Stretched-exponential Model Research Articles

Monoexponential, biexponential and stretched-exponential models based diffusion weighted imaging: a comparative study in the differential diagnosis of benign and malignant breast lesions

Objective To investgate the value of various parameters obtained from monoexponential, biexponential, and stretched exponential diffusion-weighted imaging models in the differential diagnosis of breast lesions. Methods A retrospective study performed in 54 patients with pathologically confirmed malignant tumors(n=30), benign lesions(n=34) and normal fibroglandular tissues (n=30). All patients underwent T1WI, T2WI, dynamic enhancement and diffusion weighted MRI with multi-b values at a 3.0 T magnetic resonance imaging unit. All parameters were measured at a workstation. ADC was calculated by using monoexponential analysis(b=0, 800 s/mm2). Slow apparent diffusion coefficient (ADC- slow), fast apparent diffusion coefficient (ADC- fast), and perfusion fraction (f) were calculated using the biexponential model. Distributed diffusion coefficient (DDC) and water molecular diffusion heterogeneity index (α) were obtained from diffusion-weighted images using the stretched exponential model. All parameters were statistically compared among normal fibroglandular tissues, benign lesions and malignant tumors using Kruskal- Wallis rank sum test. Mann- Whitney U test were used for further comparisons between specific group pairs. ADC values were compared with ADC-slow and DDC for different groups by paired Wilcoxon test. Correlations between ADC-value, ADC-slow and DDC were assessed by using Spearman rank correlation coefficient. Receiver operating characteristic curve was used to analyze and compare the ability of these parameters in differentiation of benign and malignant breast lesions. Results The ADC, ADC-slow, f, DDC and α values were significantly different among the normal fibroglandular tissues, benign tumors and malignant tumors (P<0.05). Further differential comparisons of the four parameters between each pair showed that the ADC, ADC-slow, f, DDC and α values were significantly lower in malignant tumors than both in normal fibroglandular tissues and benign tumors(P<0.016 7). The ADC values of normal fibroglandular tissues, benign tumors and malignant tumors were significantly higher than ADC- slow and DDC (P<0.05). The f and DDC had higher area under the receiver operating characteristic curve (0.688 and 0.657 respectively). The optimal cutoff values for ADC, ADC- slow, f, DDC and α were 1.235 × 10-3mm2/s, 0.428×10-3mm2/s, 57.8%, 1.175×10-3mm2/s and 0.721, respectively. The α value showed higher specificity (65.5% ) and the f value had higher sensitivity (82.9%). Conclusion The parameters derived from biexponential and stretched exponential DWI could be helpful for differentiation between benign and malignant breast tumors. Key words: Breast neoplasms; Magnetic resonance imaging; Comparative study

Incorporating Density and Temperature in the Stretched Exponential Model for Predicting Stress Relaxation Behavior of Polymer Foams

This paper discusses an approach to incorporate density and temperature terms in the well-known stretched exponential (SE) model for predicting the stress relaxation behavior of polymer foams. We have developed this approach for closed-cell polyurethane foams (PUFs) and verified using experimental data for accuracy. The SE model was first examined using short-term experimental data to predict long-term stress relaxation behavior of PU solid (PUS). The corresponding model parameters were then extracted for PUS and two PUFs with different densities (PU404 and PU415) at three different test temperatures. Finally, an expression was developed in conjunction with the modified Gibson–Ashby relationship and the Arrhenius equation and validated for other foam density (PU420) and test temperatures. The predictions were found to be reasonably good with more than 90% accuracy.

