Excerpt from the Proceedings of the 2014 COMSOL Conference in Cambridge Determination of the Mechanical Properties in the Avian Middle Ear by Inverse Analysis P. Muyshondt *1 , D. De Greef 1 , J. Soons 1 , J Peacock 1 , and J.J.J. Dirckx 1 1 University of Antwerp, Laboratory of Biomedical Physics *Groenenborgerlaan 171, B-2020 Antwerp, Belgium, [email protected]Abstract: This paper presents the study of the avian middle ear as a biomechanical system, which is typically made up of a single hearing ossicle, the columella. So far, only few is known about the functioning of the avian middle ear. To gain new information about the mechanical properties of this system, a finite element model was created using a viscoelastic characterization, for which the geometry was extracted from µCT scans recorded from the middle ear of a mallard duck. Some of the unknown model parameters were determined by performing an inverse analysis, in which the model output is compared with the outcome of optical interferometric experiments, like stroboscopic digital holography and laser Doppler vibrometry. As a result of this procedure, several parameter values of different middle ear structures could be found. Keywords: middle ear mechanics, finite element modeling, optical interferometry, inverse analysis. 1. Introduction The avian middle ear is a peculiar biomechanical system that serves as an impedance match between incoming sound waves in air and acoustic waves in the inner ear fluid. In contrast to the mammalian middle ear, which contains three ossicles and a number of muscles and ligaments, the avian middle ear only contains a single ossicle, called the columella, one muscle and one prominent ligament (see Fig. 1). Despite this far simpler design, birds are able to perceive sound signals in a frequency range that is almost as broad as mammals [1, 2]. Despite these interesting properties, the avian middle ear has not been given the same research attention as the mammalian middle ear. This paper presents the current state of our research of avian middle ear mechanics through stroboscopic digital holography, laser Doppler vibrometry (LDV) and finite element modeling. The model’s geometry is deduced from CT measurements and its parameters are optimized using the experimental results. The work will provide novel insights in the functioning of this mechanically simpler variant to mammal middle ears, and therefore have important consequences in the development of middle ear ossicular replacement prostheses. Because some of the current middle ear prostheses designs (such as a TORP - Total Ossicle Replacement Prosthesis) qualitatively resemble the avian middle ear [3], studying this system will assist in determining the optimal shape, parameters, material choice and placement of these prostheses. 2. Methods 2.1 Numerical Model To start with, the model's geometry was obtained from CT measurements at the UGCT, UGhent [4], performed on a segment of the left skull half of a dead mallard duck, with a resolution of 7.5 µm. In order to enhance the X- ray contrast of different types of soft tissue, the sample was stained in a daily refreshed 2.5% PTA (Phosphotungstic acid) solution in deionized water for 48 hours before the scan. From these data, different middle ear structures were segmented using Amira (Visage Imaging) to create a surface model of the middle ear which is needed to create a realistic numerical model. Within the surface model, as depicted on Fig. 2, five different structures could be distinguished: the tympanic membrane, Platner’s ligament, the cartilaginous extracolumella and the bony columella with the footplate bounded by an annular ligament. Other ligaments mentioned in literature were not observed and therefore not considered in the geometry. The final geometrical surface model, consisting of 15000 triangle-shaped faces after decimation and smoothing of the surface, was exported as an STL-file that could be imported in finite element software (COMSOL Multiphysics 4.3b, The Structural Mechanics Module) in order to create a mechanical model.
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Excerpt from the Proceedings of the 2014 COMSOL Conference in Cambridge
Determination of the Mechanical Properties in the Avian Middle Ear by Inverse Analysis P. Muyshondt*1, D. De Greef1, J. Soons1, J Peacock1, and J.J.J. Dirckx1 1University of Antwerp, Laboratory of Biomedical Physics *Groenenborgerlaan 171, B-2020 Antwerp, Belgium, [email protected] Abstract: This paper presents the study of the avian middle ear as a biomechanical system, which is typically made up of a single hearing ossicle, the columella. So far, only few is known about the functioning of the avian middle ear. To gain new information about the mechanical properties of this system, a finite element model was created using a viscoelastic characterization, for which the geometry was extracted from µCT scans recorded from the middle ear of a mallard duck. Some of the unknown model parameters were determined by performing an inverse analysis, in which the model output is compared with the outcome of optical interferometric experiments, like stroboscopic digital holography and laser Doppler vibrometry. As a result of this procedure, several parameter values of different middle ear structures could be found. Keywords: middle ear mechanics, finite element modeling, optical interferometry, inverse analysis. 1. Introduction
The avian middle ear is a peculiar biomechanical system that serves as an impedance match between incoming sound waves in air and acoustic waves in the inner ear fluid. In contrast to the mammalian middle ear, which contains three ossicles and a number of muscles and ligaments, the avian middle ear only contains a single ossicle, called the columella, one muscle and one prominent ligament (see Fig. 1). Despite this far simpler design, birds are able to perceive sound signals in a frequency range that is almost as broad as mammals [1, 2]. Despite these interesting properties, the avian middle ear has not been given the same research attention as the mammalian middle ear.
