modeling and simulation of auditory pathway · 2017-10-16 · of the human auditory pathway is...

Modeling and Simulationof the Auditory Pathway

INTERIM REPORT:Computational Models for the Study of Hearing and Language Impairement in Children

Alok BakshiSchool of Industrial EngineeringPurdue University, West Lafayette, IN [email protected]

Aditya P. MathurDepartment of Computer SciencePurdue University, West Lafayette, IN [email protected]

January 20, 2007

This work is supported by NSF Award 0536258.

CONTENTS 2 Interim Report: Modeling the Auditory Pathway

Contents

Abstract 4

1 Introduction 51.1 Progress summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51.2 Model: granular or aggregate? . . . . . . . . . . . . . . . . . . . . . . . . . . 51.3 Limitations of the cellular approach to modeling . . . . . . . . . . . . . . . . . 6

2 Background 62.1 Auditory pathway . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72.2 Ear . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8

2.2.1 External ear . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82.2.2 Middle ear . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82.2.3 Inner ear: the cochlea . . . . . . . . . . . . . . . . . . . . . . . . . . . 9

2.3 Auditory neuron . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92.4 Cochlear nucleus . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10

2.4.1 Primary-like responses . . . . . . . . . . . . . . . . . . . . . . . . . . 112.4.2 Onset responses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 122.4.3 Chopper responses . . . . . . . . . . . . . . . . . . . . . . . . . . . . 122.4.4 Pauser and buildup responses . . . . . . . . . . . . . . . . . . . . . . 132.4.5 Inhibitory responses . . . . . . . . . . . . . . . . . . . . . . . . . . . 13

2.5 Superior olivary complex . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 132.5.1 Medial superior olive . . . . . . . . . . . . . . . . . . . . . . . . . . . 142.5.2 Lateral superior olive . . . . . . . . . . . . . . . . . . . . . . . . . . . 14

2.6 Inferior colliculus . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 142.7 Medial geniculate body . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 142.8 Encoding of sound characteristics . . . . . . . . . . . . . . . . . . . . . . . . 15

3 Modeling 153.1 Hodgkin-Huxley model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 163.2 Models with stochastic Na+ channels . . . . . . . . . . . . . . . . . . . . . . 173.3 Auditory neurons . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 173.4 Cochlear nucleus . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18

3.4.1 Bushy cell . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 183.4.2 Fusiform cell . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 213.4.3 Octopus cell . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 233.4.4 Pyramidal cell . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 263.4.5 Stellate cell . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27

4 Progress 304.1 Octopus cell model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 314.2 Bushy cell model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 314.3 Fusiform cell model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32

This work is supported by NSF Award 0536258: Computational Models for the Study of Hearing and LanguageImpairement in Children.

CONTENTS 3 Interim Report: Modeling the Auditory Pathway

5 Related work 335.1 Auditory Neuron . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 355.2 Cochlear Nucleus . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35

5.2.1 Bushy Cell . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 365.2.2 Octopus Cell . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36

6 Future Work 36

Acknowledgements 36

References 37


1. Introduction 4 Interim Report: Modeling the Auditory Pathway

Abstract

The objective of the work reported here is to develop a detailed cell-level computational modelof the human auditory pathway is under development. The model, once fully developed andvalidated against experimental data, will assist in the study of neural plasticity observed inthe central auditory pathway as a consequence of auditory training in children with learningand attention deficit disorders. Researchers have quantified the effect of auditory training bythe brainstem evoked auditory potential, which the proposed complete computational model isexpected to reproduce. Specifically, a complete and validated computational model will be usedas a tool to assist in understanding the effect of (a) non-intrusive treatments in children withlearning disabilities, and (b) the fault tolerance of the pathway to time varying defects in itscellular substance and structure. This report summarizes the progress made towards the statedobjective.Keywords: Auditory pathway, auditory training, computational model, dyslexia, brainstemevoked auditory potential, learning disorders in children.

1 Introduction

The objective of our exploratory research is to construct and validate a computational modelthat (a) mimics experimental results of auditory processing tasks in children diagnosed withauditory processing disorders and learning disabilities and (b) experiment with the validatedmodel to understand the impact of treatments on children with auditory disorders and learningdisabilities. Rather than assume any apriori knowledge about the nature and/or location of themalfunction in auditory processing in these children, we will explicitly perform parametric ma-nipulation of models of different parts of the auditory system and compare the model responseto that observed in experiments. Parameters under our control relate to individual cells and theirinterconnections (see Section 3).

Note that the long term focus of our research is on children who suffer from various disor-ders related to the auditory pathway. While one set of researchers study the cause and effect ofsuch disorders [3, 17, 21, 22], we propose to use the observations reported by these researchersto validate our computational models and in turn use the validated models to ask and answer“what if” questions. Our belief is that the proposed approach to modeling and validation againstthe observed behavior, e.g. the brainstem evoked auditory potential, will lead to a better under-standing of what defects in the auditory pathway lead to dyslexic behavior and how treatments,that lead to changes in the cellular parameters and structure, might bring the behavior back tonormality.

1.1 Progress summary

Towards our objective, we have completed the following tasks: (a) study the anatomy andphysiological nature of various stages in the auditory pathway, (b) select, implement and val-idate models of the auditory neurons, bushy cell, fusiform cell, and the octopus cell. Severalresearchers have focused on the development of models of various types of cells found at differ-ent stages in the auditory pathway. Rather than build our own model for each cell, we decidedto study and then select one model of each cell type, when available.


1.2. Model: granular or aggregate? 5 Interim Report: Modeling the Auditory Pathway

Thus so far our contribution has been an integration of the different models in the cochlearnucleus with that of the auditory neurons. We implement in MATLAB each model, test it, andthen integrate it with the models for other cells in the auditory pathway. We plan to follow thisapproach until we have an integrated cellular model of the entire complex.

1.2 Model: granular or aggregate?

A key question in modeling a complex system such as the auditory pathway, is “How granularshould the model be ?” The following paragraphs dwell on this question.

The human auditory pathway leading from the cochlea to the auditory complex is a mar-velously naturally engineered subsystem in the brain. Researchers have been studying fordecades its anatomy and physiological behavior. A variety of computational models have alsobeen developed with the goals of reproducing various aspects of the behavior of the auditorypathway. For example, Travis has reported a computational model of one pathway in the catsubcortical auditory system [20]. Travis has argued that “While traditional neural networks havemade inroads to understanding cognitive functions, more realism (in the form of structural, dy-namic and connectivity constraints) is likely required to explain processes such as vision andaudition.” Travis models a basilar membrane nerve fiber unit and the subcortical auditory nu-clei. His model is stochastic in that inter-neuron connectivity is determined randomly, whileaccounting for physiologic constraints. Components of the pathway, e.g the Medial GeniculateBody ventral division, are modeled using a set of coupled first order differential equations.

While Travis’ model is detailed in that it treats each neuron as a distinct entity, aggregatebehavioral models have also been proposed. For example, Wrigley and Brown have proposala computational model of auditory selective attention [23]. Their model is motivated by thefinding “that attention plays a key role in the formation of auditory streams.” The model it-self consists of a network of neural oscillators where the “attentional interest is modeled as aGaussian distribution in frequency.”

Works by Travis, and Wrigley and Brown, are similar in that both focus on modeling por-tions of the auditory pathway. They are quite different, however, in their granularity. WhileTravis’ model is cellular and hence highly granular, Wrigley and Brown’s model is aggregateand phenomenological.

