Journal of Cerebral Blood Flow and Metabolism 10:147-148 © 1990 Raven Press, Ltd., New York
Letters to the Editor To the Editor:
with time. The constants in question relate to the movement of materials between brain compart ments. There is no physiological steady-state model that corresponds to an ever-changing set of con stants. b. It ignores the possibility that different adjust ments in the "constants" may have to be made un der different experimental conditions of glucose concentrations, distribution of isotope, and meta bolic rates, even at 45 min. c. It assumes that the rate constant for loss is the same in all brain regions. The range of values for DG is not great (1.1-1.3%/min) in 8 selected regions (Redies and Diksic, 1989), but is wider (0.9-1.4%) in the complete set of 18 regions (Redies et aI., 1989). The range for FDG is 0.8-1.7%. Interestingly, there is a significant correlation between the rate con stants of phosphorylation and dephosphorylation reported for DG and FDG (Fig. 1). In summary, these articles show that dephospho rylation of DG-phosphate and FDG-phosphate oc curs at rates that must be accounted for in the typ ical 45 min autoradiography experiment. They do not show any advantage to working with a mathe matical model that accounts for this loss by ignoring the rate constant for loss and instead making com pensatory changes in the other "constants" so as to achieve the same mathematical result at a single point in time. On the other hand, there are definite risks to using such a model under different experi mental conditions.
Recent articles by Redies and associates in this journal and elsewhere provide interesting data on the kinetics of deoxyglucose (DG) and fluorodeox yglucose (FDG) metabolism in rat and ferret brain (Redies et aI., 1987a,b; Redies and Diksic, 1989; Redies et aI., 1989). Their findings with regard to loss of phosphorylated DG and FDG from brain may be summarized as follows: (a) the rate constant for this loss is, on average, somewhat greater than 1 %/min; (b) loss occurs from the beginning of the experiment (there is no delay); and (c) there is sig nificant regional variation in the rate constants of loss. One might reasonably conclude from these ob servations that experimenters using the deoxyglu cose method should use a mathematical model that takes into account loss of product, on a regional basis. Given the range of brain regional rate con stants for FDG loss of 0.8-1.7% (Redies et aI., 1989), failure to account for loss will result in un derestimates of regional rates of glucose utilization of approximately 25-50% at 45 min after intrave nous FDG. The range for DG, 0.9-1.4% (Redies et aI., 1989), will cause underestimates of approxi mately 28-42%. The authors accept the need to account for loss of product in long experiments (120--180 min) but ar gue that this is unnecessary in 45 min experiments. Instead, they state that at 45 min one can ignore the rate constant for loss and use different values for the rate constants for transport out, for phosphory lation, and for the lumped constant (the ratio of the unidirectional rate of tracer phosphorylation to the net rate of glucose phosphorylation). This approach is unsatisfactory for three reasons.
Alexander L. Miller, M.D. Department of Psychiatry The University of Texas Health Science Center San Antonio, Texas
a. It uses "constants" as variables that change
Richard A. Hawkins, Ph.D. 40
Department of Physiology •
30
r =
0.61
• • •
.
k3
0
20
%/min •
•
0
0
North Chicago, Illinois
0 • •
•
REFERENCES
•
0 10
•
The Chicago Medical School
•
• •
0
§
Redies C, Matsuda M, Diksic M, Meyer E, Yamamoto YL (1987a) In vivo measurement of [18Flfluorodeoxyglucose rate constants in rat brain by external coincidence counting.
0
0 0 0.5
1.5
1.0 k
.
4
Neuroscience 22:593-599
2.0
Redies C, Diksic M, Evans AC, Gjedde A, Yamamoto YL (l987b) Double-label autoradiographic deoxyglucose method for sequential measurement of regional cerebral glu cose utilization. Neuroscience 22:601-619
%/min
FIG. 1. Plot of k; versus k: for DG (_) and FDG (e). DG points (1.2, 16) and (1.3, 13) are duplicated. For the entire data set r = 0.61 (p < 0.01). Data from Figure 1 of Redies et aI., 1989.
