Download impedance audiometry lectures

Tymp Lecture Handout
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Syllabus for Impedance
Audiometry, CD 5704
Robert de Jonge, Ph.D., Mar
58
Text: Clinical Impedance Audiometry, 2nd
Ed., JJ Jerger & JL Northern
Supplements:
•RH Margolis and LL Hunter,
"Acoustic Immittance Measurements,"
Chapter 17 in Audiology: Diagnosis, RJ
Roeser, M Valente, and H Hosford-Dunn
(eds).
•American Speech-Language-Hearing Association (1997). Guidelines for Audiologic Screening, 15-22. This is the
section dealing with screening children (birth through 18 years) for outer and middle ear disorders.
•"Tympanometry for evaluating middle ear disease in children," RR de Jonge
•Acoustic Impedance and Admittance, AS Feldman & LA Wilbur
•Selected Readings in Impedance Audiometry, JL Northern
Exams: There will be two exams, a mid-term and a final exam. Each exam will have the same weight in determining the
final grade.
Attendance: Class attendance policy is consistent with University policy. In addition, four absences are allowed for
whatever reason (approved or not, at your discretion). Beyond this the final grade is reduced by 1/4 of a letter grade for
each additional absence. The final grade will be increased by 1/4 for each of the allowed absences that is not used. Perfect
attendance improves performance by one full letter grade.
Course Outline
Introduction to the Impedance Battery
I.
Tympanometry, general principles
•what happens to the middle ear during tympanometry
•the tympanogram and its axes: admittance and static pressure
•parameters derived from the tympanogram: peak Y, TPP, TW, Vec
•relationship between tympanometric parameters and middle ear pathology
II.
Acoustic reflexes
•brief overview of the acoustic reflex arc
•general effects of conductive, cochlear, and retrocochlear pathology upon the reflex
•acoustic reflex decay
Principles of Impedance
I.
Introduction to the concept of impedance, admittance, immittance.
•the relationship between "force-like" and "flow-like" quantities in systems
•energy flow through systems
•The basic model: mass, stiffness,friction, with a sinusoidally oscillating force applied
II.
Simpler systems containing only friction, responding to DC force
•mechanical, acoustical, electrical systems
Tymp Lecture Handout
III.
A more complex mechanical system, the basic model revisited
•define Z, R and X
•R, resistance, energy lost from system in heat, friction
•X, reactance, energy stored in system, Xm and Xk
•Xm, mass reactance, kinetic energy, angular velocity
•Xk, stiffness reactance, potential energy, Hooke's Law, springs, stiffness and compliance
•the impedance equations, and a particular examples
IV.
Impedance as a vector quantity, the phase angle
•defining fo, the resonant frequency, tympanogram notching
•Impedance as a complex quantity (real & imaginary parts)
V.
Y, the admittance
•conductance, G and susceptance, B
•describing Y, G, B in terms of Z, R, X
VI.
Analogous components in mechanical, acoustical, electrical systems
•mass, tubes, inductors
•stiffness (compliance), volumes, capacitors
•friction, acoustical resistance, resistors
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Midterm exam
Readings:
•Jerger & Northern, preface to first edition, chapter 1
•Feldman & Wilbur, chapter 3 is required (chapters 1 &12 are supplemental)
• Margolis & Hunter, "Acoustic Immittance Measurements," read p. 381-408, the information up to the section on
The Acoustic Stapedial Reflex.
VII.
Zwislocki's middle ear model
•energy flow through model
•input impedance or admittance (tympanogram peak), energy flow through cochlea (audiogram)
•putting the tympanogram & audiogram together to uniquely define middle ear pathology
VIII.
The functional blocks of Zwislocki's middle ear model, relating components to normal middle ear structures,
pathology, the effects upon the audiogram and tympanogram. The functional blocks:
•cochlea: relation to Meniere's disease & VIII N. tumors
•stapes branch: otosclerosis
•incudo-stapedial joint: ossicular discontinuity
•malleo-incudal complex: inflammatory disease of the middle ear
•drum shunt: atrophic tympanic membrane
•middle ear spaces: fluid and tympanometric rounding, gradient
Performing and Interpreting the Impedance Evaluation
I.
Tympanometry, the parameters: peak Y, TPP, TW, Vec
•normative data, interpreting abnormal results
•predicting middle ear effusion from tympanometric parameters, immittance screening
•evaluating tympanostomy (PE) tubes, Eustachian tube evaluation
II.
Acoustic reflexes
•basic neuroanatomy
•ipsi vs. contralateral reflexes with conductive hearing loss
•reflex sensation level and hearing level with conductive, cochlear, VIII N. pathology
•acoustic reflex decay for VIII N. lesions
•facial nerve paralysis
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•predicting hearing sensitivity
III.
Clinical examples, interpretation
Final exam
Readings:
•Feldman & Wilbur, chapter 4 is required
•Jerger & Northern, chapters 2, 4, 5, 6, 7, 8, 10
• RH Margolis & LL Hunter, "Acoustic Immittance Measurements," read p. 408-413, the section on The Acoustic
Stapedial Reflex.
