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  <front>
    <journal-meta>
      <journal-id journal-id-type="publisher-id">abc</journal-id>
      <journal-title-group>
        <journal-title>Arquivos Brasileiros de Cardiologia</journal-title>
        <abbrev-journal-title abbrev-type="publisher">Arq. Bras. Cardiol.</abbrev-journal-title>
      </journal-title-group>
      <issn pub-type="ppub">0066-782X</issn>
      <issn pub-type="epub">1678-4170</issn>
      <publisher>
        <publisher-name>Sociedade Brasileira de Cardiologia - SBC</publisher-name>
        <publisher-loc>S&#227;o Paulo, SP, Brazil</publisher-loc>
      </publisher>
    </journal-meta>
    <article-meta>
      <article-id pub-id-type="publisher-id" specific-use="scielo-v3">wGSRY7VppmxYMKDMjfXTvSL</article-id>
      <article-id pub-id-type="other">00007</article-id>
      <article-id pub-id-type="publisher-id" specific-use="scielo-v2">S0066-782X2011001100007</article-id>
      <article-id pub-id-type="publisher-id" specific-use="scielo-v1">S0066-782X(11)09700207</article-id>
      <article-id pub-id-type="doi">10.1590/S0066-782X2011005000078</article-id>
      <article-categories>
        <subj-group subj-group-type="heading">
          <subject>Artigos Originais</subject>
        </subj-group>
      </article-categories>
      <title-group>
        <article-title>Validade das equa&#231;&#245;es preditivas da frequ&#234;ncia card&#237;aca m&#225;xima para crian&#231;as e adolescentes</article-title>
      </title-group>
      <contrib-group>
        <contrib contrib-type="author">
          <name>
            <surname>Machado</surname>
            <given-names>Fabiana Andrade</given-names>
          </name>
          <xref ref-type="aff" rid="aff01"/>
        </contrib>
        <contrib contrib-type="author">
          <name>
            <surname>Denadai</surname>
            <given-names>Benedito S&#233;rgio</given-names>
          </name>
          <xref ref-type="aff" rid="aff02"/>
        </contrib>
      </contrib-group>
      <aff id="aff01">
        <addr-line>
          <named-content content-type="city">Maring&#225;</named-content>
          <named-content content-type="state">Paran&#225;</named-content>
        </addr-line>
        <institution content-type="orgname">Universidade Estadual de Maring&#225;</institution>
        <institution content-type="orgdiv1">Departamento de Educa&#231;&#227;o F&#237;sica </institution>
        <country country="BR">Brazil</country>
      </aff>
      <aff id="aff02">
        <addr-line>
          <named-content content-type="city">Rio-Claro</named-content>
          <named-content content-type="state">S&#227;o Paulo</named-content>
        </addr-line>
        <institution content-type="orgname">Universidade Estadual Paulista</institution>
        <institution content-type="orgdiv1">Departamento de Educa&#231;&#227;o F&#237;sica </institution>
        <country country="BR">Brazil</country>
      </aff>
      <pub-date date-type="collection" publication-format="electronic">
        <month>08</month>
        <year>2011</year>
      </pub-date>
      <volume>97</volume>
      <issue>2</issue>
      <fpage>136</fpage>
      <lpage>140</lpage>
      <history>
        <date date-type="rev-recd">
          <day>14</day>
          <month>10</month>
          <year>2011</year>
        </date>
        <date date-type="received">
          <day>09</day>
          <month>10</month>
          <year>2010</year>
        </date>
        <date date-type="accepted">
          <day>11</day>
          <month>04</month>
          <year>2011</year>
        </date>
      </history>
      <permissions>
        <license license-type="open-access" xlink:href="http://creativecommons.org/licenses/by-nc/4.0/" xml:lang="en">
          <license-p>This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.</license-p>
        </license>
      </permissions>
      <abstract>
        <p>FUNDAMENTO: Aus&#234;ncia de estudos na literatura validando equa&#231;&#245;es preditivas da frequ&#234;ncia card&#237;aca m&#225;xima (FCm&#225;x) em crian&#231;as e adolescentes. OBJETIVO: Analisar a validade das equa&#231;&#245;es preditivas da FCm&#225;x "220 - idade" e "208 - (0,7 x idade)" em meninos com idades entre 10 e 16 anos. M&#201;TODOS: Um teste progressivo de esfor&#231;o m&#225;ximo foi realizado em 69 meninos com idades entre 10 e 16 anos, aparentemente saud&#225;veis e ativos. A velocidade inicial do teste foi de 9 km/h com incrementos de 1 km/h a cada tr&#234;s minutos. O teste foi mantido at&#233; a exaust&#227;o volunt&#225;ria, considerando-se como FCm&#225;x a maior frequ&#234;ncia card&#237;aca atingida durante o teste. A FCm&#225;x medida foi comparada com os valores preditos pelas equa&#231;&#245;es "220 - idade" e "208 - (0,7 x idade)" atrav&#233;s da ANOVA, medidas repetidas. Resultados: Os valores m&#233;dios da FCm&#225;x (bpm) foram: 200,2 &#177; 8,0 (medida), 207,4 &#177; 1,5 ("220 - idade") e 199,2 &#177; 1,1 ("208 - (0,7 x idade)"). A FCm&#225;x predita pela equa&#231;&#227;o "220 - idade" foi significantemente maior (p &lt; 0,001) que a FCm&#225;x medida e que a FCm&#225;x predita pela equa&#231;&#227;o ("208 - (0,7 x idade)"). A correla&#231;&#227;o entre a FCm&#225;x medida e a idade n&#227;o foi estatisticamente significativa (r = 0,096; p &gt; 0,05). CONCLUS&#195;O: A equa&#231;&#227;o "220 - idade" superestimou a FCm&#225;x medida e n&#227;o se mostrou v&#225;lida para essa popula&#231;&#227;o. A equa&#231;&#227;o "208 - (0,7 x idade)" se mostrou v&#225;lida apresentando resultados bastante pr&#243;ximos da FCm&#225;x medida. Estudos futuros estudos com amostras maiores poder&#227;o comprovar se a FCm&#225;x n&#227;o depende da idade para essa popula&#231;&#227;o, situa&#231;&#227;o em que o valor constante de 200 bpm seria mais apropriado para a FCm&#225;x.</p>
      </abstract>
      <kwd-group xml:lang="pt" kwd-group-type="author-generated">
        <kwd>Frequ&#234;ncia card&#237;aca</kwd>
        <kwd>crian&#231;a</kwd>
        <kwd>adolescente</kwd>
        <kwd>cora&#231;&#227;o</kwd>
      </kwd-group>
      <pub-date publication-format="electronic" date-type="pub">
        <day>01</day>
        <month>07</month>
        <year>2011</year>
      </pub-date>
    </article-meta>
  </front>
  <body>
    <p>
      <bold>Validade das equa&#231;&#245;es preditivas da frequ&#234;ncia card&#237;aca m&#225;xima para crian&#231;as e adolescentes</bold>
    </p>
    <p>
      <bold>Validity of maximum heart rate prediction equations for children and adolescents</bold>
    </p>
    <p>
      <bold>Fabiana Andrade Machado<sup>I</sup>; Benedito S&#233;rgio Denadai<sup>II</sup></bold>
    </p>
    <p><sup>I</sup>Departamento de Educa&#231;&#227;o F&#237;sica - Universidade Estadual de Maring&#225; (UEM) - Maring&#225;, PR </p>
    <p><sup>II</sup>Departamento de Educa&#231;&#227;o F&#237;sica - Universidade Estadual Paulista (UNESP) - Rio-Claro, SP - Brasil</p>
    <p>
      <xref ref-type="corresp" rid="back">Correspond&#234;ncia</xref>
    </p>
    <p>
      <bold>RESUMO</bold>
    </p>
    <p><bold>FUNDAMENTO:</bold> Aus&#234;ncia de estudos na literatura validando equa&#231;&#245;es preditivas da frequ&#234;ncia card&#237;aca m&#225;xima (FCm&#225;x) em crian&#231;as e adolescentes. </p>
    <p><bold>OBJETIVO:</bold> Analisar a validade das equa&#231;&#245;es preditivas da FCm&#225;x "220 - idade" e "208 - (0,7 x idade)" em meninos com idades entre 10 e 16 anos. </p>
    <p><bold>M&#201;TODOS:</bold> Um teste progressivo de esfor&#231;o m&#225;ximo foi realizado em 69 meninos com idades entre 10 e 16 anos, aparentemente saud&#225;veis e ativos. A velocidade inicial do teste foi de 9 km/h com incrementos de 1 km/h a cada tr&#234;s minutos. O teste foi mantido at&#233; a exaust&#227;o volunt&#225;ria, considerando-se como FCm&#225;x a maior frequ&#234;ncia card&#237;aca atingida durante o teste. A FCm&#225;x medida foi comparada com os valores preditos pelas equa&#231;&#245;es "220 - idade" e "208 - (0,7 x idade)" atrav&#233;s da ANOVA, medidas repetidas. </p>
    <p> Resultados: Os valores m&#233;dios da FCm&#225;x (bpm) foram: 200,2 &#177; 8,0 (medida), 207,4 &#177; 1,5 ("220 - idade") e 199,2 &#177; 1,1 ("208 - (0,7 x idade)"). A FCm&#225;x predita pela equa&#231;&#227;o "220 - idade" foi significantemente maior (p &lt; 0,001) que a FCm&#225;x medida e que a FCm&#225;x predita pela equa&#231;&#227;o ("208 - (0,7 x idade)"). A correla&#231;&#227;o entre a FCm&#225;x medida e a idade n&#227;o foi estatisticamente significativa (r = 0,096; p &gt; 0,05). </p>
    <p><bold>CONCLUS&#195;O:</bold> A equa&#231;&#227;o "220 - idade" superestimou a FCm&#225;x medida e n&#227;o se mostrou v&#225;lida para essa popula&#231;&#227;o. A equa&#231;&#227;o "208 - (0,7 x idade)" se mostrou v&#225;lida apresentando resultados bastante pr&#243;ximos da FCm&#225;x medida. Estudos futuros estudos com amostras maiores poder&#227;o comprovar se a FCm&#225;x n&#227;o depende da idade para essa popula&#231;&#227;o, situa&#231;&#227;o em que o valor constante de 200 bpm seria mais apropriado para a FCm&#225;x. (Arq Bras Cardiol. 2011; [online].ahead print, PP.0-0)</p>