Our approach to modeling the auditory pathway is similar to that proposed and implementedby Travis. We are interested in constructing a detailed cellular model of the entire auditorypathway from the output of the cochlea to the auditory cortex including all the stages describedin Section 2. We believe that a detailed cellular level model will aid in reproducing the observedbehavior at different stages of the pathway thereby allowing us to study the impact of minor andmajor faults in the cellular substance and structure.

1.3 Limitations of the cellular approach to modeling

We face two major problems when using the modeling approach described above. One is relatedto the computational effort required to solve the cellular model and the other is the lack of, ordifficulty in finding, the cell inter-connnection data, especially along the descending auditorypathway.

So far our work has focused on modeling individual cells and connecting the models, alsofor single cells, across the cochlea and the cochlear nucleus. In the next phase of our researchwe plan to replicate cell models and incorporate intercellular connections. The computational


2. Background 6 Interim Report: Modeling the Auditory Pathway

requirements of the resulting interconnections of cellular models will likely force us to movethe computation to a supercomputer. Whenever we fail to find anatomical details of intercellularconnections, we will explore using a Travis-like approach of (intelligently) establishing randomconnections and select and validate a suitable connection structure against the physiologicallyobserved behavior.

2 Background

This section covers background material necessary for an understanding of the computationalmodels described subsequently. The material in this section is heavily based on two books:“The Central Auditory System” by Ehret et. al. [2] and “An Introduction to the Physiology ofHearing” by Pickles [14].

Numerous models of the individual neurons exist. These are shown to have specific func-tions in the auditory pathway, such as decoding of pitch and sound localizaton information.Nevertheless, we lack a complete model of the auditory pathway, from which we can under-stand exactly how the information is decoded and relayed to the brain. There are models whichattempt to simulate the entire nuclei, without going down to the level of individual neurons.Though such models capture few properties of the auditory pathway without much computa-tion effort, we do need a detailed computational model of the auditory pathway. The detailedmodel can be used for computing a correlation between defect types in the nuclei and malfunc-tion of the auditory pathway. Such correlation in turn will likely be useful in the diagnosis andtreatment of auditory disorders in children.

Next we explain the pathway as a whole and the individual nuclei (group of nerve cellbodies), as well as nerve cells which process and relay the auditory information in the pathway:

2.1 Auditory pathway

The central auditory pathway transfers auditory signals from the ear to the auditory cortex. Theauditory pathway can be categorized broadly into the following two parts.

Ascending Auditory Pathway Auditory information received through the ear is sent to theauditory cortex along this pathway that contains the intermediate nuclei.

Descending Auditory Pathway This pathway is responsible for the feedback signals that em-anate from higher nuclei (group of nerve cell bodies) back to the lower nuclei.

The feedback mechanism from higher to lower nuclei is not well understood. Hence currentlywe model only the ascending pathway; the descending pathway will be ignored in the currentphase of our research. The impact of this simplification will be reviewed after the computationalmodel is built and validated.

As shown in Figure 1, the ascending auditory pathway consists of a series of nuclei con-nected by fiber tracts (axons of the nerve cells). There are specialized cells in the nuclei whichprocess specific auditory information encoded in the form of nerve impulses, while few cellsin the nuclei simply relay the information to the higher nuclei without any processing. Thesound, which we hear is the travelling pressure wave in the air, which is picked up by theouter ear. The outer ear transfers the vibration to tympanic membrane (eardrum). The middleear transmits vibrations from tympanic membrane to oval windows in cochlea by three bones


2.1. Auditory pathway 7 Interim Report: Modeling the Auditory Pathway

Figure 1: Ascending auditory pathway.

known as ossicles. These vibrations cause displacement of basilar membrane resulting from themovement of cochlear fluids. The high frequency and low frequency tones generate vibrations,which peak at the base and apex of the cochlea respectively. The inner and outer hair cells firebecause of movement of basilar membrane and their response is carried by auditory neurons tothe auditory pathway.

The auditory neurons provide input to brainstem nuclei known as the cochlear nucleus.The cochlear nucleus encodes the input data in various forms and transfers the information tocontralateral superior olivary complex and ipsilateral lateral lemniscus. From there the neuralresponse goes to higher centers, namely, the inferior colliculus, medial geniculate body, andultimately to auditory cortex. The brainstem nuclei in the auditory pathway decode information,i.e., sound location, while the auditory cortex interprets its meaning.

“Brainstem auditory evoked potential” (BAEP) is the electrical potential recorded from thescalp after presenting the stimulus. The abnormal brainstem auditory evoked potential (BAEP)reflects the faults in either functioning of the ear or in the various nuclei present in the auditorypathway [9]. The BAEP is the resultant of the response generated by all the nuclei present inauditory pathway. The peaks labeled I through V in Figure 2 are generated by the auditorynerve fibers and nuclei till lateral lemniscus, which come in the ascending auditory pathway[11]. The effect of each nuclei in auditory pathway on the BAEP is shown in Figure 2.


2.2. Ear 8 Interim Report: Modeling the Auditory Pathway

Figure 2: Brainstem auditory evoked potential.

2.2 Ear

The ear converts the sound waves, which it receives in the form of waves from the external ear,into the neural impulses of the AN fibers in innner ear. We will now describe briefly the threesignificant parts of the human ear.

2.2.1 External ear

The human pinna amplifies high frequency sound depending on its angle of incidence. Thebrain interprets these changes as direction of the sound source. Thus it serves to localize theauditory signal.

2.2.2 Middle ear

Vibrations are transmitted effectively into the fluid of the cochlea from the eardrum by themiddle ear. It requires turning a large amplitude vibration in air into smaller amplitude vibrationwithout a significant loss of energy. The large area of the eardrum, as well as the lever action ofthree small bones, helps in achieving the reduction of amplitude.

2.2.3 Inner ear: the cochlea

The cochlea is filled with liquid that actuates in response to the vibration of the middle ear.There are specialized cells called “hair cells” in the cochlea, that transform the mechanicalmovement of the fluid into the electrical signals of auditory neurons via neurotransmitters. Theauditory neurons have cell bodies in the spiral ganglion and carry the impules from the cochleato the higher nuclei in the auditory pathway.


2.3. Auditory neuron 9 Interim Report: Modeling the Auditory Pathway

2.3 Auditory neuron

The auditory neurons receive input from hair cells and carry it to the cochlear nucleus. Thesoma of AN fibers lie in the Spiral Ganglion. The properties of AN fibers can be summarizedas follows.

1. Most AN fibers have a moderate spontaneous activity that appears to be abolished by haircell destruction. AN fibers are characterized in the following three categories based onSA (Spontaneous Activity):

• High spontaneous activity

• Medium spontaneous activity

• Low spontaneous activity

2. There is a single excitatory best frequency to which the fibers respond at the lowest inten-sity, which is called characteristic frequency of that fiber (see Figure 3).The fibers have asimple V- or U-shaped excitatory tuning curve surrounding the characteristic frequency.

3. The fibers display a monotonic increase in their respective firing rate up to a maximallevel as the intensity of the preferred tone is increased and then show a constant or slightlyreduced firing rate.

Figure 3: Tuning curve of fibres.

