## INTRODUCTION

Moderate hypotensive resuscitation ("permissive hypotension") (^{1, 2}) with low-volume hypertonic solutions (^{3-5}) has been shown to promote hemodynamic and cardiovascular function and improve survival after injuries involving penetrating trauma and severe hemorrhage. However, the potential trade-off is that end-organ perfusion may not be adequately restored after resuscitation with a low-volume agent. Inadequate resuscitation greatly increases the risk of multiple end-organ failure and death (^{6}). Thus, there is a requirement for a rapid and sensitive indicator of both the amount of physiological derangement resulting from severe hemorrhage and the adequacy of subsequent resuscitation efforts. Arterial lactate has been proposed as such a marker, in part because of its relationship to oxygen debt, which has in turn been shown to be a far more reliable measure of physiological compromise than the traditional end points of resuscitation such as heart rate, pulse pressure, and systemic blood pressure (^{7, 8}). Trends in lactate have been used in clinical studies of both trauma and sepsis subjects to predict the probability of mortality and morbidity; lactate levels are higher, and time to normalization of lactate longer, in nonsurvivors compared with survivors (^{9, 10}). However in the experimental setting, there are few or no examples of serial lactate profiles being used to assess competing resuscitation therapies.

There are at least 3 problems associated with the quantification of serial lactate profiles for use in between-group assessments. First, there will be considerable intersubject variability in response to the hemorrhage process itself, which will in turn influence both lactate kinetics and overall survival. For example, if physiological compromise during hemorrhage is too extreme for a given subject, there may be irreparable tissue or microvascular injury, and, thus, no demonstrable effect of therapy; because subjects differ in response to this initial insult, there will be increased variability for the treatment group. Second, sequential lactate data contain repeated measurements on the same subject. As a result, there will be correlation among observations obtained from the same subject, resulting in biased standard error estimates of parameters and invalidation of subsequent statistical hypothesis tests. Finally, not all subjects will have a complete set of measurements for each sampling time. Data sets may be either truncated because of the death or removal of the subject before the end of each experimental trial or contain missing values; therefore, standard repeated-measures ANOVA cannot be used.

We have previously reported improved 3-h survival and MAP support in conscious rats after acute severe hemorrhage when infused with a novel hemoglobin polymer (OxyVita) in a cocktail of hypertonic saline and Hextend (HBOC-C) in comparison to standard Hextend (HEX) alone (^{11}). We postulated that the improved outcome in HBOC-C rats might be attributed to increased rates of lactate clearance relative to HEX rats. Therefore, the objective for this study was to evaluate the relative efficacy of HBOC-C compared with standard HEX support in patterns of lactate accumulation and resolution. We predicted that increased survival times exhibited by the HBOC-C animals would be associated with more rapid rates of lactate disappearance from the arterial blood. Furthermore, we surmount the disadvantages in the quantification of lactate profiles during the hemorrhage-resuscitation cycle with the use of mixed-effects model analyses. Mixed-effects models incorporate both fixed effects attributed to the experimental treatments and random effects associated with subject variation; they provide a flexible means of accounting for within-subject correlation present in longitudinal data and handle both balanced and unbalanced data. Mixed models have been underused in biomedical animal physiological studies, although they are relatively common in the plant agriculture literature (^{12, 13}), and in studies of tumor growth, disease progression, and pharmacokinetic modelling (^{14, 15}).

## METHODS

### Data collection and experimental design

This study was approved in advance by the Institutional Care and Use Committee of Virginia Commonwealth University and conforms to the Public Health Service Policy on Humane Care and Use of Laboratory Animals (2002). The data presented in this study were collected as part of a Defense Advanced Research Projects Agency (DARPA) Surviving Blood Loss program investigating competing resuscitation therapies on 3-h survival of rats after severe acute hemorrhagic shock. Details of animal husbandry, surgical procedures, and hemorrhage protocol have been reported previously (^{11}) and are briefly described here. Young (∼8 weeks old) male Long Evans rats weighing 314 (SD 12) g were surgically cannulated under sterile conditions. Arterial and venous catheters were implanted by surgical isolation and cannulation of the femoral artery, carotid artery, and jugular vein, with the right carotid artery reserved for hemorrhage, the right jugular vein for measurement of central venous pressure and infusion, and the right femoral artery for measurement of MAP.

