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  <front>
    <journal-meta>
      <journal-id journal-id-type="nlm-ta">Arq Bras Cardiol</journal-id>
      <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>
    </journal-meta>
    <article-meta>
      <article-id specific-use="scielo-v3" pub-id-type="publisher-id">G57TD6ysWgZ4kWmT66r5ZXD</article-id>
      <article-id specific-use="scielo-v2" pub-id-type="publisher-id">S0066-782X2026000704201</article-id>
      <article-id pub-id-type="other">04201</article-id>
      <article-id pub-id-type="doi">10.36660/abc.20260239</article-id>
      <article-categories>
        <subj-group subj-group-type="heading">
          <subject>Carta ao Editor</subject>
        </subj-group>
      </article-categories>
      <title-group>
        <article-title>Modelos Geom&#233;tricos na Bifurca&#231;&#227;o do Tronco da Coron&#225;ria Esquerda: Precis&#227;o Matem&#225;tica versus Complexidade Biol&#243;gica</article-title>
      </title-group>
      <contrib-group>
        <contrib contrib-type="author">
          <contrib-id contrib-id-type="orcid">0009-0005-4268-2964</contrib-id>
          <name>
            <surname>Ara&#250;jo</surname>
            <given-names>Guilherme O.</given-names>
          </name>
          <xref ref-type="aff" rid="aff1">
            <sup>1</sup>
          </xref>
        </contrib>
        <contrib contrib-type="author">
          <contrib-id contrib-id-type="orcid">0000-0003-1273-1823</contrib-id>
          <name>
            <surname>Ribeiro</surname>
            <given-names>Henrique Barbosa</given-names>
          </name>
          <xref ref-type="aff" rid="aff1">
            <sup>1</sup>
          </xref>
        </contrib>
      </contrib-group>
      <aff id="aff1">
        <label>1</label>
        <institution content-type="orgdiv2">Hospital das Cl&#237;nicas</institution>
        <institution content-type="orgdiv1">Faculdade de Medicina</institution>
        <institution content-type="orgname">Universidade de S&#227;o Paulo</institution>
        <addr-line>
          <named-content content-type="city">S&#227;o Paulo</named-content>
          <named-content content-type="state">SP</named-content>
        </addr-line>
        <country country="BR">Brasil</country>
        <institution content-type="original">Instituto do Cora&#231;&#227;o do Hospital das Cl&#237;nicas da Faculdade de Medicina da Universidade de S&#227;o Paulo, S&#227;o Paulo, SP &#8211; Brasil</institution>
      </aff>
      <author-notes>
        <corresp id="c01"><label>Correspond&#234;ncia:</label> Henrique Barbosa Ribeiro Instituto do Cora&#231;&#227;o do Hospital das Cl&#237;nicas da Faculdade de Medicina da Universidade de S&#227;o Paulo - Av. Dr. En&#233;as de Carvalho Aguiar, 44. CEP 05508-900, S&#227;o Paulo, SP &#8211; Brasil E-mail: <email>hbribeiro@gmail.com</email>, <email>henrique.ribeiro@hc.fm.usp.br</email> </corresp>
      </author-notes>
      <pub-date date-type="pub" publication-format="electronic">
        <day>03</day>
        <month>08</month>
        <year>2026</year>
      </pub-date>
      <pub-date date-type="collection" publication-format="electronic">
        <year>2026</year>
      </pub-date>
      <volume>123</volume>
      <issue>7</issue>
      <elocation-id>e20260239</elocation-id>
      <history>
        <date date-type="received">
          <day>20</day>
          <month>03</month>
          <year>2026</year>
        </date>
        <date date-type="rev-recd">
          <day>25</day>
          <month>03</month>
          <year>2026</year>
        </date>
        <date date-type="accepted">
          <day>25</day>
          <month>03</month>
          <year>2026</year>
        </date>
      </history>
      <permissions>
        <license license-type="open-access" xlink:href="https://creativecommons.org/licenses/by/4.0/" xml:lang="pt">
          <license-p>Este &#233; um artigo de acesso aberto distribu&#237;do sob os termos da licen&#231;a de atribui&#231;&#227;o pelo Creative Commons</license-p>
        </license>
      </permissions>
      <related-article related-article-type="article" id="r1" xlink:href="10.36660/abc.20250605" ext-link-type="doi"/>
      <kwd-group xml:lang="pt">
        <title>Palavras-chave:</title>
        <kwd>Angiografia Coron&#225;ria</kwd>
        <kwd>Ultrassonografia de Interven&#231;&#227;o</kwd>
