Advanced diffusion models in head and neck squamous cell carcinoma patients: Goodness of fit,relationships among diffusion parameters and comparison with dynamic contrast-enhanced perfusion

PurposeWe assessed advanced fitting models of diffusion weighted imaging (DWI) in head/neck squamous cell carcinoma (HNSCC) patients to determine the best goodness of fit and correlations among diffusion parameters. We compared these results with those of dynamic contrast-enhanced (DCE) perfusion parameters.Materials and methodsWe retrospectively evaluated 32 HNSCC patients (12 sinonasal, 20 pharynx/oral cavity). The DWI acquisition used single-shot spin-echo echo-planar imaging (EPI) with 12 b-values (0 − 2000). We calculated 14 DWI parameters using mono-exponential, bi-exponential, and tri-exponential models, stretched exponential model (SEM) and diffusion kurtosis imaging (DKI) models. We compared each model's goodness of fit using the residual sum of squares (RSS), Akaike Information Criterion (AIC) and Bayesian information criterion (BIC) value. We determined the correlation between each pair of DWI parameters and between each DWI parameter and DCE perfusion parameter.ResultsThe tri-exponential fit's RSS, AIC and BIC values were significantly smaller than those for bi-exponential fit. The RSS, AIC and BIC values of the SEM fit and DKI fit were significantly smaller than mono-exponential model. Significant correlations were observed in 30 pairs (sinonasal cavity) and 31 (sinonasal cavity group) among 91 DWI parameter combinations. Significant correlations were also observed in nine pairs (both sinonasal cavity and pharynx/oral cavity group) among 64 DWI/DCE perfusion parameter pairs, in particular, high positive correlations between the tri-exponential model's intermediate diffusion fraction (f₂) and the volume of the extracellular extravascular space per unit volume of tissue (v_e) were observed in both patient groups.ConclusionWe identified several correlations between DWI parameters by advanced fitting models and correlations between DWI and DCE parameters. These will help determine HNSCC patients' detailed tissue structures.     

Diffusion tensor parameters and principal eigenvector coherence: Relation to b-value intervals and field strength

Diffusion-weighted MRI images acquired at b-value greater than 1000 s mm^− 2 measure the diffusion of a restricted pool of water molecules. High b-value images are accompanied by a reduction in signal-to-noise ratio (SNR) due to the application of large diffusion gradients. By fitting the diffusion tensor model to data acquired at incremental b-value intervals, we determined the effect of SNR on tensor parameters in normal human brains, in vivo. In addition, we also investigated the impact of field strength on the diffusion tensor model. Data were acquired at 1.5 and 3 T, at b-values 0, 1000, 2000 and 3000 s mm^− 2 in twenty diffusion-sensitised directions. Fractional anisotropy (FA), mean diffusivity (MD) and principal eigenvector coherence (κ) were calculated from diffusion tensors fitted between datasets with b-values 0–1000, 0–2000, 0–3000, 1000–2000 and 2000–3000 s mm^− 2. Field strength and b-value effects on diffusion parameters were analysed in white and grey matter regions of interest. Decreases in FA, κ and MD were found with increasing b-value in white matter. Univariate analysis showed a significant increase in FA with increasing field strength in highly organised white matter. These results suggest there are significant differences in diffusion parameters at 1.5 and 3 T and that the optimal results, in terms of the highest values of FA in white matter, are obtained at 3 T with a maximum b = 1000 s mm^− 2.     

Novel procedure for the simultaneous determination of the Debye length and electro-optic coefficient for an optically active photorefractive Bi12SiO20 crystal

