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<front>
<journal-meta>
<journal-id journal-id-type="publisher-id">Front. Bioeng. Biotechnol.</journal-id>
<journal-title>Frontiers in Bioengineering and Biotechnology</journal-title>
<abbrev-journal-title abbrev-type="pubmed">Front. Bioeng. Biotechnol.</abbrev-journal-title>
<issn pub-type="epub">2296-4185</issn>
<publisher>
<publisher-name>Frontiers Media S.A.</publisher-name>
</publisher>
</journal-meta>
<article-meta>
<article-id pub-id-type="publisher-id">837554</article-id>
<article-id pub-id-type="doi">10.3389/fbioe.2022.837554</article-id>
<article-categories>
<subj-group subj-group-type="heading">
<subject>Bioengineering and Biotechnology</subject>
<subj-group>
<subject>Original Research</subject>
</subj-group>
</subj-group>
</article-categories>
<title-group>
<article-title>Knee Joint Menisci Are Shock Absorbers: A Biomechanical <italic>In-Vitro</italic> Study on Porcine Stifle Joints</article-title>
<alt-title alt-title-type="left-running-head">Seitz et&#x20;al.</alt-title>
<alt-title alt-title-type="right-running-head">Knee Menisci are Shock Absorbers</alt-title>
</title-group>
<contrib-group>
<contrib contrib-type="author" corresp="yes">
<name>
<surname>Seitz</surname>
<given-names>Andreas M.</given-names>
</name>
<xref ref-type="corresp" rid="c001">&#x2a;</xref>
<uri xlink:href="https://loop.frontiersin.org/people/812982/overview"/>
</contrib>
<contrib contrib-type="author">
<name>
<surname>Schwer</surname>
<given-names>Jonas</given-names>
</name>
<uri xlink:href="https://loop.frontiersin.org/people/1026453/overview"/>
</contrib>
<contrib contrib-type="author">
<name>
<surname>de Roy</surname>
<given-names>Luisa</given-names>
</name>
<uri xlink:href="https://loop.frontiersin.org/people/1268695/overview"/>
</contrib>
<contrib contrib-type="author">
<name>
<surname>Warnecke</surname>
<given-names>Daniela</given-names>
</name>
<uri xlink:href="https://loop.frontiersin.org/people/568342/overview"/>
</contrib>
<contrib contrib-type="author">
<name>
<surname>Ignatius</surname>
<given-names>Anita</given-names>
</name>
<uri xlink:href="https://loop.frontiersin.org/people/605218/overview"/>
</contrib>
<contrib contrib-type="author">
<name>
<surname>D&#xfc;rselen</surname>
<given-names>Lutz</given-names>
</name>
<uri xlink:href="https://loop.frontiersin.org/people/183959/overview"/>
</contrib>
</contrib-group>
<aff>
<institution>Institute of Orthopedic Research and Biomechanics</institution>, <institution>Center of Trauma Research Ulm</institution>, <institution>Ulm University Medical Center</institution>, <addr-line>Ulm</addr-line>, <country>Germany</country>
</aff>
<author-notes>
<fn fn-type="edited-by">
<p>
<bold>Edited by:</bold> <ext-link ext-link-type="uri" xlink:href="https://loop.frontiersin.org/people/59484/overview">Tarun Goswami</ext-link>, Wright State University, United&#x20;States</p>
</fn>
<fn fn-type="edited-by">
<p>
<bold>Reviewed by:</bold> <ext-link ext-link-type="uri" xlink:href="https://loop.frontiersin.org/people/124492/overview">Rene Verdonk</ext-link>, Ghent University, Belgium</p>
<p>
<ext-link ext-link-type="uri" xlink:href="https://loop.frontiersin.org/people/1051324/overview">Matteo Berni</ext-link>, Rizzoli Orthopedic Institute (IRCCS), Italy</p>
</fn>
<corresp id="c001">&#x2a;Correspondence: Andreas M. Seitz, <email>andreas.seitz@uni-ulm.de</email>
</corresp>
<fn fn-type="other">
<p>This article was submitted to Biomechanics, a section of the journal Frontiers in Bioengineering and Biotechnology</p>
</fn>
</author-notes>
<pub-date pub-type="epub">
<day>17</day>
<month>03</month>
<year>2022</year>
</pub-date>
<pub-date pub-type="collection">
<year>2022</year>
</pub-date>
<volume>10</volume>
<elocation-id>837554</elocation-id>
<history>
<date date-type="received">
<day>16</day>
<month>12</month>
<year>2021</year>
</date>
<date date-type="accepted">
<day>14</day>
<month>02</month>
<year>2022</year>
</date>
</history>
<permissions>
<copyright-statement>Copyright &#xa9; 2022 Seitz, Schwer, de Roy, Warnecke, Ignatius and D&#xfc;rselen.</copyright-statement>
<copyright-year>2022</copyright-year>
<copyright-holder>Seitz, Schwer, de Roy, Warnecke, Ignatius and D&#xfc;rselen</copyright-holder>
<license xlink:href="http://creativecommons.org/licenses/by/4.0/">
<p>This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY). The use, distribution or reproduction in other forums is permitted, provided the original author(s) and the copyright owner(s) are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these&#x20;terms.</p>
</license>
</permissions>
<abstract>
<p>The aim of this biomechanical <italic>in&#x20;vitro</italic> study was to answer the question whether the meniscus acts as a shock absorber in the knee joint or not. The soft tissue of fourteen porcine knee joints was removed, leaving the capsuloligamentous structures intact. The joints were mounted in 45&#xb0; neutral knee flexion in a previously validated droptower setup. Six joints were exposed to an impact load of 3.54&#xa0;J, and the resultant loss factor (<italic>&#x3b7;</italic>) was calculated. Then, the setup was modified to allow sinusoidal loading under dynamic mechanical analysis (DMA) conditions. The remaining eight knee joints were exposed to 10 frequencies ranging from 0.1 to 5&#xa0;Hz at a static load of 1210&#xa0;N and a superimposed sinusoidal load of 910&#xa0;N (2.12&#x20;times body weight). Forces (F) and deformation (l) were continuously recorded, and the loss factor (tan &#x3b4;) was calculated. For both experiments, four meniscus states (intact, medial posterior root avulsion, medial meniscectomy, and total lateral and medial meniscectomy) were investigated. During the droptower experiments, the intact state indicated a loss factor of <italic>&#x3b7;</italic> &#x3d; 0.1. Except for the root avulsion state (&#x2212;15%, <italic>p</italic>&#x20;&#x3d; 0.12), the loss factor decreased (<italic>p</italic>&#x20;&#x3c; 0.046) up to 68% for the total meniscectomy state (<italic>p</italic>&#x20;&#x3d; 0.028) when compared to the intact state. Sinusoidal DMA testing revealed that knees with an intact meniscus had the highest loss factors, ranging from 0.10 to 0.15. Any surgical manipulation lowered the damping ability: Medial meniscectomy resulted in a reduction of 24%, while the resection of both menisci lowered tan &#x3b4; by 18% compared to the intact state. This biomechanical <italic>in&#x20;vitro</italic> study indicates that the shock-absorbing ability of a knee joint is lower when meniscal tissue is resected. In other words, the meniscus contributes to the shock absorption of the knee joint not only during impact loads, but also during sinusoidal loads. The findings may have an impact on the rehabilitation of young, meniscectomized patients who want to return to sports. Consequently, such patients are exposed to critical loads on the articular cartilage, especially when performing sports with recurring impact loads transmitted through the knee joint surfaces.</p>
