RESUMO
The two-dimensional sample entropy marks a significant advance in evaluating the regularity and predictability of images in the information domain. Unlike the direct computation of sample entropy, which incurs a time complexity of O(N2) for the series with N length, the Monte Carlo-based algorithm for computing one-dimensional sample entropy (MCSampEn) markedly reduces computational costs by minimizing the dependence on N. This paper extends MCSampEn to two dimensions, referred to as MCSampEn2D. This new approach substantially accelerates the estimation of two-dimensional sample entropy, outperforming the direct method by more than a thousand fold. Despite these advancements, MCSampEn2D encounters challenges with significant errors and slow convergence rates. To counter these issues, we have incorporated an upper confidence bound (UCB) strategy in MCSampEn2D. This strategy involves assigning varied upper confidence bounds in each Monte Carlo experiment iteration to enhance the algorithm's speed and accuracy. Our evaluation of this enhanced approach, dubbed UCBMCSampEn2D, involved the use of medical and natural image data sets. The experiments demonstrate that UCBMCSampEn2D achieves a 40% reduction in computational time compared to MCSampEn2D. Furthermore, the errors with UCBMCSampEn2D are only 30% of those observed in MCSampEn2D, highlighting its improved accuracy and efficiency.
RESUMO
Oxygen is a vital molecule involved in regulating development, homeostasis, and disease. The oxygen levels in tissue vary from 1 to 14% with deviations from homeostasis impacting regulation of various physiological processes. In this work, we developed an approach to encapsulate enzymes at high loading capacity, which precisely controls the oxygen content in cell culture. Here, a single microcapsule is able to locally perturb the oxygen balance, and varying the concentration and distribution of matrix-embedded microcapsules provides spatiotemporal control. We demonstrate attenuation of hypoxia signaling in populations of stem cells, cancer cells, endothelial cells, cancer spheroids, and intestinal organoids. Varying capsule placement, media formulation, and timing of replenishment yields tunable oxygen gradients, with concurrent spatial growth and morphogenesis in a single well. Capsule containing hydrogel films applied to chick chorioallantoic membranes encourages neovascularization, providing scope for topical treatments or hydrogel wound dressings. This platform can be used in a variety of formats, including deposition in hydrogels, as granular solids for 3D bioprinting, and as injectable biomaterials. Overall, this platform's simplicity and flexibility will prove useful for fundamental studies of oxygen-mediated processes in virtually any in vitro or in vivo format, with scope for inclusion in biomedical materials for treating injury or disease.
