scholarly journals Accuracies and Contrasts of Models of the Diffusion-weighted-dependent Attenuation of the Mri Signal at Intermediate B-values

2015 ◽  
Vol 8 ◽  
pp. MRI.S25301 ◽  
Author(s):  
Renaud Nicolas ◽  
Igor Sibon ◽  
Bassem Hiba
Keyword(s):  
White Matter ◽  
Akaike Information Criterion ◽  
Goodness Of Fit ◽  
Information Criterion ◽  
Exponential Model ◽  
B Values ◽  
Diffusion Weighted ◽  
Monoexponential Model ◽  
Biexponential Model ◽  
The Brain

The diffusion-weighted-dependent attenuation of the MRI signal E( b) is extremely sensitive to microstructural features. The aim of this study was to determine which mathematical model of the E( b) signal most accurately describes it in the brain. The models compared were the monoexponential model, the stretched exponential model, the truncated cumulant expansion (TCE) model, the biexponential model, and the triexponential model. Acquisition was performed with nine b-values up to 2500 s/mm2 in 12 healthy volunteers. The goodness-of-fit was studied with F-tests and with the Akaike information criterion. Tissue contrasts were differentiated with a multiple comparison corrected nonparametric analysis of variance. F-test showed that the TCE model was better than the biexponential model in gray and white matter. Corrected Akaike information criterion showed that the TCE model has the best accuracy and produced the most reliable contrasts in white matter among all models studied. In conclusion, the TCE model was found to be the best model to infer the microstructural properties of brain tissue.

Diffusion-Weighted Imaging of the Brain in Preterm Infants With Focal and Diffuse White Matter Abnormality

PEDIATRICS ◽  
2003 ◽  
Vol 112 (1) ◽  
pp. 1-7 ◽  
Author(s):  
S. J. Counsell ◽  
J. M. Allsop ◽  
M. C. Harrison ◽  
D. J. Larkman ◽  
N. L. Kennea ◽  
...  
Keyword(s):  
White Matter ◽  
Preterm Infants ◽  
Diffusion Weighted Imaging ◽  
White Matter Abnormality ◽  
Diffuse White Matter ◽  
Diffusion Weighted ◽  
The Brain

Diffusion-weighted MR Imaging in the Brain in Children: Findings in the Normal Brain and in the Brain with White Matter Diseases

Radiology ◽  
2002 ◽  
Vol 222 (2) ◽  
pp. 410-418 ◽  
Author(s):  
Volkher Engelbrecht ◽  
Axel Scherer ◽  
Margarethe Rassek ◽  
Hans J. Witsack ◽  
Ulrich Mödder
Keyword(s):  
White Matter ◽  
Mr Imaging ◽  
Normal Brain ◽  
White Matter Diseases ◽  
Diffusion Weighted ◽  
The Brain

scholarly journals Validação da estrutura fatorial do Körperkoordination Test für Kinder (KTK) em escolares de 8 a 10 anos

2020 ◽  
Vol 8 (3) ◽  
pp. 31
Author(s):  
João Otacilio Libardoni Dos Santos ◽  
Pâmella De Medeiros ◽  
Fernando Luiz Cardoso ◽  
Nilton Soares Formiga ◽  
Nayara Christine Souza ◽  
...  
Keyword(s):  
Maximum Likelihood ◽  
Root Mean Square Error ◽  
Mean Square Error ◽  
Akaike Information Criterion ◽  
Goodness Of Fit ◽  
Cross Validation ◽  
Information Criterion ◽  
Mean Square ◽  
Fit Index ◽  
Close Fit

Objetivo: Avaliar a estrutura fatorial do teste KTK em crianças em idade escolar, na faixa etária entre 8 e 10 anos, com base na estrutura unifatorial do KTK. Método: Foram avaliados 350 escolares da cidade de Manaus-AM com idade entre 8 e 10 anos de ambos os sexos. Para análise dos dados considerou-se como entrada, a matriz de covariância, tendo sido adotado o estimador ML (Maximum-Likelihood). Foram utilizados os seguintes indicadores: χ²/gl (qui-quadrado e grau de liberdade), Goodness-of-Fit Index (GFI), Adjusted Goodness-of-Fit Index (AGFI), Root-Mean-Square Error of Approximation (RMSEA), p de Close Fit (PCLOSE), Comparative Fit Index (CFI), Expected Cross-Validation Index (ECVI) e o Consistent Akaike Information Criterion (CAIC). Resultados: A análise fatorial confirmou o modelo unifatorial original da bateria de testes. Deixando livre as covariâncias (phi, φ) entre os itens, os resultados revelaram que os indicadores de qualidade de ajuste são aceitáveis para o modelo proposto, o qual é composto por quatro itens distribuídos em um único fator (χ²/gl = 1.09; GFI = 0.99; AGFI = 0.94; CFI = 0.97; TLI = 0.92; RMSEA = 0.07; PCLOSE = 0.10). Observou-se ainda que todas as saturações (Lambdas, λ), tanto estiveram dentro do intervalo esperado |0 - 1| quando foram estatisticamente diferentes de zero (t > 1.96, p < 0.05). Conclusões: Foi possível identificar aceitáveis evidências de validade baseada na estrutura interna do KTK proposto pelos autores originais confirmando a sua capacidade de investigar e classificar o nível de coordenação motora de crianças, identificando possíveis perturbações ou insuficiências na população avaliada.

