A MODEL FOR THE TRANSLATIONAL VESTIBULO-OC'I-JLAR REFLEX

A thesis submitted in confonnity of the requirements for the degree of Master of Science

~ e ~ a k m t of Physiology Universiry of Toronto

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A MODEL FOR THE TRANSLATIONAL VEsTIBUL0-OCULAR REFLEX

W~sam Musallam Master of Science

1997

Department of Physiology University of Toronto

The vestibular system is the system of baiance. The vestibulo-odar reflex (VOR) moves the

eyes in response to head movements by uMg iaformaàon from the angular motion detectors,

the semi-circular can& (AVOR), and linear motion derectors, the otolith organs (TVOR). In

order to move the eyes, the ocdomotor neurons are knawn to require signals in phase with

veloaty and position. However, the primay afferent signal canying information kom the

otolith organs is in phase with acceleration. T'o complicate matters, the TVOR is a function of

target distance and rarget position and the otoliths are also sensitive to gravity. The mode1 in

th thesis difterentiates the pximary afferent signal maklig it in phase with velocity. The signal's

gain is then adjusteci and is merged with the canal signal and it is the combination of the two

signals that will reach the motor neurons.

Tdts on the other hand cause the gravity vector to shift with the respect to the otolith organs.

How do c e n d mechaniSm ciifferenthte between an irnposed tilt and an Lnposed linear

acceleration? We have proposed that if both the otolith organs, the umde and the saccule, are

taken into account, then the arnbiguity in the signal is rernoved. A simple function is presented

that considers different cases of tilt and translations and eliminates aoy arnbiguity.

1 would iike to thank Dr David Tomluison for his endless advice, support, and understanding.

Dr. Tomlimon showed me the ~atience of a kindhearted person and 1 am very gratefd to h

1 have benefited gready kom being in his lab, both as a student and as a person. 1 am thankfùl

for the freedom he gave me to leam on my own and the support he provided dong the way.

1 would also like to thank Mary and my parents, Suleiman and Sihaoi, for th& endless support,

Peter for his inspiring belief in me, and Irene for making it all mean something.

TABLE OF CONTENTS

... Acknowledgments ....................................................................................... IU

List of Tables .................................................................................................. vi List of Figures ............................................................................................... vi List of Appendices .......................................................................................... k List of Abbreviations ....................................................................................... x 2.0 Introduction ............................................................................................ 1

1.1 Periphd Vestibular Organs ................................................................. 2 1.1.1 Blood Supply ................................................................................ 2 1.1.2 Hair Cells ...................................................................................... 2 1.1.3 The Semi&& &ah ................................................................. 3

1.1.3.2 Mechania ........................................................................ 5 ..................................................................... 1.1.4 The Ocolith Organs -8

............................................................... 1.1.4.1 Sensitiviy Veaors -8 1.1 .4.2 Mechanics .......................................................................... 1 0

1.2 Innervation of the Peripheral Vestibular Systenz ................................... 11 .......................................................................... 1.2.1 E fferent Fi bers 1 1

1.2.2 Primary afferents ........................................................................ 12 ............................ ..................... 1.2.2.1 Canal Primary afferents .. 1 5

.................................................. 1.2.2.2 Otolith Primaty Afferents 1 5 ........................ 1 . 2.3 Prirnary Afferent Input To The Vesti buIar Nudei 20

1.3 Extraocular Muscles ............................................................................ 2 1 ................................................................ 1.4 The Vestibule-Ocular Reflex 24

.................................................................. 1.4.1 Oculomotor Neurons 25 1.4.2 Pathways Linking the Horizontal Canals to the Oculomotor Neurons .............................................................................................. 26

........................................................................................ 1.4.3 AVOR 26

........................................................................................ 1.4.4 TVOR 28 1.4.4.1. Dependence of the TVOR on Target Position and

.

Distance ............................................................................... 2 9 .................................................. 1.4.4.2 AVOR-WOR Interaction 31

................................ 1.5 Cells in the Vestibular Nudei Mediahg the VOR 34 1.5.1 PW Cd.s .................................................................................. 34 1.5.2 EHV Cds ................................................................................... 35 1.5.3 Otolith O*, Cand Onh/, and &al Otolith Cells ....................... 36

1.6 M d & of the VOR ......................................................................... 3 6 ................................................. 1.6.1 Robinson's Mode1 of the AVOR 3 6

1.6.2 Models of the TVOR ................................... ... ......................... 3 6 1.7 Cancdation, suppression and adaptation ............................................. 3 8

2.0 Methods ................................................................................................ 40 ........................ ......................................... 2.1 Ocdomotor Neurons ....,. 40

................................. 2.1.1 Transfer function o f an oculomotor neuron 41 2.2 The Mode1 ........................................................................................... 43

3.1 Differences Between Tilts and Translations ......................................... -51 .................................................................................................... 3.2 W[s] 53

3.3 Hl[s] .................................................................................................... 54 3.4 ws, w] ............................................................................................... 58

......................................................................... 3.5 Ouput of Hl and HZ -62 3.6 AVOR-TVOR Interaction ............................................................ 67

.............................................................................................. 4.0 Discussion -70 4.1 Predictions and experiments ................................................................ -74

................................................................................................. Appendix A -84 Appendk B ....................... .. ......................................................................... 85

........................................................................................... REFERENCES 8 7

LIST OF TABLES

Table 1.1 Approxirnate on direction of Canals

Table 1 2 Primary afferent projeaion onto the Vesribular Nudei

Table 1.3 Effects of right eye musde activation

Table 1.4 Primary effea of canal stimulation

LIST OF FIGURES

Figure 1.1

Figure 1 2

Figure 1.3

Figure 1.4

Figure 1.5

Figure 1.6

Figure 1.7

Figure 1.8

Figure 1.9

Figure 1.10

Figure 1.11

Figure 1.U

Figure 1.13

Figure 1.14

Figure 1.15

Figure 1.16

Figure 1.17

Orientation of the semicirdar canals

Cupula deflection of the hair cells

Gain and phase of canal primary afferents

Orientation of the umcle and saccule

Histogram of the coeffiaent of Variations

Adaptation of an hegular afferent

Bode plots for Regular otolith prMary afferents

Bode plots for Irreguiar otolith prMary afferents

The vestibular nudei and its innervations

Muscular innervation of the nght eye

Horizontal canal exatatov projections

The dependence of die TVOR on target distance

Signa ambiguity in the otolith organs

Disjunctive eye movements

Eccentric rotation

Eye position for eccentric rotation for different vergence angles

Robinson's mode1 for visual-vestibular interaction

Figure 2.1 Bode plot for an ocdomotor neuron

Figure 2.2 A model for the TVOR

Figure 2.3 Prograrn that sirnulates the model Li figure 2.2

Figure 3.1 Tonional qre produced by the modd cornpared with experimentai values 55

Figure 3.2 Bode plot of Hl[s] 56

Figure 3.3 Bode plot of H,[s] cascaded with otolith primary afferents 57

Figure 3.4 Bode plot of HJs] 60

Figure 3.5 Bode plot of HLs] cascaded with otoiirh primary afferents 61

Figure 3.6 Output of the mode1 for various vergence angles 63

Figure 3.7 Model's qre veloaty divided by theoretid eye vdoaty

Figure 3.8 SensiUvities vs. Frequency of the TVOR

Figure 3.9 Sensitivities vs. Vergence of the TVOR

Figure 3.10 Firing rates of central canal and otolith neurons

Figure 4.1 Slow phase eye velocity produced by the mode1

Figure 4.2 Torsional amplitudes for various frequencies

LIST OF APPENDICES

Appendk 1 Proof that F(8,3>0

2 Lia of parameters

LIST OF ABBREVIATIONS

ATD AVOR

CA

CAOT

EHV

EPSP

FTN

g IO

IR

LR LVOR

MA

MLF

MR OT

OVAR

PVP

SO

SR

TVOR

VN

VOR

COV

Axending Tact of Deiters

Aagular Vestibulo-Ocular Reflex

M W ciinar-otolith

Eye Head VelOCity

Excitatory Post-Synaptic Potential

Floccular Target Neurons

9.8m/s2

Inferior Oblique

Inferior Rectus

Lateral R e m

Linear Vestibule-Ocdar Reflex

Mew Angles

Medial Longitudind Fasaculus

Media Reçtus

Otolith OnIy

Off Vemd Rotation

Position-Vestibh-Pause

Superior Oblique

Superior Rems

Translational Vaibulo-Ocular Reflex

Vestibular Nudei

Vestibulo-Odar Reflex

Coefficient of Variation

C h a p t e r 1

INTRODUCTION

The vestibular systern is the vstm of balance and is necessary for dear vision. It is responsible

for moving the eyes so as to compensate for motion of the head and body. This is

accomplished by uUng head movement information supplieci by the vestibular labynnth. When

the head is rorated in one direction, the vestibulo-ocular reflex F R ) generates a compensatory

eye movernenr that is in the opposite direction leaving the direction of the visual axis

unchanged Failure of the VOR results in a movement of r d images during head movernent

and in a rnarked decrease in visual acuity.

The vestibu1a.r systexn is divided into two distinct sensory organs; the semicircdar canals, which

sense head rotation, and the otolith organs, which sense linear head movernent. Because of this

distinction between stimuii, t he VOR can &O be subdivided into ~o dasses: the Translational

VOR WOR, also known as the Linear VOR &VOR)) which is mediated by the otolith organs,

and the Angular VOR (AVOR) which is mediated by the semiciradar canals. 0th- vestibuiar

reflexes indude the vestibule-colic reflex, which aaivares ne& muscles, and the postural reflexes

which active the lower limbs. The vestibular response to head rotation, or the AVOOR, is

probably the most thorougidy midieci of d eye movement systems and thus dinical testing that

can assess canal function is routine. However, due to a la& of basic research into the

mechanism of otoïth function, a dear diagnosis of otolith pathology cannot currendy be made.

The work in this thesis grew out of the interesting question of how the veaibular nudei process

signals that originate in the otolith organs. A mode1 has been written rhat takes as input linear

acceleration, processes it, and produces an output in phase witb eye velocily.

1.1 PERXPHERAL VESTIBULAR ORGANS

The vestibule is locared in the inner ear at the base of the skull jus posterior to the cochlea

which is comected CO the v&b& by the ductus reuniens. n e ves t ibh system funcsions as

a sensor of head motion, respondlig to head accderation. Each ear has three semicircular

canals: a horizontal, anterior and posterior canal, and two otolith organs, the utride and the

saccule. Both of rhese organs are capable of generating a VOR (Lysakowski et al., 1993).

Information about head movement is canied by the e&th nerve, which e n t a the vestibule via

Scarpa's ganglion kom the intemal auditory meatus. The vestibular (Scarpa's) ganglion is divided

inro a superior and an inferior secrior,. The niperior vestibular nerve associateci with the

superior ponion of Scarpa's ganglion supplies the anterior and horbnta canal and the umde,

while the inferior vestibular nerve supplies the posterior nerve and the saccule (Lysakowski et al.,

1993).

1.1.1 Blood Supply

Blood supply to the vestibular end organs is through the intemal auditory artery, which becomes

the anterior vestibular artery and the common codear artery. The anterior vesibular a r t q

provides the blood nipply to most of the uoide and to the superior and horizontal m a l s and to

a s d portion of the saccule. The common cochlear artery divides into the proper cochlear

art- and the vestibulocochlear artery, whidi gives rise to the poserior vestibular arrery. The

latter supplies pnmady the poserior canal and the saccule (Lysakowski et al., 1993).

Information from the vestibular system is initiateci by movement of cilia on hair cells (See

section 1.1.3.1). The hair ceils are mechanoreceptors wirh a resting membrane potential of

about -60 mV. The mechanoreceptive organelles of the hak c& is a stereoda bundle

numbering 40 to 200 and m g e d in a aaircase pattern bounded at the talles end by a single

kinocilium. Deflection of the aereocilia towards the k i n d u r n depolarizes the hair c d

decreasing the potencial to about -40mV; defleaion a m from the kin0Citiu.m ~~ it to -64 rnV, and a stimulus directeci perpendicular to the kinocilium should elicit no response.

This rectification gready emphasizes the excitatory response making the c d morphologicdy

polarized D e p o h z q the haL cd leads to primary afferent activation. Thus a hinctional

polarization vector exists as well (Schwan and Tomlimon, 1993).

The hair c& are divided inco Type 1 and Type II cells. Type 1 hair ceils are flask shaped, and

are concentrateci in the center of the neuroepithelium in the monkey. They are innervatecl by a

calyx shaped denciritic afferent and generdy gives rise to an ùreguiar firin% rate (see section

1.2.1) and c m be innervared by efferent synapses (Femandez et a., 1990). Type II hair cells are

phyiogenetically older and are located mostly in the periphery of the neuroepithelium They are

cylindrical in shape, are innervateci by bouton endligs, and gen* give rise to regular &g

rates (see section 1.2.1).

1.1.3 The Semicircular Canals

The semicirdar canals are arrangeci as a set of three m u e orthogonal senson with each

canal being rnammalh/ sensicive to rotations that lie in the plane of that canal. The response of

each canal is proportional to the cosine of the angle between the plane of head rotation and the

plane of the canal (Le~gh and Zee, 1991). There are two vertical canals on each side, the anterior

and posterior, rhat lie perpendicular to each other and are oriented KOU& 45 degrees to the

sagittal plane, and one horizontal canal tilted upward about 30 degrees (Figure 1.1) Qysakowski

et al., 1993). The canais are organized as funaional pairs. The ancerior canal on one side is

paired with the posterior on the opposite side while the horizontal canais form a qmergistic pair

(Table 1.1) (Leigh and Zee, 1991).

Ri& PC Left PC . . . . . .

Left AC . . >:. . . . . Rie AC

F KURE 1.1 Orientation of the semicirdar can&. The Three canais on each side of the head are m u e orthogonal ro eadi other. The Left AC and the heght PC form a synergistic pair. Likewise for the Right AC and die Left PC. The Lateral Canas dso f o m a synergistic pair and are tilted 30 degrees from the horizontal in the upright position.

Table 1.1 Approxhate 'ON' direction of canas. +:stimulation. -:inhibition. For a particular movement (yaw, pitch or roll), conjugate pairs are activated for all directions of that movements, so that sensation occun in any direction. Conjugate pairs are Lidicated by the same row number

1 1 2 2 3 3 -

Hor Right HorLeft Sup Right Post Left Sup Left Post Right

YAW right

+ - 0 O O O

YAW left

- + O O O O

PITCH forward

0 0 + - + -

PITCH backward

0 0 - +

+

ROLL right

0 0 + - - +

ROLL Ieft

O 0 - + + -

1.1.3.1 Structure

The semicircular canals can be thought of as a thin Sr& tube fillecf with endolymph that is

secreted by speaalized ceils in each sensory orgaa s i m i k to the stria vascularis of the codilea.

At one end of each canal is an enlargement known as the ampulla, which contains the cupula

and the sensoty epithelium (figure 1.Za). The lumen of the canals is ocduded by the cupula, a

gelatinous membrane which protrudes into the ampulla spanning the entire cross section of the

canal so that it stops the endolymph £rom flowing past it (Hihan, 1979). The nipula is bent by

the relative flow of the endolymph during head rotation. The three sernicircular canas

converge upon the utride which provides a 5uid conUnuiv among the three canals. Since the

saccule is in fluid continuityd the unide, then by association, it also is in continuiy with the

canais (VUidson &Jones, 1979).

At the bottom of the ampulla lies the crista ampullaris, the neuroepitheiium that gives rise to the

hair c d s embedded in the cupuia The processes of each hair cells that lie in the crista consisu

of many stereocilia and one hocilium aligned so that they respond to cupda ben* in a

specific orientation. h is the bending of the cupula that stimulates the hair cells that lie in its base

leading to the h g of the vestibular primary afferent neurom (Lysakowski et al., 1993).

Deflemon of the stereoulia towards the k i n d u m causes depolarization of the hair cell;

deflection in the opposite direction causes hyperpolarization (figure 1.2b).

