Repeatability of arterial input functions and kinetic parameters in muscle obtained by dynamic contrast enhanced MR imaging of the head and neck

BackgroundQuantification of pharmacokinetic parameters in dynamic contrast enhanced (DCE) MRI is heavily dependent on the arterial input function (AIF). In the present patient study on advanced stage head and neck squamous cell carcinoma (HNSCC) we have acquired DCE-MR images before and during chemo radiotherapy. We determined the repeatability of image-derived AIFs and of the obtained kinetic parameters in muscle and compared the repeatability of muscle kinetic parameters obtained with image-derived AIF's versus a population-based AIF.Materials and methodsWe compared image-derived AIFs obtained from the internal carotid, external carotid and vertebral arteries. Pharmacokinetic parameters (v_e, K^trans, k_ep) in muscle—located outside the radiation area—were obtained using the Tofts model with the image-derived AIFs and a population averaged AIF. Parameter values and repeatability were compared. Repeatability was calculated with the pre- and post-treatment data with the assumption of no DCE-MRI measurable biological changes between the scans.ResultsSeveral parameters describing magnitude and shape of the image-derived AIFs from the different arteries in the head and neck were significantly different. Use of image-derived AIFs led to higher pharmacokinetic parameters compared to use of a population averaged AIF. Median muscle pharmacokinetic parameters values obtained with AIFs in external carotids, internal carotids, vertebral arteries and with a population averaged AIF were respectively: v_e (0.65, 0.74, 0.58, 0.32), K^trans (0.30, 0.21, 0.13, 0.06), k_ep (0.41, 0.32, 0.24, 0.18). Repeatability of pharmacokinetic parameters was highest when a population averaged AIF was used; however, this repeatability was not significantly different from image-derived AIFs.ConclusionImage-derived AIFs in the neck region showed significant variations in the AIFs obtained from different arteries, and did not improve repeatability of the resulting pharmacokinetic parameters compared with the use of a population averaged AIF. Therefore, use of a population averaged AIF seems to be preferable for pharmacokinetic analysis using DCE-MRI in the head and neck area.     

Free-breathing radial volumetric interpolated breath-hold examination sequence and dynamic contrast-enhanced MRI combined with diffusion-weighted imaging for assessment of solitary pulmonary nodules

ObjectiveTo test the performance of free-breathing Dynamic Contrast-Enhanced MRI (DCE-MRI) using a radial volumetric interpolated breath-hold examination (VIBE) sequence combined with diffusion-weighted imaging (DWI) for quantitative solitary pulmonary nodule (SPN) assessment.MethodsA total of 67 SPN cases receiving routine MRI routine scans, DWI, and dynamic-enhanced MRI in our hospital from May 2017 to November 2018 were collected. These cases were divided into a malignant group and a benign group according to the characteristics of the SPNs. The quantitative DCE-MRI parameters (K^trans, K_ep, V_e) and apparent diffusion coefficient (ADC) values of the nodules were measured.ResultsThe K^trans and K_ep values in the malignant group were higher than those in the benign group, while the ADC values in the malignant group were lower than those in the benign group. Furthermore, the K^trans value of adenocarcinoma was higher than that of squamous cell carcinoma and small cell carcinoma (P < 0.05). The V_e value was significantly different between non-small cell carcinoma and small cell carcinoma (P < 0.05). With an ADC value of 0.98 × 10⁻³ mm²/s as the threshold, the specificity and sensitivity to diagnose benign and malignant nodules was 90.6% and 80%, respectively.ConclusionHigh-temporal-resolution DCE-MRI using the r-VIBE technique in combination with DWI could contribute to pulmonary nodule analysis and possibly serve as a potential alternative to distinguish malignant from benign nodules as well as differentiate different types of malignancies.     

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.     

A comprehensive evaluation and impact of normalization of generalized tracer kinetic model parameters to characterize blood-brain-barrier permeability in normal-appearing and tumor tissue regions of patients with glioma

Rationale and objectivesTo comprehensively evaluate robustness and variations of DCE-MRI derived generalized-tracer-kinetic-model (GTKM) parameters in healthy and tumor tissues and impact of normalization in mitigating these variations on application to glioma.Materials (patients) and methodsA retrospective study included pre-operative 31 high-grade-glioma(HGG), 22 low-grade-glioma(LGG) and 33 follow-up data from 10 patients a prospective study with 4 HGG subjects. Voxel-wise GTKM was fitted to DCE-MRI data to estimate K^trans, v_e, v_b. Simulations were used to evaluate noise sensitivity. Variation of parameters with-respect-to arterial-input-function (AIF) variation and data length were studied. Normalization of parameters with-respect-to mean values in gray-matter (GM) and white-matter (WM) regions (GM-Type-2, WM-Type-2) and mean curves (GM-Type-1, WM-Type-1) were also evaluated. Co-efficient-of-variation(CoV), relative-percentage-error (RPE), Box-Whisker plots, bar graphs and t-test were used for comparison.ResultsGTKM was fitted well in all tissue regions. K^trans and v_e in contrast-enhancing (CE) has shown improved noise sensitivity in longer data. v_b was reliable in all tissues. Mean AIF and C(t) peaks showed ~38% and ~35% variations. During simulation, normalizations have mitigated variations due to changes in AIF amplitude in K^trans and v_b.. v_e was less sensitive to normalizations. CoV of K^trans and v_b has reduced ~70% after GM-Type-1 normalization and ~80% after GM-Type-2 normalization, respectively. GM-Type-1 (p = 0.003) and GM-Type-2 (p = 0.006) normalizations have significantly improved differentiation of HGG and LGG using K^trans.ConclusionK^trans and v_b can be reliably estimated in normal-appearing brain tissues and can be used for normalization of corresponding parameters in tumor tissues for mitigating inter-subject variability due to errors in AIF. Normalized K^trans and v_b provided improved differentiation of HGG and LGG.     

Studies of pathology and VEGF expression in rabbit cerebrospinal fluid metastasis: application of dynamic contrast-enhanced MRI

Objective

The objective was to analyze the correlation of dynamic contrast-enhanced magnetic resonance imaging (DCE-MRI) with vascular endothelial growth factor (VEGF) protein expression and to assess the potential application of DCE-MRI to the rabbit cerebrospinal fluid (CSF) metastasis model.

Methods

Thirty New Zealand rabbits were divided into experimental and control groups. In the experimental group, VX2 tumor cells were injected into the subarachnoid space at the plane of cisterna magna in 24 rabbits. In the control group, physiological saline was injected into the subarachnoid space at the plane of cisterna magna in six rabbits. DCE-MRI was performed at multiple time points, and several pharmacokinetic parameters, including K^trans, K_ep and V_e, were calculated. Also, VEGF levels in plasma and CSF were evaluated by enzyme-linked immunosorbent assay prior to DCE-MRI examination. After DCE-MRI examination, the rabbits were sacrificed, and the corresponding tumor specimens were harvested. Hematoxylin–eosin staining and VEGF immunohistochemical staining were carried out, and VEGF expression in the specimens was evaluated by the immunohistochemical scoring system.

Results

Vascular endothelial growth factor positive staining was localized in the cytoplasm and cell membranes of tumor cells, as well as in a subset of epithelial cells. Both VEGF immunohistochemical scores and VEGF expression in CSF and plasma exhibited positive correlations with K^trans and K_ep values as demonstrated by rank correlation statistical analysis.

Conclusions

Vascular endothelial growth factor expression in plasma and CSF in the CSF metastasis model was higher than in normal tissues. Therefore, DCE-MRI reliably indicated VEGF expression in the rabbit CSF metastasis model.     

Effects of arterial input function selection on kinetic parameters in brain dynamic contrast-enhanced MRI

PurposeKinetic parameters derived from dynamic contrast-enhanced MRI (DCE-MRI) were suggested as a possible instrument for multi-parametric lesion characterization, but have not found their way into clinical practice yet due to inconsistent results. The quantification is heavily influenced by the definition of an appropriate arterial input functions (AIF). Regarding brain tumor DCE-MRI, there are currently several co-existing methods to determine the AIF frequently including different brain vessels as sources. This study quantitatively and qualitatively analyzes the impact of AIF source selection on kinetic parameters derived from commonly selected AIF source vessels compared to a population-based AIF model.Material and methods74 patients with brain lesions underwent 3D DCE-MRI. Kinetic parameters [transfer constants of contrast agent efflux and reflux K^trans and k_ep and, their ratio, v_e, that is used to measure extravascular-extracellular volume fraction and plasma volume fraction v_p] were determined using extended Tofts model in 821 ROI from 4 AIF sources [the internal carotid artery (ICA), the closest artery to the lesion, the superior sagittal sinus (SSS), the population-based Parker model]. The effect of AIF source alteration on kinetic parameters was evaluated by tissue type selective intra-class correlation (ICC) and capacity to differentiate gliomas by WHO grade [area under the curve analysis (AUC)].ResultsArterial AIF more often led to implausible v_e > 100% values (p < 0.0001). AIF source alteration rendered different absolute kinetic parameters (p < 0.0001), except for k_ep. ICC between kinetic parameters of different AIF sources and tissues were variable (0.08–0.87) and only consistent > 0.5 between arterial AIF derived kinetic parameters. Differentiation between WHO III and II glioma was exclusively possible with v_p derived from an AIF in the SSS (p = 0.03; AUC 0.74).ConclusionThe AIF source has a significant impact on absolute kinetic parameters in DCE-MRI, which limits the comparability of kinetic parameters derived from different AIF sources. The effect is also tissue-dependent. The SSS appears to be the best choice for AIF source vessel selection in brain tumor DCE-MRI as it exclusively allowed for WHO grades II/III and III/IV glioma distinction (by v_p) and showed the least number of implausible v_e values.     

Differentiation of bone metastases from prostate cancer and benign red marrow depositions of the pelvic bone with multiparametric MRI

PurposeTo investigate the diagnostic utilities of imaging parameters derived from T1-weighted imaging (T1WI), diffusion-weighted imaging (DWI) and dynamic contrast-enhanced magnetic resonance imaging (DCE-MRI) to differentiate bone metastases from prostate cancer and benign red marrow depositions of the pelvic bone.Materials and methodsThirty-six lesions from 36 patients with prostate cancer were analyzed with T1WI, DWI, and DCE-MRI. The lesions were classified in the bone metastases (n = 22) and benign red marrow depositions (n = 14). Lesion-muscle ratio (LMR), apparent diffusion coefficient (ADC), volume transfer constant (K^trans), reflux rate (Kep), and volume fraction of the extravascular extracellular matrix (Ve) values were obtained from the lesions. The imaging parameters of the both groups were compared using the Mann-Whitney U test, receiver operating characteristics (ROC) curves were analyzed. For the ROC curves, area under the curves (AUCs) were compared.ResultsThe ADC, K^trans, K_ep, and V_e values of bone metastases were significantly higher than those of benign red marrow depositions (Mann-Whitney U test, p < 0.05). However, there was no significant difference in LMR between the two groups (Mann-Whitney U test, p = 0.360). The AUCs of K^trans_, K_ep, ADC, V_e, and LMR were 0.896, 0.844, 0.812, 0.724, and 0.448, respectively. In the pairwise comparison of ROC curves, the AUCs of K^trans and K_ep was significantly higher than LMR.ConclusionsK^trans, K_ep, V_e, and ADC values can be used as imaging tools to differentiate bone metastases from prostate cancer and benign red marrow depositions of the pelvic bone.     

Dynamic contrast-enhanced MRI of gastric cancer: Correlations of the pharmacokinetic parameters with histological type,Lauren classification,and angiogenesis

PurposeTo compare the pharmacokinetic parameters derived from dynamic contrast-enhanced magnetic resonance imaging (DCE-MRI) in gastric cancers of different histological type and Lauren classification, and to investigate whether DCE-MRI parameters correlate with vascular endothelial growth factor (VEGF) expression levels in gastric cancer.MethodsIncluded were 32 patients with gastric cancer who underwent DCE-MRI of the upper abdomen before tumor resection. DCE-MRI parameters including the volume transfer coefficient (K^trans), reverse reflux rate constant (K_ep), and extracellular extravascular volume fraction (V_e) were calculated from the tumor region. Post-operative specimens were used for determination of histological differentiation (i.e., non-mucinous, mucinous, or signet-ring-cell adenocarcinoma) as well as Lauren classification (intestinal type or diffuse type). VEGF expression was examined for assessing angiogenesis. DCE-MRI parameters with different histological type and Lauren classification were compared using independent samples t-test and analysis of variance, respectively. Correlations between DCE-MRI parameters and VEGF expression grades were tested using Spearman correlation analysis.ResultsAmong gastric adenocarcinomas of three different histological types, mucinous adenocarcinomas showed a higher V_e and lower K^trans than the others (P < 0.01). Between the two Lauren classifications, the diffuse type showed a higher V_e than the intestinal type (P < 0.001). The mean K^trans showed a significantly positive correlation with VEGF (r = 0.762, P < 0.001).ConclusionDCE-MRI permits noninvasive prediction of tumor histological type and Lauren classification and estimation of tumor angiogenesis in gastric cancer. DCE-MRI parameters can be used as imaging biomarkers to predict the biologic aggressiveness of a tumor as well as patient prognosis.     

Prediction of early response to concurrent chemoradiotherapy in cervical cancer: Value of multi-parameter MRI combined with clinical prognostic factors

PurposeThis study aimed to investigate the prediction of early response to concurrent chemoradiotherapy (CCRT) through a combination of pretreatment multi-parametric magnetic resonance imaging (MRI) with clinical prognostic factors (CPF) in cervical cancer patients.MethodsEighty-five patients with pathologically confirmed cervical cancer underwent conventional MRI, intravoxel incoherent motion diffusion weighted imaging (IVIM-DWI), and dynamic contrast-enhanced MRI (DCE-MRI) before CCRT. The patients were divided into non- and residual tumor groups according to post-treatment MRI. Univariable and multivariable analyses were performed to pretreatment MRI parameters and CPF between the two groups, and optimal thresholds and predictive performance for post-treatment residual tumor occurrence were estimated by drawing the receiver operating characteristic (ROC) curve.ResultsThere were 52 patients in non- and 33 in residual group. The residual group showed a lower perfusion fraction (f) value and volume transfer constant (K^trans) value, a higher apparent diffusion coefficient (ADC) value, diffusion coefficient (D) value and volume fraction of extravascular extracellular space (V_e) value, and a higher stage than the non-residual tumor group (all P < .05). D, K^trans, V_e and stage were independent prognostic factors. The combination of D, K^trans and V_e improved the diagnostic performance compared with individual MRI parameters. A further combination of these three MRI parameters with stage exhibited the highest predictive performance.ConclusionsPretreatment D, K^trans, V_e and stage were independent prognostic factors for cervical cancer. The predictive capacity of multi-parametric MRI was superior to individual MRI parameters. The combination of multi-parametric MRI with CPF further improved the predictive performance.     

Early responses assessment of neoadjuvant chemotherapy in nasopharyngeal carcinoma by serial dynamic contrast-enhanced MR imaging

PurposeTo evaluate the feasibility of utilizing serial dynamic contrast-enhanced magnetic resonance imaging (DCE-MRI) prospectively for early prediction of neoadjuvant chemotherapy (NAC) response in nasopharyngeal carcinoma (NPC) patients.Materials and methodsSixty-three advanced NPC patients were recruited and received three DCE-MRI exams before treatment (Pre-Tx), 3 days (Day3-Tx) and 20 days (Day20-Tx) after initiation of chemotherapy (one NAC cycle). Early response to NAC was determined based on the third MRI scan and classified partial response (PR) as responders and stable disease (SD) as non-responders. After intensity-modulated radiotherapy (IMRT), complete response (CR) patients were classified as responders. The kinetic parameters (K^trans, K_ep, v_e, and v_p) derived from extended Tofts' model analysis and their corresponding changes ΔMetrics_(0–X) (X = 3 or 20 days) were compared between the responders and non-responders using the Student's T-test or Mann–Whitney U test.ResultsCompared to the SD group, the PR group after one NAC cycle presented significantly higher mean K^trans values at baseline (P = 0.011) and larger ΔK^trans_(0–3) and ΔK_ep(0–3) values (P = 0.003 and 0.031). For the above parameters, we gained acceptable sensitivity (range: 66.8–75.0%) and specificity (range: 60.0–66.7%) to distinguish the non-responders from the responders and their corresponding diagnosis efficacy (range: 0.703–0.767). The PR group patients after one NAC cycle showed persistent inhibition of tumor perfusion by NAC as explored by DCE-MRI parameters comparing to the SD group (P < 0.05) and presented a higher cure ratio after IMRT than those who did not (83.3% vs. 73.8%).ConclusionsThis primarily DCE-MRI based study showed that the early changes of the kinetic parameters during therapy were potential imaging markers to predicting response right after one NAC cycle for NPC patients.     

Assessment of a combined spin- and gradient-echo (SAGE) DSC-MRI method for preclinical neuroimaging

The goal of this study was to optimize and validate a combined spin- and gradient-echo (SAGE) sequence for dynamic susceptibility-contrast magnetic resonance imaging to obtain hemodynamic parameters in a preclinical setting. The SAGE EPI sequence was applied in phantoms and in vivo rat brain (normal, tumor, and stroke tissue). Partial and full Fourier encoding schemes were implemented and characterized. Maps of cerebral blood volume (CBV), cerebral blood flow (CBF), mean transit time (MTT), vessel size index (VSI), volume transfer constant (K^trans), and volume fraction of the extravascular extracellular space (v_e) were obtained. Partial Fourier encoding provided shortened echo times with acceptable signal-to-noise ratio and temporal stability, thus enabling reliable characterization of T₂, T₂^? and T₁ in both phantoms and rat brain. The hemodynamic parameters CBV, CBF, and MTT for gradient-echo and spin-echo contrast were determined in tumor and stroke; VSI, K^trans, and v_e were also computed in tumor tissue. The SAGE EPI sequence allows the acquisition of multiple gradient- and spin-echoes, from which measures of perfusion, permeability, and vessel size can be obtained in a preclinical setting. Partial Fourier encoding can be used to minimize SAGE echo times and reliably quantify dynamic T₂ and T₂^? changes. This acquisition provides a more comprehensive assessment of hemodynamic status in brain tissue with vascular and perfusion abnormalities.     

Dynamic contrast-enhanced MRI with Gd-EOB-DTPA for the quantitative assessment of early-stage liver fibrosis induced by carbon tetrachloride in rabbits

PurposeTo explore quantitative parameters obtained by dynamic contrast-enhanced magnetic resonance imaging (DCE MRI) with Gd-EOB-DTPA in discriminating early-stage liver fibrosis (LF) in a rabbit model.Materials and methodsLF was established in 60 rabbits by the injection of 50% CCl₄ oil solution, whereas 30 rabbits served as the control group. All rabbits underwent pathological examination to determine the LF stage using the METAVIR classification system. DCE MRI was performed, and quantitative parameters, including K^trans, K_ep, V_e, V_p and Re were measured and evaluated among the different LF stages using spearman correlation coefficients and receiver operating characteristic curve.ResultsIn all, 24, 25, and 22 rabbits had stage F0, stage F1, and stage F2 LF, respectively. K^trans (r = 0.803) increased, and K_ep (r = −0.495) and Re (r = −0.701) decreased with LF stage progression (P < 0.001), while no significant correlation was found for V_e or V_p. K^trans and Re were significantly different between all LF stage pairs compared (F0 vs. F1, F0 vs. F2, F1 vs. F2, F0 vs. F1-F2, P < 0.05). With the exception of F0 vs. F1, K_ep differed significantly between stages (P < 0.05). The AUC of K^trans was higher than that of other quantitative parameters, with an AUC of 0.92, 0.99, 0.94 and 0.92 for staging F0 vs. F1, F0 vs. F2, F1 vs. F2, and F0 vs. F1-F2, respectively.ConclusionAmong quantitative parameters of Gd-EOB-DTPA DCE MRI, K^trans was the best predictor for quantitatively differentiating early-stage LF.     

Reconstruction of dynamic contrast enhanced magnetic resonance imaging of the breast with temporal constraints

A number of methods using temporal and spatial constraints have been proposed for reconstruction of undersampled dynamic magnetic resonance imaging (MRI) data. The complex data can be constrained or regularized in a number of different ways, for example, the time derivative of the magnitude and phase image voxels can be constrained separately or jointly. Intuitively, the performance of different regularizations will depend on both the data and the chosen temporal constraints. Here, a complex temporal total variation (TV) constraint was compared to the use of separate real and imaginary constraints, and to a magnitude constraint alone. Projection onto Convex Sets (POCS) with a gradient descent method was used to implement the diverse temporal constraints in reconstructions of DCE MRI data. For breast DCE data, serial POCS with separate real and imaginary TV constraints was found to give relatively poor results while serial/parallel POCS with a complex temporal TV constraint and serial POCS with a magnitude-only temporal TV constraint performed well with an acceleration factor as large as R=6. In the tumor area, the best method was found to be parallel POCS with complex temporal TV constraint. This method resulted in estimates for the pharmacokinetic parameters that were linearly correlated to those estimated from the fully-sampled data, with K^trans,R=6=0.97 K^trans,R=1+0.00 with correlation coefficient r=0.98, k_ep,R=6=0.95 k_ep,R=1+0.00 (r=0.85). These results suggest that it is possible to acquire highly undersampled breast DCE-MRI data with improved spatial and/or temporal resolution with minimal loss of image quality.     