This paper presents the current state of our research of avian middle ear mechanics through stroboscopic digital holography, laser Doppler vibrometry (LDV) and finite element modeling. The model’s geometry is deduced from CT measurements and its parameters are optimized
using the experimental results. The work will provide novel insights in the functioning of this mechanically simpler variant to mammal middle ears, and therefore have important consequences in the development of middle ear ossicular replacement prostheses. Because some of the current middle ear prostheses designs (such as a TORP - Total Ossicle Replacement Prosthesis) qualitatively resemble the avian middle ear [3], studying this system will assist in determining the optimal shape, parameters, material choice and placement of these prostheses. 2. Methods
2.1 Numerical Model
To start with, the model's geometry was
obtained from CT measurements at the UGCT, UGhent [4], performed on a segment of the left skull half of a dead mallard duck, with a resolution of 7.5 µm. In order to enhance the X-ray contrast of different types of soft tissue, the sample was stained in a daily refreshed 2.5% PTA (Phosphotungstic acid) solution in deionized water for 48 hours before the scan. From these data, different middle ear structures were segmented using Amira (Visage Imaging) to create a surface model of the middle ear which is needed to create a realistic numerical model.
Within the surface model, as depicted on Fig. 2, five different structures could be distinguished: the tympanic membrane, Platner’s ligament, the cartilaginous extracolumella and the bony columella with the footplate bounded by an annular ligament. Other ligaments mentioned in literature were not observed and therefore not considered in the geometry. The final geometrical surface model, consisting of 15000 triangle-shaped faces after decimation and smoothing of the surface, was exported as an STL-file that could be imported in finite element software (COMSOL Multiphysics 4.3b, The Structural Mechanics Module) in order to create a mechanical model.
Figure 1middle ear of a mallard duck, reconstructed from
measurements. The different components and
Finite element studies of the human middle
ear have indicated that a viscoelasticcharacterization of the soft tissue structures is necessaryTherefore, we chose to introduce a complex elastic modulus with an isotropic loss factor. Since there are no literature values available for the elastic parahuman and other viscoelastic material parameters were used as initial values instead. As explained in the next section, some of these parameters will be optimized using the experimental data. In table all components were chosen i
Table 1:
finite element modelPoisson's ratios Young
[7]; b
[10
Component
TM ColumellaExtracol.Platner’s lig.Annular lig.
Excerpt from the Proceedings of the 2014 COMSOL Conference in Cambridge
Figure 1. Geometrical surfamiddle ear of a mallard duck, reconstructed from
measurements. The different components and anatomical orientations are indicated
Finite element studies of the human middle ear have indicated that a viscoelasticcharacterization of the soft tissue structures is necessary to predict the observed behavior [6Therefore, we chose to introduce a complex elastic modulus with an isotropic loss factor. Since there are no literature values available for the elastic parameters of the avian middle ear, human and other viscoelastic material parameters were used as initial values instead. As explained in the next section, some of these parameters will be optimized using the experimental data. In table 1 starting values for dall components are listedwere chosen isotropic.
Table 1: Starting finite element model
Poisson's ratios ν are taken from [7Young's modulus E
Excerpt from the Proceedings of the 2014 COMSOL Conference in Cambridge
eometrical surface model of themiddle ear of a mallard duck, reconstructed from
measurements. The different components and anatomical orientations are indicated
Finite element studies of the human middle ear have indicated that a viscoelasticcharacterization of the soft tissue structures is
predict the observed behavior [6Therefore, we chose to introduce a complex elastic modulus with an isotropic loss factor. Since there are no literature values available for
meters of the avian middle ear, human and other viscoelastic material parameters were used as initial values instead. As explained in the next section, some of these parameters will be optimized using the experimental data. In
values for different parameters of are listed. Initially, all
sotropic.
material parameters finite element model. All mass densities
are taken from [7E indicated with ]; c taken from [9
. All loss factors ηs come from [6], except for coming from [10].
ρ kg/m³]
E [MPa]
1.2E3 20a
2.2E3 14101.2E3 39.2b
1.2E3 21c 1.2E3 0.0412
Excerpt from the Proceedings of the 2014 COMSOL Conference in Cambridge
ce model of the leftmiddle ear of a mallard duck, reconstructed from
measurements. The different components and anatomical orientations are indicated [5].
Finite element studies of the human middle ear have indicated that a viscoelasticcharacterization of the soft tissue structures is
predict the observed behavior [6Therefore, we chose to introduce a complex elastic modulus with an isotropic loss factor. Since there are no literature values available for
meters of the avian middle ear, human and other viscoelastic material parameters were used as initial values instead. As explained in the next section, some of these parameters will be optimized using the experimental data. In
ifferent parameters of Initially, all parameters
material parameters used in the. All mass densities ρ and
are taken from [7]. Values for the indicated with a are taken from taken from [9] and d taken from
come from [6], except for ].
