INTRODUCTION

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THERE HAVE BEEN SEVERAL recent advances in our understanding of cold-water near-drowning, a condition where victims survive cold-water submersion for as long as 66 min with full or partial neurological recovery (2). Explanation of this phenomenon relates to the mechanisms for, and amounts of, body/brain cooling that occur and the mechanisms for the protective effects of this cooling.

It is commonly accepted that the cerebral protection is due to the decreased metabolic requirements of the cold brain tissues. This protective effect of low tissue temperature is demonstrated by the fact that induced hypothermia with brain cooling has been successfully used during brain surgery or surgery to repair congenital heart defects to protect against hypoxic brain damage. However, it seems unlikely that survival from prolonged cold-water submersion can be based solely on a decrease in cerebral metabolic requirements for O₂ (for review see Ref. 12). Several recent studies directed mainly toward protection of the brain during or after cerebral ischemic events have demonstrated that even moderate brain cooling to between 35 and 33°C provides substantial cerebral protection from 10-20 min of total cerebral ischemia in rats (for review see Ref. 13). It is proposed that an additional mechanism for cold protection from anoxia involves decreased glutamate and hydroxyl radical production.

Inasmuch as irreversible brain damage usually occurs in humans within 4-6 min of anoxia, it is likely that the brain would have to cool 3°C within 5 min to explain the intact survival of prolonged cold-water submersion.

The ability to withstand prolonged total submersion, especially in cold water, seems to be more evident in children. Reports of children surviving total submersion in cold water are commonly known in all northern countries (2, 5). Unfortunately, these reports often are given as individual case reports, or information is based only on circumstantial evidence without the necessary details for complete analysis.

Investigation of the thermal changes occurring in the brain of a person submerged in cold water is thus of clinical importance. The rate of brain cooling basically depends on external heat exchange (i.e., heat loss from the head surface to cold water), internal heat exchange (i.e., heat transfer within the head), and local brain metabolic heat production. Internal heat exchange occurs through heat conduction from the deep brain tissues to the outer boundaries and convective heat exchange via blood flow between brain tissue and the body core. Conductive and convective cooling are influenced by boundary conditions (i.e., water temperature and heat transfer coefficient), blood circulation, brain metabolism, respiratory ventilation of water, and head size. The quantitative contributions of these factors to brain cooling have not been determined. Inasmuch as experimental research with human subjects is not possible, a mathematical modeling approach is an acceptable alternative for analysis. Dexter and Hindman (7) developed a one-dimensional model for brain cooling during cardiopulmonary bypass, and Olsen et al. (20) developed a model for brain cooling during hypothermia and circulatory arrest. The aim of the present work is to develop a model to estimate the contributions of the different avenues of brain cooling during cold-water submersion.

	METHODS

Geometrical Representation

View larger version (25K): [in this window] [in a new window]   Fig. 1.   Schematic representation of brain cooling model.

Mathematical Model

(1)

1

1

1

3

3

1

Boundary 1

(2)

2

1

Boundary 2

Insulated. Boundary 2 is insulated, and there is no water in the upper airway. Consequently, heat transfer at boundary 2 is expressed as

(3)

Heat transfer into cold water. Boundary 2 is assumed to be totally exposed to cold water in the upper airway (see Conductive cooling). The surface area across boundary 2 is ~168 cm², whereas the real surface for the nasopharynx is ~15-20 cm². The heat transfer is then expressed as

(4)

where ₂ is heat transfer coefficient (W · m² · °C¹) and T_w2 is temperature of cold water in the upper airway (°C).

Parameters

The physical and physiological parameters (Table 2) used in the calculation are as follows. The heat conductivity, heat capacity, and metabolic rate were obtained from the literature and summarized by Werner and Buse (27). Skin values were uniformly applied to all soft tissue.

Numerical Methods

Equations 1 and 4 contain singularities at r = 0. This problem is circumvented by substituting the spherical coordinate system with the rectangular coordinate system at r = 0, and then each equation can be represented by a solvable difference equation (24).

