Left Ventricular Volume in Bovines: The Correlation between Teichholz’s Medical Mathematical Method and the Volume of the Truncated Prolate Spheroid
Abstract
1. Introduction
2. The Manufacturing of the Molds and Collection of Measurements
3. Results and Discussions
4. Conclusions
Author Contributions
Acknowledgments
Conflicts of Interest
Abbreviations
TPS | Truncated prolate spheroid |
LV | Left ventricle |
LVV | Left ventricular volume |
RV | real left ventricular volume |
References
- Galrinho, A.; Branco, L.M.; Soares, R.M.; Miranda, F.E.; Leal, A.; Ferreira, R.C. Volume da aurícula esquerda: Um velho cálculo ecocardiográfico com uma importância prognóstica renovada. Um estudo em doentes com miocardiopatia dilatada. Revista Portuguesa de Cardiologia 2009, 28, 1049–1060. (In Portuguese) [Google Scholar] [PubMed]
- Martins, E.; Silva-Cardoso, J.; Bicho, M.; Bourbon, M.; Ceia, F.; Rebocho, M.J.; Moura, B.; Fonseca, C.; Correia, M.J.; Brito, D.; et al. Study Portuguese in Dilated Myocardiopathies Family: The FATIMA Study. Rev. Port. Cardiol. 2008, 27, 1029–1042. [Google Scholar] [PubMed]
- Filho, P.R.P.F. Padrões de Hipertrofia e Geometria do Ventrículo Esquerdo pela Ecocardiografia Transtorácica. Revista Brasileira de Ecocardiografia e Imagem Cardiovascular 2012, 25, 103–115. (In Portuguese) [Google Scholar]
- Domingues, J.S.; Barbosa, M.P.; Vale, M.P. Mathematical and Computational Aspects in Partial Ventriculectomy. In Proceedings of the 8th International Conference on Advanced Computational Engineering and Experimenting, Paris, France, 30 June–3 July 2014. [Google Scholar]
- Domingues, J.S.; Vale, M.P.; Barbosa, M.P. Partial left ventriculectomy: Have well-succeeded cases and innovations in the procedure been observed in the last 10 years? Braz. J. Cardiovasc. Surg. 2015, 30, 579–585. [Google Scholar] [CrossRef] [PubMed]
- Teichholz, L.E.; Kreulen, T.; Herman, M.V.; Gorlin, R. Problems in Echocardiographic Volume Determinations: Echocardiographic-Angiographic Correlations in the Presence or Absence of Asynergy. Am. J. Cardiol. 1976, 37, 7–11. [Google Scholar] [CrossRef]
- Lang, R.M.; Badano, L.P.; Mor-Avi, V.; Afilalo, J.; Armstrong, A.; Ernande, L.; Flachskampf, F.A.; Foster, E.; Goldstein, S.A.; Kuznetsova, T.; et al. Recommendations for Cardiac Chamber Quantification by Echocardiography in Adults: An Update from the American Society of Echocardiography and the European Association of Cardiovascular Imaging. J. Am. Soc. Echocardiogr. 2015, 28, 1–39. [Google Scholar] [CrossRef] [PubMed]
- Wood, P.W.; Choy, J.B.; Nanda, N.C.; Becher, H. Left ventricular ejection fraction and volumes: It depends on the imaging method. Echocardiography 2014, 31, 87–100. [Google Scholar] [CrossRef] [PubMed]
- Chengode, S. Left ventricular global systolic function assessment by echocardiography. Ann. Card. Anaesth. 2016, 19, 26–34. [Google Scholar] [CrossRef] [PubMed]
- Costa, S.A. Fatores Prognósticos na Insuficiência Cardíaca Chagásica com Disfunção Ventricular Grave. Master’s Thesis, Health Sciences, Medical School, Federal University of Goiás, Goiânia, Brazil, 2016. Available online: http://repositorio.bc.ufg.br/tede/handle/tede/6083 (accessed on 10 September 2018).
- Andrade, M.F.A. Perfil Ecocardiográfico Convencional e por Strain em Pacientes com Mucopolissacaridose na Bahia-Brasil. Master’s Thesis, Institute of Health Sciences, Federal University of Bahia, Salvador, Brazil, 2016. Available online: http://repositorio.ufba.br/ri/handle/ri/22545 (accessed on 10 September 2018).
