis (Table 1). After dilution (1:2), the calculated pH in pure HCO3– buffer from halved [HCO3–] (12 mmol/l) is 7.1, according to HH (Eq. 2), and 7.154 in HCO3–/phosphate buffer (Eq. A1 in the APPENDIX and Eq. 6). In the latter, calculation of pH from pure dilution leads to paradoxical values: 7.1 from dilution of HCO3–, and 7.4 from dilution of phosphate buffer. However, this discrepancy in pH is matched by formation of HCO3– (1.6 mmol/l) from chemical reaction. Thus, in the final state, the concentrations of HCO3– (13.6 mmol/l) and also of H2PO4– (4.6 mmol/l) are increased, whereas that of HPO42– (10.4 mmol/l) is decreased with respect to their diluted values. Only the concentration of the total buffer bases (48 mmol/l) is diluted (1:2).

Whole blood in vitro.   In the calculations, the following acid-base variables from the literature were used (23): initial pH (7.4), PCO2 (40 Torr), and total plasma protein concentration (70 g/l) before dilution, and total Hb (15.2 g/dl) before and after dilution (10.7, 6.6, 3.7 g/dl) with 0.9% saline at constant PCO2. From these and the hematocrit that was calculated from the ratio of whole blood (g/dl) to MCHC (33.4 g/dl), all of the other acid-base quantities are derived (Table 2). The FP, running from 100% before to 56.4, 29.5, and 14.9% after dilution (Eq. 7), was used to calculate the diluted concentrations of the plasma proteins (39.5, 20.6, 10.4 g/l) and of the plasma HCO3– (13.69, 7.15, 3.62 mmol/l). Taking these concentrations and the hematocrit after dilution and the [HCO3–]o in the erythrocytes (13.83 mmol/l), and substituting for rC = 2.642 – 0.28 x pH in the two equations for {Delta}CE(1) and {Delta}CE(2), given in the APPENDIX for whole blood in vitro, the pH, the actual [HCO3–] in the plasma (Eq. 11), and also the BE (Van Slyke equation) were calculated. The pH is strongly shifted to the acid side (7.283, 7.128, 6.945) with large negative values (–7.52, –15.21, –21.61 mmol/l) in BE. The corresponding decrease in plasma HCO3– from 24.26 mmol/l to 18.53, 12.96, and 8.51 mmol/l is less than proportionate to plasma dilution. This is caused by formation of HCO3– from the plasma proteins (0.48, 0.58, 0.49 mmol/l) and by transfer from the erythrocytes (4.36, 5.23, 4.40 mmol/l). In the erythrocytes, the formation of HCO3– from oxyhemoglobinate by chemical reaction is strongly increased (6.58, 15.80, 27.44 mmol/l) with decreasing plasma pH; however, the fraction of the erythrocytes (hematocrit) is also decreased as hemodilution proceeds. Hence, the transfer of HCO3– from the erythrocytes to the plasma must have an optimum. This was assessed by further calculations, assuming additional [Hb] (14, 12.7, 8.6, 7.6, 2.5, 1.5 g/dl). All calculated values (pH, plasma HCO3–, and BE) are in good agreement with reported values from the literature (23).


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  		Table 2. Dilution of whole blood in vitro: acid-base values before and after dilution with 0.9% saline at constant PCO2

 
Whole body.   The basic values, used in the algorithm to predict pH, actual [HCO3–] in the plasma, and whole blood BE, were derived from the chosen clinical studies in the literature (Table 3). In the major calculations for pH from {Delta}CE(1) and {Delta}CE(2) in whole body (APPENDIX) and for the plasma [HCO3–] (Eqs. 13 and 14), these are the [HCO3–]o in the erythrocytes and in the plasma; the total plasma proteins; the D– before dilution; the FP and the FISF (FISF = ISV/ISVo); and the hematocrit, the PV, and the interstitial volume (ISV) after dilution. BVo and initial volume of the ECF (ECVo) were obtained by estimation, and RCVo was obtained by calculation from venous, not body, hematocrit. The corresponding volumes after dilution were estimated differently, depending on the special circumstances of the clinical study. In the before-infusion column of Table 3, all initial values for pH and the [HCO3–] in the plasma were corrected for end-PCO2 after dilution, and all values in the after-infusion column, except the hematocrit and the PCO2, were predicted.


