Sentinel lymph node metastasis (SLNM) is a crucial predictor for breast cancer treatment and survival. This study was designed to propose deep learning (DL) models based on grayscale ultrasound, color Doppler flow imaging (CDFI), and elastography images, and to evaluate how DL radiomics can be used to classify SLNM in breast cancer. Clinical and ultrasound data of 317 patients diagnosed with breast cancer at the Second Affiliated Hospital of Nanchang University were collected from January 2018 to December 2021 and randomly divided into training and internal validation cohorts at a ratio of 7:3. An external validation cohort comprising data from Nanchang Third Hospital with 42 patients collected. Three DL models, namely DL-grayscale, DL-CDFI, and DL-elastography, were proposed to predict SLNM by analyzing grayscale ultrasound, CDFI, and elastography images. Three DL models were compared and evaluated to assess diagnostic performance based on the area under the curve (AUC). The AUCs of the DL-grayscale were 0.855 and 0.788 in the internal and external validation cohorts, respectively. For the DL-CDFI model, the AUCs were 0.761 and 0.728, respectively. The diagnostic performance of DL-elastography was superior to that of the DL-grayscale and DL-CDFI. The AUC of the DL-elastography model was 0.879 in the internal validation cohort, with a classification accuracy of 86.13%, sensitivity of 91.60%, and specificity of 82.79%. The generalization capability of DL-elastography remained high in the external cohort, with an AUC of 0.876, and an accuracy of 85.00%. DL radiomics can be used to classify SLNM in breast cancer using ultrasound images. The proposed DL-elastography model based on elastography images achieved the best diagnostic performance and holds good potential for the management of patients with SLNM.

Misalignment in cardiac magnetic resonance (CMR) images can adversely affect three-dimensional left ventricle modelling and downstream quantitative analysis. Currently, there are two types of approaches for dealing with realignment and motion distortion problems, one image based and the other geometry based. Image-based approaches are limited by the inherent non-homogeneity and anisotropy of CMR images. Geometry-based approaches rely on idealized models and over-simplified assumptions. This study was motivated by the need for a robust and effective approach for correcting motion related distortions due to misalignment in CMR images. A cine cardiac magnetic resonance image sequence was acquired using our routine clinical imaging protocol. The left ventricular endocardium was delineated manually with software assistance on all long and short-axis images. Long and short-axis contours were projected onto a patient-based coordinate system and then realigned using iterative registration. The realigned contour points were used to reconstruct the shape of the left ventricle for quantitative validation. The method was tested on five myocardial infarction patients whose images showed substantial misalignment. Realignment time was about 16 seconds per case, using a 2.5 GHz CPU desktop with obvious elimination of the distortion in the reconstructed model. Using the long-axis contour as a reference in evaluating the reconstructed models, it was apparent that the models with realigned contours had better accuracy than the non-realigned ones. This study presents a novel, geometry-based method for correcting motion distortions in CMR images. The method incorporates (1) manual delineation, (2) registration based on a generalized, iterative closest point algorithm, and (3) reconstruction of the shape of the left ventricle for quantitative validation. The effectiveness of our approach is corroborated both visually and by quantitative assessment. We envision the use of our method in current clinical practice as a means of improving accuracy in the evaluation of cardiac function.

Residual neural ordinary differential equations (NODEs) of the form $\widehat{f}=f+h_{\theta }$ can attain small one-step prediction error yet diverge under autonomous long-horizon rollout. A recent diagnostic attributes this to the one-sided Lipschitz (OSL) constant—the supremum over visited states of the logarithmic norm ${\mu }_2(J_{\widehat{f}})={\lambda }_{\max }(\frac{1}{2}(J_{\widehat{f}}+J_{\widehat{f}}^{\top }))$—which, when positive, signals local expansion and amplifies persistent approximation error. In this work we convert this post hoc diagnostic into a train-time method by augmenting the one-step objective with a contraction penalty $\lambda {\mathbb{E}}_x[{({\mu }_2(J_{\widehat{f}}\left(x\right))-c)}_{+}]$, and we study when this improves robust forecasting across stable, expansive, marginal, and chaotic regimes under realistic sensor-corruption noise. We prove that, at the penalty’s minimizer, the empirical OSL constant is controlled on the training set. A sample-to-domain covering condition then yields, via a Gronwall-type comparison, a conditional uniform-in-time rollout-error bound, with a time-averaged variant that justifies penalizing the mean rather than the maximum log-norm. Empirically, on a six-system, four-noise benchmark the penalty reliably drives the OSL constant down by one-to-two orders of magnitude, but whether this helps long-horizon accuracy is strongly regime-dependent and $\lambda$-sensitive: a common default ($\lambda =0.1$) over-damps and degrades rollout, whereas a calibrated $\lambda \approx 0.01$ helps only for measurably expansive baselines. Under a seed-decoupled re-evaluation with 15 seeds, the benefit is robust on a near-unstable, rotation-dominated oscillator—a $2.3\times$ lower 100-step rollout error ($p=0.018$) at matched one-step error—but the apparent 5-seed improvement on a six-dimensional chemical reaction network does not replicate: with model and dataset seeds decoupled it reverses to a significant degradation, identifying the original effect as a seed-coupling artifact. The method thus yields a single robust positive result, and degrades already-contractive, conservative, and chaotic systems; for chaotic systems this is unavoidable, because enforced contraction suppresses the positive Lyapunov exponents that define the attractor. Finally, while a contraction-aware spectral penalty matches the log-norm penalty, standard ${\parallel J\parallel }_2\le 1$ spectral normalization fails on rotation-dominated dynamics ($8\times$ worse rollout, $p=0.0005$, 15 seeds), confirming that the rotation-invariance of ${\mu }_2$ is the operative property.