Volume Turnover Kinetics of Fluid Shifts after Hemorrhage, Fluid Infusion, and the Combination of Hemorrhage and Fluid Infusion in Sheep

The protocol for this study was approved by the Institutional Animal Care and Use Committee of the University of Texas Medical Branch, Galveston, Texas, and conformed to guidelines for care and use of laboratory animals. Adult female merino sheep (n = 12) weighing 39.0 ± 5.9 kg were anesthetized with halothane in oxygen. A pulmonary arterial catheter (Swan-Ganz, Baxter Edwards Critical Care, Irvine, CA) and bilateral femoral arterial and venous catheters (Intracath, Becton Dickinson, Sandy, UT) were inserted under sterile conditions. All animals underwent splenectomy through a left subcostal incision and the abdomen was closed using a three-layer closure. After surgery, catheters were connected to hemodynamic monitors via  continuously flushed transducers. Analgesia consisted of buprenorphine administered intramuscularly. The sheep were maintained in metabolic cages with free access to food and water and allowed 5 days for postoperative recovery. Twenty-four hours before each experimental procedure was performed, each animal was instrumented with a urinary bladder catheter (Sherwood Medical, St. Louis, MO) and food and water were discontinued.

Each animal was subjected to three experiments in random order with an interval of at least 48 h for recovery between experiments. At the beginning of each protocol, animals were observed without intervention for 45 min, during which time three sets of preprotocol measurements were taken. All animals were heparinized with 3000 U of heparin administered intravenously 5 min before each experiment. All infusions consisted of intravenous administration of 0.9% saline (Baxter, Irvine, CA) through a femoral venous catheter over 20 min using a high-flow roller pump (Travenol Laboratories, Morton Grove, IL).

In the first protocol (infusion only), after an initial resting period of 5 min, animals received 25 ml/kg of 0.9% saline over 20 min. In the second protocol (hemorrhage only), animals were bled 300 ml over 5 min. In the third protocol (hemorrhage plus infusion), animals were subjected to 300 ml blood loss over 5 min followed immediately by infusion of 25 ml/kg of 0.9% saline over 20 min.

Hemorrhage was accomplished over 5 min by connecting an arterial catheter to a sterile blood donation bag (Teruflex Blood Bag System, CPDA-1 Solution; Terumo Corporation, Tokyo, Japan). Accumulating blood was weighed on a balance scale (1 ml was assumed to weigh 1 g) to determine the endpoint of hemorrhage. The amount of hemorrhage (7.8 ± 1.1 ml/kg) was not adjusted to body size of the sheep. The rate of hemorrhage was controlled by regulating a pinch clamp. The laboratory environment was maintained at 20°C and physical activity of the sheep was limited by a cage.

Baseline plasma volume was measured using the Evans blue-dye technique16at the beginning of each protocol. Standard curves for the Evans blue concentration analysis were determined for each animal from the plasma collected before dye infusion.

Hematocrit and hemoglobin concentration were measured and recorded three times before the protocol was started and every 5 min during each experiment using 1.0-ml arterial blood samples (HemaVet; CDC Technologies, Oxford, CT). All experiments lasted 3 h. Before sample withdrawal, 4 ml of blood was removed from the arterial catheter to avoid sample dilution. The withdrawn blood was reinfused through the femoral venous catheter after sampling. The catheters were then flushed with 1 to 2 ml of heparinized saline.

Cardiac output (CO) was measured using iced saline thermodilution (Cardiac Output Computer Model 9530; Baxter Edwards Critical Care, Irvine, CA) and recorded in duplicate three times before the start of the protocol, immediately after bleeding, and every hour during the experiment. Urinary volumes were measured every 5 min using a 250-ml graduated cylinder. Mass balance analysis was performed according to the equations in the  appendix.

The homeostasis of an endogenous compound, such as water, is maintained by the equilibrium between uptake, production, and loss. Turnover implies a steady state, and the most basic model contains the turnover rate (k  ⁱⁿ ), fractional turnover rate (k  ^out ), and the amount of the compound in the body (A ). It should be noted that k  ⁱⁿ is often a zero-order process while k  ^out is a first-order process.14,17The turnover of a system is mathematically described by:

At a steady state, dA/dt = 0. Then, the baseline value A  ⁰ can be calculated under the assumption that k  ⁱⁿ and k  ^out are time-independent parameters:

If the subject of modeling is a fluid volume (fig. 1A), the basic turnover model can be written as

To explore that model and to estimate the turnover parameters, it is necessary to disturb the system by an exogenous supply of the compound under controlled conditions. In this study, the system was disturbed by introducing hemorrhage, infusing 0.9% saline, and combining hemorrhage and infusion.

