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A new integrated statistical approach to the diagnostic use of two-dimensional maps.

Two-dimensional (2-D) electrophoresis is a very useful technique for the analysis of proteins in biological tissues. The complexity of the 2-D maps obtained causes many difficulties in the comparison of different samples. A new method is proposed for comparing different 2-D maps, based on five steps: (i) the digitalisation of the image; (ii) the transformation of the digitalised map in a fuzzy entity, in order to consider the variability of the 2-D electrophoretic separation; (iii) the calculation of a similarity index for each pair of maps; (iv) the analysis by multidimensional scaling of the previously obtained similarity matrix; (v) the analysis by classification or cluster analysis techniques of the resulting map co-ordinates. The method adopted was first tested on some simulated samples in order to evaluate its sensitivity to small changes in the spots position and size. The optimal setting of the method parameters was also investigated. Finally, the method was successfully applied to a series of real samples corresponding to the electrophoretic bidimensional analysis of sera from normal and nicotine-treated rats. Multidimensional scaling allowed the separation of the two classes of samples without any misclassification.

Animals↗

A split-merge-based region-growing method for fMRI activation detection.

We introduce a hybrid method for functional magnetic resonance imaging (fMRI) activation detection based on the well-developed split-merge and region-growing techniques. The proposed method includes conjoining both of the spatio-temporal priors inherent in split-merge and the prior information afforded by the hypothesis-led component of region selection. Compared to the fuzzy c-means clustering analysis, this method avoids making assumptions about the number of clusters and the computation complexity is reduced markedly. We evaluated the effectiveness of the proposed method in comparison with the general linear model and the fuzzy c-means clustering method conducted on simulated and in vivo datasets. Experimental results show that our method successfully detected expected activated regions and has advantages over the other two methods.

Acoustic Stimulation↗

Efficient fuzzy control strategies for the application of pH-stat to fed-batch cultivation of genetically engineered Escherichia coli.

In the cultivation of genetically engineered Escherichia coli it is very important to control the substrate concentration at an appropriate level in order to avoid the accumulation of acetate, thereby elevating the expression level of plasmid-encoded protein. In this paper, a pH-stat mode of fuzzy control was considered for the overexpression of beta-galactosidase in the fed-batch cultivation of recombinant E. coli. In the simple pH-stat fuzzy control, the response of pH change in the culture broth to the feeding rate of glucose was used to estimate the glucose consumption rate. In the modified pH-stat fuzzy control, the glucose consumption rate was accurately estimated by using pH change and the change in the carbon dioxide content of the exhaust gas. With this control strategy, the cell density could be increased to 72 g DCW dm-3, which was twofold higher than that attained in the cultivation with the simple pH-stat fuzzy control. The bulk beta-galactosidase concentration was increased to 4150 U cm-3, which was threefold higher than when the simple pH-stat control was used.

Carbon Dioxide↗

Determination of arterial input function using fuzzy clustering for quantification of cerebral blood flow with dynamic susceptibility contrast-enhanced MR imaging.

An accurate determination of the arterial input function (AIF) is necessary for quantification of cerebral blood flow (CBF) using dynamic susceptibility contrast-enhanced magnetic resonance imaging. In this study, we developed a method for obtaining the AIF automatically using fuzzy c-means (FCM) clustering. The validity of this approach was investigated with computer simulations. We found that this method can automatically extract the AIF, even under very noisy conditions, e.g., when the signal-to-noise ratio is 2. The simulation results also indicated that when using a manual drawing of a region of interest (ROI) (manual ROI method), the contamination of surrounding pixels (background) into ROI caused considerable overestimation of CBF. We applied this method to six subjects and compared it with the manual ROI method. The CBF values, calculated using the AIF obtained using the manual ROI method [CBF(manual)], were significantly higher than those obtained with FCM clustering [CBF(fuzzy)]. This may have been due to the contamination of non-arterial pixels into the manually drawn ROI, as suggested by simulation results. The ratio of CBF(manual) to CBF(fuzzy) ranged from 0.99-1.83 [1.31 +/- 0.26 (mean +/- SD)]. In conclusion, our FCM clustering method appears promising for determination of AIF because it allows automatic, rapid and accurate extraction of arterial pixels. J. Magn. Reson. Imaging 2001;13:797-806.

Adult↗

Quantification of white matter and gray matter volumes from T1 parametric images using fuzzy classifiers.