1.1.3.2 Mechanics

The &a and the surrounding endohph have been likened to an overdarnped torsion

pendulum (Wiion and M e H e Jones, 1979). The diameter of the seMcircular canals is s m d

compareci to their curvature G g h and Zee, 1991) so that when the canai is rotated, the flJd

lags behind because of its inema This causes the flow of the endolymph to be proportional to

head velocity maklig the canais inte&rating accelerometen. The idea that the canals

rnedianically integrate head acceieration has been confimieci electrophynologically (Goldberg

and Feniande5 197 1).

F IGURE 1.2a Hair c d s protrude from the uista into the cupuk men the head rotates, the endolymph ~ushes on the mpda which in tum deflecu the hair cells embedded in it.

1 Rotation tc the right hyper- polarizes the lek

Hair cd in its resting state.

Rotation ta the right depolarizes the right canal

FIGURE 1.2b Deflection of the stereorcilia (short lines) towards the kinocilium (da& lines) causes depolarization (ri& hair cd) . Deflection away kom the k i n d u m (Iek hair ceil) causes hyperpolarization.

The mechania of cupular and endolymph displacernent have been described by a rorsion-

pendulm rnodel (SteLihausen, 1933):

dZq d ' ~ dE I y = I - , + B - - + k E

dt- dt- dt

where 1 =2.54 x 1O4g/cm is the moment of in+ q is the anguiar displacement of the head

(or canal) in radians, B =.O8 poise is the viscous damping couple, k =.008--016 g/cm*s2 is the

elastic restoring force of the nipula and E is the angular displacement of the cupula relative to

the canal in radians (Schwarz and Tomlinson, 1993). Equation 1.1 relates the angular denecrion

of the cupula to the angular acceleration of the head The response of the cupula is

charaaerized by rwo Mie constants; r, = VI3 and T , = B/k r, defines the minimum duration of

the stimulus which can accurately be transduced by the caoals and has been calculateci to be 3

m. T , is the t h e constant of the nipula's r e m to its resting point. Since k cannot be

measured dire+, the value of T? has been inferrecl fiom primary afferent activity and iu current

accepted value is about 6 seconds (Schwarz and Tomhion, 1993).

The variables in the torsion-pendulurn mode1 are reiated to canal dimensions which v q across

species. Large animais tend to be ssluggish and require a more sensitive peripheral apparatus

with longer tirne constants. This is accomplLhed by having a large radius of m a t u r e dong

with a large lumen tadius.

There is one drawback to equation 1.1. The angular acceleration stimulus is integrated

reasonably weil for physiological kequencies and one would expect the primary afferent gain

and phase to follow the movement of the cupula fairly weil. However, at higher fiequencies,

primary afferent behaviour show a gain increase and a consistent phase lead throughout the

frequency range (figure 1.3) (Fernandez & Goldberg, 1971). Rabbit and Damiano (1991)

rnodeled the cupuk as an elastic plate and the endolymph as an incompressible Newtonian fluid

governed by the Navier-Stokes and continuity equations. They took h to account the kequency

dependence of the endolymph veloaty distribution and the fluid structure interaction at the

nipula Although they ran simulations ushg data from human infants, th& results follow the

experimental findings of Femandez & Goldberg (1971). However, sensory receptors are

7

generally sensitive to both the stimulus and its rate of change mediated by synapic dynamics. In

the vestibuIar system this would appear as a high fi-equency gain inaease and phase lead

Therefore, since ecption 1.1 does not rake into account synaptic mechanlms, we canoot

asnime that it does not corredy mode1 the endolymphapula interaction.

1.1.4 The Otolith Organs

The otolith organs sense hear acceleration in contrast to the sernicircular cands, which sense

angular acceleration. They are endolymph Med sacs with a sensory epithelium known as the

macula. The unicular macula lies approximately Li the horizontal plane and iu anterior portion

is tilted up about 25 to 30 degrees such that normal head position would orient it sornewhat

horizondy. It c m best detect d e r fore and aft or lateral translations of the head and tilts of

the h d The sacdar macula lies parallel to the sagittal plane perpendicular to the u d e with

its lowest end deflected lat* by 18 degrees. It can best detect up and down translations and

tilts of the head. The hair c& in the macula promide into a gelatinous ma& in which calcium

carbonate uystals (otoconia) are ernbedded Due to the otoconia, the specifïc gravity of the

otolithic membrane is about 2.7 &es greater than the surrounding endolymph (Money et al.,

1971). This results in a greater inertia, and causes a displacernent of the membrane, and thus a

deflection of the hair cds, in the direction opposite to an irnposed Iinear acceleration.

1.1.4.1 S e n s i t ~ g Vectors

The maLda is divided down the midline by a thin stripe known as the sviola The directional

sensitivities of the hair cells point towards the saiola in the utride and away kom the suiola in

the saccule (figure 1.4). Directional sensitivities are in h e with the morphological sensitivities

that will be descnbed in section 1.2.3. Deflemon of the ciIia dong its directional axis leads to

maximal excitation. At other angles of deflection, the response amplitude is proportional to the

response dong the directional axis rnultiplied by the cosine of the angle. Unlike the cm&, hair

cells in the macula of the utride and saccule do not face a single direction. Linear accelerations

in a l direhons could activate some hair ceh and inhibit othen (Schwarz and Tomlinson, 1993).

This dual signal might aid the brain in disceming the direction of movernent

Although it has been mggesteci that the otolith organs might respond to angular accelerations

since such a stimulus would cause a torsional motion of the membrane, Goldberg & Fernandq

(1975) found that otolith neurons are unaffeaed by angular accelerations. This can be explained

if the membrane has a hi& torsional ri@dity, or because tonional rnovements induced by

angular accelerations would deflect moa sensory hair cells in a direction perpendidar to & e h

polarization axes which is presumably ineffective.

Phase

Figure 1.3 Gain and phase in the kequency domain of canal primary afferents. The soiid lines are theoretical values while the dotted lines are the results of experhentd data and deviate from the values predicted by equation 1.1. Experimental d u e s £rom Fernandez & Goldberg, (197 1) (Adapted from Milsum, 1966).

Figure 1.4. Orientation of the utride and the saccule in the right side kom the subject's point of view. HaL cells in the saccule point away kom the striola (midline), while those in the unide point towards the suioh In the upright position, the hair c& v e n d to the striola in the saccule are continuously exated due to the presence or the gravity vector. The otolith organs on the contralateral side are the mirror image of the picture presented hue. So a d a t i o n towards the right wiU arcite the hair c d s that are lateral ro the d o l a of the uûide in the right side and =cite the hair cells that are medial to the striola in the left side.

1.1.4.2 Mechanics

The mechanics of the otolith membrane can been describeci by (Goldberg & Fernandez, 1975):

relating otoïth displacement x(t) to input acceleration a (t). me is the effective rnass of the

- Po - P c otolith membrane (1.9 x 10' g), p - - -320 is the density of the otolith membrane dative Po + Pe

to the density of the endolyrnph, b L a viscous damping constant (1 g / s ) , and k is the spring

constant (1200 dynedcm). The s d e s t detectable displacement of the otolith membrane x(t)

that can be detected by humans is 106cm. This corresponds to a human threshold for

perception of linear acceleration of 2 x lûLg (Grabiel et al., 1955).

1.2 INNERVATION OF THE PERIPHERAL VESTIBULAR SYSTEM

The Vestibular system is innematecl by both afferent and efferent fibers in the eight cranial

nerve. The bipolar ceils that make up the afferenr fiben have their c d bodies in Scarpa's

ganglion (see section 1.2). These ceils will be discussed in detail in the folowing section.

In the monkey, the few efferent fibers that supply the vestibular end organs arise lateral to the

abducens nudeus and from a region dorsolateral fiom the genu of the facial nerve (Goldberg

and Fernandez, 1980). In the bog, efferent fiber discharges have a tirne course similar to that

of the canal prirnary afferents in response to constant angular accelerauon and velociy seps.

After the cessation of an acceleration sep, the tirne coune for the falling phase of the response

was irregular and prolonged indicating possible multisenso~y convergence on efferent neurom.

These neurons dischargeci by ~assive and active limb rnovement and gentle pressure applied to

the skh or eyes (Precht et al., 1971) and aiso increase their firing rate in response to visual and

auditory stimuli.

The experimental r d t s of Precht, (1974) indicare that the efferent systern is inhibitory in

nature. Sorne possibilities for the function of the efferent system were podated by Brichta

and Goldberg (1996). They found that the efferent systern in the d e poserior aista inhibited

some Uf3its and exated others. They mggested that if the efferent system is activated in

antiapation of rnovement, then it could be used to switch the vestibular system from a

" p o d " mode to a "volitional" mode by inh ib i~g units that codd be sanuated by large head

movemeats and activating units that have large dynamic ranges. Other possible funccions were

pomilated by Schmidt et al., (1972) when they found that the efferent neurons in fish changed

th& hng rate prior to the onset of eye rnovements. Although the efferent affect on the

affixent signal has been c h a r a c t d as weak (Precht et ai., 1971) a l this evidence suggests d m

R nqht play a role in suppressing the undesireci afferent ngnal fiom the labyrinth d e n making

an active head movement accompanied by an eye movernent in the same direction ore*

1978). However, K h h et aL, (198 1) presented evidence rhat thk is not so. Tney propose that

the role of the efferent system is a global baseline +on during a wide range of stimuli This

L supporteci by 6ndings of excensive branching of efferenr fiben onro afferents (IChaLa et al.,

1981). Evidence in primates fav0urin.g this trypothesis is providecl by b u i e and Kimm, 1978).

The ~rimary afferent neurons m c d e the degree of rrirmilaaon of the perïpheral 0x-ga.n~ and

relay tbis information primdy to the vescibular nudei Ar the peripheral end of the nneuron,

the afferent can have a bouton, calyx or a dimorphic ending. Anatomidy, Qe cah/x endings

are found in the centrai regions of the neuroepirhelium and receive synapses £rom Type I haL

c& and sometimes fiom T ~ F II haïr cells (Goldberg et aL, 1990). These neurons have low

sensitivities and lead to irregular firing partm. Bouton endings are found in the peripherai

regions of the neuroepithelium and have regular rares. Dimo'phic endings can be eidier

regular or irrrgular in their finng pattem and innervare both Type 1 and Type II hair cells. The

dimorphic synapses rhar lead to regular fmng patterns are found in the peripherd zones whïle

those thar remit in in;egular firing patterns are found in the ccenter of rhe neuroepirhelium

Genedy, regardless of the innervation, irrrgular 6 m . g neurons are concentrad cenuaUy on a

neuroepithelium while reg& f k q neurons are concenmted in the ~eriphery. The different

~oabation of the fiben exhibithg different a&ty may lead to differmt c e n d d o n s

but th& ngnificance is nor yet known (Schwarz & To&on, 1993).

The primary afferents are not quiet in the absence of stimdus but mainrain a constant discharge

in response to the constanr n e u r o ~ m i t t e r rdease from the hak &. Goldberg & Femandez,

(19713 reponed and average resting dirharge rate of 90 spikes/sec. This allows for bi-

direaïonal change dependmg on the direction the hak ceh bend T?ie regulanty of dixharge is

defined by the coeffiaent of variation (COV) *ch K cornputeci as the standard daiarion

dixideci by the rnme interspike interval and is therefore somewhac arbinary because of the

different inrerspike intenrals rhar rnay be iwd At an inrerspike inferval of 17.5 ms, the mean 12

COV of all prLnary afferents was reported as p=.3072 + .O24 (mean t standard m o r mean)

(Goldberg & Femandez, 1971~). The r@ar firing fiben, which have slower conduction

veloaties and a s d e r diameter than irregular finng fibers have a COV less chan 0.1, while

irreguiar 6n.q patterns have a COV greater than 0.4.. A kequency histogram of COV is shown

for a s q d monkey uing an interspike interval of 12.5111s resulting in a mean COV of

p=.1854 t ,0139 (figure 1.5). Two peaks can be seen, one centered around COV of .O6 and a

second aroud 0.4 corresponding to regular and m;egukr fibers. The function of regular and

irreguIar newons will be discussed in section 1.2.2

The afferents innervating the canals are aaivated by head accelerations in the ipsilareral direction

and inhibitecl by rotations in the connalateral directions (Femandez & Goldberg, 1971b) with

the degree of activation being proportiond to the cosine of the angle berneen the canal plane

and the stimulus plane. Similady, in the monkey, wen though the hair cells in the umcular

macula are dimibuted around the kola , the utricular afferents have a preponderance of

afferents responding to forces directeci towardc the ipsilateral ear. However, unlike the cana

affereats, the otolith primary afferents may respond to stimuli in one or more directions

(Fernandez & Goldberg, 1976b). They also may be excited by forces directed perpendicular to

th& polarization vector. Fernandez & Goldberg, (1976b) suggested that the otolith mechanics

may involve complex non-hear mechanical interactions. Didunan et ai., (1991) &O reporteci

otolith afferems in the gerbil that responded to stimuli directed orthogonal to th& sensitivity

vectors. Angelaki (1992a) explaineci these "broadly tuneci" neurons with a mode1 utilLing the

spatio-temporal convergence berneen haL cells with different temporal and spatial propemes.

Two haL c d s with different phase characteristics and different directional sensitivities could

produce the "broadly nuied" behaviour observed in these neurons. The different phase

characteristics could be produced by the different membrane propenies of Type 1 and Type II

hair cells (Comia and Lang, 1990). This would make the dimorphic neurons suiteci to cary

" broadly nined" signal.

0.04 0.08 0.12 0.16 0.2 0.24 0.28 0.32 0.36 0.4 0.44 0.48 0.56

Coefficient of Variation

Figure 1.5 Hkogram showing the Coefficient Of Variation for the primary afferents of the squUreI monkey. Interspike intemal = 12.5ms. Reguiar ~ t s are d e h e d as having a COV< 1. Irregular units have a COV>.4. Units in between are defineci as dimorphic. Note thar the amounr of regdar units found is greater than bot . the dimorphic and the irregular. Data from Fernandez & Goldberg, 197 1c.

12.2.1 Canal b a r y afferents

Canal prMary afferent neurons carry a signal that is approximately in phase with angular veloaty

of the head (Fernandez & Goldbq, 1971). The naasfer function diat describes the behaviour

of the canal p&my afferent is:

where s is the Laplace nansfmrn The £irst part of equation 1.3 is the laplace ~ f o r m of

equation 1.1 and corresponds to the cupular dynamics. As before, T, = 6 seconds, TL= ,033

seconds. The second bracket corresponds to an adaptation operator. In the Orne domain, diis

hi& pass £'ilter is proportional to ed" so that as TA decreases, the neurons adapt faster. Even

though the value of TA varid for irregular units, th& mean is TA=34 seconds indicating a

relatively rapid adaptation. In contrast, the regular unirs' adaptation operator is ornitteci (or

equivdendy set to idnity). Figure 1.6 shows the hme course of a re~resenrative kepuiar

afferent with TA=34 seconds and TL=.08 seconds. Fin*, the last bracket indicates a high

frequency gain enhancement and phase lead, with TL =.O8 for irrqdar uni= and .O17 in reg&

uni= (Femandez & G o l d b e ~ 197 la).

1.2.2.2 Otolith k i m a r y Afferents p p p p p p p p - - - - - -

The otolith prLnary afferents are of great interest in rhis stucty since they mppk the input to the

circui~y that is being modeled. The transfer function that describes the behaviour of the otolith

prinaty afferents is giva by (Fernandez & Goldberg, 1976~):

The term H,,= L + k, (T&,s) kv is a vdocity sensitive operator with fractiond component (k,, < 4 which provides mosr of the gain enhancement and phase leab seen in irregular units. The value

of reflects the amount of differentiation that d e s place (the effemveness of the velocity

1 + k,T,s operator). The factor HA= is an adaptation operator. It contributes to the phase

1 + T,s

leads seen at low kecpenaes and to the large increase in gain observed in going fmm DC to

.O6 Hz (figure 1.8). (Note that in figures 1.7 and 1.8, the vdues from DC to .O06 where

interpolateci using eqpation 1 A.)

