INTRODUCTION

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VOLUME OF BLOOD LOSS is a major determinant of outcome after non-head injury (2). As posttrauma blood volume cannot be measured directly, the extent of blood loss is estimated from the homeostatic responses such as changes in heart rate and blood pressure. However, such changes are complex. Traditionally, a rise in heart rate and fall in blood pressure are taken as indicative of severe hemorrhage. However, in hemorrhage uncomplicated by injury (e.g., gastrointestinal bleeding), heart rate response is biphasic, with an initial tachycardia followed by a reflex bradycardia (4, 18, 21), and blood pressure is maintained until hemorrhage becomes severe (4, 18).

Determination of the extent of blood loss involves locating a patient at points on nonlinear functions (e.g., heart rate and blood pressure time trends) so that blood volume can be back calculated. However, in the emergency room, prehemorrhage status, time from onset of hemorrhage, and rate of blood loss are generally unknown, and thus the distance a patient's results lie along the response is uncertain. In such circumstances, blood loss cannot be directly inferred, and the usual approach is to observe (i.e., wait for serial measurements so that trend can be determined). A method that could accurately predict volume of blood loss from the routinely available physiological measurements, without reference to rate of loss and time-based information, would, therefore, be extremely useful.

A prediction method that is gaining popularity is known as artificial neural networks (ANN) (6). These are arrays of simultaneous equations that iteratively examine data sets according to learning rules, the most extensively studied and commonly used being the delta rule (20). The delta rule performs gradient descent optimization and is thus closely related to standard regression models. ANNs using the delta rule have been successfully applied to predicting outcomes in a variety of complex biomedical problems (5, 10).

In common with all gradient descent methods, ANNs may become stuck in local minima in the error landscape. One way this can be avoided is by applying search procedures that are known to mimic the processes of evolution known as genetic algorithms (11, 15, 19). Genetic algorithms have been used with ANNs in a variety of ways (3, 25), one of which is to select which variables are the most important predictors (16, 19; see Fig. 1).

View larger version (19K): [in this window] [in a new window]   Fig. 1.   Schematic of key processes in a genetic algorithm neural network. Random combinations of variables for a prediction model, coded according to which variables are included (genes), are generated to form a "gene pool." For each gene, code for combination of variables is used to train an artificial neural network (ANN); accuracy of predictions of ANN is called "fitness of gene" (F). Next gene pool (i.e., next generation) is derived by using genes with high F to replace those with low F. Over generations, genes with higher and higher F, i.e., combinations of variables that produce high predictive accuracy, come to dominate gene pool, i.e., prediction solution set "evolves."

In this study, we examine whether a genetic algorithm neural network (GANN) can predict volume of blood loss from standard physiological and biochemical responses in an experimental hemorrhage model in rats and we compare accuracy of prediction to stepwise linear regression (SLR).

	METHODS

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Experimental hemorrhage model. Thirty-three male Wistar rats of the Porton strain (228-258 g) were anesthetized with alphadolone/alphaxolone (Saffan, Pitman-Moore, UK; 19-23 mg · kg¹ · h¹ iv) while breathing room air. Body temperature was maintained at 38.1 ± 0.3°C by using a heated operating table and heating lamps. Arterial blood was withdrawn anaerobically from the ventral tail artery in aliquots of 0.5 ml at an overall rate of 2% estimated total blood volume per minute [total blood volume 6.06 ml/100 g body wt (13)]. Cardiovascular measurements were made after the withdrawal of each aliquot of blood, and each sample was subjected to blood-gas analysis (ABL 330, Radiometer, Denmark). The cycle was repeated until 40% of the estimated blood volume had been withdrawn. At the end of the study, the animals were killed by overdose of anesthetic.

Predictive models. The prediction data set comprised 10 predictor variables: heart period; systolic, diastolic, and mean blood pressures; hemoglobin concentration; pH; arterial PO₂ and PCO₂ (Pa_O2 and Pa_CO2, respectively); bicarbonate; and base deficit, together with the target variable estimated blood loss, at 12 time points for 33 animals (total 396 prediction cases). Volume of blood loss was estimated as percentage of the estimated total blood volume. Time was not one of the variables included. Trend in mean blood pressure and heart period is illustrated in Fig. 2.

View larger version (15K): [in this window] [in a new window]   Fig. 2.   Summary of trend in heart period (HP) and mean blood pressure (MBP) with blood volume (BV) loss during stepwise hemorrhage [i.e., blood loss as %estimated total blood volume (%BV) (15)] in 33 male Wistar rats. Error bars indicate SD values.