Initial Condition

2

1

Assumptions for Submersion

Circulation. Blood circulation eventually arrests during submersion. Fainer et al. (9) studied 160 mongrel dogs during fresh-water drowning and observed that blood pressure started to fall precipitously after a mean of 130 s and reached zero after an average of 262 s. In the present model it is assumed that blood flow to the brain is normal within the first 2 min and then decreases linearly to zero in the next minute.

Brain metabolism. Michenfelder and Milde (18) demonstrated in dogs that at brain temperatures between 37 and 27°C the metabolic rate diminished by a factor of 3 (Q₁₀ = 3.0). Thus metabolic heat production of the brain is estimated as follows

(5)

where M₀ is the reference metabolic rate at 37°C (Table 2). The metabolic heat production is also related to the cerebral blood flow. During circulatory arrest, the metabolic rate decreases proportionally with the decrease in cerebral blood flow (15). Therefore, it is assumed that the metabolic rate changes according to Q₁₀ during the first 2 min (where blood flow is still constant) but is then reduced to zero over the next 1 min as the blood flow decreases to zero.

Ventilation. Two pathways must be considered to estimate the effects of ventilation of water on brain cooling: 1) direct conductive cooling through the airway at boundary 2 and 2) indirect circulatory cooling via the lungs.

2

1

(6)

Simulation Conditions

Brain cooling is influenced by boundary conditions, blood circulation, ventilation of water, and head size. Therefore, the following simulation conditions were designed to analyze the effect of these factors, in various combinations, on brain cooling.

Condition 1: effect of conductive cooling at boundary 1 (boundary 2 insulated, without circulation or ventilation). At boundary 1, heat transfer into cold water always occurs during submersion, and therefore boundary 1 must always be considered. Circulation and ventilation are not taken into account in this nonphysiological case to show the magnitude or contribution of conductive cooling alone through boundary 1.

Condition 2: effect of conductive cooling at boundaries 1 and 2 (without circulation). Ventilation occurs, but only direct maximal conductive cooling through boundaries 1 and 2 is considered. The effects of circulatory cooling are not taken into account. This case is also nonphysiological to show the impact of additional conductive cooling through boundary 2.

Condition 3: effect of conductive cooling at boundary 1 and circulatory cooling via the lung (boundary 2 insulated, circulation intact). The circulatory cooling effect of ventilation of water is considered with boundary 2 insulated. Therefore, these results will show the effect of heat transfer in the lungs on the carotid artery and brain temperature.

Condition 4: effect of conductive cooling of boundary 1, conductive cooling of boundary 2, and circulatory cooling via the lung (circulation intact). All the possible contributions to brain cooling are considered in this case. The result will yield the maximum predicted rate of brain cooling.

Condition 5: effect of the head size. Another factor that affects brain cooling is head size. Only conditions 1 and 2 are considered in this case (see DISCUSSION for further details), but the radius of the skull and the thickness of each layer are reduced to represent a 2-yr-old child. The head radius is given as 74 mm (28), and the tissue and bone thickness were proportionally reduced from adult values.

	RESULTS

The data are presented as an average brain temperature or the two-dimensional temperature distributions within the brain hemisphere. Figure 2 shows the average brain temperatures over time for conditions 1-5. Recall that the brain cooling rate for conditions 1 and 2 depends only on the physical parameters of the tissues and geometrical parameters. The results of condition 1 indicate that conductive cooling of the brain through boundary 1 is slow. The results of condition 2 show that added conductive cooling through boundary 2 enhances brain cooling, but it is still too slow to meet the required brain cooling of 3°C within 5 min. Therefore, the overall, but isolated, effect of conductive cooling is small.

View larger version (26K): [in this window] [in a new window]   Fig. 2.   Predicted average brain temperatures for conditions (Cond.) 1-4 for adults and condition 5 (1b + 2b) for children.

These conclusions can also be deduced from the two-dimensional temperature distributions. Figure 3 shows the temperature distribution at the precooling baseline condition, after 5 min with conductive cooling only at boundary 1 (condition 1), and after conductive cooling at boundaries 1 and 2 (condition 2). After 5 min of cooling the temperature of the brain surface is reduced by conductive cooling through boundary 1, but the deep part of the brain is still not cooled. In condition 2 the temperature at boundary 2 is also reduced by conductive cooling; however, the deep part of the brain is not yet influenced.