Individual rats were randomly assigned in blocks of four using a computerized randomization algorithm (http://www.randomization.com) to one of two fluid treatments (HBOC-C or HEX) and one of two infusion schedules (titration of fluid resuscitation to a MAP of 60 mmHg) or bolus administration. The experimental design was thus a 2 × 2 factorial with four possible resuscitation combinations (HBOC-C titration, HBOC-C bolus, HEX titration, HEX bolus). There were 9 animals per treatment, for a total of 36 animals.

Animals were hemorrhaged from the carotid catheter to the target shed blood volume of 60% of total blood volume estimated from body mass (^{16}). Blood was removed in three 20% volume increments, or "stacks," at rates of 1.0, 0.5, and 0.25 mL/min, respectively; hemorrhage was paused if MAP declined to less than 40 mmHg. Hemorrhage times for all animals averaged 38 (SD, 8) min; blood volumes removed averaged 11.8 (SD, 0.5) mL. Animals were then resuscitated via the jugular catheter with either HBOC-C or HEX. Total volume of resuscitation fluid was 3 mL/kg. The hemoglobin-based oxygen carrier used in this study was a novel, large molecular weight (17 Md; average radius, 360 Å), zero-link polymerized adipoyl-cross-linked bovine hemoglobin [OXYVITA Inc., New Windsor, NY (^{17})]. The HBOC-C consisted of 7.5 g OxyVita/100 mL carrier solution; the carrier was 7.5% hypertonic saline and 50% Hextend by volume. Unaugmented Hextend solution was used as a control. The titrated treatment was initiated with a 1-mL/kg bolus at a rate of 0.05 mL/min to provide minimal fluid support; the remainder of the treatment volume was infused intermittently at 0.05 mL/min to maintain MAP at approximately 60 mmHg. Animals allocated to the bolus treatment received all resuscitation fluid at 0.05 mL/min during a 15-min push.

Lactate response to hemorrhage and resuscitation was measured on arterial blood samples taken from the carotid artery. Values were determined using a blood gas analyzer with a multiwavelength co-oximeter (ABL 725 and OSM 3; Radiometer America, Westlake, Ohio). During hemorrhage, blood was sampled in 140-μL aliquots in heparinized microcapillary tubes at baseline and after each 20% hemorrhage increment; blood removed for sampling was included in the calculated shed blood volume. Blood was then sampled at 60, 120, and 180 min from the beginning of hemorrhage. Blood sampled at these time points was replaced by an equal volume of blood taken from the first stacked volume sample; these aliquots were pretreated with 1% 1:1,000 heparin and 10% citrate-phosphate dextrose solution to prevent clotting. We obtained five to seven lactate measurements per rat.

### Model fitting and analyses

In this study, we were primarily interested in estimating the overall treatment effects of the competing resuscitation strategies, rather than individual responses *per se*. In principle, longitudinal data patterns and between-subject variability can be modeled by fitting a separate model to data for each subject, extracting the subject-specific parameter estimates, and then performing a two-way ANOVA. However, a relatively large number of estimates are required for accurate estimation, and accumulation-clearance patterns common to all subjects in the study are ignored; thus, population estimates may be poor and inefficient (^{19, 20}).

Mixed models are an extension of generalized linear models in that they incorporate both a fixed-effects term, which captures the population average behavior, and a random-effects term to account for the heterogeneity between subjects. If the experiment is properly randomized, observations from different animals are likely to be independent of each other. However, individual animals will differ in the magnitude of their response to both hemorrhage and resuscitation, and sequential observations made on each animal will be correlated and more similar than those made on different animals. Conventional repeated-measures ANOVA models cannot account for these effects. Furthermore, ANOVA models are unable to handle missing data, and individuals with missing observations are dropped from the analysis entirely. In contrast, mixed-model analyses allow construction of test statistics to account for both fixed and random effects, allow custom specification of the covariance structures for the repeated measures, and account for missing data. As a result, estimates of fixed effects gain in accuracy and precision, and results may have wider scope of inference (^{21, 22}).