Changes in plasma volume calculated from changes in hemoglobin concentration were taken as an index of the change in the volume of the central compartment, V  ^C (ml). This parameter should not be confused with total plasma volume. V  ^C represents the sampling compartment and may include the plasma of the central blood volume and some part of a rapidly equilibrating subset of interstitial fluid in highly perfused regions. The cumulative urinary output (l) is measured as the main component of the total volume eliminated from the system. Those two sets of volume-time data were fitted to a two-compartment model that includes six model parameters (fig. 1B). V  ^T is the volume of the peripheral compartment (ml) and Cl  ^d is the intercompartmental distribution parameter (ml/min) that describes fractional volume changes between the two compartments. Cl  ^bleed (ml/min) is a distribution parameter related to the recruitment of fluid into the central compartment after bleeding, either from V  ^T by mechanisms not captured by Cl  ^d or from a deeper compartment that was not otherwise characterized in these experiments. Cl  ^bleed is triggered by compensatory circulatory changes after bleeding and is therefore zero in the absence of hemorrhage. Finally, renal elimination was modeled as an exponential function comprising two model parameters: CL  ^R is baseline renal excretion at normal hydration (ml/min) and α is an exponent that describes the alteration of urinary output in response to changes of V  ^C .

V  ^C0 and V  ^T0 are the baseline (preinfusion, prehemorrhage) volumes of the central and peripheral compartments (ml), respectively, thus making all three experimental protocols subject to simultaneous data analysis. This approach requires the assumption that each sheep returned to baseline volumes between the experimental sessions. CL  ^R was permitted to vary between nonbleeding (CL  ^R1 ) and bleeding experiments (CL  ^R2 ). All other parameters were assumed to be similar between the different sessions.

The k  ⁱⁿ parameter, representing oral fluid intake governed by thirst, was set to zero because the animals were fasting throughout the experiments. Nonrenal routes of elimination and metabolic production of water were judged to be negligible. Because even small changes in V  ^C influence renal elimination, and in an effort to standardize between animals of different sizes, we chose to let the fractional volume changes of the two compartments govern both the renal excretion from V  ^C and the distribution between compartments. fV  ^C and fV  ^T are the fractional volume changes (unitless) of the central and peripheral compartments, respectively, and they were defined as:

The turnover of fluid volume in the central compartment was

Inf  is the infusion rate of 0.9% saline. Bleeding rate, b  ^rate , is the amount of bleeding divided by bleeding time. b  ^rate is corrected by baseline hematocrit, hct  ⁰ , to give the volume loss of the central compartment (i.e. , plasma loss). This term becomes zero once bleeding stops. Note that Cl  ^bleed is zero in the absence of hemorrhage. The corresponding turnover of the peripheral compartment was

Finally, the accumulated volume of renal excretion (Ae ) is increased according to

Weighting according to a constant absolute error was applied. For each sheep all six data sets, consisting of hemoglobin dilution and renal output data, respectively, from each of the three protocols, were analyzed simultaneously by a system of nine differential equations (Equations 6 through 8for each experimental session). This regression analysis was performed using WinNonlin Professional 4.0.1 software (Pharsight, Cary, NC). To check parameter identifiability, we did a systematic reduction of one model parameter at a time and compared the change in the objective function value as expressed by the total sum of squared residuals with the full seven-parameter model. Special emphasis was placed on assessment of the correlation matrix (parameter correlation) and parameter precision (CV%).

Transcapillary influx and efflux were calculated using mass balance analysis as the sum of changed plasma volume, plasma loss during hemorrhage, and accumulated urinary output minus infused volume of crystalloid. The corresponding, although not equal, total flow into V  ^C was predicted from the pharmacokinetic analysis as the sum of flow between V  ^T and V  ^C added to the volume recruitment characterized by Cl  ^bleed . To determine whether a prompt infusion of 0.9% saline could prevent some of the physiologic effects of hemorrhage, we performed a second kinetic analysis where Cl  ^bleed was allowed to vary between the two hemorrhage protocols. This volume turnover kinetic analysis contained eight parameters.