Data were divided randomly, i.e., at each time point 17 and 16 cases were randomly allocated to either the training or test sets so that, overall, the data were divided randomly in half to give a total of 198 prediction cases in both the test and training sets. The GANN has been described previously (16, 19). Briefly, for each information gene, a neural network with one hidden layer was derived. The number of nodes in the input and hidden layers in each case is equal to the two geometric means rounded to the nearest integer of a geometric progression of four terms with a common ratio of 0.5, with the first term being the number of variables in the input layer (variables active in the information gene) and the last term being one (single predictor target; volume of hemorrhage). This process is illustrated schematically in Fig. 3. Neural networks were trained by using the delta rule for back-propagation of error defined as root mean square (RMS) of actual minus predicted estimated blood volume ten times, with different initial random weights and the best (lowest) RMS error stored.

View larger version (20K): [in this window] [in a new window]   Fig. 3.   Schematic illustrating how a neural network may be derived from a genetic algorithm. Predictor variables are coded for by binary information genes. If a gene is active, then data from corresponding variable are used as an input source to a neural network. BP, blood pressure; PaO2 and PaCO2, arterial PO2 and PCO2, respectively.

The fitness function for each information gene was calculated at the end of each generation from the stored neural network prediction error divided by the sum of errors for all neural networks in the population. The genetic algorithm used a population size of 16 over 32 generations (representing one-half of the possible combinations). The initial generation was randomly generated. The information gene with highest fitness at the last generation was used to predict volume of blood loss in the test set. The GANN process was implemented by a custom-written program (Visual Basic 4.0, Microsoft) operating on a 120-MHz Pentium IBM-PC-compatible computer.

Multiple SLR was used as the control experiment. All predictor variables were allowed to enter. Variables were entered if probability from F-test was P < 0.05, and removed if P > 0.10, in a stepwise manner until no further variables could be entered or removed. The solution equation from regression, performed on the training set of data, was applied to the test set to produce predictions. Regression modeling and statistical tests were performed by using SPSS for Windows (SPSS version 6.1).

	RESULTS

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Variables selected by SLR, regression diagnostics, and variables included in GANN solution are shown in Table 1. There were a total of four variables in the SLR solution compared with three in the GANN solution. Base deficit and Pa_O2 were selected by both methods; both methods also included measurements of blood pressure: mean and systolic blood pressures with SLR and diastolic blood pressure with GANN.

Overall RMS error on the test set was 2.63% (SD 1.44) estimated blood volume with GANN and 4.22% (SD 3.48) with SLR.

Mean and SD of RMS error in prediction on the test set by GANN and SLR is shown in Fig. 4. The GANN produced significantly lower RMS error in prediction overall than SLR (paired t-test, P < 0.001). Error in prediction by both methods was normally distributed (Kolmogorov-Smirov goodness of fit, z = 1.72, two-tail, P = 0.005 for GANN; z = 1.56, two-tail, P = 0.0156 for SLR).

View larger version (15K): [in this window] [in a new window]   Fig. 4.   Prediction of estimated blood loss during stepwise hemorrhage in 33 male Wistar rats from measurements of physiological and biochemical responses by a genetic algorithm neural network () and stepwise linear regression (). Volume of blood loss is shown as a %estimated total BV (15). Time categories equal increments of 90 s. RMS, root mean square.

Time for training by the GANN was 2 h 42 min, and 2 min for SLR. Once trained, test time was <1 min for both methods.

	DISCUSSION

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The homeostatic response to hemorrhage involves complex changes in many cardiovascular and biochemical variables (4, 18, 21). There have been no previous reports of accurate prediction of dynamic blood loss without use of rate of loss and time-based information. In this study, we demonstrate that a GANN is able to use this type of data to predict volume of blood loss accurately and significantly better than SLR. Four issues arise in interpreting this finding.

First, concerns have been expressed as to the heuristic value of ANN results (23). One reason for this is that, as ANN solutions are defined by the network as a whole, feedback cannot be given about which variables are the important predictors, i.e., measurements analogous to regression coefficients are not available. An advantage of the GANN approach is that a set of optimal predictors is derived. This can be considered as analogous with a nonranked list of variables with the highest regression coefficients. However, for variables in the solution set, in this case diastolic blood pressure, base deficit, and Pa_O2, all that can be deduced is that they together carried more predictive information than other variable combinations examined. Furthermore, as with all blind genetic algorithm searches compared with exhaustive combinatorial approaches, there can be no guarantee that the arrived solution represents the global solution, as different combinations of variables could be found in subsequent searches. Interestingly, however, both SLR and GANN selected similar variables, Pa_O2, base deficit, and measurements of blood pressure. Together, these appear to be an understandable choice as they provide samples from the cardiovascular, biochemical, and respiratory variable domains of homeostatic response examined. Indeed, a recent report shows a relationship between the requirement of blood transfusion and base deficit in critically ill trauma victims (7).