    <p><bold>Palavras-chave:</bold> Frequ&#234;ncia card&#237;aca, crian&#231;a, adolescente, cora&#231;&#227;o/fisiologia.</p>
    <p>
      <bold>ABSTRACT</bold>
    </p>
    <p><bold>BACKGROUND:</bold> There are no studies in the literature to validate equations that predict maximum heart rate (HRmax) in children and adolescents. </p>
    <p><bold>OBJECTIVE:</bold> To analyze the validity of the HRmax predictive equations "220 - age" and "208 - (0.7 x age)" in boys aged 10 and 16. </p>
    <p><bold>METHODS:</bold> A progressive maximal exertion test was carried out in 69 apparently healthy boys aged 10 to 16. The initial test velocity was 9 km/h, with 1-km/h increments every three minutes. The test was maintained until maximum voluntary exertion was achieved, considering HRmax as the highest heart rate attained during the test. The measured HRmax was compared with the values predicted by the "220 - age" and "208 - (0.7 x age)" equations, using ANOVA for repeated measures. </p>
    <p><bold>RESULTS:</bold> The mean values of HRmax (bpm) were: 200.2 &#177; 8.0 (measured), 207.4 &#177; 1.5 ("220 - age") and 199.2 &#177; 1.1 ("208 - (0.7 x age)"). The HRmax predicted by the "220 - age" equation was significantly higher (p &lt; 0.001) than the measured HRmax and the HRmax predicted by the ("208 - (0.7 x age)") equation. The correlation between the measured HRmax and age was not statistically significant (r = 0.096; p &gt; 0.05). </p>
    <p><bold>CONCLUSION:</bold> The "220 - age" equation overestimated the measured HRmax and was not valid for this population. The "208 - (0.7 x age)" equation was valid for this population, showing results that were quite similar to those of measured HRmax. Future studies with larger sample sizes can verify whether the HRmax does not depend on age for this population, a situation in which the constant 200 bpm value would be more appropriate for HRmax. (Arq Bras Cardiol. 2011; [online].ahead print, PP.0-0)</p>
    <p><bold>Keywords:</bold> Heart rate; child; adolescent; heart/physiology.</p>
    <p>
      <bold>Introdu&#231;&#227;o</bold>
    </p>
    <p>A frequ&#234;ncia card&#237;aca (FC) &#233; considerada uma vari&#225;vel fisiol&#243;gica de f&#225;cil mensura&#231;&#227;o, sendo rotineiramente utilizada para avaliar a resposta cardiovascular durante o esfor&#231;o e a recupera&#231;&#227;o<sup>1,2</sup>. A frequ&#234;ncia card&#237;aca m&#225;xima (FCm&#225;x), por sua vez, &#233; considerada um dos crit&#233;rios de verifica&#231;&#227;o do esfor&#231;o m&#225;ximo em testes ergom&#233;tricos<sup>3,4</sup> e &#233; amplamente utilizada na prescri&#231;&#227;o da intensidade de exerc&#237;cios<sup>4-6</sup>.</p>
    <p>A determina&#231;&#227;o da FCm&#225;x pode ser feita de maneira direta, usualmente por meio de protocolos progressivos de esfor&#231;o m&#225;ximo, ou pode ser feita de maneira indireta com o aux&#237;lio de equa&#231;&#245;es preditivas, que constituem uma maneira de baixo custo e de f&#225;cil aplica&#231;&#227;o<sup>1,7,8</sup>.</p>
    <p>Entre as diversas equa&#231;&#245;es propostas para predizer a FCm&#225;x, a de maior destaque por ser amplamente conhecida &#233; a equa&#231;&#227;o "220 - idade"<sup>4,9,10</sup>, que curiosamente possui autoria desconhecida, apesar de muitas vezes ser citada como de autoria de Karvonen e cols.<sup>11</sup>, ainda que o trabalho elaborado por esses autores n&#227;o tenha envolvido a elabora&#231;&#227;o dessa equa&#231;&#227;o<sup>7,10,12,13</sup>. Outra equa&#231;&#227;o que merece destaque &#233; "208 - (0,7 x idade)" proposta por Tanaka e cols.<sup>4</sup>, que foi desenvolvida em um estudo de meta-an&#225;lise coletando-se dados na literatura de 18.712 sujeitos.</p>
    <p>A principal caracter&#237;stica dessas e de outras f&#243;rmulas apresentadas para predizer a FCm&#225;x &#233; a de que todas consideram que essa vari&#225;vel decresce com a idade<sup>14</sup>. Apesar de esse decr&#233;scimo ser um consenso geral para homens e mulheres, adultos saud&#225;veis, ele pode n&#227;o ser verdadeiro para crian&#231;as e adolescentes, e ainda que o seja, esse decr&#233;scimo deve ser mensurado para essa clientela espec&#237;fica, visto que a taxa de decr&#233;scimo da maioria das equa&#231;&#245;es foi determinada para uma ampla faixa et&#225;ria, englobando apenas em alguns casos crian&#231;as e adolescentes<sup>9,15,16</sup>.</p>
    <p>Assim, em raz&#227;o da import&#226;ncia do conhecimento da FCm&#225;x para que uma crian&#231;a ou adolescente n&#227;o treine em uma intensidade diferente da apropriada e planejada, e considerando a inexist&#234;ncia na literatura, segundo nosso conhecimento, de estudos validando essas duas equa&#231;&#245;es preditivas da FCm&#225;x para essa clientela, o objetivo deste estudo foi analisar a validade das equa&#231;&#245;es preditivas da FCm&#225;x "220 - idade" e "208 - (0,7 x idade)" em meninos com idades entre 10 e 16 anos.</p>
    <p>
      <bold>M&#233;todos</bold>
    </p>
    <p>
      <bold>Popula&#231;&#227;o</bold>
    </p>
    <p>Sessenta e nove meninos com idades entre 10 e 16 anos, aparentemente saud&#225;veis e ativos, participaram deste estudo. Os valores m&#233;dios &#177; desvio padr&#227;o (DP) da idade, estatura e massa corporal foram: 12,6 &#177; 1,5 anos; 152,7 &#177; 13,1 cm; 47,3 &#177; 14,1 kg, respectivamente; a mediana da idade (intervalo interquartil) foi de 12,1 anos (11,4 - 13,8). A idade foi calculada de forma centesimal considerando a data de nascimento e a data de realiza&#231;&#227;o do teste. Nenhum dos participantes estava inserido em programas sistem&#225;ticos de treinamento. Todos os procedimentos adotados foram previamente aprovados pelo Comit&#234; de &#201;tica em Pesquisa local. A participa&#231;&#227;o foi volunt&#225;ria e isenta de qualquer b&#244;nus ou &#244;nus aos sujeitos. Antes do in&#237;cio dos testes os respons&#225;veis tomaram conhecimento de todos os procedimentos a que as crian&#231;as seriam submetidas assinando o termo de consentimento livre e esclarecido referente &#224; participa&#231;&#227;o nos testes.</p>
    <p>
      <bold>Teste progressivo de esfor&#231;o m&#225;ximo</bold>
    </p>
    <p>Previamente &#224; realiza&#231;&#227;o do teste de esfor&#231;o em esteira rolante, os participantes realizaram uma visita ao laborat&#243;rio para uma sess&#227;o de adapta&#231;&#227;o ao erg&#244;metro e tamb&#233;m para a verifica&#231;&#227;o das medidas antropom&#233;tricas (massa corporal e estatura). O teste progressivo de esfor&#231;o m&#225;ximo foi realizado em esteira rolante multiprogram&#225;vel (Inbrasport Super ATL, Porto Alegre, Brasil). Ap&#243;s aquecimento inicial de tr&#234;s minutos a 5 km/h, o teste iniciou-se a 9 km/h, com incrementos de 1 km/h a cada tr&#234;s minutos. Durante todo o teste foi mantida uma inclina&#231;&#227;o contante referente a 1%. A frequ&#234;ncia card&#237;aca (FC) foi constantemente monitorada por meio de frequenc&#237;metro (Polar Vantage XL). O teste foi mantido at&#233; a exaust&#227;o volunt&#225;ria, sendo os participantes encorajados verbalmente a se manterem em exerc&#237;cio pelo maior tempo poss&#237;vel. A FCm&#225;x foi definida como a maior FC atingida durante o teste<sup>4</sup>, sendo considerada atingida (v&#225;lida) apenas quando fossem observados sinais de esfor&#231;o intenso (hiperpneia, vermelhid&#227;o facial, descompasso de passadas)<sup>17</sup>.</p>
    <p>
      <bold>An&#225;lise estat&#237;stica</bold>
    </p>
    <p>Os dados s&#227;o apresentados como m&#233;dia &#177; desvio padr&#227;o (DP) para todas as vari&#225;veis mensuradas. Os m&#233;todos foram comparados utilizando-se ANOVA para medidas repetidas com o teste <italic>post-hoc</italic> de Bonferroni. ANOVA one-way foi utilizada para comparar a FCm&#225;x medida entre as faixas et&#225;rias. O coeficiente de correla&#231;&#227;o de Pearson foi utilizado tanto para relacionar os valores medidos com os valores preditos da FCm&#225;x como para verificar a rela&#231;&#227;o entre a idade e a FCm&#225;x medida. An&#225;lise de Bland-Altman<sup>18</sup> foi utilizada para calcular os limites de concord&#226;ncia entre a FCm&#225;x medida e a predita pela idade; o n&#237;vel de signific&#226;ncia adotado foi de p &lt; 0,05.</p>
    <p>
      <bold>Resultados</bold>
    </p>
