Motion of Magnetic Microcapsules Through Capillaries in the Presence of a Magnetic Field: From a Mathematical Model to an In Vivo Experiment

In this paper, we discuss the prediction of the delivery efficiency of magnetic carriers based on their properties and field parameters. We developed a theory describing the behavior of magnetic capsules in the capillaries of living systems. A partial differential equation for the spatial distribution of magnetic capsules has been obtained. We propose to characterize the interaction between the magnetic field and the capsules using a single vector, which we call “specific magnetic force”. To test our theory, we performed experiments on a model of a capillary bed and on a living organism with two types of magnetic capsules that differ in size and amount of magnetic material. The experimental results show that the distribution of the capsules in the field correlated with the theory, but there were fewer actually accumulated capsules than predicted by the theory. In the weaker fields, the difference was more significant than in stronger ones. We proposed an explanation for this phenomenon based on the assumption that a certain level of magnetic force is needed to keep the capsules close to the capillary wall. We also suggested a formula for the relationship between the probability of capsule precipitation and the magnetic force. We found the effective value of a specific magnetic force at which all the capsules attracted by the magnet reach the capillary wall. This value can be considered as the minimum level for the field at which it is, in principle, possible to achieve a significant magnetic control effect. We demonstrated that for each type of capsule, there is a specific radius of magnet for which the effective magnetic force is achieved at the largest possible distance from the magnet’s surface. For the capsules examined in this study, the maximum distance where the effective field can be achieved does not exceed 1.5 cm. The results of the study contribute to our understanding of the behavior of magnetic particles in the capillaries of living organisms when exposed to a magnetic field.