Biomechanics and Modeling in Mechanobiology

, Volume 18, Issue 5, pp 1415–1427 | Cite as

Effects of left ventricle wall thickness uncertainties on cardiac mechanics

  • Joventino O. CamposEmail author
  • Joakim Sundnes
  • Rodrigo W. dos Santos
  • Bernardo M. Rocha
Original Paper


Computational models of the heart have reached a level of maturity that enables sophisticated patient-specific simulations and hold potential for important applications in diagnosis and therapy planning. However, such clinical use puts strict demands on the reliability and accuracy of the models and requires the sensitivity of the model predictions due to errors and uncertainty in the model inputs to be quantified. The models typically contain a large number of parameters, which are difficult to measure and therefore associated with considerable uncertainty. Additionally, patient-specific geometries are usually constructed by semi-manual processing of medical images and must be assumed to be a potential source of model uncertainty. In this paper, we assess the model accuracy by considering the impact of geometrical uncertainties, which typically occur in image-based computational geometries. An approach based on 17 AHA segments diagram is used to consider uncertainties in wall thickness and also in the material properties and fiber orientation, and we perform a comprehensive uncertainty quantification and sensitivity analysis based on polynomial chaos expansions. The quantities considered include stress, strain and global deformation parameters of the left ventricle. The results indicate that important quantities of interest may be more affected by wall thickness, and highlight the need for accurate geometry reconstructions in patient-specific cardiac mechanics models.


Uncertainty quantification Sensitivity analysis Cardiac mechanics Patient-specific left ventricle models 


Compliance with ethical standards

Conflict of Interest

The authors declare that they have no conflict of interest.