Spectral characteristics of carrier transfer from Si cluster to nanocrystal in Si-rich-oxide/SiO2 multilayer films

Si-rich-oxide/SiO2 multilayer composite films containing Si clusters and nanocrystals (NCs) have been synthesized by PECVD technique, and the carrier transfer processes from Si cluster to nanocrystal are studied by photoluminescence (PL) spectra. Compared with the references, intense PL is observed in the composite film, which is caused by the combined effect of Si clusters and NCs. Optical excitation is enhanced due to the dense Si clusters, while the carriers generated in the clusters are transferred to the Si–NCs due to their large carrier capture section. The PL excitation spectra shows that the resonance excitation energy is 3.58 eV, which corresponds to the excitation energy level of SiOX shell covering the Si clusters. Double stretched-exponential decay model is used to demonstrate the PL decay processes in the composite film, and the results suggest that the carrier transfer time is about 35.8 μs.

The productivity and potential future recovery of the Bakken formation of North Dakota

The Bakken shale and similar formations in North Dakota are a new, poorly characterized resource and the oil production potential of North Dakota is highly uncertain. To better understand this resource, we employ a least squares curve fitting method on 5773 wells in the Bakken, drilled from 2005 to mid-2013, fitting each well with hyperbolic decline (HD) and stretched exponential (SE) decline models. We characterize well productivity by vintage and location. Additionally, we construct scenarios to simulate future production by varying individual well productivity, well spacing, and drilling rate. Using the HD model, a typical Bakken well drilled to date is expected to produce 270 mbbl (mean) or 221 mbbl (median) over a 15-year life. Using the SE model these figures are slightly lower: 231 mbbl (mean), 181 mbbl (median). Over our study period, the cumulative production in the first six months of a well’s life (IP180) increased and then remained steady. EURs increased until 2010 and have decreased since 2010. It appears that wells are becoming less productive over time, with the reasons not yet fully accounted for. Our base forecast has North Dakota producing at least 1mmbbl/day for over 20years, peaking at approximately 1.7mmbbl/day in the mid-2020s. This period of high production can be shortened by faster-than-expected decline or extended by advances in technology.

Assessment of tumor response to oxygen challenge using quantitative diffusion MRI in an animal model.

To assess tumor response to oxygen challenge using quantitative diffusion magnetic resonance imaging (MRI). A well-characterized Dunning R3327-AT1 rat prostate cancer line was implanted subcutaneously in the right thigh of male Copenhagen rats (n = 8). Diffusion-weighted images (DWI) with multiple b values (0, 25, 50, 100, 150, 200, 300, 500, 1000, 1500 s/mm(2) ) in three orthogonal directions were obtained using a multishot FSE-based Stejskal-Tanner DWI sequence (FSE-DWI) at 4.7T, while rats breathed medical air (21% oxygen) and with 100% oxygen challenge. Stretched-exponential and intravoxel incoherent motion (IVIM) models were used to calculate and compare quantitative diffusion parameters: diffusion heterogeneity index (α), intravoxel distribution of diffusion coefficients (DDC), tissue diffusivity (Dt), pseudo-diffusivity (Dp), and perfusion fraction (f) on a voxel-by-voxel basis. A significant increase of α (73.9 ± 4.7% in air vs. 78.1 ± 4.5% in oxygen, P = 0.0198) and a significant decrease of f (13.4 ± 3.7% in air vs. 10.4 ± 2.7% in oxygen, P = 0.0201) were observed to accompany oxygen challenge. Correlations between f and α during both air and oxygen breathing were found; the correlation coefficients (r) were -0.90 and -0.96, respectively. Positive correlations between Dt and DDC with oxygen breathing (r = 0.95, P = 0.0003), f and DDC with air breathing were also observed (r = 0.95, P = 0.0004). Quantitative diffusion MRI demonstrated changes in tumor perfusion in response to oxygen challenge.