2.4 Cochlear nucleus

The cochlear nucleus is the first mid-brain nucleus of the ascending auditory pathway. It ismorphologically differentiated into following three sub-regions:

• Anteroventral Cochlear Nucleus (AVCN)

• Posteroventral Cochlear Nucleus (PVCN)


2.4. Cochlear nucleus 10 Interim Report: Modeling the Auditory Pathway

• Dorsal Cochlear Nucleus (DCN)

AVCN and PVCN are also collectively known as Ventral Cochlear Nucleus (VCN). These threedifferent divisions of the cochlear nucleus have different response properties as well. The AVCNneurons have similar response properties as that of the AN fibers and therefore it acts as a simplerelay for higher nuclei. While DCN neurons have complex response properties, and they projectdirectly to the lateral lemniscus and inferior colliculus bypassing the superior olivary complexaltogether. The properties of PVCN neurons intermediate of the properties of AVCN and DCNneurons.

Figure 4: Tonotopic organization (from Ryugo and Parks, 2003).

Each AN fiber bifurcates while entering the cochlear nucleus sending one branch to AVCNand the other branch to PVCN and DCN. Each subregion of cochlear nucleus has orderly ar-rangement of afferent AN fibers according to their characteristic frequency and thus preservetonotopicity.

For example the fibers originating from the cochlear base, which encode higher frequencyprojects to DCN. Whereas the fibers from cochlear apex, which encode low frequencies projectsto the VCN. The fibers having intermediate frequencies end up in between these two regions asshown in Figure 4.

Both type I and type II AN fibers project to the cochlear nucleus thus constituting the twoparallel pathways. The first pathway, consisting of type I AN fibers, originate from inner haircell of the cochlea and project to the central part of cochlear nucleus. The second pathway,consisting of type II AN fibers, originate from outer hair cells of the cochlea and project to theperipheral part of cochlear nucleus. Thus type I AN fibers transfer the main auditory input tocochlear nucleus, while type II AN fibers provide modulation for the acoustic data.

The cells of the cochlear nucleus can be differentiated morphologically or by the reponsepattern. The cochlear nucleus neurons can be classified into different categories based on the



response to the short tone bursts delivered just above the threshold and at the characterisicfrequency of the neuron. The following response types are observed in cochlear nucleus:

• Primary-like Responses

• Onset Responses

• Chopper Responses

• Pauser and Buildup Responses

• Inhibitory Responses

• Phase Locked Responses

2.4.1 Primary-like responses

Such response pattern is observed throughout in ventral cochlear nucleus, in particular in AVCNarea. The spherical bushy cells of AVCN display this kind of response. As the name suggests,the response is similar to that of auditory nerve fibers, with a peak at the onset and then gradualdecrease to a lower response for tones. There are no inhibitory sidebands in response and itresembles the tuning curve for AN fibers.

The cells showing “primary-like response” receive secure synaptic input, with short synapticdelay and hence relay the information from AN fibers to higher auditory nuclei.

Primary-like responses divide into two subtypes:

• Primary-like response

• Primary-like-notch response

The shape of PSTH (post stimulus time histogram) is similar for both these responses, butin notched response there is short disruption of firing after the initial peak of maximum firing,which is followed by the return to normalcy in firing. Spherical bushy cells generate primarylike response while globular bushy cells show notched response. The primary like response isobserved in anterior of AVCN while the notched response is observed more in posterior AVCN.

2.4.2 Onset responses

Onset response is characterized by the sharp peak in PSTH at the beginning of tone bursts anda low level of sustained acivity thereafter. This response is oberved in all over the cochlearnucleus, but more frequently in ventral cochlear nucleus. The ocopus cell area in VCN showsonly onset response and thus the octopus cell are known to have such response pattern. Theresponse is thought to be generated by the presence of excitatory input and then a delayedinhibitory input. The octopus cell area produces only onset responses and the area consistsalmost entirely of octopus cells. Thus octopus cells in this region generate onset responses. Itmight be supposed that there is an excitatory input and then a delayed inhibitory input for thesecells. This response can be further categorized into following responses:

OI Onset responses which shows transient activity are called OI. This response shows a singleaction potential per tone burst, which is given just above threshold at the characteristicfrequency.



OL Onset responses which show sustained activity after initial peak are called OL.

OC The multipolar cells of posteroventral cochlear nucleus generate such response. This re-sponse is characterized by the initial 2–4 peaks, with decreasing amplitudes at the onset.

OG This response is found in few cells of dorsal cochlear nucleus. It is characterized by thegraded decreasing of firing after the initial peak of response.

The onset response encodes the temporal coding of onset of stimulus which is necessaryfor sound localization by the comparison of arrival-time differences of sound at the twoears

2.4.3 Chopper responses

The chopper responses is observed throughout the cochlear nucleus, predominantly in the pos-teroventral cochlear nucleus and the polymorphic cell layer of the dorsal cochlear nucleus.

Chopper response is characterized by the repetitive firing during a sustained tone burst witha rate independent of the period of the stimulus waveform. The PSTH, therefore has number ofpeaks for this response.

Chopper response can be further differentiated into following three types:

• Responses having long intervals between peaks. This response is shown mainly by thecells in the dorsal cochlear nucleus.

• Responses having short intervals in between the peaks, which also have significant decre-ment in peak amplitude with the duration of the stimulus.

• Responses which shows chopper characteristic only during the onset of stimulation.

The chopper response is shown by the stellate cells present in the cochlear nucleus. As thechopper units lose the temporal information, so a likely role for such units is in the encoding ofthe intensity of stimulus.

2.4.4 Pauser and buildup responses

Pauser response is characterized by the initial onset of the response, then complete disruptionof discharge for some time and a gradual resumption to normal discharge. Buildup responseare similar to pausup response except that these units don’t show the onset of response. Thepyramidal cells present in the cochlear nucleus show these kind of responses along with thepolymorphic cell layer of the dorsal cochlear nucleus. Oftenly the cells displaying such re-sponse show other kinds of response if input parameters are changed. This is because of theinterneuronal circuits present in the DCN, which may change response of the cell from pauserto buildup response based on the intensity of the sound.

2.4.5 Inhibitory responses

In this response, there is only inhibition in the discharge rate whenever a stimulus is provided,and this inhibition continues as long as the stimulus is provided. So far, this kind of response isnot attached to any type of cell in cochlear nucleus.


2.5. Superior olivary complex 13 Interim Report: Modeling the Auditory Pathway

2.5 Superior olivary complex

Superior olivary complex is the first nucleus along the auditory pathway that receives informa-tion from both the ipsilateral and contralateral side. This nucleus plays an important role in thelocalization of sound. The localization is done based on the following two cues:

Interaural intensity difference (IID) This is the difference in intensity of sound perceived bythe ear due to the location of the sound.

Interaural time difference (ITD) This is the difference in arrival time at both ears when thesound source is not equidistant from the ears.

This nucleus is divided into the following three sub-regions:

• Medial superior olive

• Lateral superior olive

• Medial nucleus of the trapezoid body

The tonotopicity is preserved in all of these three nuclei.Medial nucleus of the trapezoid body(MNTB) provides the LSO and MSO inhibitory inputs, which represent the contralateral ear,providing thus the cues for sound localization.

2.5.1 Medial superior olive

The medial superior olive helps in sound localization by comparing difference in the arrivaltime of sounds of both the ears. The cells in MSO are most responsive to low frequency sound.It projects to ipsilateral inferior colliculus ipsilaterally, while MSO projects bilaterally to theinferior colliculus. It receives fibers mainly of the low frequency.

