#PAGE_PARAMS# #ADS_HEAD_SCRIPTS# #MICRODATA#

Mathematical modeling of cardiac function to evaluate clinical cases in adults and children


Autoři: Selim Bozkurt aff001
Působiště autorů: Institute of Cardiovascular Science, University College London, London, United Kingdom aff001
Vyšlo v časopise: PLoS ONE 14(10)
Kategorie: Research Article
doi: https://doi.org/10.1371/journal.pone.0224663

Souhrn

Time-varying elastance models can simulate only the pressure and volume signals in the heart chambers while the diagnosis of clinical cases and evaluation of different treatment techniques require more information. In this study, an extended model utilizing the geometric dimensions of the heart chambers was developed to describe the cardiac function. The new cardiac model was evaluated by simulating a healthy and dilated cardiomyopathy (DCM) condition for adults and children. The left ventricular ejection fraction, end-diastolic volume, end-diastolic diameter and diastolic sphericity index were 53.60%, 125 mL, 5.08 cm and 1.82 in the healthy adult cardiovascular system model and 23.70%, 173 mL, 6.60 cm and 1.40 in the DCM adult cardiovascular system model. In the healthy child cardiovascular system model, the left ventricular ejection fraction, end-diastolic volume, end-diastolic diameter and diastolic sphericity index were 59.70%, 92 mL, 4.10 cm and 2.26 respectively and 30.70%, 125 mL, 4.94 cm and 1.87 in the DCM child cardiovascular system model. The developed cardiovascular system model simulates the hemodynamic variables and clinical diagnostic indicators within the physiological range for healthy and DCM conditions proving the feasibility of this new model to evaluate clinical cases in adults and children.

Klíčová slova:

Blood pressure – Cardiac ventricles – Cardiovascular physiology – Ejection fraction – Child health – Simulation and modeling – Cardiac atria


Zdroje

1. Lankhaar J-W, Rövekamp FA, Steendijk P, Faes TJC, Westerhof BE, Kind T, et al. Modeling the instantaneous pressure-volume relation of the left ventricle: a comparison of six models. Ann Biomed Eng. 2009;37: 1710–1726. doi: 10.1007/s10439-009-9742-x 19554450

2. Faes TJ, Kerkhof PL. The Volume Regulation Graph versus the Ejection Fraction as Metrics of Left Ventricular Performance in Heart Failure with and without a Preserved Ejection Fraction: A Mathematical Model Study. Clin Med Insights Cardiol. 2015;9: 73–91. doi: 10.4137/CMC.S18748 26052232

3. Song Z, Gu K, Gao B, Wan F, Chang Y, Zeng Y. Hemodynamic effects of various support modes of continuous flow LVADs on the cardiovascular system: A numerical study. Med Sci Monit Int Med J Exp Clin Res. 2014;20: 733–741. doi: 10.12659/MSM.890824 24793178

4. Ellwein LM, Pope SR, Xie A, Batzel JJ, Kelley CT, Olufsen MS. Patient-specific modeling of cardiovascular and respiratory dynamics during hypercapnia. Math Biosci. 2013;241: 56–74. doi: 10.1016/j.mbs.2012.09.003 23046704

5. Gaudenzi F, Avolio AP. Lumped parameter model of cardiovascular-respiratory interaction. Conf Proc Annu Int Conf IEEE Eng Med Biol Soc IEEE Eng Med Biol Soc Annu Conf. 2013;2013: 473–476. doi: 10.1109/EMBC.2013.6609539 24109726

6. van de Vosse FN, Stergiopulos N. Pulse Wave Propagation in the Arterial Tree. Annu Rev Fluid Mech. 2011;43: 467–499. doi: 10.1146/annurev-fluid-122109-160730

7. Cox LGE, Loerakker S, Rutten MCM, de Mol BAJM, van de Vosse FN. A mathematical model to evaluate control strategies for mechanical circulatory support. Artif Organs. 2009;33: 593–603. doi: 10.1111/j.1525-1594.2009.00755.x 19558561

8. Bovendeerd PHM, Borsje P, Arts T, van De Vosse FN. Dependence of Intramyocardial Pressure and Coronary Flow on Ventricular Loading and Contractility: A Model Study. Ann Biomed Eng. 2006;34: 1833–1845. doi: 10.1007/s10439-006-9189-2 17048105

