Effects of left ventricle wall thickness uncertainties on cardiac mechanics
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Abstract
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.
Keywords
Uncertainty quantification Sensitivity analysis Cardiac mechanics Patient-specific left ventricle modelsNotes
Compliance with ethical standards
Conflict of Interest
The authors declare that they have no conflict of interest.
References
- 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
- 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. https://doi.org/10.1007/s10237-018-1028-5 CrossRefGoogle Scholar
- 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
- 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
- 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. https://doi.org/10.1007/s10237-014-0618-0 CrossRefGoogle Scholar
- 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. https://doi.org/10.1002/cnm.2948 e2948 cnm.2948MathSciNetCrossRefGoogle Scholar
- 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
- 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
- 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. https://doi.org/10.1007/s10439-015-1474-5 CrossRefGoogle Scholar
- 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
- 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
- Feinberg J, Langtangen HP (2015) Chaospy: an open source tool for designing methods of uncertainty quantification. J Comput Sci 11:46–57. https://doi.org/10.1016/j.jocs.2015.08.008 MathSciNetCrossRefGoogle Scholar
- Fishman G (2013) Monte Carlo: concepts, algorithms, and applications. Springer, BerlinzbMATHGoogle Scholar
- 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
- 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
- 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. https://doi.org/10.1016/0021-9290(94)00174-3 CrossRefGoogle Scholar
- 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
- 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
- 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
- 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
- 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
- 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
- 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. https://doi.org/10.1029/2006WR005673 CrossRefGoogle Scholar
- 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
- Osnes H, Sundnes J (2012) Uncertainty analysis of ventricular mechanics using the probabilistic collocation method. IEEE Trans Biomed Eng 59(8):2171–2179CrossRefGoogle Scholar
- 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
- 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
- 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
- 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
- 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. https://doi.org/10.1016/j.piutam.2013.01.001, iUTAM symposium on multiscale problems in stochastic mechanics
- 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. https://doi.org/10.14814/phy2.13392 CrossRefGoogle Scholar
- 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
- Smiseth OA, Aalen JM (2018) Mechanism of harm from left bundle branch block. Trends Cardiovasc Med. https://doi.org/10.1016/j.tcm.2018.10.012 CrossRefGoogle Scholar
- Sobol IM (2001) Global sensitivity indices for nonlinear mathematical models and their Monte Carlo estimates. Math Comput Simul 55(1–3):271–280MathSciNetzbMATHCrossRefGoogle Scholar
- 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
- 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
- Trayanova NA, Winslow R (2011) Whole-heart modeling: applications to cardiac electrophysiology and electromechanics. Circ Res 108(1):113–128CrossRefGoogle Scholar
- 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
- 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
- Xiu D, Karniadakis GE (2002) The Wiener–Askey polynomial chaos for stochastic differential equations. SIAM J Sci Comput 24(2):619–644MathSciNetzbMATHCrossRefGoogle Scholar
- 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. https://doi.org/10.1109/TPWRS.2018.2865548 CrossRefGoogle Scholar