<?xml version="1.0" encoding="ISO-8859-1"?><article xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance">
<front>
<journal-meta>
<journal-id>0188-9532</journal-id>
<journal-title><![CDATA[Revista mexicana de ingeniería biomédica]]></journal-title>
<abbrev-journal-title><![CDATA[Rev. mex. ing. bioméd]]></abbrev-journal-title>
<issn>0188-9532</issn>
<publisher>
<publisher-name><![CDATA[Sociedad Mexicana de Ingeniería Biomédica]]></publisher-name>
</publisher>
</journal-meta>
<article-meta>
<article-id>S0188-95322016000100029</article-id>
<article-id pub-id-type="doi">10.17488/RMIB.37.1.2</article-id>
<title-group>
<article-title xml:lang="en"><![CDATA[Solution Using Lagrange's Equation to the Model of Cochlear Micromechanics]]></article-title>
<article-title xml:lang="es"><![CDATA[Solución del modelo de la micromecánica de la cóclea usando la ecuación de Lagrange]]></article-title>
</title-group>
<contrib-group>
<contrib contrib-type="author">
<name>
<surname><![CDATA[Jiménez Hernández]]></surname>
<given-names><![CDATA[M.]]></given-names>
</name>
<xref ref-type="aff" rid="Aff"/>
</contrib>
</contrib-group>
<aff id="Af1">
<institution><![CDATA[,Instituto Politécnico Nacional Escuela Superior de Ingeniería Mecánica y Eléctrica ]]></institution>
<addr-line><![CDATA[ México D.F.]]></addr-line>
<country>Mexico</country>
</aff>
<pub-date pub-type="pub">
<day>00</day>
<month>04</month>
<year>2016</year>
</pub-date>
<pub-date pub-type="epub">
<day>00</day>
<month>04</month>
<year>2016</year>
</pub-date>
<volume>37</volume>
<numero>1</numero>
<fpage>29</fpage>
<lpage>37</lpage>
<copyright-statement/>
<copyright-year/>
<self-uri xlink:href="http://www.scielo.org.mx/scielo.php?script=sci_arttext&amp;pid=S0188-95322016000100029&amp;lng=en&amp;nrm=iso"></self-uri><self-uri xlink:href="http://www.scielo.org.mx/scielo.php?script=sci_abstract&amp;pid=S0188-95322016000100029&amp;lng=en&amp;nrm=iso"></self-uri><self-uri xlink:href="http://www.scielo.org.mx/scielo.php?script=sci_pdf&amp;pid=S0188-95322016000100029&amp;lng=en&amp;nrm=iso"></self-uri><abstract abstract-type="short" xml:lang="en"><p><![CDATA[Abstract In this paper a new solution to micromechanical model of the cochlea developed by Neely and Kim is presented using Lagrange's equation. This solution has the advantage over previous methodologies to provide a mathematical model for the displacement exercised on the outer hair cells in the organ of Corti that only depends of the mechanical characteristics in the system and the value of the excitation frequency in the inner ear. For the evaluation of this new model the parameters developed by Ku are used and is considers that the amplitude of the excitation frequency is normalized. The model developed is satisfactorily compared with the impedance method and its numerical solution proposed by Neely and Kim, the state space analysis developed by Elliot, Ku and Lineton and the physiological measurements taken from Békésy.]]></p></abstract>
<abstract abstract-type="short" xml:lang="es"><p><![CDATA[Resumen En este trabajo se presenta una nueva solución utilizando la ecuación de Lagrange al modelo micromecánico de la cóclea desarrollado por Neely y Kim. Esta solución tiene la ventaja respecto a las ya existentes de proporcionar un modelo matemático del desplazamiento ejercido a los cilios en el órgano de Corti que sólo depende de las características mecánicas del sistema y del valor de la frecuencia de excitación en el oído interno. Para su evaluación se utilizan los parámetros desarrollados por Ku y se considera que la amplitud de la frecuencia de excitación está normalizada. El modelo desarrollado se compara satisfactoriamente con el método de impedancias y su solución numérica propuesta por Neely y Kim, el método de análisis de espacio estado desarrollado por Elliot, Ku y Lineton y con las mediciones fisiológicas realizadas por Békésy.]]></p></abstract>
<kwd-group>
<kwd lng="en"><![CDATA[inner ear]]></kwd>
<kwd lng="en"><![CDATA[organ of Corti]]></kwd>
<kwd lng="en"><![CDATA[outer hair Cells]]></kwd>
<kwd lng="en"><![CDATA[Lagrange's equation]]></kwd>
<kwd lng="es"><![CDATA[oído interno]]></kwd>
<kwd lng="es"><![CDATA[cóclea]]></kwd>
<kwd lng="es"><![CDATA[órgano de corti]]></kwd>
<kwd lng="es"><![CDATA[cilios]]></kwd>
<kwd lng="es"><![CDATA[ecuación de Lagrange]]></kwd>
</kwd-group>
</article-meta>
</front><back>
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