Data are presented as mean ± SD or as median and range if significant according to the Shapiro-Wilk W test of normality. The three protocols (infusion only, hemorrhage only, hemorrhage plus infusion) were compared for transcapillary flow using the Wilcoxon signed ranks test. Cardiac output, mean arterial pressure, and plasma volume were expressed as fractional changes from baseline and were analyzed using analysis of variance for a two-factor experiment with repeated measures on significance. All effects and interactions were assessed at the 0.05 level of significance. The three protocols were compared at end of hemorrhage (5 min), the end of infusion (25 min), and at 65, 125, and 185 min after the beginning of the protocol. The outcomes at those five time points were compared with the baseline (i.e. , 1.0) for each protocol. Fisher’s least significant difference procedure was used for multiple comparisons of least squares means with 0.005 as the comparison-wise error rate to minimize type II errors. Data analysis was conducted using PROC MIXED with LSMEANS options in SAS®, Release 8.2 (SAS Institute, Cary, NC).18 

Baseline values were as follows: blood volume was 2.32 ± 0.33 l, plasma volume was 1.61 ± 0.23 l, CO was 4.3 ± 1.1 l/min, baseline hematocrit was 0.301 ± 0.037, and baseline hemoglobin concentration was 10.3 ± 1.6 g/dl. All animals tolerated the three experimental procedures well. The circulatory effects of the three protocols are summarized in figure 2, A and B. At 65 min after the start of the protocol, CO was significantly decreased in the two hemorrhage protocols compared with the infusion-only protocol. There were no significant differences in CO between the two hemorrhage protocols. Mean arterial blood pressure was transiently decreased by hemorrhage only and increased by infusion only. In the hemorrhage-plus-infusion experiment, a short-lasting effect of the infusion was seen, causing a significantly higher blood pressure at the end of fluid infusion compared with hemorrhage only.

Significant differences in fractional changes of plasma volume between the three experimental protocols are displayed in figure 2, C. Thus, antecedent hemorrhage did not increase the magnitude of the plasma dilution produced by crystalloid fluid infusion when the same preinfusion prehemorrhage baseline was used for each sheep in all three experimental sessions, although absolute dilution of hemoglobin concentration was greater in the hemorrhage-plus-infusion experiment once hemorrhage was completed. Plasma dilution at 185 min was similar between protocols. Mass balance analysis of transcapillary flow into the plasma volume during the 3-h procedure is presented in Table 1.

Cumulative urinary output was 924 ± 371 ml, 255 ± 135 ml, and 537 ± 233 ml at 180 min in the infusion-only, hemorrhage-only, and hemorrhage-plus-infusion protocols, respectively (fig. 3, A, B, C). Hemorrhage significantly decreased urinary output by 70 ± 20% and 37 ± 25%, respectively, in the two bleeding experiments compared with the infusion-only procedure. The 300-ml bleeding constituted a fraction of 0.132 ± 0.019 of the blood volume, and this fraction significantly correlated with impairment of renal excretion in the third protocol, where bleeding was followed by crystalloid infusion, (r = 0.73, P < 0.01).

Each protocol resulted in a distinctly different pattern of central volume dilution profiles with depletion of volume at the end of bleeding and maximal dilution at the end of fluid infusion followed by stabilization of central volume at a level slightly above the baseline (fig. 3 D, E, F). All six data sets (time-central compartment dilution and time-cumulative urinary output, respectively, from each of the three protocols) were analyzed simultaneously for each animal. The consistency was good between observed and predicted data for the proposed model (fig. 4). The model contained seven parameters because CL  ^R was permitted to vary between bleeding (CL  ^R2 ) and nonbleeding experiments (CL  ^R1 ). The parameter estimates for each animal are presented in Table 2. Mean V  ^C0 was 1.8 l—slightly more than the mean plasma volume measured by Evans blue; and mean V  ^T0 (≈ 7.6 l) was about four times greater than mean V  ^C0 . The mean correlation between the parameters in the regression analysis was high for V  ^C0 and Cl  ^d (−0.75 ± 0.18), CL  ^R2 and α (−0.66 ± 0.27), CL  ^R1 and α (−0.64 ± 0.27), and between CL  ^R1 and CL  ^R2 (0.62 ± 0.28). All other correlations averaged less than 0.54. In addition to the moderate covariance between parameters, model identifiability was tested by elimination of the parameter Cl  ^bleed , which resulted in a mean increase in total sum of squared residuals from 0.44 to 0.67 (+51%) for the 12 sheep (Table 3). Renal output impairment, as predicted by the applied model, related to the ratio between the amount of hemorrhage and calculated blood volume (fig. 5). The median ratio CL  ^R2 :CL  ^R1 was 0.42 (0.12–0.87).

