Modelling the effect of SPION size in a stent assisted magnetic drug targeting system with interparticle interactions.

Cancer is a leading cause of death worldwide and it is caused by the interaction of genomic, environmental, and lifestyle factors. Although chemotherapy is one way of treating cancers, it also damages healthy cells and may cause severe side effects. Therefore, it is beneficial in drug delivery in the human body to increase the proportion of the drugs at the target site while limiting its exposure at the rest of body through Magnetic Drug Targeting (MDT). Superparamagnetic iron oxide nanoparticles (SPIONs) are derived from polyol methods and coated with oleic acid and can be used as magnetic drug carrier particles (MDCPs) in an MDT system. Here, we develop a mathematical model for studying the interactions between the MDCPs enriched with three different diameters of SPIONs (6.6, 11.6, and 17.8 nm) in the MDT system with an implanted magnetizable stent using different magnetic field strengths and blood velocities. Our computational analysis allows for the optimal design of the SPIONs enriched MDCPs to be used in clinical applications.

Low-field susceptibility of classical Heisenberg chains with arbitrary and different nearest-neighbour exchange.

Interest in molecular magnets continues to grow, offering a link between the atomic and nanoscale properties. The classical Heisenberg model has been effective in modelling exchange interactions in such systems. In this, the magnetization and susceptibility are calculated through the partition function, where the Hamiltonian contains both Zeeman and exchange energy. For an ensemble of N spins, this requires integrals in 2N dimensions. For two, three and four spin nearest-neighbour chains these integrals reduce to sums of known functions. For the case of the three and four spin chains, the sums are equivalent to results of Joyce. Expanding these sums, the effect of the exchange on the linear susceptibility appears as Langevin functions with exchange term arguments. These expressions are generalized here to describe an N spin nearest-neighbour chain, where the exchange between each pair of nearest neighbours is different and arbitrary. For a common exchange constant, this reduces to the result of Fisher. The high-temperature expansion of the Langevin functions for the different exchange constants leads to agreement with the appropriate high-temperature quantum formula of Schmidt et al, when the spin number is large. Simulations are presented for open linear chains of three, four and five spins with up to four different exchange constants, illustrating how the exchange constants can be retrieved successfully.