scholarly journals A Multi-Layer Perceptron Network for Perfusion Parameter Estimation in DCE-MRI Studies of the Healthy Kidney

2020 ◽  
Vol 10 (16) ◽  
pp. 5525
Author(s):  
Artur Klepaczko ◽  
Michał Strzelecki ◽  
Marcin Kociołek ◽  
Eli Eikefjord ◽  
Arvid Lundervold
Keyword(s):  
Least Squares ◽  
Curve Fitting ◽  
Ground Truth ◽  
Optimization Techniques ◽  
Reliable Estimate ◽  
Multi Layer Perceptron ◽  
Dce Mri ◽  
Least Squares Curve Fitting ◽  
Parameter Values

Background: Dynamic contrast-enhanced magnetic resonance imaging (DCE-MRI) is an imaging technique which helps in visualizing and quantifying perfusion—one of the most important indicators of an organ’s state. This paper focuses on perfusion and filtration in the kidney, whose performance directly influences versatile functions of the body. In clinical practice, kidney function is assessed by measuring glomerular filtration rate (GFR). Estimating GFR based on DCE-MRI data requires the application of an organ-specific pharmacokinetic (PK) model. However, determination of the model parameters, and thus the characterization of GFR, is sensitive to determination of the arterial input function (AIF) and the initial choice of parameter values. Methods: This paper proposes a multi-layer perceptron network for PK model parameter determination, in order to overcome the limitations of the traditional model’s optimization techniques based on non-linear least-squares curve-fitting. As a reference method, we applied the trust-region reflective algorithm to numerically optimize the model. The effectiveness of the proposed approach was tested for 20 data sets, collected for 10 healthy volunteers whose image-derived GFR scores were compared with ground-truth blood test values. Results: The achieved mean difference between the image-derived and ground-truth GFR values was 2.35 mL/min/1.73 m2, which is comparable to the result obtained for the reference estimation method (−5.80 mL/min/1.73 m2). Conclusions: Neural networks are a feasible alternative to the least-squares curve-fitting algorithm, ensuring agreement with ground-truth measurements at a comparable level. The advantages of using a neural network are twofold. Firstly, it can estimate a GFR value without the need to determine the AIF for each individual patient. Secondly, a reliable estimate can be obtained, without the need to manually set up either the initial parameter values or the constraints thereof.

A Fourier Transform Infrared Study of Mineral Matter in Coal: The Application of a Least Squares Curve-Fitting Program

1981 ◽  
Vol 35 (1) ◽  
pp. 102-106 ◽  
Author(s):  
Paul C. Painter ◽  
Susan M. Rimmer ◽  
Randy W. Snyder ◽  
Alan Davis
Keyword(s):  
Fourier Transform ◽  
Least Squares ◽  
Curve Fitting ◽  
Fourier Transform Infrared ◽  
Mineral Matter ◽  
Infrared Study ◽  
Least Squares Curve Fitting ◽  
Mineral Mixtures ◽  
Good Agreement

The application of Fourier transform infrared spectroscopy to the quantitative determination of mineral matter in coal is discussed. The use of a least squares curve-fitting program allows a choice between standards to be made. The results of an analysis of mineral mixtures and a coal low temperature ash are presented. The results are in good agreement with known concentrations and those obtained by other methods of analysis.

Least-Squares Curve-Fitting of Fourier Transform Infrared Spectra with Applications to Polymer Systems

1977 ◽  
Vol 31 (6) ◽  
pp. 518-524 ◽  
Author(s):  
M. K. Antoon ◽  
J. H. Koenig ◽  
J. L. Koenig
Keyword(s):  
Fourier Transform ◽  
Least Squares ◽  
Infrared Spectra ◽  
Curve Fitting ◽  
Fourier Transform Infrared ◽  
Polymer Systems ◽  
Fourier Transform Infrared Spectra ◽  
Least Squares Curve Fitting ◽  
Xylene Solution

A method is presented for least-squares curve-fitting of Fourier transform infrared spectra. A demonstration of the determination of xylene solution compositions illustrates the accuracy of the method. Least-squares coefficients are shown to be valuable for the analysis of several polymer systems by digital subtraction of spectra.

scholarly journals Least squares curve fitting in Mo3d X-ray photoelectron spectra for determination of oxidation states of supported molybdenum catalysts.

