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<article xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink" article-type="research-article" dtd-version="1.0" specific-use="sps-1.6" xml:lang="en">
  <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 pub-id-type="publisher-id" specific-use="scielo-v3">P9qLqGLrnthnNBmXnRnpKWL</article-id>
      <article-id pub-id-type="publisher-id" specific-use="scielo-v2">S0066-782X2017000900231</article-id>
      <article-id pub-id-type="publisher-id" specific-use="previous-pid">S0066-782X2017005001503</article-id>
      <article-id pub-id-type="doi">10.5935/abc.20170115</article-id>
      <article-categories>
        <subj-group subj-group-type="heading">
          <subject>Original Article</subject>
        </subj-group>
      </article-categories>
      <title-group>
        <article-title>Influence of the tilt angle of Percutaneous Aortic Prosthesis on Velocity and Shear Stress Fields</article-title>
      </title-group>
      <contrib-group>
        <contrib contrib-type="author">
          <name>
            <surname>Gomes</surname>
            <given-names>Bruno Alvares de Azevedo</given-names>
          </name>
          <xref ref-type="aff" rid="aff1">1</xref>
          <xref ref-type="aff" rid="aff2">2</xref>
          <xref ref-type="aff" rid="aff3">3</xref>
        </contrib>
        <contrib contrib-type="author">
          <name>
            <surname>Camargo</surname>
            <given-names>Gabriel Cordeiro</given-names>
          </name>
          <xref ref-type="aff" rid="aff1">1</xref>
        </contrib>
        <contrib contrib-type="author">
          <name>
            <surname>Santos</surname>
            <given-names>Jorge Roberto Lopes dos</given-names>
          </name>
          <xref ref-type="aff" rid="aff2">2</xref>
        </contrib>
        <contrib contrib-type="author">
          <name>
            <surname>Azevedo</surname>
            <given-names>Luis Fernando Alzuguir</given-names>
          </name>
          <xref ref-type="aff" rid="aff2">2</xref>
        </contrib>
        <contrib contrib-type="author">
          <name>
            <surname>Nieckele</surname>
            <given-names>&#194;ngela Ourivio</given-names>
          </name>
          <xref ref-type="aff" rid="aff2">2</xref>
        </contrib>
        <contrib contrib-type="author">
          <name>
            <surname>Siqueira-Filho</surname>
            <given-names>Aristarco Gon&#231;alves</given-names>
          </name>
          <xref ref-type="aff" rid="aff1">1</xref>
        </contrib>
        <contrib contrib-type="author">
          <name>
            <surname>Oliveira</surname>
            <given-names>Glaucia Maria Moraes de</given-names>
          </name>
          <xref ref-type="aff" rid="aff1">1</xref>
          <xref ref-type="corresp" rid="c1"/>
        </contrib>
      </contrib-group>
      <aff id="aff1">
        <label>1</label>
        <institution content-type="orgname">Universidade Federal do Rio de Janeiro</institution>
        <institution content-type="orgdiv1">Programa de P&#243;s Gradua&#231;&#227;o em Cardiologia</institution>
        <addr-line>
          <named-content content-type="city">Rio de Janeiro</named-content>
          <named-content content-type="state">RJ</named-content>
        </addr-line>
        <country country="BR">Brazil</country>
        <institution content-type="original">Programa de P&#243;s Gradua&#231;&#227;o em Cardiologia - Universidade Federal do Rio de Janeiro, Rio de Janeiro, RJ - Brazil</institution>
        <institution content-type="normalized">Universidade Federal do Rio de Janeiro</institution>
      </aff>
      <aff id="aff2">
        <label>2</label>
        <institution content-type="orgname">Pontif&#237;cia Universidade Cat&#243;lica do Rio de Janeiro</institution>
        <addr-line>
          <named-content content-type="city">Rio de Janeiro</named-content>
          <named-content content-type="state">RJ</named-content>
        </addr-line>
        <country country="BR">Brazil</country>
        <institution content-type="original">Pontif&#237;cia Universidade Cat&#243;lica do Rio de Janeiro (PUC-Rio), Rio de Janeiro, RJ - Brazil</institution>
        <institution content-type="normalized">Pontif&#237;cia Universidade Cat&#243;lica do Rio de Janeiro</institution>
      </aff>
      <aff id="aff3">
        <label>3</label>
        <institution content-type="orgname">MS</institution>
        <institution content-type="orgdiv1">Instituto Nacional de Cardiologia</institution>
        <addr-line>
          <named-content content-type="city">Rio de Janeiro</named-content>
          <named-content content-type="state">RJ</named-content>
        </addr-line>
        <country country="BR">Brazil</country>
        <institution content-type="original">Instituto Nacional de Cardiologia, INC/MS, Rio de Janeiro, RJ &#8211; Brazil</institution>
        <institution content-type="normalized">Minist&#233;rio da Sa&#250;de</institution>
      </aff>
      <author-notes>
        <corresp id="c1"><bold>Mailing Address: Gl&#225;ucia Maria Moraes de Oliveira,</bold> Universidade Federal do Rio de Janeiro - R. Prof. Rodolpho P. Rocco, 255 - Pr&#233;dio do HU 8&#186; andar - sala 6, UFRJ. Postal Code 21941-913, Cidade Universit&#225;ria, RJ - Brazil. E-mail: <email>glauciam@cardiol.br</email>, <email>glauciamoraesoliveira@gmail.com</email>
				</corresp>
        <fn fn-type="con">
          <p>
            <bold>Author contributions</bold>
          </p>
          <p>Conception and design of the research: Gomes BAA, Camargo GC, Lopes J, Azevedo LFA, Oliveira GMM; Acquisition of data: Gomes BAA; Analysis and interpretation of the data: Gomes BAA, Camargo GC, Azevedo LFA, Nieckele AO, Oliveira GMM; Writing of the manuscript: Gomes BAA, Camargo GC; Critical revision of the manuscript for intellectual content: Gomes BAA, Azevedo LFA, Nieckele AO, Siqueira-Filho AG, Oliveira GMM.</p>
        </fn>
        <fn fn-type="conflict">
          <p>
            <bold>Potential Conflict of Interest</bold>
          </p>
          <p>No potential conflict of interest relevant to this article was reported.</p>
        </fn>
      </author-notes>
      <pub-date pub-type="epub">
        <day>07</day>
        <month>08</month>
        <year>2017</year>
      </pub-date>
      <pub-date pub-type="collection">
        <month>09</month>
        <year>2017</year>
      </pub-date>
      <volume>109</volume>
      <issue>3</issue>
      <fpage>231</fpage>
      <lpage>240</lpage>
      <history>
        <date date-type="received">
          <day>08</day>
          <month>03</month>
          <year>2017</year>
        </date>
        <date date-type="rev-recd">
          <day>14</day>
          <month>05</month>
          <year>2017</year>
        </date>
        <date date-type="accepted">
          <day>22</day>
          <month>05</month>
          <year>2017</year>
        </date>
      </history>
      <permissions>
        <license license-type="open-access" xlink:href="https://creativecommons.org/licenses/by/4.0/" xml:lang="en">
          <license-p>This is an Open Access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.</license-p>
        </license>
      </permissions>
      <abstract>
        <title>Abstract</title>
        <sec>
          <title>Background:</title>
          <p>Due to the nature of the percutaneous prosthesis deployment process, a variation in its final position is expected. Prosthetic valve placement will define the spatial location of its effective orifice in relation to the aortic annulus. The blood flow pattern in the ascending aorta is related to the aortic remodeling process, and depends on the spatial location of the effective orifice. The hemodynamic effect of small variations in the angle of inclination of the effective orifice has not been studied in detail.</p>
        </sec>
        <sec>
          <title>Objective:</title>
          <p>To implement an <italic>in vitro</italic> simulation to characterize the hydrodynamic blood flow pattern associated with small variations in the effective orifice inclination.</p>
        </sec>
        <sec>
          <title>Methods:</title>
          <p>A three-dimensional aortic phantom was constructed, reproducing the anatomy of one patient submitted to percutaneous aortic valve implantation. Flow analysis was performed by use of the Particle Image Velocimetry technique. The flow pattern in the ascending aorta was characterized for six flow rate levels. In addition, six angles of inclination of the effective orifice were assessed.</p>
        </sec>
        <sec>
          <title>Results:</title>
          <p>The effective orifice at the -4&#176; and -2&#176; angles directed the main flow towards the anterior wall of the aortic model, inducing asymmetric and high shear stress in that region. However, the effective orifice at the +3&#176; and +5&#176; angles mimics the physiological pattern, centralizing the main flow and promoting a symmetric distribution of shear stress.</p>
        </sec>
        <sec>
          <title>Conclusion:</title>
          <p>The measurements performed suggest that small changes in the angle of inclination of the percutaneous prosthesis aid in the generation of a physiological hemodynamic pattern, and can contribute to reduce aortic remodeling.</p>
        </sec>
      </abstract>
      <kwd-group xml:lang="en">
        <title>Keywords:</title>
        <kwd>Heart Valve Prosthesis Implantation</kwd>
        <kwd>Regional Blood Flow</kwd>
        <kwd>Hemodynamics</kwd>
        <kwd>Shear Stress</kwd>
      </kwd-group>
    </article-meta>
  </front>
  <body>
    <sec sec-type="intro">
      <title>Introduction</title>
