Magnetic resonance imaging segmentation techniques using batch-type learning vector quantization algorithms

In this article, we propose batch-type learning vector quantization (LVQ) segmentation techniques for the magnetic resonance (MR) images. Magnetic resonance imaging (MRI) segmentation is an important technique to differentiate abnormal and normal tissues in MR image data. The proposed LVQ segmentation techniques are compared with the generalized Kohonen's competitive learning (GKCL) methods, which were proposed by Lin et al. [Magn Reson Imaging 21 (2003) 863-870]. Three MRI data sets of real cases are used in this article. The first case is from a 2-year-old girl who was diagnosed with retinoblastoma in her left eye. The second case is from a 55-year-old woman who developed complete left side oculomotor palsy immediately after a motor vehicle accident. The third case is from an 84-year-old man who was diagnosed with Alzheimer disease (AD). Our comparisons are based on sensitivity of algorithm parameters, the quality of MRI segmentation with the contrast-to-noise ratio and the accuracy of the region of interest tissue. Overall, the segmentation results from batch-type LVQ algorithms present good accuracy and quality of the segmentation images, and also flexibility of algorithm parameters in all the comparison consequences. The results support that the proposed batch-type LVQ algorithms are better than the previous GKCL algorithms. Specifically, the proposed fuzzy-soft LVQ algorithm works well in segmenting AD MRI data set to accurately measure the hippocampus volume in AD MR images.     

Entropic stochastic resonance: the constructive role of the unevenness

We demonstrate the existence of stochastic resonance (SR) in confined systems arising from entropy variations associated to the presence of irregular boundaries. When the motion of a Brownian particle is constrained to a region with uneven boundaries, the presence of a periodic input may give rise to a peak in the spectral amplification factor and therefore to the appearance of the SR phenomenon. We have proved that the amplification factor depends on the shape of the region through which the particle moves and that by adjusting its characteristic geometric parameters one may optimize the response of the system. The situation in which the appearance of such entropic stochastic resonance (ESR) occurs is common for small-scale systems in which confinement and noise play an prominent role. The novel mechanism found could thus constitute an important tool for the characterization of these systems and can put to use for controlling their basic properties.     

Stochastic resonance, reverse-resonance and stochastic multi-resonance in an underdamped quartic double-well potential with noise and delay

The stochastic resonance in an underdamped quartic double-well potential with time delayed feedback is studied numerically. The signal power amplification is employed to characterize the stochastic resonance of the system. Simulation results indicate that: (i) for moderate frequency of the periodic driving, the stochastic resonance is decreased monotonically by increasing the delay time, but at high frequency, the reverse-resonance is induced to transform into a stochastic resonance by time delay; (ii) the damping coefficient has a critical value for which the stochastic resonance is optimum; (iii) a stochastic multi-resonance emerges when the signal power amplification is a function of the driving frequency.     

I/f noise in systems showing stochastic resonance

Stochastic resonator systems with input and/or output 1/f noise have been studied. Disordered magnets/dielectrics serve as examples for the case of output 1/f noise with white noise (thermal excitation) at the input of the resonators. Due to the fluctuation-dissipation theorem, the output noise is related to the out-of-phase component of the periodic peak of the output spectrum. Spin glasses and ferromagnets serve as interesting examples of coupled stochastic resonators. A proper coupling can lead to an extremely large signal-to-noise ratio. As a model system, a l/f-noise-driven Schmitt trigger has been investigated experimentally to study stochastic resonance with input 1/f noise. Under proper conditions, we have found several new nonlinearity effects, such as peaks at even harmonics, holes at even harmonics, and 1/f noise also in the output spectrum.     

Magnetic resonance image reconstruction using trained geometric directions in 2D redundant wavelets domain and non-convex optimization

Reducing scanning time is significantly important for MRI. Compressed sensing has shown promising results by undersampling the k-space data to speed up imaging. Sparsity of an image plays an important role in compressed sensing MRI to reduce the image artifacts. Recently, the method of patch-based directional wavelets (PBDW) which trains geometric directions from undersampled data has been proposed. It has better performance in preserving image edges than conventional sparsifying transforms. However, obvious artifacts are presented in the smooth region when the data are highly undersampled. In addition, the original PBDW-based method does not hold obvious improvement for radial and fully 2D random sampling patterns. In this paper, the PBDW-based MRI reconstruction is improved from two aspects: 1) An efficient non-convex minimization algorithm is modified to enhance image quality; 2) PBDW are extended into shift-invariant discrete wavelet domain to enhance the ability of transform on sparsifying piecewise smooth image features. Numerical simulation results on vivo magnetic resonance images demonstrate that the proposed method outperforms the original PBDW in terms of removing artifacts and preserving edges.     

