A strain-based finite element model for calcification progression in aortic valves

doi:10.1016/j.jbiomech.2017.10.014

Journal of Biomechanics

Volume 65, 8 December 2017, Pages 216-220

https://doi.org/10.1016/j.jbiomech.2017.10.014 Get rights and content

Abstract

Calcific aortic valve disease (CAVD) is a serious disease affecting the aging population. A complex interaction between biochemicals, cells, and mechanical cues affects CAVD initiation and progression. In this study, motivated by the progression of calcification in regions of high strain, we developed a finite element method (FEM) based spatial calcification progression model. Several cardiac cycles of transient structural FEM simulations were simulated. After each simulation cycle, calcium deposition was placed in regions of high circumferential strain. Our results show the radial expansion of calcification as spokes starting from the attachment region, agreeing very well with the reported clinical data.

Introduction

Calcific aortic valve disease (CAVD) is the major form of aortic stenosis (Otto et al., 1997), where stiffening of the valve leaflets obstructs blood flow from the left ventricle into the systemic circulation. The initiation and progression of CAVD involve various interrelated mechanobiological processes spanning multiple scales (Pawade et al., 2015). Hemodynamics phenomena play an important role in normal aortic valve function and CAVD (Sacks and Yoganathan, 2007, Balachandran et al., 2011, Gould et al., 2013, Ayoub et al., 2016). Wall shear stress exerted on the valvular endothelial cells (ECs) influences the inflammatory processes in CAVD as well as the signaling between the ECs and the valvular interstitial cells (VICs). Mechanical strains sensed by the VICs are believed to promote VIC differentiation to a calcific phenotype (Fisher et al., 2013).

Calcification is more likely to occur on the aortic side of the valve (Otto et al., 1994, Weinberg et al., 2010, Yip and Simmons, 2011), which has been attributed to the disturbed hemodynamics (Weinberg et al., 2010, Ge and Sotiropoulos, 2010) and the structural distinctions (Neufeld et al., 2014). Although progress has been made in modeling the aortic valve biomechanics, modeling CAVD progression has not received much attention. Previous biomechanical aortic valve calcification progression models have either obtained calcification progression from medical imaging data (Halevi et al., 2015), used pre-assumed simple growth laws (Weinberg et al., 2009), or have not reported the calcification growth patterns (Katayama et al., 2013).

Herein, we propose a calcification model based on the observation that mechanical strain promotes calcification in aortic valves (Balachandran et al., 2010, Hutcheson et al., 2012, Fisher et al., 2013, Hsu et al., 2016). We propose an algorithm to model the long-term evolution of calcification based on the mechanical strain on the aortic side of the valve. CAVD initiation and progression involve a complex interplay between various biochemicals, cells, and biomechanical factors (Arzani et al., 2017). In the current study, motivated by the known self-perpetuating process of calcification (Pawade et al., 2015), we simulate the spatial calcification growth patterns based on the mechanical strain obtained from a finite element model.

Section snippets

Finite element method (FEM)

The idealized aortic valve geometrical model used in prior studies (Weinberg and Mofrad, 2007, Weinberg et al., 2009) was used in this study. The model included the valve leaflet with varying thickness, the aortic root and sinus, and the ascending aorta (Fig. 1). We assumed perfect symmetry of the valve to reduce the computational domain to one-sixth of the valve, similar to previous studies (Weinberg and Mofrad, 2007, Weinberg et al., 2009, Joda et al., 2016). This is a favorable assumption

Results

The calcification algorithm was repeated until the stop criteria were reached after the 19th simulation cycle. The calcification progression results are shown in Fig. 2. The color bar represents the material constant (c) in the isotropic term of the constitutive equation, and therefore, an indicator of calcification intensity. The six snapshots (Fig. 2(a)–(f)) show the calcification progression at different steps. The first and last snapshots represent the first and last simulation cycles. It

Discussion

We presented a new strain-based FEM model for simulation of the long-term spatial progression of calcification in the aortic valve. Our model is able to replicate the clinically observed radial calcification expansion patterns (Thubrikar et al., 1986). Calcification creates a localized increase in stiffness, resulting in a compliance mismatch at the boundary of calcification that ultimately drives the observed spatial growth patterns. Interestingly, more recent studies have also shown the

Conflicts of interest

None.

Acknowledgements

This work was supported by the American Heart Association (Award 16GRNT27630015).

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Short communicationA strain-based finite element model for calcification progression in aortic valves

Abstract

Introduction

Section snippets

Finite element method (FEM)

Results

Discussion

Conflicts of interest

Acknowledgements

Am. J. Pathol.

Med. Eng. Phys.

J. Biomech.

J. Biomech.

J. Biomech.

J. Thoracic Cardiovascul. Surg.

Ann. Thoracic Surg.

Atherosclerosis

J. Am. College Cardiol.

J. Comput. Appl. Math.

J. Biomech.

Med. Eng. Phys.

Am. J. Cardiol.

Cardiovascul. Pathol.

Comparison and critical analysis of invariant-based models with respect to their ability in fitting human aortic valve data

Ann. Solid Struct. Mech.

Hemodynamics and mechanobiology of aortic valve inflammation and calcification

Int. J. Inflamm.

Computational comparison of regional stress and deformation characteristics in tricuspid and bicuspid aortic valve leaflets

Int. J. Numer. Methods Biomed. Eng.

A time integration algorithm for structural dynamics with improved numerical dissipation: the generalized-α method

J. Appl. Mech.

Short communication
A strain-based finite element model for calcification progression in aortic valves

A time integration algorithm for structural dynamics with improved numerical dissipation: the generalized- $α$ method