We have previously shown (Ref. I) the absence of variations in average cerebral blood flow, measured by the method of LASSEN, following treatment of traumatic coma by means of hyperbaric oxygenation patients presenting with brainstem contusion, during 2 hours of HBO (at 2.5 times atmospheric pressure) measurements of cerebral blood flow were made using a single detecting probe, before and two hours after terminating HBO. Measurements in 9 patients demonstrated variations in cerebral flow greater than predicted by experimental error (+/- 4%): 5 measurements (these with initial flow less than 31 ml/mn/100 g increased following OHB, while 4 measurements (these with initial flow greater than 31 ml/mn/100 g) decreased following OHB. In order to determine the significance of these variations, we studied the correlation between two methods of calculating cerebral blood flow : the exponential (bicompartimental) method, and the stochastic method, assuming lambda the coefficient of partition, tobe equal to I. These two method of calculation appear to be independant ; thus, the observed correlation (r = 0.74, p less than 0.01) tends to validite the measured variations in flow. This finding is further supported by the calculated correlation between the change in flow as measured by the exponential and that measured by the stochastic method (r = 0.684, p less than 0.05). Thus, we feel that measured changes in flow represent changes in cerebral perfusion, and cannot be attributed to the method of calculation. The bio exponential method of calculation of flow, D = Dg + Dw (with Dg = fg. Wg = "index of grey perfusion" and Dw = fw. Ww = "index of white perfusion", where fg = lambda1. (see article), and where Wg and Ww represent the percentage of the grey and white substance) permit calculation of a highly significant correlation between the change in flow and the grey perfusion index (r = 0.83, p less than 0.01). This correlation, previously described in the literature, appears to explain the observed findings in terms of the variations in perfusion of the grey compartment. However, there exists an equally significant correlation, but negative, between the variations of the grey and white perfusion index (r = 0.824, p less than 0.01). This correlation seems to indicate the presence of an inverse relationship between flow to grey and white substances, tending to minimize the variations of the total flow after OHB. We can then formulate an explanatory hypothesis: if one assumes that the diminution of intracranial pressure during OHB, by decreasing cerebral edema, hastens the recovery of perfusion in the damaged zones, then the response to therapy with hyperbaric oxygenation should differ, depending on whether the tissues were healthy or damaged. Healthy tissues should show a decrease, while damaged zones should show an increase in flow following OHB. This mechanism would appear to explain, in relation to lesions located predominantly in grey or white matter, the observed negative correlation between blood flow to the two compartments.