        <kwd>Angioplastia Coron&#225;ria com Bal&#227;o</kwd>
      </kwd-group>
      <counts>
        <fig-count count="0"/>
        <table-count count="0"/>
        <equation-count count="0"/>
        <ref-count count="11"/>
      </counts>
    </article-meta>
  </front>
  <body>
    <p>A geometria das bifurca&#231;&#245;es coron&#225;rias desempenha papel fundamental na fisiopatologia da aterosclerose e no planejamento da interven&#231;&#227;o coron&#225;ria percut&#226;nea. Entre essas estruturas, a bifurca&#231;&#227;o do tronco da coron&#225;ria esquerda (TCE) assume relev&#226;ncia singular, n&#227;o apenas pelo amplo territ&#243;rio mioc&#225;rdico irrigado, mas tamb&#233;m pela complexa intera&#231;&#227;o entre as for&#231;as hemodin&#226;micas, o remodelamento vascular e a progress&#227;o da doen&#231;a ateroscler&#243;tica. Nesse contexto, modelos geom&#233;tricos que estimam o di&#226;metro do vaso principal a partir das dimens&#245;es dos ramos distais foram propostos como ferramentas auxiliares para o dimensionamento vascular e para a otimiza&#231;&#227;o das estrat&#233;gias intervencionistas. Contudo, faltam estudos comparando, de forma sistem&#225;tica, esses modelos com o aux&#237;lio de ferramentas de imagem intravascular, que s&#227;o mais precisas na mensura&#231;&#227;o das art&#233;rias coron&#225;rias.<sup><xref ref-type="bibr" rid="B1">1</xref>-<xref ref-type="bibr" rid="B3">3</xref></sup></p>
    <p>Garzon et al.<sup><xref ref-type="bibr" rid="B1">1</xref></sup> avaliaram a confiabilidade dos modelos de Murray, Finet e Huo-Kassab na estimativa das dimens&#245;es da bifurca&#231;&#227;o do TCE em art&#233;rias com aterosclerose moderada, utilizando angiografia coron&#225;ria quantitativa (QCA) e ultrassom intracoron&#225;rio (IVUS) como m&#233;todos de refer&#234;ncia.<sup><xref ref-type="bibr" rid="B1">1</xref></sup> Os autores demonstram que os modelos de Murray e Huo-Kassab apresentam maior acur&#225;cia e precis&#227;o em compara&#231;&#227;o ao modelo de Finet, com desempenho particularmente superior do modelo de Murray quando o IVUS foi utilizado como padr&#227;o de refer&#234;ncia. Esses achados est&#227;o em conson&#226;ncia com a robustez te&#243;rica dos modelos baseados em princ&#237;pios de din&#226;mica dos fluidos e otimiza&#231;&#227;o energ&#233;tica, em contraste com o modelo de Finet, derivado empiricamente da geometria fractal angiogr&#225;fica.<sup><xref ref-type="bibr" rid="B1">1</xref>-<xref ref-type="bibr" rid="B5">5</xref></sup></p>
    <p>A superioridade do modelo de Murray observada neste estudo &#233; consistente com evid&#234;ncias experimentais e computacionais que sugerem que a rela&#231;&#227;o c&#250;bica proposta por Murray, mais simples do ponto de vista matem&#225;tico, pode ser menos sens&#237;vel a varia&#231;&#245;es nos di&#226;metros dos ramos distais.<sup><xref ref-type="bibr" rid="B2">2</xref>,<xref ref-type="bibr" rid="B4">4</xref></sup> Por outro lado, embora o modelo de Huo-Kassab incorpore princ&#237;pios fisiol&#243;gicos semelhantes, sua formula&#231;&#227;o matem&#225;tica mais complexa pode amplificar pequenas imprecis&#245;es nas medidas dos ramos distais, particularmente em art&#233;rias com aterosclerose, nas quais o remodelamento vascular altera a geometria original. Esse achado suscita hip&#243;teses relevantes acerca da robustez de modelos matematicamente mais simples em cen&#225;rios cl&#237;nicos caracterizados por variabilidade anat&#244;mica e pela presen&#231;a de doen&#231;a ateroscler&#243;tica.</p>
    <p>Outro aspecto relevante do estudo &#233; a diferen&#231;a sistem&#225;tica entre as medidas obtidas por IVUS e QCA, com o IVUS tendendo a fornecer di&#226;metros maiores. Essas diferen&#231;as refletem as limita&#231;&#245;es conhecidas da angiografia bidimensional na avalia&#231;&#227;o do l&#250;men coron&#225;rio e s&#227;o concordantes com estudos pr&#233;vios que demonstram maior acur&#225;cia da imagem intracoron&#225;ria na caracteriza&#231;&#227;o do di&#226;metro vascular e da carga de placa.<sup><xref ref-type="bibr" rid="B6">6</xref>-<xref ref-type="bibr" rid="B10">10</xref></sup> Nesse sentido, o IVUS permanece como padr&#227;o de refer&#234;ncia para o dimensionamento do TCE, estando associado a melhores desfechos cl&#237;nicos quando utilizado para guiar interven&#231;&#245;es, em especial nos procedimentos de maior complexidade, incluindo o TCE.<sup><xref ref-type="bibr" rid="B6">6</xref>-<xref ref-type="bibr" rid="B8">8</xref></sup></p>