9. Jongen GJLM, van der Hout-van der Jagt MB, Oei SG, van de Vosse FN, Bovendeerd PHM. Simulation of fetal heart rate variability with a mathematical model. Med Eng Phys. 2017;42: 55–64.28196652

10. Bozkurt S, Bozkurt S. In-silico evaluation of left ventricular unloading under varying speed continuous flow left ventricular assist device support. Biocybern Biomed Eng. 2017;37: 373–387. doi: 10.1016/j.bbe.2017.03.003

11. Bhattacharya-Ghosh B, Bozkurt S, Rutten MCM, van de Vosse FN, Díaz-Zuccarini V. An in silico case study of idiopathic dilated cardiomyopathy via a multi-scale model of the cardiovascular system. Comput Biol Med. 2014;53: 141–153. doi: 10.1016/j.compbiomed.2014.06.013 25147131

12. Bozkurt S. In-silico modeling of left ventricle to simulate dilated cardiomyopathy and cf-lvad support. J Mech Med Biol. 2017;17: 1750034. doi: 10.1142/S0219519417500348

13. Sheffer L, Santamore WP, Barnea O. Cardiovascular simulation toolbox. Cardiovasc Eng Dordr Neth. 2007;7: 81–88. doi: 10.1007/s10558-007-9030-z 17570062

14. Shimizu S, Une D, Kawada T, Hayama Y, Kamiya A, Shishido T, et al. Lumped parameter model for hemodynamic simulation of congenital heart diseases. J Physiol Sci JPS. 2018;68: 103–111. doi: 10.1007/s12576-017-0585-1 29270856

15. MacGregor J. By Janet MacGregor—Introduction to the Anatomy and Physiology of Children: A Guide for Students of Nursing, Child Care and Health. 2 edition. ROUTLEDGE; 2008.

16. Udelson JE. Left Ventricular Shape: The Forgotten Stepchild of Remodeling Parameters. JACC Heart Fail. 2017;5: 179–181. doi: 10.1016/j.jchf.2017.01.005 28254123

17. Korakianitis T, Shi Y. A concentrated parameter model for the human cardiovascular system including heart valve dynamics and atrioventricular interaction. Med Eng Phys. 2006;28: 613–628.16293439

18. Walker LA, Buttrick PM. The right ventricle: biologic insights and response to disease: updated. Curr Cardiol Rev. 2013;9: 73–81. doi: 10.2174/157340313805076296 23092273

19. Denslow S, Wiles HB. Right ventricular volumes revisited: a simple model and simple formula for echocardiographic determination. J Am Soc Echocardiogr Off Publ Am Soc Echocardiogr. 1998;11: 864–873.

20. Holland DJ, Sharman JE, Leano RL, Marwick TH. Gender differences in systolic tissue velocity: role of left ventricular length. Eur J Echocardiogr J Work Group Echocardiogr Eur Soc Cardiol. 2009;10: 941–946. doi: 10.1093/ejechocard/jep103 19720628

21. Kossaify A. Echocardiographic Assessment of the Right Ventricle, from the Conventional Approach to Speckle Tracking and Three-Dimensional Imaging, and Insights into the “Right Way” to Explore the Forgotten Chamber. Clin Med Insights Cardiol. 2015;9: 65–75. doi: 10.4137/CMC.S27462

22. Peverill RE, Chou B, Donelan L. Left ventricular long axis tissue Doppler systolic velocity is independently related to heart rate and body size. PloS One. 2017;12: e0173383. doi: 10.1371/journal.pone.0173383 28288162

23. Rudski LG, Lai WW, Afilalo J, Hua L, Handschumacher MD, Chandrasekaran K, et al. Guidelines for the echocardiographic assessment of the right heart in adults: a report from the American Society of Echocardiography endorsed by the European Association of Echocardiography, a registered branch of the European Society of Cardiology, and the Canadian Society of Echocardiography. J Am Soc Echocardiogr Off Publ Am Soc Echocardiogr. 2010;23: 685–713; quiz 786–788. doi: 10.1016/j.echo.2010.05.010 20620859

24. Ursino M. Interaction between carotid baroregulation and the pulsating heart: a mathematical model. Am J Physiol. 1998;275: H1733–1747. doi: 10.1152/ajpheart.1998.275.5.H1733 9815081