    <p>Na <xref ref-type="table" rid="t1">tabela 1</xref> s&#227;o apresentados os valores medidos e preditos da FCm&#225;x para meninos com idades entre 10 e 16 anos. Os valores apresentados pela equa&#231;&#227;o "220 - idade" foram significativamente maiores (p &lt; 0,001) que os valores medidos e que os valores estimados pela equa&#231;&#227;o "208 - (0,7 x idade)", conforme ANOVA para medidas repetidas com o teste <italic>post-hoc</italic> de Bonferroni. A correla&#231;&#227;o entre os valores da FCm&#225;x medida e os valores preditos para as duas equa&#231;&#245;es n&#227;o foi estatisticamente significante (p &gt; 0,05) apresentando o mesmo coeficiente de correla&#231;&#227;o para ambas as equa&#231;&#245;es (r = -0,096).</p>
    <table-wrap id="t1">
      <graphic xlink:href="1678-4170-abc-97-02-0136-00078-gt01.jpg"/></table-wrap>
    <p>A <xref ref-type="fig" rid="f1">figura 1</xref> apresenta os valores m&#233;dios &#177; DP da FCm&#225;x medida para as diferentes faixas et&#225;rias. ANOVA one-way n&#227;o demonstrou diferen&#231;a significativa (p &gt; 0,05) entre as faixas et&#225;rias. A correla&#231;&#227;o entre os valores da FCm&#225;x medida e a idade n&#227;o foi estatisticamente significante (r = 0,096; p &gt; 0,05). Observa-se visualmente a aus&#234;ncia de uma tend&#234;ncia de aumento ou diminui&#231;&#227;o da FCm&#225;x com a idade. Isso foi corroborado pela correla&#231;&#227;o entre essas vari&#225;veis, a qual n&#227;o foi estatisticamente diferente de zero. A variabilidade da FCm&#225;x para as diversas faixas et&#225;rias representada pelo DP na <xref ref-type="fig" rid="f1">figura 1</xref> tamb&#233;m n&#227;o apresentou nenhuma tend&#234;ncia de aumentar ou diminuir com a idade. Verificam-se ainda na <xref ref-type="fig" rid="f1">figura 1</xref> os elevados valores de DP encontrados, em que o menor e o maior DP foi de 5,1 e 9,0 bpm para as faixas et&#225;rias entre 13-14 e 14-15 anos, respectivamente.</p>
    <fig id="f1">
      <graphic xlink:href="1678-4170-abc-97-02-0136-00078-gf01.jpg"/></fig>
    <p>A <xref ref-type="fig" rid="f02">figura 2</xref> refere-se ao gr&#225;fico de dispers&#227;o dos valores da FCm&#225;x medida da amostra. Destaca-se novamente a alta dispers&#227;o dos dados corroborada pelo alto DP apresentado na <xref ref-type="table" rid="t1">tabela 1</xref> para a FCm&#225;x medida. Verifica-se tamb&#233;m que os valores preditos pela equa&#231;&#227;o "220 - idade", representados pela linha tracejada, apresentam a tend&#234;ncia de superestimar a FCm&#225;x. Por sua vez, os valores preditos pela equa&#231;&#227;o "208 - (0,7 x idade)", representados pela linha pontilhada, aparentam se ajustar muito melhor &#224; m&#233;dia da FCm&#225;x medida.</p>
    <p content-type="asset">
      <fig id="f02">
        <graphic xlink:href="1678-4170-abc-97-02-0136-00078-gf02.jpg"/></fig>
    </p>
    <p>A an&#225;lise de concord&#226;ncia entre a FCm&#225;x medida e a predita pelas f&#243;rmulas apresentou como vi&#233;s (diferen&#231;a entre as m&#233;dias) &#177; desvio padr&#227;o das diferen&#231;as: 7,1 &#177; 8,3 bpm ("220 - idade") e -1,1 &#177; 8,2 bpm ("208 - (0,7 x idade)"). Ressalta-se o alto vi&#233;s de 7,1 bpm apresentado pela diferen&#231;a entre as m&#233;dias dos valores preditos pela equa&#231;&#227;o "220 - idade" e os valores da FCm&#225;x medida, o qual conduz a uma superestima&#231;&#227;o da FCm&#225;x.</p>
    <p>
      <bold>Discuss&#227;o</bold>
    </p>
    <p>O objetivo deste estudo foi analisar a validade das equa&#231;&#245;es preditivas da FCm&#225;x "220 - idade" e "208 - (0,7 x idade)" em meninos com idades entre 10 e 16 anos. O principal achado foi que a equa&#231;&#227;o "220 - idade" superestimou na m&#233;dia os valores da FCm&#225;x n&#227;o se mostrando v&#225;lida para essa popula&#231;&#227;o, e a equa&#231;&#227;o "208 - (0,7 x idade)" se mostrou v&#225;lida para essa clientela pedi&#225;trica. Al&#233;m disso, verificamos que a FCm&#225;x se mostrou independente da idade para essa popula&#231;&#227;o espec&#237;fica, ressalvando-se que a amostra estudada (n = 69) n&#227;o permite conclus&#245;es definitivas quanto a essa independ&#234;ncia de rela&#231;&#227;o.</p>
    <p>De acordo com Almeida e cols.<sup>19</sup>, equa&#231;&#245;es preditivas s&#227;o v&#225;lidas quando aplicadas em popula&#231;&#245;es com caracter&#237;sticas semelhantes &#224;s da amostra a partir da qual a equa&#231;&#227;o foi gerada. Dessa forma, apesar de sua ampla aplica&#231;&#227;o, a f&#243;rmula "220 - idade" necessita das amostras pela qual foi gerada, visto o desconhecimento de seu autor e da faixa et&#225;ria utilizada para a sua elabora&#231;&#227;o. J&#225; a equa&#231;&#227;o "208 - (0,7 x idade)" foi gerada pela regress&#227;o linear de 18.712 sujeitos especialmente entre as idades de 20 e 70 anos.</p>
    <p>Verifica-se na <xref ref-type="table" rid="t1">tabela 1</xref> que o valor m&#233;dio da equa&#231;&#227;o "220 - idade" foi significantemente maior (p &lt; 0,001) que os valores medidos e que os valores estimados pela equa&#231;&#227;o "208 - (0,7 x idade)". Dessa forma, a equa&#231;&#227;o "220 - idade" superestima, na m&#233;dia, os valores da FCm&#225;x. Aplicando-se a equa&#231;&#227;o "220 - idade", constata-se que FCm&#225;x predita recua linearmente de 210 bpm aos 10 anos para 204 bpm aos 16 anos, superestimando ao longo da faixa et&#225;ria de 10 a 16 anos o valor m&#233;dio da FCm&#225;x medida de 200,2 bpm. Essa constata&#231;&#227;o pode ser feita visualmente pela <xref ref-type="fig" rid="f02">figura 2</xref>. Contrariamente &#224; equa&#231;&#227;o "220 - idade", n&#227;o houve diferen&#231;a significativa (p &gt; 0,05) entre os valores preditos pela equa&#231;&#227;o "208 - (0,7 x idade)" e os valores medidos. Os valores preditos pela equa&#231;&#227;o "208 - (0,7 x idade)" recuam de 201 bpm aos 10 anos para 196,8 bpm aos 16 anos de idade, apresentando valores acima (idade &lt; 11,1 anos) e abaixo (idade <underline>&gt;</underline> 11,1 anos) da m&#233;dia de 200,2 bpm da FCm&#225;x medida.</p>
    <p>Verificou-se por meio da <xref ref-type="fig" rid="f1">figura 1</xref> que n&#227;o houve diferen&#231;a significativa (p &gt; 0,05) entre as diversas faixas et&#225;rias para a FCm&#225;x medida. Corroborou para essa aus&#234;ncia de diferen&#231;a o fato de a correla&#231;&#227;o entre a FCm&#225;x medida e a idade n&#227;o ter sido estatisticamente significante. Dessa forma, por meio deste estudo, n&#227;o &#233; poss&#237;vel afirmar que a FCm&#225;x decres&#231;a com a idade para a popula&#231;&#227;o aqui estudada. Apesar de essa amostra n&#227;o ser pequena (n = 69), ela ainda n&#227;o permite obter conclus&#245;es definitivas quanto &#224; aus&#234;ncia de rela&#231;&#227;o entre a FCm&#225;x e a idade.</p>
    <p>Outro ponto interessante apresentado nos resultados foi a alta variabilidade da FCm&#225;x para as diversas faixas et&#225;rias, variabilidade representada pelo DP. Esse elevado DP tamb&#233;m n&#227;o apresentou nenhuma tend&#234;ncia de aumentar ou diminuir com a idade. Tanto na <xref ref-type="fig" rid="f1">figura 1</xref> como na <xref ref-type="fig" rid="f02">figura 2</xref>, &#233; poss&#237;vel verificar esse padr&#227;o de um elevado DP para a FCm&#225;x. Ressaltamos que n&#227;o apenas a FCm&#225;x medida apresentou um alto DP da ordem de 8 bpm, como tamb&#233;m a diferen&#231;a entre as m&#233;dias (vi&#233;s) dos valores preditos e medidos apresentou um DP dessa mesma ordem. Esses valores est&#227;o de acordo com a literatura que relata um desvio padr&#227;o da ordem de 10 bpm para os valores preditos da FCm&#225;x<sup>4,10</sup>. Analisando-se o vi&#233;s e o DP da diferen&#231;a entre os valores da FCm&#225;x preditos e medidos, verifica-se um amplo limite de concord&#226;ncia para 95% dos casos entre os valores medidos e os preditos pela equa&#231;&#227;o "220 - idade" (-9,5 a 23,7 bpm) e pela equa&#231;&#227;o "208 - (0,7 x idade)" (-17,5 a 15,3 bpm), os quais poder&#227;o resultar em erros de at&#233; +12% e -9%, respectivamente, considerando a FCm&#225;x m&#233;dia de 202,2 bpm. Diante disso, temos que a alta variabilidade da FCm&#225;x se apresenta como o principal fator limitante para a sua predi&#231;&#227;o.</p>
    <p>
      <bold>Conclus&#227;o</bold>
    </p>
    <p>Com base nesses resultados, conclui-se que a equa&#231;&#227;o "220 - idade" n&#227;o se mostra v&#225;lida e apropriada para crian&#231;as e adolescentes, j&#225; que essa superestimou na m&#233;dia os valores da FCm&#225;x para meninos na faixa et&#225;ria de 10 a 16 anos. A equa&#231;&#227;o "208 - (0,7 x idade)", por sua vez, apresentou resultados bastante pr&#243;ximos da FCm&#225;x medida, podendo ser considerada uma equa&#231;&#227;o v&#225;lida para essa clientela pedi&#225;trica. Adicionalmente, caso a FCm&#225;x seja realmente independente da idade para meninos dessa faixa et&#225;ria, o que apenas poder&#225; ser comprovado em futuros estudos com amostras maiores, o valor constante de 200 bpm poder&#225; se tornar o valor mais apropriado para a FCm&#225;x dessa popula&#231;&#227;o.</p>
    <p>
      <bold>Potencial Conflito de Interesses</bold>
    </p>
    <p>Declaro n&#227;o haver conflito de interesses pertinentes.</p>