- Domingues, J.S. Modelagem Matemática da Ventriculectomia Parcial Esquerda e Determinação de Parâmetro Cardíaco do Ventrículo Esquerdo. Ph.D. Thesis, Mechanical Engineering, Federal University of Minas Gerais, Belo Horizonte, Brazil, 2017. Available online: http://www.bibliotecadigital.ufmg.br/dspace/handle/1843/BUBD-AN5NKP (accessed on 10 September 2018).
- Lopez, L.; Colan, S.D.; Frommelt, P.C.; Ensing, G.J.; Kendall, K.; Younoszai, A.K.; Lai, W.W. Recomendações para os métodos de quantificação durante a realização do ecocardiograma pediátrico: Relatório escrito pelo grupo da Sociedade Americana de Ecocardiografia e do Conselho em Cardiopatias Congênitas. Am. Soc. Echocardiogr. 2014. Available online: http://asecho.org/wordpress/wp-content/uploads/2014/01/PedQuantification-Portuguese-5.pdf (accessed on 10 September 2018).
- Otto, C.M. Fundamentos de Ecocardiografia Clínica, 5th ed.; Elsevier: Rio de Janeiro, Brazil, 2014. [Google Scholar]
- Marks, A.R. Cardiac function and circulatory control. In Goldman’s Cecil Medicine, 24th ed.; Goldman, L., Schafer, A.I., Eds.; Elsevier: Philadelphia, PA, USA, 2011; Volume 1. [Google Scholar]
- Da Silva, A.A.; da Silva, A.F.; Ferreira, C.B.N.D.; Botelho, E.S.L.; de Vasconcellos, H.D.; de Souza, K.M.; Fernandes, M.R.; Filho, M.F.S. Ecocardiograma Transesofágico Intraoperatório. In ETI Ecocardiografia Transesofágica no Intraoperatório; Bagatini, A., Pires, O.C., Filho, M.F.S., Ferreira, C.B.N.D., Eds.; Sociedade Brasileira de Anestesiologia: Rio de Janeiro, Brazil, 2013. [Google Scholar]
- Piveta, R.B.; Hajjar, L.A.; Osella, O.F.S.; Vieira, M.L.C.; Filho, R.K. Cardiomiopatia Pós-quimioterapia. Avanços Recentes e Perspectivas da Ecocardiografia nas Cardiopatias, 1st ed.; Ramires, J.A.F., Filho, R.K., Vieira, M.L.C., Eds.; Atheneu: Rio de Janeiro, Brazil, 2016. (In Portuguese) [Google Scholar]
- Zipes, D.P.; Libby, P.; Bonow, R.O.; Mann, D.L.; Tomaselli, G.F. Braunwald’s Heart Disease: A Textbook of Cardiovascular Medicine, 11th ed.; Elsevier: New York, NY, USA, 2018. [Google Scholar]
- De Andrade, M.M.; Espinoza, B.L.M.; de Oliveira Nascimento, F.A.; Rocha, A.; Vasconcelos, D.F.; de Jesus, P.; Carvalho, H.S. Hybrid algorithm for segmentation of the left ventricle in two-dimensional echocardiography. Revista Brasileira de Engenharia Biomedica 2006, 22, 23–33. [Google Scholar]
- Melo, S.A., Jr.; Macchiavello, B.; Andrade, M.M.; Carvalho, J.L.; Carvalho, H.S.; Vasconcelos, D.F.; Berger, P.A.; da Rocha, A.F.; Nascimento, F.A.O. Semi-automatic algorithm for construction of the LV area variation curve over a complete cardiac cycle. Biomed. Eng. Online 2010, 9, 5. [Google Scholar] [CrossRef] [PubMed]
- Domingues, J.S.; Vale, M.P.; Martinez, C.B. New mathematical model for the surface area of the left ventricle by the truncated prolate spheroid. Sci. World J. 2017, 2017, 6981515. [Google Scholar] [CrossRef] [PubMed]
- Baccani, B.; Domenichini, F.; Pedrizzetti, G. Model and influence of mitral valve opening during the left ventricular filling. J. Biomech. 2003, 36, 355–361. [Google Scholar] [CrossRef]
- Nielsen, P.M.F.; Le Grice, I.J.; Smaill, B.H.; Hunter, P.J. Mathematical model of geometry and fibrous structure of the heart. Am. J. Physiol. 1991, 260 Pt 2, H1365–H1378. [Google Scholar] [CrossRef]
- Katz, T.L.; Mattos, C.F.G.; Kowatsch, I.; Vieira, M.L. Critical Analysis of Echocardiographic Measurements of Left Ventricular Mass. Revista Brasileira de ecocardiografia e Imagem Cardiovascular 2010, 23, 95–100. [Google Scholar]
- Bezerra, S.J. Um Modelo Matemático Para o Cálculo do Volume Ventricular Esquerdo. Master’s Thesis, Applied Mathematics, UNICAMP, Campinas, Brazil, 1985. Available online: http://repositorio.unicamp.br/handle/REPOSIP/307328 (accessed on 10 September 2018).