Figure 1.6 Adaptation of a canal irregular prîmary afferent ushg TA=M seconds. Gain is rnaiutained at about .2 spikes/sec/deg/sec for about 1 second

The last term &= 1/(1 +Tus) is a first order lag operator and rnay reflect the mechanics of

otolith motion. It accounts for the hi& frequency phase lags seen in regular units (figure 1.7)

and accounts for the srna1 phase lead seen in irregdar unis which are uniayr smaller than

would be prdcted sol* from the fractional veloaty operator. Figure 1.8b depicts the phase

of an meguiar afferent wirh lq-• Based on this information, the phase lead should be dose

to 40 degrees espeaally ar high beqyenaes. However, as can be seen fiom figure 1.8b, due to

H, the phase begins to dedine as the kequency increases. Femandez & Goldberg, (1976~)

estimatecl four of the parameters k, kAi TA, TJ uUng a leasr square fit to the experimental

kequency plots but held TV constant at 40 seconds. The median values reported are used

throughout the simulations in d is theses. For kegular afferents, the medians were: lq,=O.44,

k,= 1.9, TA= 101 seconds and TM=0.C09 seconds. Reg& mits had h= Ql88, k,= IL?, TA=69

seconds and TM=0.016 seconds.

Figure 1.7 and 1.8 depicr the dynmics of a regular and irregular otolirh neuron in the frequency

domain. The irregular unit increases in gain by 40 tLnes and has an average phase lead of 30

degrees with respect co head acceleration as the kequency increases from .Wb Hz m 2 Hz

Surprisigly, the regular unit shows veIy lide variation with frequency. its phase hovers around

O degrees at low £requ&es and dips to around a 20 degrees lag at higher fiequencies. The

average gain for an irregular otolith afferent is about 200 spikedsedg at 1 Hz while that for a

regular afferent is around 40 spikes/sedg at 1 Hz On average, the resting rate of otolith

afferem was found to average 60 spikedsec, considerably less than the average found for the

canal afferents (Femandez & Goldberg, 1971a).

0.001 0.01 0.1 1 Frequency (Hz)

-6 ' 0.001 0.01 o. 1 1 1 O

Frequency (Hz)

Figure 1.7 Bode plots for regular orolith p&my afferents. k,= .188, k, = Llî, TA= 695, TM= l6ms, Tv=40s. a: Gain in spikes/sec/g where =9.8m/s2. As the frequency inaeases from .O1 to 2 Hz, the gain exhibits a very flat kequency response. Compare with figure 1-82 b: Phase re acceleration in degrees. At low frequencies, the phase leads acceleration by a few degrees. After .= the phase begins ro lag and reaches -5 degrees at 2Hz

0.001 0.01 o. 1 1

Frequency (Hz)

0.001 0.01 0.1 1 10

Frwency (W Figure 1.8 Bode plots for irregdar otolith prirnary afferents. k,, = .M, k, = Lm, TA = lOls, T M = S ~ , TV=4Os. a: Gain in spikes/sec/g where g=9.8m/s'. In c o n m to the regular afferent's gain (figure 1.7a), the gain of the irregular neuron is dynamic and res~onds with a large gain for an inaease in frequency. Note the difference in s d e . b: Phase re acceleration in degrees. At low fiequencies, the phase leads acceleration as desuibed by the velociv operator. At 1 Hz, the phase begins to lag due the input of the lag operator.

19

12.3 PNnary Merent Input To The Vestibular Nuclei

There is a fundamend difference between the signals originating frorn the otolith organs and

for chose originating h m the canais. The signas are in phase with head accdemion Femandez

& Goldberg, W&), and head velocity respectively. The oculomotor neurons are known to

require input sipals propomonal to eye d o + and eye position (see section 1.4). Therefore

for the AVOR the vdocity signal is readily obtained from the semi-cucuiar c a d rnahg iu

raw signal adequate to drive the vdocity component of die oculomoror neurons. The situation

for the TVOR L more complex. Since the signai from the otolirhs is in phase with acceleration,

further processing is needed in order to obtain the necessaty commands to drive the ocular

motoneurons. The circuitry that accomplishes this feat is nor yer known but because of the high

latenaes of the TVOR, the circuiuy probably extends beyond the vestibular nudei into the

cere b d u m

The vestibular nudei occupy a large portion of the medulla and extend ros tdy into the pons.

Primary afferent fibers korn semicircular canals and the otolith organs nin into the vestibdar

division of the vestibulocochlear nerve 0 to terminare in the vestibular nudei In addition,

hi& frequency stimulation of the u m d a r nerue evoked EPSPs in the abducens rnotoneurons

with latemies between 0.9 rns and 1.2 ms. This suggests that the abducens motoneurons make

monosynaptic connections with the vestibular nerve (vchiuo et al., 1994). This is a surprising

renilt since the latency of the WOR is around 30 rns (see section1.4.4).

The vestibular nudei consists of four main nudei termeci superior, descending (iderior)), lateral

and medial nudei (figue 1.9) and several minor groups termed Y, L, F, X and Z groups

(Schwarz & Tomlinson, 1993). Each main nudei and die Y group has distinct connections with

the periphery as shown in table 1.2. AU the primary afferenrs connections are excitatoiy. The

inhibitions shown in table 1.2 are mediad by inhibitory interneurons.

The medial and niperior vestibdar nudei receive input from the semicircular canals. These

nudei partiapate in the vestibulo-ocular reflex and make monosynaptic connections with

motoneurons innervating the neck muscles and are the primiuy source of the reflex connol of

neck movements (Let& & Zee, 199 1). The medial nucleus also receive utricuiar input resulMg

in a s d amplitude response to forward and backward tilts (Gacek, 1969).

The descending vestibular nudeus receives some input kom the semicircuiar canals and a

significant input £rom the utride and correspondin& has a large response to dt ( w i o n &

M e l d e Jones, 1979). The romai part of the nudeus is believed to receive saccular input

(Gacek, 1969). The descendhg nucleus rends the majoriv of its efferents ro the vestibulospinal

pathwap and projects to the spinal cord

The lateral vestibular nudeus has main inputs from the macula of the unide, semicircular canals

(Gacek, 1969) and £rom the cerebellum and the spina cord (Wilson & MelviUe Jones, 1979).

Neurons in the lateral vestibular nucleus &O respond to tilt in one direction and deuease th&

response to tilt in the opposite direction. The mapitude of the response increases with

increasing tilt (Schor, 1974).

I I 1 Horizontal 1 Excitation 1 Media & Lateral 1

1 1

Posterior 1 Excitation 1 Medial &Lateral 1 Anterior

I 1 Inhibtnon i Supenor 1

Excitation Inhibmon

Media & Lateral Supenor

L

Utride

1 I I Table 1.2 Projections of semicVcular canals and otolith primaxy afferents onto rbe vestibular

nudei. Inhibitory mponses are due to inhibitory interneurons. Adapted from Lei& & Zee, 199 1.

Saccule

1.3 EXTRAOCULAR MUSCLES

Exatation

The eyes are innenrated by six extraocular muscles. niese are the medial and lateral recti, the

Lateral & inferior

Excitation

superior and inferior recti, and the superior and inferior obligues (figure 1.10). The effect of

y-group & Infenor

sup rÏor 7 Horizontal and

... ...-... 7 Anterior Canal

........... ...... m-- . - .

Figure 1.9 Sections of the four major vestibular nudei and its innwations. The prirrmy afferents £rom the canal terminate in all four vestibular nudei wMe the utricle terminates onto the Lzferior and lateral portions and the Saccule on the l a r d portions. Solid light line: Horizontal and anterior canal. Solid dark line: Saccule. Dashed light hue: Postenor canal. Dashed dark Eue: Utride.

Figure 1.10 Muscular innemation of the right eye from observer's point of view when looking at a subject. A: Medial recm. B: Superior Recnis. C: Lateral ~ e & . D: Inferior Recm. - E: Superior Oblique. G: hferior Oblique.

the lateral and medial recti are h o s t pu+ a horizontal rotation since these muscles are

attached in the plane of the center of rotation of the e y e But rhinps are not that well smictured

for the 0 t h muscles. The superior and inferior recti are displaced in a medial direction and

have a 1Lie of action that is displaced 23 degrees ro the visual axis in the primary position. Th&

main action in this position respectively is eiwation and depression together with a slighr

intorsion kom the superior rems and an morsion korn the inferior rems. The superior

oblique uses a pulley, the trochlea, to change its direction and inserts itself la tedy dong the top

of the Te. Iu Lue of action then is displaced 53 degrees from the wual axk in the primary

position. The inferior oblique insers itself in the heerior lateral portion of the globe wi& the

poserior section dose to the optic nwe, making its h e of action nor coinadent wirh thar of

the superior oblique. Their main action in the prirnary position respectively is intorsion wich a

secondary action of depression and exrorsion with a secondary action of elevation (Wilson &

Melde Jones, 1979). Table 1.3 Surnmanzes the actions of the ri& eye musdes for certain

movements from the primary position.

Right Eye 1 Adduction

Superior

Inferior R e m s Superior - oblique In fenor -

rable 1.3 Effects of

Abduction ( elevation 1 depression 1 intorsion 1 1

Yaw Left Pitch Pitch Roll In Roll out backward forward (069

\ I J

the activation of the nght eye musdes and the movement that stimulates them +: stimulation. -: &bition. +: main action. +: minor action. For a parti& movement k, pitch or roil), conjugate pairs are activatecl for .. .. . n .

ail drrecaons oi that movements.

CornParing table 1.3 with table 1.1, it becornes evident that each pair of canal iduences a pair

of extraocular muxles that moves the pair in the p h e of chat canai. The unide and the

saccule on the other hand cm move the qres in any direction (Fluur & MeDarom, 1970).

Primary effew of canal sarmilanon are shown in table 1.4.

6nalstimulated 1 Exates 1 Inhibits 1 -

Horizontal

I 1 1 Table 1.4 Pr* e as of canal stimulation on the extraocu1a.r mussels. i: ipsilateral, c:

condateral, M R medial recnis, LR: lateral r e m , SR: niperior r e m , IR: inferior rems, SO: superior oblique, IO: infirior oblique.

Posterior

Innervation of the six extraodar musdes originate in three nudei located in the brainstem; the

oculomor nudeus 0, the trodear n u d a 0 and the abducens nudeus 0. In the

~ M R C L R

monkey, the abducens and the trochlear nudeus each supply ody one musde, the ipsilateral

lateral recnis and condateal superior oblique respectively. The oculomotor nucleus supplies

~ L R C M R '

iS0 cIR

the other four musdes; the ipsilateal inferior recnis, i~silateral media1 rems, ipsilateral infenor

oblique and condateral superior recnrs (Warwi4 1953).

rI0 cSR

1.4 THE VESTIBULO-OCULAR. REFLEX

The vestibule-ocular reflex (VOR) generates eye movements that compensate for head

movements sensed by the vestibular systent There are nvo classes of VOR, the Angu1a.r VOR

(AVOR) govemed by the senicircular car&, and the TmIational VOR WOR) &en by die

otclith orgaos. Failure of the VOR r e s h in movement of rainai images and a mafked

decrease in vinia a&. Little is known about the TVOR since research has concentsateci on

the AVOR . This thesis will be maudy concerned with the WOR

The n70R has a IAtPncy of 3 W rns (McConde e t aL, 1996). This is beccruse the primary

afferent ngnaL require pnxewiag before thq- a n be fed to the oculomotor neurom. The

AVOR on the orher hand has a latenq- of 10-14 ms (Lsbervber, 1984) and L based on a 3

neuron arc consking oE

1. the prhmy afferent neuron,

2. rhe secondary neurons in the vestibular nucleus,

3. the ocdomotor neurons.

The prkmy afferents have air+ been described in secrion 12 d e the neurons in the

vesti* nudeus aJ1 be dexribed in che nen section The oculomotor neurons are usai

both rhe TVOR and the AVOR @ W ~ T and dl be bnefly describeci here.

The ocular motoneurons are knm- ro r+e inpm sipals proporcional ro eye veI+- and eye

position as motoneuron fkq rare can be described by the eqwuioxx

a-here R is the finng me in sph/sec, Rf is the bmg a r e d e n Ehe eye Ü in primq psiion,

E and g a r e the eye position and eye do+- respeCm-el?, k=4 spikes/seddeg, and r=.95 dt

sp3;e/seddeg/sec (Robinson, 198 1). .G can be seen, w o n 1.5 carries s@ proportional

to eye velociy and psmon. In the case of the NOR, the q e veloQs- command is

obtaiDed h m the canai signal and rhe position sgnal is obraioed bj- ùitegmion A c e n d

neural integmor has been proposeci to perform rhis m.& Fobinson, 1963). Honever, & the

AVOR, rhe u n p d otolith afferent signai is inappropriare to nipply the vel* command

for &king the motoneurons since it L in phase a-& head accelemion

1-42 Pathways Linking the Horizontal Canals to the Oculomotor Neurons

The mode1 of the TVOR presented in this thesis describes the behaviour of eye movements to

interaural translations. In the mode1 (see section 2 4 , the horizontal TVOR d e i c evenndy

ad& to information kom the labymth and uses the labynnthine pathways to the extra&

muscles. Therefore, ody a description of the pathway fÏom the horizontal canals to the

extra& m d e s will be given.

If the head k rotated to the nght, then in order to compensate for rhL rnovernent, the eyes mus

move to the left. For the nght eye, dis results in excitation of the medal r e m and inhibition of

the lateral recw. In general, srcitation of a horizontal canal on one side causes excitation of the

connalateral and inhibition of ipsïlateral abducens (table 1.4) (Precht et al., 1969). The second

order neurons that relay this information to the abducens lie in the r o d medial nudeus

(Gacek, 1971). In the car, Baker et al., (1969) showed that stimulation of the vestibular nerve

evokes EPSPs in the contralateral abducens wich a latency of 1.2-2.0 ms &g these

connections düynaptic confirming the AVOR 3 neuron arc. Intemudea. neurons in the

abducens project to the third nucleus via the medial longitudinai f a s u d u s (MLF) to contact

medial r e m neurons. Exatatory neurons in the medial vestibular nudeus cross the mimidllie at

the lwd of the abducens and synapse on the contraiateral abducens nucleus. From there,

exatatory projection is sent to the lateral r e m while other neurons cross the rnidline via the

abducens intemeurons, badc to the half of die exciteci canai, and synapse onto the hed nudeus

exciting the ipsilateral media rems. The ipsilateral medial recnis is ais0 exated via the

Ascending Tract of Dieters (ATD) which does not project ro the other side. This gives the

An> the ability to send signals to the motoneurom that do noc match those going to the

condateral lateral r e m . This is exactly what is needed for disjunctive eye movements and will be discussed further in section 1.4.4 A summary of exatatory connections for the horizontal

canal is s hown in figure 1.1 1.

1.4.3 AVOR

The AVOR L the moa thoroughly snidied vestibular reflex (see Schwarz & TomlLison, 1993

for a review). The gain of the AVOR is defined as the eye velocity divided by angular head

Figure 1.11 Horizontal canal aratatory projections. Ipsilateral vescibuk nudei neurons project contralaterly to the abdumes. In nini, the Abducens projects to the ipislaterai lateal recuts and contralate+ to the III nucleus. The ATD does not project connalatady. MLF: Medial Longitudinal Fasiculus, III: Odomotor nudeus. VI: Abducens nudeus. Lateral rectus. M E Medial Recnis. VN: Vestibular nucleus. ATD: Ascending Tract of Deiten. HE Horizontal C d .

Figure 1.12 Translation is highdy dependant on target h c e . Transla~g a distance L to the right requires the eye to move an angle ArcTan(L/D) to the left where D is the target distance. As D approaches ;nf;niy, E +O.

veloaty and the temporal difference between the output and the input is described as phase.