[MPa] ηs
0.078 1410a 0d
b 0.078 0.078
0.0412a 0.078
Excerpt from the Proceedings of the 2014 COMSOL Conference in Cambridge
left CT
measurements. The different components and
Finite element studies of the human middle ear have indicated that a viscoelastic characterization of the soft tissue structures is
predict the observed behavior [6]. Therefore, we chose to introduce a complex elastic modulus with an isotropic loss factor. Since there are no literature values available for
meters of the avian middle ear, human and other viscoelastic material parameters were used as initial values instead. As explained in the next section, some of these parameters will be optimized using the experimental data. In
ifferent parameters of parameters
sed in the and
]. Values for the taken from
taken from come from [6], except for d
ν
0.3 0.3 0.3 0.3 0.3
types of mesh elements: 2D triangleelements for the tympanic membrane, which are appropriate for thin structures, and 3D tetrahedral solid elements for the remaining middle ear componentsBecause shell elements are only twodimensional, one needs a procedure to account for the finite and variable thickness of tympanic membrane. This was realized by defining a function on the eardrum elements that interpolates the thickness distribution obtained from the original image segmentatishown on Fig.mathematical framework still account for typical threeproperties like bending stiffness and inertia.
and solid elements for the remaining
Excerpt from the Proceedings of the 2014 COMSOL Conference in Cambridge
The finite element model was built up by two types of mesh elements: 2D triangleelements for the tympanic membrane, which are appropriate for thin structures, and 3D tetrahedral solid elements for the remaining middle ear componentsBecause shell elements are only twodimensional, one needs a procedure to account for the finite and variable thickness of tympanic membrane. This was realized by defining a function on the eardrum elements that interpolates the thickness distribution obtained from the original image segmentatishown on Fig.mathematical framework still account for typical threeproperties like bending stiffness and inertia.
Figure 2. Applied mesh inShell elements are used for the tympanic membrane
and solid elements for the remainingcolor
Figure 3. Interpolation function containing the thickness distribution of the tympanic membrane
which is defined on the according shell elements
Excerpt from the Proceedings of the 2014 COMSOL Conference in Cambridge
The finite element model was built up by two types of mesh elements: 2D triangleelements for the tympanic membrane, which are appropriate for thin structures, and 3D tetrahedral solid elements for the remaining middle ear components, as depicted in Fig. 2Because shell elements are only twodimensional, one needs a procedure to account for the finite and variable thickness of tympanic membrane. This was realized by defining a function on the eardrum elements that interpolates the thickness distribution obtained from the original image segmentatishown on Fig. 3. Despite the twomathematical framework of shell elements, they still account for typical threeproperties like bending stiffness and inertia.
Applied mesh in the finite element model. Shell elements are used for the tympanic membrane
and solid elements for the remainingcolors represent element quality.
Interpolation function containing the thickness distribution of the tympanic membrane
which is defined on the according shell elementsFig. 2 [5]
Excerpt from the Proceedings of the 2014 COMSOL Conference in Cambridge
The finite element model was built up by two types of mesh elements: 2D triangle-shaped shell elements for the tympanic membrane, which are appropriate for thin structures, and 3D tetrahedral solid elements for the remaining
, as depicted in Fig. 2Because shell elements are only twodimensional, one needs a procedure to account for the finite and variable thickness of tympanic membrane. This was realized by defining a function on the eardrum elements that interpolates the thickness distribution obtained from the original image segmentation data, as
. Despite the two-dimensional of shell elements, they
still account for typical three-dimensional properties like bending stiffness and inertia.
the finite element model. Shell elements are used for the tympanic membrane
and solid elements for the remaining components. The element quality.
Interpolation function containing the thickness distribution of the tympanic membrane
which is defined on the according shell elements[5].
The finite element model was built up by two shaped shell
elements for the tympanic membrane, which are appropriate for thin structures, and 3D tetrahedral solid elements for the remaining
, as depicted in Fig. 2. Because shell elements are only two-dimensional, one needs a procedure to account for the finite and variable thickness of the tympanic membrane. This was realized by defining a function on the eardrum elements that interpolates the thickness distribution obtained
on data, as dimensional
of shell elements, they dimensional
properties like bending stiffness and inertia.
the finite element model.
Shell elements are used for the tympanic membrane components. The
Interpolation function containing the
thickness distribution of the tympanic membrane, which is defined on the according shell elements in
Excerpt from the Proceedings of the 2014 COMSOL Conference in Cambridge
To model the incident acoustic waves at the tympanic membrane, a uniform harmonic load of 1 Pa was applied at the outer (i.e. lateral) surface of the eardrum. To account for the reflection of sound energy at the tympanic membrane, an empirically measured and frequency dependent power utilization ratio [11] was defined at the eardrum, so that only a part of the acoustic waves is actually transmitted to the middle ear. The presence of the cochlea in the inner ear behind the columella footplate was simulated by a viscoelastic spring foundation that was introduced at the footplate to account for the impedance caused by the cochlear fluid [12].
The tympanic membrane was fully constrained at the edge, as well as the annular ligament and the end of Platner’s ligament. To determine the linear response from the middle ear to harmonic loads, the computations were performed in the frequency domain. From these calculations the resulting displacement magnitude and phase over the entire eardrum were deduced.
To validate the finite element model, the vibrating motion of the mallard middle ear was measured under acoustic stimulation, using both stroboscopic digital holography and laser Doppler vibrometry as experimental tools. These optical techniques allow us to measure the full-field displacement and the single-point velocity amplitude of an object's surface respectively. More detail on these techniques can be found in previous work [5, 13]. 2.2 Inverse Analysis
As mentioned before, there are no avian middle ear properties available in literature. Therefore, the mechanical parameters of the middle ear components were validated by performing an inverse analysis routine in which the finite element model is compared with the experimental results. In this procedure the aim is to optimize the model in a certain way so that it approximates the experiment as well as possible. Therefore, an intelligently defined objective function is to be minimized. The objective function that was minimized using the holography measurements is defined as
��(�) =� ������(��, �) − ����(��)��
�
+ �����(��, �) − ����(��)��
� . (1)
In this equation the summation index i runs over the number of evaluated points on the eardrum surface. The ri represent the spatial coordinates on the eardrum and p is the set of model parameters to be optimized. M represents the magnitude normalized to 1 and ϕ the vibration phase in cycles (between 0 and 1). The subscripts ‘mod’ and ‘exp’ denote model and experimental results, respectively. Magnitude maps were normalized to their respective maximal magnitude to prevent erroneously large values for the objective function.