</abstract>
<kwd-group>
<kwd>knee</kwd>
<kwd>joint</kwd>
<kwd>meniscus</kwd>
<kwd>shock absorber</kwd>
<kwd>shock</kwd>
<kwd>impact</kwd>
<kwd>dynamic mechanic analysis (DMA)</kwd>
<kwd>
<italic>in&#x20;vitro</italic>
</kwd>
</kwd-group>
</article-meta>
</front>
<body>
<sec sec-type="intro" id="s1">
<title>1 Introduction</title>
<p>Patients suffering from anterior cruciate ligament (ACL) injuries (<xref ref-type="bibr" rid="B21">Gillquist and Messner, 1999</xref>; <xref ref-type="bibr" rid="B31">Lohmander et&#x20;al., 2007</xref>; <xref ref-type="bibr" rid="B6">Bodkin et&#x20;al., 2020</xref>), meniscus tears (<xref ref-type="bibr" rid="B47">Roos et&#x20;al., 1998</xref>; <xref ref-type="bibr" rid="B46">Roos et&#x20;al., 1999</xref>; <xref ref-type="bibr" rid="B31">Lohmander et&#x20;al., 2007</xref>), or articular fractures of the knee (<xref ref-type="bibr" rid="B65">Weigel and Marsh, 2002</xref>; <xref ref-type="bibr" rid="B7">Buckwalter and Brown, 2004</xref>; <xref ref-type="bibr" rid="B8">Buckwalter et&#x20;al., 2004</xref>) are up to 20&#x20;times more likely to develop post-traumatic osteoarthritis (PTOA) (<xref ref-type="bibr" rid="B39">Muthuri et&#x20;al., 2011</xref>; <xref ref-type="bibr" rid="B9">Carbone and Rodeo, 2017</xref>; <xref ref-type="bibr" rid="B61">Thomas et&#x20;al., 2017</xref>) compared to the healthy population. Traumatic meniscal tears are a frequent cause of disability and loss of work time (<xref ref-type="bibr" rid="B35">Mccann et&#x20;al., 2009</xref>; <xref ref-type="bibr" rid="B38">Mcdermott, 2011</xref>; <xref ref-type="bibr" rid="B3">Badlani et&#x20;al., 2013</xref>; <xref ref-type="bibr" rid="B9">Carbone and Rodeo, 2017</xref>), mostly affecting patients under 40&#xa0;years of age (<xref ref-type="bibr" rid="B45">Ridley et&#x20;al., 2017</xref>) and professional athletes (<xref ref-type="bibr" rid="B34">Majewski et&#x20;al., 2006</xref>; <xref ref-type="bibr" rid="B67">Yeh et&#x20;al., 2012</xref>; <xref ref-type="bibr" rid="B57">Snoeker et&#x20;al., 2013</xref>). One of the superior goals of this active patient group is to return to work or sports as soon as possible. While arthroscopic suture repair provides a good prognosis for tears in the blood-supplied outer, so-called &#x201c;red&#x201d; and central &#x201c;red-white&#x201d; zone of the menisci, the healing potential for tears in the inner &#x201c;white zone&#x201d; is rather poor and remains a big clinical challenge (<xref ref-type="bibr" rid="B4">Bansal et&#x20;al., 2021</xref>). Although being aware about the poor clinical long-term results (<xref ref-type="bibr" rid="B1">Andersson-Molina et&#x20;al., 2002</xref>; <xref ref-type="bibr" rid="B64">Wachsmuth et&#x20;al., 2003</xref>; <xref ref-type="bibr" rid="B15">Englund and Lohmander, 2004</xref>; <xref ref-type="bibr" rid="B36">Mcdermott and Amis, 2006</xref>; <xref ref-type="bibr" rid="B24">Intema et&#x20;al., 2010</xref>; <xref ref-type="bibr" rid="B48">Salata et&#x20;al., 2010</xref>), mechanically instable tears at the white zone are still mostly treated by partial meniscectomy, in order to obtain pain relief, avoid tear progression, and allow a faster return to different activities.</p>
<p>Besides biological alterations (<xref ref-type="bibr" rid="B43">Rai et&#x20;al., 2019</xref>), biomechanical changes (<xref ref-type="bibr" rid="B5">Barton et&#x20;al., 2017</xref>; <xref ref-type="bibr" rid="B18">Fischenich et&#x20;al., 2017b</xref>) that are mainly related to the increased tibiofemoral contact pressure (<xref ref-type="bibr" rid="B54">Seitz et&#x20;al., 2012</xref>; <xref ref-type="bibr" rid="B58">Sukopp et&#x20;al., 2021</xref>) have been identified to be responsible for the amplification of PTOA progression after such meniscectomy procedures. Other than the main biomechanical function of tibiofemoral load transmission (<xref ref-type="bibr" rid="B37">Mcdermott et&#x20;al., 2008</xref>), the frequently assigned shock-absorbing function of the menisci might also affect the knee joint homeostasis after meniscectomy. &#x201c;The shocking truth about meniscus&#x201d; by <xref ref-type="bibr" rid="B2">Andrews et&#x20;al. (2011)</xref> revealed major flaws of the three most cited publications (<xref ref-type="bibr" rid="B28">Krause et&#x20;al., 1976</xref>; <xref ref-type="bibr" rid="B29">Kurosawa et&#x20;al., 1980</xref>; <xref ref-type="bibr" rid="B63">Voloshin and Wosk, 1983</xref>) that affiliate the meniscus with this shock-absorbing ability. Moreover, a recent commentary (<xref ref-type="bibr" rid="B20">Gecelter et&#x20;al., 2021</xref>) came to the conclusion that based both on the mechanical properties and the evolutionary origin, the menisci are not shock absorbers. In contrast, there is evidence assigning a shock-absorbing function directly to the meniscus material itself (<xref ref-type="bibr" rid="B40">Pereira et&#x20;al., 2014</xref>; <xref ref-type="bibr" rid="B19">Gaugler et&#x20;al., 2015</xref>; <xref ref-type="bibr" rid="B11">Coluccino et&#x20;al., 2017</xref>) and to the knee joint during activities of daily living (<xref ref-type="bibr" rid="B66">Winter, 1983</xref>; <xref ref-type="bibr" rid="B44">Ratcliffe and Holt, 1997</xref>). Therefore, the question remains whether the menisci play an active role as shock absorbers in the healthy, injured, and meniscectomized knee joints or not. Hence, the aim of this biomechanical <italic>in&#x20;vitro</italic> study was to investigate the shock-absorbing function of the meniscus as an essential integrant of the knee joint during impact and repetitive&#x20;loads.</p>
<p>Normal menisci have a highly anisotropic structure that is mainly composed of water (75%), collagen (23%), water-binding glycosaminoglycans (1%), and other matrix components leading to a time-dependent viscoelastic behavior (<xref ref-type="bibr" rid="B22">Herwig et&#x20;al., 1984</xref>; <xref ref-type="bibr" rid="B40">Pereira et&#x20;al., 2014</xref>; <xref ref-type="bibr" rid="B55">Seitz et&#x20;al., 2021</xref>). While under static equilibrium conditions (<xref ref-type="bibr" rid="B62">Tibesku et&#x20;al., 2004</xref>; <xref ref-type="bibr" rid="B53">Martin Seitz et&#x20;al., 2013</xref>; <xref ref-type="bibr" rid="B50">Schwer et&#x20;al., 2020</xref>) and repetitive loading (<xref ref-type="bibr" rid="B26">Kessler et&#x20;al., 2006</xref>), the menisci exhibit considerable axial deformation, high impact, or shock loads, as seen, e.g., during jump landings, leading to an increase in their stiffness, and thus, to a decrease in the ability to reduce the transmitted stresses. Therefore, we hypothesize that the menisci contribute significantly to knee joint shock absorption during repetitive loads, while under impact loads, this shock absorption potential is absent.</p>