The applied volume turnover model was able to explain the dynamics of volume flow into V  ^C (fig. 6). In the hemorrhage-only protocol, endogenous volume recruitment into V  ^C was most rapid during the first 15 min after the end of bleeding, and likewise, in the two infusion experiments, the rapid dynamics of flow between compartments was finalized within 15 to 30 min after cessation of fluid infusion. The model also permitted a partitioning of volume flows between V  ^C and V  ^T related to the parameter Cl  ^d and endogenous volume recruitment after hemorrhage represented by the parameter Cl  ^bleed (Table 1). However, results were inconsistent between subjects. Three sheep experienced dehydration of V  ^T in the fluid-only protocol, and in three cases, recruitment by dilution gradients dominated over Cl  ^bleed flow in the hemorrhage-plus-infusion experiment.

In the second analysis, Cl  ^bleed was allowed to vary between the hemorrhage-only (Cl  ^bleed1 ) and hemorrhage-plus-infusion (Cl  ^bleed2 ) protocols (Table 1). The model thus contained eight parameters, which decreased mean total sum of squared residuals by 9% (Table 3). No Cl  ^bleed parameter had a mean correlation to any other parameter exceeding 0.39. For 12 sheep the within-subject difference between Cl  ^bleed1 and Cl  ^bleed2 , 1.4 ± 2.7 ml/min, did not reach significance (P = 0.11).

The applied turnover approach has not been used previously in fluid shift experiments; it provides an important elaboration of existing volume kinetics. In this sheep study, hemorrhage caused an inhibition of renal output, which strongly influenced volume kinetics, regardless of subsequent fluid infusion.

In comparison with studies performed with the original volume kinetic model, the current model could predict volume changes in a broader range of perturbations that more closely resemble clinically relevant scenarios. The congruence between systemic physiology and the turnover model, in which physiologic mechanisms mediate a return to baseline volumes, is appealing. The turnover model can also incorporate explanatory response models to describe how the body achieves homeostasis. One important objective in turnover modeling is the determination of an appropriate baseline, which is essential for estimating other parameters correctly. Keeping the baseline (V  ^C0 and V  ^T0 ) constant between all three protocols permits a joint analysis of all experimental data for each subject. Thus, a certain combination of model parameters can be determined with good precision, even if they could never simultaneously be estimated by means of a single experimental data set. For example, if the hemorrhage-only protocol is analyzed without reference to the other protocols, there is little information regarding the shift between V  ^C and V  ^T . However, that does not mean that the body in this particular situation behaves as a one compartment but rather that the data from this isolated protocol are insufficient to discriminate between V  ^C and V  ^T . This approach of joint analysis suggests that the apparently greater plasma dilution effect of crystalloids after hemorrhage, reported in volunteers,13is primarily attributable to the comparison of volumes during the unstable posthemorrhagic period.

The turnover rate of water in a temperate environment is approximately 12% per day in sheep,19as compared with 7% per day in man.20,21Normally, most of the water is lost by renal excretion and respiratory losses, whereas losses to transdermal evaporation, sweat, and feces are of minor importance.21,22The impact of fasting on the state of hydration was unclear in this study because baseline data for renal excretion were not determined. Therefore, the state of hydration could vary both between and within subjects at the beginning of the three different experiments and contribute to the variations in response to fluid infusions or hemorrhage. This is, however, less likely because we provided ad libitum  water until a determined time before each experiment. In addition, the order of the experiments was randomized and at least 48 h elapsed between each experiment.