• American Speech-Language-Hearing Association (1997). Guidelines for Audiologic Screening, 15-22. This is the
section dealing with screening children (birth through 18 years) for outer and middle ear disorders.
•Tympanometry for evaluating middle ear disease in children
Supplements from Northern's selected readings:
•p. 133-138 (Brooks' article, gradient), 166-174, 175-181, 69-81, 271-277, 96-104, 44-60, 284-287, 288-297
card fld "Major Topics…"
Your objectives for the class:
•Be able to perform the admittance battery, do the tests. You will do this in clinic.
◊tympanometry
◊acoustic reflex thresholds (ARTs)
◊acoustic reflex decay (ARD)
•Be able to interpret your results. Relate tympanometric variables to the status of the external and middle ear:
◊physical volume, ear canal volume, Vec
◊static admittance or peak admittance, Yx
◊tympanometric peak pressure, TPP
◊gradient, or tympanometric width, TW
•Understand the pathogenesis of acute, serous, and secretory otitis media. At each stage of the disease, understand the
impact upon the tympanometric variables.
•Be able to predict how middle ear disease, cochlear, and retrocochlear pathology affect ARTs and ARD.
•Understand the principles of immittance (physics)
◊admittance (conductance & susceptance)
◊impedance (resistance & reactance)
◊phase angle
•Understand the basic factors underlying impedance
◊mass
◊compliance (or stiffness)
◊resistance (friction)
◊frequency
•Be able to apply these concepts to energy flow in each of the three domains
◊mechanical
◊acoustical
◊electrical
•Understand Zwislocki's middle ear model. Be able to use it simulate middle ear pathology:
◊effects of reduced middle ear volume
◊atrophic eardrum
◊middle ear effusion, negative middle ear pressure
◊ossicular discontinuity
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◊otosclerosis
•By combining the tympanogram with the audiogram it is possible to determine which pathology is affecting the middle
ear
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Inserting the probe
•the main goal is…
-tight, but comfortable
-hermetic (air tight) seal
-no blockage of probe tubes
Do
•Briefly describe what you are going to do.
With understanding, fears are allayed
•Tell them to sit still. Don't talk, move jaw, swallow during test. If you tell them not to swallow, let them know when its
Ok to swallow.
•Tell them some of the sounds will be very loud, but they won't last too long: usually one second, no more then 10
seconds
•Use the otoscope to inspect the ear for…
-signs of pathology requiring medical referral
-contraindications to performing tympanometry
-size and shape of canal
•select a probe slightly larger than canal
•fully seat probe on probe assembly
•make sure probe assembly is securely fastened together, no leaks
•pull up & back on pinna to straighten canal
•insert probe with a slight twisting motion
•push gently, but firmly to achieve seal with little discomfort to patient
•Begin test, your equipment will let you know when you don't have a seal (then you repeat the above)
Don't
•Don't tell the patient it won't hurt. This is what people say before they are going to do something painful.
•Don't do anything to clog the tubes of the probe assembly
-recently washed, wet probe tube
Tymp Lecture Handout
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-wax filled ear
-wet, draining ear
•Don't stress drum in a fragile ear
-post stapedectomy
-post myringoplasty, tympanoplasty
•Don't needlessly hurt patient
-acute otitis is painful, sometimes even to touch ear
-pathology is obvious, you can make medical referral (according to AAO guidelines)
•When doing acoustic reflex testing, don't present tones at levels which will cause acoustic trauma. Generally stop at 110
dB HL.
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About the final…
•Understand the different forms of otitis and what you would expect to find for the audiogram, tympanogram, and
acoustic reflexes
•Be able to predict what you would expect to find for the audiogram, tympanogram, and acoustic reflexes for…
√otosclerosis
√ossicular discontinuity, with and without bleeding
√negative middle ear pressure, ipsi and contra reflexes
√middle ear effusion, the inverted notch tympanogram
√the effect of reducing the volume of the middle ear cavity
√hypermobile/atrophic tympanic membranes
√Bell's palsy
√Cochlear hearing loss
√Acoustic neuroma & Meniere's disease, effect on tympanogram and ARTs and ARD
•Be able to take a G and B tympanogram and, for a particular static canal pressure, compute R, X, Z and the impedance
phase angle
•Given the mass, stiffness, resistance, and frequency driving a simple series mechanical circuit, use the stack "Impedance
Calculator" to determine G, B, Y, R, X, Z, impedance or admittance phase ange, and the resonant frequency, and
√determine whether the system is mass dominated or stiffness dominated, or at resonance
√whether you would find a notched tympanogram
•Be able to apply the ASHA recommended criteria to determine…
√failure or passing or re-check on the hearing or immittance screen
√what referral you should make
•Look at the syllabus, do the readings
Tymp Lecture Handout
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•Immittance refers to either impedance or admittance
-you cannot attach a number to immittance
•Impedance is a measure of the opposition to the flow of energy through a system
-electrical
-mechanical
-acoustical
Z = P / U, in acoustic ohms
•Admittance is the inverse of impedance
Y = 1 / Z, in mho or mmho
•Impedance is a "two-part concept" so is often spoken of as a vector quantity
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•Typical tympanogram taken of me, using the
Virtual. Only right ear is shown