Modeling of stretched-exponential and stretched-hyperbola time dependence of threshold voltage shift in thin-film transistors

To gain insight into the underlying properties of the well-known stretched-exponential and stretched-hyperbola time dependence models, I propose a numerical method to study threshold voltage (Vt) shift caused by both defect creation and charge trapping using a generic kinetic equation. It is shown that during the early phase of Vt shift, the time evolution of the shift is determined by the density of barrier states or trap sites which exponentially increases with barrier energy or trap location from a channel and is characterized by the dispersion parameter β in the models. The later phase is effectively determined by reaction rates in the kinetic equation in addition to β. In the case of the stretched-hyperbola model, the later phase is distinguished by the backward reaction and characterized by the fitting parameter α in the model. It is shown that Vt shifts in which backward reactions dominate during the later phase are represented by the stretched-exponential model and the rest is represented by the stretched-hyperbola model. The proposed method is also used to analyze the logarithmic time dependence model and cases when two instances of the models coexist in order to show that it is useful to study Vt shift of arbitrary shape. It is concluded that the shape of Vt shift is determined by the reaction rates and the density of barrier states or trap sites.

Nickel-induced enhancement of photoluminescence in nc-Si-SiOx nanostructures

The effect of nickel silicide interlayer on the intensity of photoluminescence (PL) from Si nanoclusters (nc) in normally deposited and obliquely deposited in vacuum SiOx/Ni/Si structures have been studied using spectral and time-resolved PL measurements. It has been shown that the intensity of PL band in SiOx/Ni/Si samples is essentially higher than that in reference SiOx/Si samples (without the nickel interlayer) with the same characteristics and treatment. The PL intensity enhancement factor is equal to 5.77 for normally deposited samples and 18 for obliquely deposited samples. The unchanged spectral shape of PL bands and similar position of PL maximum in samples with and without nickel silicide interlayer indicates that in the SiOx/Ni/Si structures after annealing no additional emitting centers are introduced to compare with reference one. Time-resolved measurements showed that PL decay rate was decreased from 8.210 s for SiOx/Si specimens to 2.8610 4 s for SiOx/Ni/Si one. The emission decay rate distribution was determined by fitting the experimental decay curves to the stretchedexponential model. The observed narrow decay rate distribution, decrease of the PL decay rate and enhancement of the PL intensity in SiOx/Ni/Si samples can be assigned to the processes of nickel silicide passivation of the dangling bonds at the interface of Si nanoparticles and the silicon oxide matrix, which is more effective in porous samples.

Photoluminescence decay properties of Si-rich-oxide/SiO2 multilayer films with different Si-quantum dots densities

In this work, Si-rich-oxide/SiO2 multilayer films have been deposited by adjusting the radio-frequency power in a PECVD system, and Si quantum dots (Si-QDs) are obtained in the Si-rich-oxide layer after annealing treatment. FTIR results show that phase separation between Si and SiO2 occurs after annealing treatment. TEM and Raman spectra show that the size and density of Si-QDs are larger for the multilayer films deposited at 20W. Compared with the film deposited at 40W, a 1.7 times PL enhancement is obtained for the film deposited at 20W, and the PL peak shifts toward low energy. Time-resolved PL spectra show the PL decay for the film deposited at 40W can be expressed by the multi-exponential decay model, while stretched-exponential decay model can be used to describe the carrier recombination process when the density of Si-QDs is high enough. The PL decay time increases with the red shift of wavelength firstly and decreases, which suggests that quantum confinement effect is the main PL mechanism in the short wavelength region, and localized state transition in Si clusters contributes to the optical emission in the longer wavelength region. The results are further confirmed by low temperature PL spectra.

Effects of electron trapping and interface state generation on bias stress induced in indium–gallium–zinc oxide thin-film transistors

The electrical characteristics of bias temperature stress (BTS) induced in amorphous indium–gallium–zinc oxide thin-film transistors (a-IGZO TFTs) were studied. We analyzed the threshold voltage (VTH) shift on the basis of the effects of positive bias temperature stress (PBTS) and negative bias temperature stress (NBTS), and applied it to the stretched-exponential model. Both stress temperature and bias are considered as important factors in the electrical instabilities of a-IGZO TFTs, and the stretched-exponential equation is well fitted to the stress condition. VTH for the drain current–gate voltage (IDS–VGS) curve and flat-band voltage (VFB) for the capacitance–voltage (C–V) curve move in the positive direction when PBTS is induced. However, in the case of NBTS, they move slightly in the negative direction. To clarify the VTH shift phenomenon by electron and hole injection, the average effective energy barrier (Eτ) is extracted, and the extracted values of Eτ under PBTS and NBTS are about 1.33 and 2.25 eV, respectively. The oxide trap charges (Not) of PBTS and NBTS calculated by C–V measurement are 4.4 × 1011 and 1.49 × 1011 cm−2, respectively. On the other hand, the border trap charges of PBTS and NBTS are 6.7 × 108 and 1.7 × 109 cm−2, respectively. This indicates that the increased interface trap charge, after PBTS is induced, captures electrons during detrap processing from the border trap to the conduction band, valence band, and interface trap.

