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Clinical Science Aspects

Kinetics of Ringer's Solution in Extracellular Dehydration and Hemorrhage

Hahn, Robert G.∗,†; Drobin, Dan; Li, Yuhong§; Zdolsek, Joachim||

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doi: 10.1097/SHK.0000000000001422



The two main purposes of giving intravenous (i.v.) infusions of acetated or lactated Ringer's solution are to replace losses of extracellular fluid (ECF) and of blood, that is, to treat volume depletion and hypovolemia. One can assume that a certain loss of ECF volume would require less Ringer's to be replaced than would be required with a blood loss because Ringer's overhydrates the interstitial space when used to treat hemorrhage (1–3), but a direct comparison between these volume requirements is lacking. The kidney's ability to excrete urine after fluid treatment of ECF volume depletion versus hemorrhage is also unclear.

For this purpose, we evaluated the fluid volume kinetics with mixed models software by comparing data from two volunteer studies performed in similar settings. In the first study, two Ringer's acetate volumes were used to replace a volume depletion of 1.7 L, which had been created by intravenous injections of furosemide (4). The approach was the same in the second study, in which 450 mL and 900 mL of blood were removed in volunteers just before Ringer's was infused (5). Fluids given in the normovolemic state served as controls.

The hypotheses to be tested were that the amounts of fluid required to restore the two types of fluid losses correspond to their physiological volumes (ECF and the blood). We also hypothesized that the renal excretion of fluid would be similar after fluid resuscitation in both these settings.


Dehydration study

Forty experiments were performed on 10 healthy male volunteers with a mean age of 22 years (range 19–37) and a body weight of 80 kg (range 75–100). The Ethics Committee of Linköping University approved the protocol (Ref. M114-09, Identifier NCT01062776) (4). Each volunteer gave his consent for participation after being informed about the study both orally and in writing.

The volunteers fasted after midnight before the experiment and, to prevent any dehydration, they drank 800 mL (approximately 10 mL/kg) of water at 6:00 am. The experiments started 2 h later. A cannula was placed in the cubital vein of one arm to infuse fluid and another cannula was inserted in the other arm for sampling blood. Plasma volume expansion was induced by infusing Ringer's acetate (Baxter Medical AB, Kista, Sweden) i.v. over 15 min using infusion pumps. The Ringer's solution contained sodium 130, chloride 110, acetate 30, potassium 4, calcium 2, and magnesium ions 1 mmol/L.

All 10 volunteers underwent four experiments, performed in a random order determined by the sealed envelope method, and separated by at least 2 days. The experiments comprised infusion of 5 mL/kg and 10 mL/kg of Ringer's, with or without preceding dehydration. The two series of experiments involved induction of a deliberate volume depletion by repeated small intravenous doses of 5 mg of furosemide (Furix 10 mg/mL, Nycomed, Stockholm, Sweden; mean dose 25 mg) until the urinary excretion amounted to between 1.5 L and 2.0 L. Sixty minutes elapsed between the last dose of furosemide and the subsequent infusion.

During the fluid infusion experiments, venous blood (4 mL) was withdrawn to measure the blood hemoglobin (Hb) concentration and the hematocrit on a CELL-DYN Sapphire (Abbott Diagnostics, Abbott Park, Ill). Sampling was performed every 5 min during the first 50 min, and then at 60, 70, 90, 105, and 120 min.

The subjects voided freely in the recumbent position throughout the experiments. The total urine volume was recorded at the end of the infusion experiment.

Hemorrhage study

Ten healthy men with a mean age of 28 years (range 23–33) and with a mean body weight of 76 (65–85) kg underwent three fluid infusion experiments in random order, one in the normovolemic state and the others immediately after having 450 mL and 900 mL blood withdrawn (5). The blood was removed from the circulation over a period of approximately 10 to 15 min using a blood donor set (Teruflex, Terumo Corp, Tokyo, Japan). The experiments were separated by at least 1 week. The protocol had been approved by the Ethics Committee at Huddinge University Hospital on March 6, 1995 (54/95, officer in charge Lennart Kaijser), and informed consent was obtained from all subjects.

Venous blood was collected every 5 min for 60 min and thereafter every 10 min, up to 180 min, after the infusion started. The blood Hb concentration was measured on a Technicon H2 (Bayer, Tarrytown, NY).

In both studies, a small discard volume of blood was drawn before each blood collection to preclude any admixture of rinsing solution, and 2 mL of 0.9% saline was then injected to prevent clotting. Duplicate Hb samples drawn at baseline in all experiments ensured a coefficient of variation (CV) of 0.8%.