</sec>
<sec id="s2">
<title>2 Methods</title>
<sec id="s2-1">
<title>2.1 Study Design</title>
<p>The shock-absorbing potential of six porcine knee joints was investigated using a custom developed droptower setup, which provided one degree of freedom. After successful validation of the setup using defined damping materials, the joints were impacted with a total energy of 3.54&#xa0;J.&#x20;During the tests, only the meniscus states were successively varied to be able to relate the shock absorption potential directly to the menisci. These were intact, medial meniscus posterior root avulsion, medial meniscectomy, total lateral, and medial meniscectomy. The shock absorption was interpreted by the loss factor, which was calculated <italic>via</italic> the propagation time between two integrated load&#x20;cells.</p>
<p>After modification of the test setup, a dynamic mechanical analysis (DMA) was conducted on eight porcine knees to investigate their shock-absorbing potential under repetitive, sinusoidal loads. For this purpose, a frequency scan including 10 different frequencies, ranging between 0.1&#x2013;5&#xa0;Hz at a constant load amplitude was performed while considering the four different meniscus states. The resultant shock absorption potential is calculated <italic>via</italic> the phase shift between force and displacement (strain) in order to draw conclusions about the influence of the meniscus on the damping in the knee&#x20;joint.</p>
</sec>
<sec id="s2-2">
<title>2.2 Specimen Preparation</title>
<p>Fourteen fresh porcine hind limbs (liveweight &#x2248; 100&#xa0;kg) were obtained for the experiments from a local butcher. The soft tissues were removed, leaving the capsuloligamentous knee joint structures intact. Before the tibial bone was shortened to a length of 4&#xa0;cm in distance to the knee joint gap, the head of the fibula was secured using a setscrew. A precision miter screw allowed for plane parallel resection of the femoral bone in 5&#xa0;cm distance to the joint gap and 45&#xb0; neutral knee joint flexion (<xref ref-type="bibr" rid="B41">Proffen et&#x20;al., 2012</xref>). During the preparation process, the tissues were kept moist using physiologic saline solution. After the preparation process, the specimens were wrapped in saline saturated gauze and stored at &#x2212;20&#xb0;C until the day of testing.</p>
<p>Both for the impact and for the repetitive (DMA) loading experiments, four meniscus states (intact, medial posterior root avulsion, medial meniscectomy, and total lateral and medial meniscectomy) were investigated to identify the shock-absorbing function of the meniscus (<xref ref-type="fig" rid="F1">Figure&#x20;1</xref>). The meniscus preparation steps were conducted as minimally invasive as possible by an orthopedic surgeon. During these preparation steps, the knee joints were kept in the respective testing setup to avoid a misplacement bias by disassembling and reassembling.</p>
<fig id="F1" position="float">
<label>FIGURE 1</label>
<caption>
<p>Schematic drawing of the axial view on a tibial plateau of a left knee joint. The femur is removed to allow better visualization of the four investigated meniscal states: <bold>(A)</bold> intact, <bold>(B)</bold> avulsion of the posterior medial meniscus horn, <bold>(C)</bold> medial meniscectomy, and <bold>(D)</bold> total lateral and medial meniscectomy.</p>
</caption>
<graphic xlink:href="fbioe-10-837554-g001.tif"/>
</fig>
</sec>
<sec id="s2-3">
<title>2.3 Test Setup and Validation</title>
<sec id="s2-3-1">
<title>2.3.1 Droptower Setup</title>
<p>The droptower test setup configuration consisted of a weight-adjustable (up to 200&#xa0;N), axially guided drop weight with a height stop and a hemispherical, stainless-steel impactor, which allows for pinpoint impact transmission (<xref ref-type="fig" rid="F2">Figure&#x20;2</xref>). The drop weight hit the impact pad that was mounted to the mobile upper sensor unit containing a screwed-in 10&#xa0;kN force sensor (KM30z, ME GmbH, Germany) to which the upper sample holder was connected with four knurled screws. Accurate and low-friction axial guidance of the upper sensor unit was ensured using eight linear ball bearings. The test sample was fixed between the two sample holders, while the lower sample holder was axially guided by four linear ball bearings. The lower sensor contained another screwed-in 10&#xa0;kN force sensor (KM30z, ME GmbH, Germany) that was rigidly connected to the main frame. The test setup provided only one degree of freedom in the axial direction. This was guided by a total of twelve low-friction linear ball bearings, which were in contact with the stainless-steel main&#x20;frame.</p>
<fig id="F2" position="float">
<label>FIGURE 2</label>
<caption>
<p>
<bold>(A)</bold> Technical drawing of the droptower setup in the side (left) and frontal (middle) view. The setup consisted of a height stop (ochre), which was directly connected to the axial guidance system of the drop weight. A hemisphere impactor (blue) was used to allow for pinpoint impact transmission. The upper, mobile sensor unit (red) is axially guided by eight axial ball bearings and incorporates the upper force sensor. It is further connected to an impact pad at its top end and to a sample holder at the lower end. The lower, fixed sensor unit (white) is also axially guided by four axial ball bearings and incorporates the lower force sensor. The lower end of this sensor unit is directly connected to the main frame. <bold>(B)</bold> Example of an installed porcine knee joint at the sample area at the droptower&#x20;setup.</p>
</caption>
<graphic xlink:href="fbioe-10-837554-g002.tif"/>
</fig>
<p>The two series-connected force sensors were used to determine the shock wave propagation by measuring the impact loads at the upper (F<sub>1</sub>) and lower sensor (F<sub>2</sub>) with the corresponding propagation time (&#x394;t). The measurements were used to calculate the loss factor (<inline-formula id="inf1">
<mml:math id="m1">
<mml:mi>&#x3b7;</mml:mi>
</mml:math>
</inline-formula>), which was used to interpret the damping behavior of the test sample. For damping materials, it can be assumed (<xref ref-type="bibr" rid="B25">J&#xe4;ger et&#x20;al., 2016</xref>) that<disp-formula id="e1">
<mml:math id="m2">
<mml:mrow>
<mml:mi>&#x3b7;</mml:mi>
<mml:mo>&#x2248;</mml:mo>
<mml:mn>2</mml:mn>
<mml:mi>D</mml:mi>
</mml:mrow>
</mml:math>
<label>(1)</label>
</disp-formula>while for viscoelastic materials (e.g., articular cartilage or menisci), it can be assumed that<disp-formula id="e2">
<mml:math id="m3">
<mml:mrow>
<mml:mi>&#x3b7;</mml:mi>
<mml:mo>&#x3d;</mml:mo>
<mml:mn>2</mml:mn>
<mml:mi>D</mml:mi>
<mml:mo>&#xa0;</mml:mo>
<mml:mo>&#x7c;</mml:mo>
<mml:msqrt>
<mml:mrow>
<mml:mn>1</mml:mn>
<mml:mo>&#x2212;</mml:mo>
