Accuracy of iodine quantification using dual energy CT in latest generation dual source and dual layer CT.

OBJECTIVE: To determine the accuracy of iodine quantification with dual energy computed tomography (DECT) in two high-end CT systems with different spectral imaging techniques. METHODS: Five tubes with different iodine concentrations (0, 5, 10, 15, 20 mg/ml) were analysed in an anthropomorphic thoracic phantom. Adding two phantom rings simulated increased patient size. For third-generation dual source CT (DSCT), tube voltage combinations of 150Sn and 70, 80, 90, 100 kVp were analysed. For dual layer CT (DLCT), 120 and 140 kVp were used. Scans were repeated three times. Median normalized values and interquartile ranges (IQRs) were calculated for all kVp settings and phantom sizes. RESULTS: Correlation between measured and known iodine concentrations was excellent for both systems (R = 0.999-1.000, p < 0.0001). For DSCT, median measurement errors ranged from -0.5% (IQR -2.0, 2.0%) at 150Sn/70 kVp and -2.3% (IQR -4.0, -0.1%) at 150Sn/80 kVp to -4.0% (IQR -6.0, -2.8%) at 150Sn/90 kVp. For DLCT, median measurement errors ranged from -3.3% (IQR -4.9, -1.5%) at 140 kVp to -4.6% (IQR -6.0, -3.6%) at 120 kVp. Larger phantom sizes increased variability of iodine measurements (p < 0.05). CONCLUSION: Iodine concentration can be accurately quantified with state-of-the-art DECT systems from two vendors. The lowest absolute errors were found for DSCT using the 150Sn/70 kVp or 150Sn/80 kVp combinations, which was slightly more accurate than 140 kVp in DLCT. KEY POINTS: • High-end CT scanners allow accurate iodine quantification using different DECT techniques. • Lowest measurement error was found in scans with largest photon energy separation. • Dual-source CT quantified iodine slightly more accurately than dual layer CT.

The Effects of Iodine Attenuation on Pulmonary Nodule Volumetry using Novel Dual-Layer Computed Tomography Reconstructions.

OBJECTIVES: To assess the effect of iodine attenuation on pulmonary nodule volumetry using virtual non-contrast (VNC) and mono-energetic reconstructions. METHODS: A consecutive series of patients who underwent a contrast-enhanced chest CT scan were included. Images were acquired on a novel dual-layer spectral CT system. Conventional reconstructions as well as VNC and mono-energetic images at different keV levels were used for nodule volumetry. RESULTS: Twenty-four patients with a total of 63 nodules were included. Conventional reconstructions showed a median (interquartile range) volume and diameter of 174 (87 - 253) mm3 and 6.9 (5.4 - 9.9) mm, respectively. VNC reconstructions resulted in a significant volume reduction of 5.5% (2.6 - 11.2%; p<0.001). Mono-energetic reconstructions showed a correlation between nodule attenuation and nodule volume (Spearman correlation 0.77, (0.49 - 0.94)). Lowering the keV resulted in increased volumes while higher keV levels resulted in decreased pulmonary nodule volumes compared to conventional CT. CONCLUSIONS: Novel dual-layer spectral CT offers the possibility to reconstruct VNC and mono-energetic images. Those reconstructions show that higher pulmonary nodule attenuation results in larger nodule volumes. This may explain the reported underestimation in nodule volume on non-contrast enhanced compared to contrast-enhanced acquisitions. KEY POINTS: • Pulmonary nodule volumes were measured on virtual non-contrast and mono-energetic reconstructions • Mono-energetic reconstructions showed that higher attenuation results in larger volumes • This may explain the reported nodule volume underestimation on non-contrast enhanced CT • Mostly metastatic pulmonary nodules were evaluated, results might differ for benign nodules.

Feasibility and accuracy of dual-layer spectral detector computed tomography for quantification of gadolinium: a phantom study.