For naturai head frequenaes (S-5 HZ), the gain is airnosr ideal and is dose to 1 while the phase

has a value of O degrees. Since the eye moves in the opposite direction to the head, perfea

compensation requkes a phase shift of 180 degrees (&ch by convention is taken to be O

degrees). At frequencies of rotation less than .O1 Hz, the gain decreases and a phase lead

develops. But in this range, the vinial system helps to cornpensate for the rotation

For sustained rotations at constant velocity, vestibuiar eye movement velocify declines with a

tirne constant around 15 seconds. The dedine is due to rhe elastic properries of the cupula but

15 seconds is much greater than the cupda's thne constant (5-6 seconds). The prolongation of

the signal is achieved by the velocity storage integracor which combines vestibular and

optokinetic input in a positive feedback loop @phan et al., 1978, Cohen et al., 1981). n i e

output (eye velocity) of the velocity storage is the nim of the direct vestibular pathway, direct

visual pathway (retLial slip) and the output of the positive feedback loop. The canal M i e

constant T2 would result in a new system M l e constant T,=T2/(i-y) where y is the gain of the

loop. In the monkey, y=.7 which causes Ts=3xT2 which is what is observeci (Waespe & Hem,

1977).

1.4.4 TVOR

There are several different manifestations of the otolith-ocular reflexes that are aimed at

accomplishing visual stability. These iodude counter-rolling of the eyes during head du,

contes speafic ocuiar reflexes during translation (Paige & Tornko, 1991a) and a sustained

nystagmus during Off Vertid Axis Rotation (OVAR), a paradigrn thar tilts the axk of the

rotation from the vertical. Even though the otolith primary afferents have been w d quantifiecl

(Fernaudez & Goldberg, 1976, Goldberg et al., 1990), litde is known about the TVOR reflex

and its central connections. This is pady due to the difficulty in obtaining equipment that can

produce conmiled Linear stimuli and partiy due to early TVOR results. Nwen et al., (1965)

performed experiments in darkness and found the WOR response in hurnans to be very s d .

From the geometric understanding of the reflex (figure 1.12), this is what is expected, since in

darkness the eyes are diverged as if there &ed a target at visuai infinity. Recendy, the TVOR

28

response has been shown to be a h & o n of target distance ( B u k a et ai., 1981) and furcher

experiments have shown it to be substantial when the target distance is s d (Paige, 1989, Paige

& Tomko, 1991, Schwarz et al., 1989). When the head is translateci chrough a distance L from

P, to PI, the reequire compensatory eye movement is given by ArcTan(YD) where D is the

target distance (figure 1.12).

The otolith organs respond to hear acceleration indudlig gravity. Since gravity L normally

present, it has always been asnimed that the otohth signai generated by a head tilt to one side

will be the same as that generated by translational acceleration to the other side. The ocular

wponse to a translation is a horizonta eye movernent while that to a head tilt is a tonional eye

movernent while high frequency stimuli result in horizontal ones, with considerable overlap.

The arnbiguity mentioned is mie for the utride, but is not mie if both the umde and the saccule

are taken into consideration. The utricular signal that dweiops when a subject is tilted by an

angle 8 is the same as during a translation in the opposite direction of the tilt with an

acceleration =gsin(8) where g = lag=9.8m/s2 (figure 1.13). However, during translation, the

saccule does not mudukte its discharge rate as it would during a tilt. Therefore, we condude

that if information kom both endorgans is taken into consideration by the brain, then this

would &are the ambigujr discussed above.

Signal ambiguiv can also arise with the saccule. Donoventral translation at some acceleration

a+ would cause the saccule to sense an acceleration g- q in one direction. This same acceleration

can be repeated with a tilt by an angle <p ntch that the gGs(cp) = g-a, leading to the proposed

arnbiguity. For falling, which is a dorsovenaal t&ansla~on, the cornpensatory eye movernent is

verticai but for dting it is tonional. Agaui, rhis arnbiguiity can be elMinad by considering both

otolith organs. k g dorsoventral translation, the umde does not modulate but during tilts, it

does.

1.4.4.1. Dependence of the TVOR on Target Position and Distance

In the dark, the gain of the TVOR defineci here as eye velocity d ~ d e d by head acceleration is 13

deg/sec/g at a he-equency of 1.5 Hz However, in the light, the sensitivity of the TVOR (defined

Saccules sesg 1

Figure 1.13. To the unide, tilting the head is equivalent to accelertaing interauraly with a=g*Sin(cp) leading to an arnbiguity in the signal To the saccule, no interaurd d a t i o n cm replicate the acderation it senses during tilt hence elLninabg the ambiguity once the discharge of both organs is taken into account.

Target distance (rn)

Figure 1.14 When a subject is accderated in the nasooccipitd axis, the ri& left eye move independently of each other. In th is case, the target is located in front of the right eye. As the subject approaches the target, the lek b e p s moving the amount shown while the right eye does not move. Such eye movemenu may be mediated by the ATD.

here as eye position aver head position in degreedmeter) is a funcrion of target distance. In

addition, during interaural d a t i o n s and after travelling a &ance x in one direction, the

target distance inmeases to ( L L + ( 2 + ~ ) V 2 so that the gain of the TVOR needs to be dynamic

to compensate for the changing target distance. The dependence of the TVOR on target

distance is manifested by the degree of convergence of the eyes. The stimulus to change

vergence is retioal disparity and the degree of vergence k m e m e as Meter Angles (A&%) which

is equivalent to rhe inverse of target distance.

The gain of TVOR also is a fundon of target and eye position. Consider the effect of the target

position on the gain of each eye during naso-occipital translation. If the target is located

dl+ in front of the right eye, then the ri& eye does not have to move to maintain fixation

during the movement but the left eye needs to rotate to the ri& Figure 1.14). Such changes in

the TVOR have been shown to occur by Paige & Tomko, (1991b) and may be mediated by the

fibers in the ATD. Indeed naso-ocapital translations can lead to a variety of eye movements. If

a target is located to one side of a subject as they are translateci in the naso-occipid axis, then

horizontal eye movement d result. Similady, if the ta* is located above or below the

subject, then vertical eye movements will r d t . Vergence eye movements (both eyes moving in

opposite direction towards the nose) are expected to occur during forward translation when the

target is located between die eyes. This is exacdy what is observed experimentdy Po& &

Paige, 1992).

Vergence eye movements are much faster if they occur at the same t h e widi a head or eye

movement towards a target rather thao by thernselves (Paige & Tomko, 1991b). It was believed

that vergence information is simply supeMlposed onto oculomotor neurons (Mays et d., 1986)

but this is inconsistent wirh the observed TVOR results. kistead, vergence information musr be

supplieci to central neurom that mediate the TVOR to produce the observed system behaviour.

1.4.4.2 AVOR-TVOR Interaction

Rotation about an a i s removed fiom the center of the head (eccenmc rotation) d excite both

the c a n l and the otolith organs (figure 1.15). Equations 1.6 and 1.7 desuibe the theoreticai left

and right eye movements for a 9;ve.n head movernent wirre et d., 1986).

3 1

1 (D+ R)Sin(-4) + --

0, = ArcTan 2 (D + R)Cos(+) + R

8r = ArcTan L

(D + R)COS(-$) - R

where D is the target distance, R is the radius of rotation, I is the interaual distance, <p is head

position and 8, and 0, are the left and nght eye positions respectively. Figure 1.16 depicts

movernents for the ri& eye based on equation 1.7 with R=2 maers, D1.3, -2 and .IO menes.

When the subject is facing the center of rotation as in figure 1-15, a lebard eccenaic rotation

will cause the head to rotate to the righ but translate to the lefr. Both the AVOR and the

TVOR are active but each system wams to drive the eye towarb the opposite direction. As the

target disrance goes from being farther to being doser than the axis of rotation, the eye

movement decreases and evend ly reverses. For D >R, the eyes mus rotare t o d the ri&

and the AVOR dorninates (figure 1.16) while for D<R, the eyes must rotate to the left and the

TVOR dorninates. When D-R the eye position in the head is geomeuidy not expected to

change. From figure 1.16, it can be seen that the absolute change in the amplitude of eye

position around Dz0.2 meters is e x a d y the same for D= 0.3 metres and D -0.15 meters men

though the former is 10 cm farther than the axis of rotation and the latter is 5 cm doser to the

subject than the center of rotation. However, the eye movement is a funmon of vergence angle

which is the inverse of target distance. The change in vergence mgle induced by going from

D-0.3 meters to D=.2 meteres is (1/.3)-(1/.2)= 1.667 MA This is exa* the same as going

from from D-0.2 meters to D=0.15 merers since (1/.2)-(1/.15)= 1.667 MA.

Table \ rotation direction

Right rotation

- Left Translation

Figure 1.15. Eccentric rotation arates both the canh and the otolith organs. Rotating to the lefc around an a& in fiont of the subject causes the AVOR and the LVOR to oppose each other.

Ti (seconds)

Figure 1.16 Eye position during eccentric rotation with the radius of rotation 20 un infront of the head and a frequency of 2 Hz If the gaze is ciiread at the center of rotation, then no eye movement is expected to occur. As the target distance increases, the AVOR dominates while if it deueases, the TVOR dominates.

1.5 CELLS IN THE VESTIBULAR NUCLEI MEDIATING THE VOR

Single c d recordings from the vestibular nudei have eluadated many of the mysreries

underlying the sensory to motor transformations dia1 o c m in the brain stem (McConville et al.,

1996, McConville et ai., 1994, Tomlinson et ai., 1996, Tomlinson & Robinson, 1984, Scudder &

Fuchs, 1992, Lis berger & MJes, 1980, Fuchs & KUnm, 1975). Eark classification labeled cells in

the vestibule nudei as Type I , Type II or Type III. Type 1 cells were dehed as those excited

by head rotations to the ipsilateral side, Type II were defineci as head rotations to the

contralateral side, and Type III are excited by rotations in both direcxions (Fuchs & Kimm,

1975). A different ceIl q.pe dassification identified cells according to their relevance to the

horizontal VOR @uchs & KLnm, 1975). In the rostral medial vestibular nudeus, some of these

cells are: Position Vestibular Pause (PVP), Eye Head Vdoaty 0, Burst-Tonic neurons PT) and Floccular Target Newons 0. FTN ~robably correspond to EHV cells since they have

the same behaviour and are found in the sarne region of the vestibular nudei (McConville et al.,

1996). The behaviour of these cek will be discussed in the nne~t section

Some of the other neurons found in the r o s d mediai and mediai lateral vestibular nuclei

include Canal oniy cells (CA), otolith only cds (OT), and cells that receive combined canal and

otolith input (CAOT) (I'o&on et al., 1996).

Of al1 these neurons, onty the PVP cells and the EHV (or FTN) c d s conaibute to the

vestibular information supplied to the moroneurons (Scudder and Fuchs, 1992). There are

distinct ciifferences between the behaviour and inputs of EHV and PVP neurons as discussed in

the next section.

PVP cells provide the main conmbution to the horizontai VOK Th& firing rare is

propomonai to eye position when the head is stationary and to angular head veloaty Almost

all PVP cells are Type 1, being excited for i~silateral rotations. They pause during saccades

(Scudder 8r Fuchs, 1992). Robinson (198 1) gave the foUowing ecpmion for PVP c d s for the

vertical VOR

where R is the discharge rate in spikes/sec, dE/dt is the eye velocity in degrees/sec during

pusuit of a moving target with the head stationary, dE/dt is the eye velocity during saccades

and indicates that the cd stops fhng during a l l rapid eye movements. dWdt indicates rhe

vestibular component of the signal. The presence of an eye position signal in these neurons

suggests that they receive input from the neural integrator. The PVP c d has many eye signais

converging onto it and can be assigned a function of converhg the sensory sipals from the

vestibdar systern into a motor one.

In the situation depicteci in figure 1.15, eye movments induced by the AVOR are dkected to

the left while those from the TVOR are directed to the right. Using targets with different

distances while eccenmcally rotating rhesus monkeys, McConde et al., (1996) found that the

otolith s i p a l s are supplied to P W c d s but they hst must undergo processing . As mentioned

earlier, the gain of the TVOR is mon& dependent on carget h c e . McConde et a., (1996)

observed that PVP cds did not modulate th& £king rate sigmficafltly when the target distance

was dtered during eccenmic rotation. The EHV c d s on the other hand showed a large increase

in gain and are candidates for this effect.

15.2 EHY Cells

Along with PVP c&, EHV ceils are dso known to contact motoneurom (Scudder & Fuchs,

1992). EHV c d s exhibit large changes in gain when the target distance is changed and probably

represent a dominant pathway for the TVOR. The large target distance sensitivity might be

accomplished by using floccular input kom the cerebdum (McConville et aL, 1996) and hence

may correspond to the Floccular Target Neurons 0. Snyder & King (1995) demonstrated

that the flocculus is supplied with the necessary otolith signal although it is not known whether

the EHVs receive a direct input from otolith afferents in addition to Cerebellar input. The large

modulation of EHVs to a change in target distance during otolith stimulation is easily illustrateci

by considering th& sensitivities. If the axis of rotation interseas the interauml Iine, then the

sensitMties of EHV neurons are .41 spikes/sec/deg/sec and .56 spikes/sec/deg/sec for far and

near targets respectively. But when the axis of rotation is rnoved 14 cm S o n t of the eyes, the

sensitivities become 1.36 spikes/sec/deg/sec for far targets and 2.2 spikes/sec/deg/sec for near

targets, a 62% inaease.

15.3 OtoIith Only, Canal Only, and Canal Otolith Cells.

Others cells in the media and laterai vestibular nudeus indude c d s that have response

characterktics consistent with combined cana and otolith signals (CAOT), cells rhat ody have

canal inputs (CA) and c d s that ody have otolith inputs (OT) (Tomlinson et al., 1996). These

c& had response dynamics that are intermediate between those obsenred in piimary afferents

and those requLed to drive the motoneurom and therefore may represent an intermediate stage

in the signal processing Çromlinson et al., 1996).

1.6 MODELS OF THE VOR

Several models have been designed to explali how the TVOR might operate during OVAR

(Hain, 1986; Raphan & Schnablock, 1988) and during translation (Angelala, 1992). But fïrst a

simple rnodei for the AVOR will be describecl @lobinson, 1981). The model we have written

utilizes Robinson's mode. as the final common pathway.

1.6.1 Robinson's Mode1 of the AVOR

Eye movernents are driven by vinid inputs and vestibular inputs and these two inputs genedy

act in synergy. Visually dnven eye movements indude the pursuit system, where a target in

motion is kept on the fovea, and the optokinetic system, where die eyes move in response to the

movement of the entire visually field Studies of the optokinetic system have shown that it uses

the same circuitry as the vestibular system (Robinson, 198 1). Figure 1.17 shows the model

proposed by Robinson, (198 1) in whifh the vestibular and the optoklietic system are combined.

1.6.2 Models of the TVOR

Hain, (1986) proposed a three-dimensional model that extends the idea of velocity storage

(section 1.4.3). The otolith information about the orientation of the head to gmity changes the

36

time constant of vestibular respomes by modulanng the gain of the velocity storage feedback

loop. Hain, (1986) also proposes diax otolith ugnals in response to d t i o n s are fed in10 die

vestibular system through the velocity storage integrator. The velocity norage integrator makes

up pan of the low p a s filter feedback Ioop in the velWcy storage that extends the t ime constant

of the AVOR This paper suggests diat the bias eye velocity observed during OVAR could be

estimateci by crosssorrelation of hear accelerarion signals and rheir derivaWa. Hain could

generate the bias eye velmiy during OVAR but does not take inro account the t q e t distance

dependence of the TVOR and therefore the modd is inadequate for interaural nanslanons.

Figure 1.17 Robinson's (198 1) mode1 for Wual-vesribular interaction The signal existing form OKS is inserreci in the vesribular nudei (vn). This in tum is added with the ssemicir& canal signaL OKS: Oprokinetic v e m de: retinal slip velocity. dW: Wual surround vel+ dE: eye velociry, CEE head vel+ S= switch (dosed for daylight, open for night) .