•measurement plane tympanogram, not
compensated for admittance of volume
occupied by ear canal
•in the upper right portion of the tymp is a
plot of phase angle as a function of probe
frequency
-at tympanogram peak
•a positive admittance phase angle indicates that stiffness dominates the system
•a negative admittance phase angle indicates that mass dominates the system
•a phase angle of 0° indicates that the system is in resonance
-moving most efficiently
-maximum energy transfer
•phase angle is…
-lower in loosening pathologies
-higher in stiffening pathologies
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During the course of obtaining a tymp on a
normal ear…
•pump increases static ear canal pressure
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•drum is stretched, input impedance of the middle ear increases (admittance decreases)
•flow of acoustic energy into middle ear decreases, energy in canal increases, SPL of probe tone begins to increase
•AGC circuit detects increased SPL from microphone, and automatically decreases drive current to the loudspeaker
•decreased current results in reduced SPL, back to normal 85 dB SPL
•As static ear canal pressure is reduced, admittance of middle ear increases, increased flow of acoustic energy into middle
ear causes SPL to drop in canal
•AGC circuit detects reduced SPL at microphone, increases current to loudspeaker, SPL increases to 85 dB SPL
•at tympanogram peak, flow into middle ear is maximum, loudness for listener is at maximum, drive current to
loudspeaker is at maximum, admittance is at maximum, impedance is at minimum
-The tone sounds loudest to the listener
•as static canal pressure drops further, admittance of middle ear is reduced as drum is placed under tension, SPL in canal
builds as acoustic flow into middle ear is reduced
-The tone sounds softer to the listener
•AGC circuit detects increased SPL at microphone, reduces current to loudspeaker, SPL decreases to 85 dB SPL
•and so on…
Some points about calibration…
•drive current to loudspeaker is directly proportional to admittance
-current flow in electrical systems is analogous to volume velocity in acoustical systems
•by placing probe in cavities of known admittance (i.e., known volumes), the instrument can be calibrated to read directly
in mmho
•at 226 Hz, 1 ml cavity has admittance of 1 mmho, let drive current = x
-if current of unknown cavity is 2x, then admittance = 2 mmho
•the relationship between volume and admittance depends upon atmospheric pressure
-calibration needs to be performed daily
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Increase in static pressure represented by mm
increase in fluid level
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•this is a "U" tube manometer
•increases and decreases in fluid level are
measured in millimeters
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•1.0 mm (millimeter) of water pressure equals 10 Pascals, or 1.0 daPa
•negative values indicate a pressure below ambient
•normal ambient pressure is about 100, 000 Pa (30 inches Hg)
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Volume of the ear canal
•is estimated at either tail of the tymp
•here, a pressure of -296 daPa was used
•drum is stretched (medially, or laterally)
Ytotal = Ycanal + Ymiddle ear
•impedance of the middle ear is driven to
"infinity"
-actually, it isn't
•admittance is minimum
•admittance is related to the volume associated with the cavity between the probe tip and the drum
-canal volume is overestimated
-canal volume can be measured with a syringe & alcohol (adults ≈ .56 ml vs. .9 mmho)
•at a probe frequency of 226 Hz, 1.2 mmho = 1.2 cc
•higher the volume, the larger the admittance
•Vec normally larger with hand held probes
•with perforation of drum, canal + middle ear volume is measured
•perforation usually gives very large values for Vec, except when…
-small mastoid cavity
-mastoid fluid filled
•Shanks et al. (1992) studied 334 children (age 6 weeks to 6.7 years) pre- and post-tympanostomy using GSI-33 insert
probe
-mean Vec pre-op was about .55 ml to .8 ml (canals were larger for older children). Mean value is about .9 ml for adults
-mean Vec post-op was about 1.7 to 4.2 ml (larger values for older kids)
•Using Vec ≥ 1.0 ml as criterion for perf…
-2% false positive rate (i.e., Vec ≥ 1.0 ml, but no perf)
-3.3% false negative (i.e., Vec < 1.0 ml, but had perf)
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•Using Vec (RE - LE) ≥ 0.4 ml had only 0.9% false negative rate, 1.5% false positive rate
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Peak Admittance
•a measure of the "mobility" of the middle ear
system
•more mobile systems have higher admittance
values
•Ytm is measured at the tympanogram peak
•at this point, there is no tension on the drum
•the drum is in its position of rest; it is not forced medially or laterally
•the pressure in the canal is equal to the pressure in the middle ear
•Ytm tends to be large with "loosening" pathologies: ossicular discontinuities, atrophic TMs
•Ytm is small with stiffening pathologies: middle ear effusion, otosclerosis
Tympanometric peak pressure
•the peak also estimates the "middle ear pressure," or TPP
-with negative middle ear pressure and small mastoid volume, and highly mobile drum, TPP can be much less (more
negative) than MEP
-with fluid filled ears, TPP is probably unrelated to MEP
•TPP is around 0 daPa with normals
•TPP is negative when middle ear pressure is below ambient
•TPP is associated with Eustachian tube malfunction
•TPP varies widely in children's ears that are normal
card fld "Nozza"
Middle ear effusion is an objective indicator of an ear in a diseased state requiring treatment.