Fluctuations induced extinction and stochastic resonance effect in a model of tumor growth with periodic treatment

We investigate a stochastic model of tumor growth derived from the catalytic Michaelis-Menten reaction with positional and environmental fluctuations under subthreshold periodic treatment. Firstly, the influences of environmental fluctuations on the treatable stage are analyzed numerically. Applying the standard theory of stochastic resonance derived from the two-state approach, we derive the signal-to-noise ratio (SNR) analytically, which is used to measure the stochastic resonance phenomenon. It is found that the weak environmental fluctuations could induce the extinction of tumor cells in the subthreshold periodic treatment. The positional stability is better in favor of the treatment of the tumor cells. Besides, the appropriate and feasible treatment intensity and the treatment cycle should be highlighted considered in the treatment of tumor cells.     

Evidence of stochastic resonance in the mating behavior of Nezara viridula (L.)

We investigate the role of the noise in the mating behavior between individuals of Nezara viridula (L.), by analyzing the temporal and spectral features of the non-pulsed type female calling song emitted by single individuals.We have measured the threshold level for the signal detection, by performing experiments with the calling signal at different intensities and analyzing the insect response by directionality tests performed on a group of male individuals. By using a sub-threshold signal and an acoustic Gaussian noise source, we have investigated the insect response for different levels of noise, finding behavioral activation for suitable noise intensities. In particular, the percentage of insects which react to the sub-threshold signal, shows a non-monotonic behavior, characterized by the presence of a maximum, for increasing levels of the noise intensity. This constructive interplay between external noise and calling signal is the signature of the non-dynamical stochastic resonance phenomenon. Finally, we describe the behavioral activation statistics by a soft threshold model which shows stochastic resonance. We find that the maximum of the ensemble average of the input-output cross-correlation occurs at a value of the noise intensity very close to that for which the behavioral response has a maximum.     

Detecting and quantifying temporal correlations in stochastic resonance via information theory measures

We show that Information Theory quantifiers are suitable tools for detecting and for quantifying noise-induced temporal correlations in stochastic resonance phenomena. We use the Bandt & Pompe (BP) method [Phys. Rev. Lett. 88, 174102 (2002)] to define a probability distribution, P, that fully characterizes temporal correlations. The BP method is based on a comparison of neighboring values, and here is applied to the temporal sequence of residence-time intervals generated by the paradigmatic model of a Brownian particle in a sinusoidally modulated bistable potential. The probability distribution P generated via the BP method has associated a normalized Shannon entropy, H[P], and a statistical complexity measure, C[P], which is defined as proposed by Rosso et al. [Phys. Rev. Lett. 99, 154102 (2007)]. The statistical complexity quantifies not only randomness but also the presence of correlational structures, the two extreme circumstances of maximum knowledge (“perfect order") and maximum ignorance (“complete randomness") being regarded an “trivial", and in consequence, having complexity C = 0. We show that both, H and C, display resonant features as a function of the noise intensity, i.e., for an optimal level of noise the entropy displays a minimum and the complexity, a maximum. This resonant behavior indicates noise-enhanced temporal correlations in the sequence of residence-time intervals. The methodology proposed here has great potential for the precise detection of subtle signatures of noise-induced temporal correlations in real-world complex signals.     

Equilibrium signal intensity mapping, an MRI method for fast mapping of longitudinal relaxation rates and for image enhancement

