A Rapidly Convergent Descent Method for Minimization

Fletcher, R.; Powell, M. J. D.

doi:10.1093/comjnl/6.2.163

Cited by 4,249 publications

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“…The plasma data were first fitted to an empirical exponential expression relat ing Ct to time. The parameters of this expression were calculated using the function minimization procedure of Fletcher and Powell (1963). This ex plicit expression was then used to represent ct in Eq.…”

Section: Lcmrgi Determinationmentioning

confidence: 99%

Use of 2-Deoxy-D[1-¹¹C]Glucose for the Determination of Local Cerebral Glucose Metabolism in Humans: Variation within and between Subjects

Reivich

Alavi

Wolf

et al. 1982

J Cereb Blood Flow Metab

128

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tracer for the measurement of LCMRgl and to determine its variability within subjects over a 2-h period. The kinetic rate constants for ll C-deoxyglucose were determined for gray and white matter and found to be very similar to those for 18F-fluorodeoxyglucose, suggesting that these two analogues of glu cose have similar affinities for the facilitated transport system and are similar substrates for hexokinase in the brain. The coefficient of variation of repeated measurements of LCMRgl in a series of six normal subjects was 5.5% to S.7% for various gray matter structures and 9.7% to 14.0% for white matter struc tures. The pattern of cerebral metabolic rates is relatively constant in a given individual when the conditions of the study are unchanged. The ability to make repeat measurements in the same subject reduces the variance due to between-subject differences, allowing smaller changes in LCMRgl to be de tected with confidence. Key Words: Coefficient of variation for repeat determinations-Deoxyglucose-Kinetic rate constants-Local cerebral glu cose metabolism.The 14C-2-deoxyglucose method for measuring local cerebral glucose metabolism (LCMRgl) in animals is a widely accepted technique that employs the autoradiographic determination of radioactivity concentration in tissues and allows quantitation of

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Section: Lcmrgi Determinationmentioning

confidence: 99%

Use of 2-Deoxy-D[1-¹¹C]Glucose for the Determination of Local Cerebral Glucose Metabolism in Humans: Variation within and between Subjects

Reivich

Alavi

Wolf

et al. 1982

J Cereb Blood Flow Metab

128

View full text Add to dashboard Cite

show abstract

“…A sequential quadratic programming method is employed for optimization. The optimizer updates an estimate of the Hessian of the Lagrangian at each iteration using the BFGS formula [20,21]. We set the lower and upper search bounds empirically at −2.0 • and 2.0 • for R x and R y , and at −2.0 mm and 2.0 mm for T z .…”

Section: Area Optimizationmentioning

confidence: 99%

Extraction of the Plane of Minimal Cross-Sectional Area of the Corpus Callosum Using Template-Driven Segmentation

Changizi

Hamarneh

Ishaq

et al. 2010

Medical Image Computing and Computer-Assisted Intervention – MICCAI 2010

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Abstract. Changes in corpus callosum (CC) size are typically quantified in clinical studies by measuring the CC cross-sectional area on a midsagittal plane. We propose an alternative measurement plane based on the role of the CC as a bottleneck structure in determining the rate of interhemispheric neural transmission. We designate this plane as the Minimum Corpus Callosum Area Plane (MCCAP), which captures the cross section of the CC that best represents an upper bound on interhemispheric transmission. Our MCCAP extraction method uses a nested optimization framework, segmenting the CC as it appears on each candidate plane, using registration-based segmentation. We demonstrate the robust convergence and high accuracy of our method for magnetic resonance images and present preliminary clinical results showing higher sensitivity to disease-induced atrophy.

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“…the three methods may be formulated as follows Y is usually set as an identity matrix for the first iteration and updated at each subsequent iteration, as shown by Fletcher and Powell (1963). A is reduced each time TiTTi decreases and increased when TiTTi increases (Marquardt, 1963).…”

Section: J;j == W;[i/i;ctj) -1/i?(tj)]/ Where = (Lim;) Ri /I?(t) (4)mentioning

confidence: 99%

Uncertainty and Forecasting of Water Quality

1983

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A Rapidly Convergent Descent Method for Minimization

Cited by 4,249 publications

References 0 publications

Use of 2-Deoxy-D[1-¹¹C]Glucose for the Determination of Local Cerebral Glucose Metabolism in Humans: Variation within and between Subjects

Use of 2-Deoxy-D[1-¹¹C]Glucose for the Determination of Local Cerebral Glucose Metabolism in Humans: Variation within and between Subjects

Extraction of the Plane of Minimal Cross-Sectional Area of the Corpus Callosum Using Template-Driven Segmentation

Uncertainty and Forecasting of Water Quality

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A Rapidly Convergent Descent Method for Minimization

Cited by 4,249 publications

References 0 publications

Use of 2-Deoxy-D[1-11C]Glucose for the Determination of Local Cerebral Glucose Metabolism in Humans: Variation within and between Subjects

Use of 2-Deoxy-D[1-11C]Glucose for the Determination of Local Cerebral Glucose Metabolism in Humans: Variation within and between Subjects

Extraction of the Plane of Minimal Cross-Sectional Area of the Corpus Callosum Using Template-Driven Segmentation

Uncertainty and Forecasting of Water Quality

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Use of 2-Deoxy-D[1-¹¹C]Glucose for the Determination of Local Cerebral Glucose Metabolism in Humans: Variation within and between Subjects

Use of 2-Deoxy-D[1-¹¹C]Glucose for the Determination of Local Cerebral Glucose Metabolism in Humans: Variation within and between Subjects