The general form of the mixed model is

Here, Y is the vector of lactate concentrations over time, described as a function of **X**, the matrix of experimental design factors (explanatory variables), **Z**, the random-effects matrix with the corresponding vector of random-effect parameters *U*, and sampling error *ε* _{i}. Because we are primarily interested in assessing the effects of the different treatment regimens (fluid, infusion), estimation of the mean parameters *β* are of most interest; the random-effects terms are "nuisance" variables that model the variation that occurs both within and between each animal (^{23}).

We considered two alternative model forms to describe the data: a full factorial linear additive model and a nonlinear model described below.

Initial estimation and assessment of the covariance structure for the random effects component must be performed before fitting the experimental design component (^{21, 22}). We made preliminary comparisons of three different covariance models: unstructured, compound symmetry, and spatial power structure. The unstructured model is the most complex; it assumes that the variance of within-subject responses, and, thus, the correlation between within-subject errors for each pair of times, is different for each period. The compound symmetry model assumes that correlations are equal between each pair of time points. Finally, the power structure model is most appropriate if it is likely that the correlation between observations is dependent on the time lag, and time intervals are unequally spaced. This model differs from the conventional correlated error model AR(1) in that the correlation *ρ* between observations *d* units apart is modeled as *ρd* and thus, correlation between observations declines as a function of euclidean distance between points, whereas the AR(1) model assumed the correlation between adjacent observations is a fixed value of *ρ* for adjacent observations. We assessed heterogeneity of variance between different time points by examination of group SDs at each time point, and by explicitly controlling for heterogeneity in the covariance structure by the GROUP option; however, these effects were small, and controlling for these effects made no difference to the model fit. Final selection of the most appropriate covariance model was based on comparisons of the magnitude of Akaike's Information Criterion and log likelihood (−2LL) and by residual plots for each fit.

*Linear model*

We fitted a linear additive model to the factors fluid type (HBOC-C, HEX), infusion schedule (titrated, bolus), and sampling time. In this model, time was considered a fixed effect; sampling time points were 0 (baseline), at the end of each 20% hemorrhage increment (∼3.5, 14.2, and 34.5 min from the onset of hemorrhage), and 60, 120, and 180 min from the initiation of hemorrhage. The fifth sampling point at 60 min therefore occurred approximately 20 min into the resuscitation period. The best-fit covariance model was a spatial power structure that accounts for unequally spaced longitudinal measurements. Finally, the full model with main effects and interaction terms was fitted using restricted maximum likelihood in SAS PROC MIXED v 9.1 (^{24}). Restricted maximum likelihood is preferred to maximum likelihood because variance component estimates tend to be biased downwards with the latter procedure, leading to confidence intervals that are too narrow and test statistics that are biased upwards (^{21, 22}). Estimates of means and 95% confidence intervals (CIs) for lactate concentrations and differences between lactate concentrations for treatment groups at specified time points were obtained from the LSMEANS and ESTIMATE statements, respectively, in PROC MIXED (^{24}).

We also compared responses of individual animals planned according to their survival status posthemorrhage. First, we assessed survival to 60 min from the initiation of resuscitation; all of the animals allocated to the bolus treatment groups and most of those receiving titrated infusions were expected to have completed their resuscitation regimen at this point. Thus, evaluation at this time point (phase 1 resuscitation) assesses treatment performance during resuscitation or immediately postresuscitation. Animals surviving at least 60 min from the initiation of resuscitation were coded as survivors and as nonsurvivors if they survived less than 60 min posthemorrhage. Second, we assessed survival to prescribed end of the trial (180 min from the initiation of hemorrhage; phase 2); survivors were those subjects that survived the prescribed 3 h from the initiation of hemorrhage.