      <p>Transcatheter Aortic Valve Implantation (TAVI) has been introduced by Cribier et al.<xref ref-type="bibr" rid="B1">1</xref> as an alternative to treat individuals with severe aortic valve stenosis at high surgical risk. With the development of new systems of percutaneous heart valve implantation, the use of TAVI for patients at intermediate surgical risk has been a worldwide trend.<xref ref-type="bibr" rid="B2">2</xref><sup>-</sup><xref ref-type="bibr" rid="B4">4</xref> Because of the nature of the implantation procedure, a variation in prosthetic valve placement is expected.<xref ref-type="bibr" rid="B5">5</xref> In addition, eccentric calcifications in the aortic annulus can influence the final orientation of the valve prosthesis. Valve placement will define the spatial location of its effective orifice in relation to the aortic annulus, and will determine the likelihood of generating eccentric flow in the vascular lumen.<xref ref-type="bibr" rid="B6">6</xref>
			</p>
      <p>Several studies have shown that the anatomical characteristics of the aortic root influence blood flow in the ascending aorta.<xref ref-type="bibr" rid="B7">7</xref> In addition, the changes in blood flow pattern after TAVI represent an important aspect that has not been studied in details.<xref ref-type="bibr" rid="B5">5</xref> Studies suggest that eccentric blood flow is related to the aortic remodeling process, such as dilatation and aneurysmal formations.<xref ref-type="bibr" rid="B8">8</xref><sup>-</sup><xref ref-type="bibr" rid="B10">10</xref>
			</p>
      <p><italic>In vitro</italic> simulations that preserve the anatomy of the aorta (patient-specific) can contribute to a better understanding of the blood flow changes produced by variations in the effective orifice inclination. Contrary to <italic>in vivo</italic> studies, <italic>in vitro</italic> simulations enable proper control of flow geometry and contour conditions, providing a systematic assessment of the blood flow response to valve placement variations.</p>
      <p>So far, only one study<xref ref-type="bibr" rid="B11">11</xref> using flow-sensitive cardiovascular magnetic resonance imaging (4D flow MRI)<xref ref-type="bibr" rid="B12">12</xref> has reproduced the anatomy of the aorta of a patient and has assessed the changes in blood flow produced by variations in the effective orifice inclination. The objective of the present study was to implement an <italic>in vitro</italic> simulation to characterize the hydrodynamic pattern of blood flow associated with small variations in the effective orifice inclination.</p>
    </sec>
    <sec sec-type="methods">
      <title>Methods</title>
      <p>This is a descriptive study of <italic>in vitro</italic> simulation of blood flow in a three-dimensional (3D) aortic model. For that purpose, a vascular phantom was constructed based on the tomographic angiography of the aorta of one patient submitted to TAVI. The present study was approved by the Research Ethics Committee of the institution. The patient was a 77-year-old male with severe degenerative aortic stenosis, mild ventricular dysfunction, and New York Heart Association functional class III.</p>
      <p>Tomographic angiography of the aorta was performed with a Somatom Sensation 64-channel tomography device (Siemens, Germany). Tomographic slices from the aortic annulus to the distal segment of the thoracic aorta were selected. The DICOM images were transferred to the Mimics software (Materialise, Belgium) to implement the segmentation of the aortic region of interest. After the segmentation process, the digital file was exported to.<italic>STL</italic> (stereolithography) format to perform the 3D printing, with the Stratasys Fortus 400 mc Systems equipament (Stratasys, USA), using the ABS-M30 Affordable FDM thermoplastic material (Stratasys, USA). The 3D model was printed in a real scale, and its dimensions were confirmed via measurements taken on the tomographic angiography of the aorta (<xref ref-type="fig" rid="f1">Figure 1</xref>).</p>
      <p>
        <fig id="f1">
          <label>Figure 1</label>
          <caption>
            <title>Three-dimensional aortic model. Model in ABS-M30 Affordable FDM thermoplastic material (Stratasys, USA).</title>
          </caption>
          <graphic xlink:href="1678-4170-abc-109-03-0231-70115-gf01.jpg"/></fig>
      </p>
      <p>The 3D aortic model was used to build a silicone phantom, with which the <italic>in vitro</italic> simulation of blood flow was implemented. The 3D model was positioned in a rectangular reservoire, built with plexiglass plaques. Liquid silicone elastomer was added to that reservoire, involving the aortic model. After 24 hours, the silicone elastomer was solid, allowing the extraction of the 3D model. A longitudinal cut was performed in the lateral walls of the elastomer block, dividing it into two halves. Then, the 3D model was removed from the silicone phantom, and the two halves were reconnected. To maintain proper alignment and to preserve the original anatomy of the aorta, five metallic rods, crossing the entire set, were used to guide the reassembly of the phantom. After reuniting the two halves of the phantom, connectors of the hydraulic circuit allowed the test solution to flow through the silicone model.</p>
      <p>The Sylgard 184 silicone elastomer (Dow Corning, USA) was chosen because of its optical properties, and an image technique with laser was used to measure the flow patterns. That silicone has a refraction index (n = 1,417) close to that of the test solution chosen for the assays, an aqueous mixture of glycerine (60% glycerine, n = 1,420).<xref ref-type="bibr" rid="B13">13</xref> The test solution was drained into a closed circuit through the hydraulic instalation, boosted by a constant-volume pump, NEMO 4501140 (NETZSCH of BRASIL, Brazil). The flow rate was adjusted by controlling the frequency of pump rotation, using a frequency inversor CFW 08 (WEG, Brazil).</p>
      <p>The flow was directed to the aortic phantom, with inflow in the vascular lumen occurring in the position equivalent to the aortic annulus, where a nozzle was connected to the phantom, representing the aortic prosthesis with full opening of its leaflets. The inner area of that nozzle measured 1.5 cm<sup>2</sup>, based on the effective orifice of the patient&#8217;s prosthesis, obtained via transthoracic echocardiography. The aortic phantom had the following outflow points: brachiocephalic trunk, left common carotid artery, left subclavian artery, and thoracic aorta.</p>
      <p>The Particle Image Velocimetry (PIV) technique was chosen for flow analysis.<xref ref-type="bibr" rid="B14">14</xref> The particles that served as flow tracers were constituted by silver-coated hollow glass espheres of approximately 13 &#181;m of diameter, and were addeded to the aqueous glycerine solution. A dual-cavity laser (BIG SKY Nd: YAG, 120 mJ, Quantel, USA) was the illumination source used, generating a 0.5-mm-thick light plane. A digital camera (PIVCAM 10-30, TSI, USA) captured synchronized images of the particles in the region between the aortic annulus and the middle ascending aortic segment. For each implemented hydrodynamic state, 3000 images of the tracers were captured, producing 1500 instantaneous velocity fields. The mean velocity and shear rate fields were calculated based on those instantaneous fields. Cross-correlation was the process used to determine the displacement of the tracers, by use of the INSIGHT 3G software (TSI, USA). Each velocity vector was obtained for an area of 32x32 pixels in the image, corresponding to a 2x2-mm resolution in the real flow.<xref ref-type="bibr" rid="B14">14</xref>
			</p>
      <p>The PIV technique produced two-dimensional velocity fields. To have a 3D characterization of the aortic flow, the measurements were taken in four different planes. The central measuring plane was placed as to coincide with the central line of the effective orifice, crossing the right coronary ostium, and encompassing the main flow inside the aortic phantom. In addition, the velocity measurements were taken in three other planes, 4 mm apart from each other. Two of those planes were placed towards the dorsal region and one was placed towards the ventral region.</p>
      <p>Because of the rapid blood flow acceleration at the beginning of the ventricular systole, it was hypothesized that significant changes in shear stress occur during that period.<xref ref-type="bibr" rid="B15">15</xref> Thus, the present study was designed to characterize the flow in the initial third of the ventricular systole. For that purpose, the following values of continuous flow were used: 0.8; 1.6; 2.6; 3.3; 4.0 and 5.3 liters per minute (L/min). Considering the properties of the test solution and the inner diameter of the effective orifice, the Reynolds numbers corresponding to each flow level were 195, 390, 630, 800, 970 and 1285, respectively.</p>
      <p>The variation in the inclination of the effective orifice could be assessed by building a spindle inclination mechanism, comprising a threaded rod coupled to a 0-25-mm micrometer (Mitutoyo, Japan). In one extremity of that rod, a joint allowed coupling the spindle inclination mechanism to the entrance nozzle that was connected to the aortic phantom. When a translation movement was imposed to the spindle inclination mechanism, there would be a change in the effective orifice inclination. For flows of 2.6 and 3.3 L/min, the following angles of inclination were implemented: -4&#176;, -2&#176;, 0&#176;, +1&#176;, +3&#176;, and +5&#176;. The zero angle of inclination corresponded to the coincidence of the central line of the effective orifice with the central line of the aortic annulus. The negative angles tilted the main flow towards the right coronary ostium, while the positive angles tilted the main flow towards the posterior wall (<xref ref-type="fig" rid="f2">Figure 2</xref>).</p>
      <p>
        <fig id="f2">
          <label>Figure 2</label>
          <caption>
            <title>Angle of inclination of the effective orifice. AAo: ascending aorta; RC: right coronary artery; &#952;: angle of inclination.</title>
          </caption>
          <graphic xlink:href="1678-4170-abc-109-03-0231-70115-gf02.jpg"/></fig>
      </p>
    </sec>
    <sec sec-type="results">
      <title>Results</title>