OBJECTIVES: The aim of this study was to evaluate the feasibility and accuracy of dual-layer spectral detector CT (SDCT) for the quantification of clinically encountered gadolinium concentrations. METHODS: The cardiac chamber of an anthropomorphic thoracic phantom was equipped with 14 tubular inserts containing different gadolinium concentrations, ranging from 0 to 26.3 mg/mL (0.0, 0.1, 0.2, 0.4, 0.5, 1.0, 2.0, 3.0, 4.0, 5.1, 10.6, 15.7, 20.7 and 26.3 mg/mL). Images were acquired using a novel 64-detector row SDCT system at 120 and 140 kVp. Acquisitions were repeated five times to assess reproducibility. Regions of interest (ROIs) were drawn on three slices per insert. A spectral plot was extracted for every ROI and mean attenuation profiles were fitted to known attenuation profiles of water and pure gadolinium using in-house-developed software to calculate gadolinium concentrations. RESULTS: At both 120 and 140 kVp, excellent correlations between scan repetitions and true and measured gadolinium concentrations were found (R > 0.99, P < 0.001; ICCs > 0.99, CI 0.99-1.00). Relative mean measurement errors stayed below 10% down to 2.0 mg/mL true gadolinium concentration at 120 kVp and below 5% down to 1.0 mg/mL true gadolinium concentration at 140 kVp. CONCLUSION: SDCT allows for accurate quantification of gadolinium at both 120 and 140 kVp. Lowest measurement errors were found for 140 kVp acquisitions. KEY POINTS: • Gadolinium quantification may be useful in patients with contraindication to iodine. • Dual-layer spectral detector CT allows for overall accurate quantification of gadolinium. • Interscan variability of gadolinium quantification using SDCT material decomposition is excellent.

Computed Tomography Imaging of a Hip Prosthesis Using Iterative Model-Based Reconstruction and Orthopaedic Metal Artefact Reduction: A Quantitative Analysis.

OBJECTIVES: To quantify the combined use of iterative model-based reconstruction (IMR) and orthopaedic metal artefact reduction (O-MAR) in reducing metal artefacts and improving image quality in a total hip arthroplasty phantom. METHODS: Scans acquired at several dose levels and kVps were reconstructed with filtered back-projection (FBP), iterative reconstruction (iDose) and IMR, with and without O-MAR. Computed tomography (CT) numbers, noise levels, signal-to-noise-ratios and contrast-to-noise-ratios were analysed. RESULTS: Iterative model-based reconstruction results in overall improved image quality compared to iDose and FBP (P < 0.001). Orthopaedic metal artefact reduction is most effective in reducing severe metal artefacts improving CT number accuracy by 50%, 60%, and 63% (P < 0.05) and reducing noise by 1%, 62%, and 85% (P < 0.001) whereas improving signal-to-noise-ratios by 27%, 47%, and 46% (P < 0.001) and contrast-to-noise-ratios by 16%, 25%, and 19% (P < 0.001) with FBP, iDose, and IMR, respectively. CONCLUSIONS: The combined use of IMR and O-MAR strongly improves overall image quality and strongly reduces metal artefacts in the CT imaging of a total hip arthroplasty phantom.

An automated tool for cortical feature analysis: Application to differences on 7 Tesla T2* -weighted images between young and older healthy subjects.

PURPOSE: High field T2* -weighted MR images of the cerebral cortex are increasingly used to study tissue susceptibility changes related to aging or pathologies. This paper presents a novel automated method for the computation of quantitative cortical measures and group-wise comparison using 7 Tesla T2* -weighted magnitude and phase images. METHODS: The cerebral cortex was segmented using a combination of T2* -weighted magnitude and phase information and subsequently was parcellated based on an anatomical atlas. Local gray matter (GM)/white matter (WM) contrast and cortical profiles, which depict the magnitude or phase variation across the cortex, were computed from the magnitude and phase images in each parcellated region and further used for group-wise comparison. Differences in local GM/WM contrast were assessed using linear regression analysis. Regional cortical profiles were compared both globally and locally using permutation testing. The method was applied to compare a group of 10 young volunteers with a group of 15 older subjects. RESULTS: Using local GM/WM contrast, significant differences were revealed in at least 13 of 17 studied regions. Highly significant differences between cortical profiles were shown in all regions. CONCLUSION: The proposed method can be a useful tool for studying cortical changes in normal aging and potentially in neurodegenerative diseases. Magn Reson Med 74:240-248, 2015. © 2014 Wiley Periodicals, Inc.

Use of internal references for assessing CT density measurements of the pelvis as replacement for use of an external phantom.