    <p>
      <bold>Fontes de Financiamento</bold>
    </p>
    <p>O presente estudo n&#227;o teve fontes de financiamento externas.</p>
    <p>
      <bold>Vincula&#231;&#227;o Acad&#234;mica</bold>
    </p>
    <p>N&#227;o h&#225; vincula&#231;&#227;o deste estudo a programas de p&#243;s-gradua&#231;&#227;o.</p>
    <p>
      <fn id="back" fn-type="corresp">
        <p>Correspond&#234;ncia:</p>
        <p> Fabiana Andrade Machado </p>
        <p> Av. Colombo, 5790 - Bloco M06 </p>
        <p> Depto. Educa&#231;&#227;o F&#237;sica - Universidade Estadual de Maring&#225; </p>
        <p> 87020-900 - Maring&#225;, PR - Brasil </p>
        <p> Email: </p>
        <p><email xlink:href="famachado@uem.br">famachado@uem.br</email>, </p>
        <p>
          <email xlink:href="famachado_uem@hotmail.com">famachado_uem@hotmail.com</email>
        </p>
      </fn>
    </p>
    <p>Artigo recebido em 09/10/10; revisado recebido em 14/10/11; aceito em 11/04/11.</p>
  </body>
  <back>
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          <lpage>76</lpage>
          <volume>22</volume>
          <person-group person-group-type="author">
            <name>
              <surname>Armstrong</surname>
              <given-names>N</given-names>
            </name>
            <name>
              <surname>Welsman</surname>
              <given-names>JR</given-names>
            </name>
          </person-group>
        </element-citation>
      </ref>
      <ref id="B18">
        <mixed-citation>18. Bland JM, Altman    DG. Statistical methods for assessing agreement between two methods of clinical    measurement. Lancet. 1986;1(8476):307-10.</mixed-citation>
        <element-citation publication-type="journal">
          <article-title>Statistical methods for assessing agreement between two methods of clinical measurement</article-title>
          <source>Lancet</source>
          <date>
            <year>1986</year>
          </date>
          <fpage>307</fpage>
          <lpage>10</lpage>
          <issue>8476</issue>
          <volume>1</volume>
          <person-group person-group-type="author">
            <name>
              <surname>Bland</surname>
              <given-names>JM</given-names>
            </name>
            <name>
              <surname>Altman</surname>
              <given-names>DG</given-names>
            </name>
          </person-group>
        </element-citation>
      </ref>
      <ref id="B19">
        <mixed-citation>19. Almeida JA,    Campbell CSG, Pardono E, Sotero RC, Magalh&#227;es G, Sim&#245;es HG. Validade    de equa&#231;&#245;es de predi&#231;&#227;o em estimar o VO2max de brasileiros    jovens a partir do desempenho em corrida de 1.600m. Rev Bras Med Esporte. 2010;16(1):57-60.</mixed-citation>
        <element-citation publication-type="journal">
          <article-title>Validade de equa&#231;&#245;es de predi&#231;&#227;o em estimar o VO2max de brasileiros jovens a partir do desempenho em corrida de 1.600m</article-title>
          <source>Rev Bras Med Esporte</source>
          <date>
            <year>2010</year>
          </date>
          <fpage>57</fpage>
          <lpage>60</lpage>
          <issue>1</issue>
          <volume>16</volume>
          <person-group person-group-type="author">
            <name>
              <surname>Almeida</surname>
              <given-names>JA</given-names>
            </name>
            <name>
              <surname>Campbell</surname>
              <given-names>CSG</given-names>
            </name>
            <name>
              <surname>Pardono</surname>
              <given-names>E</given-names>
            </name>
            <name>
              <surname>Sotero</surname>
              <given-names>RC</given-names>
            </name>
            <name>
              <surname>Magalh&#227;es</surname>
              <given-names>G</given-names>
            </name>
            <name>
              <surname>Sim&#245;es</surname>
              <given-names>HG</given-names>
            </name>
          </person-group>
        </element-citation>
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    </ref-list>
  </back>
  <sub-article article-type="translation" id="TRen" xml:lang="en">
    <front-stub>
      <article-categories>
        <subj-group subj-group-type="heading">
          <subject>Original Articles</subject>
        </subj-group>
      </article-categories>
      <title-group>
        <article-title xml:lang="en">Validity of maximum heart rate prediction equations for children and adolescents</article-title>
      </title-group>
      <abstract xml:lang="en">
        <p>BACKGROUND: There are no studies in the literature to validate equations that predict maximum heart rate (HRmax) in children and adolescents. OBJECTIVE: To analyze the validity of the HRmax predictive equations "220 - age" and "208 - (0.7 x age)" in boys aged 10 and 16. METHODS: A progressive maximal exertion test was carried out in 69 apparently healthy boys aged 10 to 16. The initial test velocity was 9 km/h, with 1-km/h increments every three minutes. The test was maintained until maximum voluntary exertion was achieved, considering HRmax as the highest heart rate attained during the test. The measured HRmax was compared with the values predicted by the "220 - age" and "208 - (0.7 x age)" equations, using ANOVA for repeated measures. RESULTS: The mean values of HRmax (bpm) were: 200.2 &#177; 8.0 (measured), 207.4 &#177; 1.5 ("220 - age") and 199.2 &#177; 1.1 ("208 - (0.7 x age)"). The HRmax predicted by the "220 - age" equation was significantly higher (p &lt; 0.001) than the measured HRmax and the HRmax predicted by the ("208 - (0.7 x age)") equation. The correlation between the measured HRmax and age was not statistically significant (r = 0.096; p &gt; 0.05). CONCLUSION: The "220 - age" equation overestimated the measured HRmax and was not valid for this population. The "208 - (0.7 x age)" equation was valid for this population, showing results that were quite similar to those of measured HRmax. Future studies with larger sample sizes can verify whether the HRmax does not depend on age for this population, a situation in which the constant 200 bpm value would be more appropriate for HRmax.</p>
      </abstract>
      <kwd-group xml:lang="en">
        <kwd>Heart rate</kwd>
        <kwd>child</kwd>
        <kwd>adolescent</kwd>
        <kwd>heart</kwd>
      </kwd-group>
    </front-stub>
    <body>
      <p>
        <fn id="top-body2">
          <label>
            <bold>Validity of maximum heart rate prediction equations for children and adolescents</bold>
          </label>
          <p>
            <bold>Fabiana Andrade Machado<sup>I</sup>; Benedito S&#233;rgio Denadai<sup>II</sup></bold>
          </p>
        </fn>
      </p>
      <p><sup>I</sup>Departamento de Educa&#231;&#227;o F&#237;sica - Universidade Estadual de Maring&#225; (UEM) - Maring&#225;, PR</p>
      <p><sup>II</sup>Departamento de Educa&#231;&#227;o F&#237;sica - Universidade Estadual Paulista (UNESP) - Rio-Claro, SP - Brazil</p>
      <p>Mailing address</p>
      <p>
        <bold>ABSTRACT</bold>
      </p>
      <p><bold>BACKGROUND:</bold> There are no studies in the literature to validate equations that predict maximum heart rate (HRmax) in children and adolescents.</p>
      <p><bold>OBJECTIVE:</bold> To analyze the validity of the HRmax predictive equations "220 - age" and "208 - (0.7 x age)" in boys aged 10 and 16.</p>
      <p> Methods: A progressive maximal exertion test was carried out in 69 apparently healthy boys aged 10 to 16. The initial test velocity was 9 km/h, with 1-km/h increments every three minutes. The test was maintained until maximum voluntary exertion was achieved, considering HRmax as the highest heart rate attained during the test. The measured HRmax was compared with the values predicted by the "220 - age" and "208 - (0.7 x age)" equations, using ANOVA for repeated measures.</p>
      <p><bold>RESULTS:</bold> The mean values of HRmax (bpm) were: 200.2 &#177; 8.0 (measured), 207.4 &#177; 1.5 ("220 - age") and 199.2 &#177; 1.1 ("208 - (0.7 x age)"). The HRmax predicted by the "220 - age" equation was significantly higher (p &lt; 0.001) than the measured HRmax and the HRmax predicted by the ("208 - (0.7 x age)") equation. The correlation between the measured HRmax and age was not statistically significant (r = 0.096; p &gt; 0.05).</p>
      <p><bold>CONCLUSION:</bold> The "220 - age" equation overestimated the measured HRmax and was not valid for this population. The "208 - (0.7 x age)" equation was valid for this population, showing results that were quite similar to those of measured HRmax. Future studies with larger sample sizes can verify whether the HRmax does not depend on age for this population, a situation in which the constant 200 bpm value would be more appropriate for HRmax. (Arq Bras Cardiol. 2011; [online].ahead print, PP.0-0)</p>
