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Objective.Mutual information (MI) is consolidated as a robust similarity metric often used for medical image registration. Although MI provides a robust registration, it usually fails when the transform needed to register an image is too large due to MI local minima traps. This paper proposes and evaluates Generalized MI (GMI), using Tsallis entropy, to improve affine registration.Approach.We assessed the GMI metric output space using separable affine transforms to seek a better gradient space. The range used was 150 mm for translations, 360° for rotations, [0.5, 2] for scaling, and [-1, 1] for skewness. The data were evaluated using 3D visualization of gradient and contour curves. A simulated gradient descent algorithm was also used to calculate the registration capability. The improvements detected were then tested through Monte Carlo simulation of actual registrations with brain T1 and T2 MRI from the HCP dataset.Main results.Results show significantly prolonged registration ranges, without local minima in the metric space, with a registration capability of 100% for translations, 88.2% for rotations, 100% for scaling and 100% for skewness. Tsallis entropy obtained 99.75% success in the Monte Carlo simulation of 2000 translation registrations with 1113 double randomized subjects T1 and T2 brain MRI against 56.5% success for the Shannon entropy.Significance.Tsallis entropy can improve brain MRI MI affine registration with long-range translation registration, lower-cost interpolation, and faster registrations through a better gradient space.

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Multiscale entropy (MSE) analysis is a fundamental approach to access the complexity of a time series by estimating its information creation over a range of temporal scales. However, MSE may not be accurate or valid for short time series. This is why previous studies applied different kinds of algorithm derivations to short-term time series. However, no study has systematically analyzed and compared their reliabilities. This study compares the MSE algorithm variations adapted to short time series on both human and rat heart rate variability (HRV) time series using long-term MSE as reference. The most used variations of MSE are studied: composite MSE (CMSE), refined composite MSE (RCMSE), modified MSE (MMSE), and their fuzzy versions. We also analyze the errors in MSE estimations for a range of incorporated fuzzy exponents. The results show that fuzzy MSE versions-as a function of time series length-present minimal errors compared to the non-fuzzy algorithms. The traditional multiscale entropy algorithm with fuzzy counting (MFE) has similar accuracy to alternative algorithms with better computing performance. For the best accuracy, the findings suggest different fuzzy exponents according to the time series length.

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The introduction of the multiscale entropy (MSE) method was a milestone in the field of complex physiological signal analysis. However, since MSE is inapplicable for short signals, several variants of MSE have been proposed. One of the most important variants of MSE is the modified multiscale entropy (MMSE), even though it can still produce biased estimates due to the hard similarity criteria of sample entropy. Taking the advantages of MMSE and the concept of fuzzy entropy, we propose the modified multiscale fuzzy entropy (MMFE). We evaluated the robustness of MMSE and MMFE using segmented stochastic noises and actual heart rate variability series and compared it with the classical MSE results obtained with the full signals. Results show that MMFE is much more robust than MMSE for short physiological time series, resembling MSE for series as shorter as 400 samples. We also show the existence of an exponential relationship between the MMFE fuzzy parameter and the signal size. We suggest the use of this relationship to choose the optimal MMFE parameter as part of the method.

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Heart rate variability (HRV) analysis is widely used to investigate the autonomic regulation of the cardiovascular system. HRV is often analyzed using RR time series, which can be affected by different types of artifacts. Although there are several artifact correction methods, there is no study that compares their performances in actual experimental contexts. This work aimed to evaluate the impact of different artifact correction methods on several HRV parameters. Initially, 36 ECG recordings of control rats or rats with heart failure or hypertension were analyzed to characterize artifact occurrence rates and distributions, to be mimicked in simulations. After a rigorous analysis, only 16 recordings ( n = 16) with artifact-free segments of at least 10,000 beats were selected. RR interval losses were then simulated in the artifact-free (reference) time series according to real observations. Correction methods applied to simulated series were deletion, linear interpolation, cubic spline interpolation, modified moving average window, and nonlinear predictive interpolation. Linear (time- and frequency-domain) and nonlinear HRV parameters were calculated from corrupted-corrected time series, as well as for reference series to evaluate the accuracy of each correction method. Results show that NPI provides the overall best performance. However, several correction approaches, for example the simple deletion procedure, can provide good performance in some situations, depending on the HRV parameters under consideration. NEW & NOTEWORTHY This work analyzes the performance of some correction techniques commonly applied to the missing beats problem in RR time series. From artifact-free RR series, spurious values were inserted based on actual data of experimental settings. We intend our work to be a guide to show how artifacts should be corrected to preserve as much as possible the original heart rate variability properties.

