Computational Modeling of Electromagnetic and Thermal Effects for a Dual-Unit Retinal Prosthesis: Inductive Telemetry, Temperature Increase, and Current Densities in the Retina - Artificial Sight: Basic Research, Biomedical Engineering, and Clinical Advances - page 281

here as examples for the retinal prosthesis under consideration. However, the
methods discussed and presented are general and applicable to many different
coil configurations and applications.
There have been several approaches to the analysis and design of inductively
coupled transcutaneous links, with the goal of minimizing misalignment effects
and maximizing the coupling efficiency [6-10]. In many cases, an analytical
static approximation, based on the Partial Inductance concept [11], can be used
successfully to calculate the mutual and self-inductance of coupled coils. The
PIM can only provide an estimate for the coupling between external coils and
coils implanted inside the eye of a human head model since it ignores the
presence of the human tissue. However, at low frequencies it is very suitable for
maximizing the coupling efficiency of inductive links and observing the effects
of implant motion and misalignment. This method provides a very simple and
efficient free-space analysis of inductively coupled wire traces and, due to its
simplicity and capabilities, will be briefly illustrated here.

Partial Inductance Method
The inductive interaction between conductors carrying currents is caused by
electrodynamic effects, which take place concurrently: currents flowing through
conductors create magnetic fields (Ampere's Law); time-varying magnetic fields
create induced electric fields (Faraday's Law). The inductive coupling of
complex geometric structures and open loops can be calculated using the Partial
Inductance concept [11-13]. Figure 15.1 illustrates two inductively coupled
current loops.
The inductance between two wire loops i and j is be defined as L ij ≡

ij
I j

, where

a i i a i A ij · a j j a j

I j d l j da j

1

4

the mutually coupled flux is ij =

r ij is
the magnetic vector potential in loop i due to the current in loop j. Thus, the
mutual inductance between two wires can be written as

d l i da i . A ij =

d l j • d l i

4a i a j

L ij = da j da i (1)

r ij a i a j l i l j

Figure 15.1. Decomposition of current loops into segments of partial inductances.