Skip to main content

Using machine learning to characterize heart failure across the scales

Abstract

Heart failure is a progressive chronic condition in which the heart undergoes detrimental changes in structure and function across multiple scales in time and space. Multiscale models of cardiac growth can provide a patient-specific window into the progression of heart failure and guide personalized treatment planning. Yet, the predictive potential of cardiac growth models remains poorly understood. Here, we quantify predictive power of a stretch-driven growth model using a chronic porcine heart failure model, subject-specific multiscale simulation, and machine learning techniques. We combine hierarchical modeling, Bayesian inference, and Gaussian process regression to quantify the uncertainty of our experimental measurements during an 8-week long study of volume overload in six pigs. We then propagate the experimental uncertainties from the organ scale through our computational growth model and quantify the agreement between experimentally measured and computationally predicted alterations on the cellular scale. Our study suggests that stretch is the major stimulus for myocyte lengthening and demonstrates that a stretch-driven growth model alone can explain \(52.7\%\) of the observed changes in myocyte morphology. We anticipate that our approach will allow us to design, calibrate, and validate a new generation of multiscale cardiac growth models to explore the interplay of various subcellular-, cellular-, and organ-level contributors to heart failure. Using machine learning in heart failure research has the potential to combine information from different sources, subjects, and scales to provide a more holistic picture of the failing heart and point toward new treatment strategies.

This is a preview of subscription content, access via your institution.

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11

References

  • Ambrosi D, Ateshian GA, Arruda EM, Cowin SC, Dumais J, Goriely A, Holzapfel GA, Humphrey JD, Kemkemer R, Kuhl E, Olberding JE, Taber LA, Garikipati K (2011) Perspectives on biological growth and remodeling. J Mech Phys Solids 59:863–883

    MathSciNet  MATH  Article  Google Scholar 

  • Arts T, Delhaas T, Bovendeerd P, Verbeek X, Prinzen FW (2005) Adaptation to mechanical load determines shape and properties of heart and circulation: the CircAdapt model. Am J Phys Heart Circ Phys 288:H1943–H1954

    Google Scholar 

  • Baillargeon B, Rebelo N, Fox DD, Taylor RL, Kuhl E (2014) The Living Heart Project: a robust and integrative simulator for human heart function. Eur J Mech A/Solids 48:38–47

    MathSciNet  MATH  Article  Google Scholar 

  • Bray MA, Sheehy SP, Parker KK (2008) Sarcomere alignment is regulated by myocyte shape. Cell Motil Cytoskel 65:641–651

    Article  Google Scholar 

  • Campos JO, Sundnes J, dos Santos RW, Rocha BM (2019) Effects of left ventricle wall thickness uncertainties on cardiac mechanics. Biomech Model Mechanobiol. https://doi.org/10.1007/s10237-019-01153-1

    Article  Google Scholar 

  • Chabiniok R, Wang V, Hadjicharalambous M, Asner L, Lee J, Sermesant M, Kuhl E, Young A, Moireau P, Nash M, Chapelle D, Nordsletten DA (2016) Multiphysics and multiscale modeling, data-model fusion and integration of organ physiology in the clinic: ventricular cardiac mechanics. Interface Focus 6:20150083

    Article  Google Scholar 

  • Choy JS, Leng S, Awakeem Y, Sack K.L, Dabiri Y, Zhong L, Guccione JM, Kassab GS Mechanical stretch as stimulus for growth and remodeling in mitral regurgitation. submitted for publication

  • Dassault Systèmes SIMULIA (2018) Abaqus 2018. Documentation, Dassault Systèmes, Rhode Island

  • Dokos S, Smaill BH, Young AA, LeGrice IJ (2002) Shear properties of passive ventricular myocardium. Am J Physiol Heart Circ Physiol 283:H2650–H2659

    Article  Google Scholar 

  • Eriksson TSE, Prassl AJ, Plank G, Holzapfel GA (2013) Influence of myocardial fiber/sheet orientations on left ventricular mechanical contraction. Math Mech Solids 18:592–606

    MathSciNet  Article  Google Scholar 

  • Gelman A (2006) Prior distributions for variance parameters in hierarchical models. Bayesian Anal 1:515–534

    MathSciNet  MATH  Article  Google Scholar 

  • Gelman A, Hill J (2006) Data analysis using regression and multilevel/hierarchical models. Cambridge University Press, Cambridge