25. Heldt T, Shim EB, Kamm RD, Mark RG. Computational modeling of cardiovascular response to orthostatic stress. J Appl Physiol Bethesda Md 1985. 2002;92: 1239–1254. doi: 10.1152/japplphysiol.00241.2001 11842064

26. Pinsky MR. The right ventricle: interaction with the pulmonary circulation. Crit Care. 2016;20: 266. doi: 10.1186/s13054-016-1440-0 27613549

27. Hall JE. Guyton and Hall Textbook of Medical Physiology, 13e. 13 edition. Philadelphia, PA: Saunders; 2015.

28. Blanco PJ, Feijóo RA. A 3D-1D-0D Computational Model for the Entire Cardiovascular System. Mecánica Comput. 2010;29: 5887–5911.

29. Albanese A, Cheng L, Ursino M, Chbat NW. An integrated mathematical model of the human cardiopulmonary system: model development. Am J Physiol Heart Circ Physiol. 2016;310: H899–921. doi: 10.1152/ajpheart.00230.2014 26683899

30. Shi Y, Lawford P, Hose R. Review of Zero-D and 1-D Models of Blood Flow in the Cardiovascular System. Biomed Eng OnLine. 2011;10: 33. doi: 10.1186/1475-925X-10-33 21521508

31. El Edelbi R, Lindemalm S, Eksborg S. Estimation of body surface area in various childhood ages—validation of the Mosteller formula. Acta Paediatr Oslo Nor 1992. 2012;101: 540–544. doi: 10.1111/j.1651-2227.2011.02580.x

32. Kiani A, Shakibi JG. Normal value of left ventricular end-systolic elastance in infants and children. Iran J Med Sci. 2003;28: 169–172.

33. Regen DM, Graham TP, Wyse RK, Deanfield J, Franklin RC. Left-ventricular cavity dimensions in children with normal and dilated hearts. Pediatr Cardiol. 1988;9: 17–24. doi: 10.1007/BF02279878 2964589

34. Poutanen T, Jokinen E, Sairanen H, Tikanoja T. Left atrial and left ventricular function in healthy children and young adults assessed by three dimensional echocardiography. Heart Br Card Soc. 2003;89: 544–549.

35. Gardner AW, Parker DE. Association between arterial compliance and age in participants 9 to 77 years old. Angiology. 2010;61: 37–41. doi: 10.1177/0003319709339588 19638351

36. Cattermole GN, Leung PYM, Ho GYL, Lau PWS, Chan CPY, Chan SSW, et al. The normal ranges of cardiovascular parameters measured using the ultrasonic cardiac output monitor. Physiol Rep. 2017;5. doi: 10.14814/phy2.13195 28320891

37. Raes A, Van Aken S, Craen M, Donckerwolcke R, Vande Walle J. A reference frame for blood volume in children and adolescents. BMC Pediatr. 2006;6: 3. doi: 10.1186/1471-2431-6-3 16503982

38. Japp AG, Gulati A, Cook SA, Cowie MR, Prasad SK. The Diagnosis and Evaluation of Dilated Cardiomyopathy. J Am Coll Cardiol. 2016;67: 2996–3010. doi: 10.1016/j.jacc.2016.03.590 27339497

39. Mathew T, Williams L, Navaratnam G, Rana B, Wheeler R, Collins K, et al. Diagnosis and assessment of dilated cardiomyopathy: a guideline protocol from the British Society of Echocardiography. Echo Res Pract. 2017;4: G1–G13. doi: 10.1530/ERP-16-0037 28592613

40. Jelenc M, Jelenc B, Vrtovec B, Kneževič I. Mitral regurgitation and axial flow left ventricular assist device: a computer simulation study. ASAIO J Am Soc Artif Intern Organs 1992. 2013;59: 405–409. doi: 10.1097/MAT.0b013e31829ff57d 23820280

41. Bozkurt S. Effect of Cerebral Flow Autoregulation Function on Cerebral Flow Rate Under Continuous Flow Left Ventricular Assist Device Support. Artif Organs. 2018;42: 800–813. doi: 10.1111/aor.13148 29726017