      <p><bold>Keywords:</bold> Heart rate; child; adolescent; heart/physiology.</p>
      <p>
        <bold>Introduction</bold>
      </p>
      <p>Heart rate (HR) is considered an easily measurable physiological variable, being routinely used to evaluate cardiovascular response during exertion and recovery<sup>1,2</sup>. Maximum heart rate (HRmax), in turn, is considered one of the criteria to assess maximum exertion in exercise tests<sup>3,4</sup> and is broadly used when prescribing exercising intensity<sup>4-6</sup>.</p>
      <p>HRmax can be directly determined, usually with progressive maximal exertion protocols or indirectly, with the help of predictive equations that constitute a low-cost and easy-to-apply method of determining it<sup>1,7,8</sup>.</p>
      <p>Among the several equations proposed to predict HRmax, the most widely known is the equation "220 - age"<sup>4,9,10</sup>, which is curiously of unknown authorship, although it is very often cited as being the work of Karvonen et al<sup>11</sup>, although the work carried out by these authors did not involve the creation of this equation<sup>7,10,12,13</sup>. Another equation worth mentioning is "208 - (0.7 x age)" proposed by Tanaka et al<sup>4</sup>, which was developed in a meta-analysis study, after collecting data from the literature on 18,712 subjects.</p>
      <p>The main characteristic of these and other formulas used to predict HRmax is that all of them consider that the variable decreases with age<sup>14</sup>. Although this decrease is a general consensus for healthy adult men and women, it might not be true for children and adolescents, and even if it is, this decrease must be measured for this specific population, considering that the decrease rates of most equations was determined for a broad age range that only included children and adolescents in some cases<sup>9,15,16</sup>.</p>
      <p>Thus, considering to the importance of HRmax knowledge, so that a child or adolescent does not undergo training at an intensity that is neither appropriate nor planned and considering the lack in the literature, as far we know, of studies validating these two HRmax prediction equations for this population, the objective of the present study was to analyze the validity of the two HRmax prediction equations - "220 - age" and "208 - (0.7 x age)" - in boys aged 10 to 16 years.</p>
      <p>
        <bold>Methods</bold>
      </p>
      <p>
        <bold>Population</bold>
      </p>
      <p>Sixty-nine apparently healthy and active boys aged 10 to 16 years were enrolled in this study. The mean values &#177; Standard Deviations (SD) of age, height and body mass were: 12.6 &#177; 1.5 years; 152.7 &#177; 13.1 cm; 47.3 &#177; 14.1 kg, respectively; the age median (interquartile interval) was 12.1 years (11.4 - 13.8). Age was calculated centesimally, considering the birth date and the date when the test was performed. None of the participants participated in regular training programs. All procedures used in the study were previously approved by the local Research Ethics Committee. Participation was voluntary, with no bonus or onus for the subjects. Before the tests were performed, the children's parents or tutors were informed of all the procedures the children would be submitted to and signed the Free and Informed Consent Form regarding test participation.</p>
      <p>
        <bold>Maximal effort exercise test</bold>
      </p>
      <p>Prior to the exercise test on a treadmill, the participants visited to lab for an ergometer adaptation session and also to have anthropometric measurements (body mass and height) taken. The progressive maximal exertion test was carried out on a multiprogrammable treadmill (Inbrasport Super ATL, Porto Alegre, Brazil).</p>
      <p>After a three-minute warm-up at 5 km/h, the test was started at 9 km/h, with 1-km/h increments every three minutes. Constant inclination was maintained at 1% throughout the test. Heart rate (HR) was constantly monitored using a heart rate monitor (Polar Vantage XL). The test was maintained until voluntary exhaustion was attained and the participants were verbally encouraged to keep the test going for as long as possible. Maximum heart rate (HRmax) was defined as the highest HR achieved during the test<sup>4</sup>, being considered attained (valid) only when signs of intense exertion (hyperpnea, facial flushing, irregular steps) were observed<sup>17</sup>.</p>
      <p>
        <bold>Statistical analysis</bold>
      </p>
      <p>Data are presented as means &#177; standard deviations (SD) for all measured variables. The methods were compared using ANOVA for repeated measures with Bonferroni post hoc test. One-way ANOVA was used to compare the HRmax measured between age ranges. Pearson's correlation coefficient was used to correlate the measured values with the predicted ones of HRmax, as well as to verify the association between age and measured HRmax.</p>
      <p>Bland-Altman analysis<sup>18</sup> was used to calculate the limits of concordance between the measured HRmax and the that predicted by age; the level of significance was set at p &lt; 0.05.</p>
      <p>
        <bold>Results</bold>
      </p>
      <p><xref ref-type="table" rid="t1-body2">Table 1</xref> shows the measured and predicted values of HRmax for boys aged 10 to 16 years. The values demonstrated by the "220 - age" equation were significantly higher (p &lt; 0.001) than the measured values and those estimated by the "208 - (0.7 x age)", according to the ANOVA for repeated measures with Bonferroni <italic>post-hoc</italic> test. The correlation between the measured HRmax and the values predicted by the two equations was not statistically significant (p &gt; 0.05), showing the same coefficient of correlation for both equations (r = -0.096).</p>
      <table-wrap id="t1-body2">
        <graphic xlink:href="1678-4170-abc-97-02-0136-00078-gt01-en.jpg"/></table-wrap>
      <p><xref ref-type="fig" rid="f1-body2">Figure 1</xref> shows the mean values &#177; SD of HRmax for the different age ranges. One-way ANOVA did not show any significant different (p &gt; 0.05) between the age ranges. The correlation between the measured HRmax values and age was not statistically significant (r = 0.096; p &gt; 0.05). The absence of a tendency toward the increase or decrease of HRmax with age was observed visually. This was corroborated by the correlation between these variables, which was not statistically different from zero. HRmax variability for the several age ranges, represented by the SD in <xref ref-type="fig" rid="f1-body2">Figure 1</xref>, did not show any tendency toward increase or decrease with age, either. <xref ref-type="fig" rid="f1-body2">Figure 1</xref> also shows the high SD values observed, in which the lowest and the highest values were 5.1 and 9.0 bpm for the age ranges of 13-14 and 14-15 years, respectively.</p>
      <fig id="f1-body2">
        <graphic xlink:href="1678-4170-abc-97-02-0136-00078-gf01-en.jpg"/></fig>
      <p><xref ref-type="fig" rid="en_06911f02-body2">Figure 2</xref> shows the dispersion charts of measured HRmax values in the sample. It is noteworthy the high dispersion of data corroborated by the high SD shown in <xref ref-type="table" rid="t1-body2">Table 1</xref> for measured HRmax. It can also be observed that the values predicted by the "220 - age" equation, represented by the dashed line, show a tendency toward HRmax overestimation. Additionally, the values predicted by the "208 - (0.7 x age)" equation, represented by the dotted line, seem to be better adjusted to the measured HRmax mean.</p>
      <p content-type="asset">
        <fig id="en_06911f02-body2">
          <graphic xlink:href="1678-4170-abc-97-02-0136-00078-gf02-en.jpg"/></fig>
      </p>
      <p>The analysis of concordance between the measured HRmax and that predicted by the equations showed as bias (difference between the means) &#177; SD of differences: 7.1 &#177; 8.3 bpm ("220 - age") and -1.1 &#177; 8.2 bpm ("208 - (0.7 x age)"). It is worth mentioning the high bias of 7.1 bpm demonstrated by the difference between the means of values predicted by the "220 - age" equation and the measured HRmax values, which is in agreement with the overestimation of HRmax.</p>
      <p>
        <bold>Discussion</bold>
      </p>
      <p>The objective of the present study was to analyze the validity of two predictive equations for HRmax, "220 - age" and "208 - (0.7 x age)", in boys aged 10 to 16 years. The main finding was that the "220-age" equation overestimated HRmax values on average, thus demonstrating that it is not valid for this population, whereas the "208 - (0.7 x age)" equation showed to be valid for this pediatric population. Moreover, we verified that HRmax was independent from age for this specific population, although it is important to emphasize that the studied sample (n = 69) does not allow definitive conclusions to be drawn regarding this absence of association.</p>
