Shear Modulus of the vocal fold Goodyer et al
The Shear Modulus of the Human Vocal Fold, Preliminary Results from 20
Larynges
Eric Goodyer (1), Sandra Hemmerich (2), Frank Müller (2), James B. Kobler (3),
Markus Hess (2)
This project received financial support from the Engineering Physics & Science
Research Council of Great Britain (EPSRC)
Eric Goodyer eg@dmu.ac.uk
Markus Hess hess@uke.uni-hamburg.de
(1) The Centre for Computational Intelligence - Bioinformatics Group, DeMontfort
University, The Gateway, Leicester LE1 9BH UK. 44-1162-551-551 x 8493
(2) University Medical Centre Hamburg-Eppendorf, Department of Phoniatrics and
Pediatric Audiology, Hamburg, Martinistr. 52, D-20246 Hamburg/Germany
(3) Center for Laryngeal Surgery and Voice Rehabilitation, Massachusetts General
Hospital, One Bowdoin Sq., Boston MA 02114
Abstract:
Objective:
Quantification of the elastic properties of the human vocal fold
provides invaluable data for researchers deriving mathematical models of phonation,
developing tissue engineering therapies, and as normative data for comparison
between healthy and scarred tissue. This study measured the shear modulus excised
cadaver vocal folds from twenty subjects.
Methods:
Twenty freshly excised human larynxes were evaluated less than 4
days post-mortem. The larynxes were split along the saggital plane and mounted
without tension. Shear modulus data was obtained by two different methods using a
Linear Skin Rheometer (LSR). For method 1 cyclical shear stress was applied
tangentially to the mid-membranous portion of the vocal fold and shear modulus was
derived by applying a simple shear model. For method 2 the apparatus was configured
as an indentometer and the shear modulus was obtained from the stress/strain by
applying an established analysis technique.
Results:
Method 1 yielded shear moduli ranging from 327 to 3516 Pascals for
female larynxes and from 296 to 4582 Pascals for male larynxes. Method 2 yielded a
range of 555 to 2088 Pascals for female larynxes and from 556 to 2987 Pascals for
male larynxes.
There is insufficient data at this time to make any generalised conclusions or perform
statistical analysis. However the results obtained by the two methods correlate fairly
well with a correlation factor of 0.65. Comparing left hand side to right hand side the
correlation factor using the shear model is 0.38 and for the indentometer model 0.54.
Conclusions: We have successfully demonstrated two methodologies that are
capable of directly measuring the shear modulus of the human vocal fold, without the
need to dissect out the vocal fold cover tissue. The sample size of 9 female and 11
male larynxes is too small to validate a general conclusion. The high degree of
variability in this small cohort of subjects indicates that factors such as age, health
status and post-mortem delay may be significant. There must also be a natural
Shear Modulus of the vocal fold Goodyer et al
variation present in any group of samples. Therefore a far larger sample size is
required for valid normative data.
Key Words: Elasticity, Shear Modulus, Vocal Fold Biomechanics
Shear Modulus of the vocal fold
Shear Modulus of the vocal fold Goodyer et al
Introduction:
Intraoperative measurements of vocal fold pliability would be very useful in the
practice of phonosurgery. As a preliminary step in designing a system to make such
measurements we conducted a study on fresh cadaver vocal folds. The purpose of this
study was to obtain some preliminary data regarding the range of normal shear
modulus values for male and female vocal folds and to compare two methods for
obtaining this data. Two different techniques were developed to measure the shear
modulus of the tissue at the mid-membranous position without the need to dissect the
vocal fold out of the larynx. One method was the application of cyclical shear stress
tangential to the axis between the vocal process and the anterior commisure (what is
the tangent to a straight line? Do you mean parallel to the axis?) ; the resultant
stress/strain characteristics are used to derive the tissue modulus using a simple shear
model. The second method was the use of an indentometer to compress the tissue
normal to the surface; the mathematical model developed by Hayes [12] can then be
applied to the resultant stress/strain data to obtain another measure of the tissue
modulus.