Second, in common with many other ANN studies (5), we find a GANN to have significantly greater predictive accuracy than a comparable standard statistical method. This does not suggest that a GANN is "superior" to SLR in that, like regression models, ANNs implicitly require data to have a regular (but not necessarily Gaussian) distribution about the output function (20). They are also as prone as regression methods to overlearning the training set (see fourth point below). If the correct interaction terms are used in a regression then, by definition, neither an ANN or any other method can predict better. Rather, the finding of better accuracy with the GANN model implies that the SLR model was nonoptimally specified. Specification of regression methods is a major problem that occurs where, as in this study, a number of variables are found to be important predictors together, and complex relations must be accounted for by a priori inclusion of combination terms (1). The difficulty that arises is that there is no analytical method for determining a priori how covariates should be combined for a regression. For example, if a, b, and c interact, should the interaction term be a * b * c or a/b * c or â b/c? In fact, all possible interactions should be explored. The key advantage of ANNs, which explains the better accuracy of prediction results in this study, is that they do not require a priori specification to account for complex covariate interactions. This property allows ANNs to solve any well-behaved continuous function to within an arbitrary degree of error (22). By implication, the superior prediction results by GANN compared with SLR in this study suggest that important complex intervariable relationships exist between diastolic blood pressure, base excess, Pa_O2, and blood volume. This is not an unexpected finding, since, as discussed, cardiovascular and biochemical responses to hemorrhage are known to be complexly related.

Third, ANN and, particularly, GANN procedures are computationally slow compared with standard statistical analyses. Training the GANN process in this study took over 80 times as long as the SLR. This is due to the serial nature of processing on a desktop computer being used to implement the essentially parallel GANN task of evaluating multiple ANNs. If efficiency is evaluated in terms of serial speed, SLR is clearly superior. The GANN process, however, offers a valuable paradigm for parallel computation (17) and, if a GANN procedure were implemented on a parallel computer, speed differences would be much less. This may be important in furthering the biological analogy of ANNs, as population genetics-controlled selection of neural groups has been suggested to be a key mechanism underlying the processes of neural development and learning in humans (12). Once the GANN has been trained, the time to make a prediction is similar to the SLR method (both <1 min).

Fourth, in common with all predictive studies, the wider applicability of results can be questioned (24). One reason for this is that prediction results are critically dependent on training data being representative of subsequent test set. Both a GANN and SLR may produce spuriously optimistic prediction results when tested but fail catastrophically in practice if a new case is drawn from a significantly different sample of the population (23). Earlier computational approaches to this problem focused on searches for global solutions. Three factors suggest that this should no longer be a target and that a GANN process may be valuable as a practical clinical prediction tool. 1) As illustrated by the difficulties encountered by De Dombal and associates (9) in their pioneering work on diagnosis of the acute abdomen, general transferable prediction systems may be impossible to achieve, because of the subjective, variable nature of many clinical measurements (8). 2) Obtaining general solutions may not be desirable, as a system dependent on such may not have the ability to adapt to changing circumstances (14). 3) Since the equivalent of £100,000 of specialist center-based computational power in De Dombal's era is now available for less than £1,000 and is available in most medical departments, it is possible for solutions to be evolved locally. Together, these arguments suggest that ANN-type solutions should be implemented locally and at each site and as staff, practices, and patients change be retrained to ensure optimization of prediction for that site. Considering that the GANN method, as used in this study, will operate on any modern desktop PC, prospective examination appears to be warranted. For this to be done in practice, many other variables, e.g., medical history, gender, medications, type of injury, will have to be included in the predictive model.

We conclude that in the studied experimental model of hemorrhage in rats a GANN can predict volume of hemorrhage highly accurately and significantly better than SLR can, without knowledge of prehemorrhage status or trend in physiological variables. We suggest that this merits further investigation as it may hold promise for prediction of blood loss in clinical practice. GANN approaches may also be applicable to prediction of responses in other complex physiological systems.