Redies C, Diksic M (1989) The deoxyglucose method in the ferret
147
LE TTERS TO THE EDITOR
148
brain. 1. Methodological considerations. J Cereb Blood Flow
Metab 9:35-42 Redies C, Diksic M, Y amamoto YL (1989) The deoxyglucose method in the ferret brain. II. Glucose utilization images and normal values. J Cereb Blood Flow Metab 9:43-52 and 247-
248
Reply:
The kinetic models described and used in our pa pers should be taken as the mathematical approxi mations of the biological reality. The rate constants in the models are, strictly speaking, transfer coeffi cients that describe the movement of tracer be tween the compartments of the model. These com partments do not necessarily have to correspond to a specific biochemical compartment. The aim of the deoxyglucose method is not to determine rate con stants but to measure brain glucose utilization (Sokoloff et aI., 1977; Redies and Diksic, 1989). Rate constants allow the calculation of glucose uti lization irrespective of whether or not their specific biochemical correlates are identified. We showed that failure to account for loss of me tabolized tracer (deoxyglucose phosphate) results in negligible errors in calculating glucose utilization in deoxyglucose experiments lasting 45 min (Redies and Diksic, 1989). For the purpose of measuring glucose utilization, the Kj-kj model and the Kj-k! model are therefore equivalent for this experimental period. From this practical point of view, we dis agree with Drs. Miller and Hawkins' conclusion that loss of metabolized tracer must be taken into account in 45 min experiments. Drs. Miller and Hawkins correctly point out that the equivalence of the two models does not necessarily apply to exper imental conditions different from those we de scribed (Redies and Diksic, 1989). We doubt, how ever, that our conclusion would be invalid in many other cases. Furthermore, we would like to clarify the following points:
of glucose utilization of 25-50% if loss of metabo lized tracer is neglected. Certainly this conclusion does not derive from our paper. We show that an analysis that is consistent throughout yields a neg ligible underestimation (Redies and Diksic, 1989). c. The constants used by us in the Kj-kj and the Kj-k! model are indeed constants in these respec tive models. In all calculations, we applied either the Kj-kj model or the Kj-k! model but never mixed the two. d. The correlation between kj and k! is not sur prising. Other rate constants are usually also corre lated (for example, Kj and k!, and k! and kj). Such correlations are best evaluated and even more ap parent in the correlation matrices obtained in the individual fits. e. Drs. Miller and Hawkins point out the similar ity of the k! values for the 8 brain structures used in the simulation compared with the much wider range in the complete list of 18 brain structures. We sug gest that, for the problem studied, it is more rele vant to look at loss of metabolized tracer relative to the reaction it counteracts, i.e., tracer metabolism ("phosphorylation"). With a k!lkj ratio larger than those used in the simulation one would perhaps ex pect larger discrepancies between the glucose utili zation values calculated in the two models. The range of k!lkj ratios is 0.06--0.14 for the simulation study and reflects a wide range of metabolic rates. In the complete list for DG, there are only three brain structures that have k!lkj ratios beyond this range (0.05, 0.16, and 0.20). For FDG, all ratios are within the simulation range or slightly lower (0.040.13). The use of the Kj-kj model does not require that loss of metabolized tracer be the same in all brain structures. Christoph Redies, M.D., Ph.D. Department of Brain and Cognitive Sciences Massachusetts Institute of Technology Cambridge, Massachusetts
a. It is an assumption in the Kj-k! model that loss occurs from the beginning of the experiment. Whether loss sets in immediately in brain tissue is very difficult to determine from our data and the method we used (Redies and Diksic, 1989). In any event, the loss of metabolized tracer from the brain tissue is very small during the first 10-20 min and has a small effect on the total tissue radioactivity curve. Although this issue may have some interest from a biochemical point of view, it is irrelevant for the determination of glucose utilization with the de oxyglucose method. b. We are not sure how Drs. Miller and Hawkins arrive at the large underestimation in regional rates J Cereb Blood Flow Metab, Vol. 10, No.1, 1990
Mirko Diksic, Ph.D. Montreal Neurological Insitute and Department of Neurology and Neurosurgery McGill University Montreal, Quebec, Canada
REFERENCES Redies C, Diksic M (1989) The deoxyglucose method in the ferret brain.!. Methodological considerations. J Cereb Blood Flow
Metab 9:35-42 SokoloffL, Reivich M, Kennedy C, Des Rosiers MH, Patlak CS, Pettigrew KD, Sakurada 0 and Shinohara M (1977) The 14C_ deoxyglucose method for the measurement of local glucose utilization: theory, procedure, and normal values in the con scious and anesthetized albino rat. J Neurochem 28:897-916
Letters to the Editor To the Editor:
with time. The constants in question relate to the movement of materials between brain compart ments. There is no physiological steady-state model that corresponds to an ever-changing set of con stants. b. It ignores the possibility that different adjust ments in the "constants" may have to be made un der different experimental conditions of glucose concentrations, distribution of isotope, and meta bolic rates, even at 45 min. c. It assumes that the rate constant for loss is the same in all brain regions. The range of values for DG is not great (1.1-1.3%/min) in 8 selected regions (Redies and Diksic, 1989), but is wider (0.9-1.4%) in the complete set of 18 regions (Redies et aI., 1989). The range for FDG is 0.8-1.7%. Interestingly, there is a significant correlation between the rate con stants of phosphorylation and dephosphorylation reported for DG and FDG (Fig. 1). In summary, these articles show that dephospho rylation of DG-phosphate and FDG-phosphate oc curs at rates that must be accounted for in the typ ical 45 min autoradiography experiment. They do not show any advantage to working with a mathe matical model that accounts for this loss by ignoring the rate constant for loss and instead making com pensatory changes in the other "constants" so as to achieve the same mathematical result at a single point in time. On the other hand, there are definite risks to using such a model under different experi mental conditions.
