# Sensory Systems/Vestibular Signal Processing

## Signal Processing

### Peripheral Signal Transduction

#### Transduction of Linear Acceleration

The hair cells of the otolith organs are responsible for the transduction of a mechanical force induced by linear acceleration into an electrical signal. Since this force is the product of gravity plus linear movements of the head

${\displaystyle {\vec {F}}={\vec {F}}_{g}+{\vec {F}}_{inertial}=m({\vec {g}}-{\frac {d^{2}{\vec {x}}}{dt^{2}}})}$

it is therefore sometimes referred to as gravito-inertial force. The mechanism of transduction works roughly as follows: The otoconia, calcium carbonate crystals in the top layer of the otoconia membrane, have a higher specific density than the surrounding materials. Thus a linear acceleration leads to a displacement of the otoconia layer relative to the connective tissue. The displacement is sensed by the hair cells. The bending of the hairs then polarizes the cell and induces afferent excitation or inhibition.

Excitation (red) and inhibition (blue) on utricle (left) and saccule (right), when the head is in a right-ear-down orientation. The displacement of the otoliths was calculated with the finite element technique, and the orientation of the haircells was taken from the literature.

While each of the three semicircular canals senses only one-dimensional component of rotational acceleration, linear acceleration may produce a complex pattern of inhibition and excitation across the maculae of both the utricle and saccule. The saccule is located on the medial wall of the vestibule of the labyrinth in the spherical recess and has its macula oriented vertically. The utricle is located above the saccule in the elliptical recess of the vestibule, and its macula is oriented roughly horizontally when the head is upright. Within each macula, the kinocilia of the hair cells are oriented in all possible directions.

Therefore, under linear acceleration with the head in the upright position, the saccular macula is sensing acceleration components in the vertical plane, while the utricular macula is encoding acceleration in all directions in the horizontal plane. The otolthic membrane is soft enough that each hair cell is deflected proportional to the local force direction. If denotes the direction of maximum sensitivity or on-direction of the hair cell, and the gravito-inertial force, the stimulation by static accelerations is given by

${\displaystyle stim_{otolith}={\vec {F}}\cdot {\vec {n}}}$

The direction and magnitude of the total acceleration is then determined from the excitation pattern on the otolith maculae.

#### Transduction of Angular Acceleration

The three semicircular canals are responsible for the sensing of angular accelerations. When the head accelerates in the plane of a semicircular canal, inertia causes the endolymph in the canal to lag behind the motion of the membranous canal. Relative to the canal walls, the endolymph effectively moves in the opposite direction as the head, pushing and distorting the elastic cupula. Hair cells are arrayed beneath the cupula on the surface of the crista and have their stereocilia projecting into the cupula. They are therefore excited or inhibited depending on the direction of the acceleration.

The stimulation of a human semicircular canal is proportional to the scalar product between a vector n (which is perpendicular to the plane of the canal), and the vector omega indicating the angular velocity.

This facilitates the interpretation of canal signals: if the orientation of a semicircular canal is described by the unit vector ${\displaystyle {\vec {n}}}$, the stimulation of the canal is proportional to the projection of the angular velocity ${\displaystyle {\vec {\omega }}}$ onto this canal

${\displaystyle stim_{canal}={\vec {\omega }}\cdot {\vec {n}}}$

The horizontal semicircular canal is responsible for sensing accelerations around a vertical axis, i.e. the neck. The anterior and posterior semicircular canals detect rotations of the head in the sagittal plane, as when nodding, and in the frontal plane, as when cartwheeling.

In a given cupula, all the hair cells are oriented in the same direction. The semicircular canals of both sides also work as a push-pull system. For example, because the right and the left horizontal canal cristae are “mirror opposites” of each other, they always have opposing (push-pull principle) responses to horizontal rotations of the head. Rapid rotation of the head toward the left causes depolarization of hair cells in the left horizontal canal's ampulla and increased firing of action potentials in the neurons that innervate the left horizontal canal. That same leftward rotation of the head simultaneously causes a hyperpolarization of the hair cells in the right horizontal canal's ampulla and decreases the rate of firing of action potentials in the neurons that innervate the horizontal canal of the right ear. Because of this mirror configuration, not only the right and left horizontal canals form a push-pull pair but also the right anterior canal with the left posterior canal (RALP), and the left anterior with the right posterior (LARP).

### Central Vestibular Pathways

The information resulting from the vestibular system is carried to the brain, together with the auditory information from the cochlea, by the vestibulocochlear nerve, which is the eighth of twelve cranial nerves. The cell bodies of the bipolar afferent neurons that innervate the hair cells in the maculae and cristae in the vestibular labyrinth reside near the internal auditory meatus in the vestibular ganglion (also called Scarpa's ganglion, Figure Figure 10.1). The centrally projecting axons from the vestibular ganglion come together with axons projecting from the auditory neurons to form the eighth nerve, which runs through the internal auditory meatus together with the facial nerve. The primary afferent vestibular neurons project to the four vestibular nuclei that constitute the vestibular nuclear complex in the brainstem.

### Vestibulo-Ocular Reflex (VOR)

An extensively studied example of function of the vestibular system is the vestibulo-ocular reflex (VOR). The function of the VOR is to stabilize the image during rotation of the head. This requires the maintenance of stable eye position during horizontal, vertical and torsional head rotations. When the head rotates with a certain speed and direction, the eyes rotate with the same speed but in the opposite direction. Since head movements are present all the time, the VOR is very important for stabilizing vision.

How does the VOR work? The vestibular system signals how fast the head is rotating and the oculomotor system uses this information to stabilize the eyes in order to keep the visual image motionless on the retina. The vestibular nerves project from the vestibular ganglion to the vestibular nuclear complex, where the vestibular nuclei integrate signals from the vestibular organs with those from the spinal cord, cerebellum, and the visual system. From these nuclei, fibers cross to the contralateral abducens nucleus. There they synapse with two additional pathways. One pathway projects directly to the lateral rectus muscle of eye via the abducens nerve. Another nerve tract projects from the abducens nucleus by the abducens interneurons to the oculomotor nuclei, which contain motor neurons that drive eye muscle activity, specifically activating the medial rectus muscles of the eye through the oculomotor nerve. This short latency connection is sometimes referred to as three-neuron-arc, and allows an eye movement within less than 10 ms after the onset of the head movement.

For example, when the head rotates rightward, the following occurs. The right horizontal canal hair cells depolarize and the left hyperpolarize. The right vestibular afferent activity therefore increases while the left decreases. The vestibulocochlear nerve then carries this information to the brainstem and the right vestibular nuclei activity increases while the left decreases. This makes in turn neurons of the left abducens nucleus and the right oculomotor nucleus fire at higher rate. Those in the left oculomotor nucleus and the right abducens nucleus fire at a lower rate. This results in the fact than the left lateral rectus extraocular muscle and the right medial rectus contract while the left medial rectus and the right lateral rectus relax. Thus, both eyes rotate leftward.

The gain of the VOR is defined as the change in the eye angle divided by the change in the head angle during the head turn

${\displaystyle gain={\frac {\Delta _{Eye}}{\Delta _{Head}}}}$

If the gain of the VOR is wrong, that is, different than one, then head movements result in image motion on the retina, resulting in blurred vision. Under such conditions, motor learning adjusts the gain of the VOR to produce more accurate eye motion. Thereby the cerebellum plays an important role in motor learning.