View larger version (72K): [in this window] [in a new window]   Fig. 3.   Predicted 2-dimensional temperature distribution for precooling baseline and after 5 min of cooling in conditions 1 and 2.

With the blood circulation intact, brain temperature becomes sensitive to central blood temperature and flow rate. Condition 3 describes brain cooling primarily as a consequence of decreased central blood temperature, inasmuch as cold water is ventilated and heat is transferred within the lung and, secondarily, to conductive heat loss at boundary 1. Condition 4 more accurately depicts the situation when water is respired, inasmuch as the additional effect of conductive heat transfer with the cold water in the upper airways is included. The large and continual decrease in brain temperature is qualitatively comparable to the decrease in carotid artery temperature in the study of Conn et al. (6).

Figure 4 shows the temperature distribution after 2 min of cooling under conditions 2-4. The results for conditions 3 and 4 confirm that deep parts of the brain can be rapidly cooled by circulatory cooling via the lung.

View larger version (64K): [in this window] [in a new window]   Fig. 4.   Predicted temperature distribution for conditions 2-4 after 2 min of cooling.

As expected, the size of the head also affects the brain cooling rate. The results for condition 5 (Fig. 2, 1b + 2b) show a great difference in conductive cooling between the adult's head and the smaller child's head. After 5 min of cooling the average brain temperature of the child's head is ~0.8°C lower than that of the adult's head when only conductive cooling through boundary 1 is considered (Fig. 2, 1b). The average brain temperature can be reduced below 34°C within 5 min when conductive cooling through boundary 2 is also included (Fig. 2, 2b).

	DISCUSSION

The present model predicts that conductive brain cooling through boundaries 1 and 2 is minimal and that ventilation of cold water greatly enhances brain cooling through circulatory cooling. The minimal conductive cooling can be explained by the low heat conductivity of human tissue. Furthermore, heat conduction through boundary 2 is probably overestimated, since only part of this surface is exposed to water and its temperature in the upper airway should rise above the ambient value.

These results are consistent with Mellergard's observation (17). He studied different ways to lower patients' brain temperature and observed that isolated head cooling, whether with frozen liquid or a cooling helmet, had a very limited effect. Also, Dexter and Hindman (7) developed a one-dimensional mathematical model to analyze brain cooling during cardiopulmonary bypass. They investigated the direct effects of conduction, convection, and metabolism and demonstrated that conductive heat loss, when the head was packed in ice, was minimal. Brain temperature was dependent on convective cooling in proportion to rate of blood flow and inflow temperature. They also showed that brain metabolism had a minimal direct effect on the rate of brain cooling. Small infant head size resulted in greater conductive cooling; however, there was no additional advantage when convective blood cooling was considered. Inasmuch as our results were in close agreement with this previous study, we did not perform analyses for effects of convection on a small child-sized head, nor did we separately determine the effect of changes in brain metabolism (Fig. 2).

Conn et al. (6) submersed dogs in cold water and noted that the dogs actually continued to ventilate under the water, allowing the lungs to act as a heat exchanger, causing rapid and significant decreases in carotid artery temperature. These data were used in our model, which indeed does predict a significant effect of water breathing on brain temperature. We are not sure of the extent to which dog and human responses are comparable. Dogs have a carotid rete that will not affect convective heat loss in the lung due to water ventilation but may affect conductive heat loss from the upper airways (boundary 2).

To test whether Eq. 6 is reasonable for human simulation, consider the potential decrease in the central blood temperature on breathing water. With the assumption that breathing water exchanges heat only with central blood in the lung and that the heat exchange effectiveness is 100%, central blood cooling can be estimated by the following simple heat balance equation

(7)

where m_b is total volume of the central blood (liters), _w is volume of ventilated water (l/min), and (c)_w is heat capacity of water (kJ · m³ · °C¹). Further assume that total volume of the central blood is 5 and 1.6 liters for an adult and a 2-yr-old child, respectively. Equation 7 indicates that central blood temperature will decrease by 6°C within 2 min in an adult exchanging 500 ml/min (i.e., volume of ventilated water) and in a child exchanging 150 ml/min of water in the lung. These decreases surpass the prediction of Eq. 6, thus suggesting that the use of Eq. 6 is reasonable.