Recent articles by Redies and associates in this journal and elsewhere provide interesting data on the kinetics of deoxyglucose (DG) and fluorodeox yglucose (FDG) metabolism in rat and ferret brain (Redies et aI., 1987a,b; Redies and Diksic, 1989; Redies et aI., 1989). Their findings with regard to loss of phosphorylated DG and FDG from brain may be summarized as follows: (a) the rate constant for this loss is, on average, somewhat greater than 1 %/min; (b) loss occurs from the beginning of the experiment (there is no delay); and (c) there is sig nificant regional variation in the rate constants of loss. One might reasonably conclude from these ob servations that experimenters using the deoxyglu cose method should use a mathematical model that takes into account loss of product, on a regional basis. Given the range of brain regional rate con stants for FDG loss of 0.8-1.7% (Redies et aI., 1989), failure to account for loss will result in un derestimates of regional rates of glucose utilization of approximately 25-50% at 45 min after intrave nous FDG. The range for DG, 0.9-1.4% (Redies et aI., 1989), will cause underestimates of approxi mately 28-42%. The authors accept the need to account for loss of product in long experiments (120--180 min) but ar gue that this is unnecessary in 45 min experiments. Instead, they state that at 45 min one can ignore the rate constant for loss and use different values for the rate constants for transport out, for phosphory lation, and for the lumped constant (the ratio of the unidirectional rate of tracer phosphorylation to the net rate of glucose phosphorylation). This approach is unsatisfactory for three reasons.
Alexander L. Miller, M.D. Department of Psychiatry The University of Texas Health Science Center San Antonio, Texas
a. It uses "constants" as variables that change
Richard A. Hawkins, Ph.D. 40
Department of Physiology •
30
r =
0.61
• • •
.
k3
0
20
%/min •
•
0
0
North Chicago, Illinois
0 • •
•
REFERENCES
•
0 10
•
The Chicago Medical School
•
• •
0
§
Redies C, Matsuda M, Diksic M, Meyer E, Yamamoto YL (1987a) In vivo measurement of [18Flfluorodeoxyglucose rate constants in rat brain by external coincidence counting.
0
0 0 0.5
1.5
1.0 k
.
4
Neuroscience 22:593-599
2.0
Redies C, Diksic M, Evans AC, Gjedde A, Yamamoto YL (l987b) Double-label autoradiographic deoxyglucose method for sequential measurement of regional cerebral glu cose utilization. Neuroscience 22:601-619
%/min
FIG. 1. Plot of k; versus k: for DG (_) and FDG (e). DG points (1.2, 16) and (1.3, 13) are duplicated. For the entire data set r = 0.61 (p < 0.01). Data from Figure 1 of Redies et aI., 1989.