White matter (WM) and gray matter (GM) were accurately measured using a technique based on a single standardized fuzzy classifier (FC) for each tissue. Fuzzy classifier development was based on experts' visual assessments of WM and GM boundaries from a set of T1 parametric MR images. The fuzzy classifier method's accuracy was validated and optimized by a set of T1 phantom images that were based on hand-detailed human brain cryosection images. Nine sets of axial T1 images of varying thickness equally distributed throughout the brain were simulated. All T1 data sets were mapped to the standardized FCs and rapidly segmented into WM and GM voxel fraction images. Resulting volumes revealed that, in most cases, the difference between measured and actual volumes was less than 5%. This was consistent throughout most of the brain, and as expected, the accuracy improved to generally less than 2% for the 1-mm simulated brain slices.

Artifacts↗

Fuzzy clustering of gradient-echo functional MRI in the human visual cortex. Part I: reproducibility.

Reproducibility of human functional MRI (fMRI) studies is essential for clinical and neuroresearch applications of this new human brain mapping method. Based on a recently presented study on reproducibility of gradient-echo fMRI in the human visual cortex (Moser et al. Magn Reson Imaging 1996; 14:567-579), comparing the performance of three different threshold strategies for correlation analysis, we demonstrate that (a) fuzzy clustering is a robust, model-independent method to extract functional information in time and space; (b) intertrial reproducibility of cortical activation is significantly improved by the capability of fuzzy clustering to separate signal contributions from larger vessels, running perpendicular to the slice orientation, from activation apparently close to the primary visual cortex; and (c) for repeated single subject studies, SDs of <20% for signal enhancement in approximately 80% of the studies and SDs of <30% for activated area size in approximately 65% of the studies are obtained. This, however, depends also on signal-to-noise ratio, (motion) artifacts, and subject cooperation.

Adult↗

Fuzzy clustering of gradient-echo functional MRI in the human visual cortex. Part II: quantification.

Fuzzy cluster analysis (FCA) is a new exploratory method for analyzing fMRI data. Using simulated functional MRI (fMRI) data, the performance of FCA, as implemented in the software package Evident, was tested and a quantitative comparison with correlation analysis is presented. Furthermore, the fMRI model fit allows separation and quantification of flow and blood oxygen level dependent (BOLD) contributions in the human visual cortex. In gradient-recalled echo fMRI at 1.5 T (TR = 60 ms, TE = 42 ms, radiofrequency excitation flip angle [theta] = 10 degrees-60 degrees) total signal enhancement in the human visual cortex, ie, flow-enhanced BOLD plus inflow contributions, on average varies from 5% to 10% in or close to the visual cortex (average cerebral blood volume [CBV] = 4%) and from 100% to 20% in areas containing medium-sized vessels (ie, average CBV = 12% per voxel), respectively. Inflow enhancement, however, is restricted to intravascular space (= CBV) and increases with increasing radiofrequency (RF) flip angle, whereas BOLD contributions may be obtained from a region up to three times larger and, applying an unspoiled gradient-echo (GRE) sequence, also show a flip angle dependency with a minimum at approximately 30 degrees. This result suggests that a localized hemodynamic response from the microvasculature at 1.5 T may be extracted via fuzzy clustering. In summary, fuzzy clustering of fMRI data, as realized in the Evident software, is a robust and efficient method to (a) separate functional brain activation from noise or other sources resulting in time-dependent signal changes as proven by simulated fMRI data analysis and in vivo data from the visual cortex, and (b) allows separation of different levels of activation even if the temporal pattern is indistinguishable. Combining fuzzy cluster separation of brain activation with appropriate model calculations allows quantification of flow and (flow-enhanced) BOLD contributions in areas with different vascularization.

Adult↗

An accurate and robust method for unsupervised assessment of abdominal fat by MRI.

PURPOSE: To describe and evaluate an automatic and unsupervised method for assessing the quantity and distribution of abdominal adipose tissue by MRI. MATERIAL AND METHODS: A total of 20 patients underwent whole-abdomen MRI. A total of 32 transverse T1-weighted images were acquired from each subject. The data collected were transferred to a dedicated workstation and analyzed by both our unsupervised method and a manual procedure. The proposed methodology allows the automatic processing of MRI axial images, segmenting the adipose tissue by fuzzy clustering approach. The use of an active contour algorithm on image masks provided by the fuzzy clustering algorithm allows the separation of subcutaneous fat from visceral fat. Finally, an automated procedure based on automatic image histogram analysis identifies the visceral fat. RESULTS: The accuracy, reproducibility, and speed of our automatic method were compared with the state-of-the-art manual approach. The unsupervised analysis correlated well with the manual analysis, and was significantly faster than manual tracing. Moreover, the unsupervised method was not affected by intraobserver and interobserver variability. CONCLUSION: The results obtained demonstrate that the proposed method can provide the volume of subcutaneous adipose tissue, visceral adipose tissue, global adipose tissue, and the ratio between subcutaneous and visceral fat in an unsupervised and effective manner.

