I. BELI^ et al.: A STUDY OF THE SONIC RESONANCE OF THE FEMORAL PART OF HIP ENDOPROSTHESIS
15–18
A STUDY OF THE SONIC RESONANCE OF THE FEMORAL PART
OF HIP ENDOPROSTHESIS
[TUDIJA ZVO^NE RESONANCE STEGNENI^NEGA DELA
KOL^NE PROTEZE
Igor Beli~
1*
, Beno Klop~i~
2
, Andra` Logar
2
, Monika Jenko
1,3
, Drago Dolinar
4,3
,
Matev` Goren{ek
5,3
, Bo{tjan Kocjan~i~
4
1
Institute of Metals and Technology, Lepi pot 11, 1000 Ljubljana, Slovenia
2
BOSCH REXROTH d.o.o., Kidri~eva 81, 4220 [kofja Loka, Slovenia
3
MD-RI Institute for Materials Research in Medicine, Bohori~eva Street 5, 1000 Ljubljana, Slovenia
4
Department for Orthopaedic Surgeon, University Medical Centre Ljubljana, Zalo{ka 9, 1000 Ljubljana, Slovenia
5
MD-Medicina Ljubljana, Bohori~eva Street 5, 1000 Ljubljana, Slovenia
Prejem rokopisa – received: 2020-06-09; sprejem za objavo – accepted for publication: 2020-07-24
doi:10.17222/mit.2020.108
Mechanical resonance is the property of a mechanical system that responds to the oscillations coming from the outside of the
observed system. The response amplitude of the system is the highest when the frequency of the oscillations matches the sys-
tem’s natural frequency (its resonance frequency). It is known that resonance can cause swaying motions and even catastrophic
failure in improperly constructed structures. The phenomenon is known as resonance disaster. Sonic energy enters the system
through excitation and is dissipated through damping. Damping can be internal (within the material) or external (mounting of an
object). Six retrieved stems of hip endoprostheses were studied. For each of them sonograms were made, showing very distinc-
tive and narrow resonance curves with one major resonance peak followed by several higher harmonic peaks. Simulation of
endoprostheses standing waves was also performed resulting in the demonstration of various standing wave modes depending on
the observed frequency. Results clearly show that, due to the geometry and the used material, the observed endoprostheses have
very distinctive sonic resonance characteristics. The resonance is excited by the sound coming from outside (or inside) of the
human body. The energy of resonance movement of the endoprosthesis is dissipated through the endoprosthesis–bone interface.
A long-term exposure to the resonance oscillations might contribute to other causes of aseptic loosening of endoprostheses.
Keywords: femoral part of hip endoprosthesis, vibration analysis, resonance, aseptic loosening
Mehanska resonanca je lastnost sistema, ki se odziva na zvo~na nihanja, izvirajo~a iz zunanjosti opazovanega sistema.
Amplituda odziva sistema je najve~ja, ~e se frekvenca nihanj ujema z naravno frekvenco sistema (njegova resonan~na
frekvenca). Znano je, da lahko resonanca povzro~i zvijanje sistema ali celo poru{itev pri nepravilno na~rtovanih konstrukcijah.
Pojav je znan kot resonan~na katastrofa. Zvo~na energija vstopi v sistem z vzbujanjem in se disipira z du{enjem. Du{enje
nihanja je lahko notranje (znotraj sistema) ali zunanje (vpetje - namestitev sistema). [tudirali smo {est stegneni~nih delov
endoprotez kolka. Za vsakega od njih so bili narejeni sonogrami, ki prikazujejo zelo izrazite in ozke resonan~ne krivulje z enim
glavnim resonan~nim vrhom, ki mu sledi ve~ vi{je-harmonskih vrhov. Izvedena je bila tudi simulacija stoje~ih valov, ki so
pokazale razli~ne na~ine stojnega valovanja in sicer glede na opazovano frekvenco. Rezultati jasno ka`ejo, da imajo
endoproteze zaradi geometrije in uporabljenega materiala zelo izra`eno zvo~no resonanco. Resonanco vzbuja zvok, ki prihaja
od zunaj (ali znotraj) ~love{kega telesa. Energija resonan~nega gibanja endoproteze se disipira preko spoja endoproteza-kost.