      <p>According to Almeida et al<sup>19</sup>, predictive equations are valid when applied to populations with characteristics that are similar to those of the sample for which the equation was developed. Hence, although broadly applied, the "220 - age" equation requires the samples for which it was generated, considering the author remains unknown as well as the age range used when it was created. Regarding the "208 - (0.7 x age)" equation, it was generated by the linear regression of 18,712 subjects, especially between ages 20 and 70 years.</p>
      <p><xref ref-type="table" rid="t1-body2">Table 1</xref> showed that the mean value obtained with the "220 - age" equation was significantly higher (p &lt; 0.001) than the measured values and those estimated by the "208 - (0,7 x age)" equation. Therefore, the "220 - age" equation overestimates, on average, HRmax values. When applying the "220 - age" equation, one can verify that the predicted HRmax linearly decreases from 210 bpm at 10 years to 204 bpm at 16 years, overestimating the mean value of measured HRmax of 200.2 bpm throughout the age range 10 to 16 years. This can be verified visually in <xref ref-type="fig" rid="en_06911f02-body2">Figure 2</xref>. Contrarily to the "220 - age" equation, there was no significant difference (p &gt; 0.05) between the values predicted by the "208 - (0.7 x age)" equation and the measured values. The values predicted by the "208 - (0.7 x age)" equation decrease from 201 bpm at 10 years to 196.8 bpm at 16 years of age, showing values that are above (age &lt; 11.1 years) and below (age <underline>&gt;</underline> 11.1 years) the mean of 200.2 bpm of the measured HRmax.</p>
      <p><xref ref-type="fig" rid="f1-body2">Figure 1</xref> showed there was no significant difference (p &gt; 0.05) among the several age ranges for the measured HRmax. This absence of difference was corroborated by the fact that the correlation between the measured HRmax and age was not statistically significant. Therefore, the present study does not allow us to affirm that HRmax decreases with age in the studied population. Although the sample was not small (n = 69), it does not allow us to draw definitive conclusions regarding the absence of association between HRmax and age.</p>
      <p>Another interesting point demonstrated by the results was the high HRmax variability across the several age ranges, which was represented by the SD. This high SD showed no tendency toward increase or decrease with age, either. Both <xref ref-type="fig" rid="f1-body2">Figure 1</xref> and <xref ref-type="fig" rid="en_06911f02-body2">Figure 2</xref> show this high SD pattern for HRmax. It is noteworthy the fact that not only the measured HRmax showed a high SD, of around 8 bpm, but the difference between the means (bias) of predicted and measured values also showed an equally high SD.</p>
      <p>These values are in accordance with the literature, which reports a standard deviation value of 10 bpm for the predicted HRmax values<sup>4,10</sup>. When the bias and the SD of the difference between the predicted and measured HRmax values are analyzed, one can observe a broad limit of agreement for 95% of cases between measured values and those predicted by the "220 - age" (-9.5 to 23.7 bpm) and by the "208 - (0.7 x age)" equations (-17.5 to 15.3 bpm), which can result in errors of up to +12% and -9%, respectively, considering the mean HRmax of 202.2 bpm. Therefore, one can conclude that the high variability of HRmax is the main limiting factor for its prediction.</p>
      <p>
        <bold>Conclusion</bold>
      </p>
      <p>Based on these results, we conclude that the "220 - age" equation is not valid and appropriate for children and adolescents, as it overestimated, on average, the HRmax values for boys at the age range of 10 to 16 years. The "208 - (0.7 x age)" equation, in turn, showed results that were quite close to those of the measured HRmax and can be considered a valid equation for this pediatric age range. Moreover, if the age range is really independent from age for boys at this age range, which can be verified in future studies with larger sample sizes, the constant value of 200 bpm can become the most appropriate value for HRmax in this population.</p>
      <p>
        <bold>Potential Conflict of Interest</bold>
      </p>
      <p>No potential conflict of interest relevant to this article was reported.</p>
      <p>
        <bold>Sources of Funding</bold>
      </p>
      <p>There were no external funding sources for this study.</p>
      <p>
        <bold>Study Association</bold>
      </p>
      <p>This study is not associated with any post-graduation program.</p>
      <p>
        <bold>References</bold>
      </p>
    </body>
  </sub-article>
  <sub-article article-type="translation" id="TRes" xml:lang="es">
    <front-stub>
      <article-categories/>
      <title-group>
        <article-title xml:lang="es">Validez de las ecuaciones predictivas de la frecuencia card&#237;aca m&#225;xima para ni&#241;os y adolescentes</article-title>
      </title-group>
      <abstract xml:lang="es">
        <p>FUNDAMENTO: Ausencia de estudios en la literatura validando ecuaciones predictivas de la frecuencia card&#237;aca m&#225;xima (FCm&#225;x) en ni&#241;os y adolescentes. OBJETIVO: Analizar la validez de las ecuaciones predictivas de la FCm&#225;x "220 - edad" y "208 - (0,7 x edad)" en ni&#241;os con edades entre los 10 y los 16 a&#241;os. M&#201;TODOS: Un test progresivo de esfuerzo m&#225;ximo fue realizado en 69 ni&#241;os con edades entre los 10 y los 16 a&#241;os, aparentemente sanos y activos. La velocidad inicial del test fue de 9 km/h con incrementos de 1 km/h a cada tres minutos. El test se mantuvo hasta el agotamiento voluntario, considerando como FCm&#225;x la mayor frecuencia card&#237;aca alcanzada durante el test. La FCm&#225;x medida se compar&#243; con los valores previstos por las ecuaciones "220 - edad" y "208 - (0,7 x edad)" a trav&#233;s de ANOVA, medidas repetidas. RESULTADOS: Los valores promedios de la FCm&#225;x (lpm) fueron: 200,2 &#177; 8,0 (medida), 207,4 &#177; 1,5 ("220 - edad") y 199,2 &#177; 1,1 ("208 - (0,7 x edad)"). La FCm&#225;x de predicci&#243;n por la ecuaci&#243;n "220 - edad" fue significantemente mayor (p &lt; 0,001) que la FCm&#225;x medida y que la FCm&#225;x de predicci&#243;n por la ecuaci&#243;n ("208 - (0,7 x edad)"). La correlaci&#243;n entre la FCm&#225;x medida y la edad no fue estad&#237;sticamente significativa (r = 0,096; p &gt; 0,05). CONCLUSI&#211;N: La ecuaci&#243;n "220 -edad" supervalor&#243; la FCm&#225;x medida y no se mostr&#243; v&#225;lida para esa poblaci&#243;n. La ecuaci&#243;n "208 - (0,7 x edad)" fue v&#225;lida presentando resultados bastante pr&#243;ximos a la FCm&#225;x medida. Estudios futuros con muestras mayores podr&#225;n comprobar si la FCm&#225;x no depende de la edad para esa poblaci&#243;n, situaci&#243;n en que el valor constante de 200 lpm ser&#237;a el m&#225;s apropiado para la FCm&#225;x.</p>
      </abstract>
      <kwd-group xml:lang="es">
        <kwd>Frecuencia card&#237;aca</kwd>
        <kwd>ni&#241;o</kwd>
        <kwd>adolescente</kwd>
        <kwd>coraz&#243;n</kwd>
      </kwd-group>
    </front-stub>
    <body>
      <p>
        <bold>ART&#205;CULO ESPECIAL</bold>
      </p>
      <p>
        <fn id="nota_1-body3">
          <label>
            <bold>Validez de las ecuaciones predictivas de la frecuencia card&#237;aca m&#225;xima para ni&#241;os y adolescentes</bold>
          </label>
          <p>
            <bold>Fabiana Andrade Machado<sup>I</sup>; Benedito S&#233;rgio Denadai<sup>II</sup></bold>
          </p>
        </fn>
      </p>
      <p><sup>I</sup>Departamento de Educa&#231;&#227;o F&#237;sica - Universidade Estadual de Maring&#225; (UEM) - Maring&#225;, PR</p>
      <p><sup>II</sup>Departamento de Educa&#231;&#227;o F&#237;sica - Universidade Estadual Paulista (UNESP) - Rio-Claro, SP - Brasil</p>
      <p>Correspondencia</p>
      <p>
        <bold>RESUMEN</bold>
      </p>
      <p><bold>FUNDAMENTO:</bold> Ausencia de estudios en la literatura validando ecuaciones predictivas de la frecuencia card&#237;aca m&#225;xima (FCm&#225;x) en ni&#241;os y adolescentes.</p>
      <p><bold>OBJETIVO:</bold> Analizar la validez de las ecuaciones predictivas de la FCm&#225;x "220 - edad" y "208 - (0,7 x edad)" en ni&#241;os con edades entre los 10 y los 16 a&#241;os.</p>
      <p><bold>M&#201;TODOS:</bold> Un test progresivo de esfuerzo m&#225;ximo fue realizado en 69 ni&#241;os con edades entre los 10 y los 16 a&#241;os, aparentemente sanos y activos. La velocidad inicial del test fue de 9 km/h con incrementos de 1 km/h a cada tres minutos. El test se mantuvo hasta el agotamiento voluntario, considerando como FCm&#225;x la mayor frecuencia card&#237;aca alcanzada durante el test. La FCm&#225;x medida se compar&#243; con los valores previstos por las ecuaciones "220 - edad" y "208 - (0,7 x edad)" a trav&#233;s de ANOVA, medidas repetidas.</p>
