The development of hyperglycaemia soon after burning has been related to body burn surface area (BSA) and the depth of the wound. Hyperglycaemia is not an isolated phemonenon. It appears in a scenario of changes of amino acids, free fatty acids, triglycerides, insulin, human growth hormone, cortisol, glucagori, and adrenalin concentrations, Hypermetabolism, hyperpyrexia, immunodepression,' increased production of endogenous glucose, amino acid and fatty acid mobilization, and water retention are all characteristics of the immediate response to a major burn injury, A physiological reset occurs in response to stress that alters the hormonal milieu. The hypennetabolic response to thermal injury is maximum in burns as small as 20% total 13SA and increases with additional burn size from heat loss.' These temporal changes are adaptive to noxious stimuli, but eventually result in progressive catabolism and deterioration. Hypovolaemia-related cardiovascular dysfunction can occur during this time owing to increased vascular permeability.
In the absence of sepsis, most cases of post-burn hyperglycaemia require no specific therapy. Clinical and experimental studies on glucose kinetics after a burn injury are related to its plasma concentration. The quotient between total plasma glucose and plasma volume, in a situation with abrupt changes in the extracellular volume distribution, is not an adequate indicator of carbohydrate metabolism.
Different fluid resuscitation guidelines have been designed for the treatment of burn patients. Most of these solutions include carbohydrates. The effect of intravenous infusion of these substances in a hyperglycaemic situation is not well documented.
The complexity of the problem has originated this algorithm approach, which allows us to analyse extracellullar glucose behaviour during the first hours after a major burn.

Material and methods

1. Computational methods and theory
We base our algorithms on the physical law of mass conservation. In order to determine plasma and interstitial volumes in the burn patient, our algorithms use data such as age, sex, weight, height, body BSA, fluid inputs, diuresis, haematocrit, and plasma protein concentration.We presume that plasma glucose concentration is equal to extracellular concentration. This assumption is consistent with most metabolic studies. Fig. I presents a flow diagram including these variables and the relations considered in this study. On the basis of this hypothesis, we infer the differential equations that control the plasma and interstitial glucose turnover:

and

We can thus deduce:

Both equations can be expressed as:

and

As glucose concentration data are discreet, we transform the differential equations to equations in differences. Thus, using the Euler method, we obtain:

TPG (k) = TPG(k-l) + DTX [ GI(k-l) - PGCO(k-l) - GDI (k-l) ] (6)

TGIN (k) = TGIN(k-l) + DTX [GDPI (k-l) - GDIC(k-l) - GLEX (k-l) ] (7)

Glucose concentration, exogenous input glucose, and glucose loss by exudation values are calculated by means of linear interpolation of clinical data. From equation (2) we know the net balances between glucose supplies and elimination in the plasma and interstitial compartments.
Thus:

adding (3) and (4) we obtain:

ECGNB(k-l) = GI(k-l) - ECGU(k-l) + INGNB(k-l)  (10)

2. Clinical application of the algorithm
As an example of the validity and utility of the algorithm the clinical data of 36 non-diabetic burn patients were retrospectively analysed. Patients were divided in two groups according to the resuscitation guidelines applied. Patients in Group 1 were resuscitated with the Parkland guideline (lactated Ringer 4 tnl/kg/% BSA during the first 24 h, half of this volume infused during the first 8 h and the other half in the following 16 h).
Patients in Group II were resuscitated according to the BET guideline (human seroalburnin in factated Ringer, with a decreasing concentration from 10 to 7.5, 5, 2.5 and 0%, depending on the post-burn time, (0-8 h, 8-16 h, 16-24 h, 24-40 h and over 40 h, respectively), with an infusion rate of 220 ml/m²/BSA/h.

Fig. I - Simplified diagram of the variables and their relations considered in the analysis of extfacellular glucose exchanges after burn injury.

Thirty-six patients were included in the study: 15 in Group I and 21 in Group II. The characteristics of these patients. The mean values of BSA, age, sex, height, weight, and body mass index of both groups were comparable.

Fig. 2 - Haemoconcentration is a consequence of burn injury. Its level is related to BSA. The mean value of venous haematocrit was higher in the group of patients treated according to the Parkland guideline (Group 1) than in the group treated according to the BET guideline (Group II).

Haernoconcentration was related to both BSA and resuscitation therapy and was higher in Group I than in Group 11. Plasma protein concentration decreased in all cases, in relation to BSA and the type of fluid used during the resuscitation period.'-" Plasma volume was higher in Group 11 (Fig. 3a). The interstitial volume, obtained by the algorithm, increased in Group I more than in Group 11 (Fig. 3b).
Plasma glucose concentration increased above its normal value immediately after injury and remained at that level throughout the period considered. There were no significant differences between the two groups of patients (Fig. 4).

