# Multifidelity-CMA: a multifidelity approach for efficient personalisation of 3D cardiac electromechanical models

## Abstract

Personalised computational models of the heart are of increasing interest for clinical applications due to their discriminative and predictive abilities. However, the simulation of a single heartbeat with a 3D cardiac electromechanical model can be long and computationally expensive, which makes some practical applications, such as the estimation of model parameters from clinical data (the personalisation), very slow. Here we introduce an original multifidelity approach between a 3D cardiac model and a simplified “0D” version of this model, which enables to get reliable (and extremely fast) approximations of the global behaviour of the 3D model using 0D simulations. We then use this multifidelity approximation to speed-up an efficient parameter estimation algorithm, leading to a fast and computationally efficient personalisation method of the 3D model. In particular, we show results on a cohort of 121 different heart geometries and measurements. Finally, an exploitable code of the 0D model with scripts to perform parameter estimation will be released to the community.

## Keywords

Cardiac electromechanical modelling Reduced model Multifidelity modelling Parameter estimation Finite element mechanical modelling## Notes

### Acknowledgements

This work has been partially funded by the European Union FP7-funded project MD-Paedigree (Grant Agreement 600932) and contributes to the objectives of the European Research Council advanced Grant MedYMA (2011-291080).

### Compliance with ethical standards

### Conflicts of interest

The authors declare that they have no conflict of interest.

### Informed consent

Informed consent was obtained from the subjects, and the protocol was approved by the local research ethics committee.