The subjects voided in the recumbent position and the total volume was measured at the end of the study.

The systolic and diastolic arterial pressures and the heart rate were measured on a noninvasive hemodynamic device at the beginning and at end of each infusion (dehydration study) or at 15 to 30 min intervals (hemorrhage study). Mean arterial pressure (MAP) was taken as the diastolic pressure plus one-third of the difference between the systolic and diastolic pressure.

Kinetic analysis

A two-volume kinetic model with three rate constants (k12, k21, and k10) and one scaling factor between dilution and volume (Vc, central volume) were fitted to the dependent variables (frequently measured plasma dilution and total urinary excretion) in all experiments on a single occasion (base model) using the Phoenix software for nonlinear mixed effects (NLME), version 1.3 (Pharsight, St. Louis, Mo). The influence of various covariates on the model parameters was then tested sequentially, as guided by a reduction in the residual error, to form the full model.

In the base model, fluid is infused into the plasma (Vc) from where it is distributed to (k12) and redistributed from (k21) the extravascular space (Vt). Elimination occurs from Vc by urinary excretion (k10) (7, 8). All flows are proportional by the value of a rate constant to the volume expansion of the respective body fluid space (Fig. 1A). For example, the flow of fluid from Vc to Vt is determined by the rate constant k12 multiplied by volume expansion of Vc in any given moment.

Fig. 1
Fig. 1:
Kinetic analysis of Ringer's acetate.

Covariates consider individual-specific variations in the base model parameters. Their inclusion allows that a more precise prediction of the dependent variable (here, the plasma dilution) in an individual can be made than in the traditional situation, where only the mean parameter value for the population is used. If hemorrhage changes the flow of fluid from Vc to Vt, the value of k12 in an individual volunteer (ind) can be expressed as: 

where Cov is the computer-estimated value of the covariate effect. The shown so-called linear covariate model allows for the possibility that the hemorrhage is zero. Hence, Cov modifies k12 in each individual depending on the amount of withdrawn blood, if any.

The covariates examined in the present study included the furosemide-stimulated diuresis, removed blood volume, body weight, infusion rate, arterial pressures (systolic, diastolic, and MAP), and the heart rate at the onset of the infusion.

The Hb-derived fractional plasma dilution was used to indicate the volume expansion of Vc resulting from the infusion and, together with the measured urinary excretion, served as input in the calculations. A minor correction was made for the effects of blood sampling on the plasma dilution (6).

Differential equations for the kinetic model and the criteria for inclusion of covariates are given in Supplemental Digital Content 1, All data used for the kinetic analysis are given in Supplemental Digital Content 2,

Computer simulations using MATLAB R2013b (Math Works, Inc., Natick, Mass) were used to illustrate the influence of the key covariates on the distribution of fluid between plasma (Vc) and the extravascular fluid space (Vt).

Demographic results were reported as the mean (standard deviation) and the kinetic data were reported as the mean (95% confidence interval). The significance levels for inclusion of the covariates were taken from the Phoenix program. P < 0.05 was considered statistically significant.


Table 1 shows the fluid balance and the hemodynamic parameters when the infusions started. The two-volume model was successfully fitted to the 1,356 data points, which were derived from 69 experiments in the 20 male volunteers (Table 2, top). One experiment had been excluded from the original 70 due to missing data. Two routes of elimination, which were relevant in previous work (7, 8), did not improve the base model.

Table 1
Table 1:
Fluid balance and hemodynamics at the time of initiation of the infusion
Table 2
Table 2:
Population kinetic parameters in the final model


The search for covariates showed that hemorrhage changed all parameters in the base model (k12, k21, k10, and Vc), whereas dehydration affected only k21 and k10, and that both the infusion rate and the hemorrhage influenced Vc (Table 2, bottom).

These covariate effects imply that dehydration and hemorrhage accelerate a redistribution of fluid while slowing down the elimination.

How the covariate effects mathematically influenced the fixed parameters is explained in the Supplemental Digital Content 1,

Goodness-of-fit and simulations

The residual plots shown in Figure 1, B and C illustrate the ability of the fixed parameters in the base model (Table 2, top) to recreate the measured plasma dilution for each data point in the study. The final curve-fit is given in Figure 1D and the improved precision of the model to predict the urinary excretion on inclusion of the covariates from Table 2 is illustrated in Figure 1, E and F.