#### Nonlinear model

We fitted a mechanistic four-parameter model that modeled the trajectories of both lactate accumulation and decline with a quantitatively defined turning point in between. This turning point explicitly marks the transition between lactate accumulation during hemorrhage and lactate decline during resuscitation. We adapted a model originally developed for describing the growth of plant components such as leaf area that typically increase and then decrease during the course of the growing season (^{25}). This model implicitly assumes that the observed change in arterial lactate over time (*dy*/*dt*) can be described as the difference between the relative rate of accumulation of lactate in arterial blood during hemorrhage (*αy*) and relative rate of lactate disappearance from the arterial blood subsequent to resuscitation (*βy*)

If *α* − *β* is represented by *δ*, then *δ* is the net relative rate of change of lactate concentration. It is assumed that *δ* decays exponentially at a rate proportional to the difference between the initial rate of lactate concentration change at time *t* (*δ* _{0}) and the final net relative rate (*δ* _{min}) as *t* approaches infinity. Therefore, *δ* _{min} determines how fast lactate concentration declines after reaching its maximum. Integrating the above gives the expression for lactate concentration *y* as

where *t* is time (min), *y* _{0} is lactate concentration at time *t* _{0}, *δ* _{0} is the initial relative rate of lactate change, and *δ* _{min} is the final net rate of lactate concentration change (^{25}). The rate constant *κ* is a measure of the overall "steepness" or curvature of the function such that the greater the curvature, the smaller the time frame over which lactate changes. The characteristic turning point of the function is thus determined by both *δ* _{0} and *δ* _{min}. Both peak lactate concentration (*y* _{max}) and the time at which it occurred (*t* _{max}) can then be derived from the solved function as:

and

so that

If lactate does not decline during resuscitation, then *δ* _{min} is zero.

To perform statistical comparisons of the fixed treatment effects, we assigned coded coefficients (−1 or 1) to each level of treatment. The resulting array of dummy variables *zi* were then used to estimate main effects and interactions by embedding them in the parameter estimates (^{12, 26}):

where *βι* is the parameter estimate, *z* _{1} = 1 if fluid was HBOC-C, and *z* _{1} = -1 for HEX; *z* _{2} = 1 for titrated infusion and *z* _{2} = -1 for bolus infusion, and *z* _{3} coded for the interaction between fixed treatment effects (*z* _{1} × *z* _{2}).The coefficients γ_{1} represented the main effect of fluid type, γ_{2} was the main effect for infusion, and γ_{3} was the interaction effect (fluid × infusion). We also compared the lactate responses between groups designated by their survival status posthemorrhage: *z* = 0 if animals for nonsurvivors and *z* = 1 for survivors; parameter estimates were coded accordingly.

Preliminary estimates for the nonlinear mixed model parameters were obtained by transforming Eq. 4 to the linear form *Y* = *A* + *Bt* + C·*e* ^{-} *κ* *t*, where *Y* = ln(*y*). Estimates for *A*, *B*, and *C* can then be used to obtain preliminary estimates by back-transforming from the relations ln (*y* _{max}) = *A* + *B* (1 / *κ* + *t* _{max}), *B* = *δ* _{min}, and *t* _{max} = (1 / *κ*) ln (*κ C* / *B*). Initial nonlinear model fits using these parameter estimates were then performed in SAS PROC NLIN V. 9.1 (^{24}) using a modified Levenberg-Marquardt method. This step enables estimation of reasonable starting values necessary for convergence of the nonlinear mixed model but ignores the repeated measures effects. The full model was then fitted to the data using the nonlinear mixed-models procedure in SAS PROC NLMIXED (SAS V. 9.1) (^{24}). NLINMIXED solves the functional equation for all 16 parameters and accounts for the within-subject repeated measures by using an iterative approach based on the estimated initial values. This model maximizes the approximate likelihood function integrated over the random effects; the integral was approximated by adaptive Gaussian quadrature. Preliminary model fits suggested that parameters describing lactate concentration (*y* _{0}, *y* _{max}) can be treated as random and the remaining parameters as fixed. Estimates and 95% CIs for *y* _{max} and *t* _{max} were obtained from the PREDICT statement in SAS PROC NLMIXED (^{24}). Model fit was evaluated by the log-likelihood (-2 LL), Akaike Information Criterion, the gradient vector of first-order partial derivatives at the optimization solution, and residual plots. Approximate 95% CIs and *t* values for each parameter estimate were derived from the final Hessian matrix (^{24}). Treatment effects and interactions were assessed by examination of the *t* value for the respective coefficient estimate.

