scholarly journals Model of Kinetic Behavior of Deoxyglucose in Heterogeneous Tissues in Brain: A Reinterpretation of the Significance of Parameters Fitted to Homogeneous Tissue Models

1991 ◽  
Vol 11 (1) ◽  
pp. 10-24 ◽  
Author(s):  
K. Schmidt ◽  
G. Mies ◽  
L. Sokoloff
Keyword(s):  
Rate Constant ◽  
Weighted Average ◽  
Effective Rate Constant ◽  
Direct Consequence ◽  
Experimental Period ◽  
Tissue Heterogeneity ◽  
Product Loss ◽  
Dg Method ◽  
Heterogeneous Tissue ◽  
Homogeneous Tissue

Effects of tissue heterogeneity on regional CMRglc (rCMRglc) calculated by use of the deoxyglucose (DG) method at 45 min following the pulse of DG were evaluated in simulation studies. A theoretical model was developed to describe the kinetics of DG uptake and metabolism in heterogeneous brain tissues. Rate constants were fitted to simulation data for mixed tissue and rCMRglc computed on the basis of this tissue heterogeneity model. The results were compared with those obtained by use of the original model of the DG method for homogeneous tissue, both without (3K model) and with (4K model) a term to describe an apparent loss of deoxyglucose-6-phosphate (DG-6-P). As a direct consequence of tissue heterogeneity, the effective rate constant for phosphorylation of DG, k*3, declined with time. To compensate for the time-changing k*3, estimates of the dephosphorylation rate constant, k*4, were artifactually high when the 4K model was used, even though no dephosphorylation of DG-6-P actually occurred. The present study demonstrates that the finding of a significant k*4, at least within 45 min following a pulse of DG, may not represent dephosphorylation at all, but rather the consequence of measuring radioactivity in a heterogeneous tissue and applying a model designed for a homogeneous tissue. Furthermore, the high estimates of k*4 resulted in significant overestimation of rCMRglc. When rCMRglc was computed with the conventional single-scan or autoradiographic method at 45 min after a pulse of DG, the 3K and tissue heterogeneity models yielded values that were within 5% of the true weighted average value for the heterogeneous tissue as a whole. We conclude that the effects of tissue heterogeneity alone can give the appearance of product loss, even when none occurs, and that the use of the 4K model with the assumption of product loss in the 45-min experimental period recommended for the DG method may lead to overestimation of the rates of glucose utilization.

scholarly journals Errors Introduced by Tissue Heterogeneity in Estimation of Local Cerebral Glucose Utilization with Current Kinetic Models of the [18F]Fluorodeoxyglucose Method

1992 ◽  
Vol 12 (5) ◽  
pp. 823-834 ◽  
Author(s):  
K. Schmidt ◽  
G. Lucignani ◽  
R. M. Moresco ◽  
G. Rizzo ◽  
M. C. Gilardi ◽  
...  
Keyword(s):  
Rate Constant ◽  
Kinetic Models ◽  
Time Course ◽  
Glucose Utilization ◽  
Experimental Period ◽  
Tissue Heterogeneity ◽  
Cerebral Glucose Utilization ◽  
Positron Emission ◽  
Normal Humans ◽  
Homogeneous Tissue

The effects of tissue heterogeneity on the estimation of regional cerebral glucose utilization (rCMRglc) in normal humans with [18F]2-fluoro-2-deoxy-d-glucose ([18F]FDG) and positron emission tomography (PET) were compared with respect to the various kinetic models of the [18F]FDG method. The kinetic models were conventional homogeneous tissue models of the [18F]FDG method, with (4K Model) and without (3K Model) a rate constant to account for an apparent loss of [18F]2-fluoro-2-deoxy-d-glucose-6-phosphate ([18F]FDG-6-P), and a tissue heterogeneity model (TH Model). When either of the kinetic models designed for homogeneous tissues was applied to heterogeneous tissues, estimates of the rate constant for efflux of [18F]FDG from the tissue ( k*2) and of the rate constant for phosphorylation of [18F]FDG ( k*3) decreased as the duration of the experimental period was increased. When the 4K Model was used, estimates of the rate constant for the apparent dephosphorylation of [18F]FDG-6-P ( k*4) were significantly greater than zero and fell with increasing duration of the experimental period. Although the TH Model included no term to describe an apparent dephosphorylation of [18F]FDG-6-P, the fit of the TH Model to the time course of total tissue radioactivity was at least as good as and often better than the fit of the 4K Model in the 120-min period following the pulse of [18F]FDG. Hence, the high estimates of k*4 found in PET studies of ≤120 min can be explained as the consequence of measuring radioactivity in a heterogeneous tissue and applying a model designed for a homogeneous tissue; there remains no evidence of significant dephosphorylation of [18F]FDG-6-P in this time period. Furthermore, use of the 4K Model led to an overestimation of rCMRglc; whole-brain glucose utilization calculated with the 4K Model was >20% higher than values usually obtained in normal humans by the model-independent Kety–Schmidt technique. rCMRglc was accurately estimated by the TH Model and, in experimental periods sufficiently long to minimize the effects of tissue heterogeneity, also by the original 3K Model of the deoxyglucose method.