We present a novel procedure based on an improved physical model and a versatile numerical fitting technique, to simultaneously determinate the Debye screening length and electro-optic coefficient using a thick sample of an optically active photorefractive crystal Bi₁₂SiO₂₀ (BSO). For the computation, experimental data of gain vs. grating spacing were obtained by a two-beam coupling arrangement. Unlike former calculation models, in our work, the general expression for the diffraction efficiency in the presence of self-diffraction is considered, and the influence of the optical activity in the coupling parameters is had into account for the calculation of the gain values. The fitting of the experimental data to the predicted theoretical behavior by our model is achieved by finding the closest theoretical curve to a set of data sampled from a spline-smoothed curve of the experimental data. Both, the Debye screening length l_s and the electro-optic coefficient r₄₁ are used as fitting parameters by searching in a rather wide range for each one of the parameters, so that, the estimation of their values is obtained in a more reliable and direct way from the same experiment. The calculations are performed in diffusion regimen and the procedure leads to l_s = 0.22 μm and r₄₁ = 4.5 × 10 ^− 12m/V. Because the optical activity can alter the maximum gain and self-diffraction effects influence the energy exchange, the procedure reveals to be physically appropriated for the simultaneous determination of these physical parameters when thick photorefractive crystals with high optical activity are considered.     

Equilibrium and kinetic modeling of adsorptive sulfur removal from gasoline by synthesized Ce-Y zeolite

In this research, the adsorption of a model sulfur compound, thiophene, from a simulated gasoline onto Ce-Y zeolite in pellet and powder forms was investigated. For this purpose, zeolite Na-Y was synthesized, and Ce-Y zeolite was prepared via solid-state ion-exchanged (SSIE) method. Adsorptive desulfurization of model gasoline was conducted in a batch reactor at ambient conditions to evaluate the equilibrium and kinetics of thiophene adsorption onto Ce-Y zeolite. The equilibrium data were fitted to Langmuire and Toth models. Pseudo-n-order and modified n-order models, LDF-base model, and intra-particle diffusion model were evaluated to fit the kinetic of the adsorption process and to determine the mechanism of it. The corresponding parameters and/or correlation coefficients of each model were reported. The LDF-base model was used also to fit the mass transfer coefficient for both powder and pellet forms of the adsorbent. The best fit estimates for the mass transfer coefficient were obtained 4 × 10⁻¹¹ m/s and k = 3.1 × 10⁻¹²[exp( − t/τ) + 1/(t + 10⁻⁴)], for powder and pellet form adsorbents, respectively.     

Thermodynamic and kinetic parameters of ciprofloxacin adsorption onto modified coal fly ash from aqueous solution

Batch adsorption experiments were carried out for the removal of ciprofloxacin from aqueous solution using modified coal fly ash as adsorbent. The effects of various parameters such as contact time, initial solution concentration and temperature on the adsorption system were investigated. The optimum contact time was found to be 100 min. The isotherm adsorption data fit well with the Langmuir model, and the kinetic data fit well with the pseudo-second order and the intra-particle diffusion model. Intra-particle diffusion analysis demonstrates that ciprofloxacin diffuses quickly among the particles at the beginning of the adsorption process, and then the diffusion slows down and stabilizes. Thermodynamic parameters such as ΔG, ΔH and ΔS were also calculated. The negative Gibbs free energy change and the positive enthalpy change indicated the spontaneous and endothermic nature of the adsorption, and the positive entropy change indicated that the adsorption process was aided by increased randomness.     

Optimization of MR diffusion-weighted imaging acquisitions for pancreatic cancer at 3.0 T

Objectives

To investigate and optimize diffusion-weighted imaging (DWI) acquisitions for pancreatic cancer at 3.0 T.

Methods

Forty-five patients with pancreatic cancer were examined by four DWI acquisitions with b values = 0 and 600 s/mm² at 3.0 T, including breath-holding DWI (BH-DWI), respiratory-triggered DWI (TRIG-DWI), respiratory-triggered DWI with inversion–recovery technique (TRIGIR-DWI), and free-breathing DWI with inversion–recovery technique (FBIR-DWI). Artifacts, contrast ratio (CR), contrast-to-noise ratio (CNR) and apparent diffusion coefficient (ADC) of pancreatic cancer were statistically compared among DWI acquisitions.

Results

TRIGIR-DWI displayed the lowest artifacts and highest CR compared to other DWI acquisitions. CNRs of pancreatic cancer in TRIG-DWI and TRIGIR-DWI were statistically higher than that in FBIR-DWI and BH-DWI. Different ADCs between pancreatic cancer and noncancerous pancreatic tissues were noticed by a paired-samples T test in TRIG-DWI (p = 0.017), TRIGIR-DWI (p = 0.00001) and FBIR-DWI (p = 0.000041).