Criterion for separating ears with and without effusion, based upon Ytm…
Ytm
Ytm
Ytm
Ytm
Ytm
Ytm
mmho
= 0
≤ 0.1
≤ 0.2
≤ 0.3
≤ 0.4
Sens%
11
26
46
70
83
Spec%
98
97
92
80
69
PPV%
88
92
88
81
76
NPV%
47
52
58
69
77
Tymp Lecture Handout
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Nozza, et al. "Identification of MEE…" Ear & Hearing, 1994, 310-323.
Population: children with a history of chronic or recurrent MEE who were candidates for tympanostomy tubes.
Given the criterion:
•Sens = % of those with disease having positive results
•Spec = % of those without disease having negative results
•PPV = % of those with a positive outcome who have the disease
•NPV = % of those with a negative outcome who do not have the disease
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Gradient
•TW is a measure of how "sharply peaked" vs.
"flattened" the tymp is
•flattened tymps associated with effusion
•TW is mainly an attempt to quantify this
qualitative observation
card fld "Nozza"
Tymp Width
daPa
Sens%
TW > 150
94
TW > 200
89
TW > 250
85
TW > 275
81
TW > 300
77
TW > 325
70
TW > 350
61
TW > 400
49
Spec%
26
47
68
82
85
88
89
96
PPV%
61
67
76
85
86
87
88
94
NPV%
78
78
78
78 <-75
71
65
61
Nozza, et al. "Identification of MEE…" Ear & Hearing, 1994, 310-323.
Population: children with a history of chronic or recurrent MEE who were candidates for tympanostomy tubes.
Given the criterion:
•Sens = % of those with disease having positive results
•Spec = % of those without disease having negative results
•PPV = % of those with a positive outcome who have the disease
•NPV = % of those with a negative outcome who do not have the disease
Comment
•PPV and NPV depend upon the frequency of MEE (and normals) within the population.
Nozza's (Nozza et al., 1992 Ear & Hearing, 442-453) recommendation for criteria representing ears of children in the
general population:
Sens%
TW > 250 or
Spec%
PPV%
NPV%
Tymp Lecture Handout
Ytm < 0.3
78
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99
88
99
•ASHA's (1997) screening guidelines:
Infants (above 7 months):
Ytm < 0.2 mmho or TW > 235 daPa
One year to school age:
Ytm < 0.3 mmho or TW > 200 daPa
School age:
Ytm < 0.4 mmho or TW > 200 daPa
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For OME children 1-3 yrs of age, AAO guidelines…
•Tube is an option if…
◊HL ≥ 20 dB, better ear
◊OME duration ≥ 3 months
•Tube is recommended if…
◊HL ≥ 20 dB, better ear
◊OME duration ≥ 4-6 months
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Scale sensitivity
•same tymp as in previous displays, but with
a different scale
•makes tymp easier to interpret
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Hydrops ex vacuo…
•A theory for describing the pathogenesis of
otitis media
1. Occlusion of the orifice of the Eustachian
tube
•Hypertrophy of nasopharyngeal adenoid
tissue
•allergic tubo-tympanitis
•viral or bacterial nasopharyngitis
Regardless of the cause, the Eustachian tube swells, and no longer ventilates the middle ear
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Hydrops ex vacuo…
2. Reduced middle ear pressure
•the mucous membrane lining the middle ear
(mucoperiosteum) is the same tissue lining the
entire respiratory tract (including the lungs)
•the mucoperiosteum absorbs gas (mostly
oxygen) from the normally air-filled
("pneumatized" is a synonym) middle ear
cavity at a rate up to 50 daPa per hour
•this results in a negative middle ear pressure (that is, a pressure below the ambient barometric pressure); a partial
vacuum
•the eardrum is pulled medially into a retracted position
•a Jerger type C tympanogram would result
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Hydrops ex vacuo…
3. Development of the transudate
•the negative middle ear pressure passively
"sucks" fluid (transudate) from the
mucoperiosteum
•the fluid derives from blood plasma
•the fluid is clear, watery, not viscous, and
may have an amber cast to it
•bubbles, or a meniscus may be visible during otoscopy
•the shape of the tymp is changing from a type C to a Jerger type B as mobility is reduced
•this is a serous otitis media
•appearance of the drum on otoscopy may be quite normal
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Tymp Lecture Handout
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Hydrops ex vacuo…
4. Serous becomes secretory, or mucoid
•as time goes on, secretions from the mucus
glands (of the mucoperiosteum) increase
viscosity of the fluid; becoming the
consistency of egg white
•eventually, the fluid can become very thick,
tenacious, and "glue-like"; a mucoid otitis, or
"glue-ear"
•the tympanogram becomes very flat
•otoscopy will show a dull, opaque drum with a loss of landmarks
•most effective treatment is tympanostomy
tubes
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Acute Otitis Media
•a serous/secretory otitis often sets the stage
for a bacterial infection
•main treatment is antibiotics
1. Stage of hyperemia
•a bacterial inflammation causes the
Eustachian tube to swell and become dysfunctional, incapable of aerating the middle ear
•the inflammation migrates from the tube to the mucoperiosteum lining the tympanum
•blood vessels of the drum are "injected"
•the drum is red
•the ear is painful