2.5.2 Lateral superior olive

The lateral superior olive helps in sound localization by comparing difference in the inten-sity of sound on both the ears. It receives direct high frequency inputs from the ipsilateralAVCN(spherical Bushy cells) and indirectly from the globular cells of the contralateral ventralcochlear nucleus, which pass through the nucleus of trapezoid body. The LSO neurons are ex-cited by the direct connections i.e. from ipsilateral AVCN while the indirect input is inhibitory.

2.6 Inferior colliculus

The inferior colliculus is a nucleus situated in midbrain, which is present in both ascending aswell as descending auditory pathway. It consists of following subregions:

• Central Nucleus

• Pericentral Nucle

• External Nucleus


2.7. Medial geniculate body 14 Interim Report: Modeling the Auditory Pathway

Central Nucleus, which is a principal subregion, consists of principal neurons, characterizedby flat dendritic tree and multipolar neurons, which are interneurons and thus modulate thelocal circuit. Central Nucleus receives contralateral ascending inputs from cochlear nucleus andsuperior olive complex, while it receives ipsilateral ascending inputs from lateral superior oliveand medial superior olive. The lateral superior olive projects high CF neurons to contralteralinferior colliculus and low CF inhibitory input to ipsilateral olivary complex.

2.7 Medial geniculate body

The medial geniculate body contains “thalamic auditory relay”, which receives inputs frominferior colliculus and projects to the auditory cortex. There are three subregions for MGB,which are connected to the inferior colliculus from three parallel pathways. The subregions ofMGB are:

ventral MGB It receives projection from central nucleus of inferior colliculus, which formthe pathway named tonotopic pathway. The pathway is named so because of the spatialarrangement of neurons according to their frequency.

dorsal MGB The projection from inferior colliculus to this sub-region lack tonotopic organi-zation, so they form the pathway named diffused pathway.

medial MGB It receives projections from lateral part of inferior colliculus, which form pol-ysensory pathway. The pathway is named so because lateral part of inferior colliculusreceives projection outside from the auditory pathway.

There exists some overlap as well as interconnections between these three parallel pathways.

2.8 Encoding of sound characteristics

The mechanism by which basic properties of the sound, for example pitch and localization, isgiven below in brief:

Earlier two seperate theories were proposed for the mechanism by which frequency of theauditory information is decoded. The current theory is somewhat a combination of the followingtwo:

Frequency theory The basilar membrane vibrates in sync with a sound causing the auditorynerve axons to produce action potentials with the same frequency.

Place theory Each area of the basilar membrane is tuned to a specific frequency and vibratesif that frequency is present.

The current thoery postulates the following encoding of frequency:

1. Frequency of action potentials in the auditory nerve directly correlates with the frequencyof the sound in case of low frequency sound.

2. Volleys of responses across many receptors can lead to the encoding of sounds of fre-quency up to 5000 Hz in the whole auditory nerve even though no individual axon canfire with that frequency.


3. Modeling 15 Interim Report: Modeling the Auditory Pathway

3. Higher frequency sounds are characterized by area of greatest response along the basilarmembrane due to location of peaks of the travelling wave in the basilar membrane.

The sound is localized by following two different mechanisms:

1. Loudness difference between ears is used to detect the sound location for high frequencysound.

2. Differences in phase between ears is used to detect the sound location for low frequencysound.

3 Modeling

Next discuss models already built and verified for the individual neurons by other researchers.In the first two subsections, we discuss the generic models, which we use whenever the specificmodel of a neuron is not available. The first generic model is the Hodgkin Huxley model,which simulates the neuron through voltage gated ion channels, while the others model the cellbehavior using stochastic ion channels.

3.1 Hodgkin-Huxley model

The model [5] computes different types of ion current, for example Na+, K+, and a leakagecurrent consisting mainly of Cl− ions. Specific voltage dependent ion channels, one for Na+

and another one for K+, control the flow of those ions through the cell membrane. The leakcurrent takes care of other channel types which are not described explicitly. The circuit diagramfor the model is shown in the Figure 5.

Here is the brief description of the variables and constants which are present in the differ-ential equation setup for the model:

I The total ionic current across the membrane

m The probability that 1 of the 3 required activation particles has contributed to the activationof the Na gate (m3 : the probability that all 3 activation particles have produced an openchannel)

h The probability that the 1 inactivation particle has not caused the Na gate to close

GNa Maximum possible Sodium Conductance (about 120 mOhms−1/cm2)

E Total membrane potential (about -60 mV)

ENa Na membrane potential (about 55 mV)

n The probability that 1 of 4 activation particles has influenced the state of the K gate.

GK Maximum possible Potassium Conductance (about 36 mOhms−1/cm2)

EK K membrane potential (about -72 mV)

GL Maximum possible Leakage Conductance (about .3 mOhms−1/cm2)


3.2. Models with stochastic Na+ channels 16 Interim Report: Modeling the Auditory Pathway

Figure 5: Hodgkin Huxley Model [5].

EL Leakage membrane potential (about -50 mV)

The voltage of the membrane depends on the ion channels by following relation

−CmdE

dt= m3hGNa(E − ENa) + n4GK(E − EK) + GL(E − EL)

The probability associated with each gate i at any given instant, depends in turn on the mem-brane potential at that time. So here aI ’s and bi’s depend on the membrane potential and the iongate probability satisfied following differential equations:

dm

dt= am(1−m)− bmm

dn

dt= an(1− n)− bnn

dh

dt= ah(1− h)− bhh

3.2 Models with stochastic Na+ channels

Nonlinear deterministic models such as Hodgkin Huxley model fails to take account of the spiketiming and threshold fluctuations. The fluctuations of Na+ current accounts for the stochasticnature of spike timing and threshold. The stochastic nature of Na+ ions can be modelled ascontinuous time, discrete state Markov jumping processes.

The Na+ channel has three activating gates(denoted by m) with four different states, andone inactivating gate(denoted by h)with two distinct states according to the Hodgkin Huxlymodel. Therefore, the resultant markov process has 4× 2 = 8 states, and 20 transition states asshown in Figure 6.

Such models are computationally intensive owing to their biophysical complexity.The algorithms for stochastic simulation can be grouped into

1. Approximation algorithms of the differential equation using Langevin’s equation (F al-gorithm)


3.3. Auditory neurons 17 Interim Report: Modeling the Auditory Pathway

2. Exact algorithms, which can be further subdivided into two categories:

Channel state tracking (CST) algorithms This algorithm tracks the state of each chan-nel and superimposes individual channel currents corresponding to the states in or-der to generate sodium channel current fluctuations. This algorithm is computation-ally very intensive, and is implemented in SD algorithm, R algorithm.

Channel number tracking (CNT) algorithms This algorithm (CW algorithm) tracksthe number of channels in each state, assuming that all the channels are independentand memoryless. It has much greater efficiency compared to the other one.

Figure 6: Kinetic scheme for stochastic models.

Comparing the algorithms [4], we find that the CNT algorithm (CW) is computationally mostefficient and robust.

3.3 Auditory neurons

A phenomenological model of the Auditory Neurons is implemented [24], which describes theresponses of high SA auditory neuron fibers, including several non linear properties.

The general scheme of AN model implementation is shown in the Figure 7. The model takesthe instantaneous pressure waveform of the stimulus, without taking into account the effect ofexternal and middle ear. As shown in the figure, non linear filtering section of the model are thesignal path and the feedforward control path, so that the model gives same type of non linearresponse as observed in the experiment.