INTRODUCTION: Inhomogeneity of magnetic fields, both B(0) and B(1), has been a major challenge in magnetic resonance imaging (MRI). Field inhomogeneity leads to image artifacts and unreliability of signal intensity (SI) measurements. This work proposes and shows the feasibility of generating equilibrium signal intensity (SI(Eq)) maps that can be utilized either to speed up relaxation-rate measurement or to enhance image quality and relaxation-rate-based weighting in various applications. METHODS: A 1.5-T MRI scanner was used. In canines (n=4), myocardial infarction was induced, and 48 h after the administration of 0.05 mmol kg(-1) Gd(ABE-DTTA), a contrast agent with slow tissue kinetics, in vivo R(1) mapping was carried out using an inversion recovery (IR)-prepared, fast gradient-echo sequence with varying inversion times (TIs). To test the SI(Eq) mapping method without the confounding effects of motion and blood flow, we carried out ex vivo R(1) mapping after the administration of 0.2 mmol kg(-1) Gd(DTPA) using an IR-prepared, fast spin-echo sequence in another group of dogs (n=2). R(1,full) maps and SI(Eq) maps were generated from the data from both sequences by three-parameter nonlinear curve fitting of the SI versus TI dependence. R(1,full) maps served as the reference standard. Raw IR images were then divided by the SI(Eq) maps, yielding corrected SI maps (COSIMs). Additionally, R(1) values were calculated from each single-TI image separately, using the SI(Eq) value and a one-parameter curve-fitting procedure (R(1,single)). Voxelwise correlation analysis was carried out for the COSIMs and the R(1,single) maps, both versus the standard R(1,full) maps. Deviations of R(1,single) from R(1,full) were statistically evaluated. RESULTS: In vivo, COSIM versus R(1,full) showed significantly (P<.05) better correlation [correlation coefficient (CC)=0.95] than SI versus R(1,full) with a TI=700-800 ms, which is 200-300 ms longer than the tau(null) (500 ms) of viable myocardium. With such TIs, SI versus R(1,full) yielded CCs of 0.86-0.88. R(1,single) versus R(1,full) yielded a peak CC of 0.96 at TI=700-900 ms. Mean deviations of R(1,single) from R(1,full) were below 5% for TIs between 500 and 1000 ms. Ex vivo, where tau(null) was 300 ms, the advantage of correction with SI(Eq) was not in the improvement of linear correlation but more in the reduction of scatter. Peak CCs for SI versus R(1,full) and COSIM versus R(1,full) at TI=500 ms were 0.96 for both. The ex vivo CC for R(1,single) versus R(1,full) at TI=500 ms was 0.98. Mean deviations of R(1,single) from R(1,full) were below 5% for TIs between 400 and 700 ms. CONCLUSIONS: Once the corresponding SI(Eq) map is obtained from a control stack, R(1) can be obtained accurately, using only a single IR image and without the need for a stack of TI-varied images. This approach could be applied in various dynamic MRI studies where short measurement time, once the dynamics has started, is of essence. When using this method with IR-prepared T(1)-weighted images, it is essential that the single TI be chosen such that the longitudinal relaxation in all voxels of interest would have passed tau(null). SI(Eq) maps are also useful in eliminating confounders from MR images to allow obtaining SI values that reflect more faithfully the relaxation parameter (R(1)) sought.     

Contrast changes in portal vein and bile duct between centric and linear k-space ordering on three-dimensional segmented true fast imaging with steady-state precession magnetic resonance imaging

Purpose

To compare the degree of visualization of the bile duct and portal vein in terms of the difference in k-space ordering on a three-dimensional (3D) segmented true fast imaging with steady-state precession (trueFISP) sequence.

Materials and Methods

A breath-hold coronal 3D segmented trueFISP sequence was prospectively performed on 14 healthy volunteers. Images obtained with centric and linear k-space ordering in the k(x)–k(y) plane were compared by two independent radiologists qualitatively with depiction scores on a five-point scale (1=not seen to 5=excellent depiction) using the Wilcoxon signed-rank test. Images were also compared quantitatively using relative contrast values for the bile duct and portal vein against the hepatic parenchyma using a paired t-test.

Results

With centric ordering, both the mean depiction scores and relative contrast values for the portal vein were significantly lower than those with linear ordering (1.5 vs. 3.5, P<.01; and 0.08±0.19 vs. 0.51±0.10, P<.01, respectively). However, in the bile duct, there were no significant differences, only slight differences were found among the results obtained with centric and linear ordering (3.9 vs. 3.8, P=.72; and 0.59±0.06 vs. 0.68±0.06, P<.01, respectively).

Conclusion

For visualizing the bile duct, centric k-space ordering on 3D segmented trueFISP sequence is recommended, while linear ordering is recommended for portal vein visualization.     

