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Using the Maxwell Stress Tensor to Move Towards Predictive Magnetic Field Shaping in 3D

A Shutler*, I Rutel , University of Oklahoma Health Science Center, Oklahoma City, OK


(Sunday, 7/29/2018) 4:00 PM - 4:30 PM

Room: Exhibit Hall | Forum 9

Purpose: By understanding how to manipulate the equivalent-force vectors of a magnetic field space, we can move towards predictive techniques of field shaping to applying the force gradient of our choosing to a point in space. We can use this with targeted drug delivery therapies involving superparamagnetic iron oxide nanoparticles (SPION) in order to provide a non-invasive technique to isolate a tissue target.

Methods: We demonstrate computation of the force equivalent vector field by applying a simplified Maxwell stress tensor (MST) to a 3D magnetic field space (setting electric fields to zero). From this generalized force equation, we then apply the tensor and compute the forward derivative to arrive at the equivalent force. To compute the gradient, we implement a next-next nearest neighbor (NNNN) method to increase computational efficiency while performing computations in all directions. Data handling techniques for large amounts of vector field spaces are also explored. The method is demonstrated by performed calculations across a simulated magnetic field space, and then practical applications using an experimental set up are shown.

Results: For a sample 5x5x5 magnetic field that grows isotropically, the MST method is found to produce equivalent force vectors in the appropriate direction with a constant gradient. The MST method can be applied to physical magnets to show how the process of magnetization produces a field that varies along all directions, but when collapsed down via projections to a single axis, produces results stated by the manufacturer. This is an important result to use and understand when trying to develop a physical system of magnets to use for field-shaping.

Conclusion: This work provides the underlying work for computing force fields in any space where the step size between measurements is known, and can be generalized to any arbitrary time-invariant electromagnetic fields in 1-, 2-, or 3D.


Magnetic Fields, Simulation, Software


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