The cooling of the blood that perfuses the brain via the carotid artery is not necessarily confined to heat exchange with ventilated water at the lung level. Cool venous return from the skin of the body will also contribute. Consider, for example, scalp blood flow, which remains relatively high during exposure to cold air (11). If it is assumed that the venous blood temperature is equal to the temperature of the scalp, the following heat balance between the scalp venous return and central blood applies

(8)

where _skin is scalp blood flow (ml/min) and T_skin is scalp temperature (°C). Further assume that the adult total blood volume is 5 liters, scalp blood flow is 13.5 ml/min on the basis of data from Tables 1 and 2, and scalp tissue temperature was equal to skin temperature. A simulation was conducted under condition 3, except carotid artery temperature was changed according to Eq. 8 instead of Eq. 6. The simulation results indicate that carotid blood temperature decreases by only 0.1°C after 5 min of submersion in 2°C water. One other study (10) has shown scalp cooling to decrease extracerebral blood flow by up to 25%. This would decrease the convective cooling effect further. Consequently, the cooling of scalp blood flow has a negligible effect on central blood cooling and can be ignored. The venous return from other surfaces of the body would also likely contribute little to central blood cooling relative to the effect of ventilated water at the lung level.

Various groups of authors have demonstrated that moderate cooling of the rat brain to 35 and 33°C greatly reduces or even eliminates histopathological neuronal damage caused by 10-20 min of total cerebral ischemia (3, 19, 23). Mechanisms in addition to decreased brain metabolism are as follows: 1) cooling the brain to 34°C delays terminal depolarization and reduces the initial rate of rise of extracellular K⁺ (15); 2) ischemia performed in rats with brain temperatures of 33 or 30°C results in the complete suppression of glutamate release and a 60% reduction in the peak release of dopamine (4); and 3) cooling during ischemia also attenuates the ischemia-induced damage to endothelial cells and increases in blood-brain barrier permeability (8), reduces hydroxyl radial production (14), and improves postischemia glucose utilization (13).

The purpose of the present mathematical model is to help determine the mechanisms by which sufficient brain cooling could occur to provide protection against anoxia. According to the data reviewed above, we have set a threshold for significant cerebral protection at a minimum decrease in temperature of 3°C within 5 min. On the basis of overall average brain temperature, ventilation of water would be required for an adult to reach this threshold and a child would at least have to have water in the upper airway to cool effectively. When temperature distributions within the brain are considered, ventilation of water would again be required to quickly decrease the temperature of all brain tissue. However, conductive cooling would provide some cooling to superficial layers of the brain (near boundary 1) and the brain stem (near boundary 2). The gray matter of the high motor and sensory centers is most susceptible to hypoxic damage and constitutes the outer layer of the brain; in addition, the brain stem is responsible for autonomic control of many vital systems. Therefore, it is possible that localized graded cooling from conduction alone may provide some important protection from anoxia.

On submersion, central blood temperature may be mainly affected by ventilation of water, whereas the effect of convective cooling of venous blood in the scalp is negligible. In submersed dogs, respiratory movements have been shown to continue for an average of 71 s in water at room temperature (9) and to peak at 1 min and last as long as 4 min in cold water (6). In the latter study, ventilation of 4°C water resulted in a decrease in carotid artery temperature of 8°C within 2 min compared with only a 1°C decrease when dogs were prevented from ventilating the water.

Our model indicates that, during the first 2 min of submersion, ventilation rates of 500 ml/min for an adult and 150 ml/min for a child are required to reduce the central blood temperature by 6°C. This amount should be considered as a minimal requirement, inasmuch as effectiveness of heat exchange between water and central blood cannot be 100%, and the blood temperature could be affected by venous return from other parts of the body. The amount of water that can be aspirated/ventilated that is compatible with life is not known; however, cold-water near-drowning survivors have been shown to have water in the airways and lungs (5). It was demonstrated that as many as 61% of submersed dogs were revived after breathing room-temperature water for an extended period of 75 s (9).

