Multi-parametric MRI-based machine learning model for prediction of pathological grade of renal injury in a rat kidney cold ischemia-reperfusion injury model.

BACKGROUND: Renal cold ischemia-reperfusion injury (CIRI), a pathological process during kidney transplantation, may result in delayed graft function and negatively impact graft survival and function. There is a lack of an accurate and non-invasive tool for evaluating the degree of CIRI. Multi-parametric MRI has been widely used to detect and evaluate kidney injury. The machine learning algorithms introduced the opportunity to combine biomarkers from different MRI metrics into a single classifier. OBJECTIVE: To evaluate the performance of multi-parametric magnetic resonance imaging for grading renal injury in a rat model of renal cold ischemia-reperfusion injury using a machine learning approach. METHODS: Eighty male SD rats were selected to establish a renal cold ischemia -reperfusion model, and all performed multiparametric MRI scans (DWI, IVIM, DKI, BOLD, T1mapping and ASL), followed by pathological analysis. A total of 25 parameters of renal cortex and medulla were analyzed as features. The pathology scores were divided into 3 groups using K-means clustering method. Lasso regression was applied for the initial selecting of features. The optimal features and the best techniques for pathological grading were obtained. Multiple classifiers were used to construct models to evaluate the predictive value for pathology grading. RESULTS: All rats were categorized into mild, moderate, and severe injury group according the pathologic scores. The 8 features that correlated better with the pathologic classification were medullary and cortical Dp, cortical T2*, cortical Fp, medullary T2*, ∆T1, cortical RBF, medullary T1. The accuracy(0.83, 0.850, 0.81, respectively) and AUC (0.95, 0.93, 0.90, respectively) for pathologic classification of the logistic regression, SVM, and RF are significantly higher than other classifiers. For the logistic model and combining logistic, RF and SVM model of different techniques for pathology grading, the stable and perform are both well. Based on logistic regression, IVIM has the highest AUC (0.93) for pathological grading, followed by BOLD(0.90). CONCLUSION: The multi-parametric MRI-based machine learning model could be valuable for noninvasive assessment of the degree of renal injury.

Heat transport in Rayleigh-Bénard convection with linear marginality.

Recent direct numerical simulations (DNS) and computations of exact steady solutions suggest that the heat transport in Rayleigh-Bénard convection (RBC) exhibits the classical [Formula: see text] scaling as the Rayleigh number [Formula: see text] with Prandtl number unity, consistent with Malkus-Howard's marginally stable boundary layer theory. Here, we construct conditional upper and lower bounds for heat transport in two-dimensional RBC subject to a physically motivated marginal linear-stability constraint. The upper estimate is derived using the Constantin-Doering-Hopf (CDH) variational framework for RBC with stress-free boundary conditions, while the lower estimate is developed for both stress-free and no-slip boundary conditions. The resulting optimization problems are solved numerically using a time-stepping algorithm. Our results indicate that the upper heat-flux estimate follows the same [Formula: see text] scaling as the rigorous CDH upper bound for the two-dimensional stress-free case, indicating that the linear-stability constraint fails to modify the boundary-layer thickness of the mean temperature profile. By contrast, the lower estimate successfully captures the [Formula: see text] scaling for both the stress-free and no-slip cases. These estimates are tested using marginally-stable equilibrium solutions obtained under the quasi-linear approximation, steady roll solutions and DNS data. This article is part of the theme issue 'Mathematical problems in physical fluid dynamics (part 1)'.

Time-stepping approach for solving upper-bound problems: Application to two-dimensional Rayleigh-Bénard convection.

An alternative computational procedure for numerically solving a class of variational problems arising from rigorous upper-bound analysis of forced-dissipative infinite-dimensional nonlinear dynamical systems, including the Navier-Stokes and Oberbeck-Boussinesq equations, is analyzed and applied to Rayleigh-Bénard convection. A proof that the only steady state to which this numerical algorithm can converge is the required global optimal of the relevant variational problem is given for three canonical flow configurations. In contrast with most other numerical schemes for computing the optimal bounds on transported quantities (e.g., heat or momentum) within the "background field" variational framework, which employ variants of Newton's method and hence require very accurate initial iterates, the new computational method is easy to implement and, crucially, does not require numerical continuation. The algorithm is used to determine the optimal background-method bound on the heat transport enhancement factor, i.e., the Nusselt number (Nu), as a function of the Rayleigh number (Ra), Prandtl number (Pr), and domain aspect ratio L in two-dimensional Rayleigh-Bénard convection between stress-free isothermal boundaries (Rayleigh's original 1916 model of convection). The result of the computation is significant because analyses, laboratory experiments, and numerical simulations have suggested a range of exponents α and ß in the presumed Nu∼Pr(α)Ra(ß) scaling relation. The computations clearly show that for Ra≤10(10) at fixed L=2√[2],Nu≤0.106Pr(0)Ra(5/12), which indicates that molecular transport cannot generally be neglected in the "ultimate" high-Ra regime.