Statistically robust evidence of stochastic resonance in human auditory perceptual system

In human perception, exogenous noise is known to yield a masking effect, i.e. an increase of the perceptual threshold relative to a stimulus acting on the same modality. However, somehow counter-intuitively, the opposite mechanism can occasionally occur: a decrease of the perceptual threshold for a non-vanishing, virtuous amount of noise. This mechanism, called stochastic resonance, is deemed to provide important information about the role of noise in the human brain. In this paper, we investigate stochastic resonance in a detection task in the auditory modality. Normal-hearing participants were asked to judge the presence of acoustic stimuli of different intensity and superimposed to different levels of white noise. The matrix-like outcomes of a behavioural experiment were fitted by a two-dimensional, noise-dependent psychometric function. The fit revealed a statistically significant stochastic resonance in 43% of the experimental runs. We conclude that, in the auditory modality, stochastic resonance is a tiny effect that, under conventional circumstances, is largely overrun by standard masking.     

Stochastic resonance in bistable confining potentials

We study the effects of the confining conditions on the occurrence of stochastic resonance (SR) in continuous bistable systems. We model such systems by means of double-well potentials that diverge like |x|^q for |x|↦∞. For super-harmonic (hard) potentials with q > 2 the SR peak sharpens with increasing q, whereas for sub-harmonic (soft) potentials, q < 2, it gets suppressed.     

Magnetic resonance imaging on CO(2) miscible and immiscible displacement in oil-saturated glass beads pack

In this study, the displacement processes were observed as gaseous or supercritical CO₂ was injected into n-decane-saturated glass beads packs using a 400-MHz magnetic resonance imaging (MRI) system. Two-dimensional images of oil distribution in the vertical median section were obtained using a spin-echo pulse sequence. Gas channeling and viscous fingering appeared obviously in immiscible gaseous CO₂ displacement. A piston-like displacement front was detected in miscible supercritical CO₂ displacement that provided high sweep efficiency. MRI images were processed with image intensity analysis methods to obtain the saturation profiles. Final oil residual saturations and displacement coefficients were also estimated using this imaging intensity analysis. It was proved that miscible displacement can enhance the efficiency of CO₂ displacement notably. Finally, a special coreflood analysis method was applied to estimate the effects of capillary, viscosity and buoyancy based on the obtained saturation data.     

Nonstationary stochastic resonance viewed through the lens of information theory

In biological systems, information is frequentlytransferred with Poisson like spike processes (shot noise) modulatedin time by information-carrying signals. How then to quantifyinformation transfer by such processes for nonstationary inputsignals of finite duration? Is there some minimal length of theinput signal duration versus its strength? Can such signals bebetter detected when immersed in noise stemming from thesurroundings by increasing the stochastic intensity? These are somebasic questions which we attempt to address within an analyticaltheory based on the Kullback-Leibler information concept applied torandom processes.     

Improvement of signal-to-noise ratio by stochastic resonance in sigmoid function threshold systems, demonstrated using a CMOS inverter

Stochastic resonance (SR) has become a well-known phenomenon that can enhance weak periodic signals with the help of noise. SR is an interesting phenomenon when applied to signal processing. Although it has been proven that SR does not always improve the signal-to-noise ratio (SNR), in a strongly nonlinear system such as simple threshold system, SR does in fact improve SNR for noisy pulsed signals at appropriate noise strength. However, even in such cases, when noise is weak, the SNR is degraded. Since the noise strength cannot be known in advance, it is difficult to apply SR to real signal processing. In this paper, we focused on the shape of the threshold at which SR did not degrade the SNR when noise was weak. To achieve output change when noise was weak, we numerically analyzed a sigmoid function threshold system. When the slope around the threshold was appropriate, SNR did not degrade when noise was weak and instead was improved at suitable noise strength. We also demonstrated SNR improvement for noisy pulsed voltages using a CMOS inverter, a very common threshold device. The input-output property of a CMOS inverter resembles the sigmoid function. By inputting the noisy signal voltage to a CMOS inverter, we measured the input and output voltages and analyzed the SNRs. The results showed that SNR was effectively improved over a wide range of noise strengths.     