  1. Bai W, Shi W, de Marvao A, Dawes TJ, O’Regan DP, Cook SA, Rueckert D (2015) A bi-ventricular cardiac atlas built from 1000+ high resolution mr images of healthy subjects and an analysis of shape and motion. Med Image Anal 26(1):133–145CrossRefGoogle Scholar
  2. Balaban G, Finsberg H, Funke S, Håland TF, Hopp E, Sundnes J, Wall S, Rognes ME (2018) In vivo estimation of elastic heterogeneity in an infarcted human heart. Biomech Model Mechanobiol 17(5):1317–1329. CrossRefGoogle Scholar
  3. Bayer JD, Blake RC, Plank G, Trayanova NA (2012) A novel rule-based algorithm for assigning myocardial fiber orientation to computational heart models. Ann Biomed Eng 40(10):2243–2254CrossRefGoogle Scholar
  4. Biehler J, Wall W (2017) The impact of personalized probabilistic wall thickness models on peak wall stress in abdominal aortic aneurysms. Int J Numer Methods Biomed Eng 34(2):2922CrossRefGoogle Scholar
  5. Biehler J, Gee MW, Wall WA (2015) Towards efficient uncertainty quantification in complex and large-scale biomechanical problems based on a Bayesian multi-fidelity scheme. Biomech Model Mechanobiol 14(3):489–513. CrossRefGoogle Scholar
  6. Campos JO, Santos RW, Sundnes J, Rocha BM (2017) Preconditioned augmented Lagrangian formulation for nearly incompressible cardiac mechanics. Int J Numer Methods Biomed Eng 34(4):e2948. e2948 cnm.2948MathSciNetCrossRefGoogle Scholar
  7. Cerqueira MD, Weissman NJ, Dilsizian V, Jacobs AK, Kaul S, Laskey WK, Pennell DJ, Rumberger JA, Ryan T, Verani MS et al (2002) Standardized myocardial segmentation and nomenclature for tomographic imaging of the heart. Circulation 105(4):539–542CrossRefGoogle Scholar
  8. Choi HF, Dhooge J, Rademakers F, Claus P (2010) Influence of left-ventricular shape on passive filling properties and end-diastolic fiber stress and strain. J Biomech 43(9):1745–1753CrossRefGoogle Scholar
  9. Crozier A, Augustin CM, Neic A, Prassl AJ, Holler M, Fastl TE, Hennemuth A, Bredies K, Kuehne T, Bishop MJ, Niederer SA, Plank G (2016) Image-based personalization of cardiac anatomy for coupled electromechanical modeling. Ann Biomed Eng 44(1):58–70. CrossRefGoogle Scholar
  10. Duong PLT, Ali W, Kwok E, Lee M (2016) Uncertainty quantification and global sensitivity analysis of complex chemical process using a generalized polynomial chaos approach. Comput Chem Eng 90:23–30CrossRefGoogle Scholar
  11. Eck VG, Donders WP, Sturdy J, Feinberg J, Delhaas T, Hellevik LR, Huberts W (2016) A guide to uncertainty quantification and sensitivity analysis for cardiovascular applications. Int J Numer Methods Biomed Eng 32(8):2755MathSciNetCrossRefGoogle Scholar
  12. Feinberg J, Langtangen HP (2015) Chaospy: an open source tool for designing methods of uncertainty quantification. J Comput Sci 11:46–57. MathSciNetCrossRefGoogle Scholar
  13. Fishman G (2013) Monte Carlo: concepts, algorithms, and applications. Springer, BerlinzbMATHGoogle Scholar
  14. Gao H, Feng L, Qi N, Berry C, Griffith BE, Luo X (2017) A coupled mitral valve-left ventricle model with fluid-structure interaction. Med Eng Phys 47:128–136CrossRefGoogle Scholar
  15. Geuzaine C, Remacle JF (2009) Gmsh: a 3-d finite element mesh generator with built-in pre-and post-processing facilities. Int J Numer Methods Eng 79(11):1309–1331MathSciNetzbMATHCrossRefGoogle Scholar
  16. Guccione JM, Costa KD, McCulloch AD (1995) Finite element stress analysis of left ventricular mechanics in the beating dog heart. J Biomech 28(10):1167–1177. CrossRefGoogle Scholar
  17. Holzapfel GA, Gasser TC, Ogden RW (2000) A new constitutive framework for arterial wall mechanics and a comparative study of material models. J Elast Phys Sci Solids 61(1–3):1–48MathSciNetzbMATHGoogle Scholar
  18. Hosder S, Walters R, Balch M (2007) Efficient sampling for non-intrusive polynomial chaos applications with multiple uncertain input variables. In: 48th AIAA/ASME/ASCE/AHS/ASC structures, structural dynamics, and materials conference, p 1939Google Scholar
  19. Huberts W, Donders W, Delhaas T, Vosse F (2014) Applicability of the polynomial chaos expansion method for personalization of a cardiovascular pulse wave propagation model. Int J Numer Methods Biomed Eng 30(12):1679–1704CrossRefGoogle Scholar
  20. Hurtado DE, Castro S, Madrid P (2017) Uncertainty quantification of two models of cardiac electromechanics. Int J Numer Methods Biomed Eng 33(12):2894CrossRefGoogle Scholar
  21. Land S, Gurev V, Arens S, Augustin CM, Baron L, Blake R, Bradley C, Castro S, Crozier A, Favino M et al (2015) Verification of cardiac mechanics software: benchmark problems and solutions for testing active and passive material behaviour. Proc R Soc A 471((2184)):20150–641Google Scholar
  22. Lee LC, Wall ST, Genet M, Hinson A, Guccione JM (2014) Bioinjection treatment: effects of post-injection residual stress on left ventricular wall stress. J Biomech 47(12):3115–3119CrossRefGoogle Scholar