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  		Table 3. Baseline data and calculated intermediate values used in the algorithm for dilution in whole body

 
In the clinical study by Waters and Bernstein (21), all participants within the same group of healthy volunteers received comparable amounts of two different colloids by infusion: 6% hydroxyethyl starch (HES) solution (Hetastarch: 1.095 liter), and, 4 wk later, 5% albumin solution (5% HA: 1.094 liter). Because there was no blood loss, the RCVo was conserved in the Hetastarch group (2.089 liters) and in the HA group (2.063 liters), and the approximated BV values (RCV/Hct) after dilution were 5.303 and 5.033 liters, respectively. The volumes after dilution are estimated as follows: ECV = ECVo + Vin, PV = BV – RCV, and ISV = ECV – PV.

The clinical study by Scheingraber et al. (14) featured two randomized groups of patients with gynecological surgery, blood loss, and infusion of crystalloids: 0.9% saline and lactated Ringer solution. In this case, the volumes after dilution were estimated in another way: RCV = RCVo – RCVout, where RCVout = BVout·Hctout is the volume of the lost erythrocytes in the 2 h of surgery and infusion, and Hctout is the mean hematocrit before (Hcto) and after dilution (Hct); BV = RCV/Hct; PV = BV – RCV; ECV = ECVo + Vin – PVout – UV, where PVout = BVout·(1 – Hctout) is the lost PV, and UV is urine volume. In both the saline and the Ringer group, all estimated volumes of the blood, plasma, and ISF are expanded and hypervolemic.

The characteristic in the clinical study by Rehm et al. (12) was ANH, with the same colloids as in the study by Waters and Bernstein (21), before surgery in two randomized groups of female patients, receiving either 6% HES solution (HES group) or 5% albumin solution (HA group). Because, during ANH, BV before (BVo) and after hemodilution (BV) is assumed to be the same, all other volumes were estimated as follows: RCV = BVo·Hct; PV = BVo – RCV; ECV = ECVo + Vin – BVout·(1 – Hctout); and ISV = ECV – PV.

With the values from Table 3, pH, plasma [HCO3–], BE, and change in ({Delta}) BE in the different clinical studies after infusion were calculated and compared with reported values. The agreement was good in the Hetastarch group: slight negative change in BE predicted ({Delta}BE: –1.81 mmol/l) and reported ({Delta}BE: –1.54 mmol/l); in the saline group: strongly predicted acidosis ({Delta}BE: –6.48 mmol/l) and reported ({Delta}BE: –6.61 mmol/l); and in the HES group: moderately predicted acidosis ({Delta}BE: –2.81 mmol/l) and reported ({Delta}BE: –2.38 mmol/l) (Table 4). In Table 3, the estimated volumes before and after hemodilution are within the experimental range (plus/minus %variation) of the values determined by Rehm et al. (11, 12) for plasma (±12.9%), erythrocytes (±14.6%), and blood (±11.6%), as well as for estimated total plasma protein (±7.9%) and albumin (±10.6%) concentration. If taking for calculation in the HES group the original values by Rehm et al. (12), instead of the estimated ones before and after hemodilution, the results are similar for pH, 7.322; actual HCO3–, 21.14 mmol/l; BE, –4.29 mmol/l; and {Delta}BE, –3.29 mmol/l. However, it was contradictory in the HA group studied by Waters and Bernstein (21), no agreement between slight changes in BE predicted ({Delta}BE: –1.83 mmol/l) and reported ({Delta}BE: +0.64 mmol/l), and by Rehm et al. (12), excellent agreement between moderately predicted acidosis ({Delta}BE: –2.93 mmol/l) and reported ({Delta}BE: –2.97 mmol/l). Also, in the Ringer group, studied by Scheingraber et al. (14), there was no agreement: strongly predicted acidosis ({Delta}BE: –5.81 mmol/l) vs. reported normal BE ({Delta}BE: –0.48 mmol/l).


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  		Table 4. Predicted and reported acid-base values after infusion from different clinical studies

 
In the clinical study by Singbartl et al. (18), a great number of patients (n = 127) who underwent ANH preoperatively were classified according to the mean infused volumes of a colloid solution (Haemaccel): 0, 1, 2, 3, 4, 5, and 5.5 liters. The basic values necessary for prediction of pH, plasma [HCO3–], and BE were calculated in the same way as in the study by Rehm et al. (12); however, the final calculations were performed in consecutive steps without PCO2 corrections (0 to 1, 1 to 2, 2 to 3, etc., and not 0 to 1, 0 to 2, 0 to 3, etc.) (Table 5). The BVo (4.435 liters) before ANH was calculated from the mean body weight (see MATERIALS AND METHODS) and was weighted by the number of the male (n = 49) and female (n = 78) patients. To keep the patients normovolemic, the Vin of the colloid was larger than the volume of the replaced blood (BVout = Vin/1.3) by ANH. In each group, the plasma lactate concentration was also measured and did not change significantly (<1 mmol/l), even under extreme hemodilution. The agreement between predicted and reported values in pH, plasma [HCO3–], BE, and {Delta}BE at the end of ANH is excellent.