PURPOSE: The purpose of this research is to study the use of an internal reference standard for fat- and muscle as a replacement for an external reference standard with a phantom. By using a phantomless internal reference standard, Hounsfield unit (HU) measurements of various tissues can potentially be assessed in patients with a CT scan of the pelvis without an added phantom at time of CT acquisition. This paves the way for development of a tool for quantification of the change in tissue density in one patient over time and between patients. This could make every CT scan made without contrast available for research purposes. MATERIALS AND METHODS: Fifty patients with unilateral metal-on-metal total hip replacements, scanned together with a calibration reference phantom used in bone mineral density measurements, were included in this study. On computed tomography scans of the pelvis without the use of intravenous iodine contrast, reference values for fat and muscle were measured in the phantom as well as within the patient's body. The conformity between the references was examined with the intra-class correlation coefficient. RESULTS: The mean HU (± SD) of reference values for fat for the internal- and phantom references were -91.5 (±7.0) and -90.9 (±7.8), respectively. For muscle, the mean HU (± SD) for the internal- and phantom references were 59.2 (±6.2) and 60.0 (±7.2), respectively. The intra-class correlation coefficients for fat and muscle were 0.90 and 0.84 respectively and show excellent agreement between the phantom and internal references. CONCLUSION: Internal references can be used with similar accuracy as references from an external phantom. There is no need to use an external phantom to asses CT density measurements of body tissue.

Texture analysis of ultrahigh field T2*-weighted MR images of the brain: application to Huntington's disease.

PURPOSE: To develop a framework for quantitative detection of between-group textural differences in ultrahigh field T2*-weighted MR images of the brain. MATERIALS AND METHODS: MR images were acquired using a three-dimensional (3D) T2*-weighted gradient echo sequence on a 7 Tesla MRI system. The phase images were high-pass filtered to remove phase wraps. Thirteen textural features were computed for both the magnitude and phase images of a region of interest based on 3D Gray-Level Co-occurrence Matrix, and subsequently evaluated to detect between-group differences using a Mann-Whitney U-test. We applied the framework to study textural differences in subcortical structures between premanifest Huntington's disease (HD), manifest HD patients, and controls. RESULTS: In premanifest HD, four phase-based features showed a difference in the caudate nucleus. In manifest HD, 7 magnitude-based features showed a difference in the pallidum, 6 phase-based features in the caudate nucleus, and 10 phase-based features in the putamen. After multiple comparison correction, significant differences were shown in the putamen in manifest HD by two phase-based features (both adjusted P values=0.04). CONCLUSION: This study provides the first evidence of textural heterogeneity of subcortical structures in HD. Texture analysis of ultrahigh field T2*-weighted MR images can be useful for noninvasive monitoring of neurodegenerative diseases.

Hippocampal atrophy in people with memory deficits: results from the population-based IPREA study.

BACKGROUND: Clinical studies have shown that hippocampal atrophy is present before dementia in people with memory deficits and can predict dementia development. The question remains whether this association holds in the general population. This is of interest for the possible use of hippocampal atrophy to screen population for preventive interventions. The aim of this study was to assess hippocampal volume and shape abnormalities in elderly adults with memory deficits in a cross-sectional population-based study. METHODS: We included individuals participating in the Italian Project on the Epidemiology of Alzheimer Disease (IPREA) study: 75 cognitively normal individuals (HC), 31 individuals with memory deficits (MEM), and 31 individuals with memory deficits not otherwise specified (MEMnos). Hippocampal volumes and shape were extracted through manual tracing and the growing and adaptive meshes (GAMEs) shape-modeling algorithm. We investigated between-group differences in hippocampal volume and shape, and correlations with memory deficits. RESULTS: In MEM participants, hippocampal volumes were significantly smaller than in HC and were mildly associated with worse memory scores. Memory-associated shape changes mapped to the anterior hippocampus. Shape-based analysis detected no significant difference between MEM and HC, while MEMnos showed shape changes in the posterior hippocampus compared with HC and MEM groups. CONCLUSIONS: These findings support the discriminant validity of hippocampal volumetry as a biomarker of memory impairment in the general population. The detection of shape changes in MEMnos but not in MEM participants suggests that shape-based biomarkers might lack sensitivity to detect Alzheimer's-like pathology in the general population.

Cortical phase changes in Alzheimer's disease at 7T MRI: a novel imaging marker.

