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Vestibular system – A Tutorial

[Sara Kangarloo, Masters student at K. N. Toosi University of Technology Contact: s.kangarloo@email.kntu.ac.ir]

Most kids learn about the 5 basic extrinsic senses of sight, sound, taste, touch, and

smell. Many, however, are not as familiar with two hidden intrinsic senses: the balance and proprioceptive senses. The balance sense is one of the first to develop in a growing. By only 5 months in utero, this system is well developed and provides a great deal of sensory information to a growing fetal brain. It is very important to relay information to the brain as to where a person is in space, as related to gravity; whether they are moving or still, if they are moving how quickly, and in what direction. It is a reflex system that allows us to maintain awareness of our spatial orientation at all times, and react to it. Without it, we could not walk upright or follow objects with our eyes when we are moving.

Balance

A body is balanced when it is stationary. That means there must be no net force or torque. Hence, any forces and/or torques on the body must be canceled or balanced by opposing forces and/or torques.

Stability is the ability of a body to restore its balance after a disturbance (change in position or orientation). The quality of the stability is determined by how large a disturbance the body can withstand before the balance is lost. A body that is precariously balanced can withstand only a small disturbance and so has low stability. A body that is solidly balanced can be disturbed greatly and so has high stability.

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Gyroscope

Gyroscope physics is one of the most difficult to understand in related to the balance concept. But it can be useful to learn about the way to balance your body.

But before getting into the details of that, it's a good idea to see how a gyroscope works (if you haven't already). As you've probably noticed, a gyroscope can behave very similar to a spinning top. Therefore, the physics of gyroscopes can be applied directly to a spinning top.

To start off, let's illustrate a typical gyroscope using a schematic as shown below.

Figure1. Typical gyro (https://www.real-world-physics-problems.com)

Where:

ws is the constant rate of spin of the wheel, in radians/second

wp is the constant rate of precession, in radians/second

L is the length of the rod

r is the radius of the wheel θ is the angle between the vertical and the rod (a constant)

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As the wheel spins at a rate ws, the gyroscope precesses at a rate wp about the pivot

at the base (with θ constant).

The question is why doesn't the gyroscope fall down due to gravity?! The reason is this:

Due to the combined rotation ws and wp, the particles in the top half of the spinning

wheel experience a component of acceleration a1 normal to the wheel (with distribution

as shown in the figure below), and the particles in the bottom half of the wheel experience a component of acceleration a2 normal to the wheel in the opposite direction

(with distribution as shown). Due to Newton’s second law, this means that a net force F1 must act on the particles in the top half of the wheel, and a net force F2 must

act on the particles in the bottom half of the wheel. These forces act in opposite directions. Therefore a clockwise torque M is needed to sustain these forces. The force

of gravity pulling down on the gyroscope creates the necessary clockwise torque M.

Figure2. Gyro acceleration and force (https://www.real-world-physics-problems.com)

In other words, due to the nature of the kinematics, the particles in the wheel experience

acceleration in such a way that the force of gravity is able to maintain the angle θ of the

gyroscope as it precesses. This is the most basic explanation behind the gyroscope physics. As an analogy, consider a particle moving around in a circle at a constant velocity. The acceleration of the particle is towards the center of the circle (centripetal acceleration), which is perpendicular to the velocity of the particle (tangent to the circle). This may seem counter-intuitive, but the lesson here is that the acceleration of an object can act

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in a direction that is very different from the direction of motion. This can result in some

interesting physics, such as a gyroscope not falling over due to gravity as it precesses. So now that we have an intuitive "feel" for the physics, we can analyze it in full using a mathematical approach. We will hence determine the equation of motion for the gyroscope.

Gyroscope Physics – Analysis

The general schematic for analyzing the physics is shown below.

Figure3. The Gyro analysis (https://www.real-world-physics-problems.com)

Where g is the acceleration due to gravity, point G is the center of mass of the wheel,

and point P is the pivot location at the base.

The global axes XYZ is fixed to ground and has origin at P. I, J, and K are defined as unit vectors pointing along the positive X, Y, and Z axis

respectively.