    <p>Apesar do desempenho relativamente satisfat&#243;rio, nenhum dos modelos reproduziu com exatid&#227;o as dimens&#245;es observadas, com diferen&#231;as que podem atingir magnitudes clinicamente relevantes. Em interven&#231;&#245;es no TCE, discrep&#226;ncias aparentemente pequenas podem resultar em subexpans&#227;o ou superdimensionamento dos stents, aumentando o risco de malaposi&#231;&#227;o, dissec&#231;&#227;o e reestenose, eventos associados a piores desfechos cl&#237;nicos.<sup><xref ref-type="bibr" rid="B5">5</xref>-<xref ref-type="bibr" rid="B7">7</xref></sup> Nesse sentido, embora matematicamente elegantes, os modelos geom&#233;tricos devem ser interpretados como ferramentas auxiliares, e n&#227;o como substitutos da avalia&#231;&#227;o direta por imagem intracoron&#225;ria.</p>
    <p>Estudos pr&#233;vios demonstram que nenhuma lei de escala &#233; capaz de equilibrar completamente as for&#231;as hemodin&#226;micas em bifurca&#231;&#245;es coron&#225;rias reais, o que ressalta que tais modelos representam aproxima&#231;&#245;es da complexa intera&#231;&#227;o entre anatomia, fluxo e doen&#231;a ateroscler&#243;tica.<sup><xref ref-type="bibr" rid="B4">4</xref>,<xref ref-type="bibr" rid="B11">11</xref></sup> Ainda assim, em ambientes com acesso limitado &#224; imagem intracoron&#225;ria, essas ferramentas podem contribuir para a identifica&#231;&#227;o de desvios geom&#233;tricos e fornecer estimativas iniciais para o dimensionamento vascular. Esse aspecto torna ainda mais relevante o presente estudo em pa&#237;ses em desenvolvimento como o Brasil, com acesso limitado a ferramentas de imagem intravascular.</p>
    <p>&#192; medida que a cardiologia intervencionista evolui em dire&#231;&#227;o &#224; personaliza&#231;&#227;o terap&#234;utica, a integra&#231;&#227;o entre modelagem computacional, imagem intracoron&#225;ria e avalia&#231;&#227;o fisiol&#243;gica configura-se como um caminho promissor para o planejamento de interven&#231;&#245;es em bifurca&#231;&#245;es complexas. Estudos futuros com amostras maiores, reconstru&#231;&#245;es tridimensionais e incorpora&#231;&#227;o de vari&#225;veis relacionadas &#224; carga ateroscler&#243;tica poder&#227;o esclarecer se modelos ajustados &#224; doen&#231;a arterial podem proporcionar maior precis&#227;o e relev&#226;ncia cl&#237;nica.</p>
    <p>Apesar das limita&#231;&#245;es inerentes ao estudo de Garzon et al.<sup><xref ref-type="bibr" rid="B1">1</xref></sup>, incluindo o tamanho amostral relativamente reduzido, a an&#225;lise restrita a bifurca&#231;&#245;es do TCE com doen&#231;a arterial coron&#225;ria de grau moderado e a aus&#234;ncia de segmentos livres de doen&#231;a ou com carga ateroscler&#243;tica extensa &#8212; o trabalho acrescenta contribui&#231;&#245;es relevantes &#224; literatura. Os resultados demonstram que, em bifurca&#231;&#245;es do TCE com aterosclerose moderada, os modelos geom&#233;tricos de Murray e de Huo-Kassab apresentam melhor desempenho em rela&#231;&#227;o ao modelo de Finet, com destaque para o modelo de Murray, quando comparados &#224;s medidas obtidas por IVUS.</p>
    <p>Todavia, entre a eleg&#226;ncia dos modelos matem&#225;ticos e a complexidade da biologia vascular, permanece clara a necessidade de integrar tais constructos te&#243;ricos &#224;s modalidades contempor&#226;neas de imagem intravascular, de modo a aprimorar a precis&#227;o do planejamento e a seguran&#231;a das interven&#231;&#245;es coron&#225;rias. Nesse contexto, o estudo tamb&#233;m refor&#231;a o papel central da imagem intravascular na pr&#225;tica cl&#237;nica, em conson&#226;ncia com as recentes atualiza&#231;&#245;es das diretrizes internacionais, que recomendam sua utiliza&#231;&#227;o rotineira na otimiza&#231;&#227;o dos procedimentos coron&#225;rios complexos.</p>
  </body>
  <back>
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  <sub-article article-type="translation" id="TRen" xml:lang="en">
    <front-stub>
      <article-id pub-id-type="doi">10.36660/abc.20260239i</article-id>
      <article-categories>
        <subj-group subj-group-type="heading">
          <subject>Letter to the Editor</subject>
        </subj-group>
      </article-categories>
      <title-group>
