Convergence Properties of the Nelder--Mead Simplex Method in Low Dimensions

Lagarias, Jeffrey C.; Reeds, James A.; Wright, Margaret H.; Wright, Paul E.

doi:10.1137/s1052623496303470

Cited by 6,324 publications

(3,675 citation statements)

References 7 publications

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“…All optimization was implemented in MATLAB R2010a (The MathWorks, Natick, MA, USA) using a constrained Nelder-Mead simplex algorithm, 25 with initial parameter values chosen from a uniform random distribution.…”

Section: Optimization and Data Analysismentioning

confidence: 99%

Extra Permeability is Required to Model Dynamic Oxygen Measurements: Evidence for Functional Recruitment?

Barrett

Suresh

2013

J Cereb Blood Flow Metab

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Neural activation triggers a rapid, focal increase in blood flow and thus oxygen delivery. Local oxygen consumption also increases, although not to the same extent as oxygen delivery. This 'uncoupling' enables a number of widely-used functional neuroimaging techniques; however, the physiologic mechanisms that govern oxygen transport under these conditions remain unclear. Here, we explore this dynamic process using a new mathematical model. Motivated by experimental observations and previous modeling, we hypothesized that functional recruitment of capillaries has an important role during neural activation. Using conventional mechanisms alone, the model predictions were inconsistent with in vivo measurements of oxygen partial pressure. However, dynamically increasing net capillary permeability, a simple description of functional recruitment, led to predictions consistent with the data. Increasing permeability in all vessel types had the same effect, but two alternative mechanisms were unable to produce predictions consistent with the data. These results are further evidence that conventional models of oxygen transport are not sufficient to predict dynamic experimental data. The data and modeling suggest that it is necessary to include a mechanism that dynamically increases net vascular permeability. While the model cannot distinguish between the different possibilities, we speculate that functional recruitment could have this effect in vivo.

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Section: Optimization and Data Analysismentioning

confidence: 99%

Extra Permeability is Required to Model Dynamic Oxygen Measurements: Evidence for Functional Recruitment?

Barrett

Suresh

2013

J Cereb Blood Flow Metab

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“…The set of rate constants from the random search that produced the smallest deviation, was used as the seed for the fminsearch function of the MATLAB optimization toolbox. The fminsearch function is a directed search algorithm that uses the Nelder-Mead simplex method (Lagarias et al, 1998). The co-occurrence matrices and the corresponding sets of rate constants that produced the smallest deviation are reported in the Results section.…”

Section: Optimization Proceduresmentioning

confidence: 99%

Evaluation of pathways for progression of heterogeneous breast tumors

Sontag

Axelrod

2005

Journal of Theoretical Biology

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“…Two metrics [TA and rTTP (rTTP ¼ TTP-TA)] were determined using gamma variate fit through the first passage and the other metric (FWHM) was determined directly from the DR 2 * profile. The gamma variate function was fitted to the data with the Nelder-Mead simplex algorithm by minimization of the sum-of-squared differences between the data and the modeled gamma variate function (27). The TA is one of the fitting parameters and the TTP is determined as the time of the maximum signal of the fitted gamma variate function.…”

Section: In Vivo Postprocessingmentioning

confidence: 99%

Evaluation of signal formation in local arterial input function measurements of dynamic susceptibility contrast MRI

Bleeker

Webb

Walderveen

et al. 2011

Magnetic Resonance in Med

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Correct arterial input function (AIF) measurements in dynamic susceptibility contrast-MRI are crucial for quantification of the hemodynamic parameters. Often a single global AIF is selected near a large brain-feeding artery. Alternatively, local AIF measurements aim for voxel-specific AIFs from smaller arteries. Because local AIFs are measured higher in the arterial-tree, it is assumed that these will reflect the true input of the microvasculature much better. However, do the measured local AIFs reflect the true concentration-time curves of small arteries? To answer this question, in vivo data were used to evaluate local AIF candidates selected based on two different types of angiograms. For interpretation purposes, a 3D numerical model that simulated partial-volume effects in local AIF measurements was created and the simulated local AIFs were compared to the ground truth. The findings are 2-fold. First, the in vivo data showed that the shape-characteristics of local AIFs are similar to the shape-characteristics of gray matter concentration-time curves. Second, these findings are supported by the simulations showing broadening of the measured local AIFs compared to the ground truth. These findings are suggesting that local AIF measurements do not necessarily reflect the true concentration-time curve in small arteries. Magn Reson Med 67:1324-1331,

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Convergence Properties of the Nelder--Mead Simplex Method in Low Dimensions

Cited by 6,324 publications

References 7 publications

Extra Permeability is Required to Model Dynamic Oxygen Measurements: Evidence for Functional Recruitment?

Extra Permeability is Required to Model Dynamic Oxygen Measurements: Evidence for Functional Recruitment?

Evaluation of pathways for progression of heterogeneous breast tumors

Evaluation of signal formation in local arterial input function measurements of dynamic susceptibility contrast MRI

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