42. Porter GA, Makuck RF, Rivkees SA. Intracellular calcium plays an essential role in cardiac development. Dev Dyn. 2003;227: 280–290. doi: 10.1002/dvdy.10307 12761855

43. Brown SB, Raina A, Katz D, Szerlip M, Wiegers SE, Forfia PR. Longitudinal shortening accounts for the majority of right ventricular contraction and improves after pulmonary vasodilator therapy in normal subjects and patients with pulmonary arterial hypertension. Chest. 2011;140: 27–33. doi: 10.1378/chest.10-1136 21106653

44. Veronesi F, Corsi C, Caiani EG, Sarti A, Lamberti C. Tracking of left ventricular long axis from real-time three-dimensional echocardiography using optical flow techniques. IEEE Trans Inf Technol Biomed Publ IEEE Eng Med Biol Soc. 2006;10: 174–181.

45. Ostenfeld E, Flachskampf FA. Assessment of right ventricular volumes and ejection fraction by echocardiography: from geometric approximations to realistic shapes. Echo Res Pract. 2015;2: R1–R11. doi: 10.1530/ERP-14-0077 26693327

46. Jorstig S, Waldenborg M, Lidén M, Wodecki M, Thunberg P. Determination of Right Ventricular Volume by Combining Echocardiographic Distance Measurements. Echocardiogr Mt Kisco N. 2016;33: 844–853. doi: 10.1111/echo.13173 26841195

47. Jorstig S, Waldenborg M, Lidén M, Thunberg P. Right ventricular ejection fraction measurements using two-dimensional transthoracic echocardiography by applying an ellipsoid model. Cardiovasc Ultrasound. 2017;15: 4. doi: 10.1186/s12947-017-0096-5 28270161

48. Fukuta H, Little WC. The cardiac cycle and the physiologic basis of left ventricular contraction, ejection, relaxation, and filling. Heart Fail Clin. 2008;4: 1–11. doi: 10.1016/j.hfc.2007.10.004 18313620

49. Kovalova S, Necas J, Vespalec J. What is a “normal” right ventricle? Eur J Echocardiogr. 2006;7: 293–297. doi: 10.1016/j.euje.2005.06.010

50. Hudsmith LE, Petersen SE, Francis JM, Robson MD, Neubauer S. Normal human left and right ventricular and left atrial dimensions using steady state free precession magnetic resonance imaging. J Cardiovasc Magn Reson Off J Soc Cardiovasc Magn Reson. 2005;7: 775–782.

51. Kawel-Boehm N, Maceira A, Valsangiacomo-Buechel ER, Vogel-Claussen J, Turkbey EB, Williams R, et al. Normal values for cardiovascular magnetic resonance in adults and children. J Cardiovasc Magn Reson Off J Soc Cardiovasc Magn Reson. 2015;17: 29. doi: 10.1186/s12968-015-0111-7 25928314

52. El Missiri AM, El Meniawy KAL, Sakr SAS, Mohamed ASE. Normal reference values of echocardiographic measurements in young Egyptian adults. Egypt Heart J. 2016;68: 209–215. doi: 10.1016/j.ehj.2016.01.002

53. Gibson PH, Becher H, Choy JB. Classification of left ventricular size: diameter or volume with contrast echocardiography? Open Heart. 2014;1: e000147. doi: 10.1136/openhrt-2014-000147 25525505

54. Ho SY, Nihoyannopoulos P. Anatomy, echocardiography, and normal right ventricular dimensions. Heart. 2006;92: i2–i13. doi: 10.1136/hrt.2005.077875 16543598

55. Kossaify A. Echocardiographic Assessment of the Right Ventricle, from the Conventional Approach to Speckle Tracking and Three-Dimensional Imaging, and Insights into the “Right Way” to Explore the Forgotten Chamber. Clin Med Insights Cardiol. 2015;9: 65–75. doi: 10.4137/CMC.S27462

56. Kou S, Caballero L, Dulgheru R, Voilliot D, De Sousa C, Kacharava G, et al. Echocardiographic reference ranges for normal cardiac chamber size: results from the NORRE study. Eur Heart J Cardiovasc Imaging. 2014;15: 680–690. doi: 10.1093/ehjci/jet284 24451180

