Esophageal cancer is one of the most common cancer types in humans worldwide. Photodynamic therapy (PDT) is a promising therapeutic strategy for the treatment of cancer. However, its underlying mechanism needs to be studied thoroughly. The present study focused on the antitumor effect and underlying mechanism of the use of hematoporphyrin derivative (HpD)‑PDT against human esophageal squamous cell carcinoma cells via regulation of the PI3K/AKT/mTOR signaling pathway. A Cell Counting Kit‑8 assay was used to measure cell viability. Migration was evaluated using a wound healing assay. An annexin V‑FITC/PI kit was used to determine cell apoptosis rates. Protein expression levels were analyzed via western blotting. Reverse transcription‑quantitative PCR was used to detect gene expression levels. A 2',7'‑dichlorodihydrofluorescein diacetate kit was chosen to evaluate intracellular reactive oxygen species levels via flow cytometry. Cell viability and migration were decreased in KYSE‑150 cells after HpD‑PDT treatment. Cellular apoptosis was induced after HpD‑PDT treatment, and the same trend was observed for autophagy. Furthermore, the PI3K/AKT/mTOR signaling pathway was inhibited. The viability and migration of KYSE‑150 cells were significantly inhibited, and apoptosis was induced more effectively following treatment with a combination of HpD‑PDT and the PI3K inhibitor, a final concentration of 20 µM LY294002. In conclusion, HpD‑PDT could suppress esophageal cancer cell viability, induce apoptosis and inhibit migration by downregulating the PI3K/AKT/mTOR signaling pathway. Combination of HpD‑PDT with PI3K inhibitor (LY294002) could enhance the therapeutic efficacy compared with that demonstrated by HpD‑PDT alone. Further studies on combination therapy are required to achieve improved clinical outcomes.

The rupture degree of a noncomplete connected graph G is defined by r(G) = max{/spl omega/(G - X) - |X| - m(G - X) : X /spl sub/ V(G), /spl omega/(G - X) /spl ges/ 2}, where /spl omega/(G - X) denotes the number of components in the graph G - X. For a complete graph K/sub n/, we define r(K/sub n/) = 1 - n. This parameter can be used to measure the vulnerability of a graph. To some extent, it represents a trade-off between the amount of work done to damage the network and how badly the network is damaged. In this paper, we prove that the problem of computing the rupture degree of a graph is NP-complete. We obtain the rupture degree of the Cartesian product of some special graphs and also give the exact values or bounds for the rupture degrees of Harary graphs.

The relationship between the spatial cell and the object is unknown for the Cartesian grid using the immersed boundary method. For the researches about complex geometry or multi-body relative motion, grid generation is a very time-consuming work, and the consumption is mainly concentrated in the position determination of the Cartesian cells, which we called the cell type determination. In this study, based on the axis-aligned bounding box method and the ray casting method, we employed the dot product method and the painting algorithm to investigate the acceleration method for Cartesian grid generation. The octree structure is used to store the Cartesian cells, and the k-dimensional tree is used to store the object surface. These data management strategy can minimize the CPU’s resource while have a small memory usage. The grid generation results show that the strategy we proposed has a high efficiency and well robustness, and the time consume can reduce more than 50% compare with the original method. When dealing with a enough complex problem, the time consume can even reaches several orders of magnitude difference compared with the original method.