<mml:msup>
<mml:mi>D</mml:mi>
<mml:mn>2</mml:mn>
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<mml:mo>&#xb2;</mml:mo>
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</mml:msqrt>
<mml:mo>&#x7c;</mml:mo>
</mml:mrow>
</mml:math>
<label>(2)</label>
</disp-formula>where <italic>D</italic> is the damping factor and calculated by<disp-formula id="e3">
<mml:math id="m4">
<mml:mrow>
<mml:mi>D</mml:mi>
<mml:mo>&#x3d;</mml:mo>
<mml:mfrac>
<mml:mtext>&#x39b;</mml:mtext>
<mml:mrow>
<mml:msqrt>
<mml:mrow>
<mml:mn>4</mml:mn>
<mml:msup>
<mml:mi>&#x3c0;</mml:mi>
<mml:mn>2</mml:mn>
</mml:msup>
<mml:mo>&#x2b;</mml:mo>
<mml:mtext>&#x39b;</mml:mtext>
<mml:msup>
<mml:mo>&#xb2;</mml:mo>
<mml:mn>2</mml:mn>
</mml:msup>
</mml:mrow>
</mml:msqrt>
</mml:mrow>
</mml:mfrac>
</mml:mrow>
</mml:math>
<label>(3)</label>
</disp-formula>with <inline-formula id="inf2">
<mml:math id="m5">
<mml:mi>&#x39b;</mml:mi>
</mml:math>
</inline-formula> as the logarithmic decrement, while <inline-formula id="inf3">
<mml:math id="m6">
<mml:mi>&#x39b;</mml:mi>
</mml:math>
</inline-formula> can be determined by two consecutively measured maxima x<sub>n</sub>:<disp-formula id="e4">
<mml:math id="m7">
<mml:mrow>
<mml:msub>
<mml:mtext>x</mml:mtext>
<mml:mrow>
<mml:mtext>n</mml:mtext>
<mml:mo>&#x2b;</mml:mo>
<mml:mn>1</mml:mn>
</mml:mrow>
</mml:msub>
<mml:mtext>:&#xa0;</mml:mtext>
<mml:mi>&#x39b;</mml:mi>
<mml:mo>&#x3d;</mml:mo>
<mml:mi>ln</mml:mi>
<mml:mrow>
<mml:mo>(</mml:mo>
<mml:mfrac>
<mml:mrow>
<mml:msub>
<mml:mi>x</mml:mi>
<mml:mi>n</mml:mi>
</mml:msub>
</mml:mrow>
<mml:mrow>
<mml:msub>
<mml:mi>x</mml:mi>
<mml:mrow>
<mml:mi>n</mml:mi>
<mml:mo>&#x2b;</mml:mo>
<mml:mn>1</mml:mn>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:mfrac>
<mml:mo>)</mml:mo>
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<label>(4)</label>
</disp-formula>
</p>
<p>We used the maxima at the lower force sensor (F<sub>2</sub>), as they equal to the reaction force, and thus, vary in accordance with the shock absorption ability of the test samples (<xref ref-type="fig" rid="F3">Figure&#x20;3</xref>). Based on pretests identifying the potential impact frequencies and following the Nyquist theorem, the sampling rate was set to 30&#xa0;kHz. Validation of the test setup was conducted using seven special damping materials made of polyurethane foam, indicating specific damping properties and a known loss factor (<inline-formula id="inf4">
<mml:math id="m8">
<mml:mi>&#x3b7;</mml:mi>
</mml:math>
</inline-formula>) ranging from <inline-formula id="inf5">
<mml:math id="m9">
<mml:mi>&#x3b7;</mml:mi>
</mml:math>
</inline-formula> &#x3d; 0.11 (PUR RF220, REGUPOL BSW GmbH, Bad Berleburg, Germany) to <inline-formula id="inf6">
<mml:math id="m10">
<mml:mi>&#x3b7;</mml:mi>
</mml:math>
</inline-formula> &#x3d; 0.22 (PUR RF740). Each damping material was tested 60&#x20;times at two consecutive days by applying an impact of 3.54&#xa0;J resulting from dropping 2.1&#xa0;kg at a drop height of 172&#xa0;mm, which is double of that used by Hoshino et&#x20;al. (1.77&#xa0;J) in their experiments (<xref ref-type="bibr" rid="B23">Hoshino and Wallace, 1987</xref>). Then, the experimental loss factor was compared to the given loss factor. The resultant Pearson&#x2019;s correlation coefficient (<italic>r</italic>&#x20;&#x3d; 0.93) indicated excellent correlations. Thus, successful validation of the droptower setup configuration was confirmed.</p>
<fig id="F3" position="float">
<label>FIGURE 3</label>
<caption>
<p>Result graph of a droptower validation test using a known damping material (RF220). The blue arrows indicate automatically determined local maxima (x<sub>n</sub>: blue arrows) at the lower force sensor (F<sub>2</sub>). The force is given over the discrete sample points at a sampling rate of 20&#xa0;kHz.</p>
</caption>
<graphic xlink:href="fbioe-10-837554-g003.tif"/>
</fig>
</sec>
<sec id="s2-3-2">
<title>2.3.2 Dynamic Mechanical Analysis Setup</title>
<p>The modular design of the test setup allows for a fast removal of the height stop and drop weight assembly. This is necessary to allow for an integration of the test setup in the work space of a standard hydraulic dynamic materials testing machine (Instron 8871, Norwood MS, United&#x20;States) with a total capacity of 10&#xa0;kN. A multiaxial ball bearing was placed between the upper sensor unit and the actuator of the dynamic materials testing machine (<xref ref-type="fig" rid="F4">Figure&#x20;4</xref>) to protect the load cell. The setup was centered and rigidly clamped to the base plate of the materials testing machine. An external high-precision laser length transducer (accuracy:&#x20;&#xb1; 0.6&#xa0;&#x3bc;m; optoNCDT 2201, Micro-Epsilon Eltrotec GmbH, G&#xf6;ppingen, Germany), which was installed at the lower sensor unit, was used together with its reflection plate counterpart that was firmly connected to the upper sensor unit to measure the sample deflection (l). During the DMA tests, the phase angle (&#x3b4;), the applied oscillation input (force) amplitude (F<sub>2,A</sub>), and the resultant oscillation output (deflection) amplitude (l<sub>A</sub>) were continuously recorded (<xref ref-type="fig" rid="F5">Figure&#x20;5</xref>). Based on these three parameters, the storage modulus (M&#x2032;) was determined (<xref ref-type="bibr" rid="B14">Ehrenstein et&#x20;al., 2004</xref>) by<disp-formula id="e5">
<mml:math id="m11">
<mml:mrow>
<mml:msup>
<mml:mi>M</mml:mi>
<mml:mrow>
<mml:mo>&#x2032;</mml:mo>
<mml:mo>&#xa0;</mml:mo>
</mml:mrow>
</mml:msup>
<mml:mo>&#x3d;</mml:mo>
<mml:mrow>
<mml:mo>(</mml:mo>
<mml:mrow>
<mml:mfrac>
<mml:mrow>
<mml:msub>
<mml:mi>F</mml:mi>
<mml:mrow>
<mml:mn>2</mml:mn>
<mml:mi>A</mml:mi>
</mml:mrow>
</mml:msub>
</mml:mrow>
<mml:mrow>
<mml:msub>
<mml:mi>l</mml:mi>
<mml:mi>A</mml:mi>
</mml:msub>
</mml:mrow>
</mml:mfrac>
</mml:mrow>
<mml:mo>)</mml:mo>
</mml:mrow>
<mml:mi>c</mml:mi>
<mml:mi>o</mml:mi>
<mml:mi>s</mml:mi>
<mml:mi>&#x3b4;</mml:mi>
</mml:mrow>
</mml:math>
<label>(5)</label>
</disp-formula>while the loss modulus (M&#x2033;) is calculated by<disp-formula id="e6">
<mml:math id="m12">
<mml:mrow>
<mml:msup>
<mml:mi>M</mml:mi>
<mml:mrow>
<mml:mo>&#x2033;</mml:mo>
</mml:mrow>
</mml:msup>
<mml:mo>&#x3d;</mml:mo>
<mml:mo>&#xa0;</mml:mo>
<mml:mrow>
<mml:mo>(</mml:mo>
<mml:mrow>
<mml:mfrac>
<mml:mrow>
<mml:msub>
<mml:mi>F</mml:mi>
<mml:mrow>
<mml:mn>2</mml:mn>
<mml:mi>A</mml:mi>
</mml:mrow>
</mml:msub>
</mml:mrow>
<mml:mrow>
<mml:msub>
<mml:mi>l</mml:mi>
<mml:mi>A</mml:mi>
</mml:msub>
</mml:mrow>
</mml:mfrac>
</mml:mrow>
<mml:mo>)</mml:mo>
</mml:mrow>
<mml:mi>s</mml:mi>
<mml:mi>i</mml:mi>
<mml:mi>n</mml:mi>
<mml:mi>&#x3b4;</mml:mi>
</mml:mrow>
</mml:math>
<label>(6)</label>
</disp-formula>
</p>
<fig id="F4" position="float">
<label>FIGURE 4</label>
<caption>
<p>