      <p>The results of the analysis of the flow between the aortic annulus and the middle ascending aortic segment are now presented. Because the software used to implement the PIV technique provides no information on the physical boundaries limiting the flow, an image of the vascular model was overlapped with a typical velocity field. <xref ref-type="fig" rid="f3">Figure 3</xref> shows the anatomical structures close to the flow area in the aortic phantom.</p>
      <p>
        <fig id="f3">
          <label>Figure 3</label>
          <caption>
            <title>Velocity field measured inside the aortic phantom.</title>
          </caption>
          <graphic xlink:href="1678-4170-abc-109-03-0231-70115-gf03.jpg"/></fig>
      </p>
      <p>The following results include the velocity and shear rate fields for the four measurement planes described. For each plane, the results are presented for six flow rate values, ranging from 0.8 to 5.3 L/min. Subsequently, for the central plane, the results will explore the effect of the variation in the effective orifice tilt angle.</p>
      <sec>
        <title>Velocity field</title>
        <p><xref ref-type="fig" rid="f4">Figure 4</xref> shows the results for the mean velocity fields measured in the aortic phantom for four different planes. For each plane, six flow rate values are shown. The velocity vectors are colored according to their magnitude (meters per second - m/s), based on the scale at the right side of the figure.</p>
        <p>
          <fig id="f4">
            <label>Figure 4</label>
            <caption>
              <title>Velocity fields in the measurement planes. Velocity fields in the (a) 4-mm ventral, (b) central, (c) 4-mm dorsal, and (d) 8-mm dorsal planes. Velocity magnitude in meters per second.</title>
            </caption>
            <graphic xlink:href="1678-4170-abc-109-03-0231-70115-gf04.jpg"/></fig>
        </p>
        <p>The experimental tests represented the initial third of the ventricular systole, reaching maximum instantaneous velocities of approximately 1.2 m/s. For all velocity fields, the color scale of magnitude was maintained fixed, aiming at comparig between the different hydrodynamic states. Although the measures reached 1.2 m/s, the color scale was adjusted between 0 and 0.4 m/s, enabling the comparison between different cases, because, in the ventral plane, the low velocity values predominated. For each plane of measurement, one qualitative analysis of flow is shown.</p>
        <p><bold>4-mm ventral plane.</bold> For the flow rates of 2.6 and 3.3 L/min, the flow is directed towards the anterior wall. As the flow rate increases to 4.0 and 5.3 L/min, a larger part of the main jet acquires a centralized configuration, reaching a velocity of 0.4 m/s, at a flow rate of 5.3 L/min (<xref ref-type="fig" rid="f4">Figure 4a</xref>).</p>
        <p><bold>Central plane.</bold> In this plane, the main jet is well defined to the flow rate of 1.6 L/min, and markedly inclined towards the anterior wall. As the flow rate increases, the main jet widens, showing a mild trend towards flow centralization (<xref ref-type="fig" rid="f4">Figure 4b</xref>).</p>
        <p><bold>4-mm dorsal plane.</bold> In the first dorsal plane, the main jet is well defined as a dominant flow structure. From the flow rate of 3.3 L/min, maximum velocity is observed from the sinotubular junction to the middle ascending aortic segment. As the flow rate increases to 4.0 and 5.3 L/min, the maximum velocity region increases, seen as the dominance of the red color region (<xref ref-type="fig" rid="f4">Figure 4c</xref>).</p>
        <p><bold>8-mm dorsal plane.</bold> In this plane, a continuous maximum velocity region is observed for the flow rate of 2.6 L/min, occupying the area from the sinotubular junction to the middle ascending aortic segment. In this plane, for all flow rate levels, left inclination towards the anterior wall is seen. The analysis of the velocity field for the flow rate of 5.3 L/min clearly shows that the main jet falls on the anterior wall, as seen by the large maximum velocity area (<xref ref-type="fig" rid="f4">Figure 4d</xref>).</p>
      </sec>
      <sec>
        <title>Shear rate</title>
        <p>The shear rate fields, calculated from the velocity fields shown in <xref ref-type="fig" rid="f4">Figure 4</xref>, are now presented. As previously performed for the velocity fields, in <xref ref-type="fig" rid="f5">Figure 5</xref>, an image of the vascular phantom was overlapped with a shear rate field to make the interpretation of results easier.</p>
        <p>
          <fig id="f5">
            <label>Figure 5</label>
            <caption>
              <title>Shear rate inside the aortic phantom.</title>
            </caption>
            <graphic xlink:href="1678-4170-abc-109-03-0231-70115-gf05.jpg"/></fig>
        </p>
        <p>The results of shear rate are shown in <xref ref-type="fig" rid="f6">Figure 6</xref>, being exhibited for the same planes and flow rates of the velocity fields. The color scale in the figure represents the shear rate magnitude, ranging from 0 to 15 s<sup>-1</sup>.</p>
        <p>
          <fig id="f6">
            <label>Figure 6</label>
            <caption>
              <title>Shear rate in the measurement planes. Shear rate in the (a) 4-mm ventral, (b) central, (c) 4-mm dorsal, and (d) 8-mm dorsal planes. Shear rate magnitude in s<sup>-1</sup>.</title>
            </caption>
            <graphic xlink:href="1678-4170-abc-109-03-0231-70115-gf06.jpg"/></fig>
        </p>
        <p><bold>4-mm ventral plane.</bold> In the ventral plane, a high shear rate region is identified at the flow rate of 2.6 L/min. At 3.3 L/min, maximum shear rate occurs, as indicated by the red band, which is elongated and leans towards the anterior wall. At higher flow rates, 4.0 and 5.3 L/min, the red band extends from the top to the bottom of the image. High shear rate regions are found close to the effective orifice, in the lower part of the figure (<xref ref-type="fig" rid="f6">Figure 6a</xref>).</p>
        <p><bold>Central plane.</bold> In this plane, maximum shear is already identified, even in an incipient manner, at the flow rate of 0.8 L/min. From the flow rate of 1.6 L/min, the maximum shear stress band occupies the entire extension of the images. At subsequent flow rates, progressive widening of that area is seen (<xref ref-type="fig" rid="f6">Figure 6b</xref>).</p>
        <p><bold>4-mm dorsal plane.</bold> From the flow rate of 2.6 L/min, maximum shear stress bends towards the anterior wall. In addition, expressive widening of that band is observed as the flow rate increases. Despite the pattern of inclination to the left, it is worth noting the presence of a small sector with maximum shear stress at the right upper part of the images, beginning at the flow rate of 2.6 L/min (<xref ref-type="fig" rid="f6">Figure 6c</xref>).</p>
        <p><bold>8-mm dorsal plane.</bold> In this plane, widening of the maximum shear region is also seen from the flow rate of 2.6 L/min. The inclination of the high shear region towards the left upper part of the images remains, showing a preferential direction towards the anterior wall (<xref ref-type="fig" rid="f6">Figure 6d</xref>).</p>
      </sec>
      <sec>
        <title>Influence of the angle of inclination of the effective orifice</title>
        <p>The influence of the inclination of the effective orifice on flow characteristics was assessed by use of measurements taken in the central plane, for the flow rates of 2.6 and 3.3 L/min. The angles of inclination ranged from -4&#176; to +5&#176;, as shown in <xref ref-type="fig" rid="f2">Figure 2</xref>.</p>
      </sec>
      <sec>
        <title>Velocity and shear rate fields</title>
        <p><xref ref-type="fig" rid="f7">Figure 7</xref> shows the influence of the angle of inclination of the effective orifice on the velocity and shear rate fields. For 2.6 L/min, at a zero angle of inclination, the main flow was directed to the left, reaching the anterior wall in the middle ascending aortic segment. When the effective orifice was placed at negative inclinations (-4&#176; and -2&#176;), that flow eccentricity was exacerbated. For small positive inclinations (+1&#176;, +3&#176; and +5&#176;), a trend towards flow centralization was observed. With that mild change in inclination, the main flow is directed to the posterolateral wall (<xref ref-type="fig" rid="f7">Figure 7a</xref>).</p>
        <p>
          <fig id="f7">
            <label>Figure 7</label>
            <caption>
              <title>Velocity and shear rate fields for (a, c) 2.6 L/min and (b, d) 3.3 L/min. Inclination of the effective orifice: -4&#176;, -2&#176;, 0&#176;, +1&#176;, +3&#176;, and +5&#176;.</title>
            </caption>
            <graphic xlink:href="1678-4170-abc-109-03-0231-70115-gf07.jpg"/></fig>
        </p>
        <p>At 3.3 L/min, the velocity fields show that, for the negative angles, the main jet decreased its width as compared to that at zero angle of inclination. The negative angles show similar velocity magnitudes, with a left inclination. When the inclination reaches positive values, a trend towards centralization of the main jet is observed. Thus, higher velocity values appear inside the jet, as seen by the red colored regions. The velocity patterns are similar at the angles +1&#176; and +3&#176;, maintaining a left inclination in the upper half of the image. The +5&#176; angle of inclination shows a more significant centralization of the main jet (<xref ref-type="fig" rid="f7">Figure 7b</xref>).</p>
        <p><xref ref-type="fig" rid="f7">Figures 7c</xref> and <xref ref-type="fig" rid="f7">7d</xref> show the results for shear rate. At 2.6 L/min, for the negative inclinations, the red color bands are narrower as compared to those of other angle positions. For positive inclinations, maximum shear area widening and centralization are seen (+3&#176; and +5&#176;). For the +5&#176; inclination, the maximum shear region is maintained close to the central line of the aortic model (<xref ref-type="fig" rid="f7">Figure 7c</xref>).</p>