        <article-title>Geometric Models in Left Main Coronary Bifurcation: Mathematical Accuracy and Clinical Limits in the Era of Intravascular Imaging</article-title>
      </title-group>
      <contrib-group>
        <contrib contrib-type="author">
          <contrib-id contrib-id-type="orcid">0009-0005-4268-2964</contrib-id>
          <name>
            <surname>Ara&#250;jo</surname>
            <given-names>Guilherme O.</given-names>
          </name>
          <xref ref-type="aff" rid="aff1001">
            <sup>1</sup>
          </xref>
        </contrib>
        <contrib contrib-type="author">
          <contrib-id contrib-id-type="orcid">0000-0003-1273-1823</contrib-id>
          <name>
            <surname>Ribeiro</surname>
            <given-names>Henrique Barbosa</given-names>
          </name>
          <xref ref-type="aff" rid="aff1001">
            <sup>1</sup>
          </xref>
        </contrib>
      </contrib-group>
      <aff id="aff1001">
        <label>1</label>
        <country country="BR">Brazil</country>
        <institution content-type="original">Instituto do Cora&#231;&#227;o do Hospital das Cl&#237;nicas da Faculdade de Medicina da Universidade de S&#227;o Paulo, S&#227;o Paulo, SP &#8211; Brazil</institution>
      </aff>
      <author-notes>
        <corresp id="c01001"><label>Mailing Address:</label> Henrique Barbosa Ribeiro Instituto do Cora&#231;&#227;o do Hospital das Cl&#237;nicas da Faculdade de Medicina da Universidade de S&#227;o Paulo - Av. Dr. En&#233;as de Carvalho Aguiar, 44. Postal Code 05508-900, S&#227;o Paulo, SP &#8211; Brazil E-mail: hbribeiro@gmail.com, henrique.ribeiro@hc.fm.usp.br </corresp>
      </author-notes>
      <related-article related-article-type="article" id="r1-en" xlink:href="10.36660/abc.20250605i" ext-link-type="doi"/>
      <kwd-group xml:lang="en">
        <title>Keywords:</title>
        <kwd>Coronary Angiography</kwd>
        <kwd>Interventional Ultrasonography</kwd>
        <kwd>Angioplasty, Balloon, Coronary</kwd>
      </kwd-group>
    </front-stub>
    <body>
      <p>The geometry of coronary bifurcations plays a fundamental role in the pathophysiology of atherosclerosis and in the planning of percutaneous coronary intervention. Among these structures, the bifurcation of the left main coronary artery (LMCA) assumes singular relevance, not only due to the large myocardial territory it irrigates, but also due to the complex interaction between hemodynamic forces, vascular remodeling, and the progression of atherosclerotic disease. In this context, geometric models that estimate the diameter of the main vessel from the dimensions of the distal branches have been proposed as auxiliary tools for vessel sizing and for optimizing interventional strategies. However, studies systematically comparing these models with intravascular imaging tools, which are more precise in measuring coronary arteries, are lacking.<sup><xref ref-type="bibr" rid="B1">1</xref>-<xref ref-type="bibr" rid="B3">3</xref></sup></p>
      <p>Garzon et al.<sup><xref ref-type="bibr" rid="B1">1</xref></sup> evaluated the reliability of the Murray, Finet, and Huo-Kassab models in estimating the dimensions of the LMCA bifurcation in arteries with moderate atherosclerosis, using quantitative coronary angiography (QCA) and Intravascular ultrasound (IVUS) as reference methods.<sup><xref ref-type="bibr" rid="B1">1</xref></sup>The authors demonstrated that the Murray and Huo-Kassab models exhibit greater accuracy and precision compared to the Finet model, with the Murray model performing particularly better when IVUS is used as the reference standard. These findings are consistent with the theoretical robustness of models based on fluid dynamics principles and energy optimization, in contrast to the Finet model, which is empirically derived from angiographic fractal geometry.<sup><xref ref-type="bibr" rid="B1">1</xref>-<xref ref-type="bibr" rid="B5">5</xref></sup></p>
      <p>The superiority of Murray&#8217;s model observed in this study is consistent with experimental and computational evidence suggesting that the cubic relationship proposed by Murray, simpler from a mathematical point of view, may be less sensitive to variations in the diameters of the distal branches.<sup><xref ref-type="bibr" rid="B2">2</xref>,<xref ref-type="bibr" rid="B4">4</xref></sup>On the other hand, although the Huo-Kassab model incorporates similar physiological principles, its more complex mathematical formulation may amplify small inaccuracies in the measurements of distal branches, particularly in arteries with atherosclerosis, where vascular remodeling alters the original geometry. This finding raises relevant hypotheses about the robustness of mathematically simpler models in clinical scenarios characterized by anatomical variability and the presence of atherosclerotic disease.</p>