scholarly journals Statistical Evaluation of Different Mathematical Models for Diffusion Weighted Imaging of Prostate Cancer Xenografts in Mice

2021 ◽  
Vol 11 ◽  
Author(s):  
Harri Merisaari ◽  
Hanne Laakso ◽  
Heidi Liljenbäck ◽  
Helena Virtanen ◽  
Hannu J. Aronen ◽  
...  
Keyword(s):  
Prostate Cancer ◽  
Tumor Growth ◽  
Mathematical Models ◽  
Diffusion Weighted Imaging ◽  
Exponential Model ◽  
Information Criteria ◽  
B Values ◽  
Stretched Exponential ◽  
Diffusion Weighted ◽  
Mouse Xenograft Model

PurposeTo evaluate fitting quality and repeatability of four mathematical models for diffusion weighted imaging (DWI) during tumor progression in mouse xenograft model of prostate cancer.MethodsHuman prostate cancer cells (PC-3) were implanted subcutaneously in right hind limbs of 11 immunodeficient mice. Tumor growth was followed by weekly DWI examinations using a 7T MR scanner. Additional DWI examination was performed after repositioning following the fourth DWI examination to evaluate short term repeatability. DWI was performed using 15 and 12 b-values in the ranges of 0-500 and 0-2000 s/mm2, respectively. Corrected Akaike information criteria and F-ratio were used to evaluate fitting quality of each model (mono-exponential, stretched exponential, kurtosis, and bi-exponential).ResultsSignificant changes were observed in DWI data during the tumor growth, indicated by ADCm, ADCs, and ADCk. Similar results were obtained using low as well as high b-values. No marked changes in model preference were present between the weeks 1−4. The parameters of the mono-exponential, stretched exponential, and kurtosis models had smaller confidence interval and coefficient of repeatability values than the parameters of the bi-exponential model.ConclusionStretched exponential and kurtosis models showed better fit to DWI data than the mono-exponential model and presented with good repeatability.

scholarly journals Simulation of the occurrence of drought events via copulas

RBRH ◽  
2020 ◽  
Vol 25 ◽  
Author(s):  
Rogério de Almeida ◽  
Paulo Sérgio Franco Barbosa
Keyword(s):  
Akaike Information Criterion ◽  
Goodness Of Fit ◽  
Probabilistic Models ◽  
Historical Data ◽  
Probability Distributions ◽  
Information Criterion ◽  
Bivariate Analysis ◽  
Kolmogorov Smirnov ◽  
Hydrological Droughts ◽  
Smirnov Test

ABSTRACT This study presents a method based on Archimedean and Gaussian copulas to simulate the occurrence of hydrological droughts. The droughts were characterized by theory of runs for four threshold levels and six univariate probability distributions were evaluated to represent the probabilistic behavior of their severities and durations. The Akaike Information Criterion was used to select the better univariate probabilistic models, while their hypotheses of goodness-of-fit to the historical data were evaluated by Kolmogorov-Smirnov test. Based on the univariate probability distributions of severities and durations, Archimedean and Gaussian copulas were used in the bivariate analysis of the drought events. The proposed method proves to be a useful tool to simulate the occurrence of drought events, preserving the laws of probability of the severities and durations and the dependency between both.

scholarly journals Volumetric analysis of syringomyelia following hindbrain decompression for Chiari malformation Type I: syringomyelia resolution follows exponential kinetics

2011 ◽  
Vol 31 (3) ◽  
pp. E4 ◽  
Author(s):  
Jean-Valery Coumans ◽  
Brian P. Walcott ◽  
William E. Butler ◽  
Brian V. Nahed ◽  
Kristopher T. Kahle
Keyword(s):  
Least Squares ◽  
Chiari Malformation ◽  
Goodness Of Fit ◽  
Three Dimensional ◽  
Information Criterion ◽  
Exponential Model ◽  
Type I ◽  
Chiari Malformation Type I ◽  
Data Set ◽  
Over Time

Object Resolution of syringomyelia is common following hindbrain decompression for Chiari malformation, yet little is known about the kinetics governing this process. The authors sought to establish the volumetric rate of syringomyelia resolution. Methods A retrospective cohort of patients undergoing hindbrain decompression for a Chiari malformation Type I with preoperative cervical or thoracic syringomyelia was identified. Patients were included in the study if they had at least 3 neuroimaging studies that detailed the entirety of their preoperative syringomyelia over a minimum of 6 months postoperatively. The authors reconstructed the MR images in 3 dimensions and calculated the volume of the syringomyelia. They plotted the syringomyelia volume over time and constructed regression models using the method of least squares. The Akaike information criterion and Bayesian information criterion were used to calculate the relative goodness of fit. The coefficients of determination R2 (unadjusted and adjusted) were calculated to describe the proportion of variability in each individual data set accounted for by the statistical model. Results Two patients were identified as meeting inclusion criteria. Plots of the least-squares best fit were identified as 4.01459e−0.0180804x and 13.2556e−0.00615859x. Decay of the syringomyelia followed an exponential model in both patients (R2 = 0.989582 and 0.948864). Conclusions Three-dimensional analysis of syringomyelia resolution over time enables the kinetics to be estimated. This technique is yet to be validated in a large cohort. Because syringomyelia is the final common pathway for a number of different pathological processes, it is possible that this exponential only applies to syringomyelia related to treatment of Chiari malformation Type I.