        <p>The analysis of the shear rate results at the 3.3-L/min flow rate indicates that, for negative inclinations, maximum shear shows a left inclination. In the positive inclinations of +1&#176; and +3&#176;, maximum shear is located in the central region. Proximity of the high shear region to the posterolateral wall is observed at the +5&#176; angle, because the red band occupies the right side of the image (<xref ref-type="fig" rid="f7">Figure 7d</xref>).</p>
      </sec>
    </sec>
    <sec sec-type="discussion">
      <title>Discussion</title>
      <p>In the present study, an <italic>in vitro</italic> simulation was performed to characterize the hydrodynamic pattern of blood flow during ventricular systole in a 3D aortic model representing the anatomy of a patient submitted to TAVI. In addition, by use of velocity and shear rate fields, we identified flow changes due to six variations in the angle of inclination of the effective orifice.</p>
      <p>The optimization of percutaneous valve prosthesis implantation, in addition to its placement according to the patient&#8217;s native flow pattern, can be a means of ensuring its best performance after TAVI.<xref ref-type="bibr" rid="B16">16</xref><sup>,</sup><xref ref-type="bibr" rid="B17">17</xref> The generation of a blood flow with a hemodynamic pattern closer to the physiological one can have a beneficial impact on the patients&#8217; survival.<xref ref-type="bibr" rid="B18">18</xref><sup>,</sup><xref ref-type="bibr" rid="B19">19</xref>
			</p>
      <p>The qualitative analysis of the velocity and shear rate fields for each plane analysed in the present study clearly shows the 3D nature of the flow inside the aortic model. These data stress the importance of using realistic models of aorta geometry, in addition to the limitations of <italic>in vitro</italic> studies that represent the aorta using circular and axisymmetric models.<xref ref-type="bibr" rid="B5">5</xref>
			</p>
      <p>Groves et al.<xref ref-type="bibr" rid="B5">5</xref> have studied the effect of the variations in the axial placement of percutaneous prostheses. The aorta was represented with an plexiglass circular tube of 30-mm inner diameter. For a 4-L/min flow rate, only the 5-mm displacement below the aortic annulus resulted in low shear stress values, in addition to a symmetrical distribution.<xref ref-type="bibr" rid="B5">5</xref> In the present study, the effective orifice remained positioned less than 5 mm from the aortic annulus. However, because our model preserved the aorta anatomy, the results differed with respect to the planes assessed, which were not axisymmetric as in the study by Groves et al.<xref ref-type="bibr" rid="B5">5</xref>
			</p>
      <p>Groves et al.<xref ref-type="bibr" rid="B5">5</xref> and Wilton et al.<xref ref-type="bibr" rid="B20">20</xref> have considered the hypothesis that high shear stress, in addition to its asymmetric distribution, would be related to aortic dilatation and a higher chance of dissection.<xref ref-type="bibr" rid="B5">5</xref><sup>,</sup><xref ref-type="bibr" rid="B10">10</xref><sup>,</sup><xref ref-type="bibr" rid="B20">20</xref><sup>,</sup><xref ref-type="bibr" rid="B21">21</xref> Based on that hypothesis, optimizing the axial placement and the effective orifice inclination would be desirable, so that symmetric and low-magnitude shear stress distribution would be obtained. An axial placement of less than 5 mm from the aortic annulus associated with positive angles of inclination would be suggested in this particular case. In addition, Groves et al.<xref ref-type="bibr" rid="B5">5</xref> have reiterated that high shear stress levels downstream the prosthesis could contribute to reduce its durability, because of higher mechanical stress, emphasizing the importance of optimizing the prosthesis placement.</p>
      <p>Trauzeddel et al.<xref ref-type="bibr" rid="B7">7</xref> have assessed post-TAVI ascending aortic blood flow patterns, which were compared to those of patients submitted to conventional stented aortic valve replacement (AVR) and those of healthy individuals. That study showed that both TAVI and AVR resulted in maximum shear stress values in the right anterior wall, while minimum shear stress values were found in the left posterior wall. Healthy individuals, however, showed physiological central blood flow and a symmetric distribution of shear stress along the aortic circumference.<xref ref-type="bibr" rid="B7">7</xref> The maximum shear stress distribution in the anterior wall of patients submitted to TAVI and AVR coincides with the results of the <italic>in vitro</italic> simulation of the present study for the negative angles of inclination of the effective orifice. In the experimental model, that angle of inclination could be modified in the search for a configuration that produced a central blood flow pattern. As the results presented indicate, a decrease in shear stress in the anterior wall was obtained with small positive inclinations. For example, at the +3&#176; angle, the maximum shear stress region remained restricted to the central portion of the aortic phantom. When the angle of inclination was increased to +5&#176;, the maximum shear stress region approached the posterolateral wall.</p>
      <p>The present analysis was limited to the anatomic findings of one patient. This simulation, however, represented a real 3D anatomy, providing a significant advance in relation to the circular and axisymmetric models used in previous studies.<xref ref-type="bibr" rid="B5">5</xref><sup>,</sup><xref ref-type="bibr" rid="B6">6</xref>
			</p>
      <p>In the present study, only the initial third of the ventricular systole was represented. However, the highest prevalence of high shear stress values in the ascending aorta is known to occur during the systole. In addition, because that period of the cardiac cycle is characterized by sudden changes in velocity, a rapid variation in shear stress values is also expected.<xref ref-type="bibr" rid="B15">15</xref> In this study, a segment of pulsatile blood flow, more precisely the initial third of the ventricular systole, was represented by six different continuous blood flow levels. With this approach, some structures of secondary blood flow might not have been captured. However, in cardiovascular science, the various stages of pulsatile blood flow are commonly modelled with an increasing sequence of continuous blood flow values.<xref ref-type="bibr" rid="B11">11</xref><sup>,</sup><xref ref-type="bibr" rid="B22">22</xref>
			</p>
      <p>Based on these findings, projects of new prostheses, with the ability to change the angle of inclination of the effective orifice, can be proposed, enabling the generation of a centralized blood flow in the ascending aorta, mimicking a physiological hemodynamic pattern.</p>
    </sec>
    <sec sec-type="conclusions">
      <title>Conclusion</title>
      <p>The present study evidenced the 3D character of the blood flow pattern inside the vascular phantom, and identified a range of optimized values for the angle of inclination of the effective orifice. For small positive inclinations, a physiological centralized blood flow was obtained in the middle ascending aortic segment, eliminating the high mechanical shear stress values in the anterior wall, which prevailed in the negative inclinations of the effective orifice (-4&#176; and -2&#176;). In the placements with positive inclinations, the regions with high shear stress levels were maintained close to the central line of the vascular phantom.</p>
    </sec>
  </body>
  <back>
    <fn-group>
      <fn fn-type="supported-by">
        <p>
          <bold>Sources of Funding</bold>
        </p>
        <p>There were no external funding sources for this study.</p>
      </fn>
      <fn fn-type="other">
        <p>
          <bold>Study Association</bold>
        </p>
        <p>This article is part of the thesis of Doctoral submitted by Bruno Alvares de Azevedo Gomes, from Universidade Federal do Rio de Janeiro.</p>
      </fn>
    </fn-group>
    <ack>
      <title>Acknowledgments</title>
      <p>The authors would like to thank Carolina Azevedo for designing the artwork.</p>
    </ack>
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  <sub-article article-type="translation" id="s1" xml:lang="pt">
    <front-stub>
      <article-categories>
        <subj-group subj-group-type="heading">
          <subject>Artigos</subject>
        </subj-group>
      </article-categories>
      <title-group>
        <article-title>Influ&#234;ncia do &#194;ngulo de Inclina&#231;&#227;o da Pr&#243;tese Percut&#226;nea A&#243;rtica no Campo de Velocidade e Estresse de Cisalhamento</article-title>
      </title-group>
      <contrib-group>
        <contrib contrib-type="author">
          <name>
            <surname>Gomes</surname>
            <given-names>Bruno Alvares de Azevedo</given-names>
          </name>
          <xref ref-type="aff" rid="aff4">1</xref>
          <xref ref-type="aff" rid="aff5">2</xref>
          <xref ref-type="aff" rid="aff6">3</xref>
        </contrib>
        <contrib contrib-type="author">
          <name>
            <surname>Camargo</surname>
            <given-names>Gabriel Cordeiro</given-names>
          </name>
          <xref ref-type="aff" rid="aff4">1</xref>
        </contrib>
        <contrib contrib-type="author">
          <name>
            <surname>Santos</surname>
            <given-names>Jorge Roberto Lopes dos</given-names>
          </name>
          <xref ref-type="aff" rid="aff5">2</xref>
        </contrib>
        <contrib contrib-type="author">
          <name>
            <surname>Azevedo</surname>
            <given-names>Luis Fernando Alzuguir</given-names>
          </name>
          <xref ref-type="aff" rid="aff5">2</xref>
        </contrib>
        <contrib contrib-type="author">
          <name>
            <surname>Nieckele</surname>
            <given-names>&#194;ngela Ourivio</given-names>
          </name>
          <xref ref-type="aff" rid="aff5">2</xref>
        </contrib>
        <contrib contrib-type="author">
          <name>
            <surname>Siqueira-Filho</surname>
            <given-names>Aristarco Gon&#231;alves</given-names>