Measurement of bone cyst fluid volume using k-means clustering

We designed a semiautomatic segmentation method to easily measure the volume of a bone cyst (simple or aneurysmal) from magnetic resonance imaging (MRI). This method only considers the fluid part of the cyst, even when there are several fluid intensities (fluid-fluid levels) or the cyst is multi-loculated. The nonhomogeneity phenomenon inherent in MRI was handled by a k-means clustering algorithm that classified all of the voxels corresponding to the cyst fluid as the same voxel intensity. Level-set segmentation was expanded into the whole cyst volume and the resulting segmented volume provided the measured cyst volume. The semiautomatic method was compared with the usual manual method (manual contour tracing) in terms of its ability to measure a known volume of water (gold standard) as well as the volume of 29 bone cysts. Both methods were equivalent with regards to the gold standard, but the semiautomatic method was more accurate. In terms of the experimental measurements, the semiautomatic method was more repeatable and reproducible, and less time-consuming and fastidious than the manual method. Our semiautomatic method uses only freeware and can be used routinely whenever measurement of a bone cyst volume is needed.     

A 3D trajectory for undersampling k-space in MRSI applications

Magnetic resonance spectroscopic imaging (MRSI) is a noninvasive technique for producing spatially localized spectra. MRSI presents the important challenge of reducing the scan time while maintaining the spatial resolution. The preferred approach for this is to use time-varying readout gradients to collect the spatial and chemical-shift information. Fast, three-dimensional (3D) spatial encoded methods also reduce the scan time. Despite the existence of several new and faster 3D encoded methods, or k-space trajectories, for magnetic resonance imaging (MRI), only stack of spirals and echo planar have been studied in 3D MRSI. A novel formulation for designing fast, 3D k-space trajectory applicable to 3D MRSI is presented. This approach is simple and consists of rays expanding from the origin of k-space into a revolving sphere, collecting spectral data of all 3D spatial k-space at different times in the same scan. This article describes this new method and presents some results of its application to 3D MRSI. This technique allows some degree of undersampling; hence, it is possible to reconstruct high-quality undersampled spectroscopic imaging in order to recognize different compounds in short scan times. Additionally, the method is tested in regular 3D MRI. This proposed method can also be used for dynamic undersampled imaging.     

Feasibility of using limited-population-based average R10 for pharmacokinetic modeling of osteosarcoma dynamic contrast-enhanced magnetic resonance imaging data

Retrospective analyses of clinical dynamic contrast-enhanced (DCE) MRI studies may be limited by failure to measure the longitudinal relaxation rate constant (R₁) initially, which is necessary for quantitative analysis. In addition, errors in R₁ estimation in each individual experiment can cause inconsistent results in derivations of pharmacokinetic parameters, K^trans and v_e, by kinetic modeling of the DCE-MRI time course data. A total of 18 patients with lower extremity osteosarcomas underwent multislice DCE-MRI prior to surgery. For the individual R₁ measurement approach, the R₁ time course was obtained using the two-point R₁ determination method. For the average R₁₀ (precontrast R₁) approach, the R₁ time course was derived using the DCE-MRI pulse sequence signal intensity equation and the average R₁₀ value of this population. The whole tumor and histogram median K^trans (0.57±0.37 and 0.45±0.32 min⁻¹) and v_e (0.59±0.20 and 0.56±0.17) obtained with the individual R₁ measurement approach are not significantly different (paired t test) from those (K^trans: 0.61±0.46 and 0.44±0.33 min⁻¹; v_e: 0.61±0.19 and 0.55±0.14) obtained with the average R₁₀ approach. The results suggest that it is feasible, as well as practical, to use a limited-population-based average R₁₀ for pharmacokinetic modeling of osteosarcoma DCE-MRI data.     

Noise color and asymmetry in stochastic resonance with silicon nanomechanical resonators

Stochastic resonance with white noise has been well established as a potential signal amplification mechanism in nanomechanical two-state systems. While white noise represents the archetypal stimulus for stochastic resonance, typical operating environments for nanomechanical devices often contain different classes of noise, particularly colored noise with a 1/f spectrum. As a result, improved understanding of the effects of noise color will be helpful in maximizing device performance. Here we report measurements of stochastic resonance in a silicon nanomechanical resonator using 1/f noise and Ornstein-Uhlenbeck noise types. Power spectral densities and residence time distributions provide insight into asymmetry of the bistable amplitude states, and the data sets suggest that 1/f^α noise spectra with increasing noise color (i.e. α) may lead to increasing asymmetry in the system, reducing the achievable amplification. Furthermore, we explore the effects of correlation time τ on stochastic resonance with the use of exponentially correlated noise. We find monotonic suppression of the spectral amplification as the correlation time increases.