      <p><bold>RESULTADOS:</bold> Los valores promedios de la FCm&#225;x (lpm) fueron: 200,2 &#177; 8,0 (medida), 207,4 &#177; 1,5 ("220 - edad") y 199,2 &#177; 1,1 ("208 - (0,7 x edad)"). La FCm&#225;x de predicci&#243;n por la ecuaci&#243;n "220 - edad" fue significantemente mayor (p &lt; 0,001) que la FCm&#225;x medida y que la FCm&#225;x de predicci&#243;n por la ecuaci&#243;n ("208 - (0,7 x edad)"). La correlaci&#243;n entre la FCm&#225;x medida y la edad no fue estad&#237;sticamente significativa (r = 0,096; p &gt; 0,05).</p>
      <p><bold>CONCLUSI&#211;N:</bold> La ecuaci&#243;n "220 -edad" supervalor&#243; la FCm&#225;x medida y no se mostr&#243; v&#225;lida para esa poblaci&#243;n. La ecuaci&#243;n "208 - (0,7 x edad)" fue v&#225;lida presentando resultados bastante pr&#243;ximos a la FCm&#225;x medida. Estudios futuros con muestras mayores podr&#225;n comprobar si la FCm&#225;x no depende de la edad para esa poblaci&#243;n, situaci&#243;n en que el valor constante de 200 lpm ser&#237;a el m&#225;s apropiado para la FCm&#225;x.</p>
      <p><bold>Palabras clave:</bold> Frecuencia card&#237;aca, ni&#241;o, adolescente, coraz&#243;n/fisiolog&#237;a.</p>
      <p>
        <bold>Introducci&#243;n</bold>
      </p>
      <p>La frecuencia card&#237;aca (FC) est&#225; considerada como una variable fisiol&#243;gica de f&#225;cil mensuraci&#243;n, siendo utilizada como rutina para evaluar la respuesta cardiovascular durante el esfuerzo y la recuperaci&#243;n<sup>1,2</sup>. La frecuencia card&#237;aca m&#225;xima (FCm&#225;x) a su vez, est&#225; considerada como uno de los criterios de verificaci&#243;n del esfuerzo m&#225;ximo en test ergom&#233;tricos<sup>3,4 </sup>y es extensamente utilizada en la prescripci&#243;n de la intensidad de los ejercicios<sup>4-6</sup>.</p>
      <p>La determinaci&#243;n de la FCm&#225;x puede ser hecha de manera directa, generalmente por medio de protocolos progresivos de esfuerzo m&#225;ximo, o puede ser hecha indirectamente, con la ayuda de ecuaciones predictivas que constituyen una manera de conseguir el bajo coste y son de f&#225;cil aplicaci&#243;n<sup>1,7,8</sup>.</p>
      <p>Entre las diversas ecuaciones propuestas para predecir la FCm&#225;x, la de mayor destaque por ser ampliamente conocida es la ecuaci&#243;n "220 - edad"<sup>4,9,10</sup>, a la que curiosamente no se le conoce la autor&#237;a, a pesar de que muchas veces haya sido citada como siendo su autor Karvonen et al<sup>11</sup>, incluso cuando el trabajo elaborado por esos autores no haya involucrado la elaboraci&#243;n de esa ecuaci&#243;n<sup>7,10,12,13</sup>. Otra ecuaci&#243;n que merece destaque es "208 - (0,7 x edad)" que fue propuesta por Tanaka et al<sup>4</sup>, y desarrollada en un estudio de metan&#225;lisis recolectando datos en la literatura de 18.712 sujetos.</p>
      <p>La principal caracter&#237;stica de esas y de otras f&#243;rmulas presentadas para predecir la FCm&#225;x, es la de que todas consideran que esa variable disminuye con la edad<sup>14</sup>. A pesar de que ese descenso sea un consenso general para hombres y mujeres y adultos sanos, &#233;l puede no ser verdadero para ni&#241;os y adolescentes, e incluso si&#233;ndolo, ese descenso debe ser mensurado para esa poblaci&#243;n espec&#237;fica, visto que la tasa de descenso de la mayor&#237;a de las ecuaciones estuvo determinada para una amplia franja etaria, englobando solamente y en algunos casos, a ni&#241;os y adolescentes<sup>9,15,16</sup>.</p>
      <p>Por tanto, y en raz&#243;n de la importancia del conocimiento de la FCm&#225;x para que un ni&#241;o o adolescente no entrene en una intensidad diferente a la apropiada y planificada, y considerando la inexistencia en la literatura, seg&#250;n nuestro conocimiento, de estudios validando esas dos ecuaciones predictivas de la FCm&#225;x para esa poblaci&#243;n, el objetivo de este estudio fue analizar la validez de las ecuaciones predictivas de la FCm&#225;x "220 - edad" y "208 - (0,7 x edad)" en ni&#241;os con edades entre los 10 y los 16 a&#241;os.</p>
      <p>
        <bold>M&#233;todo</bold>
      </p>
      <p>
        <bold>Poblaci&#243;n</bold>
      </p>
      <p>Sesenta y nueve ni&#241;os con edades entre 10 y 16 a&#241;os, aparentemente sanos y activos, participaron en este estudio. Los valores promedios &#177; desviaci&#243;n est&#225;ndar (DP) de la edad, estatura y masa corporal fueron: 12,6 &#177; 1,5 a&#241;os; 152,7 &#177; 13,1 cm; 47,3 &#177; 14,1 kg, respectivamente; la mediana de la edad (intervalo intercuartil), fue de 12,1 a&#241;os (11,4 - 13,8). La edad se calcul&#243; de forma centesimal considerando la fecha de nacimiento y la fecha de realizaci&#243;n del test. Ninguno de los participantes estaba en programas sistem&#225;ticos de entrenamiento. Todos los procedimientos adoptados fueron previamente aprobados por el Comit&#233; de &#201;tica en Investigaci&#243;n Local. La participaci&#243;n fue voluntaria y estuvo exenta de todo tipo de bonos o encargos para los participantes. Antes de iniciar los test, los responsables estuvieron concientes de todos los procedimientos a los que los ni&#241;os se someter&#237;an, y firmaron el T&#233;rmino de Consentimiento Informado referente a su participaci&#243;n en los test.</p>
      <p>
        <bold>Test progresivo de esfuerzo m&#225;ximo</bold>
      </p>
      <p>Antes de la realizaci&#243;n del test de esfuerzo en cinta sin fin (o tapiz rodante), los participantes realizaron una visita al laboratorio para una sesi&#243;n de adaptaci&#243;n al erg&#243;metro y tambi&#233;n para la verificaci&#243;n de las medidas antropom&#233;tricas (masa corporal y estatura). El test progresivo de esfuerzo m&#225;ximo fue realizado en una cinta sin fin de multiprogramaci&#243;n (Inbrasport Super ATL, Porto Alegre, Brasil). Despu&#233;s del calentamiento inicial de tres minutos a 5 km/h, el test se inici&#243; a 9 km/h, con incrementos de 1 km/h a cada tres minutos. Durante todo el test se mantuvo una inclinaci&#243;n constante referente a 1%. La frecuencia card&#237;aca (FC) fue constantemente monitorizada por medio de un frecuenc&#237;metro (Polar Vantage XL). El test se mantuvo hasta el agotamiento voluntario, y a los participantes se les motiv&#243; verbalmente para que se mantuvieran haciendo ejercicios durante el mayor tiempo posible. La FCm&#225;x fue definida como la mayor FC alcanzada durante el test<sup>4</sup>, siendo considerada alcanzada (v&#225;lida), apenas cuando fuesen observadas se&#241;ales de esfuerzo intenso (hiperpnea, enrojecimiento facial, descomp&#225;s en la marcha)<sup>17</sup>.</p>
      <p>
        <bold>An&#225;lisis estad&#237;stico</bold>
      </p>
      <p>Los datos fueron presentados como promedio &#177; desviaci&#243;n est&#225;ndar (DP), para todas las variables mensuradas. Los m&#233;todos se compararon utilizando ANOVA para medidas repetidas con el test <italic>post-hoc</italic> de Bonferroni. La ANOVA <italic>one-way</italic> fue utilizada para comparar la FCm&#225;x medida entre las franjas etarias. El coeficiente de correlaci&#243;n de Pearson fue utilizado tanto para relacionar los valores medidos con los valores de predicci&#243;n de la FCm&#225;x, como para verificar la relaci&#243;n entre la edad y la FCm&#225;x medida. El an&#225;lisis de Bland- Altman18 se us&#243; para calcular los l&#237;mites de concordancia entre la FCm&#225;x medida y la predicci&#243;n por edad. El nivel de significancia adoptado fue de p &lt; 0,05.</p>
      <p>
        <bold>Resultado</bold>
      </p>
      <p>En la <xref ref-type="table" rid="tab1-body3">tabla 1</xref> aparecen los valores medidos y con predicci&#243;n de la FCm&#225;x para los ni&#241;os con edades entre 10 y 16 a&#241;os. Los valores presentados por la ecuaci&#243;n "220 - edad", fueron significativamente mayores (p &lt; 0,001) que los valores medidos y que los valores estimados por la ecuaci&#243;n "208 - (0,7 x edad)", conforme a la ANOVA para medidas repetidas con el test post-hoc de Bonferroni. La correlaci&#243;n entre los valores de la FCm&#225;x medida, y los valores de predicci&#243;n para las dos ecuaciones, no fue estad&#237;sticamente significativa (p &gt; 0,05) presentando el mismo coeficiente de correlaci&#243;n para ambas ecuaciones (r = -0,096).</p>
      <table-wrap id="tab1-body3">
        <graphic xlink:href="1678-4170-abc-97-02-0136-00078-gt01-es.jpg"/></table-wrap>
