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We mathematically extended the law of Laplace to estimate aortic wall stress within this cloverleaf region, simultaneously identifying a new metric of aortic root dimension that can be applied to clinical measurement of the aortic root and sinuses of Valsalva on clinical computerized tomographic scans. Enforcing equilibrium between blood pressure and wall stress, finite element computations were performed to evaluate the mathematical derivation. The resulting Laplace diameter was compared with existing methods of aortic root measurement across four patient groups: non-syndromic aneurysm, bicuspid aortic valve, Marfan syndrome, and non-dilated root patients (total 106 patients, 62\u00a0M, 44 F). (1)\n                    <jats:italic>Wall stress<\/jats:italic>\n                    : Mean wall stress at the depth of the sinuses followed this equation: Wall stress\u2009=\u2009BP\u2009\u00d7\u2009Circumscribing circle diameter\/(2\u2009\u00d7\u2009Aortic wall thickness). Therefore, the diameter of the circle enclosing the root cloverleaf, that is, twice the distance between the center, where the sinus-to-commissure lines coincide, and the depth of the sinuses, may replace diameter in the Laplace relation for a cloverleaf cross-section (or any shaped cross-section with two or more planes of symmetry). This mathematically derived result was verified by computational finite element analyses. (2)\n                    <jats:italic>Diameters<\/jats:italic>\n                    : CT scan measurements showed a significant difference between this new metric, the Laplace diameter, and the sinus-to-commissure, mid-sinus-to-mid-sinus, and coronal measurements in all four groups (\n                    <jats:italic>p-value<\/jats:italic>\n                    \u2009&lt;\u20090.05). The average Laplace diameter measurements differed significantly from the other measurements in all patient groups. Among the various possible measurements within the aortic root, the diameter of the circumscribing circle, enclosing the cloverleaf, represents the diameter most closely related to wall stress. This diameter is larger than the other measurements, indicating an underestimation of wall stress by prior measurements, and otherwise provides an unbiased, convenient, consistent, physics-based measurement for clinical use.\n                  <\/jats:p>\n                  <jats:p>\n                    <jats:bold>Graphical abstract<\/jats:bold>\n                  <\/jats:p>\n                  <jats:p>\n                    \u201cDiameter\u201d applies to circles. Our mathematical derivation of an extension of the law of Laplace, from\n                    <jats:italic>circular<\/jats:italic>\n                    to\n                    <jats:italic>cloverleaf<\/jats:italic>\n                    cross-sectional geometries of the aortic root, has implications for measurement of aortic root \u201cdiameter.\u201d The suggested method is as follows: (1) the \u201ccenter\u201d of the aortic root is identified by drawing three sinus-to-commissure lines. The intersection of these three lines identifies the \u201ccenter\u201d of the cloverleaf. (2) The largest radius from this center point to any of the sinuses is identified as the \u201cradius\u201d of the aortic root. (3) This radius is doubled to give the \u201cdiameter\u201d of the aortic root. We find that this diameter best corresponds to maximal wall stress in the aortic root. Please note that this diameter defines the smallest circle that completely encloses the cloverleaf shape, touching the depths of all three sinuses.\n                  <\/jats:p>","DOI":"10.1007\/s10554-023-02847-5","type":"journal-article","created":{"date-parts":[[2023,4,12]],"date-time":"2023-04-12T15:02:35Z","timestamp":1681311755000},"page":"1345-1356","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":12,"title":["Extended law of laplace for measurement of the cloverleaf anatomy of the aortic root"],"prefix":"10.1007","volume":"39","author":[{"given":"Ehsan","family":"Ban","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Paris-Dimitrios","family":"Kalogerakos","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Ramak","family":"Khosravi","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Bulat A.","family":"Ziganshin","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Hesham","family":"Ellauzi","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Abhay B.","family":"Ramachandra","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Mohammad A.","family":"Zafar","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Jay D.","family":"Humphrey","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-6255-8139","authenticated-orcid":false,"given":"John A.","family":"Elefteriades","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"297","published-online":{"date-parts":[[2023,4,12]]},"reference":[{"issue":"5","key":"2847_CR1","doi-asserted-by":"publisher","first-page":"203","DOI":"10.1016\/j.cpcardiol.2008.01.004","volume":"33","author":"JA Elefteriades","year":"2008","unstructured":"Elefteriades JA (2008) Thoracic aortic aneurysm: reading the enemy\u2019s playbook. 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Ban, Kalogerakos, Khosravi, Ziganshin, Ellauzi, Ramachandra, and Zafar have no disclosures. \nJ.D. Humphrey: Member of the Scientific Advisory Board who also receives consulting fees from HeartFlow, Inc., a company using computational modeling to assess coronary artery disease. \nJ.A. Elefteriades:  Principal, CoolSpine. CoolSpine has no clinical products.","order":2,"name":"Ethics","group":{"name":"EthicsHeading","label":"Competing interests"}},{"value":"Drs. Ban, Kalogerakos, Khosravi, Ziganshin, Ellauzi, Ramachandra, and Zafar have no disclosures. J.D. Humphrey:\u00a0Member of the Scientific Advisory Board who also receives consulting fees from HeartFlow, Inc., a company using computational modeling to assess coronary artery disease. J.A. Elefteriades: Principal, CoolSpine. CoolSpine has no clinical products.","order":3,"name":"Ethics","group":{"name":"EthicsHeading","label":"Conflict of interest"}},{"value":"This study was approved by the Yale University Human Investigation Committee.","order":4,"name":"Ethics","group":{"name":"EthicsHeading","label":"Ethical approval"}}]}}