Conclusions

TRIGIR-DWI may be the optimal acquisition of DWI for pancreatic cancer at 3.0 T.     

MRI quantification of diffusion and perfusion in bone marrow by intravoxel incoherent motion (IVIM) and non-negative least square (NNLS) analysis

Object

To assess the feasibility of measuring diffusion and perfusion fraction in vertebral bone marrow using the intravoxel incoherent motion (IVIM) approach and to compare two fitting methods, i.e., the non-negative least squares (NNLS) algorithm and the more commonly used Levenberg–Marquardt (LM) non-linear least squares algorithm, for the analysis of IVIM data.

Materials and Methods

MRI experiments were performed on fifteen healthy volunteers, with a diffusion-weighted echo-planar imaging (EPI) sequence at five different b-values (0, 50, 100, 200, 600 s/mm²), in combination with an STIR module to suppress the lipid signal. Diffusion signal decays in the first lumbar vertebra (L1) were fitted to a bi-exponential function using the LM algorithm and further analyzed with the NNLS algorithm to calculate the values of the apparent diffusion coefficient (ADC), pseudo-diffusion coefficient (D*) and perfusion fraction.

Results

The NNLS analysis revealed two diffusion components only in seven out of fifteen volunteers, with ADC = 0.60 ± 0.09 (10^− 3 mm²/s), D* = 28 ± 9 (10^− 3 mm²/s) and perfusion fraction = 14% ± 6%. The values obtained by the LM bi-exponential fit were: ADC = 0.45 ± 0.27 (10^− 3 mm²/s), D* = 63 ± 145 (10^− 3 mm²/s) and perfusion fraction = 27% ± 17%. Furthermore, the LM algorithm yielded values of perfusion fraction in cases where the decay was not bi-exponential, as assessed by NNLS analysis.

Conclusion

The IVIM approach allows for measuring diffusion and perfusion fraction in vertebral bone marrow; its reliability can be improved by using the NNLS, which identifies the diffusion decays that display a bi-exponential behavior.     

Changes in diffusion tensor imaging (DTI) eigenvalues of skeletal muscle due to hybrid exercise training

Several studies have proposed the cell membrane as the main water diffusion restricting factor in the skeletal muscle cell. We sought to establish whether a particular form of exercise training (which is likely to affect only intracellular components) could affect water diffusion. The purpose of this study is to characterise prospectively the changes in diffusion tensor imaging (DTI) eigenvalues of thigh muscle resulting from hybrid training (HYBT) in patients with non-alcoholic fatty liver disease (NAFLD). Twenty-one NAFLD patients underwent HYBT for 30 minutes per day, twice a week for 6 months. Patients were scanned using DTI of the thigh pre- and post-HYBT. Fractional anisotropy (FA), apparent diffusion coefficient (ADC), the three eigenvalues lambda 1 (λ1), λ2, λ3, and the maximal cross sectional area (CSA) were measured in bilateral thigh muscles: knee flexors (biceps femoris (BF), semitendinosus (ST), semimembranous (SM)) and knee extensors (medial vastus (MV), intermediate vastus (IV), lateral vastus (LV), and rectus femoris (RF)), and compared pre- and post-HYBT by paired t-test. Muscle strength of extensors (P < 0.01), but not flexors, increased significantly post-HYBT. For FA, ADC and eigenvalues, the overall picture was of increase. Some (P < 0.05 in λ2 and P < 0.01 in λ1) eigenvalues of flexors and all (λ1-λ3) eigenvalues of extensors increased significantly (P < 0.01) post-HYBT. HYBT increased all 3 eigenvalues. We suggest this might be caused by enlargement of muscle intracellular space.     

Comparison of accuracy of intravoxel incoherent motion and apparent diffusion coefficient techniques for predicting malignancy of head and neck tumors using half-Fourier single-shot turbo spin-echo diffusion-weighted imaging

Purpose

To evaluate the use of the intravoxel incoherent motion (IVIM) technique in half-Fourier single-shot turbo spin-echo (HASTE) diffusion-weighted imaging (DWI), and to compare its accuracy to that of apparent diffusion coefficient (ADC) to predict malignancy in head and neck tumors.