Abdominal Cavity↗

Functional magnetic resonance imaging activation detection: fuzzy cluster analysis in wavelet and multiwavelet domains.

PURPOSE: To present novel feature spaces, based on multiscale decompositions obtained by scalar wavelet and multiwavelet transforms, to remedy problems associated with high dimension of functional magnetic resonance imaging (fMRI) time series (when they are used directly in clustering algorithms) and their poor signal-to-noise ratio (SNR) that limits accurate classification of fMRI time series according to their activation contents. MATERIALS AND METHODS: Using randomization, the proposed method finds wavelet/multiwavelet coefficients that represent the activation content of fMRI time series and combines them to define new feature spaces. Using simulated and experimental fMRI data sets, the proposed feature spaces are compared to the cross-correlation (CC) feature space and their performances are evaluated. In these studies, the false positive detection rate is controlled using randomization. To compare different methods, several points of the receiver operating characteristics (ROC) curves, using simulated data, are estimated and compared. RESULTS: The proposed features suppress the effects of confounding signals and improve activation detection sensitivity. Experimental results show improved sensitivity and robustness of the proposed method compared to the conventional CC analysis. CONCLUSION: More accurate and sensitive activation detection can be achieved using the proposed feature spaces compared to CC feature space. Multiwavelet features show superior detection sensitivity compared to the scalar wavelet features.

Algorithms↗

Automatic identification of the left ventricle in cardiac cine-MR images: dual-contrast cluster analysis and scout-geometry approaches.

PURPOSE: To evaluate the technical feasibility of two approaches--dual-contrast (DC) cluster analysis, and scout geometry (SG)--for automatic identification of the left ventricular (LV) cavity in short-axis (SA) cine-MR images. MATERIALS AND METHODS: The DC algorithm uses Fuzzy C-Means (FCM) cluster analysis of SA images from a black-blood double-inversion recovery turbo spin-echo (dual IR TSE) sequence, and bright-blood images from a steady-state free precession (SSFP) sequence. The SG algorithm employs geometric information from scout views (i.e., vertical long-axis (VLA) and four-chamber (4CH) views). Both algorithms incorporate additional geometric continuity constraints along with LV region segmentation to identify the LV. The performance of both algorithms was compared on images of eight healthy volunteers, and the SG algorithm was further evaluated on images of 13 clinical patients. RESULTS: The DC algorithm identified the LV in 89% (72/75 at end-diastole (ED) and 47/59 at end-systole (ES)) of the images from healthy volunteers, compared to 98% (74/75 at ED and 57/59 at ES) by the SG algorithm. Both methods are robust against interslice signal variations and misalignment. The DC method suffers from misregistration between the dual IR TSE and SSFP images near the apex at ES. The SG method identified the LV in 91% (112/122 at ED and 91/102 at ES) of the images from clinical patients. CONCLUSION: The SG method requires no additional scan, is robust and accurate, and performs better than the DC method for automatic identification of the LV.

Adult↗

Characterization of coronary atherosclerotic plaque using multicontrast MRI acquired under simulated in vivo conditions.

PURPOSE: To compare coronary atherosclerotic plaque characterization using multicontrast MRI on: 1) freshly excised vessels under simulated in vivo conditions, and 2) preserved vessels. MATERIALS AND METHODS: T1-weighted (T1W), T2-weighted (T2W), proton density-weighted (PDW), and diffusion-weighted (DW) MR images were acquired on 13 freshly excised human coronary arteries from explanted hearts. Vessels were imaged in an MR-compatible tissue culture chamber using a 4.7 Tesla small-bore MR scanner. Eight vessels were then preserved in buffered formalin and rescanned following the same imaging protocol. A three-dimensional spatially penalized fuzzy C-means (3D-SPFCM) technique was applied to classify different plaque constituents. The classification results from vessels under "fresh" and "preserved" conditions were compared with corresponding histological sections. RESULTS: For most plaque constituents, the plaque characterization results show no significant difference between fresh and preserved scans, and little difference between scans and the histological reference standard. In the case of thrombus, apparent signal changes between fresh and preserved images were identified. Overall, MR scans conducted under preserved conditions provided a 1.8% to 17.5% greater signal-to-noise ratio (SNR) than those conducted in the fresh stage. CONCLUSION: Preservation of coronary vessels did not alter the contrast between plaque tissues on multicontrast MRI, and did not significantly change the results of plaque constituent characterization.