57. Lang RM, Badano LP, Mor-Avi V, Afilalo J, Armstrong A, Ernande L, 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 Off Publ Am Soc Echocardiogr. 2015;28: 1–39.e14. doi: 10.1016/j.echo.2014.10.003 25559473

58. Lang RM, Bierig M, Devereux RB, Flachskampf FA, Foster E, Pellikka PA, et al. Recommendations for chamber quantification. Eur J Echocardiogr J Work Group Echocardiogr Eur Soc Cardiol. 2006;7: 79–108. doi: 10.1016/j.euje.2005.12.014 16458610

59. Gavazzi A, De Maria R, Renosto G, Moro A, Borgia M, Caroli A, et al. The spectrum of left ventricular size in dilated cardiomyopathy: clinical correlates and prognostic implications. SPIC (Italian Multicenter Cardiomyopathy Study) Group. Am Heart J. 1993;125: 410–422. doi: 10.1016/0002-8703(93)90020-a 8427135

60. Matsumura Y, Elliott PM, Mahon NG, Virdee MS, Doi Y, McKenna WJ. Familial dilated cardiomyopathy: assessment of left ventricular systolic and diastolic function using Doppler tissue imaging in asymptomatic relatives with left ventricular enlargement. Heart. 2006;92: 405–406. doi: 10.1136/hrt.2005.065474 16501207

61. Weintraub RG, Semsarian C, Macdonald P. Dilated cardiomyopathy. The Lancet. 2017;390: 400–414. doi: 10.1016/S0140-6736(16)31713-5

62. Niemeijer MN, Leening MJG, van den Berg ME, Hofman A, Franco OH, Deckers JW, et al. Subclinical Abnormalities in Echocardiographic Parameters and Risk of Sudden Cardiac Death in a General Population: The Rotterdam Study. J Card Fail. 2016;22: 17–23. doi: 10.1016/j.cardfail.2015.06.007 26093333

63. Ferreira F, Galrinho A, Soares R, Branco L, Abreu J, Feliciano J, et al. Prognostic value of left atrial volume in patients with dilated cardiomyopathy. Rev Port Cardiol Orgao Of Soc Port Cardiol Port J Cardiol Off J Port Soc Cardiol. 2013;32: 865–872. doi: 10.1016/j.repc.2012.12.017 24119867

64. Gopal D, Wang J, Han Y. Determinants of Normal Left Atrial Volume in Heart Failure with Moderate-to-Severely Reduced Ejection Fraction. In: Cardiology Research and Practice [Internet]. 2018 [cited 4 Nov 2018]. doi: 10.1155/2018/7512758 29850229

65. Parcharidou DG, Giannakoulas G, Efthimiadis GK, Karvounis H, Papadopoulou KN, Dalamanga E, et al. Right ventricular function in ischemic or idiopathic dilated cardiomyopathy. Circ J Off J Jpn Circ Soc. 2008;72: 238–244.

66. Tissot C, Singh Y, Sekarski N. Echocardiographic Evaluation of Ventricular Function—For the Neonatologist and Pediatric Intensivist. Front Pediatr. 2018;6. doi: 10.3389/fped.2018.00006

67. de Simone G, Devereux RB, Kimball TR, Roman MJ, Palmieri V, Celentano A, et al. Relation of heart rate to left ventricular dimensions in normotensive, normal-weight children, adolescents and adults. Ital Heart J Off J Ital Fed Cardiol. 2001;2: 599–604.

68. Krovetz LJ, McLoughlin TG, Mitchell MB, Schiebler GL. Hemodynamic findings in normal children. Pediatr Res. 1967;1: 122–130. doi: 10.1203/00006450-196703000-00006 6029810

69. Koestenberger M, Nagel B, Ravekes W, Avian A, Burmas A, Grangl G, et al. Reference values and calculation of z-scores of echocardiographic measurements of the normal pediatric right ventricle. Am J Cardiol. 2014;114: 1590–1598. doi: 10.1016/j.amjcard.2014.08.028 25248810

70. Majonga ED, Rehman AM, McHugh G, Mujuru HA, Nathoo K, Patel MS, et al. Echocardiographic reference ranges in older children and adolescents in sub-Saharan Africa. Int J Cardiol. 2017;248: 409–413. doi: 10.1016/j.ijcard.2017.06.109 28711335