The performance of the model is evaluated by predictive checks in Figure 2.

Fig. 2
Fig. 2:
Predictive check based on 1,000 simulations using a built-in function in the Phoenix software.

Simulations based on the optimal estimates of the kinetic parameters, according to Table 2, illustrated how dehydration (Fig. 3) and hemorrhage (Fig. 4) influence the distribution and elimination of fluid when administered over three arbitrary time periods.

Fig. 3
Fig. 3:
Volume expansion of V c (plasma; top row) and V t (extravascular space; middle row) and the cumulative urinary excretion (bottom row) when 1.5 L of Ringer's acetate is infused in volunteers (weight 80 kg) in the euvolemic state (green lines) and after being dehydrated by 0.5 L (red lines), 1.0 L (blue lines), and 1.7 L (magenta-colored line).
Fig. 4
Fig. 4:
Volume expansion of V c (plasma; top row) and V t (extravascular; middle row) and the cumulative urinary excretion (bottom row) when 1.5 L of Ringer's acetate is infused in volunteers in the normovolemic state (green lines) and just after being subjected to hemorrhage of 0.5 L (red lines) and 1.0 L (blue lines).

When compared with dehydration, each milliliter of hemorrhage had an approximately 3 times greater influence on the elimination half-life of the infused fluid (Fig. 5A).

Fig. 5
Fig. 5:
Effects of increasing degrees of fluid deficits on the kinetics of Ringer's acetate.

All degrees of fluid deficit reduced the finally attained ratio Vt/Vc, that is, reduced the tendency of the infused fluid to be allocated extravascularly (Fig. 5B).

Suitable rates of infusion to restore deficits in the fluid balance were simulated. We suggest that one may start with a rate of infusion of 40 mL/min and let the duration then depend on the type and severity of the fluid balance disorder, as suggested by Figure 6. A slow continued drip would prevent rebound hypovolemia.

Fig. 6
Fig. 6:
Infusion rates suitable for restoring and maintaining.


Two different types of fluid balance disorders—extracellular dehydration (volume depletion) and hemorrhage—were deliberately induced in volunteers, followed by replacement of the assumed hypovolemia by Ringer's acetate. The kinetics of the infused fluid volume were then analyzed by a mixed models approach (7). The fixed parameters in the base model were well estimated, with narrow confidence intervals and interindividual CV being 10% at the most.

The most interesting outcomes were derived from the subsequent covariate analysis, which demonstrates how the two fluid balance disorders changed the fixed parameters in the model describing the kinetics of Ringer's acetate. The “best estimates” of these covariates reveal the strength and direction of the influences found (Table 2).

Kinetic effects

The negative covariance between dehydration, hemorrhage, and k10 implies that the urinary excretion was inhibited twice as much by every milliliter of lost blood than by every milliliter of fluid lost by volume depletion. This can also be illustrated graphically as the elimination half-life for increasing fluid deficits (Fig. 5A).

The covariance effect of hemorrhage on k12 indicates that a blood loss of 1 L doubled the rate of distribution, whereas a reduction of MAP from 110 mmHg to 70 mmHg reduced the rate of distribution by 50%.

Both dehydration and blood loss accelerated the return of distributed fluid to the plasma by increasing the rate constant k21; this might be logical as an acute fluid deficit reduces central venous pressures.

The negative covariance between hemorrhage and Vc was expected, as blood loss means that the plasma volume becomes smaller.

The simulations shown in Figures 3 and 4 illustrate the well-known distribution effect for Ringer's, which is most apparent when the infusion time is short and which continues for 30 min after an infusion ends (4–9). The plasma volume is largest at the end of infusion, when it amounts to 50% of the administered volume after a 30-min infusion.

The preference for fluid to accumulate in the extravascular space was greater in the presence of hemorrhage than of dehydration (Fig. 5B). From a physiological point of view, this finding is contrary to what the body should ideally strive for, as most of the fluid deficit in volume depletion stems from extravascular sources. In normotensive hemorrhage only a small and gradual decrease of the extravascular volume by “capillary refill” is expected to occur (10, 11).

Study hypotheses

The simulations allow us to answer the two study hypotheses.

Figure 6A shows that a dehydration of 1 L requires a replacement of 1.2 L and a further 0.9 L to maintain euhydration up to the end of the second hour.

Figure 6B suggests that 2.4 L of Ringer's is required to restore hemorrhage of 1 L and a further 1.2 L to maintain normovolemia for another hour.