Patients and methods

HASTE DW images of 33 patients with head and neck tumors (10 benign and 23 malignant) were evaluated. Using the IVIM technique, parameters (D, true diffusion coefficient; f, perfusion fraction; D*, pseudodiffusion coefficient) were calculated for each tumor. ADC values were measured over a range of b values from 0 to 1000 s/mm². IVIM parameters and ADC values in benign and malignant tumors were compared using Student's t test, receiver operating characteristics (ROC) analysis, and multivariate logistic regression modeling.

Results

Mean ADC and D values of malignant tumors were significantly lower than those of benign tumors (P < 0.05). Mean D* values of malignant tumors were significantly higher than those of benign tumors (P < 0.05). There was no significant difference in mean f values between malignant and benign tumors (P > 0.05). The technique of combining D and D* was the best for predicting malignancy; accuracy for this model was higher than that for ADC.

Conclusions

The IVIM technique may be applied in HASTE DWI as a diagnostic tool to predict malignancy in head and neck masses. The use of D and D* in combination increases the diagnostic accuracy in comparison with ADC.     

Segmentation of the brain using direction-averaged signal of DWI images

Segmentation of brain tissue in diffusion MRI image space has some unique advantages. A novel segmentation method using the direction-averaged diffusion weighted imaging (DWI) signal is proposed. Two images can be obtained from the fitting of the direction-averaged DWI signal as a function of b-value: one with superior contrast between the gray matter and white matter; one with prominent CSF contrast. A pseudo T1 weighted image can be constructed and standard segmentation tools can be applied. The method was tested on the HCP dataset using SPM12, and showed good agreement with segmentation using the T1 weighted image with the same resolution. The Dice score was all greater than 0.88 for GM or WM with full DWI data and very stable against subsampling of the DWI data in number of diffusion directions, number of shells, and spatial resolution.     

Assessment of early response to concurrent chemoradiotherapy in cervical cancer: value of diffusion-weighted and dynamic contrast-enhanced MR imaging

Purpose

To investigate diffusion-weighted (DWI) and dynamic contrast-enhanced MR imaging (DCE-MRI) as early response predictors in cervical cancer patients who received concurrent chemoradiotherapy (CCRT).

Materials and methods

Sixteen patients with cervical cancer underwent DWI and DCE-MRI before CCRT (preTx), at 1 week (postT1) and 4 weeks (postT2) after initiating treatment, and 1 month after the end of treatment (postT3). At each point, apparent diffusion coefficient (ADC) and DCE-MRI parameters were measured in tumors and gluteus muscles (GM). Tumor response was correlated with imaging parameters or changes in imaging parameters at each point.

Results

At each point, ADC, K^trans and V_e in tumors showed significant changes (P < 0.05), as compared with those of GM (P > 0.05). PostT1 tumor ADCs showed a significant correlation with tumor size response at postT2 (P = 0.041), and changes in tumor ADCs at postT1 had a significant correlation with tumor size (P = 0.04) and volume response (P = 0.003) at postT2. In tumors, preTx K^trans and V_e showed significant correlations with tumor size at postT3 (P = 0.011) and tumor size response at postT2 (P = 0.019), respectively.

Conclusion

DWI and DCE-MRI, as early biomarkers, have the potential to evaluate therapeutic responses to CCRT in cervical cancers.     

Variational multiple-tensor fitting of fiber-ambiguous diffusion-weighted magnetic resonance imaging voxels

Partial volume effects are often experienced in diffusion-weighted MRI of biologic tissue. This is when the signal attenuation reflects a mixture of diffusion processes, originating from different tissue compartments, residing in the same voxel. Decomposing the mixture requires elaborated models that account for multiple compartments, yet the fitting problem for those models is usually ill posed. We suggest a novel approach for stabilizing the fitting problem of the multiple-tensors model by a variational framework that adds biologically oriented assumption of neighborhood alignments. The framework is designed to address fiber ambiguity caused by a number of neuronal fiber compartments residing in the same voxel. The method requires diffusion data acquired by common, clinically feasible MRI sequences, and is able to derive familiar tensor quantities for each compartment. Neighborhood alignment is performed by adding piece-wise smooth regularization constraints to an energy function. Minimization with the gradient descent method produces a set of diffusion-reaction partial differential equations that describe a tensor-preserving flow towards a best approximation of the data while maintaining the constraints. We analyze fiber compartment separation capabilities on a synthetic model of crossing fibers and on brain areas known to have crossing fibers. We compare the results with diffusion tensor imaging analysis and discuss applications for the framework.     