Using the LDV measurements as input for the inverse analysis instead, the objective function can be defined as
��(�) =� �����(��, �)−����(��)��
�. (2)
In this equation V represents the velocity magnitude at the center of the columella. The summation no longer runs over the space coordinates ri, but over the applied stimulus frequencies ωi.
The technique that is employed to perform the optimization is called surrogate modeling, for which we used the MATLAB Surrogate Modeling (SUMO) Toolbox, developed by INTEC, UGhent [14]. To operate COMSOL and SUMO simultaneously, we made use of the COMSOL LiveLink for MATLAB. The surrogate modeling technique creates a model of a certain system for which we only know the input and output. The software achieves this by first choosing a set of initial input samples, based on a so called Latin Hypercube Design, and calculating the according output. It then builds a model through the resulting evaluated samples by use of the Kriging Modeling technique. From the obtained model the software chooses new samples to evaluate in order to improve the current surrogate model. The way these new samples are chosen is done by the Local Linear Adaptive Sampling Algorithm (LOLA), which identifies nonlinear regions in the current surrogate model to evaluate them more densely. A second routine, called the Dividing Rectangles Algorithm, determines the current minima of the model and evaluates them. This procedure is repeated until a certain tolerance is reached or when a maximum number of samples have been evaluated. The complete workflow is summarized on Fig. 4.
The parameters that are to be optimized still have to be chosen. This is done by the
application of the change changing theparameventually be optimized.results, tand therefore also the resulting optimization, will be computed for the different applied sound frequencies separately, since viscoelastic parameters are known to be frequency dependent.
Figure 4.routine for a certain system with input and output.
Taken from the SUMO Toolbox Tutorial, Ivo
3. Results 3.1 Experimental Results
In order to interpret the results from digital holography, to the timeare obtained from the experiments. From this analysis, vibration magnitude and phase relative to the sound signal at the TM are calculated for each object point. The results are presenteFig. 5 as magnitude and phase maps for stimulus frequencies.
Figmeasurements on the cfootplate. The figure presents footplate velocity magnitudesoundfrequencies. The two distinct resonance peaks of roughly the same height are remarkable, as mammaltypically feature only one high resonance peak and multiple subsequent smaller peaksfrequencies.
Excerpt from the Proceedings of the 2014 COMSOL Conference in Cambridge
application of manual sensitivity tests, in which the change in mochanging the inputparameters that influenceeventually be optimized.results, the total objectand therefore also the resulting optimization, will be computed for the different applied sound frequencies separately, since viscoelastic parameters are known to be frequency dependent.
Figure 4. The workflow of a surrogroutine for a certain system with input and output.
Taken from the SUMO Toolbox Tutorial, Ivo Couckuyt, INTEC UGhent
Results
3.1 Experimental Results
In order to interpret the results from digital holography, a temporalto the time-dependent are obtained from the experiments. From this analysis, vibration magnitude and phase relative to the sound signal at the TM are calculated for each object point. The results are presente
5 as magnitude and phase maps for stimulus frequencies.
Fig. 6 shows the result from LDV measurements on the cfootplate. The figure presents footplate velocity magnitude as a function of input frequency. The sound pressure was kept at 90 dB frequencies. The two distinct resonance peaks of roughly the same height are remarkable, as mammalian middle ear transfer functions typically feature only one high resonance peak and multiple subsequent smaller peaksfrequencies.
Excerpt from the Proceedings of the 2014 COMSOL Conference in Cambridge
manual sensitivity tests, in which model output is evaluatinput parameterinfluence the output
eventually be optimized. For the holography objective function
and therefore also the resulting optimization, will be computed for the different applied sound frequencies separately, since viscoelastic parameters are known to be frequency
he workflow of a surrogroutine for a certain system with input and output.
Taken from the SUMO Toolbox Tutorial, Ivo Couckuyt, INTEC UGhent
3.1 Experimental Results
In order to interpret the results from digital a temporal FFT-analysis is applied dependent displacement maps that
are obtained from the experiments. From this analysis, vibration magnitude and phase relative to the sound signal at the TM are calculated for each object point. The results are presente
5 as magnitude and phase maps for stimulus frequencies.
6 shows the result from LDV measurements on the center of the cfootplate. The figure presents footplate velocity
as a function of input frequency. The pressure was kept at 90 dB
frequencies. The two distinct resonance peaks of roughly the same height are remarkable, as
middle ear transfer functions typically feature only one high resonance peak and multiple subsequent smaller peaks
Excerpt from the Proceedings of the 2014 COMSOL Conference in Cambridge
manual sensitivity tests, in which del output is evaluated after
parameter values. The the output most, will For the holography function of Eq.
and therefore also the resulting optimization, will be computed for the different applied sound frequencies separately, since viscoelastic parameters are known to be frequency
he workflow of a surrogate modeling routine for a certain system with input and output.