          </name>
          <xref ref-type="aff" rid="aff4">1</xref>
        </contrib>
        <contrib contrib-type="author">
          <name>
            <surname>Oliveira</surname>
            <given-names>Glaucia Maria Moraes de</given-names>
          </name>
          <xref ref-type="aff" rid="aff6">1</xref>
          <xref ref-type="corresp" rid="c2"/>
        </contrib>
      </contrib-group>
      <aff id="aff4">
        <label>1</label>
        <institution content-type="original">Programa de P&#243;s Gradua&#231;&#227;o em Cardiologia - Universidade Federal do Rio de Janeiro, Rio de Janeiro, RJ - Brasil</institution>
      </aff>
      <aff id="aff5">
        <label>2</label>
        <institution content-type="original">Pontif&#237;cia Universidade Cat&#243;lica do Rio de Janeiro (PUC-Rio), Rio de Janeiro, RJ &#8211; Brasil</institution>
      </aff>
      <aff id="aff6">
        <label>3</label>
        <institution content-type="original">Instituto Nacional de Cardiologia, INC/MS, Rio de Janeiro, RJ &#8211; Brasil</institution>
      </aff>
      <author-notes>
        <corresp id="c2"><bold>Correspond&#234;ncia: Gl&#225;ucia Maria Moraes de Oliveira,</bold> Universidade Federal do Rio de Janeiro - R. Prof. Rodolpho P. Rocco, 255 - Pr&#233;dio do HU 8&#186; andar - sala 6, UFRJ. CEP 21941-913, Cidade Universit&#225;ria, RJ - Brasi. E-mail: <email>glauciam@cardiol.br</email>, <email>glauciamoraesoliveira@gmail.com</email>
				</corresp>
        <fn fn-type="con">
          <p>
            <bold>Contribui&#231;&#227;o dos autores</bold>
          </p>
          <p>Concep&#231;&#227;o e desenho da pesquisa: Gomes BAA, Camargo GC, Lopes J, Azevedo LFA, Oliveira GMM; Obten&#231;&#227;o de dados: Gomes BAA; An&#225;lise e interpreta&#231;&#227;o dos dados: Gomes BAA, Camargo GC, Azevedo LFA, Nieckele AO, Oliveira GMM; Reda&#231;&#227;o do manuscrito: Gomes BAA, Camargo GC; Revis&#227;o cr&#237;tica do manuscrito quanto ao conte&#250;do intelectual importante: Gomes BAA, Azevedo LFA, Nieckele AO, Siqueira-Filho AG, Oliveira GMM.</p>
        </fn>
        <fn fn-type="conflict">
          <p>
            <bold>Potencial conflito de interesses</bold>
          </p>
          <p>Declaro n&#227;o haver conflito de interesses pertinentes.</p>
        </fn>
      </author-notes>
      <abstract>
        <title>Resumo</title>
        <sec>
          <title>Fundamento:</title>
          <p>Devido &#224; natureza do processo de libera&#231;&#227;o da pr&#243;tese percut&#226;nea, &#233; esperada uma variabilidade do posicionamento final da v&#225;lvula. A localiza&#231;&#227;o da pr&#243;tese ir&#225; definir a posi&#231;&#227;o espacial do seu orif&#237;cio efetivo em rela&#231;&#227;o ao &#226;nulo a&#243;rtico. O padr&#227;o do fluxo sangu&#237;neo em aorta ascendente est&#225; relacionado ao processo de remodelamento a&#243;rtico, al&#233;m de ser dependente da disposi&#231;&#227;o espacial do orif&#237;cio efetivo. O efeito hemodin&#226;mico de pequenas varia&#231;&#245;es na angula&#231;&#227;o do orif&#237;cio efetivo ainda n&#227;o foi estudado em detalhes.</p>
        </sec>
        <sec>
          <title>Objetivo:</title>
          <p>O objetivo do presente trabalho foi implementar uma simula&#231;&#227;o <italic>in vitro</italic> do fluxo sangu&#237;neo para caracteriza&#231;&#227;o do padr&#227;o hidrodin&#226;mico, associado a pequenas varia&#231;&#245;es na inclina&#231;&#227;o do orif&#237;cio efetivo.</p>
        </sec>
        <sec>
          <title>M&#233;todos:</title>
          <p>Para esse fim, foi constru&#237;do um fantoma a&#243;rtico tridimensional, que reproduziu a anatomia de um paciente submetido ao implante valvar percut&#226;neo. A an&#225;lise de fluxo foi realizada atrav&#233;s da t&#233;cnica de Velocimetria por Imagens de Part&#237;cula. O padr&#227;o de escoamento em aorta ascendente foi caracterizado para seis n&#237;veis de vaz&#227;o de fluxo. Al&#233;m disso, foram estudados seis inclina&#231;&#245;es do orif&#237;cio efetivo.</p>
        </sec>
        <sec>
          <title>Resultados:</title>
          <p>O estudo demonstrou que o orif&#237;cio efetivo nos &#226;ngulos -4&#176; e -2&#176; direcionaram o fluxo principal para a parede anterior do modelo a&#243;rtico, induzindo um cisalhamento assim&#233;trico e elevado nessa regi&#227;o. Por outro lado, os &#226;ngulos +3&#176; e +5&#176; mimetizam o padr&#227;o fisiol&#243;gico, centralizando o fluxo principal e promovendo uma distribui&#231;&#227;o sim&#233;trica do cisalhamento.</p>
        </sec>
        <sec>
          <title>Conclus&#227;o:</title>
          <p>As medi&#231;&#245;es realizadas sugerem que pequenas altera&#231;&#245;es angulares na pr&#243;tese percut&#226;nea auxiliam na gera&#231;&#227;o de um padr&#227;o hemodin&#226;mico fisiol&#243;gico, podendo contribuir para menor remodelamento a&#243;rtico.</p>
        </sec>
      </abstract>
      <kwd-group xml:lang="pt">
        <title>Palavras-chave:</title>
        <kwd>Implante de Pr&#243;tese de Valva Card&#237;aca</kwd>
        <kwd>Fluxo Sangu&#237;neo Regional</kwd>
        <kwd>Hemodin&#226;mica</kwd>
        <kwd>Estresse de Cisalhamento</kwd>
      </kwd-group>
    </front-stub>
    <body>
      <sec sec-type="intro">
        <title>Introdu&#231;&#227;o</title>
        <p>O implante valvar percut&#226;neo (<italic>Transcatheter Aortic Valve Implantation</italic> - TAVI) foi apresentado por Cribier et al.<xref ref-type="bibr" rid="B1">1</xref> como uma alternativa para o tratamento de indiv&#237;duos com estenose a&#243;rtica grave e alto risco cir&#250;rgico. Com o desenvolvimento de novos sistemas de implante percut&#226;neo, tem havido uma tend&#234;ncia mundial para o uso da TAVI em pacientes com risco cir&#250;rgico intermedi&#225;rio.<xref ref-type="bibr" rid="B2">2</xref><sup>-</sup><xref ref-type="bibr" rid="B4">4</xref> Devido &#224; natureza do procedimento de implante, &#233; esperada uma variabilidade do posicionamento da pr&#243;tese.<xref ref-type="bibr" rid="B5">5</xref> Al&#233;m disso, calcifica&#231;&#245;es exc&#234;ntricas presentes no &#226;nulo a&#243;rtico podem influenciar a orienta&#231;&#227;o final da pr&#243;tese. O posicionamento da v&#225;lvula definir&#225; a posi&#231;&#227;o espacial do seu orif&#237;cio efetivo em rela&#231;&#227;o ao &#226;nulo a&#243;rtico e determinar&#225; a possibilidade de gera&#231;&#227;o de fluxo exc&#234;ntrico no l&#250;men vascular.<xref ref-type="bibr" rid="B6">6</xref>
				</p>
        <p>Diversos estudos j&#225; demonstraram que as caracter&#237;sticas anat&#244;micas da raiz da aorta ir&#227;o influenciar o fluxo sangu&#237;neo no segmento ascendente.<xref ref-type="bibr" rid="B7">7</xref> As modifica&#231;&#245;es no padr&#227;o de fluxo ap&#243;s a TAVI tamb&#233;m representam um importante aspecto que ainda n&#227;o foi estudado em detalhes.<xref ref-type="bibr" rid="B5">5</xref> Evid&#234;ncias na literatura sugerem que o fluxo sangu&#237;neo exc&#234;ntrico est&#225; relacionado ao processo de remodelamento a&#243;rtico, tais como dilata&#231;&#227;o e forma&#231;&#245;es aneurism&#225;ticas.<xref ref-type="bibr" rid="B8">8</xref><sup>-</sup><xref ref-type="bibr" rid="B10">10</xref>
				</p>
        <p>Simula&#231;&#245;es <italic>in vitro</italic> que preservam a anatomia da aorta (paciente-espec&#237;fico) podem contribuir para uma melhor compreens&#227;o das altera&#231;&#245;es de fluxo produzidas por modifica&#231;&#245;es na angula&#231;&#227;o do orif&#237;cio efetivo. Contrariamente aos estudos <italic>in vivo</italic>, simula&#231;&#245;es <italic>in vitro</italic> permitem um controle adequado da geometria de fluxo e condi&#231;&#245;es de contorno, o que possibilita uma avalia&#231;&#227;o sistem&#225;tica da resposta do fluxo &#224;s varia&#231;&#245;es de posicionamento da v&#225;lvula.</p>
        <p>At&#233; o momento, apenas um estudo<xref ref-type="bibr" rid="B11">11</xref> utilizando resson&#226;ncia magn&#233;tica sens&#237;vel ao fluxo - 4D Flow,<xref ref-type="bibr" rid="B12">12</xref> reproduziu a anatomia da aorta de um paciente e avaliou as altera&#231;&#245;es de fluxo produzidas por modifica&#231;&#245;es na inclina&#231;&#227;o do orif&#237;cio efetivo. O objetivo do presente trabalho foi implementar uma simula&#231;&#227;o <italic>in vitro</italic> do fluxo sangu&#237;neo para caracteriza&#231;&#227;o do padr&#227;o hidrodin&#226;mico associado a pequenas varia&#231;&#245;es na inclina&#231;&#227;o do orif&#237;cio efetivo.</p>
      </sec>
      <sec sec-type="methods">
        <title>M&#233;todos</title>
        <p>Estudo descritivo de simula&#231;&#227;o <italic>in vitro</italic> do fluxo sangu&#237;neo em modelo a&#243;rtico tridimensional (3D). Para tal prop&#243;sito, um fantoma vascular foi constru&#237;do a partir da angiotomografia de aorta de um paciente que foi submetido a TAVI. O presente trabalho foi aprovado pelo Comit&#234; de &#201;tica em Pesquisa da institui&#231;&#227;o participante. O paciente do estudo foi um homem de 77 anos, portador de estenose a&#243;rtica grave de etiologia degenerativa, apresentando disfun&#231;&#227;o ventricular leve e classe funcional III (<italic>New York Heart Association</italic>).</p>
        <p>A angiotomografia de aorta foi realizada em um tom&#243;grafo Somatom Sensation 64 canais (Siemens, Alemanha). Foram selecionados cortes tomogr&#225;ficos que contemplavam desde o &#226;nulo a&#243;rtico at&#233; o segmento distal da aorta tor&#225;cica. As imagens DICOM foram transferidas ao <italic>software</italic> Mimics (Materialise, B&#233;lgica) para implementar a segmenta&#231;&#227;o da regi&#227;o a&#243;rtica de interesse. Ap&#243;s o processo de segmenta&#231;&#227;o, o arquivo digital foi exportado no formato. <italic>STL</italic> (<italic>stereolithography</italic>) para realiza&#231;&#227;o da impress&#227;o 3D, com o equipamento Stratasys Fortus 400 mc Systems (Stratasys, EUA), utilizando o material termopl&#225;stico ABS-M30 Affordable FDM (Stratasys, EUA). O modelo 3D foi impresso em escala real e suas dimens&#245;es confirmadas atrav&#233;s das medidas adquiridas pela angiotomografia de aorta (<xref ref-type="fig" rid="f8">Figura 1</xref>).</p>