    Book  Google Scholar 

  • Genet M, Lee LC, Baillargeon B, Guccione JM, Kuhl E (2016) Modeling pathologies of systolic and diastolic heart failure. Ann Biomed Eng 44:112–127

    Article  Google Scholar 

  • Gerdes AM, Kellerman SE, Moore JA, Muffly KE, Clark LC, Reaves PY, Malec KB, Mc Keown PP, Schocken DD (1992) Structural remodeling of cardiac myocytes in patients with ischemic cardiomyopathy. Circulation 86:426–430

    Article  Google Scholar 

  • Gerdes AM, Capasso JM (1995) Structural remodeling and mechanical dysfunction of cardiac myocytes in heart failure. J Mol Cell Cardiol 27:849–856

    Article  Google Scholar 

  • Göktepe S, Abilez OJ, Kuhl E (2010) A generic approach towards finite growth with examples of athlete’s heart, cardiac dilation, and cardiac wall thickening. J Mech Phys Solids 58:1661–1680

    MathSciNet  MATH  Article  Google Scholar 

  • Göktepe S, Abilez OJ, Parker KK, Kuhl E (2010) A multiscale model for eccentric and concentric cardiac growth through sarcomerogenesis. J Theor Biol 265:433–442

    MATH  Article  Google Scholar 

  • Göktepe S, Acharya SNS, Wong J, Kuhl E (2011) Computational modeling of passive myocardium. Int J Num Meth Biomed Eng 27:1–12

    MathSciNet  MATH  Article  Google Scholar 

  • Grossman W, Jones D, McLaurin LP (1975) Wall stress and patterns of hypertrophy in the human left ventricle. J Clin Invest 56:56–64

    Article  Google Scholar 

  • Grossman W (1980) Cardiac hypertrophy: useful adaptation or pathologic process? Am J Med 69:576–584

    Article  Google Scholar 

  • Holmes JW (2004) Candidate mechanical stimuli for hypertrophy during volume overload. J Appl Physiol 97:1453–1460

    Article  Google Scholar 

  • Holzapfel GA, Ogden RW (2009) Constitutive modelling of passive myocardium: a structurally based framework for material characterization. Philos Trans A Math Phys Eng Sci 367:3445–3475

    MathSciNet  MATH  Article  Google Scholar 

  • Inman HF, Bradley EL Jr (1989) The overlapping coefficient as a measure of agreement between probability distributions and point estimation of the overlap of two normal densities. Commun Stat Methods 18:3851–3874

    MathSciNet  MATH  Article  Google Scholar 

  • Jones E, Oliphant T, Peterson P (2014) SciPy: open source scientific tools for Python. http://www.scipy.org/

  • Kerckhoffs RCP, Omens JH, McCulloch AD (2012) A single strain-based growth law predicts concentric and eccentric cardiac growth during pressure and volume overload. Mech Res Commun 42:40–50

    Article  Google Scholar 

  • Kerkhof PLM (2015) Characterizing heart failure in the ventricular volume domain. Clin Med Ins Cardiol 9:11–31

    Google Scholar 

  • Kleiber M (1947) Body size and metabolic rate. Physiol Rev 27:511–541

    MATH  Article  Google Scholar 

  • Klotz S, Hay I, Dickstein ML, Yi G-H, Wang J, Maurer MS, Kass DA, Burkhoff D (2006) Single-beat estimation of end-diastolic pressure-volume relationship: a novel method with potential for noninvasive application. Am J Physiol Circ Physiol 291:H403–H412

    Article  Google Scholar 

  • Kroon W, Delhaas T, Arts T, Bovendeerd P (2009) Computational modeling of volumetric soft tissue growth: application to the cardiac left ventricle. Biomech Model Mechanobiol 8:301–309

    Article  Google Scholar 

  • Kuhl E (2014) Growing matter—a review of growth in living systems. J Mech Behavior Biomed Mat 29:529–543

    Article  Google Scholar 

  • Kumar V, Abbas AK, Aster JC (2015) Robbins and Cotran pathologic basis of disease, 9th edn. Elsevier, Amsterdam

    Google Scholar 

  • Lee JD, Sasayama S, Kihara Y, Ohyagi A, Fujisawa A, Yui Y, Kawai C (1985) Adaptations of the left ventricle to chronic volume overload induced by mitral regurgitation in conscious dogs. Heart Vessels 1:9–15