Taken from the SUMO Toolbox Tutorial, Ivo Couckuyt, INTEC UGhent [14].
In order to interpret the results from digital analysis is applied
displacement maps that are obtained from the experiments. From this analysis, vibration magnitude and phase relative to the sound signal at the TM are calculated for each object point. The results are presented in
5 as magnitude and phase maps for different
6 shows the result from LDV enter of the columella
footplate. The figure presents footplate velocity as a function of input frequency. The
pressure was kept at 90 dB SPL for all frequencies. The two distinct resonance peaks of roughly the same height are remarkable, as
middle ear transfer functions typically feature only one high resonance peak and multiple subsequent smaller peaks at higher
Excerpt from the Proceedings of the 2014 COMSOL Conference in Cambridge
manual sensitivity tests, in which ed after
The will
For the holography (1),
and therefore also the resulting optimization, will be computed for the different applied sound frequencies separately, since viscoelastic parameters are known to be frequency
ate modeling
routine for a certain system with input and output. Taken from the SUMO Toolbox Tutorial, Ivo
In order to interpret the results from digital analysis is applied
displacement maps that are obtained from the experiments. From this analysis, vibration magnitude and phase relative to the sound signal at the TM are calculated for
d in different
6 shows the result from LDV olumella
footplate. The figure presents footplate velocity as a function of input frequency. The
for all frequencies. The two distinct resonance peaks of roughly the same height are remarkable, as
middle ear transfer functions typically feature only one high resonance peak
at higher
Figure 5.
Figure 6
sound pressure
3.2
analysis on the the holography and LDV allon the experimentparameters incorporated in this procedure were chosen to be theand the extracolumella, as a sensitivity tests
Excerpt from the Proceedings of the 2014 COMSOL Conference in Cambridge
Figure 5. Displacement magnitude and phase maps of the duck eardrum, extracted from digital holography
data at different frequencies.
Figure 6. Velocity of the center point of the columella footplate, derived from LDV measure
sound pressure for all frequencies was
3.2 Model Results
This section contains results of the inverse analysis on the the holography and LDV all, a surrogate modeling routine was carried out on the objectiveexperiment, as defined byparameters incorporated in this procedure were chosen to be theand the extracolumella, as a sensitivity tests
Excerpt from the Proceedings of the 2014 COMSOL Conference in Cambridge
Displacement magnitude and phase maps of the duck eardrum, extracted from digital holography
data at different frequencies.
Velocity of the center point of the columella footplate, derived from LDV measure
for all frequencies was
Model Results
This section contains results of the inverse analysis on the finite element model, based on the holography and LDV measurements
surrogate modeling routine was carried out ive function between model and
as defined by parameters incorporated in this procedure were chosen to be the Young’s moduli of the eardand the extracolumella, as a sensitivity tests. The calculations were executed
Excerpt from the Proceedings of the 2014 COMSOL Conference in Cambridge
Displacement magnitude and phase maps of the duck eardrum, extracted from digital holography
data at different frequencies.
Velocity of the center point of the columella footplate, derived from LDV measurements.
for all frequencies was 90 dB SPL
This section contains results of the inverse ite element model, based on
measurements. surrogate modeling routine was carried out
function between model and Eq. (1). The input
parameters incorporated in this procedure were Young’s moduli of the eard
and the extracolumella, as a result of the . The calculations were executed
Displacement magnitude and phase maps of
the duck eardrum, extracted from digital holography
Velocity of the center point of the columella
ments. The 90 dB SPL [5].
This section contains results of the inverse ite element model, based on
. First of surrogate modeling routine was carried out
function between model and . The input
parameters incorporated in this procedure were Young’s moduli of the eardrum
result of the . The calculations were executed
for the different applied sound frequencies separately, and results are shown for frequency
Figure 7the tympani(EC) at obtained by a surrogate modeling routine built with 64
samples. function
Figure 8the tympanic membrane, compared for the results of
the holography measurements andelement model. The optimized model parameters were
chosen to be [Hz. Notice that the inverse analysis was obtained only by considering the
in contrast to the absolute displacements
The plots of the
that the eardrum Young’s modulusbigger influence on the the modulusnot unexpected as we considered the eardrum displacements in our analysis. The optimal output values of the model lie on a curve inside a
Excerpt from the Proceedings of the 2014 COMSOL Conference in Cambridge
for the different applied sound frequencies separately, and results are shown for frequency of 1600 Hz in Fig. 7.
Figure 7. Inverse analysis on the Young's moduli of the tympanic membrane (TM) and the extracolumella (EC) at the sound frequencyobtained by a surrogate modeling routine built with 64
samples. Colors on the plot represent function between model and experiment
Figure 8. The displacement the tympanic membrane, compared for the results of
the holography measurements andelement model. The optimized model parameters were
chosen to be [ETM, Hz. Notice that the inverse analysis was obtained only by considering the normalized
in contrast to the absolute displacements
The plots of the at the eardrum Young’s modulus
bigger influence on the the modulus of the extracolumella not unexpected as we considered the eardrum displacements in our analysis. The optimal output values of the model lie on a curve inside a
Excerpt from the Proceedings of the 2014 COMSOL Conference in Cambridge
for the different applied sound frequencies separately, and results are shown for
of 1600 Hz in Fig. 7.