Simple tools for forecasting waterflood performance

Empirical and/or semianalytical tools are frequently applied in most waterflood operations, although grid-based models are also often used. This paper examines the performance of some commonly used tools, such as the water–oil ratio (WOR), Y-function, and Arps. Besides those tools, we introduce a semianalytical approach, which is a modified version of the Y-function formulation. Two other tools that have gained significant traction in unconventional-reservoir performance forecasting, the stretched-exponential decline model (SEDM) and the capacitance–resistance model (CRM) are also used here. Based on synthetic and field data, the results show that the Arps method is remarkably accurate in all flooding situations, regardless of the underlying physical mechanisms; other published data tend to support this notion. Similarly, both the SEDM and the proposed modified-Y-function method also yield solutions with good accuracy. The latter solutions tend to be pessimistic, however.

Non-Gaussian diffusion imaging for enhanced contrast of brain tissue affected by ischemic stroke.

Recent diffusion MRI studies of stroke in humans and animals have shown that the quantitative parameters characterising the degree of non-Gaussianity of the diffusion process are much more sensitive to ischemic changes than the apparent diffusion coefficient (ADC) considered so far as the “gold standard”. The observed changes exceeded that of the ADC by a remarkable factor of 2 to 3. These studies were based on the novel non-Gaussian methods, such as diffusion kurtosis imaging (DKI) and log-normal distribution function imaging (LNDFI). As shown in our previous work investigating the animal stroke model, a combined analysis using two methods, DKI and LNDFI provides valuable complimentary information. In the present work, we report the application of three non-Gaussian diffusion models to quantify the deviations from the Gaussian behaviour in stroke induced by transient middle cerebral artery occlusion in rat brains: the gamma-distribution function (GDF), the stretched exponential model (SEM), and the biexponential model. The main goal was to compare the sensitivity of various non-Gaussian metrics to ischemic changes and to investigate if a combined application of several models will provide added value in the assessment of stroke. We have shown that two models, GDF and SEM, exhibit a better performance than the conventional method and allow for a significantly enhanced visualization of lesions. Furthermore, we showed that valuable information regarding spatial properties of stroke lesions can be obtained. In particular, we observed a stratified cortex structure in the lesions that were well visible in the maps of the GDF and SEM metrics, but poorly distinguishable in the ADC-maps. Our results provided evidence that cortical layers tend to be differently affected by ischemic processes.

Non-Gaussian Analysis of Diffusion Weighted Imaging in Head and Neck at 3T: A Pilot Study in Patients with Nasopharyngeal Carcinoma

PurposeTo technically investigate the non-Gaussian diffusion of head and neck diffusion weighted imaging (DWI) at 3 Tesla and compare advanced non-Gaussian diffusion models, including diffusion kurtosis imaging (DKI), stretched-exponential model (SEM), intravoxel incoherent motion (IVIM) and statistical model in the patients with nasopharyngeal carcinoma (NPC).Materials and MethodsAfter ethics approval was granted, 16 patients with NPC were examined using DWI performed at 3T employing an extended b-value range from 0 to 1500 s/mm2. DWI signals were fitted to the mono-exponential and non-Gaussian diffusion models on primary tumor, metastatic node, spinal cord and muscle. Non-Gaussian parameter maps were generated and compared to apparent diffusion coefficient (ADC) maps in NPC.ResultsDiffusion in NPC exhibited non-Gaussian behavior at the extended b-value range. Non-Gaussian models achieved significantly better fitting of DWI signal than the mono-exponential model. Non-Gaussian diffusion coefficients were substantially different from mono-exponential ADC both in magnitude and histogram distribution.ConclusionNon-Gaussian diffusivity in head and neck tissues and NPC lesions could be assessed by using non-Gaussian diffusion models. Non-Gaussian DWI analysis may reveal additional tissue properties beyond ADC and holds potentials to be used as a complementary tool for NPC characterization.