      <p>La <xref ref-type="fig" rid="es_a07fig01-body3">figura 1</xref> presenta los valores promedios &#177; DP de la FCm&#225;x medida para las diferentes franjas etarias. ANOVA one-way no demostr&#243; diferencia significativa (p &gt; 0,05) entre las franjas etarias. La correlaci&#243;n entre los valores de la FCm&#225;x medida y la edad, no fue estad&#237;sticamente significativa (r = 0,096; p &gt; 0,05). Visualmente comprobamos la ausencia de una tendencia al aumento o a la disminuci&#243;n de la FCm&#225;x con la edad. Eso fue corroborado por la correlaci&#243;n entre esas variables, la cual no fue estad&#237;sticamente diferente a cero. La variabilidad de la FCm&#225;x para las diversas franjas etarias representada por el DP en la <xref ref-type="fig" rid="es_a07fig01-body3">figura 1</xref>, tampoco present&#243; ninguna tendencia a aumentar o disminuir con la edad. Tambi&#233;n verificamos en la <xref ref-type="fig" rid="es_a07fig01-body3">figura 1</xref>, los elevados valores de DP encontrados, en que el menor y el mayor DP fue de 5,1 y 9,0 lpm para las franjas etarias entre 13-14 y 14-15 a&#241;os, respectivamente.</p>
      <p content-type="asset">
        <fig id="es_a07fig01-body3">
          <graphic xlink:href="1678-4170-abc-97-02-0136-00078-gf01-es.jpg"/></fig>
      </p>
      <p>La <xref ref-type="fig" rid="es_a07fig02-body3">figura 2</xref> hace referencia al gr&#225;fico de dispersi&#243;n de los valores de la FCm&#225;x medida de la muestra. Destacamos nuevamente la alta dispersi&#243;n de los datos corroborada por el alto DP presentado en la <xref ref-type="table" rid="tab1-body3">tabla 1</xref> para la FCm&#225;x medida. Tambi&#233;n verificamos que los valores de predicci&#243;n por la ecuaci&#243;n "220 - edad", representados por la l&#237;nea con trazos, presentan la tendencia de superestimar la FCm&#225;x. A su vez, los valores de predicci&#243;n por la ecuaci&#243;n "208 - (0,7 x edad)", representados por la l&#237;nea de puntos, parece que se ajustan mucho mejor al promedio de la FCm&#225;x medida.</p>
      <p content-type="asset">
        <fig id="es_a07fig02-body3">
          <graphic xlink:href="1678-4170-abc-97-02-0136-00078-gf02-es.jpg"/></fig>
      </p>
      <p>El an&#225;lisis de concordancia entre la FCm&#225;x medida y la predicci&#243;n por la f&#243;rmulas, present&#243; como sesgo (diferencia entre los promedios) &#177; desviaci&#243;n est&#225;ndar de las diferencias: 7,1 &#177; 8,3 lpm ("220 - edad") y -1,1 &#177; 8,2 lpm ("208 - (0,7 x edad)"). Destacamos el alto sesgo de 7,1 lpm presentado en funci&#243;n de la diferencia entre los promedios de los valores de predicci&#243;n por la ecuaci&#243;n "220 - edad" y los valores de la FCm&#225;x medida, lo cual conduce a una superestimaci&#243;n de la FCm&#225;x.</p>
      <p>
        <bold>Discusi&#243;n</bold>
      </p>
      <p>El objetivo de este estudio fue analizar la validez de las ecuaciones predictivas de la FCm&#225;x "220 - edad" y "208 - (0,7 x edad)" en ni&#241;os con edades entre los 10 y los 16 a&#241;os. El principal hallazgo fue que la ecuaci&#243;n "220 - edad" supervalor&#243; en el promedio los valores de la FCm&#225;x, no siendo v&#225;lida para esa poblaci&#243;n, y la ecuaci&#243;n "208 - (0,7 x edad)" s&#237; que fue v&#225;lida para esa poblaci&#243;n pedi&#225;trica. Adem&#225;s, verificamos que la FCm&#225;x fue independiente de la edad para esa poblaci&#243;n espec&#237;fica, destacando que la muestra estudiada (n = 69), no permite conclusiones definitivas en cuanto a esa independencia de relaci&#243;n.</p>
      <p>De acuerdo con Almeida et al<sup>19</sup>, las ecuaciones predictivas son v&#225;lidas cuando se aplican en poblaciones con caracter&#237;sticas similares a las de la muestra a partir de la cual la ecuaci&#243;n se gener&#243;. As&#237;, y a pesar de su extensa aplicaci&#243;n, la f&#243;rmula "220 - edad", necesita muestras para saber d&#243;nde se gener&#243;, habida cuenta del desconocimiento de su autor y de la franja etaria utilizada para su elaboraci&#243;n. Ya la ecuaci&#243;n "208 -(0,7 x edad)", fue generada por la regresi&#243;n lineal de 18.712 sujetos especialmente entre las edades de 20 y 70 a&#241;os.</p>
      <p>En la <xref ref-type="table" rid="tab1-body3">tabla 1</xref> verificamos que el valor promedio de la ecuaci&#243;n "220 -edad" fue significantemente mayor (p &lt; 0,001), que los valores medidos y que los valores estimados por la ecuaci&#243;n "208 - (0,7 x edad)". Por tanto, la ecuaci&#243;n "220 - edad" supervalora, en el promedio, los valores de la FCm&#225;x. Aplicando la ecuaci&#243;n "220 - edad", comprobamos que FCm&#225;x hace una predicci&#243;n de retroceso lineal de los 210 lpm a los 10 a&#241;os, para los 204 lpm a los 16 a&#241;os, supervalorando, a lo largo de la franja etaria de 10 a 16 a&#241;os, el valor promedio de la FCm&#225;x medida de 200,2 lpm. Esa constataci&#243;n puede hacerse visualmente en la <xref ref-type="fig" rid="es_a07fig02-body3">figura 2</xref>. Al contrario de la ecuaci&#243;n "220 - edad", no hubo diferencia significativa (p &gt; 0,05) entre los valores de predicci&#243;n por la ecuaci&#243;n "208 - (0,7 x edad)" y los valores medidos. Los valores de predicci&#243;n por la ecuaci&#243;n "208 - (0,7 x edad)" retroceden de 201 lpm a los 10 a&#241;os, para 196,8 lpm a los 16 a&#241;os de edad, presentando valores por encima (edad &lt; 11,1 a&#241;os) y por debajo (edad <underline>&gt;</underline> 11,1 a&#241;os), del promedio de 200,2 lpm de la FCm&#225;x medida.</p>
      <p>Por medio de la <xref ref-type="fig" rid="es_a07fig01-body3">figura 1</xref>, verificamos que no hubo diferencia significativa (p &gt; 0,05) entre las diversas franjas etarias para la FCm&#225;x medida. Fue un factor de comprobaci&#243;n para esa ausencia de diferencia, el hecho de que la correlaci&#243;n entre la FCm&#225;x medida y la edad no haya sido estad&#237;sticamente significativa. Por tanto, por medio de este estudio, no fue posible afirmar que la FCm&#225;x disminuya con la edad para la poblaci&#243;n aqu&#237; estudiada. Y pese a que esa muestra no sea peque&#241;a (n = 69), todav&#237;a no permite obtener conclusiones definitivas en cuanto a la ausencia de relaci&#243;n entre la FCm&#225;x y la edad.</p>
      <p>Otro punto interesante presentado en los resultados fue la alta variabilidad de la FCm&#225;x para las diversas franjas etarias, variabilidad representada por el DP. Ese elevado DP tampoco present&#243; ninguna tendencia a aumentar o disminuir con la edad. Tanto en la <xref ref-type="fig" rid="es_a07fig01-body3">figura 1</xref> como en la <xref ref-type="fig" rid="es_a07fig02-body3">figura 2</xref>, se puede verificar ese est&#225;ndar de un elevado DP para la FCm&#225;x. Remarcamos el hecho de que no solamente la FCm&#225;x medida tuvo un alto DP en el umbral de 8 lpm, sino tambi&#233;n que la diferencia entre los promedios (sesgos), de los valores de predicci&#243;n y los medidos, present&#243; un DP en ese mismo nivel. Esos valores est&#225;n a tono con la literatura, que relata una desviaci&#243;n est&#225;ndar en el umbral de 10 lpm para los valores de predicci&#243;n de la FCm&#225;x<sup>4,10</sup>. Si analizamos el sesgo y el DP de la diferencia entre los valores de la FCm&#225;x de predicci&#243;n y los medidos, verificamos un amplio l&#237;mite de concordancia para un 95% de los casos entre los valores medidos y los predictivos por la ecuaci&#243;n "220 -edad" (-9,5 a 23,7 lpm), y por la ecuaci&#243;n "208 -(0,7 x edad)" (-17,5 a 15,3 lpm), los cuales podr&#225;n traer resultados equivocados de hasta +12% y -9%, respectivamente, considerando la FCm&#225;x promedio de 202,2 lpm. Frente a eso, tenemos que la alta variabilidad de la FCm&#225;x aparece como el principal factor limitante para su predicci&#243;n.</p>
      <p>
        <bold>Conclusi&#243;n</bold>
      </p>
      <p>Sobre la base de esos resultados podemos concluir, que la ecuaci&#243;n "220 -edad" no es v&#225;lida ni apropiada para ni&#241;os y adolescentes, porque supervalor&#243; en su promedio, los valores de la FCm&#225;x para ni&#241;os en la franja etaria de 10 a 16 a&#241;os. La ecuaci&#243;n "208 - (0,7 x edad)" a su vez, present&#243; resultados bastante cercanos a la FCm&#225;x medida, y puede ser considerada una ecuaci&#243;n v&#225;lida para esa poblaci&#243;n pedi&#225;trica. Por a&#241;adidura, en el caso de que la FCm&#225;x sea realmente independiente de la edad para ni&#241;os en esa franja etaria, (lo que casi no podr&#225; ser comprobado en futuros estudios con muestras m&#225;s extensas), el valor que consta de 200 lpm podr&#225; convertirse en el valor m&#225;s apropiado para la FCm&#225;x de esa poblaci&#243;n.</p>
      <p>
        <bold>Potencial Conflicto de Intereses</bold>
      </p>
      <p>Declaro no haber conflicto de intereses pertinentes.</p>
      <p>
        <bold>Fuentes de Financiaci&#243;n</bold>
      </p>
      <p>El presente estudio no tuve fuentes de financiaci&#243;n externas.</p>
      <p>
        <bold>Vinculaci&#243;n Acad&#233;mica</bold>
      </p>
      <p>No hay vinculaci&#243;n de este estudio a programas de postgrado.</p>
      <p>
        <bold>Referencias</bold>
      </p>
    </body>
  </sub-article>
</article>