Inverse analysis on the Young's moduli of c membrane (TM) and the extracolumella
the sound frequency of 1600 Hz. The result is obtained by a surrogate modeling routine built with 64
Colors on the plot represent between model and experiment
Eq. (1) [5].
The displacement amplitudethe tympanic membrane, compared for the results of
the holography measurements and theelement model. The optimized model parameters were
, EEC] = [40.3, 39.6] Hz. Notice that the inverse analysis was obtained only
normalized displacement patterns, in contrast to the absolute displacements
The plots of the objective function make clear at the eardrum Young’s modulus
bigger influence on the objectiveof the extracolumella
not unexpected as we considered the eardrum displacements in our analysis. The optimal output values of the model lie on a curve inside a
Excerpt from the Proceedings of the 2014 COMSOL Conference in Cambridge
for the different applied sound frequencies separately, and results are shown for the example
Inverse analysis on the Young's moduli of c membrane (TM) and the extracolumella
of 1600 Hz. The result is obtained by a surrogate modeling routine built with 64
Colors on the plot represent the objective between model and experiment as defined by
amplitude and phase of the tympanic membrane, compared for the results of
the optimized finite element model. The optimized model parameters were
] = [40.3, 39.6] MPa at 1600 Hz. Notice that the inverse analysis was obtained only
displacement patterns, in contrast to the absolute displacements [5].
function make clear at the eardrum Young’s modulus ETM has
ive function than of the extracolumella EEC, which is
not unexpected as we considered the eardrum displacements in our analysis. The optimal output values of the model lie on a curve inside a
Excerpt from the Proceedings of the 2014 COMSOL Conference in Cambridge
for the different applied sound frequencies the example
Inverse analysis on the Young's moduli of c membrane (TM) and the extracolumella
of 1600 Hz. The result is obtained by a surrogate modeling routine built with 64
objective as defined by
and phase of
the tympanic membrane, compared for the results of optimized finite
element model. The optimized model parameters were MPa at 1600
Hz. Notice that the inverse analysis was obtained only displacement patterns,
function make clear has a
function than , which is
not unexpected as we considered the eardrum displacements in our analysis. The optimal output values of the model lie on a curve inside a
finite region of thecurve a fit was carried out using a second order polynomial with two parameters minimizing the line integral along the curve. The equation describing this polynomial is The optimal values fo[cfrequencyvalue alonEthe displacement tympanic membrane are compared for the holography measurements and the optimized finite el
performed using the LDV results as input, in which the objective function is defined by Eq. (2). The input parameters are chosen to be the Young's moduli of the tympanic membrane and the annular ligament surrogate model is shown in Fig. 9.
ligament
modeling ro
identify a minithe parameter values MPaLDV measurements and the optimized finite element model.the footplate since tmeasurementsprocedure
Excerpt from the Proceedings of the 2014 COMSOL Conference in Cambridge
finite region of thecurve a fit was carried out using a second order polynomial with two parameters minimizing the line integral along the curve. The equation describing this polynomial is �The optimal values foc1, c2] = [5.
frequency. The minimum objectvalue along the fitted line was found atEEC] = [40.3, 39.6] MPa for 1600 Hz. In the displacement tympanic membrane are compared for the holography measurements and the optimized finite element model.
In addition, an inverse analysis was performed using the LDV results as input, in which the objective function is defined by Eq. (2). The input parameters are chosen to be the Young's moduli of the tympanic membrane and the annular ligament surrogate model is shown in Fig. 9.
Figure 9. Inverse analysis on the Young's moduli of the tympanic memb
ligament (AL), using 10 of the 66 stimulus frequencies as input. The result is obtained by a surrogat
modeling routine built with 48plot represent the
and experiment
In the obtained
identify a minithe parameter values MPa. Fig. 10 shows a comparison between the LDV measurements and the optimized finite element model.the footplate since the cochlea had to be removed formeasurements procedure.
Excerpt from the Proceedings of the 2014 COMSOL Conference in Cambridge
finite region of the input domain. To find this curve a fit was carried out using a second order polynomial with two parameters minimizing the line integral along the curve. The equation describing this polynomial is
��� = ��(���The optimal values for the two parameters are
] = [5.92E-7, 4.85. The minimum objectg the fitted line was found at
] = [40.3, 39.6] MPa for 1600 Hz. In the displacement magnitudetympanic membrane are compared for the holography measurements and the optimized
ement model. In addition, an inverse analysis was
performed using the LDV results as input, in which the objective function is defined by Eq. (2). The input parameters are chosen to be the Young's moduli of the tympanic membrane and the annular ligament surrogate model is shown in Fig. 9.
Inverse analysis on the Young's moduli of the tympanic membrane (TM) and the annular
using 10 of the 66 stimulus frequencies . The result is obtained by a surrogatutine built with 48
the objective function and experiment as defined by Eq. (2).
the obtained surrogaidentify a minimum, which is characterized by the parameter values [ETM,
Fig. 10 shows a comparison between the LDV measurements and the optimized finite element model. Notice that the cochlear load the footplate was disabled in this calculation,
he cochlea had to be removed for that served as input for this
Excerpt from the Proceedings of the 2014 COMSOL Conference in Cambridge
input domain. To find this curve a fit was carried out using a second order polynomial with two parameters c1 and minimizing the line integral along the curve. The equation describing this polynomial is
( − ��)�.
r the two parameters are 85E7] at the chosen
. The minimum objective function g the fitted line was found at
] = [40.3, 39.6] MPa for 1600 Hz. In magnitude and phase of the
tympanic membrane are compared for the holography measurements and the optimized
In addition, an inverse analysis was performed using the LDV results as input, in which the objective function is defined by Eq. (2). The input parameters are chosen to be the Young's moduli of the tympanic membrane and the annular ligament EAL. The resurrogate model is shown in Fig. 9.