        <p>
          <fig id="f8">
            <label>Figura 1</label>
            <caption>
              <title>Modelo a&#243;rtico tridimensional. Modelo em material termopl&#225;stico ABS-M30 Affordable FDM (Stratasys, EUA).</title>
            </caption>
            <graphic xlink:href="1678-4170-abc-109-03-0231-70115-gf01-pt.jpg"/></fig>
        </p>
        <p>O modelo a&#243;rtico 3D foi utilizado para constru&#231;&#227;o de um fantoma de silicone, atrav&#233;s do qual a simula&#231;&#227;o <italic>in vitro</italic> do fluxo sangu&#237;neo foi implementada. O modelo 3D foi posicionado em um reservat&#243;rio retangular, constitu&#237;do por placas de acr&#237;lico. O elast&#244;mero de silicone, em estado l&#237;quido, foi adicionado a este reservat&#243;rio, envolvendo o modelo a&#243;rtico. Ap&#243;s 24 horas, o elast&#244;mero de silicone j&#225; se encontrava em estado s&#243;lido, permitindo o processo de retirada do modelo 3D do seu interior. Um corte longitudinal foi feito nas paredes laterais do bloco de elast&#244;mero, com o objetivo de permitir sua separa&#231;&#227;o em duas metades. Ap&#243;s essa manobra, o modelo a&#243;rtico 3D foi removido do interior do fantoma de silicone. As duas metades do conjunto foram reconectadas. A fim de manter o alinhamento correto e preservar a anatomia original da aorta, cinco tirantes met&#225;licos, que atravessaram todo o conjunto, foram utilizados para guiar a remontagem do fantoma. Ap&#243;s as duas metades do fantoma terem sido unidas, conectores do circuito hidr&#225;ulico permitiram que a solu&#231;&#227;o de teste flu&#237;sse para dentro do modelo de silicone.</p>
        <p>O elast&#244;mero de silicone, Sylgard 184 (Dow Corning, EUA), foi selecionado devido &#224;s suas propriedades &#243;pticas, uma vez que uma t&#233;cnica de imagem com utiliza&#231;&#227;o de laser foi empregada para medi&#231;&#227;o dos padr&#245;es de fluxo. Esse silicone possui um &#237;ndice de refra&#231;&#227;o (n = 1.417) pr&#243;ximo ao da solu&#231;&#227;o de teste escolhida para os ensaios, uma mistura aquosa de glicerina (60%, glicerina, n = 1.420).<xref ref-type="bibr" rid="B13">13</xref> A solu&#231;&#227;o de teste escoava em circuito fechado pela instala&#231;&#227;o hidr&#225;ulica, impulsionada por uma bomba de volume constante, NEMO 4501140 (NETZSCH da BRASIL, Brasil). A taxa de fluxo foi ajustada controlando a frequ&#234;ncia de rota&#231;&#227;o da bomba, utilizando um inversor de frequ&#234;ncia CFW 08 (WEG, Brasil).</p>
        <p>O fluxo foi direcionado para o fantoma a&#243;rtico, com seu influxo no l&#250;men vascular ocorrendo na posi&#231;&#227;o equivalente ao &#226;nulo a&#243;rtico. Nesse ponto, um bocal foi conectado ao fantoma, representando a pr&#243;tese a&#243;rtica com a abertura completa de seus folhetos. A &#225;rea interna deste bocal era de 1,5 cm<sup>2</sup>, baseado no orif&#237;cio efetivo da pr&#243;tese do paciente, obtido por meio de um exame ecocardiogr&#225;fico transtor&#225;cico. O fantoma a&#243;rtico possu&#237;a os seguintes pontos de sa&#237;da de fluxo: tronco braquiocef&#225;lico, art&#233;ria car&#243;tida comum esquerda, art&#233;ria subcl&#225;via esquerda e aorta tor&#225;cica.</p>
        <p>A t&#233;cnica de Velocimetria por Imagens de Part&#237;cula (<italic>Particle Image Velocimetry</italic>, PIV) foi escolhida para a an&#225;lise de fluxo.<xref ref-type="bibr" rid="B14">14</xref> As part&#237;culas que serviam como tra&#231;adores do fluxo eram constitu&#237;das por esferas de vidro ocas revestidas de prata, de aproximadamente 13 &#181;m de di&#226;metro, e foram adicionadas &#224; solu&#231;&#227;o de &#225;gua-glicerina. Como fonte de ilumina&#231;&#227;o, utilizou-se um laser de dupla cavidade (BIG SKY Nd: YAG, 120 mJ, Quantel, EUA), gerando um plano de luz com espessura de aproximadamente 0,5 mm. A c&#226;mara digital (PIVCAM 10-30, TSI, EUA) capturava imagens sincronizadas das part&#237;culas na regi&#227;o compreendida entre o &#226;nulo a&#243;rtico e o segmento m&#233;dio ascendente. Para cada estado hidrodin&#226;mico implementado, foram capturadas 3000 imagens das part&#237;culas, produzindo 1500 campos instant&#226;neos de velocidade. Os campos m&#233;dios de velocidade e taxa de cisalhamento foram calculados a partir desses campos instant&#226;neos. O processo de <italic>correla&#231;&#227;o cruzada</italic> foi utilizado para determinar o deslocamento das part&#237;culas tra&#231;adoras, atrav&#233;s do <italic>software</italic> INSIGHT 3G (TSI, EUA). Cada vetor velocidade era obtido para uma &#225;rea de 32 x 32 pixels na imagem, correspondendo a uma resolu&#231;&#227;o de medi&#231;&#227;o de 2 x 2 mm no fluxo real.<xref ref-type="bibr" rid="B14">14</xref>
				</p>
        <p>A t&#233;cnica PIV produziu campos bidimensionais de velocidade. Para caracteriza&#231;&#227;o 3D do fluxo na aorta, as medidas foram realizadas em quatro diferentes planos. O plano de medi&#231;&#227;o central foi posicionado de modo a coincidir com a linha de centro do orif&#237;cio efetivo, atravessando o &#243;stio coronariano direito e contemplando o fluxo principal no interior do fantoma a&#243;rtico. Al&#233;m desse, as medi&#231;&#245;es de velocidade foram realizadas em tr&#234;s outros planos, distando 4 mm entre si. Dois desses planos foram posicionados em dire&#231;&#227;o &#224; regi&#227;o dorsal e um em dire&#231;&#227;o &#224; regi&#227;o ventral.</p>
        <p>Devido &#224; r&#225;pida acelera&#231;&#227;o do fluxo sangu&#237;neo no in&#237;cio da s&#237;stole ventricular, foi formulada a hip&#243;tese de que mudan&#231;as significativas no estresse de cisalhamento ocorrem durante esse per&#237;odo.<xref ref-type="bibr" rid="B15">15</xref> Desse modo, o presente estudo foi projetado para caracteriza&#231;&#227;o do fluxo no ter&#231;o inicial da s&#237;stole ventricular. Para esse fim, foram utilizados os seguintes valores de fluxo cont&#237;nuo: 0,8; 1,6; 2,6; 3,3; 4,0 e 5,3 litros por minuto (l/min). Considerando as propriedades da solu&#231;&#227;o de teste e o di&#226;metro interno do orif&#237;cio efetivo, os n&#250;meros de Reynolds correspondentes a cada n&#237;vel de fluxo foram, respectivamente, 195, 390, 630, 800, 970 e 1285.</p>
        <p>A varia&#231;&#227;o da inclina&#231;&#227;o do orif&#237;cio efetivo foi poss&#237;vel gra&#231;as &#224; constru&#231;&#227;o de um mecanismo chamado <italic>fuso de inclina&#231;&#227;o</italic>, constitu&#237;do por uma haste roscada acoplada a um micr&#244;metro de 0-25 mm (Mitutoyo, Jap&#227;o). Em uma das extremidades dessa haste, uma junta permitia o acoplamento do <italic>fuso de inclina&#231;&#227;o</italic> ao bocal de entrada que estava conectado ao fantoma a&#243;rtico. Ao impor um movimento de transla&#231;&#227;o no <italic>fuso de inclina&#231;&#227;o</italic>, era obtida uma altera&#231;&#227;o na inclina&#231;&#227;o do orif&#237;cio efetivo. Para as vaz&#245;es de fluxo de 2,6 e 3,3 l/min, os seguintes &#226;ngulos de inclina&#231;&#227;o foram implementados: -4&#186;, -2&#186;, 0&#186;, +1&#186;, +3&#186; e +5&#186;. O &#226;ngulo zero de inclina&#231;&#227;o correspondia &#224; coincid&#234;ncia da linha de centro do orif&#237;cio efetivo com a linha de centro do &#226;nulo a&#243;rtico. Os &#226;ngulos com valores negativos inclinavam o fluxo principal em dire&#231;&#227;oao &#243;stio coronariano direito. Por outro lado, &#226;ngulos com valores positivos direcionaram o fluxo principal para a parede posterior (<xref ref-type="fig" rid="f9">Figura 2</xref>).</p>
        <p>
          <fig id="f9">
            <label>Figura 2</label>
            <caption>
              <title>&#194;ngulo de inclina&#231;&#227;o do orif&#237;cio efetivo. AAo: aorta ascendente. CD: art&#233;ria coron&#225;ria direita. &#952;, &#226;ngulo de inclina&#231;&#227;o.</title>
            </caption>
            <graphic xlink:href="1678-4170-abc-109-03-0231-70115-gf02-pt.jpg"/></fig>
        </p>
      </sec>
      <sec sec-type="results">
        <title>Resultados</title>
        <p>Os resultados da an&#225;lise de fluxo entre o &#226;nulo a&#243;rtico e o segmento m&#233;dio ascendente ser&#227;o agora apresentados. A <xref ref-type="fig" rid="f10">Figura 3</xref> foi preparada para auxiliar na interpreta&#231;&#227;o dos resultados. Uma vez que o <italic>software</italic> utilizado para implementa&#231;&#227;o da t&#233;cnica PIV n&#227;o fornece informa&#231;&#245;es sobre os limites f&#237;sicos que limitam o fluxo, uma imagem do modelo vascular foi sobreposta em um campo de velocidade t&#237;pico. As legendas na <xref ref-type="fig" rid="f10">Figura 3</xref> indicam as estruturas anat&#244;micas na vizinhan&#231;a da &#225;rea de fluxo no fantoma a&#243;rtico.</p>
        <p>
          <fig id="f10">
            <label>Figura 3</label>
            <caption>
              <title>Campo de velocidade medido no interior do fantoma a&#243;rtico.</title>
            </caption>
            <graphic xlink:href="1678-4170-abc-109-03-0231-70115-gf03-pt.jpg"/></fig>
        </p>
        <p>A apresenta&#231;&#227;o dos resultados que se seguem abranger&#225; os campos de velocidades e taxa de cisalhamento para os quatro planos de medi&#231;&#227;o descritos. Para cada plano, os resultados s&#227;o apresentados para seis valores de vaz&#227;o de fluxo, variando de 0,8 a 5,3 l/min. Subsequentemente, para o plano central, os resultados ir&#227;o explorar o efeito da varia&#231;&#227;o do &#226;ngulo de inclina&#231;&#227;o do orif&#237;cio efetivo.</p>
        <sec>
          <title>Campo de velocidade</title>
          <p>A <xref ref-type="fig" rid="f11">Figura 4</xref> apresenta os resultados para os campos m&#233;dios de velocidade medidos no fantoma a&#243;rtico para os quatro diferentes planos. Para cada plano, os seis valores de vaz&#227;o de fluxo s&#227;o indicados na figura. Os vetores de velocidade na figura s&#227;o coloridos por sua magnitude, em metros por segundo (m/s), de acordo com a escala &#224; direita da figura.</p>
          <p>