## RESULTS

Arterial lactate concentrations at baseline averaged 0.65 (95% CI, 0.01-1.31) mM. Lactate concentrations increased exponentially over the course of the hemorrhage, averaging 0.88 (95% CI, 0.22-1.54) mM after 20% blood volume removal, 3.64 (95% CI, 2.98-4.30) mM after 40% removal, and 11.43 (95% CI, 10.77-12.09) mM at the end of the third stacked bleed, when 60% of the estimated total blood volume had been removed. The fifth lactate measurement was obtained at 60 min from the initiation of hemorrhage (*t* _{60}) or approximately 20 (SD 8) min from the initiation of resuscitation. All bolus treatments were completed in 15 min; total titration time was 68 min for HBOC-C and 25 min for HEX (^{11}). That meant that 16 of 18 animals in both bolus infusion groups, but only 1 of 18 animals in both titration groups, had received their entire allotted volume of resuscitation fluid at this sampling point. Nine animals showed no reduction in lactate concentrations during the entire resuscitation period; eight were animals receiving titrated infusions (4/9 HBOC-C titration, and 4/9 HEX titration); and one animal in the HEX bolus group.

### Treatment effects

Twenty-one animals survived at least 1 h posthemorrhage (12/18 HBOC-C and 9/11 HEX animals). Five HBOC-C animals, but none of the animals in either HEX group, survived the entire DARPA-prescribed 3-h period from the initiation of hemorrhage to cardiovascular collapse (^{11}). Lactate profiles were similar between resuscitation treatments (Fig. 1). Nine animals exhibited increased, rather than decreased, lactate levels after resuscitation; these were from 8 of 18 titration animals and 1 bolus treatment animal. The linear model did not discriminate statistically between lactate concentrations as a result of either resuscitation fluid type (HBOC-C vs. HEX; *F* = 0.37; *P* = 0.548) or infusion schedule (titration vs. bolus; *F* = 0.38; *P* = 0.540) at any time point; interaction effects were not significant (*P* > 0.4 for all interactions).

Lactate parameters, and their respective confidence intervals, estimated from the nonlinear model (Table 1) showed considerable overlap between treatment groups. Therefore, pooling over groups, the combined nonlinear model for lactate concentrations over the course of hemorrhage and resuscitation, was:

SE = 4.595, *s* _{rat} = 0.653. Estimated mean peak lactate concentration was 11.43 (10.77-12.11) mM, and mean time to peak lactate concentration was 45 min (41-50); mean relative initial net rate of lactate accumulation was 0.28 (0.19-0.38) mM/min, and mean relative final net rate was −0.006 (−0.009 to −0.004) mM/min.

### Survival

Regardless of resuscitation treatment, animals surviving at least 60 min from the end of hemorrhage can be distinguished from nonsurvivors in having lower accumulated lactate loads at the end of hemorrhage (Fig. 2 and Table 2). Both the linear and nonlinear models provided good estimates of peak lactates in comparison to observed values. The linear model estimated peak lactates 1.4 (95% CI, 0.1-2.6) mM lower for phase 1 survivors compared with nonsurvivors (*P* = 0.034) at the end of hemorrhage and 3.8 (95% CI, 2.4-5.1) mM lower at *t* _{60} (*P* < 0.0001) when resuscitation was underway. Peak lactates and lactate concentrations at *t* _{60} were 3.5 mM lower than nonsurvivors (*P* < 0.001). The five animals surviving to the prescribed 3-h end point averaged lactate concentrations approximately 1.8 (95% CI, 0.07-3.60) mM lower than nonsurvivors (*P* = 0.08) at the end of hemorrhage and 3.34 (95% CI, 1.3-5.4) mM lower at *t* _{60} (*P* = 0.002). The nonlinear model indicated that survivors and nonsurvivors differed only in peak lactate concentrations, averaging 2.6 mM lower in survivors. Other parameter estimates did not differ statistically between survivors and nonsurvivors for either phase 1 or phase 2.