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Acute Otitis Media
2. Stage of Exudation
•an active outpouring of fluid (exudate)
•this is a natural part of the body's immune
system's response to the bacteria
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•phagocytic leucocytes (white blood cells) engulf and destroy the bacteria, causing them to lyse
•the debris, by-products of the infection forms the mucopus
•the exudate is under pressure, the drum can bulge
•pain is increasing
•fever is increasing as the body absorbs the toxic by-products of the infection; this is a systemic response
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Acute Otitis Media
3. Stage of suppuration
•the drum spontaneously perforates, allowing
the infection to externalize itself
•pain is less, temperature is reduced
•the perforation stays small, and will usually
heal by itself
•a large perforation indicates a more serious condition; a chronic otitis media
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Acute Otitis Media
4. Stage of coalescence & surgical mastoiditis
•If the infection has not resolved itself (as was
more common in the pre-antibiotic era) the
bony tissue of the mastoid could become
infected
•consequences of the infection were
potentially serious, even causing death
•mastoid air cells would coalesce into a large infection filled cavity, the abscess
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•surgical intervention is indicated
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Acute Otitis Media
5. Resolution
•all tissues return to normal, within 4 to 6
weeks
•thickened mucoperiosteum sloughs off
•fluid is absorbed
•perforation heals
•it is important to follow the disease long enough to make certain that the ear returns to normal
•the ear may return to a serous/secretory state
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Acute Recurrent Otitis Media
•similar to acute otitis but ear progresses from
one infection to another so that the child
(usually, a child) seems to always have an
infection
•treated with prophylactic antibiotics,
tympanostomy tubes
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•The ART is measured with the ear in its
"most compliant state"
•Ear canal pressure is adjusted to equal
middle ear pressure
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•A stimulus presented to one ear activates the reflex arc bilaterally. Both stapedius muscles contract.
•Conventionally, the AR is determined for the ear activating the reflex; i.e., the ear the stimulus is presented to
•The AR may be measured (∆Y) in the same ear as the stimulus (ipsi) or the opposite ear (contra)
•For example,
-An ipsi ART of 90 dB HL was obtained for the RE
√Signal to RE, probe in RE
-A contralateral ART was obtained for the LE at 100 dB HL
√Signal to LE, probe in RE
A reflex may be absent…
•because the reflex arc is not activated, or
•because the reflex arc is activated, but the contraction of the stapedius muscle produces negligible change in the
admittance of the ear; i.e., it is not measured
•a reflex may be absent with conductive, cochlear, or retrocochlear pathology
•reflexes are absent in many otherwise normal ears, too
•A reflex may be absent in Bell's palsy, provided the lesion is not distal to the branch of the facial nerve innervating the
stapedius
Normal reflex (For normal hearing)…
•A normal ART is 85 dB HL for all frequencies between 250-8000 Hz
•The SD is about 7 dB
•Most reflexes should be present at 100 dB HL, or less
•An ART > 100 dB HL is an elevated HL, but see next 3 cards for effects of hearing loss
Effects of cochlear hearing loss
•Behavior of the ART is predictable from what you would expect to happen with recruitment and loudness growth
(Audiogram Threshold - 40 dB HL) = X
if X < 0 then X = 0
ART = X/2 + 85 dB HL
•For example, with 40 dB HL cochlear hearing loss, you would expect the reflex to be present at 85 dB HL
•Jerger found that even with cochlear hearing loss of 85 dB HL, 50% of the reflexes are still present
•Major characteristic of ART is reduced reflex SL re: audiogram threshold
•ART SL ≤ 60 dB suggests cochlear pathology, Jerger's original rule
•So, cochlear pathology can abolish reflexes
- By inhibiting activation of the arc
Tymp Lecture Handout
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-If the loss is quite severe
Effects of retrocochlear pathology
•VIII N. pathology can abolish reflex by preventing activation of the arc
•Usually the AR is absent, or present at an elevated HL
Major retrocochlear signs:
•The reflex is elevated (or absent) in the presence of relatively mild SN hearing loss
•If present, the reflex decays (ARD)
Effects of conductive pathology
•Conductive pathology will abolish the reflex by
-preventing activation of the arc, or
-preventing its measurement
•Every dB of ABG elevates the ART by one dB
ART** = 85 dB HL + ABG
**This is the stimulus level needed to activate the AR
•So, if the maximum output level is 110 dB, 50% of the reflexes are absent with ABG = 25 dB
•The conductive component attenuates the signal
•The AR may be absent (even if the reflex arc is activated)
-When the stapedius pulls on the ossicular chain, no discernable change occurs in the admittance (like pulling on a
locked door).