            <fig id="f11">
              <label>Figura 4</label>
              <caption>
                <title>Campos de velocidade nos planos de medi&#231;&#227;o. Campos de velocidade nos planos (a) ventral 4 mm, (b) central, (c) dorsal 4 mm e (d) dorsal 8 mm. Magnitude da velocidade em metros por segundo.</title>
              </caption>
              <graphic xlink:href="1678-4170-abc-109-03-0231-70115-gf04-pt.jpg"/></fig>
          </p>
          <p>Os testes experimentais representaram o ter&#231;o inicial da s&#237;stole ventricular, atingindo velocidades instant&#226;neas m&#225;ximas de aproximadamente 1,2 m/s. Para todos os campos de velocidade apresentados, foi escolhido manter fixa a escala de cor da magnitude, visando facilitar a compara&#231;&#227;o entre os diferentes estados hidrodin&#226;micos. Embora os valores medidos tenham atingido 1,2 m/s, a escala de cores foi ajustada entre 0 e 0,4 m/s, possibilitando a compara&#231;&#227;o entre diferentes casos, uma vez que no plano ventral predominaram os valores com baixa velocidade. Para cada plano de medi&#231;&#227;o, uma an&#225;lise de fluxo qualitativa &#233; agora apresentada.</p>
          <p><bold>Plano ventral 4 mm.</bold> Para as vaz&#245;es de 2,6 e 3,3 l/min, verifica-se que o fluxo &#233; direcionado para a parede anterior. &#192; medida que a vaz&#227;o aumenta para 4,0 e 5,3 l/min, uma maior por&#231;&#227;o do jato principal adquire uma configura&#231;&#227;o centralizada, atingindo uma velocidade de 0,4 m/s, a uma taxa de fluxo de 5,3 l/min (<xref ref-type="fig" rid="f11">Figura 4a</xref>).</p>
          <p><bold>Plano central.</bold> Neste plano, o jato principal j&#225; est&#225; bem definido para a vaz&#227;o de 1,6 l/min, com a sua orienta&#231;&#227;o apresentando um declive acentuado em dire&#231;&#227;o &#224; parede anterior. &#192; medida que a vaz&#227;o aumenta, observa-se um alargamento do jato principal, juntamente com uma ligeira tend&#234;ncia de centraliza&#231;&#227;o do fluxo (<xref ref-type="fig" rid="f11">Figura 4b</xref>).</p>
          <p><bold>Plano dorsal 4 mm.</bold> No primeiro plano dorsal, o jato principal est&#225; bem definido como uma estrutura de fluxo dominante. A partir da taxa de fluxo de 3,3 l/min, observa-se a velocidade m&#225;xima desde a jun&#231;&#227;o sinotubular at&#233; o segmento m&#233;dio ascendente. &#192; medida que a vaz&#227;o aumenta para 4,0 e 5,3 l/min, a regi&#227;o de velocidade m&#225;xima aumenta, como pode ser visto pela domin&#226;ncia da regi&#227;o de colora&#231;&#227;o vermelha (<xref ref-type="fig" rid="f11">Figura 4c</xref>).</p>
          <p><bold>Plano dorsal 8 mm.</bold> Neste plano, observa-se uma regi&#227;o cont&#237;nua de velocidade m&#225;xima para a vaz&#227;o de 2,6 l/min, ocupando a &#225;rea que vai desde a jun&#231;&#227;o sinotubular at&#233; o segmento m&#233;dio ascendente. Neste plano, para todos os n&#237;veis de vaz&#227;o, observa-se um declive esquerdo em dire&#231;&#227;o &#224; parede anterior. Uma an&#225;lise do campo de velocidade para a vaz&#227;o de 5,3 l/min mostra claramente que o jato principal incide sobre a parede anterior, como pode ser verificado pela grande &#225;rea de velocidade m&#225;xima nessa regi&#227;o (<xref ref-type="fig" rid="f11">Figura 4d</xref>).</p>
        </sec>
        <sec>
          <title>Taxa de cisalhamento</title>
          <p>Os campos da taxa de cisalhamento, calculados a partir dos campos de velocidade expostos na <xref ref-type="fig" rid="f11">Figura 4</xref>, ser&#227;o agora apresentados. Como realizado anteriormente para o campo de velocidade, na <xref ref-type="fig" rid="f12">Figura 5</xref>, uma imagem do fantoma vascular foi sobreposta ao campo de cisalhamento para facilitar a interpreta&#231;&#227;o dos resultados.</p>
          <p>
            <fig id="f12">
              <label>Figura 5</label>
              <caption>
                <title>Taxa de cisalhamento no interior do fantoma a&#243;rtico.</title>
              </caption>
              <graphic xlink:href="1678-4170-abc-109-03-0231-70115-gf05-pt.jpg"/></fig>
          </p>
          <p>Os resultados para a taxa de cisalhamento s&#227;o mostrados na <xref ref-type="fig" rid="f13">Figura 6</xref>, sendo exibidos para os mesmos planos e vaz&#245;es de fluxo que os resultados do campo de velocidade. A escala de cores na figura representa a magnitude da taxa de cisalhamento, variando de 0 a 15 s<sup>-1</sup>.</p>
          <p>
            <fig id="f13">
              <label>Figura 6</label>
              <caption>
                <title>Taxa de cisalhamento nos planos de medi&#231;&#227;o. Nos planos (a) ventral 4 mm, (b) central, (c) dorsal 4 mm e (d) dorsal 8 mm. Magnitude da taxa de cisalhamento em s<sup>-1</sup>.</title>
              </caption>
              <graphic xlink:href="1678-4170-abc-109-03-0231-70115-gf06-pt.jpg"/></fig>
          </p>
          <p><bold>Plano ventral 4 mm.</bold> No plano ventral, uma regi&#227;o de cisalhamento elevado &#233; identificada na vaz&#227;o de 2,6 l/min. A 3,3 l/min, ocorre um valor m&#225;ximo de cisalhamento, como indicado pela faixa vermelha. Essa faixa &#233; visualizada de forma alongada, inclinada em dire&#231;&#227;o &#224; parede anterior. Em vaz&#245;es maiores, 4,0 e 5,3 l/min, a faixa vermelha se estende desde o topo da imagem at&#233; a parte inferior. Regi&#245;es de alto cisalhamento s&#227;o encontrados perto do orif&#237;cio efetivo, na parte inferior das figuras (<xref ref-type="fig" rid="f13">Figura 6a</xref>).</p>
          <p><bold>Plano central.</bold> Neste plano, o cisalhamento m&#225;ximo j&#225; &#233; identificado, mesmo de modo incipiente, com a vaz&#227;o de 0,8 l/min. A partir da vaz&#227;o de 1,6 l/min, a faixa de cisalhamento m&#225;ximo ocupa toda a extens&#227;o das imagens. Em n&#237;veis de fluxo subsequentes, observa-se um alargamento progressivo dessa &#225;rea (<xref ref-type="fig" rid="f13">Figura 6b</xref>).</p>
          <p><bold>Plano dorsal 4 mm.</bold> A partir de 2,6 l/min, o cisalhamento m&#225;ximo apresenta uma inclina&#231;&#227;o para a parede anterior. Al&#233;m disso, est&#225; presente um alargamento expressivo dessa faixa &#224; medida que a vaz&#227;o aumenta. Apesar do padr&#227;o de inclina&#231;&#227;o para a esquerda, vale ressaltar a ocorr&#234;ncia de um pequeno setor com cisalhamento m&#225;ximo no canto superior direito das imagens, iniciando com a vaz&#227;o de 2,6 l/min (<xref ref-type="fig" rid="f13">Figura 6c</xref>).</p>
          <p><bold>Plano dorsal 8 mm.</bold> Neste plano, o alargamento da regi&#227;o de m&#225;ximo cisalhamento tamb&#233;m &#233; percebido a partir da vaz&#227;o de 2,6 l/min. A inclina&#231;&#227;o da regi&#227;o de alto cisalhamento em dire&#231;&#227;o ao canto superior esquerdo das imagens permanece, mostrando ainda uma dire&#231;&#227;o preferencial para a parede anterior (<xref ref-type="fig" rid="f13">Figura 6d</xref>).</p>
        </sec>
        <sec>
          <title>Influ&#234;ncia do &#226;ngulo de inclina&#231;&#227;o do orif&#237;cio efetivo</title>
          <p>A influ&#234;ncia da inclina&#231;&#227;o do orif&#237;cio efetivo sobre as caracter&#237;sticas de fluxo foi avaliada por medi&#231;&#245;es realizadas no plano central, para as vaz&#245;es de 2,6 e 3,3 l/min. Os &#226;ngulos de inclina&#231;&#227;o variaram de -4&#176; a +5&#176;, de acordo com a nota&#231;&#227;o da <xref ref-type="fig" rid="f9">Figura 2</xref>.</p>
        </sec>
        <sec>
          <title>Campos de velocidade e taxa de cisalhamento</title>
          <p>A <xref ref-type="fig" rid="f14">Figura 7</xref> apresenta os resultados para a influ&#234;ncia da inclina&#231;&#227;o do orif&#237;cio efetivo nos campos de velocidade e taxa de cisalhamento. Para 2,6 l/min, em &#226;ngulo de inclina&#231;&#227;o zero, o fluxo principal foi direcionado para a esquerda, atingindo a parede anterior na por&#231;&#227;o m&#233;dio ascendente. Quando o orif&#237;cio efetivo foi posicionado em valores negativos, -4&#176; e -2&#176;, essa excentricidade de fluxo foi pronunciada. Para pequenas inclina&#231;&#245;es com valores positivos, +1&#186;, +3&#186; e +5&#186;, verificou-se uma tend&#234;ncia &#224; centraliza&#231;&#227;o do fluxo. Com esta pequena altera&#231;&#227;o de inclina&#231;&#227;o, o fluxo principal &#233; dirigido para a parede posterolateral (<xref ref-type="fig" rid="f14">Figura 7a</xref>).</p>
          <p>
            <fig id="f14">
              <label>Figura 7</label>
              <caption>
                <title>Campos de velocidade e taxa de cisalhamento para (a, c) 2,6 l/min e (b, d) 3,3 l/min. Inclina&#231;&#227;o do orif&#237;cio efetivo: -4&#176;, -2&#176;, 0&#176;, +1&#176;, +3&#176; e +5&#176;.</title>
              </caption>
              <graphic xlink:href="1678-4170-abc-109-03-0231-70115-gf07-pt.jpg"/></fig>
          </p>
          <p>Em 3,3 l/min, os campos de velocidade mostram que, para os &#226;ngulos negativos, o jato principal evolui com uma largura diminu&#237;da em compara&#231;&#227;o com o &#226;ngulo zero. Os &#226;ngulos negativos apresentam magnitudes de velocidade semelhantes, com um declive esquerdo. Quando a inclina&#231;&#227;o alcan&#231;a valores positivos, observa-se uma tend&#234;ncia para centraliza&#231;&#227;o do jato principal. Como consequ&#234;ncia, valores mais altos de velocidade surgem no interior do jato, como pode ser visto pelo surgimento das regi&#245;es de colora&#231;&#227;o vermelha. Os padr&#245;es de velocidade s&#227;o semelhantes para os &#226;ngulos +1&#176; e +3&#176;, mantendo um declive esquerdo na metade superior da imagem. A inclina&#231;&#227;o +5&#176; mostra uma centraliza&#231;&#227;o mais significativa do jato principal (<xref ref-type="fig" rid="f14">Figura 7b</xref>).</p>
