A Three-Dimensional Circuit Model of the Middle Ear

A circuit model with lumped elements has been developed that is able to predict spatial vibrations in the middle ear. The model focuses on the ossicular chain, not on the eardrum. It describes translational and rotational velocities, forces, and torques at various locations. Basically the model uses three main units: it treats the eardrum as "source", malleus and incus as "interposition", and the stapes as "load".

The spatial components are associated with ports as used in classical network theory. According to the six degrees of freedom, the source and the load have six ports for three rotational and three translational components. The interposition has six input and six output ports. This basic SIL- (Source/Interposition/Load-) structure can be extended to include further details, such as joints and additional suspensions by ligaments and muscles.

The movements of each unit are described in its own reference frame. The relative position of the different units can be varied by rotation of reference frames. This operation can also be interpreted as a linear system with six input and six output ports; it thus preserves the structure of a circuit model. To analyze the circuit, all units and operations are best described by matrix equations. A single matrix inversion is necessary to obtain all mechanical quantities desired.

As an example of an application, we investigated what happens if the ossicles are not coupled in their normal position, but obliquely. It turns out that the normal middle ear is very insensitive to oblique coupling of stapes and incus.