Stalna izpostavljenost resonan~nim nihanjem {e dodatno prispeva k asepti~nemu omajanju endoprotez.
Klju~ne besede: stegneni~ni del proteze kolka, vibracijska analiza, resonanca, asepti~no popu{~anje
1 INTRODUCTION
1.1 Known causes for the aseptic loosening of endo-
prostheses
There are many reasons for aseptic loosening of
endoprostheses. There are also several theories about the
causes of aseptic loosening (i.e., osteolysis) resulting in
loosening of the implant.
1
Particle disease. The particle disease theory is cur-
rently the prevailing one. Endoprosthesis wear products
directly activate macrophages and osteoclasts, thus initi-
ating the bone resorption. The bone resorption enlarges
the interface volume between the bone and endo-
prosthesis, leading to higher joint fluid flows, providing
higher transportation capacity of the wear material. The
consequence of the process is the loosening of the im-
plant.
1,2
Cement. Possible problems with PMMA cement
(polymethylmethacrylate) are wear related. The first
problem is de-bonding, another one is cracking, which
produces debris in a joint region. Aging of the cement
causes it to become more brittle, and thus the possibility
of cracking becomes higher.
3
Polyethylene. UHMWPE (ultra-high-molecu-
lar-weight polyethylene) is the most common material
for an endoprosthesis bearing. It was found out that the
particles UHMWPE alone could cause bone resorption,
even in the absence of motion and infection.
1,4,5
Metal. Metal-to-metal implants exhibit less wear
than metal-to-UHMWPE implants. Titanium alloys have
Materiali in tehnologije / Materials and technology 55 (2021) 1, 15–18 15
UDK 616:534.321.8:615.477.2 ISSN 1580-2949
Original scientific article/Izvirni znanstveni ~lanek MTAEC9, 55(1)15(2021)
*Corresponding author's e-mail:
igor.belic@imt.si (Igor Beli~)

reduced the risk of debris production to a minimum.
Metal particles also cause grinding wear, producing more
and more wear particles. Metal particles are considered
to have the capacity to participate in the processes lead-
ing to aseptic loosening.
5
Ceramic. Even if the amounts of ceramic particles
are generally small, they are also being considered as
possible generators of aseptic loosening.
5,6
Micromotion. This is the phenomenon that describes
small movements between an implant and the surround-
ing bone. The actual registration of implant movement is
the consequence of many prior events that led to such a
situation. Micromotion is a consequence of a bad osseo-
integration or cement de-bonding. References reveal that
even a short daily micromotion period suffices to prevent
osseointegration.
1,7
Stress shielding. Stress shielding refers to the bone
structure’s adaption according to the load. Implant pro-
duces new loading conditions to the bone, which can
lead to bone loss around the implant. In such cases the
osteolysis is caused by the bone adaption to the newly
emerged load conditions.
8,9
High fluid pressure. Oscillating joint fluid pressure
might affect the interstitial osteoclasts and osteoblasts,
leading to bone loss, thus producing osteolysis.
10
Individual or genetic variations. There are individ-
ual genetic variations that lead to the very adverse cellu-
lar responses on such issues as particle disease, stress
shielding and high fluid pressure. Such variations are to
some extent responsible for implant-loosening pro-
cesses.
11,12
Sealed interface. Wear products can affect the inter-
faces around implants. Sealing off the interface is very
important for the longevity of the implant. Early micro-
motion affects the sealing of the interface.
1
Recent research of our group added further issues
that might contribute to the aseptic loosening of an im-
plant.
13
Remnants of the implant surface sand blasting.
Implants are sand blasted to provide better osseointeg-
ration. The implant surface thus becomes very rough.