Hence, 60% as much Ringer is needed to replace volume depletion as hemorrhage over a 2-h period. One reason why the fluid requirement differs is that extravascular overloading is necessary when treating hemorrhage, which is not the case with dehydration. This percentage is still higher than expected based on the difference in size between the ECF (≈16 L) and blood volumes (≈5.5 L).

The second hypothesis was that the urinary excretion would be similar after the two types of fluid deficit. This was not the case. The urinary excretion was inhibited by hemorrhage, which is a factor that reduces the difference in fluid requirement between the two types of fluid balance disorders.

Urinary excretion

The fairly brisk urinary excretion, despite the presence of apparent body fluid deficiencies, is still surprising. One might expect that the body would accept the volume corrections offered by the Ringer infusions when used to treat acute fluid balance disturbances, but this does not seem to be the case. All infusions induced a urine flow that did not differ much from what was measured during the control infusions. The kidneys actually seem to recreate the fluid balance disturbances by excreting half of the infused volume within 3 h.

Compensatory responses for volume depletion involve an acute, sympathetically mediated vasoconstriction and a slower, baroreceptor-mediated neurohumoral defense involving nonosmotic stimulus of vasopressin, norepinephrine, and the renin-angiotensin system (12, 13). Reasons for the brisk diuresis probably include a reset of cardiovascular volume receptors and decrease in plasma vasopressin (14). Nonhypotensive hemorrhage is compensated by almost immediate vasoconstriction, release or norepinephrine, and activation of the renin-angiotensin system (15, 16). Here, too, the fluid therapy is expected to alleviate the physiological compensation, although normalization was not complete during the study as shown by the prolonged half-life of Ringer's after hemorrhage (Fig. 5A).

A part of the problem might be that a bolus infusion of Ringer's causes transient hypervolemia, which promotes diuresis. Rebound hypovolemia might even occur despite full correction of a blood volume deficit (17). We speculate that equilibration with the albumin stores in the lymph is needed for permanent restoration of the baseline body volumes, as a bolus infusion of Ringer's does not seem to be sufficient. In the meantime, a slow drip of Ringer's should be continued to maintain the normovolemia (Fig. 6).

Experimental model

Both vascular and extravascular volumes (plasma and interstitial fluid) are lost in volume depletion. Blood withdrawal causes only loss of plasma, albeit also a cellular component (the red cells) is removed. Hence, the studied fluid balance disorders both cause hypovolemia but the severity is less in volume depletion due to the discrepancy in physiological volume between the ECF and the blood. This difference formed the rationale for inducing a greater loss of body fluid by furosemide than by blood withdrawal.

Based on changes in blood Hb concentration, the original publication of the furosemide-induced volume depletion experiments claimed that the hypovolemia amounted to 0.5 L after dehydration of 1.7 L (4). The plasma volume deficit would then be only half as great after dehydration of 1 L than after hemorrhage of 1 L (0.3 L vs. 0.6 L). As the plasma is in balance with the extravascular (interstitial) fluid volume, this difference might promote a more pronounced extravascular accumulation of infused fluid after hemorrhage. The plasma protein pool was reduced by the hemorrhage, which would also facilitate extravascular leakage of a larger fraction of the infused fluid.

The short follow-up time makes the present experimental model unsuitable for studying the time course of the normal physiological compensation of volume depletion and blood loss, as these are not completed until the next day (11).

Kinetic model

The volume kinetic approach we used is a dynamic method that models continuous changes in volume expansion over time. The volume of infused fluid that is present in Vc and Vt at any given time is calculated based on three rate constants (k12, k21, and k10) that are the inverse of the half-lives for the transfer of fluid between these spaces. These rate constants are mainly derived from the pattern of blood hemoglobin changes. They indicate the traffic of water volumes across a resistant wall, which probably represents the capillary membrane and the resistance of the adjacent interstitial matrix to volume expansion. The magnitude of the hemoglobin changes, the blood volume, and the volume of distribution of the hemoglobin are not important to these calculations.

Clinical relevance

The urine excreted after furosemide injections has a sodium concentration that is quite similar to the ECF fluid (18), which means that furosemide induces extracellular dehydration (volume depletion) of the same type as in secretory diarrhea and vomiting. The condition should not be confused with whole-body dehydration resulting from insufficient water intake, and which is characterized by hyperosmolality (13).