Several AN response properties were not included in the model. For example, the modeldoes not incorporate the tails of tuning curve, the effects of efferents on the rate and timing ofAN discharges, and low and medium spontaneous activity. The implication of these limitationswill be assessed after the completion of model.

3.4 Cochlear nucleus

The cochlear nucleus is the first site of the neuronal processing of the newly converted“digita”data from the inner ear. The information is brought via the auditory nerve. The lower frequencyaxons innervats the ventral portions of the dorsal cochlear nucleus and the ventrolateral portionsof the anteroventral cochlear nucleus. In contrast, the axons from the higher frequency organ



Figure 7: Block diagram of the AN Model [24].

of corti hair cells project to the dorsal portion of the anteroventral cochlear nucleus and theuppermost dorsal portions of the dorsal cochlear nucleus. The mid frequency projections endup in between the two extremes, in this way the frequency spectrum is preserved. The differenttypes of cells present in the cochlear nucleus are listed in Table 1.

There are three major projections from the cochlear nucleus. Through the medulla, one pro-jection bifurcates, and shoots to the contralateral the superior olivary complex via the trapezoidbody, whilst the other half shoots to the ipsilateral SOC( Superior Olive Complex). Anotherprojection rises above the medulla into the pons where it meets the nucleus of the lateral lem-niscus.

3.4.1 Bushy cell

Bushy cells of anteroventral cochlear nucleus (AVCN) receive inputs from AN fibers and phacelock to the characteristic frequency thus preserving the temporal information. Bushy cells passinformation to the superior olivary complex (SOC), which is the center for sound localization.For sound localization, inter-aural time difference is used, the accuracy of which is ensured byBushy cells because the temporal information related to input waveform is preserved by it.



Table 1: Types of cells in the Cochlear Nucleus.Cell Origin Location Projection Activity Temporal Receptive

Types Patterns FieldsSpherical AVCN Rostral LSO(ipsi) Excitatory Primary-like Type I

Bushy MSO(bil)VNTB(contra)

LNTB(bil)VNLL(contra)

Globular AVCN Caudal MNTB(contra) Excitatory Primary-like Type IBushy VNTB(contra) and

Periolivary N. Primary-like(bil) notch

Stellate\ PVCN Anterior Periolivary N. Inhibitory Chopper Types I,Multipolar PVCN (bil.) and III, I/III

AVCN Excitatory OC

Posterior VNLL(contra)PVCN IC(contra)

Octopus PVCN Anterior Periolivary N. Excitatory OI TypesPVCN (bil.) and I/III, IV

VNLL(contra) OL

IC(contra)Stellate DCN Molecular and Pyramidal Cells Inhibitory Chopper Types III

Pyramidal Cartwheel Cells and I/III, IIcell layers Stellate Cells OC

Pyramidal DCN Pyramidal VNLL and IC Excitatory Buildup-Pauser Types III,cell layer (contra) and Chopper IV

Here we have taken the model of Bushy cell [16] which successfully simulates the behaviorof Spherical Bushy Cells.

The model consists of a single compartment including three voltage sensitive ion channels.The model is adendritic and anaxonal, in which only the soma of Bushy cell is modeled.The membrane conductances in the soma are:

GB Slow low-threshold potassium conductance

GK Fast high-threshold potassium conductance

GL Passive leakage conductance

GI Inhibitory synaptic conductance

GE Excitatory synaptic conductance

The cell potential V is described by the following equation:

CSdV

dt+ GB(V − EK) + GK(V − EK) + GNa(V − ENa) + GL(V − EL)

+ GI(V − EI) + GE(V − EE) = Iext



Table 2: Values of model parameters at temperature 30oC.

CS = 23 pFd EE = −10 mVGL = 5.2 nS EL = 2.8 mVGB = 86.6 nS EI = −66.5 mVGK = 173.3 nS EK = −77 mVGNa = 985.2 nS ENa = 55 mV

Here ENa, EK , EI , and EE are reversal potentials for the corresponding ions, while CS is themembrane capacitance and GL is leakage potential, the values of whom are given in the Table 2.

Because all the rate constants wre defined for 22oC, So Q0 factor is used, which scales themback to normal body temp(38oC).

Tf (Q10) = Q(T−22)/1010

The three membrane conductances GB, GK , and GNa are modeled with activation variablesw, n, and m, and inactivation variable h, which themselves depend on membrane potential andtime through α and β

αw =0.107 Tf (3)

1 + exp −(V + 33)/13.1βw = 0.01881 Tf (3) exp −(V + 30)/30.3

αn =0.0282 Tf (3) (V + 9)

1− exp 1− (V + 9)/12

βn = 6 Tf (3) exp −(V + 144)/30+6 Tf (3)

1 + exp (V + 62)

αm =0.36 Tf (3) (V + 49)

1− exp −(V + 49)/3

βm =−0.4 Tf (3) (V + 58)

1− exp (V + 58)/20

αh =2.4 Tf (3)

1 + exp (V + 68)/3+

0.8 Tf (10)1 + exp V + 61.3

βh =3.6 Tf (3)

1 + exp −(V + 21)/10



Auditory Neuron inputs are modeled by excitatory synaptic conductance GE . If spikesarrives at the time tn the conductance reaches its peak value of AE at time tn +tp. As suggestedby the paper [16], tp was chosen as constant 0.5 ms.

GB = GBw GK = GKn GNa = GNam2h

dη

dt= αη(1− η) + βηη for η = w, n,m, and h

GE = AEt− tn

tpexp

1− t− tn

tp

for t > tn

3.4.2 Fusiform cell

The fusiform cells in Dorsal Cochlear Nucleus (DCN) are responsible for the pauser and buildupresponse. At present, the synaptic organization and intrinsic membrane properties of these cellsis not known, so a Hodgkin-Huxley based model [8] is taken which reproduce the responsepattern of cell without taking into account the calcium based conductances.

As shown in the Figure 8 the cell is modeled by an electrical network where current sourcerepresents the synapse input signal, and each of the branch represents nonlinear conductance .The conductances are of following types:

• Delayed rectifier potassium conductance

• Inward/anomalous rectifier potassium conductance

• A transient outward “A” type potassium conductance

• Transient, rapidly inactivating sodium conductance

• Persistent, noninactivating sodium conductance

Figure 8: A model of the fusiform cell [8].



Table 3: Parameter values for the Fusiform Cell model.

Eion gmax τA τB dA dB

gion,type (mV) (nS) x y (ms) (ms) cA cB (mV) (mV)gK,DR -65 18000 4 1 4.5 15 0.4 0.4 -47 -55gK,DR -65 40 1 · · · 20 · · · 0.3 · · · -67 · · ·gK,A -65 700 4 1 3.5 30 0.5 0.4 -60 -71gNa,T 50 600000 3 1 0.075 0.4 1.0 0.4 -51 -68.5gNa,P 50 560 3 · · · 8.0 · · · 0.3 · · · -50 · · ·

gL -58 23 · · · · · · · · · · · · · · · · · · · · · · · ·

The potential of soma is given by the equation below, where Is is the input current forthe model and Eion represents the equilibrium potential for corresponding ion. Also gion,type

represents the conductance for a particluar ion of a particular type.

dE(t)dt

=1C

[EK − E(t)][gK,IR(t) + gK,A(t) + gK,DR(t)]

+ [ENa − E(t)][gNa,P (t) + gNa,T (t)]

+ [Eleak − E(t)]gleak + Is(t)

The conductances in the model, depend on the voltage by following equations:

gK,DR(E, t) = gK,DR,maxAxK,DR(E, t)By

K,DR(E, t)

dAK,DR(E, t)dt

=1

τAK,DR

[AK,DR(E,∞)−AK,DR(E, t)]

AK,DR(E,∞) =1

1 + exp [cAK,DR(d− EAK,DR

)]dBK,DR(E, t)

dt=

1τBK,DR

[BK,DR(E,∞)−BK,DR(E, t)]

BK,DR(E,∞) =1

1 + exp [cBK,DR(dBK,DR

− E)]

Here τN denotes the time constant for N , while ∞ denotes the steady state value for the corre-sponding parameter. Aion,type and Bion,type denote the activation and inactivation componentfor the corresponding conductances. c′Ns and d′Ns give slope and position for the N versuspotential graph, where N represents the activation/inactivation component of the conductance.