scholarly journals Model Selection in Continuous Test Norming With GAMLSS

Assessment ◽  
2017 ◽  
Vol 26 (7) ◽  
pp. 1329-1346 ◽  
Author(s):  
Lieke Voncken ◽  
Casper J. Albers ◽  
Marieke E. Timmerman
Keyword(s):  
Model Selection ◽  
Sample Size ◽  
Akaike Information Criterion ◽  
Reference Group ◽  
Generalized Additive Models ◽  
Selection Procedure ◽  
Information Criterion ◽  
Exponential Model ◽  
Additive Models ◽  
Model Selection Procedure

To compute norms from reference group test scores, continuous norming is preferred over traditional norming. A suitable continuous norming approach for continuous data is the use of the Box–Cox Power Exponential model, which is found in the generalized additive models for location, scale, and shape. Applying the Box–Cox Power Exponential model for test norming requires model selection, but it is unknown how well this can be done with an automatic selection procedure. In a simulation study, we compared the performance of two stepwise model selection procedures combined with four model-fit criteria (Akaike information criterion, Bayesian information criterion, generalized Akaike information criterion (3), cross-validation), varying data complexity, sampling design, and sample size in a fully crossed design. The new procedure combined with one of the generalized Akaike information criterion was the most efficient model selection procedure (i.e., required the smallest sample size). The advocated model selection procedure is illustrated with norming data of an intelligence test.

Frequency analysis of low flows using the Akaike information criterion

1996 ◽  
Vol 23 (6) ◽  
pp. 1180-1189 ◽  
Author(s):  
Semiu A. Lawal ◽  
W. Edgar Watt
Keyword(s):  
Lower Bound ◽  
Frequency Analysis ◽  
Akaike Information Criterion ◽  
Goodness Of Fit ◽  
Current Practice ◽  
Information Criterion ◽  
Low Flow ◽  
Parameter Distribution ◽  
Two Parameter ◽  
Parameter Distributions

It is the current practice in frequency analysis of low flows to consider only three-parameter distributions in which one of the parameters represents a nonzero lower bound. When applied to the small samples typically available, this practice results in incorrect low flow estimates. These errors are related to errors in the estimated lower bound. To preclude this possibility, it is proposed that the current practice be changed to include the selection of a two-parameter distribution in certain situations. To assess this proposal, the Akaike information criterion (AIC) is used to compare the suitability of the most commonly used three-parameter distribution (three-parameter Weibull) and three two-parameter distributions (two-parameter Weibull, Gumbel, and lognormal) to low flow data for 51 long-term hydrometric stations across Canada. For 75% of the stations, a two-parameter distribution is selected over the three-parameter distribution if the selection criterion is minimum AIC. In about one third of the remaining 25% of the stations where the three-parameter Weibull distribution gave the minimum AIC, the estimated lower bound is sufficiently close to the minimum observed low flow to indicate overfitting and hence unreliable quantile estimates. When the AIC is supplemented with visual examination of goodness of fit on probability plots, it is found that the lognormal distribution could very well fit those cases where the AIC selected the three-parameter Weibull distribution. Key words: low flow frequency, goodness of fit, information criterion, probability plot.

scholarly journals Discrimination between a group of three-parameter distributions for hydro-meteorological frequency modeling

2018 ◽  
Vol 45 (5) ◽  
pp. 351-365 ◽  
Author(s):  
Ismaila Ba ◽  
Fahim Ashkar
Keyword(s):  
Correlation Coefficient ◽  
Akaike Information Criterion ◽  
Bayesian Information Criterion ◽  
Goodness Of Fit ◽  
Information Criterion ◽  
Extreme Value ◽  
Generalized Extreme Value ◽  
Discrimination Power ◽  
Pearson Type ◽  
Parameter Distributions

We recommend methods of discrimination between some three-parameter distributions used in hydro-meteorological frequency modeling. Discriminations are between model pairs belonging to the group (generalized extreme value (GEV), Pearson Type III (P3), generalized logistic (GLO)). To assess the fit of these distributions to data, the Akaike information criterion, Bayesian information criterion, and (or) goodness-of-fit measures are commonly employed. However, it is difficult to estimate the discrimination power and bias of these methods when used with three-parameter distributions. Consequently, we propose two alternative tools and assess their performance. Both tools are based on a sample transformation to normality followed by applying a powerful statistic for testing normality, such as the Shapiro-Wilk or the probability plot correlation coefficient statistic. While arriving at recommendations for discriminating between the (GEV, GLO) and (P3, GLO) pairs of models, we show that the discrimination power between the P3 and GEV distributions can be rather low.

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