<bold>(A)</bold> Technical drawing of the modified dynamic mechanical analysis (DMA) setup in side (left) and frontal (middle) view. The upper, mobile sensor unit (red) is axially guided by eight axial ball bearings and incorporates the upper force sensor. On its top, there is a multiaxial ball bearing to protect the load cell of the dynamic testing machine, while at the lower end, there is a reflector plate (green) for a laser transducer installed. The lower, fixed sensor unit (white) is axially guided by four axial ball bearings and incorporates the lower force sensor as well as an external, high-precision laser length transducer. The lower end of this sensor unit is directly connected to the main frame. <bold>(B)</bold> Example of an installed porcine knee joint at the sample area at the DMA&#x20;setup.</p>
</caption>
<graphic xlink:href="fbioe-10-837554-g004.tif"/>
</fig>
<fig id="F5" position="float">
<label>FIGURE 5</label>
<caption>
<p>
<bold>(A)</bold> Representative force-induced sinusoidal oscillation (F) and the respective deflection response (l) of a viscoelastic material. The time-dependent, characteristic shift (&#x3b4;/2&#x3c0;f) of the force (F<sub>A</sub>) versus the deflection (l<sub>A</sub>) amplitudes are&#x20;plotted over the time (t). <bold>(B)</bold> Relation between the storage modulus M&#x2032;, the loss modulus M&#x2033;, the phase angle &#x3b4;, and the magnitude (<italic>M</italic>) of the complex modulus M&#x2a;. Images are in accordance with DIN EN ISO 6721-1:2018-03.</p>
</caption>
<graphic xlink:href="fbioe-10-837554-g005.tif"/>
</fig>
<p>Based on both moduli, the loss factor (tan &#x3b4;) can be calculated by<disp-formula id="e7">
<mml:math id="m13">
<mml:mrow>
<mml:mi>t</mml:mi>
<mml:mi>a</mml:mi>
<mml:mi>n</mml:mi>
<mml:mo>&#xa0;</mml:mo>
<mml:mi>&#x3b4;</mml:mi>
<mml:mo>&#x3d;</mml:mo>
<mml:mo>&#xa0;</mml:mo>
<mml:mfrac>
<mml:mrow>
<mml:mi>M</mml:mi>
<mml:mo>&#x2033;</mml:mo>
</mml:mrow>
<mml:mrow>
<mml:mi>M</mml:mi>
<mml:mo>&#x2032;</mml:mo>
</mml:mrow>
</mml:mfrac>
</mml:mrow>
</mml:math>
<label>(7)</label>
</disp-formula>
</p>
<p>In addition, the complex modulus E&#x2a; results from the storage modulus (M&#x2032;) and the imaginary part (1) of the loss modulus (M&#x2033;). It is also called dynamic modulus and indicates the behavior of stress to strain under oscillating loads:<disp-formula id="e8">
<mml:math id="m14">
<mml:mrow>
<mml:msup>
<mml:mi>M</mml:mi>
<mml:mo>&#x2217;</mml:mo>
</mml:msup>
<mml:mo>&#x3d;</mml:mo>
<mml:mi>M</mml:mi>
<mml:mo>&#x2032;</mml:mo>
<mml:mo>&#x2b;</mml:mo>
<mml:mi>i</mml:mi>
<mml:mo>&#x2217;</mml:mo>
<mml:mi>M</mml:mi>
<mml:mo>&#x2033;</mml:mo>
<mml:mo>&#x3d;</mml:mo>
<mml:mo>&#xa0;</mml:mo>
<mml:mfrac>
<mml:mrow>
<mml:msub>
<mml:mi>F</mml:mi>
<mml:mrow>
<mml:mn>2</mml:mn>
<mml:mi>A</mml:mi>
</mml:mrow>
</mml:msub>
</mml:mrow>
<mml:mrow>
<mml:msub>
<mml:mi>l</mml:mi>
<mml:mi>A</mml:mi>
</mml:msub>
</mml:mrow>
</mml:mfrac>
</mml:mrow>
</mml:math>
<label>(8)</label>
</disp-formula>
</p>
<p>Validation of the DMA test setup was conducted using the same seven damping materials (PUR RF, REGUPOL BSW GmbH, Bad Berleburg, Germany) as those for the droptower setup validation with a known loss factor (<inline-formula id="inf7">
<mml:math id="m15">
<mml:mrow>
<mml:mi>&#x3b7;</mml:mi>
<mml:mo>&#x3d;</mml:mo>
<mml:mo>&#xa0;</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula> tan&#x3b4;). Each damping material was tested three times at 5&#xa0;Hz sinusoidal loading and a stroke length of &#xb1;1.25&#xa0;mm for 20 cycles. During these validation experiments, the sampling rate was set to 1&#xa0;kHz. Then, the experimental loss factor was compared to the given loss factor by the manufacturer. The resultant Pearson&#x2019;s correlation coefficient (<italic>r</italic>&#x20;&#x3d; 0.99) indicated excellent correlations. Thus, successful validation of the DMA setup configuration could be confirmed.</p>
<p>Synchronized data acquisition for both the droptower (F<sub>1</sub>, F<sub>2</sub>, &#x394;t) and DMA (F<sub>1</sub>, F<sub>2</sub>, l, and force/displacement output of the materials testing machine) setup measurements was achieved using a USB data acquisition card (USB-6218, NI Corp., Austin TX, United&#x20;States) and a customized LabVIEW software (LabVIEW 2019; NI Corp., Austin TX, United&#x20;States). Subsequent data postprocessing was performed using customized MATLAB scripts (MATLAB 2019b; The MathWorks Inc., Natick MA, United&#x20;States).</p>
</sec>
</sec>
<sec id="s2-4">
<title>2.4 Droptower Experiments</title>
<p>Based on the results of a study investigating the impact-absorbing properties of a healthy and meniscectomized knee joint (<xref ref-type="bibr" rid="B23">Hoshino and Wallace, 1987</xref>), an <italic>a priori</italic> sample size calculation [G<sup>&#x2217;</sup>Power 3.1.9.2 (<xref ref-type="bibr" rid="B16">Faul et&#x20;al., 2007</xref>): <italic>&#x3b1;</italic> &#x3d; 0.05, Power (1 &#x2013; <italic>&#x3b2;</italic>) &#x3d; 0.95, effect size (dz) &#x3d; 2.79, <italic>n</italic>&#x20;&#x3d; 4] was performed to ensure sufficient statistical power [Actual power&#x20;&#x3d; 0.98] of the study. In order to be able to identify differences after simulating a meniscus tear, the sample size was increased to <italic>n</italic>&#x20;&#x3d;&#x20;6.</p>
<p>At the day of testing, the joints were thawed at room temperature and subsequently centrally mounted between the two sample holders using 4&#x2013;6 proximal and eight distal screws in 45&#xb0; neutral knee joint flexion (<xref ref-type="bibr" rid="B41">Proffen et&#x20;al., 2012</xref>). To account for the viscoelastic behavior of the knee soft tissues, the joints were loaded 12&#xa0;min prior to testing with 120&#xa0;N, following an established protocol (<xref ref-type="bibr" rid="B33">Maher et&#x20;al., 2017</xref>). During preconditioning, the drop height was adjusted to 172&#xa0;mm and the drop weight was adjusted to 2.1&#xa0;kg, resulting in an impact energy of 3.54&#xa0;J, which is double of that used by Hoshino et&#x20;al. (1.77&#xa0;J) (<xref ref-type="bibr" rid="B23">Hoshino and Wallace, 1987</xref>). After application of the impact and successful crosscheck of the data recording, the joint was unloaded and allowed to undergo relaxation for 12&#xa0;min. The tests were repeated three times, resulting in a total test time of 90&#xa0;min for each meniscus state. The mean values of these three measurements were used for further analyses. Then, the next meniscus preparation step was performed and the experiments were repeated. After each preparation step the joint capsule incision was fixed by surgical sutures. The sampling rate during the droptower experiments was set to 30&#xa0;kHz. During the tests, the joints were kept moist by constantly misting physiological saline solution.</p>
</sec>
<sec id="s2-5">
<title>2.5 Dynamic Mechanical Analysis</title>