The results below don’t belong in the introduction. However a little more background
on previous attempts to measure human vocal fold properties seems needed.
There ar every few published reports that give the shear modulus for a group of
human vocal folds. Those that do exist use a range of different techniques, such as
ultrasonics, optical and mechanical. The ultrasonic and optical methods infer shear
modulus, wheras the mechanical methods diorectly measured the biomechnical
respons of the the tissue. Our results compare favourable with those obtained by other
reserchers, from human tissue using mechanical methodologies.
In all, 9 female and 11 male larynxes were examined. The range of results using the
shear method for female larynxes is 327 to 3516 Pascal for female larynxes and from
296 to 4582 Pascal for male larynxes. The range of results using the indentometer is
555 to 2088 Pascal for female larynxes and 556 to 2987 for male larynxes.
The average values were very similar. For male larynxes being 1286 Pascal (shear
model) and 1087 Pascal (indentometer model). For female larynxes being 1447 Pascal
(shear model) and 1337 Pascal (indentometer).
It can be seen that both methods yield data sets with similar ranges.. The data sets are
still too small to be considered statistically valid to draw general conclusions;
however the initial results are promising and we will continue our study to expand the
data sets.
Shear Modulus of the vocal fold Goodyer et al
Materials and Methods:
All measurements were made with a Linear Skin Rheometer (LSR) [5,18]. The LSR
is a precision instrument originally designed to measure the visco-elastic properties
of the stratum corneum [2,19,21]. Based upon the concept developed by Hargens in
the 1960’s (The Gas Bearing Electrodynanometer or GBE) [5,8,11], the LSR uses
modern micro-mechanical components to achieve force feedback control in real time,
and precision position measurement. It has recently been successfully used to measure
the more delicate tissue of the vocal fold [9,10,13,14,15].
Method 1: Simple Shear Model
A sinusoidal force F is applied to the material under test and the resultant
displacement P is logged.
(1) F = FmaxSin(t)
(2) P = PmaxSin(t+T)
Where
F = instantaneous force
Fmax = the maximum force
t = time over one cycle in radians
P = instantaneous displacement
Pmax = the maximum displacement
T = the phase shift in radians.
The Dynamic Spring Rate (DSR) of the tissue is F max / P max, and is expressed in
units of grams force per millimetre. The DSR can then be used to determine the shear
modulus using knowledge of the geometry of the test site as follows:
The stress  is the applied force F per unit area A given by
(3)  = F / A
The resultant strain is given by lateral displacement P per material thickness T.
(4) P / T
Shear modulus G is defined as stress per unit strain
(5) G = 
(6) G = (F / P) * (T / A)
As DSR = F / P then
(7) G = DSR * T / A
Data are obtained by gluing the flat tip of a probe arm to the tissue with what kind of
glue?. The area of attachment (A) is determined by direct measurement. The simple
shear model does not take account of tissue that is attached to the column that is
directly stressed, which was observed to be typically 0.5mm around the area of direct
attachment. The Hayes formulae provides a mathematically rigorous correction for
Shear Modulus of the vocal fold Goodyer et al
indentometer data, which in addition to compressing tissue with the indentor, also
exterts shear stresses to surrounding tissue. No such similar rigorous solution has been
found for pure shear stresses.
MORE TO DO HERE
To take account of the adjoining tissue and errors in the direct measurement of
attachment area, the dimensions were increased by between 0.25 and 0.75mm on all 4
sides. The thickness of the vocal fold tissue (T) is typically 1mm.
Using these geometric values a range of shear moduli can be derived for each sample.
Ten readings were taken from each test site and middle of each range was averaged.
These results are referred to as the ‘Shear Model’ in the text.
