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Oxygen transport in the bullfrog retina
Exp. Eye Res. (1980) 31, 725-726 LETTER
TO T t t E
EDITOI~S
Oxygen Transport in the Bullfrog Retina The main purpose of Zuekerman and Weiter's paper (1980) is to provide evidence of the role of the receptor's O~ consumption on the oxygenation profile of the vertebrate retina. This is an interesting problem but their results are not sufficient to provide a clear answer to the question they have asked. More important, the way they interpret the results is unequivocally wrong. Their basic result is presented in Fig. 5 of their paper, in which they have plotted d P o J d x as a function of distance (x). By this plot they have obtained a complicated curve with a clear peak at a distance of about 70/~m from the pigment epithelium which corresponded, according to the authors, to the inner segment of the photoreceptors. This was interpreted by the authors as showing "the relative contribution of the various layers in the total oxygen consumption", and further "within the photoreceptor layer the major oxygen consumption is found at the level of the photoreceptor inner segment". This is by no means true for the following reasons: Assuming that the system stuclied can be described by the one-dimensional model of diffusion (although the possible influence of the paper draping (see their Fig. 2) the retina does not seem to have been investigated), the steady-state Po~ (P) and the local oxygen consumption Q are related by the equation
Q = dx [D ~(~zP)],
(1)
where ~ and D are the solubility and the diffusion coefficients, respectively. Considering the particular case where Q, a and D are all constant, the equation (1) becomes (Hill, 1928) d~p Q = Da-d-~x ~. (2) Under experimental conditions similar to those examined here, this equation implies that P(x) is a parabola and that Q can be estimated from the slope of the straight line obtained when plotting [P(0) - P(x)]/x vs. x (Ganfield, Nair and Whalen, 1970). This is of course not the only way to estimate Q: for example, according to equation (2) above, a plot of d2P/dx~ vs. x could be used as well to this end. However, it can be observed that a plot of dP/dx vs. x will give, in this particular case, a straight line of slope - Q/Da, thus showing that the information provided by such a plot is fundamentally different from that the authors claimed to obtain. A possible interpretation of the curve presented in their Fig. 5 could be that in the region between 0 and 100 #m the O2 solubility and diffusion coefficients change dramatically. In the case where D and a remain constant and Q changes the curve dPoJdx vs. x is expected (equation 2) to be a monotonically declining curve, i.e. without peaks. Apparently Zuckerman and Welter (1980) are not aware of these problems and provide wrong information to the readers of the Experimental Eye Research. The aim of our letter is to avoid the transfer of ambiguous information tothe international scientific society
Experimental OphthalmologyLaboratory, Department of Physioloqy, University of Geneva, Medical School, Geneva, Switzerland (Received 8 April 1980, New York)
M. TSACOPOVLOSA~CDS. POITRY
0014-4835/80/120725+02 $01.00/0 (~ 1980 Academic Press Inc. (London) Limited 725
726
L E T T E R TO THE E D I T O R S REFERENCES
Ganfield, 1~. A., Nair, P. and Whalen, W. J. (1970). Mass transfer storage, and utilization of 02 in cat cerebral cortex. Am. J. Physiol. 219, 814-21. Hill, A. V. (1928). The diffusion of oxygen and lactic acid through tissues. Proc. Roy. Soc. London. Set. B. 104, 38-96. Zuckerman, R. and Weiter, J. (1980). Oxygen transport in the bullfrog retina. Exp. Eye Res. 30, 117-27.
TO T t t E
EDITOI~S
Oxygen Transport in the Bullfrog Retina The main purpose of Zuekerman and Weiter's paper (1980) is to provide evidence of the role of the receptor's O~ consumption on the oxygenation profile of the vertebrate retina. This is an interesting problem but their results are not sufficient to provide a clear answer to the question they have asked. More important, the way they interpret the results is unequivocally wrong. Their basic result is presented in Fig. 5 of their paper, in which they have plotted d P o J d x as a function of distance (x). By this plot they have obtained a complicated curve with a clear peak at a distance of about 70/~m from the pigment epithelium which corresponded, according to the authors, to the inner segment of the photoreceptors. This was interpreted by the authors as showing "the relative contribution of the various layers in the total oxygen consumption", and further "within the photoreceptor layer the major oxygen consumption is found at the level of the photoreceptor inner segment". This is by no means true for the following reasons: Assuming that the system stuclied can be described by the one-dimensional model of diffusion (although the possible influence of the paper draping (see their Fig. 2) the retina does not seem to have been investigated), the steady-state Po~ (P) and the local oxygen consumption Q are related by the equation
Q = dx [D ~(~zP)],
(1)
where ~ and D are the solubility and the diffusion coefficients, respectively. Considering the particular case where Q, a and D are all constant, the equation (1) becomes (Hill, 1928) d~p Q = Da-d-~x ~. (2) Under experimental conditions similar to those examined here, this equation implies that P(x) is a parabola and that Q can be estimated from the slope of the straight line obtained when plotting [P(0) - P(x)]/x vs. x (Ganfield, Nair and Whalen, 1970). This is of course not the only way to estimate Q: for example, according to equation (2) above, a plot of d2P/dx~ vs. x could be used as well to this end. However, it can be observed that a plot of dP/dx vs. x will give, in this particular case, a straight line of slope - Q/Da, thus showing that the information provided by such a plot is fundamentally different from that the authors claimed to obtain. A possible interpretation of the curve presented in their Fig. 5 could be that in the region between 0 and 100 #m the O2 solubility and diffusion coefficients change dramatically. In the case where D and a remain constant and Q changes the curve dPoJdx vs. x is expected (equation 2) to be a monotonically declining curve, i.e. without peaks. Apparently Zuckerman and Welter (1980) are not aware of these problems and provide wrong information to the readers of the Experimental Eye Research. The aim of our letter is to avoid the transfer of ambiguous information tothe international scientific society
Experimental OphthalmologyLaboratory, Department of Physioloqy, University of Geneva, Medical School, Geneva, Switzerland (Received 8 April 1980, New York)
M. TSACOPOVLOSA~CDS. POITRY
0014-4835/80/120725+02 $01.00/0 (~ 1980 Academic Press Inc. (London) Limited 725
726
L E T T E R TO THE E D I T O R S REFERENCES
Ganfield, 1~. A., Nair, P. and Whalen, W. J. (1970). Mass transfer storage, and utilization of 02 in cat cerebral cortex. Am. J. Physiol. 219, 814-21. Hill, A. V. (1928). The diffusion of oxygen and lactic acid through tissues. Proc. Roy. Soc. London. Set. B. 104, 38-96. Zuckerman, R. and Weiter, J. (1980). Oxygen transport in the bullfrog retina. Exp. Eye Res. 30, 117-27.