    Article  Google Scholar 

  • Lee LC, Kassab GS, Guccione JM (2016) Mathematical modeling of cardiac growth and remodeling WIREs Syst. Biol Med 8:211–226

    Google Scholar 

  • Legrice IJ, Hunter PJ, Smaill BH (1997) Laminar structure of the heart: a mathematical model. Am J Physiol 272:H2466–H2476

    Google Scholar 

  • Lewandowski D, Kurowicka D, Joe H (2009) Generating random correlation matrices based on vines and extended onion method. J Multivar Anal 100:1989–2001

    MathSciNet  MATH  Article  Google Scholar 

  • Limpert E, Stahel WA, Abbt M (2001) Log-normal distribution across the sciences: Keys and clues. Bioscience 51:341–352

    Article  Google Scholar 

  • Menzel A (2005) Modelling of anisotropic growth in biological tissues. Biomech Model Mechanobio 3:147–171

    Article  Google Scholar 

  • Menzel A, Kuhl E (2012) Frontiers in growth and remodeling. Mech Res Commun 42:1–14

    Article  Google Scholar 

  • Omens JH (1998) Stress and strain as regulators of myocardial growth. Prog Biophys Mol Biol 69:559–572

    Article  Google Scholar 

  • Opie LH, Commerford PJ, Gersh BJ, Pfeffer MA (2006) Controversies in ventricular remodelling. Lancet 367:356–367

    Article  Google Scholar 

  • Peirlinck M, Sack KL, De Backer P, Morais P, Segers P, Franz T, De Beule M (2019) Kinematic boundary conditions substantially impact in silico ventricular function. Int J Num Meth Biomed Eng 35:e3151

    Article  Google Scholar 

  • Perdikaris P (2017) Gaussian processess. A hands-on tutorial. https://github.com/paraklas/GPTutorial

  • Raissi M, Perdikaris P, Karniadakis G (2017) Machine learning of linear differential equations using Gaussian processes. J Comp Phys 348:683–693

    MathSciNet  MATH  Article  Google Scholar 

  • Raissi M, Perdikaris P, Karniadakis G (2018) Numerical Gaussian processes for time-dependent and nonlinear partial differential equations. SIAM J Sci Comp 40:A172–A198

    MathSciNet  MATH  Article  Google Scholar 

  • Rausch MK, Dam A, Göktepe S, Abilez OJ, Kuhl E (2011) Computational modeling of growth: systemic and pulmonary hypertension in the heart. Biomech Model Mechanobio 10:799–811

    Article  Google Scholar 

  • Rausch MK, Zöllner AM, Genet M, Baillargeon B, Bothe W, Kuhl E (2017) A virtual sizing tool for mitral valve annuloplasty. Int J Num Meth Biomed Eng 33:e02788

    Article  Google Scholar 

  • Rodrigues JCL, Amadu AM, Dastidar AG, Szantho GV, Lyen SM, Godsave C, Ratcliffe LEK, Burchell AE, Hart EC, Hamilton MCK, Nightingale AK, Paton JFR, Manghat NE, Bucciarelli-Ducci C (2016) Comprehensive characterisation of hypertensive heart disease left ventricular phenotypes. Heart 102:1671–1679

    Article  Google Scholar 

  • Rodriguez E, Hoger A, McCulloch AD (1994) Stress-dependent finite growth in soft elastic tissues. J Biomech 27:455–467

    Article  Google 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 Num Meth Biomed Eng 35:e3178

    Google Scholar 

  • Sack KL, Aliotta E, Ennis DB, Choy JS, Kassab GS, Guccione JM, Franz T (2018) Construction and validation of subject-specific biventricular finite-element models of healthy and failing swine hearts from high-resolution DT-MRI. Front Physiol 9:539

    Article  Google Scholar 

  • Saez P, Pena E, Martinez MA, Kuhl E (2014) Computational modeling of hypertensive growth in the human carotid artery. Comp Mech 53:1183–1196

    MathSciNet  Article  Google Scholar 

  • Sahli Costabal F, Concha FA, Hurtado DE, Kuhl E (2017) The importance of mechano-electrical feedback and inertia in cardiac electromechanics. Comp Meth Appl Mech Eng 320:352–368