In this study, a moderate hemorrhage (13% of blood volume) at a rate of 60 ml/min caused a 14% decrease in mean arterial pressure. This can be compared with a 23% hemorrhage at a rate of 21 ml/min needed by other investigators to achieve a 25% decrease in blood pressure in sheep.23Interindividual variation in the changes of CO and blood pressure was considerably greater than time-equivalent changes in plasma volume, possibly because of multifactoral control of blood pressure changes and variability in determining CO by thermodilution.

In contrast with previous experiments in volunteers in whom intermittent voluntary voiding was used to quantify urinary output,11,13urinary bladder catheterization and direct measurement of urinary output provided a data set that could be fitted to the general model for direct calculations of urinary output dynamics. In healthy subjects the renal excretion rate of water can increase 20-fold or more from baseline after rapid fluid infusions even if dilution of plasma is moderate.11By modeling urinary output as an exponential function (fig. 7), we solved the problem of negative diuresis that appears in hypovolemia if a zero-order process is applied to the hemorrhage-only experiment as in previous volume kinetics.13Therefore, we predicted continued but reduced urinary output despite the volume deficit, and explained the effect of hemorrhage on urinary output by a single modified parameter, CL  ^R .

We speculate that the relationship between hemorrhage and impairment of urinary output could be described as an inhibitory I  ^max function (fig. 5). Consequently, CL  ^R would have an identical expression between protocols permitting it to be incorporated into Equations 6 and 8:

where CL  ^R0 is the baseline urinary output at V  ^C0 , fB  is the actual bleeding as a fraction of blood volume, fB  ⁵⁰ is the fractional bleeding that causes a 50% decrease in urinary output, and γ is an exponent that describes the steepness of the response. However, this speculation requires validation by performing repeated experiments in which the amount of bleeding is varied in the same subject.

Perioperative measurement of blood pressure and urinary output are commonly used endpoints for the administration of intravenous fluids. In this study, there was a marked impairment of diuresis after hemorrhage that caused an accumulation of infused crystalloids, mainly outside V  ^C , in the combined protocol. This highlights the difficulty of determining optimal blood volume substitution during surgery and hemorrhage and supports the suggestion that overhydration might be a common feature9especially if urinary output is used as a monitor of hydration.

Conventional prediction of plasma volume expansion after fluid infusion is based on the assumption that retained fluid is distributed across anatomic and physiologic body fluid spaces.22According to this, crystalloid solutions that contain sodium concentrations similar to that of normal serum, such as 0.9% saline and lactated Ringer’s solution, would be distributed proportionately throughout the extracellular fluid space expanding plasma volume and the interstitial fluid space in a ratio of approximately 1 to 4. However, this theoretical model is less informative than examining kinetic profiles of infused fluid and applying them to functional volumes of distribution. Kinetic analysis based on dilution of plasma, as was used in this study, displays the time-dependent nature of the volume effect of an infused crystalloid solution. Kinetic profiles reveal that plasma expansion is more pronounced at the end of an infusion while rapidly decreasing to a level less than conventionally predicted.11 

Differences in perfusion and compliance between various organs and tissues will contribute to the discrepancy between physiologic fluid spaces and model parameters. Even V  ^C is likely to be influenced by fluid spaces other than plasma volume because equilibration of infused fluid is much more rapid with extracellular water in highly perfused visceral organs than with the blood in low-flow organs such as resting muscles. Thus, all model parameters are strictly kinetic and should not be interpreted as representing physiologic fluid spaces, although these parameters could still be useful in describing and predicting changes in different situations of fluid balance disturbance.