  23. Li H, Zhang D (2007) Probabilistic collocation method for flow in porous media: comparisons with other stochastic methods. Water Resour Res 43(9):1–13. CrossRefGoogle Scholar
  24. Oliveira RS, Alonso S, Campos FO, Rocha BM, Fernandes JF, Kuehne T, dos Santos RW (2018) Ectopic beats arise from micro-reentries near infarct regions in simulations of a patient-specific heart model. Sci Rep 8(1):16,392CrossRefGoogle Scholar
  25. Osnes H, Sundnes J (2012) Uncertainty analysis of ventricular mechanics using the probabilistic collocation method. IEEE Trans Biomed Eng 59(8):2171–2179CrossRefGoogle Scholar
  26. Prinzen FW, Cheriex EC, Delhaas T, van Oosterhout MF, Arts T, Wellens HJ, Reneman RS (1995) Asymmetric thickness of the left ventricular wall resulting from asynchronous electric activation: a study in dogs with ventricular pacing and in patients with left bundle branch block. Am Heart J 130(5):1045–1053CrossRefGoogle Scholar
  27. Quaglino A, Pezzuto S, Koutsourelakis P, Auricchio A, Krause R (2018) Fast uncertainty quantification of activation sequences in patient-specific cardiac electrophysiology meeting clinical time constraints. Int J Numer Methods Biomed Eng 34(7):2985MathSciNetCrossRefGoogle Scholar
  28. Rodrigues J, Schmal T, Gomes JM, Rocha B, dos Santos R (2015) Patient-specific left ventricle mesh generation using the bull’s eye of the wall thickness measurements from medical images. In: VI Latin American congress on biomedical engineering CLAIB 2014, Paraná, Argentina 29, 30 & 31 Oct 2014, Springer, pp 393–396Google Scholar
  29. Rodríguez-Cantano R, Sundnes J, Rognes ME (2019) Uncertainty in cardiac myofiber orientation and stiffnesses dominate the variability of left ventricle deformation response. Int J Numer Methods Eng 79(11):1–20Google Scholar
  30. Sepahvand K, Marburg S (2013) On construction of uncertain material parameter using generalized polynomial chaos expansion from experimental data. In: Procedia IUTAM 6:4–17., iUTAM symposium on multiscale problems in stochastic mechanics
  31. Shavik SM, Wall ST, Sundnes J, Burkhoff D, Lee LC (2017) Organ-level validation of a cross-bridge cycling descriptor in a left ventricular finite element model: effects of ventricular loading on myocardial strains. Physiol Rep 5(21):1–14. CrossRefGoogle Scholar
  32. Simo JC, Taylor RL, Pister KS (1985) Variational and projection methods for the volume constraint in finite deformation elasto-plasticity. Comput Methods Appl Mech Eng 51:177–208MathSciNetzbMATHCrossRefGoogle Scholar
  33. Smiseth OA, Aalen JM (2018) Mechanism of harm from left bundle branch block. Trends Cardiovasc Med. CrossRefGoogle Scholar
  34. Sobol IM (2001) Global sensitivity indices for nonlinear mathematical models and their Monte Carlo estimates. Math Comput Simul 55(1–3):271–280MathSciNetzbMATHCrossRefGoogle Scholar
  35. Suinesiaputra A, Cowan BR, Al-Agamy AO, Elattar MA, Ayache N, Fahmy AS, Khalifa AM, Medrano-Gracia P, Jolly MP, Kadish AH et al (2014) A collaborative resource to build consensus for automated left ventricular segmentation of cardiac mr images. Med Image Anal 18(1):50–62CrossRefGoogle Scholar
  36. Tatang MA, Pan W, Prinn RG, McRae GJ (1997) An efficient method for parametric uncertainty analysis of numerical geophysical models. J Geophys Res Atmos 102(D18):21,925–21,932CrossRefGoogle Scholar
  37. Trayanova NA, Winslow R (2011) Whole-heart modeling: applications to cardiac electrophysiology and electromechanics. Circ Res 108(1):113–128CrossRefGoogle Scholar
  38. Van Oosterhout MF, Prinzen FW, Arts T, Schreuder JJ, Vanagt WY, Cleutjens JP, Reneman RS (1998) Asynchronous electrical activation induces asymmetrical hypertrophy of the left ventricular wall. Circulation 98(6):588–595CrossRefGoogle Scholar
  39. Vernooy K, Verbeek XA, Peschar M, Crijns HJ, Arts T, Cornelussen RN, Prinzen FW (2004) Left bundle branch block induces ventricular remodelling and functional septal hypoperfusion. Eur Heart J 26(1):91–98CrossRefGoogle Scholar
  40. Xiu D, Karniadakis GE (2002) The Wiener–Askey polynomial chaos for stochastic differential equations. SIAM J Sci Comput 24(2):619–644MathSciNetzbMATHCrossRefGoogle Scholar
  41. Xu Y, Mili L, Sandu A, von Spakovsky MR, Zhao J (2019) Propagating uncertainty in power system dynamic simulations using polynomial chaos. IEEE Trans Power Syst 34(1):338–348. CrossRefGoogle Scholar

Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  • Joventino O. Campos
    • 1
    Email author
  • Joakim Sundnes
    • 2
  • Rodrigo W. dos Santos
    • 3
  • Bernardo M. Rocha
    • 3
  1. 1.Centro Federal de Educação Tecnológica de Minas GeraisLeopoldinaBrazil
  2. 2.Simula Research LaboratoryLysakerNorway
  3. 3.Graduate Program in Computational ModelingUniversidade Federal de Juiz de ForaJuiz de ForaBrazil

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