The parameter values for the model are given in the Table 3. The membrance capacitanceC was chosen as 210 pF, while resting potential was taken -58.6 mV.

3.4.3 Octopus cell

Octopus Cell is found at the caudal and medial region of the PVCN. These cells are character-ized by spiking activity which happens precisely at the tone bursts over broad frequency range.



This cell has been associated with OI and OL response, however it has been demonstrated thatOctopus cells are not the only cells which exhibit these responses. Here we have implementeda computational model of the Octopus Cell [10]. It is a compartmental model in which soma,axon and dendrites are represented as compartments, where each compartment is equipotential.Following simplifications were made while implementing the model.

• Following Rall’s 3/2 power law, four dendrites were represented by single cylinder.

• Active axon was lumped into the soma.

• The single cylinder(representing four dendrites) was modeled by 15 compartments whilethe soma was modeled by two cylinders

• Dendrites were assumed to lack any active ion channels.

As shown in the Figure 9, each compartment of dendrite receives AN of the particular charac-teristic frequency shown in the figure in kHZ. The one compartment of soma receives four AN,while the other contains all the active ion channels.

Figure 9: A model of the octopus cell [10].

The constants used in the model are summarized in Table 4.The follwoing equation gives the dendritic potential for each compartment j∀ j ∈ 1 · · · 15

cmdVdj

dt=− gL(Vdj − Er)− gsyn(t)(Vdj − Esyn)

+1ra

(Vd(j+1) − Vdj)−1ra

(Vdj − Vd(j−1))

The equation written below gives the potential of passive somatic compartment

cmdVs1

dt=− gL(Vs1 − Er)−

(Vs1 − Esyn)

4∑j=1

gsyn(t)j

+1ra

(Vs2 − Vs1)−1ra

(Vs1 − Vd1)



Table 4: Octopus Cell Parameters

Description Symbol ValueDendriteNumber of compartments 15Diameter dd 17.6 µmLength ld 238 µmPeak synaptic conductance density gsyn 1.2 mS/cm2

SomaNumber of compartments 2Diameter ds 25 µmLength ls 25 µmPeak K+ conductance density gK 120.0 mS/cm2

Peak Na+ conductance density gNa 60.0 mS/cm2

Specific membrane resistivity Rm 0.5 kΩcm2

Specific axial resistivity Ra 150Ω cmSpecific membrane capacitance Cm 1 µF/cm2

Leakage conductance reversal potential Er −65 mVSynaptic input reversal potential Esyn 45 mVNa+ reversal potential ENa 45 mVK+ reversal potential EK −90 mVMaximum synaptic conductance density gsyn 0.3 mS/cm2

Compartment membrane resistance rm Rm/πdl kΩCompartment axial resistance ra 4Ral/πd2 kΩCompartment capacitance cm Cmπdl µFDendritic characteristic length λd 383 µmSomatic characteristic length λs 456 µm

The equation written below gives the potential of active somatic compartment

cmdVs2

dt=− gL(Vs2 − Er)− gNa(t)(Vs2 − ENa)

−gK(t)(Vs2 − EK)− 1ra

(Vs2 − Vs1)

The voltage dependent conductance are modeled by following differential equations:

gNa(Vm, t) = AcgNam3h gK(Vm, t) = AcgKn4

dm

dt= αm(1−m)− βmm

dh

dt= αh(1− h)− βhh

dn

dt= αn(1− n)− βnn



αm(Vm) =−0.64(Vm − Er − 13)

e−(Vm−Er−13)

4 − 1βm(Vm) =

0.56(Vm − Er − 40)

eVm−Er−40

5 − 1

αn(Vm) =−0.064(Vm − Er − 15)

e−(Vm−Er−15)

5 − 1βn(Vm) = 1.0e

−(Vm−Er−10)40

αh(Vm) = 0.256e−(Vm−Er−17)

18 βh(Vm) =8.0

e−(Vm−Er−40)

5 + 1

With one input spike at t = 0, the synaptic conductance varies with time by following differen-tial equation:

gsyn(t) = Acgsyn

ttp e

−ttp

If other spikes also occur in between, then the total conductance was taken as simply the sumof individual conductances for each spike.

3.4.4 Pyramidal cell

The pyramidal cell model [7] is represented by a single compartment, in which, membranecapacitance (Cm) is connected in parallel with voltage and time varying ionic conductances.

The membrane voltage depends on the voltage dependent ionic conductances and leakageconductance by following relation:

dVm

dt=

−1Cm

(IKIF (Vm, t) + IKIS(Vm, t) + IKNI(Vm, t) + INa(Vm, t)

+ Ih(Vm, t) + IL(Vm, t))

The rate of change of gating variable x(V, t) is given by:

dx(V, t)dt

=x∞(V, t)− x(V, t)

τx(V )

The kinteic equation for Na+ current is given below:

INa(Vm, t) = gNam2NahNa(Vm − VNa)

mNa∞(Vm) =(1 + e−[(Vm+38)/3]

)−1

hNa∞(Vm) =(1 + e(Vm+43)/3

)−1



The kinetic equation for fast and slow inactivating potassium currents IKIF and IKIS is givenbelow:

IKIF (Vm, t) = gKIF m4F hF (Vm − VK)

mF∞(Vm) =(1 + e−[(Vm+53)/25.8]

)−1

hF∞(Vm) =(1 + e(Vm+89.6)/6.7

)−1

IKIS(Vm, t) = gKISm4ShS(Vm − VK)

mS∞(Vm) =(1 + e−[(Vm+40.9)/23.7]

)−1

hS∞(Vm) =(1 + e(Vm+38.4)/9

)−1

A third potassium current IKNI , which is noninactivating is:

IKNI(Vm, t) = gKNIm2N (Vm − VK)

mN∞(Vm) =(1 + e−[(Vm+40)/3]

)−1

Hyperpolarization activated potassium current Ih behaved according to following differentialequations:

Ih(Vm, t) = ghmhnh(Vm − Vh)

mh∞(Vm) = nh∞(Vm) =(1 + e(Vm+68.9)/6.5

)−1

τmF (Vm) =(0.15 ∗ e(Vm+57)/10 + 0.3 ∗ e−[(Vm+57)/10]

)−1+ 0.5

τhF (Vm) =(0.015 ∗ e(Vm+87)/20 + 0.03 ∗ e−[(Vm+87)/20]

)−1+ 10

τmS(Vm) =(0.15 ∗ e(Vm+40)/10 + 0.3 ∗ e−[(Vm+40)/10]

)−1+ 0.5

τhS(Vm) = 200

τmh(Vm) =(1 + e(Vm+183.6)/15.24

)−1

τnh(Vm) = (1 + e(Vm+158.6)11.2) ∗ (1 + e(Vm+75)/5.5)−1

The leakage current representing resistive losses over the membrane is described by Ohm’s law:

IL(Vm) = gl(Vm − Vl)


Figure 10: A model of the stellate cell [1].