Inverse analysis on the Young's moduli of rane (TM) and the annular
using 10 of the 66 stimulus frequencies . The result is obtained by a surrogat
samples. Colors on the objective function between model
as defined by Eq. (2).
surrogate model we can mum, which is characterized by
, EAL] = [64.5, 0.156Fig. 10 shows a comparison between the
LDV measurements and the optimized finite Notice that the cochlear load
was disabled in this calculation, he cochlea had to be removed for the LDV
that served as input for this
input domain. To find this curve a fit was carried out using a second order
and c2 by minimizing the line integral along the curve. The
(3) r the two parameters are
the chosen function
g the fitted line was found at [ETM, ] = [40.3, 39.6] MPa for 1600 Hz. In Fig. 8
and phase of the tympanic membrane are compared for the holography measurements and the optimized
In addition, an inverse analysis was performed using the LDV results as input, in which the objective function is defined by Eq. (2). The input parameters are chosen to be the Young's moduli of the tympanic membrane ETM
. The resulting
Inverse analysis on the Young's moduli of
rane (TM) and the annular using 10 of the 66 stimulus frequencies
. The result is obtained by a surrogate Colors on the
between model
te model we can mum, which is characterized by
64.5, 0.156] Fig. 10 shows a comparison between the
LDV measurements and the optimized finite Notice that the cochlear load at
was disabled in this calculation, the LDV
that served as input for this
Figure 10columella footplate,
LDVmodel. The optimized model parameters were chosen to beinverse analysis was obtained by only considering the
4. Discussion and C
In order to investigate the mechanics of complex biomechanical systems such as the avian multidisciplinary approach is necessary. Therefore, a combination of optical experiments and computerized finite element modeling has been used in this workenhanced highfinite element model of the duck middle ear was constructed. Using the experimental holography and LDV were optimized by minimizingfunction between experimental and model outcome. parameters that were chosen to be optimized are the Young’s moduli of the TM and the extracolumella. The objectfound to be minimal for parameter values ofMPa (TMThese were found through an inversroutine, based on the MATLAB Surrogate Modeling (SUMO) Toolbox (INTEC, UGhent), as explained in detail.
The same procedure wasusing the LDV with thetympanic membrainput parametersnow values of 64.5 MPa (TM) and 0.156 MPa (AL).
This work is the first step in the determination of the mechanical properties of the avian mid
Excerpt from the Proceedings of the 2014 COMSOL Conference in Cambridge
Figure 10. The velocitycolumella footplate,
LDV measurements andmodel. The optimized model parameters were chosen to be [ETM, EAL] = [inverse analysis was obtained by only considering the
10 highlighted frequencies.
Discussion and C
In order to investigate the mechanics of complex biomechanical systems such as the avian middle ear, we believe that a multidisciplinary approach is necessary. Therefore, a combination of optical experiments and computerized finite element modeling has been used in this workenhanced high-resolution
e element model of the duck middle ear was constructed. Using the experimental holography and LDV data, diffewere optimized by minimizingfunction between experimental and model outcome. Using the holography resultsparameters that were chosen to be optimized are the Young’s moduli of the TM and the extracolumella. The objectfound to be minimal for parameter values ofMPa (TM) and 39.6 MPa (EC) at 1600 Hz. These were found through an inversroutine, based on the MATLAB Surrogate Modeling (SUMO) Toolbox (INTEC, UGhent), as explained in detail.
The same procedure wasusing the LDV resultswith the isotropictympanic membrane and the annular ligameinput parameters. The objective function was now found to bevalues of 64.5 MPa (TM) and 0.156 MPa (AL).
This work is the first step in the determination of the mechanical properties of the avian middle ear. Nevertheless there are several
Excerpt from the Proceedings of the 2014 COMSOL Conference in Cambridge
velocity magnitude at the center of the columella footplate, compared for the results of the
measurements and the optimized finite element model. The optimized model parameters were chosen
] = [64.5, 0.156] MPainverse analysis was obtained by only considering the
10 highlighted frequencies.
Discussion and Conclusions
In order to investigate the mechanics of complex biomechanical systems such as the
middle ear, we believe that a multidisciplinary approach is necessary. Therefore, a combination of optical experiments and computerized finite element modeling has been used in this work. Based on contrast
resolution CT measurements, a e element model of the duck middle ear was
constructed. Using the experimental holography data, different influential parameters
were optimized by minimizingfunction between experimental and model
Using the holography resultsparameters that were chosen to be optimized are the Young’s moduli of the TM and the extracolumella. The objectivefound to be minimal for parameter values of
) and 39.6 MPa (EC) at 1600 Hz. These were found through an inversroutine, based on the MATLAB Surrogate Modeling (SUMO) Toolbox (INTEC, UGhent), as explained in detail.