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  		Table 5. Dilution in whole body: baseline data and predicted vs. reported acid-base values in patients under extreme acute normovolemic hemodilution

 

   DISCUSSION
TOP
 ABSTRACT
 Glossary
 MATERIALS AND METHODS
 RESULTS
 DISCUSSION
APPENDIX
 REFERENCES
 
Based on the dilution concept, nonrespiratory acidosis was predicted for all hypothetical and clinical examples treated in this study: both from dilution with 0.9% saline (simple buffer solutions, whole blood in vitro), and also in whole body from infusion with different colloid (6% HES, 5% HA, polygelatin) or crystalloid solutions (0.9% saline, lactated Ringer). It was also shown that hemodilution cannot be correctly described by simple dilution without taking into account all processes in which HCO3– is involved in response to addition or infusion of a diluent. However, it must be emphasized that, for all predictions, additional concentrations of the plasma electrolytes were not necessary.

The algorithm that was derived stepwise for hemodilution in whole body (3-fluid compartment) is the most general. Therefore, the algorithms for dilution of whole blood in vitro, plasma, or simple buffer solutions can be derived if the special limiting conditions are considered. For example, for HCO3–/phosphate buffer (1-fluid compartment), Eq. 14 reduces to [HCO3–(P)] = [HCO3–(P)]dil + x(P), by setting ISV = 0, RCV = 0, and replacing the HCO3– formation term of the plasma proteins by phosphate. For dilution in whole body, the predictions depend on the validity of several assumptions [3-fluid compartment, HCO3– distribution functions (rC, D–), no HCO3– loss in the urine, no metabolic HCO3– formation, HCO3–-free diluents] and on the inaccuracy of the measured or estimated variables. An assumed variance in initial pH (±0.01) and in both initial and final PCO2 (±1.5 Torr), respectively, greatly affect calculated pH (±0.010 and ±0.021), plasma HCO3– (±0.50 and ±0.72 mmol/l), and BE (±0.65 and ±0.86 mmol/l), whereas those in estimated volume of blood and ECF are of minor influence. Hence, initial pH and plasma HCO3– were corrected for end PCO2 (Tables 3 and 4). The close agreement with reported values in whole body from different clinical studies (Tables 4 and 5) indicates that the observed nonrespiratory acidosis is of dilutional origin, and, where it does not agree (lactated Ringer), it is secondary to other causes and must be diagnosed further. The dilution concept is not restricted to the HCO3–. If the Stewart approach is used for prediction of the dependent variables of pH or HCO3– after hemodilution, the SID must also be predicted from dilution. This, however, requires several ions (sodium, potassium, chloride, lactate), in contrast to the revised dilution concept, in which electrolytes other than HCO3– are not necessary.

Dilutional acidosis.   For whole blood in vitro, the extent of dilutional acidosis can be predicted from volume expansion, with 0.9% saline in the whole range from initial (15.2 g/dl) to infinite dilution. In Fig. 1, this is expressed in a plot of plasma [HCO3–] (mmol/l) vs. relative Hb (%) after hemodilution at constant PCO2 = 40 Torr. The actual concentration (first curve) is the sum of the decreased HCO3– from plasma dilution (second curve), plus the increment of HCO3– formation from the plasma proteins (fourth curve), plus the increment of HCO3– formation from Hb and transfer from the erythrocytes (third curve). The contributions from the plasma proteins are negligible (<1 mmol/l); only those of the erythrocytes with a broad maximum diminish the strong acidosis from pure plasma dilution. For example, in half-diluted blood (1:2), the predicted [HCO3–] is 14.38 mmol/l, consisting of 8.56 mmol/l from plasma dilution (59.5%), 5.24 mmol/l from transfer from the erythrocytes (36.4%), and 0.58 mmol/l from the plasma proteins (4.0%). The percent decrease in plasma HCO3– (40.7%) agrees with the extrapolated value (39.8%), obtained from an empirical formula for whole blood by Garella et al. (4). Also, the predicted BE (–13.2 mmol/l) is comparable to a recent value (–11.0 ± 2.2 mmol/l) from dilution of blood with 0.9% saline (BE = 1.4506·[Hb] – 22.47) (8).