Coronary Artery Disease↗

Interpretation of surface EMGs in children with cerebral palsy: An initial study using a fuzzy expert system.

Surface EMG detected simultaneously at different muscles has become an important tool for analysing the gait of children with cerebral palsy (CP), as it offers essential information about muscular coordination. However, the interpretation of surface EMG is a difficult task that assumes extensive knowledge and experience. As such, this noninvasive procedure is not frequently used in the general clinical routine. An Artificial Intelligence (AI) system for interpreting surface EMG signals and the resulting muscular coordination patterns could overcome these limitations. To support such interpretation, an expert system based on fuzzy inference methodology was developed. The knowledge-base of the system implemented 15 rules, from which the fuzzy inference methodology performs a prediction of the effectiveness of the muscular coordination during gait. Our aim was to assess the feasibility and value of such an expert system in clinical applications. Surface EMG signals were recorded from the tibialis anterior, soleus muscle, and gastrocnemius muscles of children with CP to assess muscular coordination patterns of ankle movement during gait. Nineteen children underwent 114 surface EMG measurements. Simultaneously, the gait cycles of each patient were determined using foot switches and videotapes. From the EMG signals, the effectiveness of the ankle movement was predicted by the expert system, and predictions were classified using a three-point ordinal scale. In 91 cases (80%), the clinical findings matched the predictions of the expert system. In 23 cases (20%) the predictions of the expert system differed from the clinical findings with 12 cases revealing worse and 11 cases revealing better results in comparison to the clinical findings. As this study is a first attempt to verify the feasibility and correctness of this expert system, the results are promising. Further study is required to assess the correlation with the kinematic data and to include the whole leg.

Cerebral Palsy↗

Computerized consensus diagnosis: a classification strategy for the robust analysis of MR spectra. I. Application to 1H spectra of thyroid neoplasms.

We introduce and apply a new classification strategy we call computerized consensus diagnosis (CCD). Its purpose is to provide robust, reliable classification of biomedical data. The strategy involves the cross-validated training of several classifiers of diverse conceptual and methodological origin on the same data, and appropriately combining their outcomes. The strategy is tested on proton magnetic resonance spectra of human thyroid biopsies, which are successfully allocated to normal or carcinoma classes. We used Linear Discriminant Analysis, a Neural Net-based method, and Genetic Programming as independent classifiers on two spectral regions, and chose the median of the six classification outcomes as the consensus. This procedure yielded 100% specificity and 100% sensitivity on the training sets, and 100% specificity and 98% sensitivity on samples of known malignancy in the test sets. We discuss the necessary steps any classification approach must take to guarantee reliability, and stress the importance of fuzziness and undecidability in robust classification.

Adenocarcinoma, Follicular↗

Neuro-fuzzy structural classification of proteins for improved protein secondary structure prediction.

Fourier transform infrared (FTIR) spectroscopy is a very flexible technique for characterization of protein secondary structure. Measurements can be carried out rapidly in a number of different environments based on only small quantities of proteins. For this technique to become more widely used for protein secondary structure characterization, however, further developments in methods to accurately quantify protein secondary structure are necessary. Here we propose a structural classification of proteins (SCOP) class specialized neural networks architecture combining an adaptive neuro-fuzzy inference system (ANFIS) with SCOP class specialized backpropagation neural networks for improved protein secondary structure prediction. Our study shows that proteins can be accurately classified into two main classes "all alpha proteins" and "all beta proteins" merely based on the amide I band maximum position of their FTIR spectra. ANFIS is employed to perform the classification task to demonstrate the potential of this architecture with moderately complex problems. Based on studies using a reference set of 17 proteins and an evaluation set of 4 proteins, improved predictions were achieved compared to a conventional neural network approach, where structure specialized neural networks are trained based on protein spectra of both "all alpha" and "all beta" proteins. The standard errors of prediction (SEPs) in % structure were improved by 4.05% for helix structure, by 5.91% for sheet structure, by 2.68% for turn structure, and by 2.15% for bend structure. For other structure, an increase of SEP by 2.43% was observed. Those results were confirmed by a "leave-one-out" run with the combined set of 21 FTIR spectra of proteins.

Fuzzy Logic↗

Numerical approaches for quantitative analysis of two-dimensional maps: a review of commercial software and home-made systems.