Raphan gL Sch~bolk, (1988) proposeci that during OVAR, a dynamic pattern of neural

activ&on produced by the sequential activation of regular otolah neurons wirh different

polarizacion vectors by the rotating gravity vector resembles a traveling wave rhar c m be

detected centraüy. The velocity of the travellLig wave is then used to drive the velocity srorage

integrator. Again this mode1 simulates OVAR and not i n t e r a d nanslaxions and assumes that

there eMrts a delayed signal that drives the system. However, temporal properties of central

vesribular neurons show no such tirne delays (Schor et al., 1985).

Angelaki, (1992) suggested that otolith afferents with different dynamics and polarization

vectors might be nimmed in such a way as to produce a signal proportional to translatiod

velouty. Before the Angelaki mdd, vestibular nudei neurons were desaibed to behave as one-

dimensional linear accelerorneters c h a r a a d by a response dong the neurods polarization

vector. Angelalci, (1992) tramforms the response vector into a response plane having

complicated spatial characteristics Otolith afferents with different polarkation vectors and

dynarntcs wouid converge onto central neurons produchg a neuron that exhibits a responses

rhat rnap out this plane, defined as a response ellipse. These neurons respond to the component

of a stimulus vector on a plane rather than on a single axis characteripng neual response in two

rather than one dimension. Stimulation in the direction of the miwr axis of the ellipse produces

a response that is in phase d jerk while stimulation dong the major axis wodd produce a

response in phase with acceleration. The velouty vecror is then encoded as the vector that is

normal to the response plane.

During eccentric rotations, otolirh organs are exciteci by the tangentid acceleration and the

caoals are exated by the rotation. Howwer, there also acists centripetal acceleration, which

occurs at twice the kequency of tangentid acceleration. Since the neurons in Angelaci's (1992)

mode1 have a broad range of inpuh then they shodd show responses related to centripetal

acceleration. McConviUe et ai., (1996) fded ro find evidence of neurons r n o d d a ~ g at twice the

frequency But these r ed t s are incondusive since the stimulus intensity was very low leading to

the explanation that the stimulus was too weak to eliat any such response. More experiments

are needed to determine whaher the Angelalsi mode1 is correct.

1.7 CANCELLATION, SUPPRESSION AND ADAPTATION

If a target is pursued with the head and not with the eyes, then the VOR needs to be elimliated.

There are two ways that this can be done. Canceliation refen to a central process where the

target veloaty as interpreted by smooth purniit is nibtracted fiom the head veloaty as

38

interpreted by the vestibuiar system. Tomlinson & Robinson (1984) showed that secondas,

vertical VOR neurons do not show a linex addition of the vestibular and pursuit signais during

cancellation of the VOR Instead, the cancellation may be provided by cells that receive

cerebellar input (Chubb & Fuchs, 1982). A second way to eIiminate the vestibular connibution

is by way of suppression. This method ~ m s down the gain of the VOR It is likely diar the

system uses a combination of these methob to elimioare the VOR (Lei& & Zee, 1991).

If retinal slip ina-eases, then the VOR will adjust its gain as to minimïz the slip. Adaptation

refers to the ab* of the vestibular synem to adjust its gaLi in response to long tenn changes in

stimulus. Miles et aL, (1980) proved that VOR adaptation was motor leaming by recording the

gain of the VOR aker a xZ lenses where placed on monkeys. Appropriately, the VOR gain

inaeased reaching an asymptote after 4 days of wearing the lenses. Ito, (1972) suggested that

the site of these adaptive changes reside in the cerebellum Speafidy, Ito proposed that the

coincident excitation of paralle1 fibers and Purkinje c ek in the Nodulo-Floccular lobe of the

cerebellum could strengthen the synapse responsible for VOR motor leaming. The Purkinje

cells would then keep the modulation of the Media Vestibular neurons down. Therefore, to

inuease the gain of the VOR, decrease the Purkinje c a s finn% rate. This was investigated by

Lisberger & Fuchs, (1978) by recording £rom PurkLije c& in the cerebdum duriog the VOR,

pursuit and cancdation. These authors found that the firing rate of the Purkinje cells was

proportional to gaze veiociry (head veloaty + eye velociry). Therefore for a low gain

cancellation, chL gaze veloaty Purkinje c d should show a slight modukcion in the direction of

head movement. Miles et aL, (1986) found that the Purkinje cells modulated but in the wrong

direction with a long latency disproving Ito's trypothesis. Lisberger, (1984) searched for the site

of adaptive changes to the vaibular nudeus and showed that PVP cells have very linle change

in th& gain response when the gain of the VOR changed. However, Lisberger found that

Floccular Tqet Neurons (FTN, which might indude EHVs ~cConvi l le et al., 1996)) changed

th& discharge rate early enough to be responsible for motor learning m&g the bralisrem a

likely place for motor 1earni.q.

C h a p t e r 2

2.0 METHODS

The TVOR systern can be viewed as a connol system for eye movements. Single c d

recordings fiom dert animals romlinson et al., 1996, McConville et a., 1996, Fuchs et al., 1975

to narne a few,) coupled with experimentai data on eye movements and some simplifying

features of the eye (Robinson, 1981), have made rhis system id& for a quantitative an.h/"cal

methods that describe odomotor c o n d There are five major systems for ocdomotor

control These are the vestibule-ocular system, vergence, pursuit, saccadic, optokinetic and the

pursuit system The function of each of these systems is known and dierefore one c m

concentrate on how the s y s t e ~ l l ~ achieves its results (Robinson, 1981). Because of its simpliaty,

we d firn use control systems an+ to derive a tramfer funmon for the firing rate of an

oculomotor neuron before proceeding to a description of the mode1 presented here.

2.1 OCULOMOTOR NEURONS

The discharge rate of oculomotor neuron depends on eye position and eye velocrn/ verin &

Cohen, 1973). For an abducens motoneuron, the discharge rate increases as a subject looks

ipsilatedy and decreases for condateral eye positions. The equation for the firing rate of a

typid motomeuron in the monkey was presented on page 25 as equation 1.5 as is repeated

bdow as equation 2.1.

Where R is rhe firing rate, & is the r-g discharge. E and - are the eye position and eye dt

vdoaty respectiv*, kk-4 spiies/sec/deg and r= 1 spike/sec/deg/sec. Each extra-ocuiar musde

is defhed as having an on direction and an off direction. When the monkey is £ixating at a

target located straight ahead, so that eye position is zero and eye veloaty is zero, then the firing

40

rate of the motomeuron is jusc & - 100 spikes/sec (Robinson, 1981). If the rnonkey fixates a

target locared in a panicular muxle's on direction or off direction then R d increase by kE or

decreases by kE respectively. For example, if a monkey fixates at a rarget located 20 degrees in

the on-direction, then R= 180 spikedsec but if the monkqr b t e s 25 degrees in the off-

direction, then the R-O. If the eye is in motion, R will M e r change by r -. Therefore if the dt

eye is passimg the position where E=O with a velocity of 150 deg/sec, then R= 250 spikedsec.

In appiying control systems analysis to ocular motoneurons, we m u t regard the eyebd and irs

muscles simpJy as a device to be controlled so that we may observe its behaviour to any signal

that reaches the motoneurom. By using equation 2.1, we can say that given any signal that

teaches the motoneuon, we know what eye movemenc E it will produce.

Another way to describe how a system will respond to a variay of sipals is by use of frequency

analys- The ratio berween the input and the output is represented by the uansfer funaion

H(s) where 5 is the complex frequency (having a real and an imagliary part). If one ciehvers a

sinusoidal signal with complex frequency s to a hear system (such as equation 2. l), &en the

output will &O be a sinusoid of frequency S. The amplitude of the output divided by the

amplitude of the inpur is termeci the gain of the system while the ArcTangent of the irnagliary

pan of H divided by the real part of H defines the phase shifi. AU signals c m be thought of as

sums of sinusoids. Therefore, the gain of H will defke how the systern wiJl respond to different

signas at al l frequencies.

The transfer funaion of a differential equation is readdy obtained by the use of Laplace

Transfom. The transfer function of equation 2.1 defines the change in eye position in

response to a change in finng rare and is defined as

Figure 2.1 GaLi and phase Li the fiequency domain of equation 2.2. The gain (a) and phase (b) are representative of a low pass filter. As the frequency inaeases, the g i n decreases and the phase leads by 90 degrees.

where T is the time constant dehed as r/k=.E seconds. The tirne constant describes how

rapidly the eye wiU respond to changes in the £inng rate and represenrs the tirne needed for the

eye to reach 63% of its hal destination. This response is exponentid If for acample, the

.firing rate in equation 2.1 changes suddedy, the eye wiU respond with an exponend

movement with a &ne constant of 2 5 seconb. Figure 2.1 shows the gain and phase of

equation 2.2. As the frequency inaeases, the gain reduces to (sT)-I with the output la%ejng the

input by 90 degrees. While at very low kequency, the gain is jus one and no phase shift is seen.

2.2 THE MODEL

The program to simulate the model presented in figure 2.2 was written in Mathernarica Student

Version 2.2 on a Pentium-166 with 32 MB of RAM Mathematka was chosen over 0th

simulation software because of its portabiliry and its ability to cary out neural network

simularions which we plan to do in the future- Simulation t h e ranged between a few seconds

to about 5 minutes. The program that implemented the ?IrOR for interaural translations and

eccenaic rotations is shown in figure 2.2

Several models were investigated before the final design of figure 2.2 was deaded upon. Ail

models had the following inputs:

1) They received both regular and irregular otolith inputs as described by Fernandez &

Goldberg, 1976~.

2) They received information regarding vergence angle.

The output of the model had to meet certain uiteria so that it might be consistent with

experimend data These uiteria were:

1) The outpur had to be a linear hinaion of the vergence angle.

2) The output (slow h hase eye veloaty) had to lead head velociy by approxirnately 50 degrees

below 1 Hz and approach head velociry as the frequency inaeased.

Both of these output criterions were satisfied by h g the model in figure 2.2. In order to

obtain a signal in phase with velocity from an acceleration signai, we pamally differentiated the

outputs of the primary afferents and adjusted the sensitivities of the resultaat jerk vector. At

htgh fiequenaes, where the Otolith-Ocular Reflex (OOR) is most robust, the irregdar otolith

afferent signal was a i r e partially differentiated making it more suited for M e r

differentiation raher than integration as is mathematically rrqiured htegration of the signal

would lead to a low pass filtering effect, an amibute not observed for the TVOR

Although the otolith-ocular reflex is a bilateral system, the model presented here assumes it is

driving a cyclopean eye. Our moa important goal was to design a model to see if utilizlig the

jerk vector could in fact reproduce experimental data. Many nansfer functions were designed

thar took advantage of the phase lead exhibiteci by the primary afferents and differentiated this

signal as a funaion of frequency. The ones chosen for rhis thesis do not provide the best fit for

the data but are a compromise berween cornpliateci funcrions and accurate resulu. Indeed

some n;uisfer functions that reproduced the means of the experimental data accufately were

functions of real and complex frequency and even had the laplace m s f o r m s raiseci to the 4'

power which inueased simulation rime considerably. One must remember that the

experimental dara is subject to variation and dthough the model presented here does not

accuately reproduce the experimental means (see figure 3.8), its output is contalied between the

maximum and the minimum sensitivities obtained in experiments by Telford et d, (subrnirced).

The easiest of the uansfer functions to design was chat for the torsional eye movements

(ept ion 3.2). We sirnply started with a low pass ater and wrote a simple program in C that

would itiratively mise the laplace nansfom in the denominator to various powers less than one.

The program wodd then check the gain of the transfer function using a least square method

approximation to a logarithmic fit of the experimentai data (ïelford et al., submitced). Figure

3.1 shows the output of this transfer function cascaded with regular afferent input as a function

of frequeacy dong with the firced expeMlental values for the gain of the torsional eye

movements. Vere gain is defined such that a gain of one is a 90-degree torsional eye

movernent).

The irregular afferents were not induded in the design of the torsional system for several

rasons. Upon tilting, the verticai can& cause the eye ro undergo torsion while the otolith

systern a m + maintains the torted position The Cty..m;cs of the irregular afferenrs is not

suited for mainrainlig a position because it is too phasic. Recd that the irregular afferents are

very highiy sensitive to changes in frequency and they adapt very fast (see figure 1.7). The

regulars, with their s m d gains and poor kequency dependence proved more than adequate to

serve as the peripherd signal that can sutain torsion.

HLs] and HJs,w] were obtained in a similar way to HJs] but th& derivation was not as simple.

Marry variables had to be considered in designing these two functions. The output of the mode1

is a cascade of four transfer functions so that as the design process continued, the interaction

between the four funmons needed to be monitored. Therefore, both H,[s] and HJs,w]

designeci simultaneoudy. The reason behind HJs,w]s dependence on both cornplex and real

frequency is discussed later in the Results and Discussion.

Not ody are we interested in the question of how the Orolith-Ocular reflex obtains a velocity

signal, but dso in the interaction between the rVOR and the AVOR As shown in figure 4.1,

the WOR is non-ided. Even at 4 Hz where it is most robust, it only reaches 60% of the

theoretical value. This may be a consequence of the system's inability to properly adjw the

sensitivity after differentiating to a jerk vector. We believe that the TVOR is more robw if the

canals are stimulated (such as during eccentric rotations). This gives the vstm the abiliry to

measure the relative quality of the otolith signal in cornparison to the canal signal. Central canal

neurons already have at th& disposai information about fiequency giving them a good measure

of how mu& enhancement the otolith signal d need Rc,o] is acniay. another network (or

several cascading aansfer functions) that wiU accomplish this ta& A sirnplified version of this

network was used for the purposes of this thesis but a tirne sampling mistake alexted us to the

muitidirnensionaliry and complexiry of F[c,o]. This sïmpEed equation corredy siiulated

AVOR+TVOR for a particular kequency and vergence but my adjustments made to the

variables caused a matked imtability which proved this equation to be useless and warrants no

more explanations. One consequence of rhL attempt is that the AVOR+TVOR reflex is not a

hear funmon of vergence. This idea will be presented in more detail in the Discussion.

Experiments have been plaaned where single cd recordqs fiom the vestibular nudeus of

d e rhesus monkeys will help us dutidate the interaction b e e n the IWO reflexes. We will

then use this data to complae the mode1 for how the AVOR and the WOR interact.