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  		Fig. 1. Plasma bicarbonate (HCO3–; mmol/l) vs. relative Hb (%) after hemodilution with 0.9% saline in vitro. Comparison is shown of predicted ({square}) and reported ({blacksquare}) values (23) of the actual concentration (top curve), and the calculated contributions from plasma dilution ({triangledown}), plasma proteins ({triangleup}), and erythrocytes ({lozenge}).

 
In a similar plot, acidosis from hemodilution in whole body under extreme ANH with colloid solution under normocapnic conditions is demonstrated in Fig. 2. The points on the fourth curve describe the decreased plasma [HCO3–] from pure plasma dilution, to which the negligible fractions from the plasma proteins (<1 mmol/l) are successively added, from the erythrocytes (1.2–2.2 mmol/l), and from the ISF (3.3–7.2 mmol/l). In the range of hemodilution (relative Hb, 100–50%), no maxima can be observed in the contributions from the erythrocytes or from the ISF. The BE is negative for all groups, and the changes in BE under extreme hemodilution ([Hb] = 5.93 g/dl), predicted (–7.56 mmol/l) and reported (–7.46 mmol/l), obviously were not caused by lactic acidosis from oxygen deficit, but from dilution by volume replacement. The corresponding decrease in plasma HCO3– (20.81 mmol/l) with respect to the baseline value (26.13 mmol/l), predicted (20.4%) and reported (20.1%), is in good agreement with the calculated result (19.7%) from the empirical formula by Garella et al. (4) in dogs.



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  		Fig. 2. Plasma HCO3– concentration (mmol/l) vs. relative Hb (%) after acute normovolemic hemodilution in different patient groups. Comparison is shown of predicted ({square}) and reported ({blacksquare}) values (18) of the actual HCO3– (top curve), composed of the calculated HCO3– ({circ}) from plasma dilution, plus the increments from the plasma proteins (Pr), the erythrocytes (E), and the interstitial fluid (ISF) with corresponding buffers.

 
Infusion solutions and prevention of dilutional acidosis.   When dilutional acidosis was verified by experimental evidence in dogs from isotonic solutions, irrespective of whether they contained chloride or not (1), it was also demonstrated that this could be prevented by infusion of balanced HCO3– solution (in mmol/l: 140 Na+, 2.4 K+, 112.5 Cl–, and 30 HCO3–) instead of 0.9% saline (16). The acid-base effects observable from infusion on whole body greatly depend on composition of the administered fluid, as well as on its volume and rate. Hence, it is surprising that infusion solutions are badly characterized with respect to their actual acid-base properties in the body. In recent time, two attempts have been made: the one proposed by Zander (22), who transferred the conventional BE concept to infusion solutions, including also metabolic effects from HCO3– precursors such as lactate, citrate, or acetate by an additional term, called the potential BE; the other proposed by Morgan et al. (8), who used the SID concept. By the latter declaration, however, the clinical implications are not always immediately comprehensible if the [HCO3–] is not explicitly given. This is the case, e.g., in hypoproteinemic alkalosis, which is explained by a decrease in the plasma proteins, and the in vitro data of human blood from Rossing et al. (13) have been frequently cited. In the plasmalike diluent (in mmol/l: 143 Na+, 3.9 K+, 108 Cl–, 39 total CO2), the SID (Na + K – Cl) is 38.9 mmol/l and equals approximately the sum of the HCO3– + the proteinate concentration, if present in the solution. To a clinician, however, who is aware of 38.9 mmol/l of HCO3– in the solution, alkalosis is not surprising.