The small sand particles remain on the rough surface and
are later added to other particles in the joint liquid.
Small cavitation on the surface. It was shown that
the sand-blasting process produces small cavitation on
the implant surface, which can hypothetically induce
many problems regarding the implant’s lifetime.
1.2 Mechanical resonance
There is another issue that might add up to the al-
ready-known causes of implant failures. The femoral
part of the hip endoprosthesis is quite a large piece of
metal. Unfortunately, it exhibits a very distinctive acous-
tic resonance very much comparable to a music fork. If
one strikes it with the metal rod, it clings with a very
clear and loud sound of several kHz. We have decided to
make a preliminary study of the mechanical resonance of
the femoral part of the hip implant.
14
Mechanical resonance is the property of a mechanical
system that responds to the oscillations coming from the
outside of the observed system. The response amplitude
of the system is the highest when the frequency of oscil-
lations matches the system’s natural frequency (its reso-
nance frequency).
The idealized model that tries to explain the behav-
iour of an ideal mechanical system is composed of ele-
ments such as mass, spring, damper and excitation. The
first three elements describe the physical system. Energy
is stored by the system in the mass and the spring in the
form of kinetic and potential energy. Energy enters the
system through excitation and is dissipated through
damping. Damping can be internal (within the material)
or external (mounting of an object).
15
Sonic energy enters the system through excitation
and is dissipated through damping.
15
In our case the mechanical system represents the
femoral part of the hip implant. Once inserted, the sonic
energy enters the implant through the human body, the
sonic energy is dissipated through the implant/bone in-
terface.
Modal analysis is a scientific field devoted to the
study of the dynamic characteristics of mechanical struc-
tures.
16
In this paper we would like to pay attention to the
phenomenon of acoustic resonance of the hip
endoprosthesis, which by our opinion, might have the
potential to contribute to other causes of aseptic loosen-
ing. The paper is not meant as in-depth study of the phe-
nomenon.
2 EXPERIMENTAL PART
Six retrieved stems
*
of hip endoprostheses were stud-
ied. For each of them sonograms were taken, using a
wide frequency range USB microphone connected to a
PC to capture the sound signal. The registered signals
were analysed with the Octave 4.2.1. software, by which
the Fourier transform of the sound signal was calculated,
transforming the time domain signal to the frequency do-
main. The acoustic signal transformed to the frequency
domain was then graphically presented in sonograms
(frequency/amplitude/time), again using Octave soft-
ware.
The next step was the simulation of the endo-
prostheses’ vibrational dynamics. The purpose of the re-
search was to establish the swaying motion of implants
that might contribute to loosening of the implant. Femo-
ral parts were 3D scanned and the vibrational properties
were studied with the Creo 4.0 software.
I. BELI^ et al.: A STUDY OF THE SONIC RESONANCE OF THE FEMORAL PART OF HIP ENDOPROSTHESIS
16 Materiali in tehnologije / Materials and technology 55 (2021) 1, 15–18
*Due to our previous research we were in possession of the re-
trieved stems. The study could have been carried out on a new
stems as well.

3 RESULTS AND DISCUSSION
3.1 Measurements of resonance
Sonograms show very distinctive and narrow reso-
nance curves with one major resonance peak (2323Hz)
followed by several higher harmonic peaks (Figures 1
and 2).
From Figures 1 and 2 it is clear that the main reso-
nance frequency at 2323 Hz remains active for a very
long time, while higher harmonic frequencies decay
faster. The resonance phenomenon happens because of
favourable conditions that are met by the given material
density and the geometrical shape of the femoral part.
Both conditions define the sonic oscillations at the reso-
nance frequency. Generally, there are two possibilities to
avoid the resonance. First, is the choice of material,
which because of the other properties that are required
for the implant, is very much limited. The density of the
material can be controlled though the porosity (some-
thing that can be compared to the bone structure) and can
nowadays be achieved using 3D-printed metals. Another
choice to avoid the resonance is the geometry of the im-
plant. Again, the shape of the implant does not give
much free space. The only reasonable solution seems to
be the 3D printed internally porous titanium alloy im-
plant with a non-porous surface. Such a structure does
not have a distinctive resonance frequency.