Fig. 3a - The mean value of the plasma volume variable calculated by the algorithm was higher in patients in Group 11 Fig. 3b - The interstitial volume increased  much more in Group I patients. Fig. 4 - The values of plasma glucose concentration were elevated immediately post-injury and remained elevated during the period analysed. There were no significant differences between the groups.

The total glucose in plasma and the interstitial compartments can be calculated from the relative volumes and concentrations. Patients resuscitated with the BET guideline (Group 11) showed higher values of total plasma glucose (Fig. 5) and lower values of total interstitial glucose (Fig. 6).

Fig. 5 - The values of the variable total of plasma glucose was higher in patients resuscitated with colloids (Group 11). Fig. 6 - The values of the total interstitial glucose were higher than normal in both groups, but less so in Group II.

Fluid loss through burn wounds is related to BSA." Its composition is comparable with interstitial volume. Glucose concentration in the exudation fluid is assumed to be equal to that of plasma. The glucose loss values in the exudate can be estimated on the basis of these assumptions (Fig. 7). These losses are substantial in patients with major BSA.

Relations between plasma and interstitial glucose flows, exogenous glucose inputs and endogenous glucose production can be defined as plasma glucose net balance (PGNB). This variable oscillated close to normal values (zero g) in the patients (Fig. 8). Oscillations from a positive to a negative glucose balance were related to the time interval post-injury and resuscitation therapy. These behaviours were not justified by the exogenous infusion of carbohydrates during the resuscitation period.

Fig. 8 - The plasma net glucose balance, which shows the glucose flows between plasma and the interstitial compartments and exogenous and endogenous glucose inputs, oscillates close to normal values, zero grams, in the period analysed.

In the immediate post-burn period phase, there is a decrease in nutrient flow and oxygen delivery to cells. The pyrocatechol discharge and the glucagon, insulin and corticosteroid release are part of the response to injury. Carbohydrate metabolism is altered in burn Patients during the shock phase in relation to the severity of the injury." Although glucose production increases and peripheral uptake is normal, the entrance of glucose into the Krebs cycle is reduced. In these stress states, the administration of excess glucose can have detrimental metabolic effects.
A transition occurs from the immediate post-burn phase to the flow phase. The latter is characterized by catabolism, hypermetabolism, and a negative nitrogen balance. Although the initial glucose intolerance begins to resolve, hyperglycaemia may still be evident.` This transient period has not been analysed in detail, probably because it has been considered irrelevant.
Our algorithm demonstrates that a change exists in the glucose stock in the patient's interstitial compartment, depending on the type of resuscitation guideline used. Similar behaviour was observed in the interstitial volume, which was higher in Group I than in Group II patients. The stock of extracellular glucose was related to the post-burn increase in the interstitial volume and to the resuscitation therapy selected.
The interstitial compartment acts as a mattress for the carbohydrates, in a clinical situation where changes in plasma and interstitial volume are frequent and considerable. Most of these carbohydrates are endogenous. The exogenous administration of lactate, at least in our patients, is not relevant, if we consider the glucose eliminated with the exudate. However, hyperglycaemia and glucosuria have been described with glucose infusions during this period.
In order to observe an increment in extracellular glucose in the burn patient, it is necessary to have a lower glucose turnover. Glucose utilization in these patients must be decreased, as it is related to burn severity. These findings are confirmed by clinical and experimental data published by different authors and validate our algorithm. Some behaviours obtained still require analysis. The control mechanisms that regulate net glucose exchanges between plasma, interstitium and intracellular compartments are not yet included in the algorithm.

Conclusion

In our opinion, the algorithm that we present is a simplc follow-up method for metabolic carbohydrate disorders in the post-burn shock stage. Its most striking aspect is its simplicity for obtaining relevant behaviours of non-accessible variables that are very indicative of the state of the system and very difficult to obtain in daily clinical practice.

RESUME. La brûlure augmente la concentration du glucose plasmatique et diminue le volume du glucose. Dans cette situation, la glycémie n'est pas un indicateur exact du comportement dynamique du glucose extracellulaire. Les Auteurs présentent un algorithme pour l'analyse du comportement du glucose extracellulaire chez 36 patients brûlés pendant la phase du choc: la réanimation a été effectuée en 15 cas avec un taux et un volume élevé d'une solution crystalloïde libre de colloides et en 21 cas avec un taux et un volume moyen d,une solution colloïde et crystalloïde. L'algorithme présenté permet d'analyser le comportement dynamique du glucose extracellulaire après la brûlure, dans une période caractérisée par des changements rapides des volumes extracellulaires.

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