3.4.5 Stellate cell

The stellate or mulipolar cells are found in the AVCN. These cells exhibit the chopper responsepattern if given the short CF tone bursts.

In the model, which we have adopted [1], the electrical network is used to represent the cell.The whole dendritic tree of the cell is collapsed into a single cylinder following Rall’s 3/2 powerlaw. Because of lack of information, it was assumed that dendrites don’t have any active ionchannels.

As shown in the Figure 10, the single dendritic cylinder is modeled by ten compartments.Soma and axon are also modeled with single compartment. Each compartment, in turn is mod-eled by an electrical circuit.

The inactivating sodium conductance gNa depends on membrance potential V and time tby the relation

gNa = goNam

3(V, t)h(V, t)S


Table 5: Stellate cell model parameters (continued in the next table).

Name Symbol ValueAnatomicalDendrite Diameter dd 2.2µmDendrite Length ld 600µmSoma Diameter ds 25µmAxon Diameter da 3.0µmAxon Segment Length la 70µmElectricalMembrane Resistivity Rm 10KΩ− cm2

Axial Resistivity Ri 150Ω− cmMembrance Capacitance/Area Cm 1.0µF/cm2

Dendritic Space Constant λd =√

ddRm

4Ri600µm

Dendritic Electronic Length Ld = ldλd

1.0Equivalent Cylindrical

Equivalent Dendrite Diameter deq = (6(dd)3/2)2/3 7.3µm

Dendritic Space Constant λeq =√

deqRm

4Ri1100µm

Dendritic Electronic Length Leq = Ld 1.0CompartmentalNumber of Compartments N 10Electronic Length ∆Zi = Ieq/N 0.1Metric Length li = λeq/N 110Membrane Capacitance ci = πdeqliCm 0.25 ∗ 10−4µF

Conductance between i to j gij = πd2eq

4R−ili0.25 ∗ 10−6S

Excitatory Reversal Potential Ee 0mVInhibitory Reversal Potential Ei −68mV

where S is the membrane surface area of the soma or axon, and m,h are the activation andinactivation variables respectively.

The activation variable m follows following differential equation:

τmdm

dt+ m = m∞



Table 6: Model parameters (continued from the previous table).

Name Symbol ValueSomaMembrane Surface Area S = πd2

s 0.20 ∗ 10−4cm2

Membrane Capacitance cs = CmS 0.20 ∗ 10−4µF

Axial Conductance between gs1 = πd2eq

4Rili/2 0.50 ∗ 10−6S

Soma and First CompartmentMax. Leakage Conductance/area go

1 0.090S/cm2

Leakage Conductance gl = gol S 0.18 ∗ 10−8

Leakage Equilibrium Poential El −53mVSodium Equilibrium Poential ENa 55mVPotassium Equilibrium Potential EK −80mVAxonMembrane Surface Area Sa = πd2

a 0.66 ∗ 10−5cm2

Membrance Capacitance ca = CmSa 0.66 ∗ 10−5µF

Axial Conductance between gas = πd2a

4Rila/2 0.13 ∗ 10−6S

Axon and SomaMax. Leakage Conductance/Area go

l 0.025S/cm2

Leakage Conductance gl = gol Sa 0.16 ∗ 10−9S

where

τm =1/Tfac

αm + βm

m∞ =αm

αm + βm

αm =−0.1(V + 37 + MSH

exp−(V +37+MSH)

10

− 1

βm = 4exp

−(V + 62 + MSH)

18

Similarly inactivation variable h follows the following differential equations:

τhdh

dt+ h = h∞

τh =1/Tfac

αh + βh

αh = 0.07exp

−(V + 62 + MSH)

20

βh =

1

exp−(V +32+MSH)

10

− 1


4. Progress 30 Interim Report: Modeling the Auditory Pathway

The delayed rectifier potassium conductance depends on V , and t as in equation:

gK = goKn4(V, t)S

where the inactivation variable n is defined as:

τndn

dt+ n = n∞

τn =1/Tfac

δ(V )(αn + βn)

n∞ =αn

αn + βn

αn =−0.01(V + 52 + NSH)

exp−(V +52+NSH)

10

− 1

βn = 0.125exp

−(V + 62 + NSH)

80

δ(V ) = 0.19 + 0.0087(1− 0.19)(V − Er)

4 Progress

Table 7 summarizes the work done so far. The table lists the neuronal models implementedand ones yet to be implemented. The auditory pathway consists of different nuclei and eachnucleus in turn contains different types of neurons having specific response and that communi-cate among themselves through interneurons. Figure 11 shows the ascending audiory pathwayhighlighted with the neurons we have implemented so far withing each nuclei.

Table 7: Status in modeling auditory pathway.

Nuclei StatusAN Fibers ImplementedCochlear Nucleus Partially Implemented

Bushy Cell ImplementedFusiform Cell ImplementedOctopus Cell ImplementedPyramidal Cell Not ImplementedStellate Cell Not Implemented

Superior Olivary Complex Not ImplementedInferior Colliculus Not ImplementedMedial Geniculate Body Not Implemented

Now we discuss the models of each individual nuclei of auditory pathway in detail.


4.1. Octopus cell model 31 Interim Report: Modeling the Auditory Pathway

SUPERIOR OLIVARY COMPLEX

Medial Supe-

rior Olive

Lateral Supe-

rior Olive

Medial Nucleus

of the

Trapezoid Body

COCHLEAR NUCLEUS

Cochlea

Bushy

Cell

Octopus

Cell

Fusiform

Cell

Pyramidal

Cell

Stellate

Cell

Inter-Neurons

Not

Implemented

Implemented

INFERIOR COLLICULUS Not

Implemented

Not

Implemented

Unknown

Connection

Known

Connection

Nucleus

Boundary

AN Fibers

Figure 11: Modeled nuclei in auditory pathway.

4.1 Octopus cell model

The model for the AN fibers was implemented as described by Zhang et. al. [24]. The octopuscell model by Levy et al. [10] was implemented by solving the differential equations in MAT-LAB given in Section 3.4.3. Output from the AN model was fed to the model for the octopuscell.

The response characteristic of the octopus cell is shown in Figure 12, in which the potentialof the soma (in mV) is shown against time (msec) for the given pattern in which AN fibers in-nervate the octopus cell. The characteristic frequency of AN fibers which innervate a particularoctopus cell has a bandwidth of 1/3rd of the entire range (from 20Hz to 20kHz). Hence alloctopus cells can be simulated by this method assuming we know the types and numbers of ANfibers which it receives.

There is always some variability in the response of octopus cell due to intrinsic variation in


4.2. Bushy cell model 32 Interim Report: Modeling the Auditory Pathway

Figure 12: Response observed from a computational model of the octopus cell.

the individual octopus cell and the experimental procedure. Therefore, the model was verifiedby demonstrating that somatic potential lies withing a biologically plausible range, which wefound to be so in simulation. As shown in Figure 12, the response curve of the octopus cellimplementation (on the right) is compared against that of the model implemented by Levy et.al. [10]. Here the somatic potential is compared for 20 dB, 40 dB, and 60 dB respectively forthe CF tone bursts.

4.2 Bushy cell model

The model of the bushy cell selected for this research is by Rothman et. al. [16]. The differentialequations were implemented in MATLAB as described in Section 3.4.1.