The same procedure was results as experimental
isotropic Young's moduli of the ne and the annular ligame
. The objective function was o be minimal for the parameter
values of 64.5 MPa (TM) and 0.156 MPa (AL).This work is the first step in the
determination of the mechanical properties of the dle ear. Nevertheless there are several
Excerpt from the Proceedings of the 2014 COMSOL Conference in Cambridge
magnitude at the center of the compared for the results of the
optimized finite element model. The optimized model parameters were chosen
0.156] MPa. Notice that the inverse analysis was obtained by only considering the
10 highlighted frequencies.
onclusions
In order to investigate the mechanics of complex biomechanical systems such as the
middle ear, we believe that a multidisciplinary approach is necessary. Therefore, a combination of optical experiments and computerized finite element modeling has
Based on contrastCT measurements, a
e element model of the duck middle ear was constructed. Using the experimental holography
rent influential parameters were optimized by minimizing an objectfunction between experimental and model
Using the holography results, tparameters that were chosen to be optimized are the Young’s moduli of the TM and the
ive function was found to be minimal for parameter values of 40.3
) and 39.6 MPa (EC) at 1600 Hz. These were found through an inverse analysis routine, based on the MATLAB Surrogate Modeling (SUMO) Toolbox (INTEC, UGhent),
also carried out experimental input,
Young's moduli of the ne and the annular ligament as
. The objective function was minimal for the parameter
values of 64.5 MPa (TM) and 0.156 MPa (AL).This work is the first step in the
determination of the mechanical properties of the dle ear. Nevertheless there are several
Excerpt from the Proceedings of the 2014 COMSOL Conference in Cambridge
magnitude at the center of the
compared for the results of the optimized finite element
model. The optimized model parameters were chosen that the
inverse analysis was obtained by only considering the
In order to investigate the mechanics of complex biomechanical systems such as the
middle ear, we believe that a multidisciplinary approach is necessary. Therefore, a combination of optical experiments and computerized finite element modeling has
Based on contrast-CT measurements, a
e element model of the duck middle ear was constructed. Using the experimental holography
rent influential parameters an objective
function between experimental and model , the
parameters that were chosen to be optimized are the Young’s moduli of the TM and the
ion was 40.3
) and 39.6 MPa (EC) at 1600 Hz. e analysis
routine, based on the MATLAB Surrogate Modeling (SUMO) Toolbox (INTEC, UGhent),
carried out input,
Young's moduli of the nt as
. The objective function was minimal for the parameter
values of 64.5 MPa (TM) and 0.156 MPa (AL). This work is the first step in the
determination of the mechanical properties of the dle ear. Nevertheless there are several
possible improvementsthe acoustic stimulation of the middle ear could be modeled by acousticof applying a uniform harmonic load at the eardrum surface. Furthermorinfluenceparameters sensitivity and uncertainty analyses. anisotropic, frequency dependent properties minto account invalidatedexperiments.
5 1. of wind tMaryland2. B. Moore, PIssues(2007)3. I. Arechvo et al., The ostrich middle ear for developing an ideal ossicular replacement prosthesis, (1)4quantifiUGCT, 5805validation tools for finite element modeling of biomechanical ear research6the human tympanic membrane studied with stroboscopic holography and finite element modeling, 7.pressurization on middleconduction responses, (2010).8. G. Spahn et al., Biomechanical properties of hyaline cartilage under axial load, Chir.9. K. Homma et al., Ossicular resonance modes of the human middle ear for boneconduction, (2009).10. H. Cai et al., A biological gear in the human middle ear, Conference
Excerpt from the Proceedings of the 2014 COMSOL Conference in Cambridge
possible improvementsthe acoustic stimulation of the middle ear could be modeled by acousticof applying a uniform harmonic load at the eardrum surface. Furthermorinfluence and uncertainty of the different model parameters cansensitivity and uncertainty analyses. anisotropic, inhomogeneousfrequency dependent properties minto account invalidated by novelexperiments.
5. References 1. R. Dooling, of wind turbinesMaryland, Colorado2. B. Moore, Physiological, Psychological and Technical Issues. John Wiley & Sons Ltd.,(2007). 3. I. Arechvo et al., The ostrich middle ear for developing an ideal ossicular replacement prosthesis, Eur(1), 37 (2013).4. B.C. Masschaele et al.,quantification of XUGCT, Nucl. Instr580, 442 (2007).5. P. Muyshondt validation tools for finite element modeling of biomechanical ear research, AIP Proceedings6. D. De Greef et althe human tympanic membrane studied with stroboscopic holography and finite element modeling, Hear. Res.7. K. Homma et al., Effects of earpressurization on middleconduction responses, (2010). 8. G. Spahn et al., Biomechanical properties of hyaline cartilage under axial load, Chir., 128, 78 (2003).9. K. Homma et al., Ossicular resonance modes of the human middle ear for boneconduction, J. Acoust. Soc. Am.(2009). 10. H. Cai et al., A biological gear in the human middle ear, Conference, Boston (2010)
Excerpt from the Proceedings of the 2014 COMSOL Conference in Cambridge
possible improvements to bethe acoustic stimulation of the middle ear could be modeled by acoustic-shell interaction instead of applying a uniform harmonic load at the eardrum surface. Furthermor
and uncertainty of the different model can be mapp
sensitivity and uncertainty analyses. inhomogeneous
frequency dependent properties minto account in the numerical model, that can
by novel static and dynamic
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. Cochlear Hearing Loss:
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6. Acknowledgements
This work was financially supported by the Research Foundation Flanders (FWO) and the University of Antwerp.