•The acoustic reflex is usually absent when the probe is in an ear with conductive pathology
-with ABG < 10 dB, more than 50% of the reflexes are absent
Figure this out…
•If you have only one ear with conductive hearing
loss, you can use contralateral ARTs to predict
audiogram
•If the only abnormality in an ear is negative middle
ear pressure, then ARTs can be normal ipsi, but
elevated contra
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Tymp Lecture Handout
Card number_____ 33
Card number_____ 34
Card number_____ 35
card fld "Inertia"
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Tymp Lecture Handout
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Inertia is a property of mass…
•An object at rest stays at rest unless acted upon by an external force.
•An object in motion stays in motion unless acted upon by an external force.
card fld "Elasticity"
An elastic deformation: a deforming force causes a body to change shape. When the deforming force is removed, body
returns to its original size.
•eg, a spring moving a distance when a mass is suspended from it
•stiffness: the ratio of the applied force to the displacement
stiffness = force / displacement
•compliance: the inverse of stiffness
compliance = displacement / force
card fld "Info…"
•Impedance (Z): opposition to the flow of energy through a system
-units: ohm
-eg: a tube of toothpaste with a very small orifice, hard squeeze (large force), small flow
-impedance concept is applicable to acoustic, mechanical, and electrical systems
•Admittance (Y): the inverse of impedance
-units: mho, or mmho
-admittance is the ordinate of the tympanogram
-eg: same tube of toothpaste with a large opening, same force, larger flow
•Immittance: a term for referring to either impedance or admittance.
-units: none
•mass (m): property of matter relating to inertia
-units: CGS, gm; MKS, kg
•stiffness (k): property of matter relating to elasticity
-units: dyne/cm or newton/m
-eg: you pull with great force on a spring, it moves very little. It is stiff.
•compliance (C): inverse of stiffness
-units: cm/dyne or m/newton
-eg: you pull with the same amount of force on another spring, it moves a lot. It is more compliant.
-a volume of air behaves (acoustically) as a spring. The larger the volume, the more compliant the spring.
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•frequency (f): impedance (and admittance) are influenced by the frequency of the force driving the system
-units: Hz
•Reactance (X): one of the two components of the impedance. Energy is stored, not lost in the reactive portion of
impedance
-units: ohm
X = Xm + Xk
•Mass reactance (Xm): kinetic energy stored in the inertia of mass
-units: ohm
•Stiffness (or compliant) reactance (Xk, Xc): potential energy stored in the compression or expansion of springs
-units: ohm
•Resistance (R): the other main component of the impedance. Energy is lost in the resistive component of the impedance,
commonly in friction, dissipated as heat.
-units: ohm
•Susceptance (B): one of the two main components of the admittance. Related to inverse of reactance.
-units: mho or mmho
B = Bm + Bc
•Mass susceptance (Bm): related to inverse of mass reactance.
-units: mho or mmho
•Compliant susceptance (Bc): related to inverse of stiffness reactance.
-units: mho or mmho
•Conductance (G): other main component of Admittance, related to inverse of resistance.
-units: mho or mmho
•Phase angle (q): the "direction" of the impedance, or admittance vector
-units: degrees
-Z and Y are both vector quantities. They have both magnitude and direction.
-a complete description of Z includes both its magnitude and direction (same for Y)
-eg: the system has an impedance of 975 ohms, and a phase angle of -75°
-eg: the system has an admittance of 1.03 mmho, and a phase angle of +75°
-the admittance phase angle is the reverse (opposite) of the impedance phase angle
card fld "Basic Parameters"
The four basic parameters:
•Mass, inertia
•Elasticity (stiffness/compliance)
•Friction (resistance)
•Frequency
We'll put them together into a simple circuit.
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Card number_____ 36
card fld "Info…"
•These equations describe impedance and
admittance relationships for a simple
mechanical circuit
•See the "Impedance Calculator" stack for
applications of these equations.
card fld "Assignment"
Try this out…
1. Obtain a G and B tympanogram. Display
them as measurement plane tympanograms, Cartesian (not Polar) coordinate system (From Virtual's Graphics menu,
choose Measurement Plane and Cartesian menu items).
2. Determine values for G and B at the tymp peak.
3. Compute Y. Also compute Z, R, X, and the
phase angle. Draw a phasor diagram.
4. Label it "My first ear" and put in on the
refrigerator. Use a magnet.
Card number_____ 37
Card number_____ 38
Tymp Lecture Handout
Card number_____ 39
Card number_____ 40
Card number_____ 41
card fld "Henry…"
The physicist and scientific administrator
Joseph Henry, b. Albany, N.Y., Dec. 17, 1797,
d. May 13, 1878, is known for his discovery of
ELECTROMAGNETIC INDUCTION and selfinduction. Largely self-educated, Henry
studied at the Albany, N.Y., Academy (1819-
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22), where he taught from 1826 until 1832, when he accepted a chair at the College of New Jersey (now Princeton
University).
His experimental work in chemistry, electricity, and magnetism reflected only a small portion of his broad scientific
interests. In 1846 he became the first secretary of the newly organized Smithsonian Institution, where he established a
continuing tradition of research.
