To compare the volume-expanding efficacy of the study fluids, simulations based on the mean variable estimates shown in Tables 1 and 3 (top) were used to compare the fluid volumes of NS and HSD required to obtain 3 predetermined dilution limits at the end of a theoretical 10-, 20-, 40-, or 60-min infusion of each fluid (Fig. 6 [left]). The ratio between the rates obtained by these computer simulations indicate that approximately three times more NS than HSD must be administered to achieve the same plasma dilution if the infusion time is only 10 min. In contrast, approximately 10 times more NS than HSD is required to obtain the same dilution if the infusion time is 40 min (Fig. 6 [right]).
These data are the first to demonstrate that analysis of small, rapidly infused boluses of a conventional crystalloid provides a reliable estimate of kinetic variables calculated from larger, slower infusions. They are also the first to demonstrate that analysis of rapid infusions of a hypertonic solution provides a reliable estimate of kinetic variables calculated from a slower infusion of equal volume. Because these experiments used extremes of volume and infusion rates, they demonstrate that volume kinetic analysis is sufficiently robust to function under typical clinical circumstances. Despite the range of durations and infusion rates, the variable estimates between isotonic fluid protocols in sheep and those from other experiments in humans are similar. When these variables were used to simulate responses to theoretical infusions of various lengths and volumes, virtually identical dilution-time curves resulted (Figs. 3 and 5). This suggests that the disposition of infused fluid can be predicted from one short or long infusion and give similar results.
Constant kinetic variables for various durations of infusions of the same volume of crystalloids have previously been found in both male and female volunteers. In men, 25 mL/kg of acetated Ringer’s solution was infused over 15 and 30 minutes (9), and in women, 25 mL/kg of acetated Ringer’s solution was infused over 15, 30, 45, and 80 minutes (13). Preliminary data from other studies indicate that V1 might increase during massive fluid infusions. However, no previous volume kinetic studies have compared small volumes of isotonic crystalloid infusion over a brief interval.
This study demonstrates, through simulations comparing these data in sheep with previous data in humans, that conclusions drawn from volume kinetic studies in sheep may be extrapolated to humans and vice versa. This permits analysis of fluid administration regimens that may be often required in clinical situations but are not practically or ethically possible in volunteers. The kinetics of isotonic or nearly isotonic fluids are dependent on the state of hydration (9), whereas the plasma dilution in response to HSD seems to agree very closely between sheep and humans (Table 4).
These data also suggest the possibility that small, rapid boluses can be used as diagnostic tests to define whether additional crystalloid fluid is likely to remain in the circulation, based on the previous observation that mild or moderate hypovolemia in volunteers markedly delays the loss of infusion-induced dilution of [Hb](4). Smaller boluses of NS could provide diagnostic information because a larger proportion of an infused volume of isotonic crystalloids such as NS remains in the circulation at the conclusion of a shorter infusion than at the conclusion of a longer infusion. Fluids such as HSD, which are less rapidly eliminated from the circulation, are less well suited for small, diagnostic infusions.
If a predetermined plasma dilution (e.g., 10%) is desired, kinetic variables derived from bolus studies can be used to simulate the infusion rates of NS and HSD that are required to obtain and maintain that degree of dilution. In effect, the simulations calculate the volumes and infusion rates required to offset excretion and redistribution. Such simulations have previously been accomplished using crystalloid solutions in volunteers (4,14). As expected, faster infusion rates of both fluids would be required to obtain greater dilution than we achieved in this study, and the rates must also be faster to allow for the predetermined dilution to be reached within a short period of time. Empirical testing of these concepts is required.
This comparative study between NS and HSD expands the observations from a previous comparison of lactated Ringer’s solution with HSD in sheep (8). In that report, analyzed by the indicator-dilution technique, 30-minute infusions of lactated Ringer’s solution—a solution approximately 90% of the tonicity of NS—were compared with 30-minute infusions of HSD in sheep. The initial volume expanding efficiency HSD was seven-fold more than that of lactated Ringer’s solution (i.e., for each milliliter of lactated Ringer’s solution infused, intravascular volume increased only 0.27 mL). In contrast, for each milliliter of HSD infused, intravascular volume increased 1.8 mL. At 30 minutes after completing the infusion, for each milliliter of lactated Ringer’s solution infused, intravascular volume increased by only 0.07 mL. In contrast, for each milliliter of HSD infused, intravascular volume increased 1.3 mL—a 20-fold difference in volume expanding efficiency. Ninety minutes after completing the infusions, for each milliliter of lactated Ringer’s solution infused, intravascular volume increased only by 0.07 mL, whereas for each milliliter of HSD infused, intravascular volume increased by 0.8 mL—again, a 20-fold difference.