71. Oran B, Bodur AS, Arslan D, Çımen D, Güvenç O. Normal M mode values in healthy Turkish children. Turk J Med Sci. 2014;44: 756–763. 25539541

72. Cain PA, Ahl R, Hedstrom E, Ugander M, Allansdotter-Johnsson A, Friberg P, et al. Age and gender specific normal values of left ventricular mass, volume and function for gradient echo magnetic resonance imaging: a cross sectional study. BMC Med Imaging. 2009;9: 2. doi: 10.1186/1471-2342-9-2 19159437

73. Friedberg MK. Chapter 9—Echocardiographic Quantitation of Ventricular Function. In: Jefferies JL, Chang AC, Rossano JW, Shaddy RE, Towbin JA, editors. Heart Failure in the Child and Young Adult. Boston: Academic Press; 2018. pp. 105–124. doi: 10.1016/B978-0-12-802393-8.00009-0

74. Muscogiuri G, Ciliberti P, Mastrodicasa D, Chinali M, Rinelli G, Santangelo TP, et al. Results of Late Gadolinium Enhancement in Children Affected by Dilated Cardiomyopathy. Front Pediatr. 2017;5: 13. doi: 10.3389/fped.2017.00013 28220144

75. Lee CK, Margossian R, Sleeper LA, Canter CE, Chen S, Tani LY, et al. Variability of M-mode versus two-dimensional echocardiography measurements in children with dilated cardiomyopathy. Pediatr Cardiol. 2014;35: 658–667. doi: 10.1007/s00246-013-0835-9 24265000

76. Bozkurt S, van de Vosse FN, Rutten MCM. Improving arterial pulsatility by feedback control of a continuous flow left ventricular assist device via in silico modeling. Int J Artif Organs. 2014;37: 773–785. doi: 10.5301/ijao.5000328 24970558

77. Granegger M, Masetti M, Laohasurayodhin R, Schloeglhofer T, Zimpfer D, Schima H, et al. Continuous Monitoring of Aortic Valve Opening in Rotary Blood Pump Patients. IEEE Trans Biomed Eng. 2016;63: 1201–1207. doi: 10.1109/TBME.2015.2489188 26461795

78. Mann Douglas L, Bristow Michael R. Mechanisms and Models in Heart Failure. Circulation. 2005;111: 2837–2849. doi: 10.1161/CIRCULATIONAHA.104.500546 15927992

79. Jackson G, Gibbs CR, Davies MK, Lip GYH. Pathophysiology. BMJ. 2000;320: 167–170. doi: 10.1136/bmj.320.7228.167 10634740

80. Su JA, Menteer J. Outcomes of Berlin Heart EXCOR® pediatric ventricular assist device support in patients with restrictive and hypertrophic cardiomyopathy. Pediatr Transplant. 2017;21. doi: 10.1111/petr.13048

81. Anwer LA, Poddi S, Tchantchaleishvili V, Daly RC, Toeg H, Strand JJ, et al. Left Ventricular Assist Devices: How Do We Define Success? ASAIO J Am Soc Artif Intern Organs 1992. 2019;65: 430–435. doi: 10.1097/MAT.0000000000000894 30312213


Článek vyšel v časopise

PLOS One


2019 Číslo 10
Nejčtenější tento týden
Nejčtenější v tomto čísle
Kurzy

Zvyšte si kvalifikaci online z pohodlí domova

KOST
Koncepce osteologické péče pro gynekology a praktické lékaře
nový kurz
Autoři: MUDr. František Šenk

Sekvenční léčba schizofrenie
Autoři: MUDr. Jana Hořínková

Hypertenze a hypercholesterolémie – synergický efekt léčby
Autoři: prof. MUDr. Hana Rosolová, DrSc.

Svět praktické medicíny 5/2023 (znalostní test z časopisu)

Imunopatologie? … a co my s tím???
Autoři: doc. MUDr. Helena Lahoda Brodská, Ph.D.

Všechny kurzy
Kurzy Podcasty Doporučená témata Časopisy
Přihlášení
Zapomenuté heslo

Zadejte e-mailovou adresu, se kterou jste vytvářel(a) účet, budou Vám na ni zaslány informace k nastavení nového hesla.

Přihlášení

Nemáte účet?  Registrujte se

#ADS_BOTTOM_SCRIPTS#