Many nonsurvivors were refractory to low-volume resuscitation, exhibiting an increase, rather than a decrease, in lactate concentrations until death. These responses were mirrored in estimates for phase 1 *δ* _{min}. The *δ* _{min} values for survivors and nonsurvivors differed qualitatively, although they could not be discriminated statistically; whereas survivors were characterized by relatively uniform and precise net relative rates of disappearance, *δ* _{min}, of nonsurvivors were highly variable with positive values (Fig. 2 and Table 2).

## DISCUSSION

We have previously reported for a rat model of acute severe hemorrhage that low-volume resuscitation with an HBOC-C, combined with a large molecular weight, tetrameric HBOC (OxyVita), was superior to HEX alone in promoting both survival to 180 min from hemorrhage initiation and MAP support to at least 60 mmHg (^{11}). The 3-h survival threshold was mandated by DARPA with the goal of identifying the resuscitation strategy immediately after a 60% hemorrhage that best promotes survival for 3 h without conventional large-volume crystalloid support. The MAP of 60 mmHg approaches the minimum level compatible with cerebral perfusion in rats but below the rebleeding threshold established for a swine model of uncontrolled hemorrhage (^{27}). Hextend is the standard of care for the US Special Operations Forces for resuscitation of battlefield casualties with hemorrhagic shock (^{3}); HBOC supplementation has been recommended to augment oxygen-carrying capacity and reduce transfusion requirements (^{6, 28, 29}). We hypothesized that the increased survival times exhibited by the HBOC-C animals would be associated with lower accumulated oxygen debt, and, thus, lower lactate loads and improved lactate resolution. In this study, quantification of lactate kinetics by both linear and nonlinear models failed to demonstrate a clear difference in lactate profiles between resuscitation treatments despite the demonstrable survival advantage of the HBOC-C. Nevertheless, a significant survival advantage was conferred to animals that both exhibited relatively lower lactate loads at the end of hemorrhage and before resuscitation and responded to resuscitation by a reduction in lactate. Conversely, all of the animals that failed to show reductions in arterial lactate during resuscitation did not survive to the 60-min time point.

Several animal studies have demonstrated that HBOC administration results in improved survival relative to HEX (^{28-30}), although one rat study of low-volume resuscitation after severe hemorrhage reported that HBOC-treated animals performed no better than nonresuscitated controls (^{31}). The finding of no differences in lactate concentration between HBOC and HEX during low-volume resuscitation is consistent with prior swine studies (^{28, 29}), although in these studies, tissue oxygenation was greater and more rapidly restored posthemorrhage when animals were infused with HBOC (^{29, 32}). However, comparisons between studies are difficult because of differences in the HBOC preparations used, differences in the amounts and timing of supplementary resuscitation fluid administered, the type of hemorrhage protocol (e.g., volume vs. pressure bleed or conscious vs. anesthetized preparation), and, not least, the amount and severity of the preceding hemorrhage. The high lactate levels exhibited posthemorrhage by animals in this study indicated the severity of this model; lactate levels more than 9 mM are generally associated with severe, if not irreversible, oxygen debt (^{33, 34}). A limited survey of several papers using rat hemorrhage models show that posthemorrhage/preresuscitation lactate levels range from less than 3 (^{35}) to greater than 15 (^{36}) mM. These values indicate the lack of standardization between hemorrhage protocols and further suggests that comparing outcomes of given resuscitation therapies between studies may be extremely problematical.

Even within studies, variability of individual response to hemorrhage, and the resulting differences in physiological compromise, greatly influence outcome to the point where differences between therapeutic treatments may be masked or annihilated (^{11}). In this study, we did not detect statistically significant differences in lactate profiles between either the type of fluid or the different infusion schedules. As a result, differences in lactate reduction cannot be used to explain the improved survival noted for the HBOC-C treated animals. Most early deaths were uniformly distributed across groups, indicating the severity of the model. However, subsequently, there was a moderate association between infusion schedule and whether animals exhibited a reduction in lactate with resuscitation. We observed that almost half of animals receiving titrated infusions failed to show a decrease in lactate (8/18), whereas nearly all animals receiving a bolus infusion did show reduced lactate concentrations (17/18). If it is assumed that lactate levels are indicative of oxygen debt, then it is clear that bolus infusions should be preferred to pressure titrations, especially in field or tactical situations, where ease of administration may be a priority. Conversely, gradual infusion of resuscitation fluid to a given MAP may not be sufficient to prevent cell damage, as indicated by the continued increase, rather than decrease, of lactate during the resuscitation process. However, overall survival was coupled most closely by events occurring before resuscitation, as indicated by peak lactate loads measured at the end of hemorrhage. Animals with posthemorrhage lactate concentrations greater than 10 mM did poorly, independent of subsequent resuscitation treatment, whether lactate subsequently showed any reduction at all with resuscitation, or the rate at which lactate levels declined from peak values.