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𝒘𝒘⃗⃗⃗⃗⃗⃗ = (𝒘𝒔 𝐬𝐢𝐧𝜽)�̂� + (𝒘𝒔 𝐜𝐨𝐬𝜽 + 𝒘𝒑 )𝑲 ̂ [𝟏]

The angular velocity of the wheel, with respect to ground, is

𝒂𝒘⃗⃗⃗⃗ ⃗ =

𝒅𝒘𝒘⃗⃗⃗⃗⃗⃗

𝒅𝒕=

𝒅[(𝒘𝒔 𝒔𝒊𝒏𝜽)�̂� + (𝒘𝒔 𝐜𝐨𝐬 𝜽 + 𝒘𝒑 )�̂�]

𝒅𝒕

=𝒅[(𝒘𝒔 𝐬𝐢𝐧𝜽)�̂�]

𝒅𝒕+

𝒅[(𝒘𝒔 𝐜𝐨𝐬𝜽 + 𝒘𝒑 )�̂�]

𝒅𝒕 [𝟐]

Looking at the first term:

𝒅[(𝒘𝒔 𝐬𝐢𝐧𝜽)�̂�]

𝒅𝒕

=𝒅[(𝒘𝒔 𝐬𝐢𝐧𝜽)]

𝒅𝒕�̂� + 𝒘𝒔 𝐬𝐢𝐧𝜽

𝒅�̂�

𝒅𝒕 [𝟑]

= 0 = −𝑤𝑝�̂�

Looking at the second term:

𝒅[(𝒘𝒔 𝐜𝐨𝐬𝜽 +𝒘𝒑)�̂�]

𝒅𝒕

=𝒅[(𝒘𝒔 𝐜𝐨𝐬𝜽 +𝒘𝒑)]

𝒅𝒕 �̂� + (𝒘𝒔 𝐜𝐨𝐬𝜽 +𝒘𝒑)

𝒅�̂�

𝒅𝒕 [𝟒]

= 0 = 0

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Therefore,

𝒂𝒘⃗⃗⃗⃗ ⃗ = −𝒘𝒔𝒘𝒑 𝐬𝐢𝐧 𝜽 �̂� [𝟓]

The angular velocity of the rod, with respect to ground, is

𝒘𝒓⃗⃗⃗⃗ ⃗ = 𝒘𝒑�̂� [𝟔]

The angular acceleration of the rod, with respect to ground, is zero since wr is constant

and does not change direction.

Note that the terms dJ

dt and

dK

dt (given above) are calculated using vector

differentiation.

All living organisms monitor their environment and one important aspect of that

environment is gravity and the orientation of the body with respect to gravity. In addition,

animals that locomote must be able to adjust their orientation with respect to self-

generated movements, as well as forces that are exerted upon them from the outside

world.

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Balance in human is achieved and maintained by a complex set of sensorimotor

control systems that include sensory input from vision (sight), proprioception (touch), and the vestibular system (motion, equilibrium, spatial orientation); integration of that sensory input; and motor output to the eye and body muscles. Injury, disease, certain drugs, or the aging process can affect one or more of these components.

In addition to the contribution of sensory information, there may also be psychological factors that impair our sense of balance.

Figure4. Contribution of sensory information in case of balance and motor control (https://neupsykey.com/vestibular-system-disorders)

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Vestibular System

The vestibular system engages a number of reflex pathways that are responsible for making compensatory movements and adjustments in body position. It also engages pathways that project to the cortex to provide perceptions of gravity and movement. At first we begin with a description of the components of the peripheral sensory apparatus and describe the ways in which specialized receptors transduce mechanical signals into electrical events. At second describe the projections of the vestibular afferents to the vestibular nuclei, and projection pathways from the vestibular nuclei to other brain structures such as the cerebellum.

Figure5. Structure of the ear (https://slideplayer.com)

The membranous labyrinth of the inner ear consists of three semicircular ducts (horizontal, anterior and posterior), two otolith organs (saccule and utricle), and the cochlea (which is discussed in Auditory System: Structure and Function).

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The Semicircular Ducts

These sensory organs respond to angular acceleration. The ampulla is a localized dilatation at one end of the semicircular duct. A patch of innervated hair cells is found at the base of the ampulla in a structure termed a crista (meaning crest). The crista contains hair cells with stereocilia oriented in a consistent direction. The cupula, a thin vane, sits atop this crest, filling the lumen of the semicircular duct. The stereocilia of the hair cells are embedded in the gelatinous cupula.

As the head rotates in one direction, inertia of the fluid causes it to lag, and hence generate relative motion in the semicircular duct in the direction opposite that of the head movement. This moving fluid bends the broad vane of the cupula. The stereocilia of the hair cells are bent because they are embedded in the gelatinous cupula.

Figure6. Each type of head movements is registered by a corresponding semicircular canal in the same plane of rotation. (https://2e.mindsmachine.com)

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Figure7. The semicircular canals detect angular accelerations of the head through displacement of the cupula This push-pull system allows us to sense all directions of rotation: while the right horizontal canal gets stimulated during head rotations to the right, the left horizontal canal gets stimulated by head rotations to the left. (www.dizziness-and-balance.com)

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Shearing of the hair cells opens potassium channels, as discussed previously. (See Figure 8).