In the chosen clinical studies, all infusion solutions contained high-sodium (>142 mmol/l) and high-chloride (>102 mmol/l) concentrations, except for lactated Ringer solution (in mmol/l: 130 Na+, 112 Cl–, and 27 lactate) by Scheingraber et al. (14) and 5% albumin solution by Waters and Bernstein (21), suspected to contain HCO3– of unknown amounts (in mmol/l: 150 Na+, 93 Cl–, and <50 HCO3–). For the latter two solutions, however, acidosis was predicted, in contrast to the reported normal acid-base state. These obvious discrepancies are good examples, demonstrating how the dilution concept can successfully be applied. Because in the organism HCO3– can be metabolically generated from lactate, lactated Ringer solution is only apparently HCO3– free. Analyzing the acid-base state before and after infusion with lactated Ringer solution, the difference in {Delta}BE between actual (–0.48) and predicted (–5.81) is +5.33 mmol/l. Hence, the amount of base to compensate for dilutional acidosis in the Ringer group must be 82.5 mmol [= 0.2·BE (mmol/l)·body weight (kg)]. From a simple balance of converted and total infused lactate (5.2 l x 27 mmol/l = 140 mmol) at the end of 2 h, the concentration of lactate in the ECF (19.0 liter) is ~3.1 mmol/l, close to the measured plasma concentration of 2.0 mmol/l. Hence, iatrogenically caused dilutional acidosis was compensated by induced alkalinizing hepatic metabolism, which is the strategy of this widely used solution in preventing nonrespiratory acidosis. However, most solutions for use in clinical practice are not physiological (high chloride; no HCO3–) and are often a compromise due to the manufacturing conditions (sterility, stability, costs). This must lead to additional acid-base effects (dilutional acidosis, rebound alkalosis from metabolizable anions), if such solutions are administered into patients in large amounts. In the case of dilutional acidosis caused from HCO3–-free solutions, irrespective of whether they contain chloride or not, measured plasma chloride concentration may be used for additional characterization as hyper- or hypochloremic.


   APPENDIX
TOP
 ABSTRACT
 Glossary
 MATERIALS AND METHODS
 RESULTS
 DISCUSSION
 APPENDIX
REFERENCES
 
Equations for Calculation of Formed HCO3– from Phosphate Buffer at Constant PCO2

[HCO3–] as a function of pH, if x = [HCO3–]formed, is substituted from Eq. 5 into Eq. 4:

(A1)

Equations for Calculation of Formed HCO3– from Plasma Proteins and Oxygenated Hb

Equations 8 and 9 are derived from the titration curves of the plasma proteins (g/l), [Pr(P)], and of the oxygenated Hb in the erythrocytes of normal concentration, MCHC = 334 g or 20.7 mmol/l heme monomer by differentiation for pH, according to the following equations (20):

(A2)
where [Pr–(P)] is the concentration of proteinate (meq/l), and

(A3)
Because, in the erythrocytes, pH(E) = 7.19 + 0.77 x (pH – 7.40), differentiation for pH in Eq. A3 yields:

(A4)
Substituting in Eq. A4 for pH(E) and inserting MCHC = 20.7 mmol/l, the change in plasma pH from initial pHo to final pH yields Eq. 9, but without the negative sign.

Complete Equations for {Delta}CE of whole blood in vitro

From combination of Eqs. 10 and 11 and rearranging, {Delta}CE(1) is explicitly given:

All quantities are known from the baseline data and as a function of plasma pH. The empirical relationship for the distribution ratio of HCO3– as a function of pH is taken from Siggaard-Andersen (17) and was linearized: rC = 0.57 – 0.28 x (pH – 7.4) = 2.642 – 0.28 x pH.

Similarly, introduction of Eq. 11 into the HH Eq. 12 yields {Delta}CE(2):

In all calculations, the ratio RCV/PV is replaced by the hematocrit: Hct/(1 – Hct).

Complete Equations for {Delta}CE in Whole Body

From distribution of HCO3– between ISF and plasma (P):

(A5)
where [HCO3–]o in ISF is calculated from initial concentration in plasma: [HCO3–(ISF)]o = [HCO3–(P)]o/D–.

Hence from Eqs. 13 and 14, {Delta}CISF can be isolated:

(A6)
From distribution of HCO3– between erythrocytes (E) and plasma (P), and substituting for {Delta}CISF into Eq. 14:

and from the HH Eq. 12:


   FOOTNOTES
 

Address for reprint requests and other correspondence: W. Lang, Institut für Physiologie und Pathophysiologie, Johannes Gutenberg-Universität Mainz, Saarstrasse 21, 55099 Mainz, Germany (E-mail: wlang{at}uni-mainz.de)

The costs of publication of this article were defrayed in part by the payment of page charges. The article must therefore be hereby marked "advertisement" in accordance with 18 U.S.C. Section 1734 solely to indicate this fact.


   REFERENCES
TOP
 ABSTRACT
 Glossary
 MATERIALS AND METHODS
 RESULTS
 DISCUSSION
 APPENDIX
 REFERENCES
 

  1. Asano S, Kato E, Yamauchi M, Ozawa Y, Iwasa M, Wada T, and Hasegawa H. The mechanism of the acidosis caused by infusion of saline solution. Lancet 1: 1245–1246, 1966.[Medline]
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