## References

- 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 48:38–47MathSciNetCrossRefGoogle Scholar
- Caruel M, Chabiniok R, Moireau P, Lecarpentier Y, Chapelle D (2014) Dimensional reductions of a cardiac model for effective validation and calibration. Biomech Model Mechanobiol 13(4):897–914CrossRefGoogle Scholar
- Chabiniok R, Moireau P, Lesault P-F, Rahmouni A, Deux J-F, Chapelle D (2012) Estimation of tissue contractility from cardiac cine-MRI using a biomechanical heart model. Biomech Model Mechanobiol 11(5):609–630CrossRefGoogle Scholar
- Chabiniok R, Wang VY, Hadjicharalambous M, Asner L, Lee J, Sermesant M, Kuhl E, Young AA, Moireau P, Nash MP, Chapelle D, Nordsletten DA (2016) Multiphysics and multiscale modelling, data-model fusion and integration of organ physiology in the clinic: ventricular cardiac mechanics. Interface Focus 6(2):20150083CrossRefGoogle Scholar
- Chapelle D, Le Tallec P, Moireau P, Sorine M (2012) Energy-preserving muscle tissue model: formulation and compatible discretizations. Int J Multiscale Comput Eng 10(2):189–211CrossRefGoogle Scholar
- Chen Z, Cabrera-Lozoya R, Relan J, Sohal M, Shetty A, Karim R, Delingette H, Gill J, Rhode K, Ayache N, Taggart P, Rinaldi CA, Sermesant M, Razavi R (2016) Biophysical modelling predicts ventricular tachycardia inducibility and circuit morphology: a combined clinical validation and computer modelling approach. J Cardiovasc Electrophys 27(7):851–860CrossRefGoogle Scholar
- Clayton R, Bernus O, Cherry E, Dierckx H, Fenton F, Mirabella L, Panfilov A, Sachse FB, Seemann G, Zhang H (2011) Models of cardiac tissue electrophysiology: progress, challenges and open questions. Prog Biophys Mol Biol 104(1):22–48CrossRefGoogle Scholar
- Cuellar AA, Lloyd CM, Nielsen PF, Bullivant DP, Nickerson DP, Hunter PJ (2003) An overview of cellml 1.1, a biological model description language. Simulation 79(12):740–747CrossRefGoogle Scholar
- Duchateau N, De Craene M, Allain P, Saloux E, Sermesant M (2016) Infarct localization from myocardial deformation: prediction and uncertainty quantification by regression from a low-dimensional space. Trans Med Imaging 35(10):2340–2352CrossRefGoogle Scholar
- Garny A, Hunter PJ (2015) Opencor: a modular and interoperable approach to computational biology. Front Physiol 6:26CrossRefGoogle Scholar
- Geijtenbeek T, van de Panne M, van der Stappen AF (2013) Flexible muscle-based locomotion for bipedal creatures. ACM Trans Graph (TOG) 32(6):206CrossRefGoogle Scholar
- Hansen N (2006) The cma evolution strategy: a comparing review. Towards a new evolutionary computation. Springer, Berlin, Heidelberg, pp 75–102Google Scholar
- Huxley A (1957) Muscle structure and theories of contraction. Prog Biophys Biophys Chem 7:255–318Google Scholar
- Jolly M-P, Guetter C, Lu X, Xue H, Guehring J (2011) Automatic segmentation of the myocardium in cine mr images using deformable registration. International workshop on statistical atlases and computational models of the heart. Springer, Berlin, pp 98–108Google Scholar
- Kayvanpour E, Mansi T, Sedaghat-Hamedani F, Amr A, Neumann D, Georgescu B, Seegerer P, Kamen A, Haas J, Frese KS, Irawati M, Wirsz E, King V, Buss S, Mereles D, Zitron E, Keller A, Katus HA, Comaniciu D, Meder B (2015) Towards personalized cardiology: multi-scale modeling of the failing heart. PLoS ONE 10(7):e0134869CrossRefGoogle Scholar
- Kennedy MC, O’Hagan A (2000) Predicting the output from a complex computer code when fast approximations are available. Biometrika 87(1):1–13MathSciNetCrossRefzbMATHGoogle Scholar
- Marchesseau S, Heimann T, Chatelin S, Willinger R, Delingette H (2010) Multiplicative jacobian energy decomposition method for fast porous visco-hyperelastic soft tissue model. International conference on medical image computing and computer-assisted intervention. Springer, Berlin, pp 235–242Google Scholar
- Marchesseau S, Delingette H, Sermesant M, Ayache N (2013a) Fast parameter calibration of a cardiac electromechanical model from medical images based on the unscented transform. Biomech Model Mechanobiol 12(4):815–831CrossRefGoogle Scholar
- Marchesseau S, Delingette H, Sermesant M, Lozoya RC, Tobon-Gomez C, Moireau P, i Ventura RMF, Lekadir K, Hernández AI, Garreau M, Donal E, Leclercq C, Duckett SG, Rhode KS, Rinaldi CA, Frangi AF, Razavi R, Chapelle D, Ayache N (2013b) Personalization of a cardiac electromechanical model using reduced order unscented kalman filtering from regional volumes. Med Image Anal 17(7):816–829CrossRefGoogle Scholar
- Mollero R, Pennec X, Delingette H, Ayache N, Sermesant M (2016) A multiscale cardiac model for fast personalisation and exploitation. International conference on medical image computing and computer-assisted intervention. Springer, Berlin, pp 174–182Google Scholar
- Neumann D, Mansi T, Itu L, Georgescu B, Kayvanpour E, Sedaghat-Hamedani F, Amr A, Haas J, Katus H, Meder B et al (2016) A self-taught artificial agent for multi-physics computational model personalization. Med Image Anal 34:52–64CrossRefGoogle Scholar
- Panthee N, Okada J-I, Washio T, Mochizuki Y, Suzuki R, Koyama H, Ono M, Hisada T, Sugiura S (2016) Tailor-made heart simulation predicts the effect of cardiac resynchronization therapy in a canine model of heart failure. Med Image Anal 31:46–62CrossRefGoogle Scholar
- Peherstorfer B, Willcox K, Gunzburger M (2016) Survey of multifidelity methods in uncertainty propagation, inference, and optimization. Technical Report TR-16-1, Aerospace Computational Design Laboratory, Department of Aeronautics and Astronautics, Massachusetts Institute of Technology, CambridgeGoogle Scholar
- Powell MJ (2009) The bobyqa algorithm for bound constrained optimization without derivatives. Cambridge NA Report NA2009/06, University of Cambridge, CambridgeGoogle Scholar
- Schaerer J, Qian Z, Clarysse P, Metaxas D, Axel L, Magnin IE (2006) Fast and automated creation of patient-specific 3d heart model from tagged MRI. In: Proceedings of the MICCAI 2006 SA2PM workshopGoogle Scholar
- Seegerer P, Mansi T, Jolly M-P, Neumann D, Georgescu B, Kamen A, Kayvanpour E, Amr A, Sedaghat-Hamedani F, Haas J, et al. (2015) Estimation of regional electrical properties of the heart from 12-lead ECG and images, vol 8896 of LNCSGoogle Scholar
- Sermesant M, Chabiniok R, Chinchapatnam P, Mansi T, Billet F, Moireau P, Peyrat J-M, Wong KC, Relan J, Rhode KS, Ginks M, Lambiase P, Delingette H, Sorine M, Rinaldi CA, Chapelle D, Razavi R, Ayache N (2012) Patient-specific electromechanical models of the heart for prediction of the acute effects of pacing in CRT: a first validation. Med Image Anal 16(1):201–215CrossRefGoogle Scholar
- Smith N, de Vecchi A, McCormick M, Nordsletten D, Camara O, Frangi AF, Delingette H, Sermesant M, Relan J, Ayache N, Krueger MW, Schulze WHW, Hose R, Valverde I, Beerbaum P, Staicu C, Siebes M, Spaan J, Hunter P, Weese J, Lehmann H, Chapelle D, Rezavi R (2011) euheart: personalized and integrated cardiac care using patient-specific cardiovascular modelling. Interface Focus 1(3):349–364CrossRefGoogle Scholar
- Streeter DD (1979) Gross morphology and fiber geometry of the heart. Handbook of physiology. Williams & Wilkins, Baltimore, pp 61–112Google Scholar
- Wang VY, Hoogendoorn C, Frangi AF, Cowan BR, Hunter PJ, Young AA, Nash MP (2012) Automated personalised human left ventricular fe models to investigate heart failure mechanics. International workshop on statistical atlases and computational models of the heart. Springer, Berlin, pp 307–316Google Scholar
- Wang Y, Georgescu B, Chen T, Wu W, Wang P, Lu X, Ionasec R, Zheng Y, Comaniciu D (2013) Learning-based detection and tracking in medical imaging: a probabilistic approach. Deformation Models. Springer, Berlin, pp 209–235CrossRefGoogle Scholar
- Westerhof N, Bosman F, De Vries CJ, Noordergraaf A (1969) Analog studies of the human systemic arterial tree. J Biomech 2(2):121–208CrossRefGoogle Scholar
- Xi J, Lamata P, Lee J, Moireau P, Chapelle D, Smith N (2011) Myocardial transversely isotropic material parameter estimation from in-silico measurements based on a reduced-order unscented kalman filter. J Mech Behav Biomed Mater 4(7):1090–1102CrossRefGoogle Scholar
- Yu T, Lloyd CM, Nickerson DP, Cooling MT, Miller AK, Garny A, Terkildsen JR, Lawson J, Britten RD, Hunter PJ, Nielsen PMF (2011) The physiome model repository 2. Bioinformatics 27(5):743CrossRefGoogle Scholar