In a simulation based on the present study, the ratios of NS to HSD that were required to dilute plasma equally seemed to be independent of the target dilution used but were strongly dependent on infusion time. The difference in volume expanding efficiency is smallest when the infusion time is short; conversely, the difference is many times larger if both fluids are infused more slowly (Fig. 6) as they were in the previous study (8). Simulations indicate that the volume expanding efficiency of the two fluids would differ only by a factor of two if an instantaneous bolus (infusion time = 0) could be administered. This time dependence is explained by excretion of a larger proportion of infused Ringer’s solution during a prolonged infusion, whereas differences in urinary excretion minimally influence plasma dilution during a short bolus infusion. Furthermore, the plasma dilution becomes pronounced early on during a bolus infusion of NS because one third of the animals showed signs of fluid accumulation in a small central fluid space, V1. These animals are the ones in which a two-volume model applies better than a one-volume model.
However, theoretically, the volume expanding efficiency of HSD should exceed that of an isotonic crystalloid because of the ability of acute hypertonicity to osmotically attract intracellular fluid into the extracellular and vascular space. Possible reasons for the difference between predicted and actual plasma dilutions include expansion of a larger body space (between 3 L and 4 L) by HSD in comparison to expansion of a body space of only 1.5 L to 2.5 L by NS.
We speculate that plasma dilution by hypertonic fluids would be greater in hypovolemic animals or humans. Previous mass balance studies demonstrate greater plasma volume expansion with hypertonic solutions (15,16). No kinetic data for hypertonic saline solutions have been reported during hypovolemic conditions, but in volunteers subjected to moderate hemorrhage, the V1 and kr for acetated Ringer’s solution were reduced in proportion to the degree of hypovolemia (4). As indicated above, a smaller V1 promotes a more pronounced dilution in response to a bolus.
For fluids infused over a longer interval, the elimination rate is a strong factor governing plasma dilution or volume expansion. For NS, the effectiveness of urinary excretion is evidenced by the fact that most infusions in normovolemic sheep were statistically most consistent with a one-volume model, which has a high elimination rate constant (kr) in comparison to a two-volume model (7). The ratios of 0.51 and 0.36 for urinary excretion, divided by the infused fluid volume at 60 minutes for the one- and two-volume models, respectively, are similar to those found after infusions of acetated Ringer’s solution at various rates to women (13) and those noted after urological irrigating fluids were infused in male volunteers (17).
The increased urinary excretion associated with fluid infusion in experiments in which the one-volume model is statistically preferable (the majority of experiments) supports the conjecture that the determinant of whether a crystalloid infusion results in a one- or two-volume model may be related to small differences in baseline extracellular volume. In other words, if an experimental animal or volunteer is normovolemic, infused fluid will be excreted rapidly, and a one-volume model will result; if extracellular volume is slightly reduced, fluid will be eliminated more slowly, and some fluid will accumulate extravascularly.
These hypertonic saline data were analyzed according to a three-volume model for which the intermediate fluid space V2 could not be distinguished from the central space V1(3). As in humans (5), the kinetics of HSD should therefore be reported according to a distribution of fluid between two fluid spaces, V1 and V3, in which the peripheral space physiologically resembles intracellular volume (Table 3 [top]). Previously, we analyzed hypertonic saline infusions in volunteers without considering the osmotic fluid shift between V1 and V3(3), but the three-volume model applied here better represents physiological responses to HSD.
After infusion of the hypertonic solutions, the plasma volume expansion is reduced by two mechanisms: urinary excretion and return of previously osmotically translocated water back to the second peripheral space V3. The return of water to V3 is reflected by the variable k13. Although in this study, k13 was highly variable, and simulations using a range of values for this variable demonstrated that the reentry of fluid to V3 contributed relatively little to the fluid elimination (Appendix). Interestingly, urinary excretion during and after the hypertonic infusions exceeded the infused fluid volume by 400–700 mL, most of which presumably is derived from V3, given that plasma dilution had nearly returned to baseline for V1 by 180 minutes after the beginning of the infusions.
Calculations of distribution volumes using volume kinetics suggest that both isotonic saline solutions and hypertonic solutions dilute a space that is clearly smaller than total extracellular volume, which is conventionally considered to be approximately 20% of total BW or approximately 200 mL/kg (4,9,18) and which is considered on theoretical grounds to be the distribution volume for isotonic or hypertonic saline solutions. The total body fluid space (V1 +V2 or V1 +V2 +V3) expanded by the hypertonic solution in these experiments was approximately 100 mL/kg, which is similar to the volume obtained in male volunteers receiving acetated Ringer’s solution over 15 or 30 minutes (3,9). In sheep receiving NS, the total distribution volume was 100 mL/kg or less with either fluid infusion and with either the one- or two-volume models.