LE-

FIGURE 2 3 Program that &ed out the simulations of Figure 2.2

: [font = input; nowordwrap; ] (*A. Prograrn to simulate the n i rOR with stimulus inceraural trrnslations or eccentric rotation*)

('Irregular afferenc constants. See equatior. 1 . 4 . Constants are taken CO be rhe medians presented in Fernândez c Caldbero. (1976cl*) h i =.44; kai =1.9; tai =101; trni =.009; tT]i =4C) ;

(*canalf) Tl. =.C03; T2 =6; ! *Sa-ze ['constn , kri, kai. rai. imi, t-ii. krr, kar. tar. :TZ, i-rr, Tl, T2] * )

l e g u l [-,,*-] : =25. E!* (1-kar*tar*I**d) * (1,+k~rf 1 t-.rr*I*-,,-) A : c r r ) / ( (~z r* I* -~ - - : * - I fcnr*I**d+lj ) ;

Canal; [-A-] : = (L/. 003) * { I*k-*TZ*T2 j / ! I * W * T ~ ~ I ; ; I I ~e roence

! 1 1 :

I t E l [ s ] in figure 2 . 2 * 1

Return [BI 1 ;

(*HZ I s , w ! in figure 2.2*! ?JFUoON2 [w-] : =Module [ { ) ,

anplitude =.06; ( * * )

tcon : = . 4 5 ; (fseconds*~ numeratexp :=i.95; denominatexp:=numeratexp;

H: =arnplitude*Regul [w] * ( ( (I*w) ̂numeratexp/ (l+I* (tcon*w) ̂denominatexp) 1 ) ; Re turn [Hl ;

1 adjust =. 001; =ON3 [w-,verg-] :=adjuste (NEURONl [w,verg] *PEURON2 [w] ; N [Arg [NEURON3 [Pi, Il 1 1 For [i=l, icS, i++l,

N[ZUg[NEURON3 [2Pifi, 11 1 1 1

( * front Paige 1997*) sens={.l, - 2 3 , -26, .3); (*means 1,2,3,4 hz*) senupper=(.15, .4, - 4 , .4); (*upper and lower for 1,2,4 h senslower={ .Os, -12, .17 ,.S) ;

phasemode1={2.19,1.868,~.683,1.528); (*eut d o m on simulation time*) ( * the phase of the mode1 was not calculated independently of the simulations and inserted into simulations as a constant. This will cut on simulations time*) t=. For[j=l,jc8, j=j+2,

For [i=l, ic5, i=i+l, ( * go through 4 frequencies-..namely f=lHz, 2Hz, 3Hz, 4Hz * )

w=2Pi*i ; ( * used small amplitudes for al1 simulations*)

amp=.01; (*metersi) ampl=l; (*cm*)

( * stimulus*) x [te) =arnp*Sin [w*t] ; yft-I=D[x[tl , tl ; z[t-l=D[y[tl ,tl/lo;

(*r is the target distance. 4 target distances used here are r=lrn, 1/3m, 1/Sm, 1/7rnt)

r=l/ j ; (*vergence is the reciprocal of the target distance used above*)

verg=l / r ; ( * The vergence changes as the subject is txanslated. But since the amplitude used was 1 cm, then this change is negligible. v [ t l was used to show that this is true* 1

v[t_] :=(vexgA2+x[tl ̂2) ̂. 5 ; (*Print [l ; Print [namp=u, amp , "rn w=", W, " phasemol=", a [wl , llvergence=", verg] ; Print il ; )

( * Since experimental values were given in sensitivity defined as deg/cm/MA. then the firing rate corresponding to the eye velocity at a certaub sensitivity can be obtained by using the following formula: sensitivity*vergence*head~elocity*lspike/sec/deg/sec*~

(*plot [{senupper [ [il 1 *verg+arnpl* (W*COS [w*t+phase [ [ i l 1 ] + 4*Sin [w*t+phase [ [il 1 1 1 ,Abs ENEURON3 [w,v [t] 1 1 * (wA2*amp*sin [ w * t + phasemodel[[i]]]/IO-

4*w*amp*Cos [w*t+phasemodel [ [il 1 ] /l0) , ( * upper and lower sensitivities correspond to upper and lower experimental values * )

senslower [ [il 1 *verg*ampl* (W*COS (w*t+phase [ Cil I I + 4*~in(w*t+phase[ [il 11) ) , {t,O,2*~i/w), ~xes~abel->{"the ( s ) I r , trsp/sw)] ;*) t=O ; Print [Nlsenupper [ [il 1 *verg*ampl* (w*Cos [w*t+phase [ [ i l ] ] + 4*Sin(w*t+phase[[i]]])], ,N[Abs [NEURON3 ~w,vergll* (wA2*amp*sin [w*t+phasemodel [ [il ] 1 /10

- 4*w*amp*Cos [wit+phasemodel [ [il ] ] /IO) 1 , " ", N [senslower [ [il 1 *verg*amplf (w*Cos [w*t+phase [ [il ] ] + 4*Sin[w*t+phase [ [il 1 ] ) 1 , " a=w,N[amp*wA2/101, "gU, " theory=" ,N [ (w+4) *amp*lSO/Pi/r], " td=", r, "m", ",]; t=.;

(*t=O; Print [N [sens [ [il 1 *verg*ampl* (w*Cos [w* t+phase [ [il 1 1 + 4*Sin[w*t+phaseC [ i l I l 1 1 ," Ir ,N [Abs [NETIRON3 [ w , v [tl 1 1 * (wA2*amp*Sin [w*t+phasemodel [ [il 1 ] /IO- 4*w*arnp*Cos [w*t+phasemodel [ [il ] ] /10) ] , l1 ", "a=" , N lamp*wA2/10] , llgn, " theory=~,N[w*amp*l8O/Pi/r], td=", r, "mw1 ; t=. ; *)

1 1

TVOR responses where simulateci based on experimental data obtained hom Telford et al.,

(submitred). The gains and phases of the transfer functions that make up the model will now

be presented dong with the sensiwities and responses they invoke.

The TiIt/Translation box in figure 2.2 deades whatier a horizonta rnovement is being made or

the exatation of the afferents L due to a tilt. This box is not based on the accepted method that

utilizes a fiequency filter to elùMate the assumed arnbiguity in the signal (see page 28). Instead,

we have employed a method that d e s inro consideration the modulation of both the unide

and the saccule under the assurnption that there does not &st an ambiguity (actudy, the model

proposed elimliates am/ ambiguity). This signal is then used ro either tum on (allow a signai to

pas) or keep off [&bit) a pathway for horizond movements (pathway H in figure 2.2). Note

that a pathway leading to torsiond eye movemenu is aiways on (pathway through the low pass

filter HisJ see below) so that horizontal eye movements of low fiequency will &O cause some

torsion (Paige & Tomko, 1% la).

3.1 DIFFERENCES BETWEEN TILTS AND TRANSLATIONS

The fuoction that anives ar the decision about the type of rnovement takuig place is F(e,a) and

is dehed as:

The output of F(0,a) will determine whether pathway H in figure 2.2 will be m e d on or off.

We shall adopt the convention that a negative output from F will be a result of a pure tilt and

d inhibit the horizontai eye movernent pathway. Conversety, a positive output will be a r e d t

of a horizontal rnovement (either done or during a tilt) and will excite the horizontal eye

movement pathway. Work has begun on hinctions that will replace equation 3.1 and will supply

the junction at the uregular urricular afferent (figure 2.2) with a scallig factor detemiined by the

degree of tilt and the magnitude of the horizontal acceleration. Here we will only be concenieci

with whether the pathway is nuneci on and off.

Equation 3.1 m m satisfy c e conditions: 1) It m m &tain both pathways off in the

absence of a s8mulus, 2) it must inhibit the horizontal eye movement pathway during a pure tilt

so that no horizontal eye movernents (in head coordinates) can be initiateci and 3) it m u t tum

on the horizontal eye movement pathway during a horizontal d a t i o n regardless of whder a

tilt exist. Parker et al., (1985) obswed that after landing, astronauts exhibited horizontal eye

movemMts in response to a head tilt but in the absence of translation. This gives us the fourth

criterion that eqytion 3.1 must satisk namely thar 4) &er the conditions d&bed above have

been met, eqyation 3.1 mus tum on the horizontal eye movement pathway in response to a d t

but in the absence of horizontal translations in effect contradicting uiterion 2. Acsudy, it will

be shown that &er bemg in space, central mechanlm change and the behaviour of eye

movernents switch from criterion 2 to criterion 4.

Let p=(S&), where gi is an intemal memory of ig of acceleration where ig is the accderation

due to gravity measured in m i t s of 9.8 m/s2, (gi=g= L on earth under nomial conditions), let a

be the accel&on in the horizontai plane and let M e < 9 degrees be the deviation frorn the

vertical. Then S,=gCos(B)+aSin(B) is the acceleration felr by the saccule for an interaurd

mslation a after tilting an angle 8 from the verrical (S, = g in the upright psition). p will then

be defineci as the acceleration felt by the saccule relative to graviv. ALo let q=U, where

U,=gSin(e)+aCos(0) is the acceleration felt by the utride for an in terad tmslation a after

&hg an angle 0 fiom the vertid (U,=a in the upright position), then F(0,a) is a simple

function that detennifles the magnitude of the degree of tilt relative to auy in terad

acceleration.

In the absence of any tilts or horizontal translations, a = Q g = 1 and 8=û. It follows that Sa =g

and q=Ua=a=O. However, p=(Sagi)=O giWig us the r d t that F(0,O)-O satisfjmg the fmt

condition.

The second condition that ne& to be satisfied has a = O but e > 0 This gives Sa = gCo$) and

Ua=gSin(9) so that p=gCos(8)-gi =g (COS@)- 1) which is less than zero &ce Cos(@ < 1 Then,

since a = O, F(€I,O)< O and the horizontal pathway is inhibited

The third condition occurs during a translation without a tilt In the absence of a dr, a > O a d

û=O. Therefore, S,=g making p=O. Therefore, F(0,a) =&a =a >O and the pathway for

horizontal eye rnovements is m e d on.

Now suppose 8>0 and a>O, so that an earth horizontal translation is r&g place during a dt,

then S,=gCos(B) + aSin(0) and U, = gSiu(9) + aCos(e). Proof that F(0,a) >O for aU 0 and a

satisfying the thLd condition is provided in appenclk A.

Before we show that the 4' condition is also satisfied, note bst that mernory of Ig accelemion

is assurneci to &st and is subtracted from the sacde in order to obtain p (figure 2.2). We

hypothesize thar chis mernov is forgotten after being in gravity kee space so that for thts

situation and for several hows afrer landkg, p=S,.- gi where gi < g. We will assume that the

magnitude of gi continues to decrease as long as a subject is in space. Therefore after all the

memo'y is forgotten, gi = O. A head tilt in the absence of translation (a =O) would t h e . result in

p=gCos(B) and q=gSin(B) so that F(0,a)- g%os(€I)Sin(€I) >O tuming on the horizontal eye

movernent pathway in response to a pure tilt. - p p p p p p p p p p p p - - - - - - - - - - - - - - - - -

- - - -

Whesher a horizontal translation or a tilt is taking place, regular afferents c o n ~ u o u s l ~ drive

Hls] and produce torsional eye movements. In other words, the pathway to H,[s] is aiways

m e d on. It is up to the horizontal pathway to inhibit the torsional pathway once the

horizontal pathway becomes active. H,[s] is just a low pass filter defined by:

H , [s] = .05( 1

(sTtiii ).95 + 1 1

where T*=S seconds. The gain and phase of equation 3.2 after receiving regular otolith input

are shown below in figures 3.la and 3.lb. Am*, this low pass £ilter is a function of the

synapse of a collaterai that arcends from the horizontal pathway to the torsional pathway

i n h i b i ~ ~ it (see figure 2.2). So that as the horizontal pathway H is accivated, the torsional

pathway is inbited according to H&].

Pathway H in figure 2.2 represents the Horizontal TVOR pathway. Once it has been

interpreted that a horizanta1 movement is taking place, information about the amplitude of the

movement as interpreted by the irregular otolith afferents and the vergence angle of the eyes is

passed on to Hl[s]. Hls] is a high pass filter desuibed by the w f e r function:

[SI has the responsibiüty of conuolluig the gain subject ro input from t

irregdar afferents and the vergence angle. Bode plots for the gain and phase of H,[s] is shown

in figure 3.2. As can be seen, it is mer* a high pass filter that changes its phase by 45 degrees

throughout the frequency range simulatecl. The primary afferenu have th& own transfer

hinction so that Gregular prLnary afferent input into H,[s] will change its characteristics. Bode

plots for the Hl[s] after receivhg ocoïith input is shown in figure 3.3.

Figure 3.1 Gain (where a gain of 1 is a 90-degree torsional eye movement) and phase re acceleration of the torsional VOR as predicted by HJs] after receiving regdar otoiith input. Ai Gain of the Torsional VOR As the frequency hueases, the amplitude of the torsional eye movement decreases by continues with very d tilt angles lesen at high fiequenaes. Throughout the fiequency range simulateci, the output of the mode1 clos+ follows that of the experimentai values. B: The phase re acceleration of the torsional VOR As the fiequency Licreases, h e phase approaches head veiocity (the phase of the horizontai TVOR Experimental values fiom Telford et al., (subrnitted)

Figure 3.2 Gain and phase of H,[s]. A: H,[s] has the simple characteristics of a high pass @ter. B: The phase starts out at 45 degrees and approaches zero as the fiequency increases. This will become important during the discussion about HJs,w].

Figure 3.3. Gain and phase of H,[s] after it receives input fiom the irregular primary afferenrs. The ciifferences between the gain and phase presented here and that of figure 3.2 are due to the effect the lrregular afferents nansfer hinaion has on H,[sJ. A: The f ier is designeci in such a way that otolith input will increase its high pass filter characteristics. M: Merer Angles. B: Phase lead increases after otolith input and continues to lead throughout the frequency range simulatd

HLs] is designeci in such a way su& thar its produa with urrgular otolith input increases the

d t a n t corner kequency. The phase of H,[s] leads liuear accelerauon by 45 degrees at O. 1 Hz

and is in phase with acceleation at fiecpenaes greater thaa 1 Hz (figure 3.2) Due ro the phase

characteristics of the irr- otolith derents, upon irregular otolith input the phase lead is

inaeased to 70 degrees at 0.1 Hz and to around 40 degrees at 1 Hr The phase continues to

approach acceleration as the frequency increases but maintains a lead men ar high frequenaes

(figure 3.3b). This phase adjustment will become important later where simulations will show

that low fiequency trans1atiom exhibit a phase lead to head veloâty and that the phase of the

eye vdoary approaches head velociry as the kequency inaeases (see Paige et a., 199 la, 199 1 b.

Paige et al., 1991 for acperimenral resuIts). The output of H,[s] d dictate the amplitude of the

eye movement and will be one of the inputs into His,w].

H&,w] is another high p a s filter but wirh different characteristics than H,[s]. Its main goal is to

pardly differentiate incoming signals as functiom of £requency so that they are in phase with

the jerk vector (and hence vdo* see page 26). HJs,w] was designed as a funaion of 2

variables; real and complex frequency (eqyation 3.4). One of the major consequences of d i s

design is that the M i e constant of decay of a signai going h o u & Hls,w] is a b a i o n of

frequency. The ~robability for the &ence of a neuron that perseverates its signal for a longer

p e n d of rime after high fiequency stimulation in the direct TVOR pathway is prenimed low

but is unknown. Nwer-eless, this transfer function proved hi& efficient in reducing

simulation t h e and achieving its desired results. Some of its consequences wiU be describeci in

the discussion.

T,= lsecond TT= 0.1% seconds

HJs,w] receives input bom the regular otolith afferents and its output L mdtiplied by die output

of Hls]. The reguIar otolith input tums on rhis function but provides m i d high frequency

enhancement. Most of the enhancement and amphde adjustments have been taken care of by

Hls] and dierefore what is left is the appropriate phase adjutment. Bode of the gain and

phase of H&,w ] More and after receiiving reg& uaide afferent but without the input from

Hls] are shown in figures 3.4 and 3.5 respectively.

The major contribution of H&w] to the model in figure 2.2 is the phase advancement it

provides the reguiar signal dong with the signai coming out of H,[s]. At low frequencies (beïow

0.6 Hz), the phase lead is huge reaching up to 180 degrees for frequencies less than O. 1 H z This

180degree phase lead is equal to a 90-degree phase lead with respect to the jerk vector.

Howwer, as srated earlier, the jerk vector is in phase wirh velocity and hence a 90degree lead

with respea to the jerk L in fact a signal that is in phase with acceleration. In other words, if the

movement is a low Gequency movement, Jien this transfer funnions mereky maintalis the

s igna phase. As the hequency incrûases, the phase approaches that of the jerk veaor. This will ensure that the slow phase eye velocity at low fieqyenaes WU lead head veloaty.

Figure 3.4 Gain and phase of the high pass Uter HJs,w] Although rhis filter does affect the amplitude of the incoming signal (espeâaUy at low fiequenies), its main funaïon is adjusting the phase. A: Like HlsJ H&,w] retlL a simple high pas filter. B: Phase of H&,w]. As the fiequency increases, the phase hovers around 90 degrees leading acceleration.

Figure 3.5 Gain and phase of HJs,w] after receiving regular afferent input A: Unlike the cascaded gain of H,[s] wirh the irregdar input, the gain m e is ody slightly affected. B: The phase of H,Cs,w] begins to lag jerk at high fiequenaes after receiwig regular otolith input.

3.5 OUPUT OF Hl AND H2

ki the absence of canal input, the eye vela* response to a translation is detemGd

output of the jwction labeled 'jerk' in figure 2.2. At this poinq the otolirh signai has been made

to be in phase with velocisy and its sensiWity adjusteci accordligly. The veloaty commands will

then get integrated for the position co~~flallds in the box labeled "Canai Processing". Note that

the TVOR is a non-ideal system Çideal meaning behaving as is geometricalh/ rrquled) and the

sensitivity adjusmient that has taken place up to this point reflects rhis weaCness.