Shear Modulus of the vocal fold Goodyer et al
Method 2 Indentometer
In the second approach the LSR it was used as an indentometer. In this arrangement a
probe tip with a known surface area is pushed into the tissue while
force~displacement data is captured in real time. For a homogeneous material the
resultant relationship will be logarithmic; However many researcher’s have correctly
stated that indentation of a soft tissue does not follow this simple rule because
surrounding tissue remains in contact with the depressed section to which a shear
stress is applied.
One widely accepted model is that originally proposed by Y C Fung [26], from which
W C Hayes et. al. [12] developed a rigorous mathematical solution. This
mathematical device is based upon a solution for Yung’s 3D partial differential
equations that explain the deformation of soft tissue. Hayes’ solution offers a
‘correction factor’ to Yung’s equations that takes account of the shear strain
surrounding the indentation, which requires knowledge of the tissue’s Poisson’s ratio
(). is the relationship between a materials’ elongation and sheer strains. For an
incompressible material it is 0.5. Yung proposes that  is approximately 0.49 for soft
tissues.
The correction factor () is based on the ratio of the indentor radius (a), the tissue
thickness and Poisson’s ratio. The range given in our results is for a Poisson’s Ratio
of 0.45 to 0.5. Our indentor radius (a) is 0.5 mm and we assume the thickness of the
tissue to be 1mm. Hayes gives the following expression in his paper as the definition
of  together with a table of solutions.
(8)  = (F * (1 - ) )/( 4aGw)
Which can be rearranged to give
(9) G = (F/w) * (1 – ) * 9.80665) / (4a)
Where
 = the Hayes correction factor obtained from the published table
F = applied force
 = Poisson’s Ratio
a = indentor radius
G = Shear Modulus
w = depth of penetration
The 9.80665 converts the units for Shear Modulus (G) into Pascal
Each sample was indented 10 times. From the resultant stress/strain curves we select
the initial linear section, apply a least square fit and obtain the best value for F/w in
units of g/mm. All the other values are known. A range of shear moduli is given in the
results for a Poisson’s ratio of between 0.45 and 0.5. These results are referred to as
the ‘Indentometer Model’ in the text.
Shear Modulus of the vocal fold Goodyer et al
Results:
You have should refer the reader to specific figures where appropriate.
This section needs some work. There must be more to say!
How about plotting right VF vs left VF data and method 1 vs Method 2?
I find presenting the ranges to be confusing. Why not just pick one correction factor
and go with that? Then you could also take one subject and plot their moduli as a
function of changing the correction factors. That gives you something to discuss a bit
later. Also, you should discuss the variability in the repeated measurements and
across subjects a bit more. Was one method more reliable than the other?
What about pooling all males vs all females?
The graphs use the mid-point of the range of values shown in the full results tables to
show the distribution of shear modulus with respect to age. Need to describe the plots
for the reader.
Using the midpoint data from tables I and II, the results can be summarised as
follows:
Male Shear Modulus =
i)
Range = 296 - 4582 Pascal (shear model)
ii)
Average = 1286 Pascal (shear model)
iii)
556 - 2987 Pascal (indentometer model)
iv)
Average = 1087 Pascal
Female Shear Modulus =
i)
327 - 3516 Pascal (shear model)
ii)
Average = 1447 Pascal
iii)
555 - 2088 Pascal (indentometer model)
iv)
Average = 1332 Pascal
A total of 19 sets of data were obtained from both the left hand side and the right hand
side of the split larynx. To assess the corellation between left and right hand side data
the normalisd differences have been determined using the formulae
(left hand side – right hand side)/(left hand side _ right hand side)
Using the shear model 4 sets data matched within 10%, 6 within 20%, 3 within 30%,
2 within 50% and 4 within 60%. Tis means that just over half the samples gave a
value for the left and right hand sides that were within 20% of eachother.
Usinf the indentometer method the corellation between keft and right pairs improved
dramatically, with 7 pairs agreeing to within 10%, 6 within 20%, 4 within 30% and 3
within 40%
Shear Modulus of the vocal fold Goodyer et al
Discussion:
Few researchers have reported data obtained by direct measurement of the mechanical
properties of intact larynges. Results have either been inferred from observations of
acoustic or optical effects, or the vocal fold cover has been excised and tested
mechanically out of anatomical context.