The use of volume kinetics in experimental animals or humans to analyze the temporal response to fluid infusion is based on the observation that serial analysis of endogenous substances (e.g., water, albumin, and [Hb]) after fluid infusion can provide information about the disposition of infused fluid. For estimates of plasma dilution, [Hb] is particularly suitable, presumably because it is a nondiffusable tracer (3). The use of volume kinetics overcomes many of the limitations with earlier methods used to estimate physiologic spaces such as isotope dispersal (19) or measurement of hemodynamic end-points (20). Isotopes distribute within physiological spaces but may not accurately reflect the effects of an infused fluid, particularly under dynamic, non–steady-state circumstances. Hemodynamic end-points provide useful information but do not provide information about volume shifts, functional body space volumes, or mechanisms behind differences in fluid dynamics.
Volume kinetic analysis also complements mass balance analysis, which is a useful but traditional approach to describe the disposition of infused fluid (8). In mass balance analysis, dilution of [Hb] can be used to calculate plasma volume (PV) expansion based on the assumption that added fluid is evenly mixed throughout blood volume and that the sum of PV expansion, urinary output, and extravascular expansion equals infused volume. However, differences between tissues in the mixing rate of infused fluid with blood volume could influence the accuracy of the calculations. By reporting results in terms of plasma dilution rather than PV expansion, volume kinetic analysis avoids the necessity of assuming that fluid is uniformly distributed throughout blood volume and also provides estimates of clearance and intercompartmental transfer. These estimates can be used to predict responses during similar physiologic circumstances and also can be used to simulate the outcome of other rates and volumes of infusion of similar fluids. The reliability of the models and the variables calculated from those models are evident in the residual plots and performance curves (Table 4, Figs. 4 and 5). However, the kinetic approach interprets the data only in terms of the applied model and is therefore highly dependent on the assumptions inherent in that model. Because the analysis describes the average behavior of the fluid, problems with interpretation may arise if major physiological changes occur in the course of an experiment.
Both mass balance and kinetic analysis offer important insights into the application of current practices related to IV infusion of fluids, especially by illustrating the duration of plasma dilution or PV expansion produced by various fluids and by demonstrating the effects of pathophysiologic disturbances on distribution and elimination of infused fluids.
In summary, we have demonstrated that analysis of small, rapidly infused boluses of a conventional crystalloid provides a reliable estimate of kinetic variables calculated from larger, slower infusions and that analysis of rapid infusions of a hypertonic solution provides a reliable estimate of kinetic variables calculated from a slower infusion of the same volume of solution. Despite the range of durations and infusion rates, the analysis generated similar estimates of kinetic variables. We interpret these data as suggesting that the disposition of infused fluid can be adequately described using a short bolus infusion.
Kinetics for Isotonic Fluid
For NS, the volume change of the single expandable body fluid space is then indicated by the dilution of the venous plasma according to equation 1:
The existence of a peripheral body fluid space V2 is said to be statistically justified if the lowest possible average difference between the model-predicted and measured data points (mean square error) is significantly reduced by fitting the solution to Equation 2 to the measured data points instead of the solution to Equation 1. In the absence of osmotic shifts, the situation in the central body fluid space V1 and the peripheral body fluid space V2 are as follows:MATH
Solutions to these differential equations have been published in previous work (3).
Kinetics for Hypertonic Fluid
An osmotic shift of water, f (t), occurs when hypertonic fluid is infused IV. The osmotic shift occurs across the cell membrane and exchanges water from the intracellular to the extracellular fluid space, which amount to 20% and 40% of the BW, respectively (18). Using a baseline osmolality of 291 and a calculated osmolality of 2458 mOsm/kg for HSD, the translocated volume can be estimated from the following equation:MATH
This equation indicates that the first milliliter of infused HSD translocates 4.9 mL of water and that the osmotic gradient becomes progressively reduced for each subsequent volume of infused fluid as the osmolality of all body fluids gradually increases. Therefore, f (t) is entered as linear function in the analysis process where f (t) at each point in time is governed by the volume of previously infused fluid.
If an intermediate fluid space (V2) is not statistically significant, and if f (t) denotes the osmotic fluid shift and k13 denotes the return of water to V3 (intracellular space), the volume changes in V1 and V3 can be expressed as:MATHMATH
The solutions to these differential equations and also to the ones describing the three-volume model in which V2 is statistically significant have recently been published (5).
Limited Importance of k13
Simulations in which hypothetical values of kr and k13 were entered into the equations demonstrated that kr had a greater influence than k13 on the overall rate of fluid elimination from V1. Setting k13 to negligible values increased the area under the dilution-time curve by 6% and 19% during the 2-min and 20-min experiments, respectively, whereas the corresponding increases obtained by setting kr to negligible values were 45% and 73%. Thus, the power of k13 to eliminate fluid was only between 13% and 26% of the power of kr.
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© 2002 International Anesthesia Research Society
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