The firing rate of a neuron representing a veloaty signal that is to be sent to the oculomotor

nudei is shown in figure 3 . 6 ~ Recal. that the ocular motoneurom require a velocity signal and

N integral (position) as describeci by equation 1.5. Howwer, integration tends to enhance low

frequency signals and reduce the amplitude of hi& kequency ones. Since the TVOR operates

best at hi& fieqyency, then figure 3.6a is also an approximate description of the finng rate of

the oculomotor nudei as a function of acceleration and vergence since the contribution of the

position signal will be s d Figure 3.6b shows that as the frequency increases, the phase of the

slow phase eye velocity approaches head veloaty. These results compare wd with experimental

results (see Paige et al., I99 1, 199 la, 199 1 b, Telford et al., 1996, Telford et al., (nibrnitted)).

The gain of the TVOR defined as the peak slow phase eye veloay predicted by die mode1

divided by the peak theoretical slow phase eye velocity is shown in figure 3.7. From the phase

difference shown in figure 3.6b (the theoretical phase resides on the 9Odegree line), it is

apparent that the theoretical and experimentai peaks occur at different &es for a translation of

the form x(t)= ASin(w).

Figure 3.6 VeloQty cornmand that will feed the oculomotor neurons and iu phase. A: Sirnularions for 4 vdues of the vergence angle as a function of fxequency. The $em beglis responding after 0.3 Hz because of the filteMg achieved by H, and H1 B: The phase re position (90 degree line is veloaty) is independent of the vergence mgle of the eyes and approaches the jerk vector as the frequency increases

Figure 3.7 shows that the output of the mode1 is aiways less than what is expecred theoretidy

but approaches the theoretical values as the freqyency increases. At 4 Hz, it seerns that the

model's output reaches 70% of the theoreticaily ideai value but due to the phase differences, this

value is achiah/ smaller (-64%). Nevertheles, the overall shape of che curve rtiU maintaineci

and is consistent d the fact that the TVOR is not a robust system, The theoretical vaiues

where obtained fiom the fact that if we let x(t) be the position at arry time t of a subject

undergoing interaurai translation, let A be the amplitude of the in te rad translation and let d be

the target distance, then after a time t, one of the eyes has moved û degrees where

8=ArcTan( 3) (figure 1.1 1). The theoreticai slow phase eye velocity wiU then be de£ined by D

equation 3.4 as:

Note that the target distance d is also a variable of time since as a subject is translated, the

distance increases. But the simulations c d out in this thesis used k . 0 5 meters &g the

change in d negligible.

Another meanire of the performance of the TVOR is its sensitMry mea~u~ed as eye velocity

divided head velocity and is expressed as deg/cm/MA for particular accelerations. Figure 3.8

compares the sensitivicies obtained from the model (0.25% peak acceleration) to thar obtained

experimentaiy for 0.2-0.3 g accelerations. Experimental values were obtained kom

Telford et al., ( subrnitted) and represent the mean of 3 squiml monkeys. The sensieMry

predicted by the model acniay. lies within die arperimental &UII~ and minimum range.

The dope of die sensitMty cuve increases sigdcandy with increasing kequency as expected.

The ideal TVOR has a sensitiviy dope of 0.57 degrees/cm/MA (Paige et al., 1994, and the

experimental values 0bt;tined by Telford et al., (submitted) at 4 Hz averaged 0.31

degrees/un/MA, 54% of the ided value) and that of the modd 0.33 degree/cm/MA.

Figure 3.7 Peak eye velocity produced by the model divided by theoretical peak eye velouty. The sharp rise in the cuve indicates the robust hi& frequenq response of the model, reachlig 70% of the theoretical value at 4 Hz ( see texc for further dadication of rh is value). Nore that the peaks occur at different times sine the phase produced by the model leab the theoretid phase throughout the frequency simulateci. Vergence = 3MA See figure 3.6b for phase descriprion

Figure 3.9 show sensirivities as a hinction of vergence. The infiuence of vergence on die TVOR

response is deady linear. The slopes of the regression lines agree well with experirnental values

for hi& frequencies @Hz, modd: 0.340 deg/cm, experiment: 0.32 deg/cm 2Hz, model: 0.196

deg/cm, experiment: 0.19 deglun), but not for low frequencies (Hz, modd: 0.041 deg/cm,

experirnent: 0.08 deg/cm, OSHz, modd: 0.007 deg/cm, experiment: 0.02 deg /cm)

(experimental values from Telford, et al., submitted).

Figure 3.8 Sensiavities obtained fiom the mode1 compared with the experimental values Fdord, et al., submitted). Experimentd vaiues are the means of rhree monkeys.

Figure 3.9 SenSitvities produced by the mode1 as a function of vergence during Laterad translations for several freqyenaes. Acceleraton = 0.2g.

3.6 AVOR-TVOR INTERACTION

One way ro excite both the canals and the otolitb organs is by eccenmcally r o t a h a subject.

Eccentric rotation refers to rotation around an axis that is rernoved from the center of the head

and is useful in studying the interaction between the AVOR and the TVOR If a nibjecc is

eccentrïdy rotated to the left (figure 1.14, dien dis is +valent to a leftward translation and a

rightward rotation about a head-centered &. If the gaze is cikected towards the axis of

rotation, then the AVOR and the LVOR should cancel r d * in no eye movements ( V i e et

al., 1986). If the gaze is directed to a target located farther away than the center, then the AVOR

shodd dorninate and if the gaze is directed to a target located doser to the subject than the

center of rotation then the TVOR should dominate.

During eccentric rotation, the otolirh organs are stimulateci by the rendtant tangentid

acceleration, where Gpt=&~in[m]where A is the amplitude of the movement and r is the

radius of rotation. The signal generated by the mode1 in spikeshec is not suffiaenr to cancei

the AVOR signal which is proportionai to the hequency of rotation with 1 Spike/sec/deg/sec

@obimon, 1981). Evidence that the TVOR is more robust when the canals are sùnultaneously

activated was presented by Anastasopoulos a al., (1996). A network of neurons is being

developed for the mode1 in figure 2.2 that enhance the TVOR when the canais are activated.

The interaaion between the signals comlig fiom the canals and the otolith is predicted to be

non-hear. The discharge rare of secondary neurons receiving cana stimulation is proportional

to head vdocity (Robinson, 1982) which is a hear hc t ion of fiequency. However, according

to the modd in figure 2.2, the frequency characteristic of a secondary vestibdar neuron

receiving otolith input has the shape of a hi& pass filter (figure 3.6). Suppose that a mbject is

being eccenuicayl rotated at a fieqyency u , wirh the axis of rotation located r cm infiont of the

subjecr with the gaze directeci towards the center of rotation. Then the AVOR and the TVOR

should add and cancd. Now if the frequency is doubled to w , = 2 o , and the gaze is maintained

towards the axis of rotation, then the AVOR and the TVOR should again cancel. F[c,ol the

funmon whic we wiU design to handle this interaction will be both a funmon of freqyency and

vergence of the eyes. A simplifieci version of F is shown as equation 3.6.

where C is the signal that originated kom the canals and O is the signais that originated fiom

the otoliths. Simulations showed that canals signals at the junction flc,o] always dominateci the

otolith signal up to a frequency of 4 Hz so that for low at kequenaes less than 4 Hz, the ouput

of F is p a t e r chan the Orolith input Note that in the absence of canal stimulation, nich as

during a pure linear translation, or when there is a large otlith signal, such as during eccenûic

rotation with a dose target, F simply reduces to O. Figure 3.10 depicts frequency characteristics

of central Canal (Robinson, 198 1) and Otolith neurons as predicted by the mdel.

Canal

i Amplitude=B degrees P e a k 10 Peak

Radius = SOcm

? j

O 0.5 1 1.5 2 2.5 3 3.5 4 4.5

Figure 3.10. Firing rates of the central canai neurons (Robinson, 1980) cornpared to ththe predicted firing rate of central otolirh neuron for different vergence angles. The nonlinearity of the c e n d firing rate of otolith neurons force the interaction becween the AVOR and die TVOR to be nonlinear.

According the anatomy in figure 2.2, wm in the absence of an otolith signai, an increase in

vergence c m in effen increase die &charge rate of the horizontai pathway as long as the

background discharge of the Otolith prixnaxy afferent is maintaineci. It is possible then that the

AVOR receives its information about vergence from this pathway- A lesion that Mght abolish

the background discharge rate of otolith primary afferents could &en reduce the AVOR's

dependance on vergence.

Chapter 4

4.0 Discussion

This thesis presents a systems model that simulates the eye movements produced durhg

sinusoida hear i n t e r a d nanslatiofl~. This kind of modeling l ads to certain disadvanrages

since often, the signak that are created in a systems model are not found in the brain rnaklig the

mode1 ueaiistic. Another disadvantage is that such a model does not indude tbresholds or

saturation of single neurons but attempts to simuiate the population behaviour of the system.

Nevertfieless, the advantage of such modehg is the ability to understand the systern in ternis of

mathematical principles and derive experiments based on the predictions of the modd.

Two types of T W R are described The hst maintains ocular fixation during i n t e r a d

translation and the second causes torsion of the eyes in response to a head tilt. For horizontal

translations, the model ut ihs signais recorded £rom otolith afferents by Fernandez &

Goldberg, (1976) and attempts to manipulate these real signals into a form (Robinson, 1980)

that would produce compensatory eye movements. Several important variables that influence

the TVOR, induding the vergence angles of the eyes (target disrance), amphde of the

translation and the frequency of translation where rnanipikred in order to quanafy the TVOR

One of the flaws of the modd is that it is a unilateral rnodel that drives a cyclopean eye.

Contralateral otolith input might play a role in the connol of eye movements men though if

they do it is probabty mliimal. It may be that c o r n m . pathways are not a propery of the

otolirh-odar system (Wiïon & Melville Jones, 1979). If rhey are, we expect to be able to adjus

the gains of the nansfer hinaions presented here in order to accornmodate the contralateral

otolith input. Our major goal was to reproduce experirnental data (Paige et al., 1991, Paige et al.,

1991% Telford et al., subrnirted) using primary afferent input as described by Fernandez and

Goldberg (1976~) and we believe we have succeed at that task as show in figure 4.1. On the

0 t h hand, the arperimental results on which we based our model are actuaily the product of a

bilateral system. Although the architecture is ciifferent h e m the model and the red system,

our maLi concem is with procedure. Can the jerk vector be used in obtaioing an accurate

central representation of head veloaty? We believe chat it c m . With this established, some of 70

our future go& are to extend the mode1 to accommodate condateml vestibular input. Another

flaw is that we have assumeci that the population of the regular and irreguIar otolith afferent is

the same. Figure 1.5 shows a hinogram of the number of unis with a particular coeffiaent of

vanation (COV). The COV of regular and irregdar afferents are l e s than 0.1 and greater than

0.4 respemvely. It is obvious form figure 1.5 that the regular primary afferenrs oumurnber the

lrregular ones, somethlig we have not taken into consideration when designing the model. The

reason for this is we believe that the regular and irregular afferents have different functions in

drivlng the TVOR The imgulan dicrate the s k of the movement to be perforrned while the

regulars inform the system of the rype of movement that ne& to be p e r f o d R e d that

regular otoIith afferents have a flat kequenq response and we believe that the regdan are

hadequate to set the required output amplitude for different kecpenaes of stimulation. Also,

because of th& low gain, modes+ increasing cheir nurnber in the model would have little effect

on the fieqyency dependence of the system as designed. Modehg the neurons rhey feed (Hl

and HL) as we di4 led us to believe that regular afferents seme another purpose. As shown in

figure 1.6, irreguiar afferents dso adapt quite signLficmtly in a very short period of time. R e d

that the t h e constant of H&,w] is a funaion of kequency such that as the frequency

increasing, so does the time constant. The slight inmase in gain of a regular afferent due to an

increase in frequency is suffisent to alter the àme constant of HL. Therefore, thïs neuron will be

used in subsequent modeling to perswerate the signai &en by the irregular afferent so that as

the irreguiar signai adapts, the reflex w31 maintain its funcknality. RRegar otolith afferenrs

have been designed to drive HJs,w] and therefore we hypothesize that th& greater population

serves to compensate for the irreguIar otolith afferents adaptation. No work has been

undertaken to dwdop this idea but f is also part of our future goals.

One of the advamages of the model is that the prirnary afferent signals used are provided by the

transfer funaion derived by Fernandez & Goldberg, (1976~). Using the rd otolith signal made

the model more realistic and resvicted us with the kind of processing we could do on thern

since the afferents dynarnics had to be taken into consideration. The transfer fwictions shown

in chapter 3 proved to be the moa efficient and sweral predictions could be made based on

their functionality. These predictions are iisted in the next section.

Tme (sec) 1

Figure 4.1 Slow phase eye movemenrs for translations with different frequenaes. Amphde =

0.Z g for all A: For high kequency, the mode1 and experimental d u e s appro&h thar of the dieoretid but still lead in phase by less that 10 degrees. B,C: As the fie@&cy decreases, the experimental and mode1 output become even more non-ideal and inaeasetheir phase lead The mode1 and the eXpenmental values are Li good agreement for ail 3 fiequenaes simulateci

4.1 PREDICTIONS AND EXPERIMENTS

The first predictions we will mention have to do with torsional eye movements. In place of the

fiequency filter hypothesis that presumabb aliows the otolith ocular system to distingwrh

between an in re rad aanslarion and a tilt of the head (Paige et aL, 1991a), we have taken into

considerarion the modulation of both the saccule and the unide and have corne up with a

funaion (equa8on 3.1) that can distinguth between the two s t i d The modei in figure 2.2

has two independent pathways, one for the horizontal eye movements (horizontal pathway) and

one for the tonional eye movements (torsional pathway). The toruond eye movement pathway

has been modeled to continuody receive regular otolith afferent input and is therefore always

on ("on" meaning canying a signal). The signal coming lrom the regular afferents is then passed

through a low pass filter resuicting the torsional eye movements to low frequency translations

mirroring experimental results (Paige et ai., 199 la). Acsuaily, the Iow pass filter H,[s] has taken

the place of a synapse that extends from the horizontal pathway to the torsiond pathway (figure

2.2). In dis design, the torsional pathway is dways kept on during any movement in arry

direction by the modulating regular afferents, but as soon as the horizontal pathway is tumed

on, a colla~eral mending from this pathway ro the torsional one will inhibit the torsional eye

movements with low pass filtering chcteristics. Therefore, the hst prediction that is

produced from this design is that

Pl) The torsional eye movements can be inhibited ody if the horizontal eye movernent pathway

is turned on.

If P I is m e , then it is possible to activate the torsional VOR pathway with a high frequenq

signal and d ger tonional eye movements if the horizontal eye movement pathway is not

tumed on. This could be accomphhed by using galvanic CUrrents while recording torsiond eye

movements for a variety of bequencies. Irreguiar afferencs cm be selectively and revenibly

silenced by appkymg a DC a n d m e n t of 100 pA unilatedy or bilat* to both ears

(Goldberg a ai., 1992, Angelaki et al, 1992b). If in fact the horizontal pathway inhibits the

torsional pathway, then by applyhg galvanic currenrs we expect the amplitude of the torsional

TVOR to rnaintain a somewfiar constant amplitude across freqyenaes.

Accordhg to the anatomy shown in figure 2.2, the torsional VOR is at moa a di-synaptic reflex.

Evidence has already been obtained by Uchino et aL, (1994) that there do exkt connections

from otolith primary afferents onto the abducens nudeus in cats. Torsionai eye movements do

not result from abducens activation but from activation of the ocdomotor and trochlear nuclei.