    MathSciNet  Article  Google Scholar 

  • Sahli Costabal F, Choy JS, Sack KL, Guccione JM, Kassab G, Kuhl E (2019) Multiscale characterization of heart failure. Acta Biomat 86:66–76

    Article  Google Scholar 

  • Sahli Costabal F, Matsuno K, Yao J, Perdikaris P, Kuhl E (2019) Machine learning in drug development: characterizing the effect of 30 drugs on the QT interval using Gaussian process regression, sensitivity analysis, and uncertainty quantification. Comp Meth Appl Mech Eng 348:313–333

    MathSciNet  Article  Google Scholar 

  • Salvatier J, Wiecki TV, Fonnesbeck C (2016) Probabilistic programming in Python using PyMC3. Peer J Comput Sci 2:e55

    Article  Google Scholar 

  • Sandler H, Dodge HT (1963) Left ventricular tension and stress in man. Circ Res 8:437–445

    Google Scholar 

  • Sasayama S, Ross JJ, Franklin D, Bloor CM, Bishop S, Dilley RB (1976) Adaptations of the left ventricle to chronic pressure overload. Circ Res 38:172–178

    Article  Google Scholar 

  • Savinova OV, Gerdes AM (2012) Myocyte changes in heart failure. Heart Fail Clin 8:1–6

    Article  Google Scholar 

  • Sommer G, Schriefl AJ, Andre M, Sacherer M, Viertler C, Wolinski H, Holzapfel GA (2015) Biomechanical properties and microstructure of human ventricular myocardium. Acta Biomat 24:172–192

    Article  Google Scholar 

  • Tsamis A, Cheng A, Nguyen TC, Langer F, Miller DC, Kuhl E (2012) Kinematics of cardiac growth: in vivo charactierzaion of growth tensors and strains. J Mech Beh Biomed Mat 8:165–177

    Article  Google Scholar 

  • Townsend N, Wilson L, Bhatnagar P, Wickramasinghe K, Rayner M, Nichols M (2016) Cardiovascular disease in Europe: epidemiological update 2016. Eur Heart J 37:3232–3245

    Article  Google Scholar 

  • Wong J, Kuhl E (2014) Generating fiber orientation maps in human heart models using Poisson interpolation. Comp Meth Biomech Biomed Eng 17:1217–1226

    Article  Google Scholar 

  • Yoshida M, Sho E, Nanjo H, Takahashi M, Koboyashi M, Kawamura K, Honma M, Komatsu M, Sugita A, Yamauchi M, Hosoi T, Ito Y, Matsuda H (2010) Weaving hypothesis of cardiomyocyte sarcomeres. Am J Path 176:660–678

    Article  Google Scholar 

  • Wisdom KM, Delp SL, Kuhl E (2015) Use it or lose it: multiscale skeletal muscle adaptation to mechanical stimuli. Biomech Model Mechanobiol 14:195–215

    Article  Google Scholar 

  • Witzenburg CM, Holmes JW (2017) A comparison of phenomenologic growth laws for myocardial hypertrophy. J Elast 129:257–281

    MathSciNet  MATH  Article  Google Scholar 

  • Zöllner AM, Abilez OJ, Böl M, Kuhl E (2012) Stretching skeletal muscle. Chronic muscle lengthening through sarcomerogenesis. PLoS ONE 7:e45661

Download references

Acknowledgements

This work was supported by the Flanders Innovation and Entrepreneurship Agency (VLAIO) strategic basic research Grant 141014 and a travel Grant by the Flemish Fund for Scientific Research (FWO) to Mathias Peirlinck, by the Becas Chile-Fulbright Fellowship to Francisco Sahli Costabal, and by the National Institutes of Health Grant U01 HL119578 to Julius M. Guccione, Ghassan S. Kassab, and Ellen Kuhl.

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to E. Kuhl.

Ethics declarations

Conflicts of interest

The authors declare that they have no conflict of interest

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Peirlinck, M., Sahli Costabal, F., Sack, K.L. et al. Using machine learning to characterize heart failure across the scales. Biomech Model Mechanobiol 18, 1987–2001 (2019). https://doi.org/10.1007/s10237-019-01190-w

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10237-019-01190-w

Keywords

  • Machine learning
  • Gaussian process regression
  • Bayesian inference
  • Uncertainty quantification
  • Heart failure
  • Growth and remodeling
  • Multiscale