Predictive data from the present model are consistent with the general belief that children have a greater chance for survival from cold-water submersion than adults. Children have a smaller-sized head, which results in more conductive cooling. Furthermore, the studies of Ramey et al. (22) showed that the breath-hold duration was shorter in children than in adults during total submersion. If this relationship persisted during accidental cold-water submersion, children would have water in their upper airways, and possibly ventilate water, earlier than adults. Earlier conductive cooling at boundary 2 and circulatory cooling via the lungs should provide an additional survival advantage for children.

To validate the present model for condition 2 (conductive cooling at boundaries 1 and 2), calculations were compared with data obtained in human cadavers. Surface cooling of the head and irrigation of the nasopharynx with ice water lowered deep brain (hippocampus) temperature from 37 to 34°C only after 30-60 min (21; S. A. Tisherman, personal communication). The hippocampus corresponds to the area of the hemisphere model that is horizontally 14% from the vertical midaxis to the surface and vertically 35% from boundary 2 to boundary 1 (1). The calculated temperature for this area after 30 min of exposure to 2°C water was 33.5°C and is in close agreement with actual cadaver data (S. A. Tisherman, personal communication).

To validate the predicted results for central cooling via cold venous return from the scalp (Eq. 8), two experiments were conducted in our laboratory. One subject (height 183 cm, weight 83 kg) was twice immersed to the neck in a water bath at thermoneutral temperature (33°C). The subject's head was inserted through a neck seal into a rigid container suspended just above the bath water. The subject breathed through a mouthpiece that was connected to a Hans Rudolph one-way valve. Corrugated tubing was connected to the inspiratory and expiratory sides of the valve and exited the rigid container. In these experiments the head enclosure was rapidly filled with water at 12 or 18°C, and the water was circulated at constant temperature for 15 min. In this condition, esophageal temperature would only change because of direct conduction at boundary 1 and through convective heat exchange via scalp blood flow. Figure 5 compares actual with predicted data for changes in the esophageal temperature during head submersion in 12 and 18°C water. The small difference between the predicted and experimental results is largely due to two factors. 1) The increase in the core temperature at the beginning of head submersion is likely a result of peripheral vasoconstriction and central redistribution of heat. This effect was not considered in the model. 2) The central blood cannot be isolated in the experiment, and it still exchanges heat with other parts of the body. Because these factors would tend to maintain a higher core temperature as observed, the predicted values appear valid, especially when the rate of fall in esophageal temperature is compared in the later half of the experiment.

View larger version (24K): [in this window] [in a new window]   Fig. 5.   Comparison of predicted and experimental values for esophageal temperature (Tes) for central cooling via cold venous return from scalp during head-only immersion in 12 and 18°C water.

The calculated results are also affected by the physical and physiological parameters listed in Table 2. Therefore, a sensitivity analysis of these parameters was performed for data under condition 4, which includes all mechanisms of heat loss. By repeated calculation, each of these parameters was reduced by 10%, while the rest of the parameters were kept unchanged. When results are compared with the original data for condition 4, the maximal deviation was 0.26°C at the end of 5 min and 0.39°C at the end of 10 min. Therefore, our predictive model for brain temperature is minimally affected by small deviations in physical and physiological parameters.

In conclusion, a mathematical model was developed to quantify all avenues of heat loss from the human head when the entire body is submersed in cold water. The simulation indicates that conductive heat loss through the skull surface (boundary 1) or through the upper airways (boundary 2) is minimal. However, the ventilation of cold water has the potential to provide substantial brain cooling through circulatory cooling. It was further demonstrated that there are big differences in temperature between the brain surface and the deep brain when brain blood flow ceases. It is also possible that conductive cooling may provide some advantage by cooling the brain cortex peripherally and the brain stem centrally via the upper airway. Although conductive cooling is greatly enhanced with decreased head size, water breathing may be essential for the rapid rate of whole brain cooling required for cerebral protection.