Considerable amounts of extravascular fluid can be mobilized into the circulation after hemorrhage to compensate for lost blood volume.24–26Conventionally, this has been called transcapillary refill, and the contributing mechanisms include constriction of arterioli that decrease capillary hydrostatic pressure,25enhancement of lymphatic flow,27,28and osmotic attraction of fluid from the interstitium to the vascular tree because of hyperglycemia.29Furthermore, the antidiuretic effect of hemorrhage has been reported repeatedly.30,31The current study demonstrates the net effects of these multiple mechanisms as a slow increase of V  ^C over time. This analysis further showed that the Cl  ^bleed -related flow into V  ^C dominated over the expansion of V  ^C caused by Cl  ^d -related flow from V  ^T in most cases (Table 1). This suggests that equilibration of relative volume changes only played a minor role in total recruitment into the central volume. The eight-parameter analysis showed no significant blunting of volume recruitment to V  ^C by the mechanisms explained by Cl  ^bleed . However, statistical power was 36%, and a total of 32 animals would have been necessary with the current study design to reach 80% power. The strength of the Cl  ^bleed parameter is interesting. It may be that the body strives not only to restore the lost fluid volume in V  ^C but also the lost erythrocyte mass. However, incorporating this concept into the kinetic model failed to improve the overall fit. There is a parallel in the mass balance analysis in that the body strives to restore not only the plasma volume but also the blood volume. Hemorrhage also appears to translocate protein to the plasma volume in sheep32and humans.33According to this kinetic analysis, physiologic responses to hypovolemia reverse slowly. Therefore, the major effect of crystalloid infusion during hemorrhage seems to be the unwanted expansion of V  ^T . Because the infused fluid is not eliminated as urine, it is located peripherally rather than in the central volume as intended.

The most important clinical implication of these experimental studies relate to physiologic responses to volume expansion after hemorrhage. If, as suggested by these studies in sheep, urinary output is suppressed during and after hemorrhage and this cannot be affected by fluid infusion, urinary output may be a flawed monitor of the adequacy of volume reconstitution for a considerable interval after plasma volume is restored to normal or even above normal. If persistent low urinary output is interpreted as continued hypovolemia, fluid treatment may not be beneficial and may only add to increased interstitial accumulation.

The current modeling analysis raises a number of design issues that may help to improve the physiologic value of model parameters in future study protocols. First, accurate and precise turnover model parameters could be obtained by measuring intake and loss of fluid during a preexperimental observation period. This baseline analysis will capture volume turnover kinetics under unperturbed conditions. Then, the natural turnover rate k  ⁱⁿ could be assessed. The state of dehydration caused by fasting could also be incorporated into the model. Second, time-dependent turnover model parameters are physiologically attractive but require a proper sampling design. The mechanisms of renal output regulation and transcapillary refill are multifactoral, and identification and measurement of such factors would be useful.34,35Third, experiments with different volumes of bleeding are necessary to fully quantify the relationship between bleeding fraction, renal excretion, and volume recruitment (Cl  ^bleed ) in the model. Fourth, the influence of anesthesia on simple fluid infusions has been previously described by volume kinetics.12,36It would be of great clinical interest to assess the performance of the new volume turnover model during anesthesia and the combined experimental design of hypovolemia and hypervolemia. Finally, a mixed-effects modeling approach will make it possible to cross-validate the model and predict the outcome of future experiments.

In summary, we envision that the turnover concept presented improves the prediction over previous models of volume kinetics. Prediction and partitioning of the sources of fluid recruitment are possible with the dynamic approach of turnover volume kinetic modeling. Further elaboration of this concept will enhance our knowledge on the relative impact of different factors in the regulation of fluid shifts in hypovolemia and hypervolemia.

The pronounced effects on circulation, volume recruitment, and renal output during and after hemorrhage were mainly unaffected by the immediate infusion of a threefold volume of crystalloid within the observational range of 3 h. Thus, the main clinical effect of infused 0.9% saline was the undesired expansion of the peripheral compartment.

The authors thank Lillian Traber, R.N. (Laboratory Supervisor, Anesthesia Investigational Intensive Care Unit), and Jordan Kicklighter, B.A. (Editor, Department of Anesthesiology, University of Texas Medical Branch, Galveston, Texas).

Plasma dilution data were obtained using the formula

where PV  is plasma volume and Hb  is measured blood hemoglobin. The subscript 0 represents the baseline value and n represents the n^thdata point. The presence of bleeding and excessive blood sampling confuses the measured plasma dilution data and calls for a correction by mass balance calculations:

where BV  is blood volume and MHb  is total body mass of hemoglobin. BV  ⁰ is calculated from PV  ⁰ when PV  ⁰ is determined by dilution of Evans Blue but can also be approximated as a set fraction of body weight. For each new point in time, denoted n + 1, the plasma volume can be calculated using Equations A4–A6: