Eight months follow-up study on pulmonary function, lung radiographic, and related physiological characteristics in COVID-19 survivors

To describe the long-term health outcomes of patients with COVID-19 and investigate the potential risk factors. Clinical data during hospitalization and at a mean (SD) day of 249 (15) days after discharge from 40 survivors with confirmed COVID-19 (including 25 severe cases) were collected and analyzed retrospectively. At follow-up, severe cases had higher incidences of persistent symptoms, DLCO impairment, and higher abnormal CT score as compared with mild cases. CT score at follow-up was positively correlated with age, LDH level, cumulative days of oxygen treatment, total dosage of glucocorticoids used, and CT peak score during hospitalization. DLCO% at follow-up was negatively correlated with cumulative days of oxygen treatment during hospitalization. DLCO/VA% at follow-up was positively correlated with BMI, and TNF-α level. Among the three groups categorized as survivors with normal DLCO, abnormal DLCO but normal DLCO/VA, and abnormal DLCO and DLCO/VA, survivors with abnormal DLCO and DLCO/VA had the lowest serum IL-2R, IL-8, and TNF-α level, while the survivors with abnormal DLCO but normal DLCO/VA had the highest levels of inflammatory cytokines during hospitalization. Altogether, COVID-19 had a greater long-term impact on the lung physiology of severe cases. The long-term radiological abnormality maybe relate to old age and the severity of COVID-19. Either absent or excess of inflammation during COVID-19 course would lead to the impairment of pulmonary diffusion function.

Invariants for a Dynamical System with Strong Random Perturbations

In this chapter we consider the invariant method for stochastic system with strong perturbations, and its application to many different tasks related to dynamical systems with invariants. This theory allows constructing the mathematical model (deterministic and stochastic) of actual process if it has invariant functions. These models have a kind of jump-diffusion equations system (stochastic differential Itô equations with a Wiener and a Poisson paths). We show that an invariant function (with probability 1) for stochastic dynamical system under strong perturbations exists. We consider a programmed control with Prob. 1 for stochastic dynamical systems – PSP1. We study the construction of stochastic models with invariant function based on deterministic model with invariant one and show the results of numerical simulation. The concept of a first integral for stochastic differential equation Itô introduce by V. Doobko, and the generalized Itô – Wentzell formula for jump-diffusion function proved us, play the key role for this research.

Time-Dependent Fractional Diffusion and Friction Functions for Anomalous Diffusion

The precise determination of diffusive properties is presented for a system described by the generalized Langevin equation. The time-dependent fractional diffusion function and the Green-Kubo relation as well as the generalized Stokes-Einstein formula, in the spirit of ensemble averages, are reconfigured. The effective friction function is introduced as a measure of the influence of frequency-dependent friction on the evolution of the system. This is applied to the generalized Debye model, from which self-oscillation emerges as indicative of ergodicity that breaks due to high finite-frequency cutoff. Moreover, several inconsistent conclusions that have appeared in the literature are revised.

On the Theory of Entropy Solutions of Nonlinear Degenerate Parabolic Equations

We consider a second-order nonlinear degenerate parabolic equation in the case when the flux vector and the nonstrictly increasing diffusion function are merely continuous. In the case of zero diffusion, this equation degenerates into a first order quasilinear equation (conservation law). It is known that in the general case under consideration an entropy solution (in the sense of Kruzhkov-Carrillo) of the Cauchy problem can be non-unique. Therefore, it is important to study special entropy solutions of the Cauchy problem and to find additional conditions on the input data of the problem that are sufficient for uniqueness. In this paper, we obtain some new results in this direction. Namely, the existence of the largest and the smallest entropy solutions of the Cauchy problem is proved. With the help of this result, the uniqueness of the entropy solution with periodic initial data is established. More generally, the comparison principle is proved for entropy suband super-solutions, in the case when at least one of the initial functions is periodic. The obtained results are generalization of the results known for conservation laws to the parabolic case.

Diffusive acceleration in relativistic shocks: particle feedback

ABSTRACT The spectral index s of high-energy particles diffusively accelerated in a non-magnetized relativistic shock, such as in a γ-ray burst afterglow, depends on the unknown angular diffusion function $\mathcal {D}$, which itself depends on the particle distribution function f if acceleration is efficient. We develop a relaxation code to compute s and f for an arbitrary functional $\mathcal {D}$ that depends on f. A local $\mathcal {D}(f)$ dependence is motivated and shown, when rising (falling) upstream, to soften (harden) s with respect to the isotropic case, shift the angular distribution towards upstream (downstream) directions, and strengthen (weaken) the particle confinement to the shock; an opposite effect on s is found downstream. However, variations in s remain modest even when $\mathcal {D}$ is a strong function of f, so the standard, isotropic-diffusion results remain approximately applicable unless $\mathcal {D}$ is both highly anisotropic and not a local function of f. A mild, ∼0.1 softening of s, in both 2D and 3D, when $\mathcal {D}(f)$ rises sufficiently fast, may be realized in ab initio simulations.

Dim and Small Targets Detection in Sequence Images Based on Spatiotemporal Motion Characteristics

In order to effectively enhance the low detection rates of dim and small targets caused by dynamic backgrounds, this paper proposes a detection algorithm for dim and small targets in sequence images based on spatiotemporal motion characteristics. With regard to the spatial domain, this paper proposes an improved anisotropic background filtering algorithm that makes full use of the gradient differences between the target and the background pixels in the eight directions of the spatial domain and selects the mean value of the three directions with the lowest diffusion function in the eight directions as the differential filter to obtain a differential image. Then, the paper proposes a directional energy correlation enhancement algorithm in the time domain. Finally, based on the above preprocessing operations, we construct a dim and small targets detection algorithm in sequence images with local motion characteristics, which achieves target detection by determining the number of occurrences of the target, the number of displacements, and the total cumulative area in these sequential images. Experiments show that the proposed detection algorithm in this paper can effectively improve the detection of dim and small targets in dynamic scenes.

Correlation between DVH parameters and lung function changes before and after radiotherapy and the occurrence of radiation-induced lung injury (RILI)

Background: The purpose of the study was to explore the correlation between DVH parameters and lung function changes before and after radiotherapy and the occurrence of radiation-induced lung injury (RILI), and to evaluate its value in predicting the risk of RILI.Methods: 120 patients with advanced non-small cell lung cancer who had been diagnosed in Jiaozhou Central Hospital of Qingdao City in the past three years and received chest conformal (intensity modulated) radiation therapy were selected. Before radiotherapy, irradiation of 45-50 Gy, and 1 month after the end of radiotherapy, the patients were tested for lung function, and the ventilation and diffusion function of the patients were tested using the Japanese CHESTAC-8800 lung function tester. The evaluation of radiation lung injury was based on the RTOG acute radiation lung injury classification standard, and the observation end point was ≥2 grade RILI.Results: A total of 34 patients with ≥2 grade RILI among 120 patients in this study, including 23 cases of grade 2 and 11 cases of grade 3, the incidence rate was 28.33%. The difference between FVC, FEV1, FEV1 / FVC, DLCO, V5, V10, V15 before radiotherapy, 45-50 Gy, and 1 month after the end of radiotherapy were statistically significant (P <0.05). Univariate analysis showed that lung function, V5, V10, and V15 before radiotherapy were related factors for RILI (P <0.05). Multivariate logistic analysis showed that the risk of RILI was 1.855 times that of patients with higher FEV1 / FVC before radiation therapy (OR = 1.855, 95% CI = 1.199-1.946, P = 0.037), patients with V10 ≥50% were 3.673 times higher than patients with V10 <50% (OR = 3.673, 95% CI = 1.548-7.582, P = 0.039).Conclusions: V10≥50% and FEV1 / FVC are high-risk factors for RILI before radiotherapy, which has certain value in predicting the risk of RILI.

Simulation of diffusion motion of ionomers using Monte Carlo algorithm

We present a simple model of ionomers, namely a single polymer chain in a series of fixed attractors. In analogy to ionized bead’s claws of surrounding chains, the set of attractors can affectively slow down the diffusion motion of the target chain. The monomer mean-square displacement of ionomers is studied by using Monte Carlo algorithm, and compared with the prediction of the sticky Rouse model. The diffusion motion properties of ionomers are explored in three aspects, including the chain length of the polymer, the depth of the potential well and the number of ionic groups. The results show that a plateau appears in the monomer diffusion function due to the attraction of the attractors to the claws. However, comparative theoretical predictions and simulation results show that there exists some discrepancy between them. Therefore, the relaxation time distribution of polymer chain motion is explored. The simulation results confirm that the association lifetime is decreasing exponentially, and the expected values of the association lifetime satisfy the Boltzmann distribution as shown by the results. These results perfectly explain the deviation between the simulation data and the theoretical results.

Quantum-Relativistic Nanodiffusion

In this paper I present the complete technical analysis of the diffusion function in thehypothesis of quantum-relativistic effects inside a nanostructure, considering a currentanalytical model, called DS model, having a wide applicability scale range. In thepaper the nanoscale is considered, but the presence of a gauge factor inside the modelallows its application from sub-pico-level to macro-level. Both theoretical frameworkis performed and examples of application.

Non-linear Mixed Models in a Dose Response Modelling

Study designs in which an outcome is measured more than once from time to time result in longitudinal data. Most of the methodological works have been done in the setting of linear and generalized linear models, where some amount of linearity is retained. However, this still be considered a limiting factor and non-linear models is another option offering its flexibility. Non-linear model involves complexity of non-linear dependence on parameters than that in the generalized linear class. It has been utilized in many situations such as modeling of growth curves and dose-response modeling. The latter modeling will be the main interest in this study to construct a dose-response relationship, as a function of time to IBD (inflammatory bowel disease) dataset. The dataset comes from a clinical trial with 291 subjects measured during a 7 week period. Both linear and non-linear models are considered. A dose time response model with generalized diffusion function is utilized for the non-linear models. The fit of non-linear models are found to be more flexible than linear models hence able to capture more variability present in the data.Keywords: IBD; longitudinal; linear mixed model; non-linear mixed model. AbstrakDesain studi dimana hasil diukur berulang kali dari waktu ke waktu menghasilkan data longitudinal. Sebagian besar metodologi yang digunakan untuk menganalisis data longitudinal adalah model linear dan model linear umum (generalized linear model) dimana sejumlah linearitas tertentu dipertahankan. Asumsi linearitas ini masih dipandang memiliki keterbatasan dan model non-linear adalah pilihan metode lainnya yang menawarkan fleksibilitas. Model non-linear telah digunakan di berbagai macam situasi seperti model kurva pertumbuhan , model farmakokinetika, dan farmakodinamika, dan model respon-dosis. Model respon-dosis akan menjadi fokus dalam penelitian ini untuk membangun hubungan dosis-respon sebagai fungsi waktu dari data IBD dengan menggunakan model linear dan non-linear. Hasil penelitian menunjukan bahwa model non-linear lebih fleksibel daripada model linear sehingga mampu menangkap lebih banyak variabilitas yang ada di dalam data.Keywords: IBD; longitudinal; model linear; model non-linear.