Kaneko [17] and Tamura [24] amongst other have reported the derivation of viscoelastic properties using ultrasound techniques in-vivo and using excised larynxes.
However they do not offer comparable data relating to the elastic modulus.
Hsiao [16] has reported success in obtaining values for Young’s Modulus using
colour Doppler imaging in-vivo. If we assume a Poissons ratio of 0.5 then these
results translate to shear modulus ranges of 10 to 40 kPa for men and 40 to 100kPa for
women. So how does that compare with your data? If not the same, why not?
McGlashan [20] reported a method to infer vocal fold properties using an in-vivo
optical technique that generated a series of dynamic surface maps. The results so far
do not offer a value for vocal fold shear modulus, but later results have quantified the
velocity of the mucosal wave, from which a derivation of shear modulus should be
achieved.(??)
Chan & Titze [6,7] have measured shear modulus in excised tissue using a parallel
plate rheometer. Their earlier work (6) gives value of between 10 to 1000Pa for shear
modulus. Their later paper (7) reports a range of values for different subjects, taken
under differing conditions. Values ranged from as low as 10 Pa to 300Pa (?) at low
frequencies.
The ground breaking (?) in-vivo data obtained by Tran et al [25] offers a range of
shear modulus from 2.45 kPa to 29.4 kPa for low frequency (?) stimulations slow
displacements? of the vocal fold. Berke [3,4] describes the apparatus used in more
detail, and gives some results for Young’s Modulus using canine data, the medial (?)
result equates to a shear modulus of 1.45kPa. Perlmann & Titze [22,23] have obtained
canine data using excised tissue with a range of 9.46 to 41.2 kPa for a variety of
conditions. Thehe closest comparison to our test conditions being ‘in-situ 10% strain’
with a value of 34.7 kPa. Alipour’s canine results [1] gives a shear modulus of
13.96kPa.
Can you stick to using either Pascals or kPa?
Our results are indicative of a normal shear modulus for the vocal fold of between 300
and 4500 Pascal. Male tissue tends to be stiffer than female. (not mentioned in results)
As yet there is insufficient data to enable us to draw generalised conclusions; and the
difficulty of obtaining repeatable measurements from soft tissue is demonstrated by
the poor coefficients of variance relating to the original raw data. It’s hard to know
what a ‘poor’ or a ‘good’ cov is in this context. Maybe you are being too stringent. If
you think it is experimental error then you need more discussion of what is causing
the poor results.
Shear Modulus of the vocal fold Goodyer et al
We are confident that our methodologies are valid as the both techniques yielded
similar data sets for the same tissue samples. – again, why not plot one vs the other?
The results are also similar in what way? to those obtained by Chan and Titze, who
also obtained their data by direct measurement of the tissues mechanical properties
Our intention is to continue this study in order to improve the repeatability of the
results, and to expand the data sets to achieve a statistically acceptable sample size. –
not clear what the statistical test or question is. Perhaps you have at least been
successful in estimating the sensitivity range over which an in vivo instrument should
be able to work. In addition we will investigate the observed variations of elasticity
with respect to anatomical position and direction of stress.
Conclusion:
We have shown that it is possible to directly measure the shear modulus of the vocal
fold without dissecting out the tissue from its’ surroundings, using a mechanical
methodology . Thus the data obtained is more representative of the elastic response
during phonation than data obtained from dissected tissue measured in isolation.
The two techniques outlined offered similar results and therefore support each other.
They are also similar to data obtained by other researchers using direct mechanical
methodologies. In future studies we will complete the analysis by dissecting out the
vocal tissue, and measuring it in isolation a similar manner to previous published
work enabling a more direct comparison of our methodologies.
Shear Modulus of the vocal fold Goodyer et al
References:
1.