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BACKGROUND: Prostate cancer is a serious public health problem that affects quality of life and has a significant mortality rate. The aim of the present study was to quantify the fractal dimension and Shannon's entropy in the histological diagnosis of prostate cancer. METHODS: Thirty-four patients with prostate cancer aged 50 to 75 years having been submitted to radical prostatectomy participated in the study. Histological slides of normal (N), hyperplastic (H) and tumor (T) areas of the prostate were digitally photographed with three different magnifications (40x, 100x and 400x) and analyzed. The fractal dimension (FD), Shannon's entropy (SE) and number of cell nuclei (NCN) in these areas were compared. RESULTS: FD analysis demonstrated the following significant differences between groups: T vs. N and H vs. N groups (p < 0.05) at a magnification of 40x; T vs. N (p < 0.01) at 100x and H vs. N (p < 0.01) at 400x. SE analysis revealed the following significant differences groups: T vs. H and T vs. N (p < 0.05) at 100x; and T vs. H and T vs. N (p < 0.001) at 400x. NCN analysis demonstrated the following significant differences between groups: T vs. H and T vs. N (p < 0.05) at 40x; T vs. H and T vs. N (p < 0.0001) at 100x; and T vs. H and T vs. N (p < 0.01) at 400x. CONCLUSIONS: The quantification of the FD and SE, together with the number of cell nuclei, has potential clinical applications in the histological diagnosis of prostate cancer.

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We analyzed the effectiveness of linear short- and long-term variability time domain parameters, an index of sympatho-vagal balance (SDNN/RMSSD) and entropy in differentiating fetal heart rate patterns (fHRPs) on the fetal heart rate (fHR) series of 5, 3 and 2 min duration reconstructed from 46 fetal magnetocardiograms. Gestational age (GA) varied from 21 to 38 weeks. FHRPs were classified based on the fHR standard deviation. In sleep states, we observed that vagal influence increased with GA, and entropy significantly increased (decreased) with GA (SDNN/RMSSD), demonstrating that a prevalence of vagal activity with autonomous nervous system maturation may be associated with increased sleep state complexity. In active wakefulness, we observed a significant negative (positive) correlation of short-term (long-term) variability parameters with SDNN/RMSSD. ANOVA statistics demonstrated that long-term irregularity and standard deviation of normal-to-normal beat intervals (SDNN) best differentiated among fHRPs. Our results confirm that short- and long-term variability parameters are useful to differentiate between quiet and active states, and that entropy improves the characterization of sleep states. All measures differentiated fHRPs more effectively on very short HR series, as a result of the fMCG high temporal resolution and of the intrinsic timescales of the events that originate the different fHRPs.

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BACKGROUND: Matrix metalloproteinase-9 (MMP-9) and tissue inhibitor of MMP (TIMP) promote derangement of the extracellular matrix, which is ultimately reflected in plaque images seen on ultrasound. Videodensitometry can identify structural disturbances in plaques. OBJECTIVES: To establish the correlations between values determined using videodensitometry in B-mode ultrasound images of advanced carotid plaques and the total expression of MMP-9 and TIMP-1 in these removed plaques. METHODS: Thirty patients underwent ultrasonic tissue characterization of carotid plaques before surgery, using mean gray level (MGL), energy, entropy and homogeneity. Each patient was assigned preoperatively to one of 2 groups: group I, symptomatic patients (n = 16; 12 males; mean age 66.7 ± 6.8 years), and group II, asymptomatic patients (n = 14; 8 males; mean age 67.6 ± 6.81 years). Tissue specimens were analyzed for MMP-9 and TIMP-1 expression. Nine carotid arteries were used as normal tissue controls. RESULTS: MMP-9 expression levels were elevated in group II and in normal tissues compared to group I (p < 0.001). TIMP-1 levels were higher in group II than in group I, and significantly higher in normal tissues than in group I (p = 0.039). The MGL was higher in group II compared to group I (p = 0.038). Energy had greater values in group II compared to group I (p = 0.02). There were no differences between patient groups in homogeneity and entropy. Energy positively correlated with MMP-9 and TIMP-1 expression (p = 0.012 and p = 0.031 respectively). Homogeneity positively correlated with MMP-9 and TIMP-1 expression (p = 0.034 and p = 0.047 respectively). There were no correlations between protein expression and MGL or entropy. CONCLUSIONS: Videodensitometric computer analysis of ultrasound scanning images can be used to identify stable carotid plaques, which have higher total expression levels of MMP-9 and TIMP-1 than unstable plaques.

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BACKGROUND: To analyse histological composition and progression of carotid plaque. METHODS: Thirty-one patients (22 males, mean age 68.03 +/- 7.3 years) admitted for carotid endarterectomy for extracranial high-grade internal carotid artery stenosis (>or= 70% luminal narrowing) were enrolled. The patients were divided into 2 groups according to symptomatology (group I, 17 symptomatic patients; and group II, 14 asymptomatic patients). A histological analysis and inflammatory cell quantification of each excised carotid plaque was made. Nine carotid arteries were removed from human cadavers that were not preselected for carotid artery disease. These specimens were used as a control tissue without any macroscopic signs of atherosclerotic plaques. RESULTS: Fifty eight percent of all carotid plaques were classified as complex plaque with possible surface defect, hemorrhage or thrombus. The inflammatory cells concentration did not differ between the two groups. All specimens from human cadavers were classified as preatheroma with extracellular lipid pools. CONCLUSION: Asymptomatic and symptomatic patients could have the same histological components on their carotid plaques. Fibrotic and calcific plaques could become vulnerable as complex plaques with surface defect, hemorrhage and thrombus could remain silent. Asymptomatic carotid stenosis should be followed close with no invasive diagnostic methods and clinical evaluation.