Mathematical and computational models of drug transport in tumours

The ability to predict how far a drug will penetrate into the tumour microenvironment within its pharmacokinetic (PK) lifespan would provide valuable information about therapeutic response. As the PK profile is directly related to the route and schedule of drug administration, an in silico tool that can predict the drug administration schedule that results in optimal drug delivery to tumours would streamline clinical trial design. This paper investigates the application of mathematical and computational modelling techniques to help improve our understanding of the fundamental mechanisms underlying drug delivery, and compares the performance of a simple model with more complex approaches. Three models of drug transport are developed, all based on the same drug binding model and parametrized by bespoke in vitro experiments. Their predictions, compared for a ‘tumour cord’ geometry, are qualitatively and quantitatively similar. We assess the effect of varying the PK profile of the supplied drug, and the binding affinity of the drug to tumour cells, on the concentration of drug reaching cells and the accumulated exposure of cells to drug at arbitrary distances from a supplying blood vessel. This is a contribution towards developing a useful drug transport modelling tool for informing strategies for the treatment of tumour cells which are ‘pharmacokinetically resistant’ to chemotherapeutic strategies.     

Gold nanorods with finely tunable longitudinal surface plasmon resonance as SERS substrates

Advances in nanophotonics have shown the potential of colloidal metal nanoparticles with sharp tips, such as rods, to focalize plasmonic electromagnetic fields. We report on the synthesis of Au nanorods via a seed mediated approach and the influence of silver ions on the aspect ratio of the Au nanorods. The longitudinal surface plasmon resonance (LSPR) of the Au nanorods was successfully tuned with the concentration of silver ions. The surface enhanced Raman scattering (SERS) effect of 2-aminothiophenol (2-ATP) as a probe molecule on Au nanorods was systematically studied by varying the longitudinal surface plasmon resonance of the nanorods. The highest electromagnetic enhancement was observed when the longitudinal surface plasmon resonance of the Au nanorods overlapped with the laser excitation wavelength. The variation of the SERS enhancement factor with the longitudinal surface plasmon resonance and laser excitation lines is also discussed in detail.     

An Automatic Presence Service for Low Duty-Cycled Mobile Sensor Networks

We consider providing presence service for duty-cycled wireless sensor networks through a multihop approach. The presence service is to ensure automatic network monitoring by which each node would know whether the sink node is reachable or not. Towards providing such presence service, we tackle three problems: 1) efficient neighbor discovery due to not-always-awake nature of duty-cycling and the mobile environment, 2) light presence message passing from the sink node to all reachable nodes given broadcasting is expensive and difficult in an embedded duty-cycling network, and 3) automatic network monitoring if there is node failure and network partition. In our protocol, in order to save power consumption, an online node which is reachable from the sink node only book-keeps the broadcast schedule of its parent in a breadth-first-search spanning tree in order to trace the online status all along. The offline node which is not reachable from the sink node stays awake periodically based on quorum-based wakeup scheduling, and probes the beacons which may come from online nodes. The presence protocol can automatically detect link failure or network partition, and it can also automatically recover online status for each sensor node if there is a path to the sink node, which is significant for applications that are sensitive to end-to-end latency constraints. The presence protocol proposed is implemented through a layered approach so that it is independent from any specific MAC and routing protocols. We make extensive simulations in order to validate the energy efficiency and reliability of our design.     

Thermophysical studies on the binary system UO2(NO3)2·6H2O - Sr(NO3)2

Thermoanalytical (TG-DTA-EGA) and X-ray diffraction measurements have been used to study the reaction between uranyl nitrate hexahydrate and strontium nitrate. The results confirmed the absence of a direct interaction between the two compounds. The presence of strontium nitrate, however, ensured that the extent of hydrolysis and polymerisation of uranyl nitrate hexahydrate during its dehydration and decomposition to UO₃ is significantly reduced. DTA curves recorded in both heating and cooling modes gave evidence to the occurrence of a reaction between molten strontium nitrate and uranium trioxide to form nitrato-complexes of uranium and strontium. X-ray diffraction data on reaction residues obtained at different temperatures and cooled to room temperature also showed evidence for the formation of such complexes. The results obtained indicated an increase in thermal stability of these nitrato-complexes with increase in Sr/U ratio. The complex with an Sr/U ratio of 2.0 is stable up to 660 °C and the complex with Sr/U ratio of 4.0 is stable up to 680 °C. These complexes decompose at higher temperatures to give strontium uranates.     

Liquid-waste injection planning via goal programming

In this paper, applications of linear goal programming techniques to the analysis of design, management and operational problems in the deep-well injection industry are investigated. Deep-well injection is a method of hazardous waste disposal where liquid or liquefiable wastes are pumped under controlled rate and pressure into confined formations that have no other potential use. A typical liquid waste injection system is modeled as a linear goal program to study and resolve the effects of conflicting objectives such as cost, environmental regulations, equipment utilization and waste-water quality requirements before injection.

The model is validated using actual data obtained from a waste-water disposal complex in Odessa, Texas. The goal program is solved for the best disposal system design and operating policies that would not only enable the plant to meet the Environmental Protection Agency's standards, but best minimize capital investment, annual operating expense and deviations from the waste-water quality requirements before injection. Justification of the use of the model is presented by comparing the actual design and operating policies of the system with the optimal design obtained from the solution of the model. This comparison showed 40% savings in favor of the design predicted by the model.     

A Differential CMOS Current-Mode Variable Gain Amplifier with Digital dB-Linear Gain Control

A novel CMOS variable gain amplifier operating on current signals with a dB-linear gain control is presented. The gain control is achieved by multiplying a digitally synthesized exponentially varying control current signal by a differential input signal in the current domain. A current amplifier at the output sets the gain to the desired level. Current-mode operation allows for a reduced supply voltage by minimizing the voltage swing at the low impedance nodes of the circuit. Multiple circuit realizations for various blocks are presented allowing for designs meeting different constraints. Experimental realization of the variable gain amplifier shows the validity of the presented approach.     

A Multiple Objective Nurse Scheduling Model

The authors present a model for the nurse scheduling problem which works in two phases. In the first phase, the nurses are assigned their day-on/day-off pattern for the two-week scheduling horizon by a goal programming model which allows for consideration of the multiple conflicting objectives inherent in scheduling a nursing staff. The second phase makes specific shift assignments through the use of a heuristic procedure. The two-phase approach results in considerable reductions in problem size, thus reducing the solution effort. Extensions to the basic model are also examined.     

An algorithm for hidden line ruled surface display using microprocessor

A simple algorithm for hidden line Ruled Surface graphics, typically used in Radio Astronomy is discussed using low cost microcomputer system built around Motorola 6800 processor and Matrox 256**2 graphics module of raster size 256 × 256 points. Resolution of the plot can be improved by displaying on a bigger raster like 1024 × 1024 points.