<p>Based on the results of a similar study performing a DMA on human menisci (<xref ref-type="bibr" rid="B40">Pereira et&#x20;al., 2014</xref>), an <italic>a priori</italic> sample size calculation [G&#x2217;Power 3.1.9.2 (<xref ref-type="bibr" rid="B16">Faul et&#x20;al., 2007</xref>): <italic>&#x3b1;</italic> &#x3d; 0.05, Power (1&#x2212;&#x3b2;) &#x3d; 0.80, effect size (dz) &#x3d; 1.15, <italic>n</italic>&#x20;&#x3d; 7] was performed to ensure sufficient statistical power [Actual power &#x3d; 0.85] of the study. Comparators to determine the effect size dz were tan &#x3b4; values (mean&#x20;&#xb1; SD) of the anterior medial menisci and mid body medial menisci values. In order to be able to identify differences after simulating meniscus pathologies, the sample size was increased to <italic>n</italic>&#x20;&#x3d;&#x20;8.</p>
<p>At the day of testing, the porcine knee joints were thawed and centrally applied in the modified DMA test setup in 45&#xb0; neutral knee joint flexion (<xref ref-type="bibr" rid="B41">Proffen et&#x20;al., 2012</xref>). A total of 8&#x2013;12 screws were used to secure the specimen against translation. <xref ref-type="bibr" rid="B59">Taylor et&#x20;al. (2006</xref>) identified an axial knee joint loading of 2.12&#x20;times body weight (BW) during the stance phase and 0.3&#x20;times BW during the swing phase of normal gait in sheep knees. Since sheep and pigs are similar in their neutral knee position and gait (<xref ref-type="bibr" rid="B41">Proffen et&#x20;al., 2012</xref>), these values were transferred to the forces in the porcine knee, resulting in a static load of 1,210&#xa0;N and a superimposed sinusoidal load of 910N, which was applied to the porcine knee joints. As a result, peak loads of 2120&#xa0;N and minimum loads of 300&#xa0;N were identified for the sinusoidal DMA tests. Additionally, the joints were loaded 12&#xa0;min prior to testing with 300&#xa0;N to account for the viscoelastic behavior of the knee soft tissues (<xref ref-type="bibr" rid="B33">Maher et&#x20;al., 2017</xref>). A total of ten frequencies (0.1, 0.2, 0.4, 0.6, 0.8, 1, 2, 3, 4, and 5&#xa0;Hz) were arranged randomly for each knee&#x20;and scanned directly one after the other, in accordance with this randomized sequence. The frequency range was adapted from <xref ref-type="bibr" rid="B40">Pereira et&#x20;al. (2014</xref>) and cropped to the frequencies that match best to those observed during gait, running, and other daily activities (<xref ref-type="bibr" rid="B12">Danion et&#x20;al., 2003</xref>; <xref ref-type="bibr" rid="B56">Simoni et&#x20;al., 2021</xref>). The sampling rate was adapted to the respective frequency in a way that 1,000 values were recorded per single&#x20;sinusoidal oscillation, resulting in a total of 10,000 measurement points per DMA run. After the intact meniscus state investigation, the joints were allowed to undergo relaxation for 12&#xa0;min. Then, the next meniscus preparation step was performed and the experiments were repeated. After each preparation step, the joint capsule incision was fixed by surgical sutures. During the tests, the joints were continuously kept moist by constantly misting physiological saline solution.</p>
</sec>
<sec id="s2-6">
<title>2.6 Statistical Analysis</title>
<p>Gaussian distribution of the results data was tested using the Shapiro&#x2013;Wilk test, resulting in non-normally distributed data for the droptower and normally distributed data for the DMA experiments. Thus, non-parametric (droptower) and parametric (DMA) statistical analyses were performed using a statistical software package (SPSS v24, IBM Corp., Armonk, NY, United&#x20;States).</p>
<p>In detail, for the droptower experiments, F<sub>2</sub> and <inline-formula id="inf8">
<mml:math id="m16">
<mml:mi>&#x3b7;</mml:mi>
</mml:math>
</inline-formula> were elaborated by comparing the four meniscus states using a Friedman test followed by a Wilcoxon test, in which significant differences were observed. For the DMA experiments, tan &#x3b4; was elaborated by comparing the four meniscus states by means of a one-way ANOVA followed by Duncan post-hoc testing, in which significant differences were observed. In general, <italic>p</italic>&#x20;&#x3d; 0.05 was considered significant, while <italic>p</italic>-value Bonferroni correction was applied where necessary.</p>
</sec>
</sec>
<sec id="s3">
<title>3 Results</title>
<sec id="s3-1">
<title>3.1 Droptower Experiments</title>
<p>Friedman testing revealed significant differences in both the force maxima at the lower force sensor (F<sub>2</sub>; <italic>p</italic>&#x20;&#x3d; 0.02) and the loss factor (<inline-formula id="inf9">
<mml:math id="m17">
<mml:mi>&#x3b7;</mml:mi>
</mml:math>
</inline-formula>; <italic>p</italic>&#x20;&#x3d; 0.002). For the intact state, a median F<sub>2</sub> of 1187&#xa0;N was measured. Furthermore, a significant F<sub>2</sub> increase of 9% after medial meniscectomy (Wilcoxon: <italic>p</italic>&#x20;&#x3d; 0.46) and of 24% after total meniscectomy (Wilcoxon: <italic>p</italic>&#x20;&#x3d; 0.014) was identified. These findings were completed by the results of the loss factor (<xref ref-type="fig" rid="F6">Figure&#x20;6</xref>): The intact state possessed a medial loss factor of <inline-formula id="inf10">
<mml:math id="m18">
<mml:mi>&#x3b7;</mml:mi>
</mml:math>
</inline-formula>&#x20;&#x3d; 0.1. Friedman testing revealed significant differences of the loss factor (<inline-formula id="inf11">
<mml:math id="m19">
<mml:mi>&#x3b7;</mml:mi>
</mml:math>
</inline-formula>) for the meniscus states (<italic>p</italic>&#x20;&#x3d; 0.002). In detail, except for the root avulsion state (&#x2212;15%, Wilcoxon: <italic>p</italic>&#x20;&#x3d; 0.12), the loss&#x20;factor significantly decreased (Wilcoxon: <italic>p</italic>&#x20;&#x3c; 0.046) by a maximum of &#x2212;68% for the total meniscectomy state (Wilcoxon: <italic>p</italic>&#x20;&#x3d; 0.028) when compared to the intact state. The loss factor of the total meniscectomy state was always statistically lower (Wilcoxon <italic>p</italic>&#x20;&#x3d; 0.028) than those of any other state. However, there was no loss factor difference for the comparison between the posterior root avulsion and the medial meniscectomy state (Wilcoxon <italic>p</italic>&#x20;&#x3d; 0.054).</p>
<fig id="F6" position="float">
<label>FIGURE 6</label>
<caption>
<p>Minimum, median, and maximum loss factor (<inline-formula id="inf12">
<mml:math id="m20">
<mml:mi>&#x3b7;</mml:mi>
</mml:math>
</inline-formula>) values compared at the four investigated meniscus states: intact, root avulsion at the posterior horn of the medial meniscus, medial meniscectomy and total lateral and medial meniscectomy. The dotted line indicates the progression of the consecutively investigated meniscus states. <sup>&#x23;</sup>The total meniscectomy state was statistically lower than any of the other states; &#x2a;Wilcoxon test: <sup>&#x2a;,&#x23;</sup>