scholarly journals Analysis of Time Courses of Metabolic Precursors and Products in Heterogeneous Rat Brain Tissue: Limitations of Kinetic Modeling for Predictions of Intracompartmental Concentrations from Total Tissue Activity

1995 ◽  
Vol 15 (3) ◽  
pp. 474-484 ◽  
Author(s):  
Kathleen C. Schmidt ◽  
Günter Mies ◽  
Gerald A. Dienel ◽  
Nancy F. Cruz ◽  
Alison M. Crane ◽  
...  
Keyword(s):  
Rate Constant ◽  
Kinetic Models ◽  
Goodness Of Fit ◽  
Glucose Utilization ◽  
Total Radioactivity ◽  
Tissue Heterogeneity ◽  
Metabolic Products ◽  
Product Loss ◽  
Time Courses ◽  
Total Tissue

The efficacy of various kinetic models to predict time courses of total radioactivity and levels of precursor and metabolic products was evaluated in heterogeneous samples of freeze-blown brain of rats administered [14C]deoxyglucose ([14C]DG). Two kinetic models designed for homogeneous tissues, i.e., a no-product-loss, three-rate-constant (3K) model and a first-order-product-loss, four-rate-constant (4K) model, and a third kinetic model designed for heterogeneous tissues without product loss [Tissue Heterogeneity (TH) Model] were examined. In the 45-min interval following a pulse of [14C]DG, the fit of the TH Model to total tissue radioactivity was not statistically significantly better than that of the 3K Model, yet the TH Model described the time courses of [14C]DG and its metabolites more accurately. The TH- and 4K-Model-predicted time courses of [14C]DG and its metabolites were similar. Whole-brain glucose utilization (CMRglc) calculated with the TH or 3K Model, ∼75 μmol 100 g−1 min−1, was similar to values previously determined by model-independent techniques, whereas CMRglc calculated with the 4K Model was 44% higher. In a separate group of rats administered a programmed infusion to attain a constant arterial concentration of [14C]DG that minimizes effects of tissue heterogeneity as well as any product loss, CMRglc calculated with all three models was 79 μmol 100 g−1 min−1 at 45 min after initiation of the infusion. Statistical comparisons of goodness of fit of total tissue radioactivity were, therefore, not indicative of which models best describe the tissue precursor and product pools or which models provide the most accurate rates of glucose utilization.

scholarly journals Consistent Weighted Average Flux of Well-Balanced TVD-RK Discontinuous Galerkin Method for Shallow Water Flows

2015 ◽  
Vol 2015 ◽  
pp. 1-11 ◽  
Author(s):  
Thida Pongsanguansin ◽  
Montri Maleewong ◽  
Khamron Mekchay
Keyword(s):  
Shallow Water ◽  
Discontinuous Galerkin ◽  
Numerical Solutions ◽  
Order Approximation ◽  
Weighted Average ◽  
Flat Bottom ◽  
Flux Function ◽  
Dg Method ◽  
Average Flux ◽  
Steady Solutions

A well-balanced scheme with total variation diminishing Runge-Kutta discontinuous Galerkin (TVD-RK DG) method for solving shallow water equations is presented. Generally, the flux function at cell interface in the TVD-RK DG scheme is approximated by using the Harten-Lax-van Leer (HLL) method. Here, we apply the weighted average flux (WAF) which is higher order approximation instead of using the HLL in the TVD-RK DG method. The consistency property is shown. The modified well-balanced technique for flux gradient and source terms under the WAF approximations is developed. The accuracy of numerical solutions is demonstrated by simulating dam-break flows with the flat bottom. The steady solutions with shock can be captured correctly without spurious oscillations near the shock front. This presents the other flux approximations in the TVD-RK DG method for shallow water simulations.

