Numerical optimisation of chemotherapy dosage under antiangiogenic treatment in the presence of drug resistance

We consider a two-compartment model of chemotherapy resistant tumour growth under angiogenic signalling. Our model is based on the one proposed by Hahnfeldt et al. (1999), but we divide tumour cells into sensitive and resistant subpopulations. We study the influence of antiangiogenic treatment in combination with chemotherapy. The main goal is to investigate how sensitive are the theoretically optimal protocols to changes in parameters quantifying the interactions between tumour cells in the sensitive and resistant compartments, that is, the competition coefficients and mutation rates, and whether inclusion of an antiangiogenic treatment affects these results. Global existence and positivity of solutions and bifurcations (including bistability and hysteresis) with respect to the chemotherapy dose are studied. We assume that the antiangiogenic agents are supplied indefinitely and at a constant rate. Two optimisation problems are then considered. In the first problem a constant, indefinite chemotherapy dose is optimised to maximise the time needed for the tumour to reach a critical (fatal) volume. It is shown that maximum survival time is generally obtained for intermediate drug dose. Moreover, the competition coefficients have a more visible influence on survival time than the mutation rates. In the second problem, an optimal dosage over a short, 30-day time period, is found. A novel, explicit running penalty for drug resistance is included in the objective functional. It is concluded that, after an initial full-dose interval, an administration of intermediate dose is optimal over a broad range of parameters. Moreover, mutation rates play an important role in deciding which short-term protocol is optimal. These results are independent of whether antiangiogenic treatment is applied or not.     

Current air quality analytics and monitoring: A review

This review summarizes the different tools and concepts that are commonly applied in air quality monitoring. The monitoring of atmosphere is extremely important as the air quality is an important problem for large communities. Main requirements for analytical devices used for monitoring include a long period of autonomic operation and portability. These instruments, however, are often characterized by poor analytical performance. Monitoring networks are the most common tools used for monitoring, so large-scale monitoring programmes are summarized here. Biomonitoring, as a cheap and convenient alternative to traditional sample collection, is becoming more and more popular, although its main drawback is the lack of standard procedures. Telemonitoring is another approach to air monitoring, which offers some interesting opportunities, such as ease of coverage of large or remote areas, constituting a complementary approach to traditional strategies; however, it requires huge costs.     

The Effects of Ring Strain on Cyclic Tetraaryl[5]cumulenes

Cyclic tetraaryl[5]cumulenes ( 1 a–f ) have been synthesized and studied as a function of increasing ring strain. The magnitude of ring strain is approximated by the extent of bending of the cumulenic core as assessed by a combination of X-ray crystallographic analysis and DFT calculations. Trends are observed in ¹³C NMR, UV-vis, and Raman spectra associated with ring strain, but the effects are small. In particular, the experimental HOMO-LUMO gap is not appreciably affected by bending of the [5]cumulene framework from ca. 174° (λ_max=504 nm) in 1 a to ca. 178° (λ_max=494 nm) in 1 f .     

Correction to: Differences in the Efficiency of Separation of Analgesic Drugs by High-Performance Thin-Layer Chromatography with Similar Octadecyl Silica-Based Adsorbents

JPC – Journal of Planar Chromatography – Modern TLC -     

Optimal double control problem for a PDE model of goodwill dynamics

We propose a new optimal control model of product goodwill in a segmented market where the state variable behaviour is described by a partial differential equation of the Lotka–Sharp–McKendrick type. In order to maximize the sum of discounted profits over a finite time horizon, we control the marketing communication activities which influence the state equation and the boundary condition. Moreover, we introduce the mathematical representation of heterogeneous electronic word of mouth. Based on the semigroup approach, we prove the existence and uniqueness of optimal controls. Using a maximum principle, we describe a numerical algorithm to find the optimal solution. Finally, we examine several examples on the optimal goodwill model and discover two types of marketing strategies.     

The Role of Singlet Oxygen in Photoreactivity and Phototoxicity of Curcumin

Curcumin is a plant-derived yellow-orange compound widely used as a spice, dye and food additive. It is also believed to have therapeutic effects against different disorders. On the other hand, there are data showing its phototoxicity against bacteria, fungi and various mammalian cells. Since the mechanism of its phototoxic action is not fully understood, we investigated here the phototoxic potential of curcumin in liposomal model membranes and in HaCaT cells. First, detection of singlet oxygen (¹O₂) luminescence proved that curcumin generates ¹O₂ upon blue light irradiation in organic solvent and in liposomes. Then, HPLC-EC(Hg) measurements revealed that liposomal and cellular cholesterol is oxidized by ¹O₂ photogenerated by curcumin. Enrichment of liposome membranes with curcumin significantly increased the oxygen photo-consumption rate compared to the control liposomes as determined by EPR oximetry. Cytotoxicity measurements, mitochondrial membrane potential analyses and protein hydroperoxides detection confirmed strong phototoxic effects of curcumin in irradiated HaCaT cells. These data show that since curcumin is advertised as a valuable dietary supplement, or a component of cosmetics for topical use, caution should be recommended especially when skin is exposed to light.     

Investigation of Parameters Influencing Tubular-Shaped Chitosan-Hydroxyapatite Layer Electrodeposition

Tubular-shaped layer electrodeposition from chitosan-hydroxyapatite colloidal solutions has found application in the field of regeneration or replacement of cylindrical tissues and organs, especially peripheral nerve tissue regeneration. Nevertheless, the quantitative and qualitative characterisation of this phenomenon has not been described. In this work, the colloidal systems are subjected to the action of an electric current initiated at different voltages. Parameters of the electrodeposition process (i.e., total charge exchanged, gas volume, and deposit thickness) are monitored over time. Deposit structures are investigated by scanning electron microscopy (SEM) and Fourier-transform infrared spectroscopy (FTIR). The value of voltage influences structural characteristics but not thickness of deposit for the process lasting at least 20 min. The calculated number of exchanged electrons for studied conditions suggests that the mechanism of deposit formation is governed not only by water electrolysis but also interactions between formed hydroxide ions and calcium ions coordinated by chitosan chains.