      <p>Another relevant aspect of the study is the systematic difference between the measurements obtained by IVUS and QCA, with IVUS tending to provide larger diameters. These differences reflect the known limitations of two-dimensional angiography in evaluating the coronary lumen and are consistent with previous studies that demonstrate greater accuracy of intravascular imaging in characterizing vascular diameter and plaque burden.<sup><xref ref-type="bibr" rid="B6">6</xref>-<xref ref-type="bibr" rid="B10">10</xref></sup>In this sense, IVUS remains the gold standard for assessing LMCA, being associated with better clinical outcomes when used to guide interventions, especially in more complex procedures, including LMCA.<sup><xref ref-type="bibr" rid="B6">6</xref>-<xref ref-type="bibr" rid="B8">8</xref></sup></p>
      <p>Despite relatively satisfactory performance, none of the models accurately reproduced the observed dimensions, with differences that can reach clinically relevant magnitudes. In LMCA interventions, seemingly small discrepancies can result in underexpansion or oversizing of the stents, increasing the risk of malposition, dissection, and restenosis, events associated with worse clinical outcomes.<sup><xref ref-type="bibr" rid="B5">5</xref>-<xref ref-type="bibr" rid="B7">7</xref></sup>In this sense, although mathematically elegant, geometric models should be interpreted as auxiliary tools, and not as substitutes for direct evaluation by intravascular imaging.</p>
      <p>Previous studies demonstrate that no scaling law is capable of completely balancing hemodynamic forces in real coronary bifurcations, highlighting that such models represent approximations of the complex interaction between anatomy, flow, and atherosclerotic disease.<sup><xref ref-type="bibr" rid="B4">4</xref>,<xref ref-type="bibr" rid="B11">11</xref></sup>Nevertheless, in settings with limited access to intravascular imaging, these tools can contribute to the identification of geometric deviations and provide initial estimates for vascular sizing. This aspect makes the present study even more relevant in developing countries like Brazil, with limited access to intravascular imaging tools.</p>
      <p>As interventional cardiology evolves toward therapeutic personalization, the integration of computational modeling, intravascular imaging, and physiological assessment emerges as a promising path for planning interventions at complex bifurcations. Future studies with larger samples, three-dimensional reconstructions, and the incorporation of variables related to atherosclerotic burden may clarify whether models adjusted for arterial disease can provide greater accuracy and clinical relevance.</p>
      <p>Despite the inherent limitations of the study by Garzon et al.<sup><xref ref-type="bibr" rid="B1">1</xref></sup>, including the relatively small sample size, the analysis restricted to LMCA bifurcations with moderate coronary artery disease, and the absence of disease-free segments or segments with extensive atherosclerotic burden &#8212; this work makes relevant contributions to the literature. The results demonstrate that, in LMCA bifurcations with moderate atherosclerosis, the Murray and Huo-Kassab geometric models perform better than the Finet model, particularly the Murray model, when compared to measurements obtained by IVUS.</p>
      <p>However, between the elegance of mathematical models and the complexity of vascular biology, the need to integrate such theoretical constructs with contemporary intravascular imaging modalities remains clear, in order to improve the precision of planning and the safety of coronary interventions. In this context, the study also reinforces the central role of intravascular imaging in clinical practice, in line with recent updates to international guidelines, which recommend its routine use in optimizing complex coronary procedures.</p>
    </body>
  </sub-article>
</article>