          <p>As <xref ref-type="fig" rid="f14">Figuras 7c</xref> e <xref ref-type="fig" rid="f14">7d</xref> apresentam os resultados para a taxa de cisalhamento. A 2,6 l/min, os resultados indicam que para as inclina&#231;&#245;es negativas, as faixas de cor vermelha exibem uma dimens&#227;o mais estreita em rela&#231;&#227;o &#224;s outras posi&#231;&#245;es angulares. Para as inclina&#231;&#245;es positivas, observa-se um alargamento da &#225;rea de m&#225;ximo cisalhamento, al&#233;m de sua centraliza&#231;&#227;o (+3&#176; e +5&#176;). Para a inclina&#231;&#227;o +5&#176;, a regi&#227;o de m&#225;ximo cisalhamento &#233; mantida pr&#243;xima &#224; linha de centro do modelo a&#243;rtico (<xref ref-type="fig" rid="f14">Figura 7c</xref>).</p>
          <p>A an&#225;lise dos resultados do cisalhamento para a vaz&#227;o de 3,3 l/min indica que, para inclina&#231;&#245;es negativas, o cisalhamento m&#225;ximo apresenta um declive esquerdo. Nas inclina&#231;&#245;es positivas de +1&#186; e +3&#186;, o cisalhamento m&#225;ximo est&#225; localizado na por&#231;&#227;o central. A proximidade da regi&#227;o de alto cisalhamento &#224; parede posterolateral &#233; observada para o &#226;ngulo +5&#176;, uma vez que a faixa vermelha ocupa o lado direito da imagem (<xref ref-type="fig" rid="f14">Figura 7d</xref>).</p>
        </sec>
      </sec>
      <sec sec-type="discussion">
        <title>Discuss&#227;o</title>
        <p>No presente estudo, foi realizada uma simula&#231;&#227;o <italic>in vitro</italic> para caracteriza&#231;&#227;o do padr&#227;o hidrodin&#226;mico do fluxo sangu&#237;neo durante a s&#237;stole ventricular em um modelo a&#243;rtico 3D, representativo da anatomia de um paciente submetido a TAVI. Al&#233;m disso, foram identificadas as altera&#231;&#245;es de fluxo atrav&#233;s do campo de velocidade e taxa de cisalhamento devido &#224; varia&#231;&#227;o de seis &#226;ngulos de inclina&#231;&#227;o do orif&#237;cio efetivo.</p>
        <p>A otimiza&#231;&#227;o do implante da pr&#243;tese percut&#226;nea, al&#233;m do seu posicionamento de acordo com o padr&#227;o de fluxo nativo do paciente, pode ser um meio de garantir seu melhor desempenho ap&#243;s a TAVI.<xref ref-type="bibr" rid="B16">16</xref><sup>,</sup><xref ref-type="bibr" rid="B17">17</xref> A gera&#231;&#227;o de um fluxo sangu&#237;neo com um padr&#227;o hemodin&#226;mico mais pr&#243;ximo ao fisiol&#243;gico pode ter um impacto ben&#233;fico na sobreviv&#234;ncia dos pacientes.<xref ref-type="bibr" rid="B18">18</xref><sup>,</sup><xref ref-type="bibr" rid="B19">19</xref>
				</p>
        <p>A an&#225;lise qualitativa do campo de velocidade e da taxa de cisalhamento para cada plano analisado no presente estudo revela claramente a natureza 3D do fluxo no interior do modelo a&#243;rtico. Esses dados destacam a import&#226;ncia de empregar modelos realistas da geometria da aorta e as limita&#231;&#245;es de estudos <italic>in vitro</italic> que representam a aorta utilizando modelos circulares e axissim&#233;tricos.<xref ref-type="bibr" rid="B5">5</xref>
				</p>
        <p>Groves et al.<xref ref-type="bibr" rid="B5">5</xref> estudaram o efeito das varia&#231;&#245;es do posicionamento axial da pr&#243;tese percut&#226;nea. Como representa&#231;&#227;o da aorta, utilizou um tubo circular de acr&#237;lico com 30 mm de di&#226;metro interno. Para a vaz&#227;o de 4 l/min, apenas o posicionamento a 5 mm abaixo do &#226;nulo a&#243;rtico resultou em baixos valores de cisalhamento, al&#233;m de uma distribui&#231;&#227;o sim&#233;trica.<xref ref-type="bibr" rid="B5">5</xref> No presente estudo, o orif&#237;cio efetivo permaneceu posicionado a menos de 5 mm do &#226;nulo a&#243;rtico. No entanto, como nosso modelo preservou a anatomia da aorta, os resultados diferiram sobre os planos avaliados, n&#227;o sendo axissim&#233;tricos como no estudo de Groves et al.<xref ref-type="bibr" rid="B5">5</xref>
				</p>
        <p>Groves et al.<xref ref-type="bibr" rid="B5">5</xref> e Wilton e Jahangiri<xref ref-type="bibr" rid="B20">20</xref> consideram a hip&#243;tese de que o cisalhamento elevado, al&#233;m de sua distribui&#231;&#227;o assim&#233;trica, estaria relacionado &#224; dilata&#231;&#227;o a&#243;rtica e maior chance de dissec&#231;&#227;o.<xref ref-type="bibr" rid="B5">5</xref><sup>,</sup><xref ref-type="bibr" rid="B10">10</xref><sup>,</sup><xref ref-type="bibr" rid="B20">20</xref><sup>,</sup><xref ref-type="bibr" rid="B21">21</xref> Com base nessa hip&#243;tese, seria desej&#225;vel otimizar o posicionamento axial e a inclina&#231;&#227;o do orif&#237;cio efetivo, de modo que seriam obtidas distribui&#231;&#245;es de tens&#227;o de cisalhamento sim&#233;tricas e de baixa magnitude. Nesse contexto, um posicionamento axial a menos de 5 mm do &#226;nulo a&#243;rtico, associado a &#226;ngulos de inclina&#231;&#227;o positivos, seriam os valores sugeridos nesse caso particular. Groves et al.<xref ref-type="bibr" rid="B5">5</xref> tamb&#233;m reiteram que altos n&#237;veis de tens&#227;o de cisalhamento, a jusante da pr&#243;tese, poderiam contribuir para a redu&#231;&#227;o da sua durabilidade, devido ao maior estresse mec&#226;nico, o que enfatiza a import&#226;ncia da otimiza&#231;&#227;o do posicionamento da pr&#243;tese.</p>
        <p>Trauzeddel et al.<xref ref-type="bibr" rid="B7">7</xref> avaliaram os padr&#245;es de fluxo sangu&#237;neo na aorta ascendente dos pacientes ap&#243;s TAVI, comparando-os com aqueles de pacientes submetidos a troca valvar a&#243;rtica convencional (TVAo) e de indiv&#237;duos saud&#225;veis. Esse estudo mostrou que tanto a TAVI quanto a TVAo resultaram em valores m&#225;ximos de cisalhamento na parede anterior direita, enquanto valores m&#237;nimos foram encontrados na parede posterior esquerda. Os indiv&#237;duos saud&#225;veis, entretanto, exibiram um fluxo fisiol&#243;gico centralizado e uma distribui&#231;&#227;o sim&#233;trica de tens&#245;es de cisalhamento ao longo da circunfer&#234;ncia a&#243;rtica.<xref ref-type="bibr" rid="B7">7</xref> A distribui&#231;&#227;o do cisalhamento m&#225;ximo na parede anterior de pacientes submetidos a TAVI e TVAo coincide com os resultados de simula&#231;&#227;o <italic>in vitro</italic> do presente estudo para as inclina&#231;&#245;es negativas do orif&#237;cio efetivo. No modelo experimental, foi poss&#237;vel modificar essa inclina&#231;&#227;o em busca de uma configura&#231;&#227;o que produzisse um padr&#227;o de fluxo centralizado. Como os resultados apresentados indicam, uma diminui&#231;&#227;o da a&#231;&#227;o do cisalhamento na parede anterior foi obtida atrav&#233;s de pequenas inclina&#231;&#245;es positivas. Por exemplo, no &#226;ngulo de +3&#176;, a regi&#227;o que exibe os valores m&#225;ximos de cisalhamento permaneceu confinada &#224; por&#231;&#227;o central do fantoma a&#243;rtico. Quando a inclina&#231;&#227;o foi aumentada para +5&#176;, a regi&#227;o de m&#225;ximo cisalhamento aproximou-se da parede posterolateral.</p>
        <p>A presente an&#225;lise foi limitada aos achados da anatomia de um paciente. No entanto, esta simula&#231;&#227;o representou uma anatomia real e 3D, promovendo uma avan&#231;o significativo em rela&#231;&#227;o aos modelos circulares e axissim&#233;trico utilizados nos estudos anteriores.<xref ref-type="bibr" rid="B5">5</xref><sup>,</sup><xref ref-type="bibr" rid="B6">6</xref>
				</p>
        <p>Na presente pesquisa, apenas o ter&#231;o inicial da s&#237;stole ventricular foi representado. No entanto, sabe-se que durante a s&#237;stole ocorre a maior preval&#234;ncia de valores de cisalhamento elevado na aorta ascendente. Al&#233;m disso, como esse per&#237;odo do ciclo card&#237;aco &#233; caracterizado por mudan&#231;as abruptas dos valores de velocidade, consequentemente, tamb&#233;m &#233; esperada uma varia&#231;&#227;o r&#225;pida nos valores de cisalhamento.<xref ref-type="bibr" rid="B15">15</xref> Al&#233;m disso, neste estudo, um segmento de um fluxo puls&#225;til, mais precisamente, o ter&#231;o inicial da s&#237;stole ventricular, foi representado por seis diferentes n&#237;veis de fluxo cont&#237;nuo. Atrav&#233;s dessa abordagem, &#233; poss&#237;vel que algumas estruturas de fluxo secund&#225;rio n&#227;o tenham sido capturadas. No entanto, na ci&#234;ncia cardiovascular, &#233; comum modelar os v&#225;rios est&#225;gios de um fluxo puls&#225;til, por uma sequ&#234;ncia crescente de valores de fluxo cont&#237;nuo.<xref ref-type="bibr" rid="B11">11</xref><sup>,</sup><xref ref-type="bibr" rid="B22">22</xref>
				</p>
        <p>Com base nesses achados, podem ser propostos novos projetos de pr&#243;teses, com a capacidade de altera&#231;&#227;o da inclina&#231;&#227;o de seu orif&#237;cio efetivo, possibilitando a gera&#231;&#227;o de um fluxo centralizado na aorta ascendente, mimetizando um padr&#227;o hemodin&#226;mico fisiol&#243;gico.</p>
      </sec>
      <sec sec-type="conclusions">
        <title>Conclus&#227;o</title>
        <p>O presente estudo evidenciou o car&#225;ter 3D do padr&#227;o de fluxo no interior do fantoma vascular, al&#233;m de identificar uma faixa de valores otimizados para o &#226;ngulo de inclina&#231;&#227;o do orif&#237;cio efetivo. Para pequenas inclina&#231;&#245;es positivas, foi obtido um fluxo fisiol&#243;gico centralizado no segmento a&#243;rtico m&#233;dio ascendente, eliminando os altos valores de tens&#227;o mec&#226;nica da parede anterior, que prevaleceram para as orienta&#231;&#245;es negativas do orif&#237;cio efetivo (-4&#176; e -2&#176;). Nos posicionamentos com inclina&#231;&#245;es positivas, as regi&#245;es que apresentaram n&#237;veis elevados de cisalhamento foram mantidas pr&#243;ximas &#224; linha de centro do fantoma vascular.</p>
      </sec>
    </body>
    <back>
      <fn-group>
        <fn fn-type="supported-by">
          <p>
            <bold>Fontes de financiamento</bold>
          </p>
          <p>O presente estudo n&#227;o teve fontes de financiamento externas.</p>
        </fn>
        <fn fn-type="other">
          <p>
            <bold>Vincula&#231;&#227;o acad&#234;mica</bold>
          </p>
          <p>Este artigo &#233; parte de tese de Doutorado de Bruno Alvares de Azevedo Gomes pela Universidade Federal do Rio de Janeiro.</p>
        </fn>
      </fn-group>
      <ack>
        <title>Agradecimentos</title>
        <p>Os autores agradecem a Carolina Azevedo pelo trabalho art&#237;stico nas figuras do artigo.</p>
      </ack>
    </back>
  </sub-article>
</article>