Effects of mechanical strain on amorphous silicon thin-film transistor electrical stability

The electrical stability of hydrogenated amorphous silicon thin-film transistors (a-Si:H TFTs) on flexible substrates was characterized under mechanical bending. TFT lifetime until 50% reduction in IDS under moderate constant-voltage gate bias (<2 MV/cm gate field for 104 s) was estimated to be 2.56 h and 7.43 h under uniaxial applied compression and tension, respectively, compared to 4.28 h without strain. The stretched-exponential model for VT shift in a-Si:H TFTs was fitted to measurement data and used to predict how applied strain can affect TFT lifetime in practical applications. VT relaxation showed a logarithmic time dependence as would be expected for dielectric/interface charge detrapping.

Amorphous indium–gallium–zinc oxide thin-film transistors instability and stress evaluation by Stretched-Exponential model

We have successfully fabricated large sized amorphous indium–gallium–zinc-oxide based active-matrix liquid-crystal displays, which uses Molybdenum/Aluminum/Titanium as source/drain electrode. In this study, an oxygen-rich etch stop layer acts as the oxygen atom supplier and converts the titanium layer into titanium oxide layer, which is found to induce instability of the device. Sample without titanium oxide has an initial threshold voltage shift is less than ±0.1V after the repeatedly measuring over a period of two weeks. In addition, the IGZO based device demonstrated superior transfer characteristic. This paper established that the stability of the amorphous indium–gallium–zinc-oxide based active-matrix liquid-crystal display can be predicted by Stretched-Exponential model.

The γ parameter of the stretched-exponential model is influenced by internal gradients: Validation in phantoms

In this paper, we investigate the image contrast that characterizes anomalous and non-Gaussian diffusion images obtained using the stretched exponential model. This model is based on the introduction of the γ stretched parameter, which quantifies deviation from the mono-exponential decay of diffusion signal as a function of the b-value. To date, the biophysical substrate underpinning the contrast observed in γ maps, in other words, the biophysical interpretation of the γ parameter (or the fractional order derivative in space, β parameter) is still not fully understood, although it has already been applied to investigate both animal models and human brain. Due to the ability of γ maps to reflect additional microstructural information which cannot be obtained using diffusion procedures based on Gaussian diffusion, some authors propose this parameter as a measure of diffusion heterogeneity or water compartmentalization in biological tissues. Based on our recent work we suggest here that the coupling between internal and diffusion gradients provide pseudo-superdiffusion effects which are quantified by the stretching exponential parameter γ. This means that the image contrast of Mγ maps reflects local magnetic susceptibility differences (Δχm), thus highlighting better than T2∗ contrast the interface between compartments characterized by Δχm. Thanks to this characteristic, Mγ imaging may represent an interesting tool to develop contrast-enhanced MRI for molecular imaging.The spectroscopic and imaging experiments (performed in controlled micro-beads dispersion) that are reported here, strongly suggest internal gradients, and as a consequence Δχm, to be an important factor in fully understanding the source of contrast in anomalous diffusion methods that are based on a stretched exponential model analysis of diffusion data obtained at varying gradient strengths g.

