We analyse a second-order boundary value problem arising from the motion of stratified ocean flows in Antarctica. Using a Lyapunov-type function and the monotonicity properties of the density function and of the oceanic vorticity, we prove results on the existence and uniqueness of solutions of the problem under consideration. Finally, we discuss possible extensions of the model that admit unique solutions for more general cases of density distribution.

Extreme precipitation usually leads to substantial impacts. Floods in the Netherlands, Belgium and Germany in the summer of 2021 have caused loss of lives, destruction of infrastructures, and long-term effect on economics. To avoid such disasters, it is important to develop a reliable and accurate method to predict heavy rain.

To study radiotherapy-related adverse effects, detailed dose information (3D distribution) is needed for accurate dose-effect modeling. For childhood cancer survivors who underwent radiotherapy in the pre-CT era, only 2D radiographs were acquired, thus 3D dose distributions must be reconstructed from limited information. State-of-the-art methods achieve this by using 3D surrogate anatomies. These can however lack personalization and lead to coarse reconstructions. We present and validate a surrogate-free dose reconstruction method based on Machine Learning (ML). Abdominal planning CTs (n = 142) of recently-treated childhood cancer patients were gathered, their organs at risk were segmented, and 300 artificial Wilms' tumor plans were sampled automatically. Each artificial plan was automatically emulated on the 142 CTs, resulting in 42,600 3D dose distributions from which dose-volume metrics were derived. Anatomical features were extracted from digitally reconstructed radiographs simulated from the CTs to resemble historical radiographs. Further, patient and radiotherapy plan features typically available from historical treatment records were collected. An evolutionary ML algorithm was then used to link features to dose-volume metrics. Besides 5-fold cross validation, a further evaluation was done on an independent dataset of five CTs each associated with two clinical plans. Cross-validation resulted in mean absolute errors ≤ 0.6 Gy for organs completely inside or outside the field. For organs positioned at the edge of the field, mean absolute errors ≤ 1.7 Gy for Dmean, ≤ 2.9 Gy for 2cc,}, and ≤ 13% for V5 Gy10 Gy, were obtained, without systematic bias. Similar results were found for the independent dataset. To conclude, we proposed a novel organ dose reconstruction method that uses ML models to predict dose-volume metric values given patient and plan features. Our approach is not only accurate, but also efficient, as the setup of a surrogate is no longer needed.

Accurate quantification of retinal structures in 3-D optical coherence tomography data of eyes with pathologies provides clinically relevant information. We present an approach to jointly segment retinal layers and lesions in eyes with topology-disrupting retinal diseases by a loosely coupled level set framework. In the new approach, lesions are modeled as an additional space-variant layer delineated by auxiliary interfaces. Furthermore, the segmentation of interfaces is steered by local differences in the signal between adjacent retinal layers, thereby allowing the approach to handle local intensity variations. The accuracy of the proposed method of both layer and lesion segmentation has been evaluated on eyes affected by central serous retinopathy and age-related macular degeneration. In addition, layer segmentation of the proposed approach was evaluated on eyes without topology-disrupting retinal diseases. Good agreement between the segmentation performed manually by a medical doctor and results obtained from the automatic segmentation was found for all data types. The mean unsigned error for all interfaces varied between 2.3 and 11.9 μm (0.6-3.1 pixels). Furthermore, lesion segmentation showed a Dice coefficient of 0.68 for drusen and 0.89 for fluid pockets. Overall, the method provides a flexible and accurate solution to jointly segment lesions and retinal layers.

It is unclear that how subcellular organelles respond to external mechanical stimuli. Here, we investigated the molecular mechanisms by which mechanical force regulates Ca2+ signaling at endoplasmic reticulum (ER) in human mesenchymal stem cells. Without extracellular Ca2+, ER Ca2+ release is the source of intracellular Ca2+ oscillations induced by laser-tweezer-traction at the plasma membrane, providing a model to study how mechanical stimuli can be transmitted deep inside the cell body. This ER Ca2+ release upon mechanical stimulation is mediated not only by the mechanical support of cytoskeleton and actomyosin contractility, but also by mechanosensitive Ca2+ permeable channels on the plasma membrane, specifically TRPM7. However, Ca2+ influx at the plasma membrane via mechanosensitive Ca2+ permeable channels is only mediated by the passive cytoskeletal structure but not active actomyosin contractility. Thus, active actomyosin contractility is essential for the response of ER to the external mechanical stimuli, distinct from the mechanical regulation at the plasma membrane.