Kinetic Monte Carlo simulations of Pd deposition and island growth on MgO(1 0 0)

The deposition and ripening of Pd atoms on the MgO(1 0 0) surface are modeled using kinetic Monte Carlo simulations. The density of Pd islands is obtained by simulating the deposition of 0.1 ML in 3 min. Two sets of kinetic parameters are tested and compared with experiment over a 200-800 K temperature range. One model is based upon parameters obtained by fitting rate equations to experimental data and assuming the Pd monomer is the only diffusing species. The other is based upon transition rates obtained from density functional theory calculations which show that small Pd clusters are also mobile. In both models, oxygen vacancy defects on the MgO surface provide strong traps for Pd monomers and serve as nucleation sites for islands. Kinetic Monte Carlo simulations show that both models reproduce the experimentally observed island density versus temperature, despite large differences in the energetics and different diffusion mechanisms. The low temperature Pd island formation at defects is attributed to fast monomer diffusion to defects in the rate-equation-based model, whereas in the DFT-based model, small clusters form already on terraces and diffuse to defects. In the DFT-based model, the strong dimer and trimer binding energies at charged oxygen vacancy defects prevent island ripening below the experimentally observed onset temperature of 600 K.     

Multispectrum fits for line mixing in the ν3 band Q branch of methane

First-order line-mixing coefficients and model relaxation matrix element scaling factors have been obtained for allowed transitions in the ν₃ band Q branch of CH₄ broadened by H₂, He, N₂, O₂, Ar, and CH₄. The broadening, shifting, Dicke-narrowing, and line-mixing parameters are determined by simultaneous least-squares fitting of spectra at pressures from 0.014 to 66.66 kPa recorded with a high-resolution difference-frequency laser. These results confirm, improve, and extend a previous analysis of the lower pressure (?13.3 kPa) data [A.S. Pine, J. Chem. Phys. 97 (1992) 773] which yielded averaged coefficients of individually fit spectra where adjacent broadened lines are still partially resolved.     

Study of vibration-rotation levels in formamide with high resolution FTIR spectroscopy: The ν12, 2ν12, ν11, and ν9 bands

The far infrared and infrared spectra of formamide (HCONH₂) have been recorded at high resolution (0.00125 cm⁻¹) in the region of 90-1060 cm⁻¹. Over 20,000 transitions from the out-of-plane NH₂ wagging motion (n₁₂ = 1 ← 0 fundamental, n₁₂ = 2 ← 0 overtone, n₁₂ = 2 ← 1 difference bands), torsion (n₁₁ = 1 ← 0 bands), and out-of-phase NCO/NH₂ bend (n₉ = 1 ← 0 bands) have been assigned. Molecular parameters have been obtained for the ground state and the unperturbed n₁₂ = 1 state. The least-squares fit calculations were completed with the microwave data available in the literature. The complicated resonance system between the n₁₂ = 2, n₁₁ = 1, and n₉ = 1 states has been investigated carefully. Thus, we have been able to verify almost all resonances (avoided crossing) existing in the region J, K investigated. In the coupled Hamiltonian used for the fit, all Watson’s reduced parameters, including the octic ones and 16 Coriolis coupling parameters were taken into account. The rms deviation obtained from the fit was 0.000247 cm⁻¹.     

A new joint analysis of the ground and first excited torsional states of methylformate

A global fit within experimental accuracy of microwave rotational transitions in the ground and first excited torsional states (v_t = 0 and 1) of methylformate (HCOOCH₃) is reported, which combines older measurements from the literature with new measurements from Kharkov. In this study the so-called ‘‘rho axis method’’ that treats simultaneously both A and E species of the ground and first excited torsional states is used. The final fit requires 55 parameters to achieve an overall unitless weighted standard deviation of 0.71 for a total of 10533 transitions (corresponding to 9298 measured lines) with rotational quantum numbers up to J ? 62 and K_a ? 26 in the ground state and J ? 35 and K_a ? 23 in the first excited torsional state. These results represent a significant improvement over past fitting attempts, providing for the first time a fit within experimental accuracy of both ground and first excited torsional states.     