<italic>p</italic>&#x20;&#x3c; 0.05; <italic>n</italic>&#x20;&#x3d; 6.</p>
</caption>
<graphic xlink:href="fbioe-10-837554-g006.tif"/>
</fig>
</sec>
<sec id="s3-2">
<title>3.2 Dynamic Mechanical Analysis</title>
<p>Parametric statistical analyses revealed that knees with an intact&#x20;meniscus had the highest loss factors, ranging from tan &#x3b4; &#x3d; 0.10 to tan &#x3b4; &#x3d; 0.15 throughout all investigated frequencies (<xref ref-type="fig" rid="F7">Figure&#x20;7</xref>). Each consecutive simulated meniscus deterioration lowered the loss factor. Thus, after posterior medial root avulsion, the mean value of the loss factor (tan &#x3b4;) was reduced by 15%, while medial meniscectomy resulted in a reduction of 24%. The resection of both the lateral and medial menisci resulted in a reduction of 18% compared to the intact meniscus state. When comparing the meniscal states at specific frequencies in detail (<xref ref-type="fig" rid="F8">Figure&#x20;8</xref>), one-way ANOVA with Duncan post-hoc testing indicated significant differences for the comparisons of the intact state and the medial meniscectomy at 0.1, 0.2, 2, 3, and 4&#xa0;Hz (<italic>p</italic>&#x20;&#x3c; 0.04) and for the comparisons of the intact meniscus state and the total meniscectomy at 0.2&#xa0;Hz (<italic>p</italic>&#x20;&#x3d;&#x20;0.02).</p>
<fig id="F7" position="float">
<label>FIGURE 7</label>
<caption>
<p>Mean values (dashed lines) of the loss factor (tan &#x3b4;)&#x20;&#xb1; SD (represented by the envelope in the same color) plotted over the ten investigated frequencies (0.1, 0.2, 0.4, 0.6, 0.8, 1, 2, 3, 4, and 5&#xa0;Hz) at the four meniscal states (red: intact menisci; yellow: avulsion of the posterior medial meniscus horn; purple: medial meniscectomy; green: total lateral and medial meniscectomy). <italic>n</italic>&#x20;&#x3d; 8.</p>
</caption>
<graphic xlink:href="fbioe-10-837554-g007.tif"/>
</fig>
<fig id="F8" position="float">
<label>FIGURE 8</label>
<caption>
<p>Detailed representation of the loss factor (tan &#x3b4;)&#x20;&#xb1; SD at the ten investigated frequencies (0.1&#x2013;5&#xa0;Hz) and under the four investigated meniscus states: intact, root avulsion at the posterior horn of the medial meniscus, medial meniscectomy, and total lateral and medial meniscectomy. The dotted line indicates the progression of the consecutively investigated meniscus states. &#x2a;One-way ANOVA with post-hoc Duncan test: &#x2a;<italic>p</italic>&#x20;&#x3c; 0.05; <italic>n</italic>&#x20;&#x3d; 8.</p>
</caption>
<graphic xlink:href="fbioe-10-837554-g008.tif"/>
</fig>
</sec>
</sec>
<sec id="s4">
<title>4 Discussion</title>
<p>In this biomechanical <italic>in&#x20;vitro</italic> study, we investigated the shock-absorbing potential of the menisci inside porcine knee joints during impact loading and repetitive sinusoidal loads by applying a DMA. The test setup was successfully validated for both applications. Both during the impact loads and during the DMA analysis, the loss factor (<inline-formula id="inf13">
<mml:math id="m21">
<mml:mi>&#x3b7;</mml:mi>
</mml:math>
</inline-formula>) and the loss factor (tan &#x3b4;), respectively, were the highest for the intact meniscus state. During impact loading, the loss factor and, thus, the shock-absorbing potential of the menisci were reduced the more meniscus tissue was resected. Therefore, this study suggests that the menisci contribute to the shock absorption inside porcine knee joints under impact loads. During repetitive sinusoidal loads, the loss factor was lowest for the medial meniscectomy state, followed by the total lateral and medial meniscectomy state. However, both meniscectomy states indicated significantly lower loss factors compared to the intact meniscus state. Hence, it can be concluded that under sinusoidal loads in a frequency range from 0.1&#xa0;Hz up to 5&#xa0;Hz, the menisci significantly contribute to the knee joint shock absorption. In summary, the results of the present study suggest that the menisci contribute to the shock absorption during both repetitive and impact loading, refuting our hypothesis.</p>
<p>
<xref ref-type="bibr" rid="B23">Hoshino and Wallace (1987)</xref> investigated the shock absorption potential of human menisci in 20 knee joints and found a comparable reaction force increase of 21% for the comparison between the intact and the total meniscectomized knee joint. Also, for the root avulsion and medial meniscectomy conditions, our relative values were in a very similar range (108&#x2013;109%). Regarding the force at the lower sensor (F<sub>2</sub>), Hoshino et&#x20;al. determined forces of up to 1600&#xa0;N, thus being 400&#xa0;N higher compared to the F<sub>2</sub> forces of the present study. This might be due to the more pronounced curvature of the porcine tibial, potentially resulting in higher shear forces, which might be transmitted to other joint structures in the porcine knee. <xref ref-type="bibr" rid="B10">Chu et&#x20;al. (1986)</xref> investigated the shock wave propagation during dynamic loading in six human lower limbs using accelerometers and force transducers. They measured an average increase in impulse force of 11% at the tibia and 23% at the femur, after total meniscectomy and removal of the articular cartilage. In the present study, F<sub>2</sub> increased by 24% only after total meniscectomy. In contrast, Chu et&#x20;al. also removed cartilage structures. Articular cartilage has been shown to possess a 40-times higher complex modulus (E&#x2a;) (<xref ref-type="bibr" rid="B60">Temple et&#x20;al., 2016</xref>) compared to the menisci (<xref ref-type="bibr" rid="B40">Pereira et&#x20;al., 2014</xref>; <xref ref-type="bibr" rid="B17">Fischenich et&#x20;al., 2017a</xref>). This might be interpreted in a way that the menisci seem to be more responsible for the increased tibial forces in the Chu study (<xref ref-type="bibr" rid="B10">Chu et&#x20;al., 1986</xref>). Therefore, the results of Chu et&#x20;al. differ by only 1% to the results of the present study. In their work, <xref ref-type="bibr" rid="B29">Kurosawa et&#x20;al. (1980)</xref> examined a total of 14 human knee joints under quasi-static loads of 500, 1,000, and 1,500&#xa0;N at a loading rate of 5&#xa0;mm/min. They observed higher energy dissipation in meniscectomized knee joints than intact knee joints at all loading levels. These findings are in contrast to the ones obtained in the present study and to those from <xref ref-type="bibr" rid="B23">Hoshino and Wallace (1987)</xref> and <xref ref-type="bibr" rid="B10">Chu et&#x20;al. (1986)</xref>. However, compared to the other studies, the transmitted energy during the loading reached only 0.023&#xa0;J at a load of 1500&#xa0;N. Thus, the results from Kurosawa are difficult to compare with the present study and are more likely to reflect the energy absorption potential during creep loading of all viscoelastic knee joint structures.</p>