Differentiation of myeloma and metastatic cancer in the spine using dynamic contrast-enhanced MRI

Spinal myeloma and metastatic cancer cause similar symptoms and show similar imaging presentations, thus making them difficult to differentiate. In this study, dynamic contrast-enhanced magnetic resonance imaging (DCE-MRI) was performed to differentiate between 9 myelomas and 22 metastatic cancers that present as focal lesions in the spine. The characteristic DCE parameters, including the peak signal enhancement percentage (SE%), the steepest wash-in SE% during the ascending phase and the wash-out SE%, were calculated by normalizing to the precontrast signal intensity. The two-compartmental pharmacokinetic model was used to obtain K^trans and k_ep. All nine myelomas showed the wash-out DCE pattern. Of the 22 metastatic cancers, 12 showed wash-out, 7 showed plateau, and 3 showed persistent enhancing patterns. The fraction of cases that showed the wash-out pattern was significantly higher in the myeloma group than the metastatic cancer group (9/9 = 100% vs. 12/22 = 55%, P = .03). Compared to the metastatic cancer group, the myeloma group had a higher peak SE% (226% ± 72% vs. 165% ± 60%, P = .044), a higher steepest wash-in SE% (169% ± 51% vs. 111% ± 41%, P = .01), a higher K^trans (0.114 ± 0.036 vs. 0.077 ± 0.028 1/min, P = .016) and a higher k_ep (0.88 ± 0.26 vs. 0.49 ± 0.23 1/min, P = .002). The receiver operating characteristic analysis to differentiate between these two groups showed that the area under the curve was 0.798 for K^trans, 0.864 for k_ep and 0.919 for combined K^trans and k_ep. These results show that DCE-MRI may provide additional information for making differential diagnosis to aid in choosing the optimal subsequent procedures or treatments for spinal lesions.     

Vibrational relaxation in liquids

A new theory is presented for vibrational energy relaxation in a liquid. It is shown that a vibrationally excited probe molecule relaxes through interaction with the density fluctuations in the surrounding solvent fluid. This interaction occurs through a potential V(k), which is expressed in terms of the intermolecular force between the excited probe molecule and the surrounding fluid molecules. By assuming spherically symmetric solvent particles the T ₁ energy relaxation time for direct V-T processes is related to the translational dynamic structure factor for the fluid S(k, ω_v), evaluated at the vibrational resonance frequency. It is shown that this is described by gas-like particle motions on a very short distance scale corresponding to k vectors lying well beyond the first or second peaks of the fluid structure factor S(k). Such motions can be pictured as high-frequency, short-distance distortions of the local equilibrium configuration of the solvent particles around the probe. T ₁ ^-1 is found to be proportional to ρ_e T ^1/2 ω_v ^-3. The V-V energy exchange relaxation time is also calculated. This is found to be proportional to S(k, ω′) evaluated at a frequency ω′, corresponding to the vibrational energy missmatch. An energy gap law for the V-V process is derived.     

Electronic states of the c is - and trans - H3ONO molecules: a CASPT2 study

The CASPT2 calculations for the S₀, T₁, S₁, T₂, and S₂ states of the cis- and trans-CH₃ONO molecules predict the energy levels and geometries of the cis- and trans-isomers in the different states. The CASPT2 adiabatic (T ₀) and vertical (T _v) excitation energies are in good agreement with available experimental data (for the S₁ cis- and trans-isomers). The CH₃O-NO dissociation potential energy curves were calculated at the CASPT2//CASSCF level, and the CASPT2 calculations were performed for the transition states along the T₁, S₁, and T₂ dissociation paths. For the repulsive S₂ state the calculations predict the T _v values larger than 5.4 eV and dissociation products of CH₃O (1²A″) + NO (X²Π).     

The ν1 and ν3 stretching fundamental bands of PD3

The infrared (IR) spectrum of PD₃ has been recorded in the 1580–1800 cm⁻¹ range at a resolution of 0.0027 cm⁻¹. About 2400 rovibrational transitions with J^′=K^′22 have been measured and assigned to the ν₁ (A₁) and ν₃ (E) stretching fundamentals. These include 506 “perturbation-allowed” transitions with selection rules Δ(k−l)=±3. Splittings of the K^′′=3 lines have been observed. Effects of strong perturbations are evident in the spectrum. Therefore the rovibrational Hamiltonian adopted for the analysis explicitly takes into account the Coriolis and k-type interactions between the v₁=1 and v₃=1 states, and includes also several essential resonances within these states. The rotational structure in the v₁=1 and v₃=1 vibrational states up to J^′=K^′=18 was reproduced by fitting simultaneously all experimental data. Thirty-four parameters reproduced 1950 transitions retained in the final cycle with a standard deviation of the fit equal to 4.9 × 10⁻⁴ cm⁻¹ (about the precision of the experimental measurements).