BACKGROUND: Postmortem studies have indicated the potential of high-field magnetic resonance imaging (MRI) to visualize amyloid depositions in the cerebral cortex. The aim of this study is to test this hypothesis in patients with Alzheimer's disease (AD). METHODS: T2*-weighted MRI was performed in 16 AD patients and 15 control subjects. All magnetic resonance images were scored qualitatively by visual assessment, and quantitatively by measuring phase shifts in the cortical gray matter and hippocampus. Statistical analysis was performed to assess differences between groups. RESULTS: Patients with AD demonstrated an increased phase shift in the cortex in the temporoparietal, frontal, and parietal regions (P < .005), and this was associated with individual Mini-Mental State Examination scores (r = -0.54, P < .05). CONCLUSION: Increased cortical phase shift in AD patients demonstrated on 7-tesla T2*-weighted MRI is a potential new biomarker for AD, which may reflect amyloid pathology in the early stages.

Cerebral atrophy in elderly with subjective memory complaints.

PURPOSE: To evaluate ventricular shape differences along the complete surface of the lateral and third ventricles of persons with subjective memory complaints (MC). MATERIALS AND METHODS: We included 28 controls and 21 persons with MC. FLAIR, T2, and PD-weighted brain MRI scans were acquired at 1.5 Tesla, followed by semi-automated segmentation of the lateral and third ventricles, and local shape difference analysis based on growing and adaptive meshes. Ventricular meshes were used to highlight local areas with significant differences between controls and persons with MC, determined by permutation tests with a predefined threshold (P = 0.01). RESULTS: Compared with control subjects, relevant differences were found in the shape of the ventricular surface adjacent to the thalamus and corona radiata in persons with MC. Before correction for multiple comparisons, relevant differences were also found in the shape of the ventricular surface adjacent to the corpus callosum, hippocampus, and amydala. CONCLUSION: Our findings suggest the presence of localized structural brain differences in patients with subjective memory complaints in the thalamus and the corona radiata.

Toward magnetic resonance-guided electroanatomical voltage mapping for catheter ablation of scar-related ventricular tachycardia: a comparison of registration methods.

INTRODUCTION: Integration of preprocedural delayed enhanced magnetic resonance imaging (DE-MRI) with electroanatomical voltage mapping (EAVM) may provide additional high-resolution substrate information for catheter ablation of scar-related ventricular tachycardias (VT). Accurate and fast image integration of DE-MRI with EAVM is desirable for MR-guided ablation. METHODS AND RESULTS: Twenty-six VT patients with large transmural scar underwent catheter ablation and preprocedural DE-MRI. With different registration models and EAVM input, 3 image integration methods were evaluated and compared to the commercial registration module CartoMerge. The performance was evaluated both in terms of distance measure that describes surface matching, and correlation measure that describes actual scar correspondence. Compared to CartoMerge, the method that uses the translation-and-rotation model and high-density EAVM input resulted in a registration error of 4.32±0.69 mm as compared to 4.84 ± 1.07 (P <0.05); the method that uses the translation model and high-density EAVM input resulted in a registration error of 4.60 ± 0.65 mm (P = NS); and the method that uses the translation model and a single anatomical landmark input resulted in a registration error of 6.58 ± 1.63 mm (P < 0.05). No significant difference in scar correlation was observed between all 3 methods and CartoMerge (P = NS). CONCLUSIONS: During VT ablation procedures, accurate integration of EAVM and DE-MRI can be achieved using a translation registration model and a single anatomical landmark. This model allows for image integration in minimal mapping time and is likely to reduce fluoroscopy time and increase procedure efficacy.

Combined magnitude and phase-based segmentation of the cerebral cortex in 7T MR images of the elderly.

PURPOSE: To propose a new method that integrates both magnitude and phase information obtained from magnetic resonance (MR) T*(2) -weighted scans for cerebral cortex segmentation of the elderly. MATERIALS AND METHODS: This method makes use of K-means clustering on magnitude and phase images to compute an initial segmentation, which is further refined by means of transformation with reconstruction criteria. The method was evaluated against the manual segmentation of 7T in vivo MR data of 20 elderly subjects (age = 67.7 ± 10.9). The added value of combining magnitude and phase was also evaluated by comparing the performance of the proposed method with the results obtained when limiting the available data to either magnitude or phase. RESULTS: The proposed method shows good overlap agreement, as quantified by the Dice Index (0.79 ± 0.04), limited bias (average relative volume difference = 2.94%), and reasonable volumetric correlation (R = 0.555, p = 0.011). Using the combined magnitude and phase information significantly improves the segmentation accuracy compared with using either magnitude or phase. CONCLUSION: This study suggests that the proposed method is an accurate and robust approach for cerebral cortex segmentation in datasets presenting low gray/white matter contrast.