<p>
<xref ref-type="bibr" rid="B40">Pereira et&#x20;al. (2014)</xref> investigated in their study the viscoelastic response of isolated human meniscus tissue at a frequency range of 0.1&#x2013;10&#xa0;Hz under displacement-controlled conditions. They subdivided the menisci into their anatomical regions (anterior horn, pars intermedia, posterior horn) and determined variations of the loss factor (tan &#x3b4;) at 1&#xa0;Hz from 0.12&#xa0;at the posterior lateral meniscus to 0.18 in the anterior medial meniscus. In accordance to the findings of the present study, Pereira also showed a frequency dependent response: while at low frequencies (0.1&#x2013;0.6&#xa0;Hz) high loss factor values (&#x223c;0.2) and a loss factor minimum at 1&#xa0;Hz were observed, high frequencies (&#x3e;3&#xa0;Hz) again led to high loss factor values. <xref ref-type="bibr" rid="B19">Gaugler et&#x20;al. (2015</xref>) investigated in their study on isolated meniscus tissue both sinusoidal loads at a frequency of 0.1&#xa0;Hz and impact loads and found loss factors of 0.3 for sinusoidal and 0.17 for impact loads. The findings of our study are within the same range as those from Gaugler et&#x20;al. and indicate the same ratio when comparing sinusoidal and impact loads. Additionally, <xref ref-type="bibr" rid="B11">Coluccino et&#x20;al. (2017</xref>) investigated the viscoelastic response of bovine meniscus explants and found both similar ranges of the loss factor (tan &#x3b4;) of, e.g., 0.17&#xa0;at 0.1&#xa0;Hz and a similar frequency dependency of the damping response of the meniscus within the range from 0.1 to 5&#xa0;Hz.</p>
<p>Limitations should be considered when interpreting the results of the present <italic>in&#x20;vitro</italic> study. First, due to the very good availability and standardized phenotype, we used a porcine knee joint model in our study investigation. Although the porcine knee showed only acceptable appearance congruence for the ACL and lateral menisci (<xref ref-type="bibr" rid="B41">Proffen et&#x20;al., 2012</xref>) and differences in the viscoelastic properties (<xref ref-type="bibr" rid="B49">Sandmann et&#x20;al., 2013</xref>) when compared to the human knee joint, the relative comparisons were in a similar range than those observed in a human cadaver study, both for the impact (<xref ref-type="bibr" rid="B23">Hoshino and Wallace, 1987</xref>) and the DMA conditions investigating isolated menisci [tan &#x3b4; &#x223c; 0.2; (<xref ref-type="bibr" rid="B40">Pereira et&#x20;al., 2014</xref>)]. Furthermore, the test setup provided only one translational degree of freedom in the axial direction. However, during pretests, we experienced significant evasive rotational movement of the porcine knee joint under compressive loads, especially after the two meniscectomy states. In consequence, the obtained shock absorption results were significantly biased by these evasive movements and the resultant influence of the viscoelastic response of the surrounding soft tissues, while providing more physiological degrees of freedom.</p>
</sec>
<sec id="s5">
<title>5 Conclusion and Outlook</title>
<p>The results of this biomechanical <italic>in&#x20;vitro</italic> study indicate that the meniscus significantly contributes to the shock absorption of the porcine knee joint both under impact loads and under more moderate, sinusoidal loads at different frequencies. The findings may have an impact on the rehabilitation of young, meniscectomized patients that want to return to sports as soon as possible. Such patients are exposed to critical loads carried by the articular cartilage, when performing shock intensive sports like skiing, volleyball, etc. In summary, a partial meniscectomy leads not only to a reduced tibiofemoral contact area, but also to an inhibited shock-absorbing potential of the meniscus and, thus, to an increased contact pressure. Consequently, during the meniscectomy procedure, care should be taken to save as much meniscal tissue as possible, underlining the clinical findings to save the meniscus (<xref ref-type="bibr" rid="B32">Lubowitz and Poehling, 2011</xref>; <xref ref-type="bibr" rid="B51">Seil and Becker, 2016</xref>; <xref ref-type="bibr" rid="B30">Lee et&#x20;al., 2019</xref>; <xref ref-type="bibr" rid="B42">Pujol and Beaufils, 2019</xref>)&#x2014;also from a shock absorption point of view. A meniscus allograft transplantation (MAT) procedure is able to biomechanically restore the injured or (partially) meniscectomized knee joint to the original, healthy state (<xref ref-type="bibr" rid="B27">Koh et&#x20;al., 2019</xref>; <xref ref-type="bibr" rid="B52">Seitz and Durselen, 2019</xref>; <xref ref-type="bibr" rid="B68">Zaffagnini et&#x20;al., 2019</xref>). However, not only from a biomechanical point of view, but also from a clinical point of view, especially when patients present persisting post-meniscectomy syndromes, does MAT represent a viable option to decrease pain, improve knee joint function, and, thus, delay the onset of PTOA after meniscus injury (<xref ref-type="bibr" rid="B69">Zaffagnini et&#x20;al., 2016</xref>; <xref ref-type="bibr" rid="B13">De Bruycker et&#x20;al., 2017</xref>).</p>
</sec>
</body>
<back>
<sec id="s6">
<title>Data Availability Statement</title>
<p>The raw data supporting the conclusion of this article will be made available by the authors, without undue reservation.</p>
</sec>
<sec id="s7">
<title>Ethics Statement</title>
<p>Ethical review and approval was not required for the animal study because the porcine knee joints were received from a local butcher.</p>
</sec>
<sec id="s8">
<title>Author Contributions</title>
<p>AS and JS performed the specimen preparation, data analysis, and statistics. AS drafted the manuscript. DW and LdR conducted the mechanical testing. AI and LD participated in the design and coordination of the study. LD conceived the study. All authors read and approved the final manuscript.</p>
</sec>
<sec sec-type="COI-statement" id="s9">
<title>Conflict of Interest</title>
<p>The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.</p>
</sec>
<sec sec-type="disclaimer" id="s10">
<title>Publisher&#x2019;s Note</title>
<p>All claims expressed in this article are solely those of the authors and do not necessarily represent those of their affiliated organizations, or those of the publisher, the editors, and the reviewers. Any product that may be evaluated in this article, or claim that may be made by its manufacturer, is not guaranteed or endorsed by the publisher.</p>
</sec>
<ack>
<p>We thank K. Kreienbaum and L. W&#xe4;chter from the Technische Hochschule Ulm for their technical support and Patrizia Horny from the Institute of Orthopedic Research and Biomechanics Ulm for her art design support.</p>
</ack>
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