Figure8. Each type of head movements is registered by a corresponding semicircular canal in the same plane of rotation. (https://nba.uth.tmc.edu/neuroscience)

There are three pairs of semicircular ducts, which are oriented roughly 90 degrees to each other for maximum ability to detect angular rotation of the head. Each slender duct has one ampulla. When the head turns, fluid in one or more semicircular ducts pushes against the cupula and bends the cilia of the hair cells. Fluid in the corresponding semicircular duct on the opposite side of the head moves in the opposite direction.

The basic transduction mechanism is the same in the auditory and vestibular systems. A mechanical stimulus bends the cilia of the hair cells. Fine thread-like tip links connect to trap doors in the adjacent cilium. Bending the hair cells stretches the tip link, causing an influx of K+ ions and the generation of neural impulses in the VIIIth cranial nerve.

Hair cells in the vestibular system are slightly different from those in the auditory system, in that vestibular hair cells have one tallest cilium, termed the kinocilium. Bending the stereocilia toward the kinocilium depolarizes the cell and results in increased afferent activity. Bending the stereocilia away from the kinocilium hyperpolarizes the cell and results in a decrease in afferent activity.

The semicircular ducts work in pairs to detect head movements (angular acceleration). A turn of the head excites the receptors in one ampulla and inhibits receptors in the ampulla on the other side.

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Figure 9.The Counteracting Influences of Bilateral Vestibular system. (https://nba.uth.tmc.edu/neuroscience)

Figure 9 is an extension of Figure 8 to show details from the horizontal semicircular ducts on both sides of the head. Beneath the ampullae are new details, which highlight the orientation of the stereocilia in both cristae and their outputs. The kinocilia are oriented in the direction of the ampullae (ampullo fugal) within the ducts on both sides. The two sides are mirror images. There is a constant low level of ionic influx into the body of the hair cells, so there is a steady-state receptor potential and a spontaneous low-level discharge of afferent activity. These neutral neurophysiological properties are shown in graphs below each ampulla.

Figure 9 is a diagram of the cranial nerves and their nuclei that mediate interactions between the vestibular system and eye muscles appears as an inset. A constant low level of spontaneous activity keeps all the muscles slightly and equally contracted, causing the eyes to look straight ahead. When the head turns, inertia causes the fluid to move more slowly than the head, generating relative fluid motion in the semicircular duct in the opposite direction of the head turn. This moving fluid, shown by arrows in the lumens of the semicircular duct, bends the hair cells on both sides of the head. Because the two sides are mirror images, the stereocilia are bent toward their kinocilium on one side and away from their kinocilium on the other side. Shearing of the stereocilia toward the kinocilium causes a depolarization of the receptor potential and an increase in afferent action potentials. There is an opposite effect on the other side – a decrease in afferent activity. These counteracting bilateral changes in afferent activity affect the vestibular and oculomotor nuclei. The ampullo fugal movement of fluid on the patient's right (reader's left) causes an increase in afferent activity (shown in green for "go" in the

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inset). This has a positive effect on the right medial and superior vestibular nuclei, which in turn stimulate the ipsilateral oculomotor and contralateral abducens nuclei. There are exactly opposite effects on the other side (shown in red for "stop" in the inset). The result of these combined counteracting effects is a smooth movement of the eyes toward the left, keeping the visual field stable as the head turns.

The Otoliths

Figure 10 illustrates the otolithic organs, the saccule and utricle to see the utricle at the top of Figure 10 and the saccule at the bottom. These two similar organs lie against the walls of the inner ear between the semicircular ducts and the cochlea. The receptors, called maculae (meaning "spot"), are patches of hair cells topped by small, calcium carbonate crystals called otoconia. The saccule and utricle lie at 90 degrees to each other. Thus, with any position of the head, gravity will bend the cilia of one patch of hair cells, due to the weight of the otoconia to which they are attached by a gelatinous layer. This bending of the cilia produces afferent activity going through the VIIIth nerve to the brainstem.

The utricle is most sensitive to tilt when the head is upright. The saccule is most sensitive to tilt when the head is horizontal. Unlike the semicircular ducts, the kinocilia of hair cells in the maculae are not oriented in a consistent direction. The kinocilia point toward (in the utricle) or away from (in the saccule) a middle line called the striola. The striola is shown as a dashed line in Figure 10. Because hair cells are oriented in different directions, tilts in any direction will activate some afferents.