We are predicthg that these connections aLo &. Our second prediaion then States:

PZ) The latency of the torsionai eye movemmts shodd be equd to the cime it takes for a signal

to cross a synapse and for the eye muscles to be activateci. In to-d, the latency is predicted to be

less than IO m. This can O* be accomplished if there exist direct regular otolith afferent

connections onto the rrochlear and ocdomotor nudei

Torsion of the eyes is of very low amplitude during horizontal aanslation so why wen have a

torsional eye movement? During translations and upon an abrupt change in the direction of

motion, procashg delays mi& cause objects to be perceived as cwistlig causing the eye to

undergo torsional movemena. However, the error associatecl in &ping a bar vertidly on

earth is about 2-3 degrees ma+ any twisting effem that might be perceived negligible. It h o

ma/ be a by-produa of the design of the TVOR We can test this ides by noting that the

combination of Pl and P2 suggests that every horizontal eye movement is preceded Sy a

torsional one. This idea is not ody a result of the ciifferences in latenaes, but of our anatomical

design. The torsional pathway can ody be inhibited after the horizontai pathway has been

turneci on.

The torsional pathway is activated by regular otolith input. Recall that firing rate of regular

afferents is b o a constant aaoss Lequacies so that a large Licrease in kecpency would not

cause a large &ange in the amibutes of the torsional VOR if it were not for the presence of the

horizontal pathway. Regular afferents are the ody input to the torsional mechanism and this

design gives us our third prediction:

P3) Rernoving the regular orolith afferent would eliminate the torsional eye movements during

tilts and horizontal translauons. h o appiymg galvanic currents to the ear (galvanic currents

have been shown to silence the irreguiar afferents, see below) should have no effect on the

torsional eye movernents.

74

One of the consequences of rhis prediction is that the torsional T ' W R is not driven by Kreguiar

otolith afferenu. Cmentlythere is no method by which regular otolith afferem can be silenced

making this prediction diffidt to test d i r e . The experiment used to prove prediction 1

could be u t M even though this ody gives us some proof that the irreguiats do not drive

torsionai eye movernents rather than that the reguiar input drives them. The sirnulated torsional

eye movements' responses are shown in figure 4.2 for i n t e r a d translations for freqpenaes of 1

Hz and 3 Hz at an accderation of O.&

Figure 4.2 Torsional amplitutdes for various head trauslations. Accderation = 0.2g. A: Very low kequency movements yidd the highest amplitude (2.5 degrees) and a phase very dose to linear head acceleration. B,C: As the freqyency i n m e s , the phase approadies head d o + but the amplitude decreases considerably. D: A typical head veloaty profile at E3.z

Note thar there is no vergence information supplieci to these pathways (figure 2.2) maintaining

experimental consistency that the torsional part of the TVOR is not a hinaion of vergence

(T'elford et al., (submitted)). But as mentioned earlier, the degree of activation of the horizontal

pathway will dictate the degree of inhibition of the tonional VOR pathway. The TVOR is a

linear function of vergence (Paige & Tomko, 1991b). Therefore, an inaease in the vergence

angle shodd increase the a&viry of the horizonta pathway, which in ~m decreases the activity

of the torsiond pathway This amibute would rnake the torsional VOR a fundon of vergence

angle even though the effect is indirect. This leads us to our fourth prediction:

P4) The torsional VOR is a function of vergence angle onh/ duiing horizontai transIation.

This is faLty easy to test. Torsionai eye movements could be rneasured during translation with

the gaze of the subject directed at targets with different distances. As the target distance

increases, so should the amplitude of the tonional eye rnovement.

According to the model, horizontal eye movements are rnediated by regular and irregular

afferents and are a function of vergence. Both the TVOR and the AVOR use a final comrnon

pathway instead of p d e l pathways and it will be argued later that when both are active, the

AVOR enhances the TVOR Our fifth predicrion States that

P5) The AVOR and the TVOR w the same pathway and share the neural integrator. So that

demoyiag the integrator will affect the ab* to hold gaze for both translations and rotations

for a particular direction of movement.

Simulations showed that otolith vdocity signals are dways dominated by canal velouty signais

and that canal activation can enhance otolith veloaty signals. After receiving this enhancement,

the otolith signal is modeleci to add to the c d signal. Although not shown here, this cm

provide a cenaal rneasure of the robumess of the signal coming in and merging with the canal

ceh. This might even be a site for adaptation since the men& of enhancernent can be

adjusted. This idea has not be purnieci in detail but led to the idea that the merged signals

c o n ~ u e on to a cornmon integrator.

The model has the vergence angle of the eyes (or target distance) affecting the reflex at the level

where the irregular otolith afferents act in the brainsrem, we predict that:

P6) Silencing the kregular orolith afferents will also reduce the systems dependence on the

vergence angle.

According the anatomy presented in the model, this would be difficult to v&. Angelaki et al.,

(i992b) found that applymg galvanic &dation during Off Vertical Axk Rotation (OVAR)

reduced the amphde of the slow phase eye velocity by 70°h. Goldberg et al., (1992) on the

other hand showed that the effect of such a current applied to the inner ear while the mon+

was undergoing motion in a ceamfige was minimal. Simulations of the rnodel presented here

tend to agree with the Angelaci resuIt Remo-&g the irregular afferent input reduced the slow

phase eye velociv by up to 80%. Therefore a p p h g galvanic currents to the ears in order to

verïfy ~rediction 6 will not work As rnentioned earlier, the slow phase eye velocity L expeaed

to be reduced but what we would like to ascertain is how much of this reduction is due to the

silenciug of the irregular otolith afferents and how much of it is due to the reduced sensitivity to

the vergence angle. If i n f o ~ o n about vergence affected the synem at a different site, then

the reduction in eye velocity when applymg gdvanic currents can be attributed to its effea of

silencing the irregular afferents. But if information about vergence affected che system as

indicad in figure 2.2, &en the reductïon in eye velocity will dso be due to the la& of

information about vergence. The methods in which we have tied both of these variables

together make it difficult to disable one and observe the effect on the other.

Our seventh prediction deals with the contribution of the reguiar otolith afferents to the slow

phase eye velocity. SpeaficaUy, we predict that

P7) SilenQng the regular otolith afferent is predicted to reduce the slow phase eye velocity by up

to 85%.

Regular afferents can not be silenced as of yet. But like the irreguiars, s i rd t ions showed that

slow phase eye velociry was reduced by up to 85% if the regular input was removed kom the

model. This result is inciiredy supported by Goldberg et al., (1992) who supports the idea that

regular afferents drive the VOR while irreguiars drive the vestibuio-spinal tract. Their argument

is based on the reiative gains of the prirnary afferents. They argue that the UTegular afferents

have a large enough gain as to be able to move a heavy body. On the other hand, the eyes carry

77

no load (Robinson, 1980) and are easy to move so that the r&ar afferent signal is niffiaent for

their reflex.. The design we have used here use both the regular and irregular signals for the

TVOR and elimioating either one proved to reduce the slow phase eyeveloaty.

As rnentioned earlier, the model utilizes memory of a Ig accelemion in deciding whether a

movement made is a tilt or a translation. We further hypothesized t h a this mernory is forgotten

after space aght and renirns with a certain t h e constant when the astronauts rerum to earth-

Immediately after landing, the memoxy of a Ig force is at its minimum causing a tilt of the head

to be interpreted as a lin= translation (Parker et al., 1985) (how the mode1 accomplished this

was shown in the results). Other predictions that can be made fiom such a design are iisted

below but involve experiments that need to be conducteci in space. If the c d of an animal

are plugged as to e k a t e th& contribution, then on earth the amplitude of the eye velocity

during horizontal nans1auon.s with an animal in the upright position shodd be greater than the

amplitude during a horizontai translation with the animal tilted some angle û fiom the vertical

(where the vertical is defined as the axis perpendicular to the axis of translation.) If the

interaction berneen the saccule and the unide is as defined by the anaromy of the model, then

we predict that

P8) The opposite is m e Li space. Thar is, after tilting an animal, the amplitude of the slow

phase eye veloaty is expected ro increase.

This prediction relies on the absence of the lg memory in space. Recall that the funaïon of

equation 3.1 is to deude whether a tilt or a translation is taking place. Aldiough in the Results

section we treated equation 3.1 as having a digital output, its future function is to provide a

degree of activation that is dependent on the degree of tilt- We s h d u& this fact here in

providlig basis for prediction 8. The Ig mernory does not exkt in space r d t i n g in no input

fiom the sacde in the upright position reduMg equation 3.1 to a (see the ResuIts section for a

defuition of these variables). The acceleration detected by the saccule in space during a

horizontal translation while tilted an angle û hem die vertical is S, = aSin(8) reduchg equation

3.1 to a2~in(0)~s(0) + a which is de& p a t e r chan the acceleration felt in the upright

position. This is predicted to increase the activation of the horizontal pathway leading to larger

amplitude eye movements during horizontal nauslarions than during a tilr Note that the

product Sin(B)Cos(B) is gen+ a small number, and since the horizontal acceieration a is

measured in g's, the increase in the perceived accelerarion will be s d

Further predictions can be made conceming signal that could be found in the vestibular

nudeus. The mode. in figure 2.2 achieves a signal that is in phase with veloaty by differentiating

the acceleration signal and not integrating it as is mathematicah/ requVed. Integralion is not

suited for the TVOR because inteption enhances low fiecpency signals and reduces the gain

of large freqyency signais. The TVOR is known to be a hi& kequency system and if subjeaed

to a double inregration would develop daraaeristics that are inconsistent with experimentai

values. SpedcaUy, it wouid exhibit sensirivities (defines as eye veloaqdhead velocity) that are

low pass fdtered and not high p a s filtered. Therefore, signais that lead hear acceleration are

predicted to evin in the c e n d vestibular neurons. R e d thar keguiar otolith afferents show

partial differentiation in their signal since rhey lead linear acceleration by up to 30 degrees at 2

Hz (figure i.8d). Our ninth prediction involves these t hase values and states that:

P9) There exist signals in the vestibular nucleus that lead linear acceleation as a function of

frequency. As the frequency increases, so should the phase lead.

Single cell recording in the brah stem of dert a d is the only way to s e a d for these signals.

We expect to start single cd recordings by September, 1997.

Simulations of eccentric rotations where carrieci out to mich/ the AVOR-TVOR interactions. In

ail cases excepr for hequencies greater than 4 Hi, the processed otoïith signa proved inadequate

to add to the domùiating canal signal to exhibit the observed behaviours. Although linear

translations simulated eye movements thar are consistent with expMmenta1 values, eccenmc

rotations did not. After enhanhg the otolirh signal with the canal signal, we were able to

improve the simulations. Although ~relrminary results have shown that the TVOR is more

robust when the canais are amvated (Anastasopoulos et al., 1996), we found that this design is

necessary for explaining the AVOR-TVOR interaction, and spedcaUy the caucellation of eye

rnovements observed when the subject is facing the center of rotation. Contralateral otolith

input is expected to provide some of the enhancement but as mentioned earlier, high fiequency 79

rotations caused the otolith signal at the summing junction with the canals to be very large.

Contralateral input would then compound tbis problem. It is expected that both canal

enhancemenu of otolith signals and contralateral otolith signal take pan in adjmïng the signal.

We believe that the canal signal L important here since it gives the otolith signal a relative rather

than absolure measure of how w d it is doing. Based on our simuIation, we cm predict that

PIO) The centrai otolith signal is more robw when the canals are activated

We have just starteci modeling this interamon. It is expected to take the shape of a network of

neurons rhat an* the canal and otolith activation rates and provide enhancement to the

otoiith signal accordin&. As mennoneci earlier, if the target is located farther than the axis of

rotation, then the AVOR should dominate, and if the target is located doser than the axis of

rotation, then the TVOR should dominate. One of the characteristics of this network of

neurons is to provide this phase change based on information about vergence. It will dso be a

function of Lequency since the otolith require more enhancement at low fiequenaes (note that

when taking about low freqpmues, we are acniayl referring to magnitudes of about 1 Hz since

anythuig lower than that causes the purmit system to be active).

We have mentioned earlier that the AVOR and the TVOR use a 6nd cornmon pathway on their

way to the ne& integmor and to the plant. Acnially, it is the pathway of the AVOR that the

otolith signals use and therefore our next prediction is that

PII) The gain of the TVOR is predicted to decrease wirh canal lesions but the gain of the

AVOR is predicted to be unaffected by otolith organ lesions.

PluggLig the canals maintains the basellie-firing rate cauring no change in the way the TVOR

operares in the absence of canal input. But if this basellie-firing rate can be abolished, then the

gain of the TVOR is expected to decrease. During iinear d a t i o n , the junction where the

canal signal sum with the otolith signal would be affected since there is no longer a steady state

basellie £Ùing rate coming into the juncrion. Eccentric rotations would affect the TVOR to a

greater degree since the canal enhancernent of an otolith signal would dso be elirninated. The

ody way to test thk renilt is by meaniring slow phase eye movements with an animal that has a

lesioned canal

An increase in kequency (acceleration), or an increase in vergence will cause the central otolith

neurons to increase their discharge rates (Fernandez & Goldberg, 1976c, Paige et al., 1991).

Simulations showeci that inmeasing the radius of rotations during eccenmc rotation has the

sarne but opposite effecr as inaeasing the vergence angle by the same amount provided thar the

gaze is directeci at the center of roration. After further thought, it becornes dear that this L what

is geometridy expected Gnsider an eccennic rotation wirh a radius r, and vergence V= i/r,

then theoretidy there should be no eye rnovements.(vie et al., 1986) If the radius is now

increased, the frvency kept constant and the vergence decreased according to the equation

above then the eye movemem should d be zero. Therefore inaeasing the radius of rotation

(iicreasing the acceleration) and decreasing the target distance by the same amount have the

same but opposite effect on the TVOR if the gaze is directeci at the center of rotation, If gaze is

directed away kom the center of rotarion, then we do nor expect this r d to be nue.

Therefore, interaction between the cana signai and the otolith signal is expected to make the

TVOR a noalinear funmon of vergence for gazes that are directeci away fiom the center of

rotation. This carmot be k e d as a predicrion since the necwork of murons that accomplished

this task has not yer been dweloped.

Aker rnany simulations, the foilowing observation was made regarding the behaviour of eye

velocity as a funcrion of frequency.

P12) During horizontai Uanslations, the slow phase eye veiocity increases as a function of the

square root of the frequency.

In contrast to bis obswation, the AVOR is a linear function of frequency. Why the TVOR in

the model behaves chis way is not yet known but we believe this will furcher enhance our

understanding of the non-linear interaction between the AVOR and the LVOR

The model Li figure 2.2 was successhil in re~roducing most of the experimental r d t s . Its

major flaw is that it is not a bilateral sysrem and the effect of contralateral input has not yet been

81

assessed We also want to dweiop a mode1 for IF&] that will shed some light on the interaction

between the otolith organs and the canais. Neverilidess, we beliwe that the modd shows us a

way in which eye vdocity can be extracteci form the raw otolith signals without using a double

inregration.

Appendix A

PROOF THAT F(e,a)>O

Proof that F(B,a)>O when F(9,a)=(gCos(0)+aSin(B)-g)(gSin(0)+aCos(8))+a.

Multiplying through, we have:

F(û,a)=g%os(0)~in(û)+gaCos~(0)+gaSin~(û)+a*~in(B) ~os(û)-g%in(0)-ga~os(8) +a

Rearranging:

F(B,a)= ~in(O)~os(€I)(g~+a*) +ag-agCos(8)+1-g2Sin(0)

Clearly, ag>agCos(e) and since g=1, then l>g2Sin(B) making F(B,a)>O for al1 8 and a.

Appendk B

LIST OF PARAMETERS

The following parameters were used for dl sirndatioos presented in chis thesis.

arv Afferents

I r r d a r Afferents;

&= 0.44 KA= 1.9 TA= 10 1 seconds T,,= 0.009 seconds Tv=40 seconds

ar Afferents:

&=O. 188 KA= 1.12 TA= 69 seconds TM=O.O 16 second TV= 40 seconds

T,=0.27 seconds Gain = 1

T,= l second T,= 0.1% seconds

Gain = 1

H, [s] = .05( 1

(sT ) .95 + 1 1

T,=0.5 seconds Gh -0.5

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