Michael Faraday disagreed with him on theoretical grounds but found his experimental work useful. The unit of
inductance, the henry, is named in his honor.
-From Grolier Electronic Encyclopedia
card fld "Info…"
Mass Effects
Mechanical system
•The basic element is mass, which offers inertia
•When a sinusoidally varying force is applied to a mass, the mass opposes the changes in direction of the force
√i.e., when it is accelerated forward, during one half of the cycle, and attains a certain velocity, it will keep going in that
forward direction
√during the second half of the cycle, when the direction of the force is reversed, the continued forward motion of the
mass opposes this change in direction
•For any given mass…
√The opposing force becomes greater when the frequency is increased (i.e., as the direction of the applied force changes
more rapidly)
•To minimize the inertial effects…
√reduce the magnitude of the mass
√drive the mass at a lower frequency
•e.g., in stereo systems…
√tweeters with the best high frequency response are small, light
Acoustical system
•The ideal acoustical mass element is a tube (i.e., a long, small diameter tube)
•When the air column within the tube is driven by a frequency…
√the "slug" of air is not compressed, or expanded, but moves as a unit, offering the acoustical equivalent of mechanical
inertia
•the air within the tube behaves more like a large mass, when…
√the length of the tube increases
√the diameter of the tube decreases
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•long, thin tubes have a poor high frequency response
Electrical systems
•The electrical equivalent of a mass is an inductor (a simple coil of wire, sometimes wound around a ferrous core, to
increase its inductance, or inertance)
•When a voltage difference is applied across the ends of the wire (as during the first half cycle of the sine wave)…
√a current flows through the wire
√a magnetic field is generated (induced) in the wire
√the magnetic field's polarity is determined by the direction of the current flow, it "points" in the direction of current
flow
√After a magnetic field is created, it takes time to collapse
•During the second half of the cycle, the polarity of the voltage is reversed…
√the direction of current flow is reversed
√a new magnetic field is created, opposite in polarity to the old magnetic field
√the old magnetic field (before it collapses) opposes the new magnetic field, inhibiting the flow of current in the new
direction
√just as a mechanical mass opposes the change in direction of the applied force
•The unit of inductance is the Henry (H)
√1 H is equivalent to 1 gram
√a 15 mH inductor is equivalent to a 15 mg mass
The End
Card number_____ 42
card fld "Info…"
Elastic Effects
Mechanical system
•The basic element is a spring, which offers
elasticity
•When a sinusoidally varying force is applied
to a spring, the spring stores the energy used
to compress (or expand) it
•Stiffer springs will respond better (with a
greater amplitude) when driven by higher frequencies
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•The impedance of a spring decreases with frequency
•e.g., in stereo systems…
√Woofers, with the best low frequency response, have high compliance edges surrounding their mounting, so that a stiff
suspension will not limit their motion
√the fairly poor low frequency response of the ear is due to stiffness limitations of the middle ear
Acoustical system
•The ideal acoustical spring element is an enclosed volume of air
•When the enclosed volume is driven by a frequency…
√the air does not move as a unit, but it is alternately compressed or expanded, offering the acoustical equivalent of a
spring
•the air within the enclosure behaves more like a stiff spring, when…
√the volume decreases
√large volumes are equivalent to more compliant springs
Electrical systems
•The electrical equivalent of a spring is a capacitor, a device with large (surface area) metal plates separated by an
insulator.
•When a voltage difference is applied across the ends of the capacitor, during the first half cycle…
√current flows (negatively charged electrons) onto one of the parallel plates, and the plate becomes negatively charged
√electrons are repelled from the other plate, making it positively charged
√the potential difference across the plates is like a +/- charged battery, storing the electrical energy, like a spring stores
energy when it is compressed
√the ability of the plates to store charge is called "capacitance" (i.e., capacity)
√the units of capacitance are Farads (F) after Michael Farady or µF
√A 1.0 Farad capacitor can store 1 coulomb of charge for each volt placed across its terminals. One coulomb is 6.24 *
10^18 electrons (i.e., the number of electrons flowing per second with a current of 1.0 ampere).
•During the second half of the cycle, when polarity is reversed…
√the current stored is returned to the circuit (i.e., it is not lost)
√this is similar to the expansion of the previously compressed spring
The End
card fld "Faraday…"
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The English chemist and physicist Michael Faraday, b. Sept. 22, 1791, d. Aug. 25, 1867, is known for his pioneering
experiments in electricity and magnetism. Many consider him the greatest experimentalist who ever lived. Several
concepts that he derived directly from experiments, such as lines of magnetic force, have become common ideas in
modern physics.
Faraday was born at Newington, Surrey, near London. He received little more than a primary education, and at the age
of 14 he was apprenticed to a bookbinder. There he became interested in the physical and chemical works of the time.
After hearing a lecture by the famous chemist Humphry DAVY, he sent Davy the notes he had made of his lectures. As a
result Faraday was appointed, at the age of 21, assistant to Davy in the laboratory of the Royal Institution in London.