- Martin, G.; Sutton, S.J.; Plappert, T. The Echocardiographers’ Guide; Informa Healthcare: London, UK, 2006; pp. 35–42. [Google Scholar]
- Brown, D.; Garber, J. Cardiac Size. Available online: http://www.vermontveterinarycardiology.com/index.php/for-cardiologists/for-cardiologists?id=136 (accessed on 10 September 2018).
Molds | d (cm) | (cm) | c (cm) | (cm) | RV (mL) |
---|---|---|---|---|---|
1 | 5.25 | 2.63 | 7.78 | 3.89 | 144.67 |
2 | 3.40 | 1.70 | 5.04 | 2.52 | 41.67 |
3 | 6.90 | 3.45 | 10.22 | 5.11 | 212.50 |
4 | 5.07 | 2.54 | 7.51 | 3.76 | 118.32 |
5 | 5.35 | 2.68 | 7.93 | 3.96 | 158.50 |
6 | 6.20 | 3.10 | 9.19 | 4.59 | 199.10 |
7 | 5.65 | 2.83 | 8.37 | 4.19 | 175.10 |
8 | 6.00 | 3.00 | 8.89 | 4.44 | 165.20 |
9 | 4.95 | 2.48 | 7.33 | 3.67 | 119.80 |
10 | 5.35 | 2.68 | 7.93 | 3.96 | 144.90 |
Molds | (mL) | (mL) | (%) | (%) |
---|---|---|---|---|
1 | 132.41 | 168.37 | 8.47 | 16.38 |
2 | 47.43 | 45.73 | 13.82 | 9.74 |
3 | 247.35 | 382.40 | 16.40 | 79.95 |
4 | 122.12 | 151.64 | 3.21 | 28.16 |
5 | 138.31 | 168.37 | 12.74 | 6.23 |
6 | 193.99 | 277.31 | 2.57 | 39.28 |
7 | 156.84 | 209.86 | 10.43 | 19.85 |
8 | 180.00 | 251.33 | 8.97 | 52.14 |
9 | 115.51 | 141.12 | 3.58 | 17.80 |
10 | 138.31 | 178.17 | 4.48 | 22.96 |
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Domingues, J.S.; Coelho, R.A.; Bento, F.D.S.; Almeida, B.C.; De Castro, A.O. Left Ventricular Volume in Bovines: The Correlation between Teichholz’s Medical Mathematical Method and the Volume of the Truncated Prolate Spheroid. Math. Comput. Appl. 2018, 23, 50. https://doi.org/10.3390/mca23030050
Domingues JS, Coelho RA, Bento FDS, Almeida BC, De Castro AO. Left Ventricular Volume in Bovines: The Correlation between Teichholz’s Medical Mathematical Method and the Volume of the Truncated Prolate Spheroid. Mathematical and Computational Applications. 2018; 23(3):50. https://doi.org/10.3390/mca23030050
Chicago/Turabian StyleDomingues, José Sérgio, Ravel Alvarenga Coelho, Francielly Dos Santos Bento, Brenda Cristina Almeida, and Ayanne Oliveira De Castro. 2018. "Left Ventricular Volume in Bovines: The Correlation between Teichholz’s Medical Mathematical Method and the Volume of the Truncated Prolate Spheroid" Mathematical and Computational Applications 23, no. 3: 50. https://doi.org/10.3390/mca23030050
APA StyleDomingues, J. S., Coelho, R. A., Bento, F. D. S., Almeida, B. C., & De Castro, A. O. (2018). Left Ventricular Volume in Bovines: The Correlation between Teichholz’s Medical Mathematical Method and the Volume of the Truncated Prolate Spheroid. Mathematical and Computational Applications, 23(3), 50. https://doi.org/10.3390/mca23030050