The response of the bushy cell model depends on the number of auditory neurons it receivesas well as on the conductance of each input. These two inputs are modeled using two parame-


4.3. Fusiform cell model 33 Interim Report: Modeling the Auditory Pathway

Figure 13: Response from a computational model of the bushy cell for different values of AE .

ters: N and AE for, respectively, the number of innervating neurons and their conductance.In Figure 13, A–F show the response of the implemented model for different amplitude of

synaptic condcutances AE , which are 18.2, 27.3, 36.4, 54.6, 109.1, 218.3, and 327.4, respec-tively. While G shows the response curve for the model as implemented by Levy et. al.

The effect of changing the number of inputs NS and amplitude of synaptic conductanceAE on the soma potential is shown in Figure 14 . In A–D, the left part of the figure showsthe membrane potential from the implementation while the corresponding right part shows thesame from the model implemented by Levy et. al.

4.3 Fusiform cell model

The model selected for the fusiform cell is by Kim et. al. [8]. Since the model takes inputcurrent as the parameter, it is same as that described by Kim. The implementation was verifiedas described in [8]


5. Related work 34 Interim Report: Modeling the Auditory Pathway

Figure 14: Response for the Bushy Cell Model for different N and AE .

5 Related work

There exist at least three approaches for modeling the auditory pathway or a part thereof. Oneapproach is to build the model for analyzing how a particular process takes place in auditorypathway. For example the auditory pathway decodes the location, pitch, and loudness of thesound besides the other characteristics. Hence the model considers one or few of the functionsand simulates these. For example, the model for sound localization [13] explains the spacemapped representation of sound. Such models are essentially phenomenological because phys-iological details of individual neurons or nerve fibers are ignored.

In the second approach, simulation of the entire auditory pathway is carried out while ignor-ing the physiology of individual neurons and other biophysical processes [12]. This approach issuitable for studying the encoding done by “population” of neurons while ignoring the responseof individual neurons. This approach does not appear suitable for injecting faults through “para-metric manipulation,” as the parameters of the model are not based on the physiology of theneurons.

In the third approach, the auditory pathway is built up from individual neurons, and nucleiwhich constitute it. The advantages of this approach follow.

• The modelling is modular, i.e. one can change the particular model for a neuron/nucleus,whenever a superior model is available.


5.1. Auditory Neuron 35 Interim Report: Modeling the Auditory Pathway

• A particular transformation/function performed by the pathway can be analyzed from theneural output. In the former case, the modelling part itself takes care of that, and hence islimited only by our current understanding.

• We can introduce faults in different sub-systems of the pathway, and analyze how itsimpact on the output or the BAEP. Such analysis can be used in cases where only the endresult data, i.e. brainstem evoked auditory potential, is available and we want to knowwhich sub-system of the pathway is responsible for any observed aberration.

The disadvantage of the third approach is that it is computationally intensive and relies onmodels for various types of neurons that may or may not be available. However, we consider theapproach evolutionary in the sense that one can add as much detail as the available computingpower allows and replace individual models by better ones as they become available.

5.1 Auditory Neuron

We have considered two models of the AN fibers. The first model [24] we we have implementeddescribes the response of high SA AN fibers. While the other model [19], is applicable for lowas well as high SA neurons; it does not focus on two tone suppression. We plan to use thesecond model whenever we need the response for low SA neurons.

5.2 Cochlear Nucleus

There exist aggregate models that attempt to simulate the entire cochlea or a particular portionthereof which shows the same kind of response [15]. We plan to use a more detailed model,and will simulate the cochlear nucleus by simulating the individual constituent neurons as theirphysiology is reasonably well understood.

5.2.1 Bushy Cell

Two types of Bushy cells are found in ventral cochlear nucleus: spherical and globular. Thefirst model [16] we have implemented simulates the behavior of the spherical bushy cell andglobular bushy cells except for globular bushy cell with a large number of incoming AN fibers.Another model [18], which is specifically built for the globular bushy cell, which we plan to usewhen needed.

5.2.2 Octopus Cell

For the octopus cell we considered two models. The first was physiological model [10] foroctopus cell, and the other was phenomenological model [6], which models the response of theoctopus cell and in particular, the ventral cochlear nucleus. Since a physiological model is morevaluable because it gives us more options of introducing fault in the auditory pathway system,so we implemented the first model [10].

6 Future Work

A model of the auditory pathway is needed for better understanding of the mechanism by whichauditory inputs are interpreted by the brain. The current obstacles we face while building the


6. Future Work 36 Interim Report: Modeling the Auditory Pathway

model is the non-availability of mathematical models for several types of neurons. We plan tosimulate he behavior of such neurons using the generic Hodgkin-Huxley model. The secondproblem which we are likely to face is that of model verification and validation. We do haveaccess to the brainstem auditory evoked potential data for validation, but this is a combinedresponse from all of the neurons from different nuclei in the auditory pathway. Hence we needto know how the evoked potential is related to the membrane potential of different neurons.

Different models for a given type of type neuron exist and we have chosen the one whichis more detailed. The detailed model is chosen for better accuracy but it also has the disad-vantage of being more complex. Hence we have to make a trade off between the detailed andless computationally intensive models. We have deferred this question until we simulate theentire auditory pathway. At that time we may possibly use less-detailed models for the sake ofcomputational tractability.

Acknowledgements

Thanks to Professors Nina Kraus and Sumitrajit Dhar, School of Communication at Northwest-ern, for their encouragement and technical assistance throughout this project; Professor MichaelHeinz, Purdue University, for sharing the MATLAB code of the model of the auditory neurons;Arthur Baskin of Intelligent Information Technologies for his ideas on how this work possiblyrelates to fault tolerant software architecture; to all members of the SERC advisory board fortheir patient hearing of the many presentations on this topic; and to Professor Wayne Zage,Director SERC, for providing an opportunity to present this work at SERC showcases.


References 37 Interim Report: Modeling the Auditory Pathway

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[3] E. Hayes, C. M. Warrier, T. Nicol, S. G. Zecker, and N. Kraus. Neural plasticity fol-lowing auditory training in children with learning problems. Clinical Neurophysiology,114(4):673–684, April 2003.

[4] M. Hiroyuki, T. R. Jay, and A. W. John. Comparison of algorithms for the simulationof action potentials with stochastic sodium channels. Annals of Biomedical Engineering,30(4):578–587, 2002.

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[9] Alan D. Legatt. Mechanisms of intraoperative brainstem auditory evoked potentialchanges. Journal of clinical neurophysiology, 19(5):396–408, 2002.

[10] K. L. Levy and D. R. Kipke. A computational model of the cochlear nucleus octopus cell.The Journal of the Acoustical Society of America, 102(1):391–402, 1997.

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[17] N. Russo, T. Nicol, S. Zecker, E. Hayes, and N. Kraus. Auditory training improves neuraltiming in the human brainstem. Behavioural Brain Research, 156:95–103, 2005.

[18] G. A. Spirou, J. Rager, and P. B. Manis. Convergence of auditory-nerve fiber projectionsonto globular bushy cell. The Journal of Neuroscience, 136:843–863, 2005.

[19] Christian J. Sumner, Enrique A. Lopez-Poveda, Lowel P. O’Mard, and Ray Meddis. A re-vised model of the inner-hair cell and auditory-nerve complex. The Journal of the Acous-tical Society of America, 111(5), 2002.

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