Numerical optimal control of a size-structured PDE model for metastatic cancer treatment.

In this paper, we propose a unified size-structured PDE model for the growth of metastatic tumors, which extends a well-known coupled ODE-PDE dynamical model developed and studied in the literature. A treatment model based on the proposed unified PDE model is investigated via optimal control theory, where its first-order necessary optimality system characterizing the optimal control is derived. We prove that the uniqueness of the optimal control depends on the chosen objective functional, and the optimal control is of bang-bang type when it is unique. For obtaining its efficient numerical solutions, a projection gradient descent algorithm based on the characteristic scheme is developed for solving the established optimal treatment model. Several numerical examples are provided to validate our mathematical analysis and numerical algorithm, and also illustrate the biologically interesting treatment outcomes of different models and control strategies. Our simple model reveals that: (i) only the total drug dosage matters if one just cares about the final treatment output; (ii) given the same total drug dosage, the optimal bang-bang treatment plan outperforms the others in the sense that it maximally reduces the total tumor sizes during the whole period of treatment, although their final tumor sizes are the same.

Serum endocan levels are correlated with the presence and severity of coronary artery disease in patients with hypertension.

BACKGROUND: Endothelial dysfunction is one of the most important early indicators of atherosclerosis in hypertension (HT) patients. Endocan has been reported to play a role in the pathophysiology of endothelial dysfunction. OBJECTIVE: We sought to assess whether serum endocan levels are correlated with the presence and severity of coronary artery disease (CAD) in patients with HT. METHODS: We measured endocan levels in 164 patients with HT and in 55 controls. The severity of CAD was assessed by the coronary atherosclerosis index scores. RESULTS: Serum endocan levels were independently correlated with the presence and severity of CAD in HT patients. CONCLUSION: Endocan might function as a useful biomarker for monitoring the development and progression of CAD in HT patients.

In vitro study of the cytotoxicities of two mixed-ligand oxovanadium complexes on human hepatoma cells.

The cytotoxicities of two oxovanadium complexes, VOI [VO(satsc)(phen)] (satsc = salicylaldehyde thiosemicarbazone, phen = 1,10-phenanthroline) and VOII [VO(3,5-dibrsatsc)(phen)](3,5-dibrsatsc = 3,5-dibromosalicylaldehyde thiosemicarbazone), were studied by performing MTT assays on human hepatoma cell lines BEL-7402, HUH-7 and HepG2. The results showed that both the VOI and VOII complexes possess significant anti-proliferative effects. In addition, the anti-proliferative mechanism of the complexes was analyzed by cell cycle analysis and an apoptosis assay and by detecting the mitochondrial membrane potential (delta psi m). The experimental results showed that the complexes can cause a G0/G1 phase cell cycle arrest and can significantly decrease delta psi m, causing depolarization of the mitochondrial membrane. Notably, the two complexes induced apoptosis in BEL-7402 cells and displayed typical morphological apoptotic characteristics. The cytotoxicities of the VOII complex are significantly stronger than that of the VOI complex, suggesting that the cytotoxic effects of oxovanadium complexes may be associated with the electronic effects of the complexes.