An Investigation of the Different Charge Trapping Mechanisms for SiNx and SiO2 Gate Insulator in a-IGZO TFTs

We investigated the threshold voltage (VTH) shifts of a-IGZO thin-film transistors (TFTs) in which the gate-insulator was either SiO2 or SiNx. The VTH shift of the TFT using a SiO2 obeyed the stretched-exponential time model, and increased sharply according to temperature increase, whereas the SiNx device obeyed the logarithmic time model, and exhibited weak temperature dependence. We found that an inter-layer formed between the IGZO and the SiNx, whose existence can be the origin of poor bias stability and the different VTH shift behavior in a-IGZO TFTs because the inter-layer accelerates the direct charge injection from the channel.

Effect of Charge Trapping∕Detrapping on Threshold Voltage Shift of IGZO TFTs under AC Bias Stress

We have investigated the dependency of alternating current (AC) stress duty ratio on the stability of indium-gallium-zinc-oxide (IGZO) thin-film transistors (TFTs). As the duty ratio increases from 0.25 to 0.75, threshold voltage (VTH) shift under the AC gate bias stress was increased from 4.10 V to 5.01 V, without degradation of subthreshold slope and mobility. The dominant mechanism of VTH shift was considered the charge trapping and VTH shift along with time was well fitted to a stretched-exponential model. The VTH shift was suppressed with a reduction of trap density by employing N2O plasma treatment on the gate insulator.

A comparison of cartilage stress-relaxation models in unconfined compression: QLV and stretched exponential in combination with fluid flow

Cartilage exhibits nonlinear viscoelastic behaviour. Various models have been proposed to explain cartilage stress relaxation, but it is unclear whether explicit modelling of fluid flow in unconfined compression is needed. This study compared Fung's quasi-linear viscoelastic (QLV) model with a stretched-exponential model of cartilage stress relaxation and examined each of these models both alone and in combination with a fluid-flow model in unconfined compression. Cartilage explants were harvested from bovine calf patellofemoral joints and equilibrated in tissue culture for 5 days before stress-relaxation testing in unconfined compression at 5% nominal strain. The stretched exponential models fit as well as the QLV models. Furthermore, the average stretched exponential relaxation time determined by this model lies within the range of experimentally measured relaxation times for extracted proteoglycan aggregates, consistent with the hypothesis that the stretched exponential model represents polymeric mechanisms of cartilage viscoelasticity.

Reliability of bottom-gate graphene field-effect transistors prepared by using inductively coupled plasma-chemical vapor deposition

Stability degradation in bottom-gate graphene field-effect transistors prepared by using inductively coupled plasma-chemical vapor deposition method are investigated under bias, temperature and illumination stress. The stretched-exponential time dependence model, which can be derived based on the trapping/detrapping of charges to/from existing traps and continuous redistribution of charges in bulk dielectrics, is well applied in fitting the time dependence of the transfer curve shifts in all stress conditions. The stress wavelength is considered as important factors as well as the bias and temperature stress in the transfer characteristic instabilities of graphene FEFs.

Anisotropic anomalous diffusion assessed in the human brain by scalar invariant indices

A new method to investigate anomalous diffusion in human brain, inspired by the stretched-exponential model proposed by Hall and Barrick, is proposed here, together with a discussion about its potential application to cerebral white matter characterization. Aim of the work was to show the ability of anomalous diffusion indices to characterize white matter structures, whose complexity is only partially accounted by diffusion tensor imaging indices. MR signal was expressed as a stretched-exponential only along the principal axes of diffusion; whereas, in a generic direction, it was modeled as a combination of three stretched-exponentials. Indices to quantify the tissue anomalous diffusion and its anisotropy, independently of the experiment reference frame, were derived. Experimental results, obtained on 10 healthy subjects at 3T, show that the new parameters are highly correlated to intrinsic local geometry when compared with Hall and Barrick indices. Moreover, they offer a different contrast in white matter regions when compared with diffusion tensor imaging. Specifically, the new indices show a higher capability to discriminate among areas of the corpus callosum associated to different distribution in axonal densities, thus offering a new potential tool to detect more specific patterns of brain abnormalities than diffusion tensor imaging in the presence of neurological and psychiatric disorders.