Redies C, Diksic M (1989) The deoxyglucose method in the ferret
147
LE TTERS TO THE EDITOR
148
brain. 1. Methodological considerations. J Cereb Blood Flow
Metab 9:35-42 Redies C, Diksic M, Y amamoto YL (1989) The deoxyglucose method in the ferret brain. II. Glucose utilization images and normal values. J Cereb Blood Flow Metab 9:43-52 and 247-
248
Reply:
The kinetic models described and used in our pa pers should be taken as the mathematical approxi mations of the biological reality. The rate constants in the models are, strictly speaking, transfer coeffi cients that describe the movement of tracer be tween the compartments of the model. These com partments do not necessarily have to correspond to a specific biochemical compartment. The aim of the deoxyglucose method is not to determine rate con stants but to measure brain glucose utilization (Sokoloff et aI., 1977; Redies and Diksic, 1989). Rate constants allow the calculation of glucose uti lization irrespective of whether or not their specific biochemical correlates are identified. We showed that failure to account for loss of me tabolized tracer (deoxyglucose phosphate) results in negligible errors in calculating glucose utilization in deoxyglucose experiments lasting 45 min (Redies and Diksic, 1989). For the purpose of measuring glucose utilization, the Kj-kj model and the Kj-k! model are therefore equivalent for this experimental period. From this practical point of view, we dis agree with Drs. Miller and Hawkins' conclusion that loss of metabolized tracer must be taken into account in 45 min experiments. Drs. Miller and Hawkins correctly point out that the equivalence of the two models does not necessarily apply to exper imental conditions different from those we de scribed (Redies and Diksic, 1989). We doubt, how ever, that our conclusion would be invalid in many other cases. Furthermore, we would like to clarify the following points:
of glucose utilization of 25-50% if loss of metabo lized tracer is neglected. Certainly this conclusion does not derive from our paper. We show that an analysis that is consistent throughout yields a neg ligible underestimation (Redies and Diksic, 1989). c. The constants used by us in the Kj-kj and the Kj-k! model are indeed constants in these respec tive models. In all calculations, we applied either the Kj-kj model or the Kj-k! model but never mixed the two. d. The correlation between kj and k! is not sur prising. Other rate constants are usually also corre lated (for example, Kj and k!, and k! and kj). Such correlations are best evaluated and even more ap parent in the correlation matrices obtained in the individual fits. e. Drs. Miller and Hawkins point out the similar ity of the k! values for the 8 brain structures used in the simulation compared with the much wider range in the complete list of 18 brain structures. We sug gest that, for the problem studied, it is more rele vant to look at loss of metabolized tracer relative to the reaction it counteracts, i.e., tracer metabolism ("phosphorylation"). With a k!lkj ratio larger than those used in the simulation one would perhaps ex pect larger discrepancies between the glucose utili zation values calculated in the two models. The range of k!lkj ratios is 0.06--0.14 for the simulation study and reflects a wide range of metabolic rates. In the complete list for DG, there are only three brain structures that have k!lkj ratios beyond this range (0.05, 0.16, and 0.20). For FDG, all ratios are within the simulation range or slightly lower (0.040.13). The use of the Kj-kj model does not require that loss of metabolized tracer be the same in all brain structures. Christoph Redies, M.D., Ph.D. Department of Brain and Cognitive Sciences Massachusetts Institute of Technology Cambridge, Massachusetts
a. It is an assumption in the Kj-k! model that loss occurs from the beginning of the experiment. Whether loss sets in immediately in brain tissue is very difficult to determine from our data and the method we used (Redies and Diksic, 1989). In any event, the loss of metabolized tracer from the brain tissue is very small during the first 10-20 min and has a small effect on the total tissue radioactivity curve. Although this issue may have some interest from a biochemical point of view, it is irrelevant for the determination of glucose utilization with the de oxyglucose method. b. We are not sure how Drs. Miller and Hawkins arrive at the large underestimation in regional rates J Cereb Blood Flow Metab, Vol. 10, No.1, 1990
Mirko Diksic, Ph.D. Montreal Neurological Insitute and Department of Neurology and Neurosurgery McGill University Montreal, Quebec, Canada
REFERENCES Redies C, Diksic M (1989) The deoxyglucose method in the ferret brain.!. Methodological considerations. J Cereb Blood Flow
Metab 9:35-42 SokoloffL, Reivich M, Kennedy C, Des Rosiers MH, Patlak CS, Pettigrew KD, Sakurada 0 and Shinohara M (1977) The 14C_ deoxyglucose method for the measurement of local glucose utilization: theory, procedure, and normal values in the con scious and anesthetized albino rat. J Neurochem 28:897-916
