A viscoactive constitutive modeling framework with variational updates for the myocardium

We present a constitutive modeling framework for contractile cardiac mechanics by formulating a single variational principle from which incremental stress-strain relations and kinetic rate equations for active contraction and relaxation can all be derived. The variational framework seamlessly incorporates the hyperelastic behavior of the relaxed and contracted tissue along with the rate - and length - dependent generation of contractile force. We describe a three-element, Hill-type model that unifies the active tension and active deformation approaches. As in the latter approach, we multiplicatively decompose the total deformation gradient into active and elastic parts, with the active deformation parametrizing the contractile Hill element. We adopt as internal variables the fiber, cross-fiber, and sheet normal stretch ratios. The kinetics of these internal variables are modeled via definition of a kinetic potential function derived from experimental force-velocity relations. Additionally, we account for dissipation during tissue deformation by adding a Newtonian viscous potential. To model the force activation, the kinetic equations are coupled with the calcium transient obtained from a cardiomyocyte electrophysiology model. We first analyze our model at the material point level using stress and strain versus time curves for different viscosity values. Subsequently, we couple our constitutive framework with the finite element method (FEM) and study the deformation of three-dimensional tissue slabs with varying cardiac myocyte orientation. Finally, we simulate the contraction and relaxation of an ellipsoidal left ventricular model and record common kinematic measures, such as ejection fraction, and myocardial tissue volume changes

Myofiber strain in healthy humans using DENSE and cDTI

Purpose: Myofiber strain, Eff , is a mechanistically relevant metric of cardiac cell shortening and is expected to be spatially uniform in healthy populations, making it a prime candidate for the evaluation of local cardiomyocyte contractility. In this study, a new, efficient pipeline was proposed to combine microstructural cDTI and functional DENSE data in order to estimate Eff in vivo.Methods: Thirty healthy volunteers were scanned with three long-axis (LA) and three short-axis (SA) DENSE slices using 2D displacement encoding and one SA slice of cDTI. The total acquisition time was 11 minutes ± 3 minutes across volunteers. The pipeline first generates 3D SA displacements from all DENSE slices which are then combined with cDTI data to generate a cine of myofiber orientations and compute Eff . The precision of the post-processing pipeline was assessed using a computational phantom study. Transmural myofiber strain was compared to circumferential strain, Ecc , in healthy volunteers using a Wilcoxon sign rank test.Results: In vivo, computed Eff was found uniform transmurally compared to Ecc (-0.14[-0.15, -0.12] vs -0.18 [-0.20, -0.16], P < .001, -0.14 [-0.16, -0.12] vs -0.16 [-0.17, -0.13], P < .001 and -0.14 [-0.16, -0.12] vs Ecc_C = -0.14 [-0.15, -0.11], P = .002, Eff_C vs Ecc_C in the endo, mid, and epi layers, respectively).Conclusion: We demonstrate that it is possible to measure in vivo myofiber strain in a healthy human population in 10 minutes per subject. Myofiber strain was observed to be spatially uniform in healthy volunteers making it a potential biomarker for the evaluation of local cardiomyocyte contractility in assessing cardiovascular dysfunction

Myofiber strain in healthy humans using DENSE and cDTI

Purpose: Myofiber strain, Eff , is a mechanistically relevant metric of cardiac cell shortening and is expected to be spatially uniform in healthy populations, making it a prime candidate for the evaluation of local cardiomyocyte contractility. In this study, a new, efficient pipeline was proposed to combine microstructural cDTI and functional DENSE data in order to estimate Eff in vivo.Methods: Thirty healthy volunteers were scanned with three long-axis (LA) and three short-axis (SA) DENSE slices using 2D displacement encoding and one SA slice of cDTI. The total acquisition time was 11 minutes ± 3 minutes across volunteers. The pipeline first generates 3D SA displacements from all DENSE slices which are then combined with cDTI data to generate a cine of myofiber orientations and compute Eff . The precision of the post-processing pipeline was assessed using a computational phantom study. Transmural myofiber strain was compared to circumferential strain, Ecc , in healthy volunteers using a Wilcoxon sign rank test.Results: In vivo, computed Eff was found uniform transmurally compared to Ecc (-0.14[-0.15, -0.12] vs -0.18 [-0.20, -0.16], P < .001, -0.14 [-0.16, -0.12] vs -0.16 [-0.17, -0.13], P < .001 and -0.14 [-0.16, -0.12] vs Ecc_C = -0.14 [-0.15, -0.11], P = .002, Eff_C vs Ecc_C in the endo, mid, and epi layers, respectively).Conclusion: We demonstrate that it is possible to measure in vivo myofiber strain in a healthy human population in 10 minutes per subject. Myofiber strain was observed to be spatially uniform in healthy volunteers making it a potential biomarker for the evaluation of local cardiomyocyte contractility in assessing cardiovascular dysfunction