Automated segmentation of myocardial scar in late enhancement MRI using combined intensity and spatial information.

Accurate assessment of the size and distribution of a myocardial infarction (MI) from late gadolinium enhancement (LGE) MRI is of significant prognostic value for postinfarction patients. In this paper, an automatic MI identification method combining both intensity and spatial information is presented in a clear framework of (i) initialization, (ii) false acceptance removal, and (iii) false rejection removal. The method was validated on LGE MR images of 20 chronic postinfarction patients, using manually traced MI contours from two independent observers as reference. Good agreement was observed between automatic and manual MI identification. Validation results showed that the average Dice indices, which describe the percentage of overlap between two regions, were 0.83 +/- 0.07 and 0.79 +/- 0.08 between the automatic identification and the manual tracing from observer 1 and observer 2, and the errors in estimated infarct percentage were 0.0 +/- 1.9% and 3.8 +/- 4.7% compared with observer 1 and observer 2. The difference between the automatic method and manual tracing is in the order of interobserver variation. In conclusion, the developed automatic method is accurate and robust in MI delineation, providing an objective tool for quantitative assessment of MI in LGE MR imaging.

Hierarchical functional modularity in the resting-state human brain.

Functional magnetic resonance imaging (fMRI) studies have shown that anatomically distinct brain regions are functionally connected during the resting state. Basic topological properties in the brain functional connectivity (BFC) map have highlighted the BFC's small-world topology. Modularity, a more advanced topological property, has been hypothesized to be evolutionary advantageous, contributing to adaptive aspects of anatomical and functional brain connectivity. However, current definitions of modularity for complex networks focus on nonoverlapping clusters, and are seriously limited by disregarding inclusive relationships. Therefore, BFC's modularity has been mainly qualitatively investigated. Here, we introduce a new definition of modularity, based on a recently improved clustering measurement, which overcomes limitations of previous definitions, and apply it to the study of BFC in resting state fMRI of 53 healthy subjects. Results show hierarchical functional modularity in the brain.

Microstructural white matter changes preceding white matter hyperintensities in migraine.

OBJECTIVE: We used magnetization transfer imaging to assess white matter tissue integrity in migraine, to explore whether white matter microstructure was more diffusely affected beyond visible white matter hyperintensities (WMHs), and to explore whether focal invisible microstructural changes precede visible focal WMHs in migraineurs. METHODS: We included 137 migraineurs (79 with aura, 58 without aura) and 74 controls from the Cerebral Abnormalities in Migraine, an Epidemiological Risk Analysis (CAMERA) study, a longitudinal population-based study on structural brain lesions in migraine patients, who were scanned at baseline and at a 9-year follow-up. To assess microstructural brain tissue integrity, baseline magnetization transfer ratio (MTR) values were calculated for whole brain white matter. Baseline MTR values were determined for areas of normal-appearing white matter (NAWM) that had progressed into MRI-detectable WMHs at follow-up and compared to MTR values of contralateral NAWM. RESULTS: MTR values for whole brain white matter did not differ between migraineurs and controls. In migraineurs, but not in controls, NAWM that later progressed to WMHs at follow-up had lower mean MTR (mean [SD] 0.354 [0.009] vs 0.356 [0.008], p = 0.047) at baseline as compared to contralateral white matter. CONCLUSIONS: We did not find evidence for widespread microstructural white matter changes in migraineurs compared to controls. However, our findings suggest that a gradual or stepwise process might be responsible for evolution of focal invisible microstructural changes into focal migraine-related visible WMHs.

Emphysema quantification using chest CT: influence of radiation dose reduction and reconstruction technique.