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Figure10. Actions of the Static Vestibular Stimilation. (https://nba.uth.tmc.edu/neuroscience)

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Vestibulo-occular Reflex, Nystagmus, and Caloric Testing

The vestibulo-occular reflex (VOR) controls eye movements to stabilize images during head movements. As the head moves in one direction, the eyes reflexively move in the other direction. The VOR is only effective up to a speed of about 50o/sec. The action of the VOR can be seen by moving your head from side to side. The image you see is stable, despite the head movement. But as you increase the speed of oscillatory head movements, you can get to a rate of angular velocity where the VOR is no longer effective, and you will see the visual image start to shift. The VOR would occur in the dark, because the eyes move due to angular acceleration of the head.

Figure 9 shows the CNS connections involved in the VOR. This is a three-neuron circuit. One neuron is in Scarpa's (the vestibular) ganglion; one neuron is in a vestibular nucleus; and one neuron is in an extraoccular motor nucleus.

A variant of the VOR, called caloric nystagmus, is used as a test of the vestibular system. If the ear is irrigated with a fluid having a temperature different than the body (either warmer or cooler), a thermal gradient will be conduced across the small space of the middle ear.

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Figure 11 shows a caloric response. Here, cold water is put in the right ear. About 20 ml is injected over about 30 s. The cold water cools the tympanic membrane, which cools the air in the middle ear, and finally the endolymph. This primarily affects the horizontal semicircular canal because it is close to the middle ear space.

Figure 11. Caloric Testing. (https://nba.uth.tmc.edu/neuroscience)

Cooling somehow hyperpolarizes the hair cells, causing the eyes to drift slowly to the right as if the head was moving to the left. When the eyes have moved as far to the side as they can go, there is a quick resetting movement in the opposite direction. This cycle of slow and fast eye-movements is called a nystagmus. Nystagmus is labeled by the direction of the fast component. Figure 11 is an illustration of a left-beating nystagmus. Caloric vestibular testing is quantified by the magnitude and direction of the nystagmus. A useful mnemonic is COWS, meaning "cold-opposite warm-same". That is, irrigation of one ear with cold water produces a nystagmus away from the irrigated ear, while warm water produces a nystagmus toward the same ear. The normal response in a caloric vestibular test is symmetric and opposite responses in both ears. Weakness of the caloric response (eyes not moving when warm or cold water is flushed through one

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ear), or a spontaneous nystagmus (constantly moving eyes, as if the head was spinning when it is stable), indicates vestibular lesions.

Overview of Ascending and Descending Pathways

The first-order vestibular afferents have their cell bodies in the vestibular (Scarpa’s) ganglion, which is found at the distal end of the internal auditory meatus. Their axons travel in the vestibular portion of the VIIIth cranial nerve through the internal auditory meatus and enter the brain stem at the junction between the pons and the medulla where the IVth ventricle is the widest. Most of these afferents project to one of the four nearby vestibular nuclei in the rostral medulla and caudal pons. A few of the vestibular afferents go directly to the cerebellum through the inferior cerebellar peduncle. The cerebellum coordinates the movements that maintain balance. There are many

connections between the cerebellum and the vestibular nuclei.

Figure12. Caloric Testing. (https://nba.uth.tmc.edu/neuroscience)

Figure 12 shows a summary of these ascending and descending vestibular pathways. Note that the medial and inferior nuclei are usually seen together in the rostral medulla. The lateral and superior nuclei are smaller and are seen in the pons. The ascending tracts are shown in blue. These arise from the superior and medial nuclei and ascend in medial longitudinal fasciculus (MLF) to the oculomotor nuclei (III, IV, VI).The lateral vestibulospinal tract is shown in green. It descends ipsilaterally to the sacral cord. The medial vestibulospinal tract is shown in red. It descends bilaterally in the MLF to

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thoracic levels. The cerebellar afferents are not shown in this summary, but these come from the medial and inferior vestibular nuclei.

Conclusion

The vestibular system detects motion and gravity and initiates movements to maintain balance and orientation. It consists of a set of sensory organs in the inner ear, sensory afferents that link the sensory organs to the brain stem, a set of vestibular nuclei within the brain stem, and the projections of these nuclei to interneurons and motor neurons in the brain stem and spinal cord. Although the vestibular reflexes mediated by these projections are highly stereotyped, the vestibular system interacts extensively with the visual and proprioceptive systems, and its activity is influenced by the cerebellum and cortex to provide a high degree of adaptability.