The present review attempts to cover a number of methods that have appeared in the last few years for performing quantitative proteome analysis. However, due to the large number of methods described for both electrophoretic and chromatographic approaches, we have limited this review to conventional two-dimensional (2-D) map analysis which couples orthogonally a charge-based step (isoelectric focusing) to a size-based separation step (sodium dodecyl sulfate-electrophoresis). The first and oldest method applied to 2-D map data reduction is based on statistical analysis performed on sets of gels via powerful software packages, such as Melanie, PDQuest, Z3 and Z4000, Phoretix and Progenesis. This method calls for separately running a number of replicas for control and treated samples. The two sets of data are then merged and compared via a number of software packages which we describe. In addition to commercially-available systems, a number of home made approaches for 2-D map comparison have been recently described and are also reviewed. They are based on fuzzyfication of the digitized 2-D gel image coupled to linear discriminant analysis, three-way principal component analysis or a combination of principal component analysis and soft-independent modeling of class analogy. These statistical tools appear to perform well in differential proteomic studies.

Cluster Analysis↗

Fuzzy cluster analysis of simple physicochemical properties of amino acids for recognizing secondary structure in proteins.

Fuzzy cluster analysis has been applied to the 20 amino acids by using 65 physicochemical properties as a basis for classification. The clustering products, the fuzzy sets (i.e., classical sets with associated membership functions), have provided a new measure of amino acid similarities for use in protein folding studies. This work demonstrates that fuzzy sets of simple molecular attributes, when assigned to amino acid residues in a protein's sequence, can predict the secondary structure of the sequence with reasonable accuracy. An approach is presented for discriminating standard folding states, using near-optimum information splitting in half-overlapping segments of the sequence of assigned membership functions. The method is applied to a nonredundant set of 252 proteins and yields approximately 73% matching for correctly predicted and correctly rejected residues with approximately 60% overall success rate for the correctly recognized ones in three folding states: alpha-helix, beta-strand, and coil. The most useful attributes for discriminating these states appear to be related to size, polarity, and thermodynamic factors. Van der Waals volume, apparent average thickness of surrounding molecular free volume, and a measure of dimensionless surface electron density can explain approximately 95% of prediction results. hydrogen bonding and hydrophobicity induces do not yet enable clear clustering and prediction.

Algorithms↗

Measures for the assessment of fuzzy predictions of protein secondary structure.

Many of the recent secondary structure prediction methods incorporate the idea of fuzzy set theory, where instead of assigning a definite secondary structure to a query residue, probability for the residue being in each of the conformational states is estimated. Moreover, continuous assignment of conformational states to the experimentally observed protein structures can be performed in order to reflect inherent flexibility. Although various measures have been developed for evaluating performances of secondary structure prediction methods, they depend only on the most probable secondary structures. They do not assess the accuracy of the probabilities produced by fuzzy prediction methods, and they cannot incorporate information contained in continuous assignments of conformational states to observed structures. Three important measures for evaluating performance of a secondary structure prediction algorithm, Q score, Segment OVerlap (SOV) measure, and the k-state correlation coefficient (Corr), are deformed into fuzzy measures F score, Fuzzy OVerlap (FOV) measure, and the fuzzy correlation coefficient (Forr), so that the new measures not only assess probabilistic outputs of fuzzy prediction methods, but also incorporate information from continuous assignments of secondary structure. As an example of application, prediction results of four fuzzy secondary structure prediction methods, PSIPRED, PROFking, SABLE, and PREDICT, are assessed using the new fuzzy measures.

Computer Simulation↗

Fuzzy cluster analysis of molecular dynamics trajectories.

We propose fuzzy clustering as a method to analyze molecular dynamics (MD) trajectories, especially of proteins and polypeptides. A fuzzy cluster analysis locates classes of similar three-dimensional conformations explored during a molecular dynamics simulation. The method can be readily applied to results from both equilibrium and nonequilibrium simulations, with clustering on either global or local structural parameters. The potential of this technique is illustrated by results from fuzzy cluster analyses of trajectories from MD simulations of various fragments of human parathyroid hormone (PTH). For large molecules, it is more efficient to analyze the clustering of root-mean-square distances between conformations comprising the trajectory. We found that the results of the clustering analysis were unambiguous, in terms of the optimal number of clusters of conformations, for the majority of the trajectories examined. The conformation closest to the cluster center can be chosen as being representative of the class of structures making up the cluster, and can be further analyzed, for example, in terms of its secondary structure. The CPU time used by the cluster analysis was negligible compared to the MD simulation time.

Amino Acid Sequence↗