Photoelectronic characterization of n-type silicon wafers using photocarrier radiometry

Photocarrier radiometry (PCR) was used to characterize four n-type silicon wafers with different resistivity values in the 1-20 Ω cm range. Simulations of the PCR signal have been performed to study the influence of the recombination lifetime and front surface recombination velocity on them; besides, the transport parameters (carrier recombination lifetime, diffusion coefficient, and frontal surface recombination) of the wafers were obtained by means of a fitting procedure. The PCR images that are related to the lifetime are presented, and the first photoelectronic images of a porous silicon sample are obtained.     

Geometrically constrained two-tensor model for crossing tracts in DWI

MR diffusion tensor imaging (DTI) of the brain and spine provides a unique tool for both visualizing directionality and assessing intactness of white matter fiber tracts in vivo. At the spatial resolution of clinical MRI, much of primate white matter is composed of interdigitating fibers. Analyses based on an assumed single diffusion tensor per voxel yield important information about the average diffusion in the voxel but fail to reveal structure in the presence of crossing tracts. Until today, all clinical scans assume only one tensor, causing potential serious errors in tractography. Since high angular resolution imaging remains, so far, untenable for routine clinical use, a method is proposed whereby the single-tensor field is augmented with additional information gleaned from standard clinical DTI. The method effectively resolves two distinct tract directions within voxels, in which only two tracts are assumed to exist. The underlying constrained two-tensor model is fitted in two stages, utilizing the information present in the single-tensor fit. As a result, the necessary MRI time can be drastically reduced when compared with other approaches, enabling widespread clinical use. Upon evaluation in simulations and application to in vivo human brain DTI data, the method appears to be robust and practical and, if correctly applied, could elucidate tract directions at critical points of uncertainty.     

A linear relationship exists among brain diffusion eigenvalues measured by diffusion tensor magnetic resonance imaging

Diffusion in biological tissues can be measured by magnetic resonance diffusion tensor imaging The complex nature of anisotropic diffusion in the brain has been described by a diffusion tensor which contains information about the magnitude of diffusion in different directions. Each tensor contains a set of three eigenvalues which are related to the major, intermediate, and minor axes of a diffusion ellipsoid. This investigation demonstrates that the various sets of diffusion eigenvalues from different regions of the brain lie along a line in ordered eigenvalue space. Sets of ordered diffusion eigenvalues were considered points in ordered eigenvalue space. The line which best fit the data by minimizing the total squared deviations was determined. A new coordinate system was constructed through translation and rotation which spanned ordered eigenvalue space. Eigenvalues from both monkey brain and human brain were studied. It was found that the sets of eigenvalues from both species have significant linear trends. Moreover, the same line may describe the brain eigenvalues from both species. It is likely that this linear relationship of the eigenvalues observed in an ordered eigenvalue plot is related to a combination of (1) conservation of total isotropic diffusion and (2) the degree of orientational dispersion of the microfibers within each voxel.     

Diode laser spectroscopic measurements and theoretical calculations of line parameters of nitrogen-broadened water vapor overtone transitions in the 818-834 nm wavelength region

Nitrogen-broadened water vapor line parameters of the (2 1 1) ← (0 0 0) overtone band transitions in the 818-834 nm wavelength region are measured by using a tunable diode laser spectrometer. Water vapor is kept at its saturated vapor pressure at room temperature within a sample cell. Use of a balanced detector and a lock-in amplifier helps to increase the detection efficiency and the signal-to-noise ratio. The collisional broadening coefficients are extracted from the fitting of the experimental data by using a standard Voigt line profile. Collisional half-widths of water vapor lines perturbed by nitrogen are evaluated using the complex-valued implementation of the Robert-Bonamy (CRB) formalism. The rotational wave functions and the energy eigenvalues in the (2 1 1) vibrational state of water molecule are assumed on the basis of symmetry properties. Hence the outcome of this work also tests the validity of the theoretical approximations. The experimental data are compared with the corresponding theoretical values and the possible causes of deviation between the two have also been discussed.