-From Grolier Electronic Encyclopedia
Card number_____ 43
card fld "Info…"
Resistive Effects
Mechanical system
•The basic element is a dashpot, which offers
friction
•When a sinusoidally varying force is applied
to the piston, friction exists between the piston
and the walls of the cylinder
•Energy is dissipated in heat
•The impedance of a dashpot is not affected by frequency
Acoustical system
•The ideal acoustical element is a fine mesh screen
•When air flows back and forth through the screen, energy is lost in friction (molecules of air interacting with the screen)
•a tube also has acoustic resistance
√adjacent layers of air move with different velocities within the tube, creating frictional losses
√energy will also be lost as air moves in contact with the walls of the tube
•frictional losses increase with the length of the tube, and decrease as the diameter of the tube increases
√long, thin tubes offer more resistance
•the resistance of the tube is also related to the viscosity of the gas within the tube
√air has a coefficient of viscosity, µ = 0.000181 dyne sec/cm^2
Electrical systems
•The electrical equivalent of friction is a resistor
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•When a voltage difference is applied across the ends of a resistor, electrical energy is lost in heat
The End
card fld "Faraday…"
The German physicist Georg Simon Ohm, b. Mar. 16, 1789, d. July 6, 1854, for whom the unit of electrical resistance, the
ohm, was named, determined (1826) Ohm's law — the relationship between the flow of current, the voltage, and the
resistance in a closed circuit (see ELECTRICITY).
Ohm's scientific contemporaries were slow to recognize his achievement, failing to realize how closely his conclusions
were derived from careful experimental work and especially how his discovery ordered vast quantities of existing
experimental data.
For most of his life Ohm held only indifferent, poorly paid teaching jobs, but in 1852 he was given the chair of physics at
the University of Munich.
-From Grolier Electronic Encyclopedia
Card number_____ 44
card fld "Info…"
A series circuit…
•In a series circuit, the total impedance is the
ratio of the total force (Ft) to the total velocity
(Vt)
•In a series circuit, Vt is the same in each of
the circuit elements (i.e., the mass, spring, and
dashpot all move with the same velocity), but
Ft is not
√Ft is the vector sum of the forces on the
mass (Fm), spring (Fk), and friction (FR) elements
•The magnitude of each force (Fm, Fk, and FR) can vary. The phase of each force is different
√Fm is at a phase of +90° relative to the velocity
√Fk is at a phase of -90° relative to the velocity
√FR is at a phase of 0° relative to the velocity
√Ft has a unique phase which depends upon the magnitude of the other forces
•So, FR is in phase with the velocity. Fm and Fk are 180° out of phase with respect to each other
•The force across the reactive portion (the spring and the mass) is…
Fx = Fm + Fk
•When the system is driven by a particular frequency, say 226 Hz…
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√Each element (m, k, R) moves at the same frequency, 226 Hz
√The total force is applied at a rate of 226 Hz
√The resulting velocity varies at a rate of 226 Hz
•The phase angle q is the phase difference between the Ft and Vt…
q = arc tan( Fx/FR)
•In the example given on this card…
√Fm
√Fk
√FR
√Fx
√Ft
√q
=
=
=
=
=
=
50 dynes
-30 dynes
10
dynes
+20 dynes
(20^2 + 10^2)^.5 = 22.36 dynes
63.43°
•see the next card for more…
Card number_____ 45
card fld "Info…"
Phase Angle
The example on this card illustrates phase
relationships between the forces on the mass,
resistive, and spring elements for a simple
series circuit. The frequency of the force (and
the velocity) is 2000 Hz. The phase of the
velocity (i.e., the total velocity) is the same for
the mass, resistance, and spring, but…
•The component of the total force applied to
the mass has a magnitude (peak amplitude) of
50 dynes. The phase angle relative to the velocity is +90°.
•The component of the total force (peak amplitude) applied to the spring element has a magnitude of 30 dynes.
phase angle relative to the velocity is -90°.
•The component of the total force (peak amplitude) applied to the resistive element has a magnitude of 10 dynes.
phase angle relative to the velocity is 0°.
See the next card…
Card number_____ 46
card fld "Info…"
Phase Angle
The
The
Tymp Lecture Handout
•These forces are the same as those for the previous card…
Fm = 50 dynes, phase = +90°
Fk = 30 dynes, phase = -90°
FR = 10 dynes, phase = 0°
and, assume the measured velocity is…
Vt = 5 cm/sec
•The total force is a combination of the three forces.
•The reactive portion, Fx, is (Fm - Fk) = 50 - 30 = 20 dynes.
√Since the reactive portion is positive, it is at a phase angle of +90°
•The resistive portion of the total force (FR) is 10 dynes, at a phase angle of 0°
•The total force (Ft) is…
Ft^2 = FR^2 + Fx^2 = 10^2 + 20^2 = 500
•Ft = 22.36 dynes, at a phase angle of 63.43 degrees
•the impedance, Z…
|Z| = Ft / Vt = 22.36 / 5 = 4.472 ohms
q = 63.43°
•|Z| is the magnitude of the impedance, and Z = |Z|, q
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