3.2 Simulation of the femoral part’s oscillation
To simulate the oscillation of the femoral part of the
hip endoprosthesis, samples were scanned by a 3D scan-
ner. The geometric structure was captured (Figure 3) and
the simulation of its oscillation was performed.
From Figures 4 and 5 it is clear that the standing
waves produce different oscillating amplitudes at differ-
ent places of a femoral hip endoprosthesis (red colour
represents high amplitude while the dark blue colour rep-
resents low amplitude). The problem that occurs is that
the resonance frequency produces high oscillation ampli-
tudes always at the same places on the endoprosthesis.
I. BELI^ et al.: A STUDY OF THE SONIC RESONANCE OF THE FEMORAL PART OF HIP ENDOPROSTHESIS
Materiali in tehnologije / Materials and technology 55 (2021) 1, 15–18 17
Figure 2: Frequency spectra of the oscillations of a femoral part.
Figure 1: Sonogram of a femoral part of hip endoprosthesis. The
sound was excited by striking the femoral part with a metal rod.
Figure 3: 3D scanned femoral part of a hip endoprosthesis.
Figure 5: Simulated standing waves of the oscillated femoral
endoprosthesis at 7170 Hz. The colour represents the relative ampli-
tude of the oscillation.
Figure 4: Simulated standing waves of the oscillated femoral
endoprosthesis at 2323 Hz. The colour represents the relative ampli-
tude of the oscillation.

Since the endoprosthesis is mounted in a bone tissue, the
same places in the bone are being constantly subjected to
grinding. The rough surface of the endoprosthesis, which
is purposefully being roughened in order to provide
better osseointegration, due to the vibration, effectively
grinds the bone. The problem with a resonant endo-
prosthesis is that it is constantly being subjected to the
sound that is originating in a human body or it is coming
from the outside. The resonator picks the sounds and os-
cillates at the resonance frequency.
Another problem that was revealed by the simulation
is that the endoprosthesis actually sways because of the
sonic resonance. The phenomenon is an extremely inter-
esting one and might additionally worsen the conditions
at the implant/bone interface.
The results clearly show that, due to the geometry
and the used material, the observed endoprostheses have
very distinctive sonic resonance characteristics. The res-
onance is excited by the sound coming from the outside
(or inside) of the human body, from body movements
(walking, etc.). The energy of the resonance movement
of the endoprosthesis is dissipated through the endo-
prosthesis–bone interface. A long-term exposure to the
resonance oscillations adds to other causes of aseptic
loosening of the endoprostheses.
4 CONCLUSIONS
Femoral parts of the hip endoprosthesis exhibit a very
distinctive and narrow sonic resonance with one major
resonance frequency followed by several higher harmon-
ics.
The results clearly show that, due to the geometry
and the used material, the observed endoprostheses have
very distinctive sonic resonance characteristics.
The resonance is excited by the sound coming from
outside (or inside) of the human body and from the
body’s movement.
The energy of the endoprosthesis resonance is dissi-
pated through the endoprosthesis–bone interface.
A long-term exposure to the resonance oscillations
might contribute to other causes of aseptic loosening of
endoprostheses.
The only reasonable solution to avoid resonance
seems to be a 3D-printed, internally porous, titanium-al-
loy implant with a non-porous surface. Such a structure
does not have a distinctive resonance frequency.
Acknowledgement
This work was supported by the Slovenian Research
Agency Programme group P2-0056.
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I. BELI^ et al.: A STUDY OF THE SONIC RESONANCE OF THE FEMORAL PART OF HIP ENDOPROSTHESIS
18 Materiali in tehnologije / Materials and technology 55 (2021) 1, 15–18