BACKGROUND: Computed tomography (CT) emphysema quantification is affected by both radiation dose (i.e. image noise) and reconstruction technique. At reduced dose, filtered back projection (FBP) results in an overestimation of the amount of emphysema due to higher noise levels, while the use of iterative reconstruction (IR) can result in an underestimation due to reduced noise. The objective of this study was to determine the influence of dose reduction and hybrid IR (HIR) or model-based IR (MIR) on CT emphysema quantification. METHODS: Twenty-two patients underwent inspiratory chest CT scan at routine radiation dose and at 45%, 60% and 75% reduced radiation dose. Acquisitions were reconstructed with FBP, HIR and MIR. Emphysema was quantified using the 15th percentile of the attenuation curve and the percentage of voxels below -950 HU. To determine whether the use of a different percentile or HU threshold is more accurate at reduced dose levels and with IR, additional measurements were performed using different percentiles and HU thresholds to determine the optimal combination. RESULTS: Dose reduction resulted in a significant overestimation of emphysema, while HIR and MIR resulted in an underestimation. Lower HU thresholds with FBP at reduced dose and higher HU thresholds with HIR and MIR resulted in emphysema percentages comparable to the reference. The 15th percentile quantification method showed similar results as the HU threshold method. CONCLUSIONS: This within-patients study showed that CT emphysema quantification is significantly affected by dose reduction and IR. This can potentially be solved by adapting commonly used thresholds.

MRI intensity nonuniformity correction using simultaneously spatial and gray-level histogram information.

A novel approach for correcting intensity nonuniformity in magnetic resonance imaging (MRI) is presented. This approach is based on the simultaneous use of spatial and gray-level histogram information. Spatial information about intensity nonuniformity is obtained using cubic B-spline smoothing. Gray-level histogram information of the image corrupted by intensity nonuniformity is exploited from a frequential point of view. The proposed correction method is illustrated using both physical phantom and human brain images. The results are consistent with theoretical prediction, and demonstrate a new way of dealing with intensity nonuniformity problems. They are all the more significant as the ground truth on intensity nonuniformity is unknown in clinical images.

In vivo assessment of iron content of the cerebral cortex in healthy aging using 7-Tesla T2*-weighted phase imaging.

Accumulation of brain iron has been suggested as a biomarker of neurodegeneration. Increased iron has been seen in the cerebral cortex in postmortem studies of neurodegenerative diseases and healthy aging. Until recently, the diminutive thickness of the cortex and its relatively low iron content have hampered in vivo study of cortical iron accumulation. Using phase images of a T2*-weighted sequence at ultrahigh field strength (7 Tesla), we examined the iron content of 22 cortical regions in 70 healthy subjects aged 22-80 years. The cortex was automatically segmented and parcellated, and phase shift was analyzed using an in-house developed method. We found a significant increase in phase shift with age in 20 of 22 cortical regions, concurrent with current understanding of cortical iron accumulation. Our findings suggest that increased cortical iron content can be assessed in healthy aging in vivo. The high spatial resolution and sensitivity to iron of our method make it a potentially useful tool for studying cortical iron accumulation in healthy aging and neurodegenerative diseases.

Computation of transmitted and received B1 fields in magnetic resonance imaging.

Computation of B1 fields is a key issue for determination and correction of intensity nonuniformity in magnetic resonance images. This paper presents a new method for computing transmitted and received B1 fields. Our method combines a modified MRI acquisition protocol and an estimation technique based on the Levenberg-Marquardt algorithm and spatial filtering. It enables accurate estimation of transmitted and received B1 fields for both homogeneous and heterogeneous objects. The method is validated using numerical simulations and experimental data from phantom and human scans. The experimental results are in agreement with theoretical expectations.

Intensity non-uniformity correction in MRI: existing methods and their validation.

Magnetic resonance imaging is a popular and powerful non-invasive imaging technique. Automated analysis has become mandatory to efficiently cope with the large amount of data generated using this modality. However, several artifacts, such as intensity non-uniformity, can degrade the quality of acquired data. Intensity non-uniformity consists in anatomically irrelevant intensity variation throughout data. It can be induced by the choice of the radio-frequency coil, the acquisition pulse sequence and by the nature and geometry of the sample itself. Numerous methods have been proposed to correct this artifact. In this paper, we propose an overview of existing methods. We first sort them according to their location in the acquisition/processing pipeline. Sorting is then refined based on the assumptions those methods rely on. Next, we present the validation protocols used to evaluate these different correction schemes both from a qualitative and a quantitative point of view. Finally, availability and usability of the presented methods is discussed.