Diffusion‐controlled reactions: Upper bounds on the effective rate constant

1991 ◽  
Vol 94 (12) ◽  
pp. 7967-7971 ◽  
Author(s):  
J. Blawzdziewicz ◽  
G. Szamel ◽  
H. Van Beijeren
Keyword(s):  
Rate Constant ◽  
Effective Rate Constant ◽  
Effective Rate ◽  
Upper Bounds ◽  
Diffusion Controlled

Refinement of the Kinetic Model of the 2-[14C]Deoxyglucose Method to Incorporate Effects of Intracellular Compartmentation in Brain

1989 ◽  
Vol 9 (3) ◽  
pp. 290-303 ◽  
Author(s):  
K. Schmidt ◽  
G. Lucignani ◽  
K. Mori ◽  
T. Jay ◽  
E. Palombo ◽  
...  
Keyword(s):  
Endoplasmic Reticulum ◽  
Rate Constant ◽  
Step Process ◽  
Precursor Pool ◽  
Physiological Conditions ◽  
Dg Method ◽  
Yield Values ◽  
Rate Limiting ◽  
Hydrolysis Of ◽  
Deoxyglucose Method

A translocase to transport hexose phosphate formed in the cytosol into the cisterns of the endoplasmic reticulum, where the phosphatase resides, is absent in brain (Fishman and Karnovsky, 1986). 2-Deoxyglucose-6-phosphate (DG-6-P) may therefore have limited access to glucose-6-phosphatase (G-6-Pase), and transport of the DG-6-P across the endoplasmic reticular membrane may be rate limiting to its dephosphorylation. To take this compartmentation into account, a five-rate constant (5K) model was developed to describe the kinetic behavior of 2-deoxyglucose (DG) and its phosphorylated product in brain. Loss of DG-6-P was modeled as a two-step process: (a) transfer of DG-6-P from the cytosol into the cisterns of the endoplasmic reticulum; (b) hydrolysis of DG-6-P by G-6-Pase and subsequent return of the free DG to the precursor pool. Local CMRglc (LCMRglc) was calculated in the rat on the basis of this model and compared with values calculated on the basis of the three-rate constant (3K) and the four–rate constant (4K) models of the DG method. The results show that under normal physiological conditions all three models yield values of LCMRglc that are essentially equivalent for experimental periods between 25 and 45 min. Therefore, the simplest model, the 3K model, is sufficient. For experimental periods from 60 to 120 min, the 4K and 5K models do not correct completely for loss of product, but the 5K model does yield estimates of LCMRglc that are closer to the values at 45 min than those obtained with the 3K and 4K models.

Residence-time of muonium at micelles: Effect of added micelles on the reactivity of muonium towards ionic solutes in water

1988 ◽  
Vol 66 (8) ◽  
pp. 1979-1983 ◽  
Author(s):  
Krishnan Venkateswaran ◽  
Mary V. Barnabas ◽  
Bill W. Ng ◽  
David C. Walker
Keyword(s):  
Residence Time ◽  
Rate Constant ◽  
Mean Residence Time ◽  
Effective Rate Constant ◽  
Effective Rate ◽  
Diffusion Time ◽  
Water Penetration ◽  
Micellar Structure ◽  
Micelle Core ◽  
Ionic Solutes

The effective rate constant for the reaction of muonium with NO3−, S2O32−, and Tl+ ions in water is altered by the addition of micelles. There is a decrease when the charge on the micelle is the same as that of the solute and an increase when their charges are opposite. From the magnitude of the effect a mean residence-time for muonium of 2 ns has been deduced for dodecyl sulphate micelles. This suggests there is barely any preferred localization, because 2 ns is smaller, even, than the expected diffusion time if the micelle core is as viscous as reported. This use of muonium atoms to probe the dynamics of micelles seems to support the view that there are regions of low microviscosity and considerable water penetration within the micellar structure.

Effective rate constant of ferriin reduction in the Belousov–Zhabotinsky reaction

1997 ◽  
Vol 93 (1) ◽  
pp. 69-71 ◽  
Author(s):  
J. Ungvarai ◽  
Z. Nagy-Ungvarai ◽  
J. Enderlein ◽  
S. C. Müller
Keyword(s):  
Rate Constant ◽  
Effective Rate Constant ◽  
Effective Rate ◽  
Belousov Zhabotinsky Reaction
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