Nearly twice as much Ringer's was needed to replace blood loss than volume depletion in human subjects who are normotensive. Half the difference is explained by a greater extravascular distribution of infused fluid after hemorrhage. However, the distribution phase of crystalloid fluid helps to restore normovolemia faster than usually anticipated. Hypervolemia is even likely to occur if blood loss is replaced by a rapid infusion of 3 times the bled volume, which might be dangerous in uncontrolled hemorrhage (9). A stepwise correction solves this problem, and also prevents rebound hypovolemia that may result from the diuresis induced by the fluid.

These precautions have not been possible to anticipate from studies based on tracer techniques. Such approaches cannot capture the distribution phase of crystalloid fluid and have also overlooked the diuretic effect of infused fluid. Between 17% and 18% of infused crystalloid fluid has been reported to remain in the vascular compartment (3, 19), which increases to 25% after normotensive hemorrhage (11), but these fractions change greatly over time due to distribution and diuresis. The static view of the efficacy of Ringer's has motivated the recommendation that hemorrhage should be replaced by 3 to 5 times as much fluid. Although this is correct after a period of several hours, the present study shows that distribution effect of Ringer's imposes a risk of hypervolemia if the whole volume is infused over a short period of time, a view that receives support from the use of physiological endpoints in hemorrhage experiments similar to ours (16). Moreover, ongoing diuresis may cause rebound hypovolemia if the treatment is given as a bolus infusion.

Crystalloid fluid is often given to compensate dehydration and hemorrhage in trauma and surgery. Water-sparing hormones can then be expected to play a greater role compared with the volunteer situation studied here. For example, the reduced arterial pressure during general anesthesia greatly prolongs the half-life of Ringer's (7), which would reduce the risk of rebound hypovolemia but increase the risk of transient volume overload if the fluid is infused at a high rate.

The continuous change in the amount of infused fluid that remains in the vascular system is a only a minor issue with colloid fluids, which do not have a distribution phase and, therefore, maintain a more stable plasma volume expansion over time.


The limitations of the present study include that the calculations represent the integration and mathematically improved analyses of two separate papers published previously (4, 5). Both studies were strictly controlled and performed in a similar way. The infused fluid volumes differed, but they aimed to compensate for the expected degree of hypovolemia in each study. Ringer's acetate was used instead of Ringer's lactate because this buffer is used in Sweden; however, these Ringer's solutions have quite similar kinetics in euhydrated volunteers (20).

For ethical reasons, the iatrogenic disturbances of the body fluids were balanced so as to maintain a normal arterial pressure. The degree of blood loss was mild by criteria of the American College of Surgeons. Some calculations were still performed in the presence of minor hemodynamic alterations (Table 1), whereas no hypotension occurred that required vasoconstrictor treatment. However, after 900 mL of blood had been withdrawn, two volunteers became sweaty and reported transient nausea, suggesting a mild vasovagal reaction. These symptoms were promptly alleviated by infusion of the Ringer's solution. Previous work has demonstrated a strong covariance effect of MAP on the urinary excretion, particularly during general anesthesia (7), but the magnitude of the variability in MAP in the present study was apparently not sufficient to disclose MAP as a covariate, independent from dehydration and hemorrhage, of the urinary excretion.

The urinary excretion was quite similar for different degrees of dehydration (Fig. 3), despite differences in the half-life of the fluid (Fig. 5A). This can be explained by the greater plasma volume expansion for progressively greater dehydration. However, the half-lives imply that the urine flow rates must differ at a later stage, and this was quite apparent between 6 and 15 h after the infusions were initiated (simulations not shown).

The fluid infusions were initiated quite soon after the induction of dehydration and hemorrhage, which purpose was to prevent any cardiovascular instability and to limit the confounding effect of capillary refill on the results (10). Due to capillary refill, less fluid would probably be required to combat hypovolemia if the infusion had been started with a delay of 45 to 60 min (10). Elderly subjects would also require less fluid as they eliminate Ringer's acetate more slowly than young subjects (7).


The plasma volume expansion induced by Ringer's showed a marked distribution effect for approximately 30 min after the end of infusion. Dehydration and hemorrhage accelerated the redistribution and retarded the elimination of the infused fluid. Slightly more than twice as much crystalloid fluid is needed to replace blood loss than extracellular dehydration per milliliter fluid deficit in normotensive humans. The distribution effect and a brisk diuresis make it necessary to maintain the drip also after the fluid deficit has been replaced to avoid rebound hypovolemia.


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Administration and dosage; body fluids; crystalloid fluid; deficiency; pharmacokinetics; therapy

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