These data indicate that assessing physiological compromise on the basis of metabolic indices such as lactate may be more problematical than previously thought. In the experimental setting, there are few or no examples of serial lactate profiles being used specifically to compare resuscitation therapies. In the clinical setting, serial measurements of lactate have been recommended as a predictor of outcomes (such as mortality or risk of MODS), although measurements are typically obtained over fairly long periods such as days (^{9, 37}). Our data suggest that much shorter time frames may be more appropriate when early warning of physiological compromise is essential, such as occurs with trauma. In this study, we demonstrated that serial lactate measurements taken over minutes to a few hours provided a qualitative picture of subject response to both hemorrhage and resuscitation. It was clear that lactate levels that either increase subsequent to the end of hemorrhage or stabilize at relatively high concentrations indicate a poor outcome and a short survival time postinjury. The advent of point-of-care lactate monitors may now allow clinical studies of lactate kinetics by enabling more rapid sampling rates with smaller blood volumes. However, it is troubling that quantitative estimates of lactate trajectory subsequent to hemorrhage could not be used to distinguish between outcomes. In the clinical setting, the first in-hospital measurement of lactate usually occurs well after lactate levels have already been affected by the injury itself, the time between point of injury and definitive care, and any interventions already performed, as well as by subject-specific responses to hemorrhage, environment, and effects of prehemorrhage stressors. Much larger studies will be required to determine if the mechanistic nonlinear model proposed here can be applied as a subject-specific predictive tool.

Mixed models are greatly superior to the conventional ANOVA models in that this method of analysis is able to accommodate irregularly spaced time sequences within subjects and missing or truncated data and allows custom specification of the covariance structure within each time sequence. The latter consideration may not be of direct interest but is important in that it allows more efficient specification of the standard errors for estimates of the mean response (^{21, 23, 38}). In addition, correct specification of the covariance model, in conjunction with likelihood methods of estimation, will give valid estimates of mean response trends when there is high dropout of subjects over time and dropout depends upon the previous response (^{39}), as is the case here. Both linear and nonlinear models fitted to data in this study gave similar results in interpretation of treatment efficacy and estimates of peak lactates. The major advantage of the linear mixed-effects model is that the response is predicted by linear combinations of treatment and time effects so effect size is relatively easy to compute. However, because time is considered a factor, one disadvantage is that there will invariably be some loss of information because sampling time points must be standardized to allow model fit. With the nonlinear mechanistic model, the parameters and their estimates can be readily interpreted and have direct physiological meaning because the underlying functional form can be specified (^{26, 40}). However, model specification and fitting can be quite laborious because fairly rigorous specification of initial starting values is required for the model to converge and provide adequate fit.

In summary, the survival advantage previously demonstrated by HBOC-C over HEX during low-volume resuscitation does not seem to be coupled to differences in arterial lactate reduction. However, there was a clear survival advantage for animals that incurred both lower peak lactate loads during hemorrhage and exhibited reduced lactate during resuscitation independent of the specific resuscitation treatment. These observations support our contention that, at a minimum, measurements of metabolic indicators taken as close to point of injury as possible, followed by sequential measurements over relatively short time frames during resuscitation, are of value in assessing both the efficacy of therapeutic response and potential outcome.

## ACKNOWLEDGMENTS

The authors thank V. Daoud, N. Kishore, and especially M. Skaflen for excellent technical support, J. Sondeen for helpful scientific suggestions at different phases of this investigation, J. McKinney-Ketchum for extremely useful feedback regarding the statistical portions of this article, and Hanna Wollocko, M.D., of OXYVITA, Inc., for her generous contribution of the hemoglobin cocktail.

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