1989 ◽  
Vol 38 (2) ◽  
pp. 65-71
Author(s):  
Natsuo FUKUMOTO ◽  
Isao KOJIMA ◽  
Masayasu KURAHASHI ◽  
Hiromichi SHIMADA ◽  
Akio NISHIJIMA
Keyword(s):  
Least Squares ◽  
Curve Fitting ◽  
Photoelectron Spectra ◽  
Oxidation States ◽  
X Ray ◽  
Molybdenum Catalysts ◽  
Least Squares Curve Fitting ◽  
Fitting In

Statistical characterization of the random errors in the radioimmunoassay dose--response variable.

1976 ◽  
Vol 22 (3) ◽  
pp. 350-358 ◽  
Author(s):  
D Rodbard ◽  
R H Lenox ◽  
H L Wray ◽  
D Ramseth
Keyword(s):  
Least Squares ◽  
Dose Response ◽  
Curve Fitting ◽  
Response Curve ◽  
Dose Response Curve ◽  
Random Errors ◽  
Statistical Characterization ◽  
Response Variable ◽  
Least Squares Curve Fitting ◽  
The Relationship

Abstract We have developed practical methods for evaluating the magnitude of the random errors in radioimmunoassay dose--response variables, and the relationship between this error and position on the dose--response curve. This is important: to obtain appropriate weights for each point on the dose--response curve when utilizing least-squares curve-fitting methods; to evaluate whether the standards and the unknowns are subject to error of the same magnitude; for quality-control purposes; and to study the sources of errors in radioimmunoassay. Both standards and unknowns in radioimmunoassays for cAMP and cGMP were analyzed in triplicate. The same mean (Y), sample standard deviation, sy, and variance (2-y) of the response variable were calculated for each dose level. The relationship between s 2-y and y was calculated utilizing several models. Results for standards and unknowns from several assays were pooled, and a curve smoothing procedure was used to minimize random sampling errors. This pooling increased the reliability of the analysis, and confirmed the presence of the theoretically predicted nonuniformity of variance. Thus, the calculation of results from these radioimmunoassays should utilize a weighted least-squares curve-fitting program. These analyses have been computerized, and can be used as a "pre-processor" for programs for routine analysis of results of radioimmunoassay.

scholarly journals Comparative Study of Optimization Algorithms for The Optimal Reservoir Operation

2018 ◽  
Vol 246 ◽  
pp. 01003
Author(s):  
Xinyuan Liu ◽  
Yonghui Zhu ◽  
Lingyun Li ◽  
Lu Chen
Keyword(s):  
Reservoir Operation ◽  
Optimization Problems ◽  
Optimization Algorithms ◽  
Complex Problem ◽  
Optimization Techniques ◽  
Decision Variables ◽  
Handling Methods ◽  
Optimality Algorithm ◽  
Parameter Values

Apart from traditional optimization techniques, e.g. progressive optimality algorithm (POA), modern intelligence algorithms, like genetic algorithms, differential evolution have been widely used to solve optimization problems. This paper deals with comparative analysis of POA, GA and DE and their applications in a reservoir operation problem. The results show that both GA and DES are feasible to reservoir operation optimization, but they display different features. GA and DE have many parameters and are difficult in determination of these parameter values. For simple problems with mall number of decision variables, GA and DE are better than POA when adopting appropriate parameter values and constraint handling methods. But for complex problem with large number of variables, POA combined with simplex method are much superior to GA and DE in time-assuming and quality of optimal solutions. This study helps to select proper optimization algorithms and parameter values in reservoir operation.

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