Assessment of regional myocardial work through adjoint-based data assimilation

Introduction

To achieve efficient pumping of blood to the body, the healthy heart contracts in a synchronous manner. However, heart disease can alter how the heart is activated during a beat, and dyssynchronous contraction can occur, reducing the overall pumping efficiency. Advanced treatments exist for such cases, but selecting patients likely to respond can be challenging. The existing selection criteria, based on organ level measures of activation and contraction, have relatively low specificity.  It is therefore of interest to extract new biomarkers to help better identify potential responders. Here we explore one example of a potential biomarker, the regional myocardial work [1], a measure of cardiac efficiency, using a computational model of cardiac mechanics optimized to patient specific data using a high level adjoint based data assimilation method.  

Methods

Left ventricular (LV) geometry was obtained from 4D echocardiography, and the segmented chamber was modelled as an incompressible, continuous hyperelastic body described via an transversely isotropic material law[2].  Active force development was modeled through additively decomposing stress into passive and active stresses, the latter added along the cardiac fiber direction, defined by a rule based architecture.  

The model was fit to 4D imaging of the LV through the cardiac cycle using an adjoint-based data assimilation technique, which automatically solves for the gradient of the solution with respect to local active stress, for highly efficient minimization of model misfit against collected data. Simulations were optimized both globally and regionally in 17 delineated segments[3]. With these simulations, the amount of mechanical work performed between time point tm and tn could be regionally calculated through -

W(tm, tn) = ∫ S: ∂tE dt = ∑i S(ti-½): dE(ti-½) 

where 

S(ti-½) = 0.5*(S(ti)+S(ti-1))  

and  

dE(ti-½) = E(ti)-E(ti-1) 

Here subscript t indicates the time point, S is the Second Piola-Kirchhoff stress tensor and E is the Green-Lagrange strain tensor. 

Results

We tested the method on healthy control subjects and patients suffering from left bundle branch block (LBBB). The results show an excellent fit between measured and simulated strain (R^2 = 0.8) and volume (R^2 = 1.0). The estimated regional myocardial work, assessed in these segments, shows clear differences between the healthy and diseased patients (e.g Mid Septal longitudinal wasted work ratio[1]: 1.45 (LBBB), 0.24(Healthy)) and can potentially be used as a biomarker to map regional cardiac dysfunction. 

References

[1] doi:10.1152/ajpheart.00191.2013 

[2] doi:10.1098/rsta.2009.0091 

[3] doi:10.1002/cnm.2863

An emerging class of models has been developed in recent years to predict cardiac growth and remodeling. We recently developed a cardiac constitutive model that predicts remodeling in response to elevated hemodynamics loading, and a subsequent reversal of the remodeling process when the loading is reduced. Here, we describe the integration of this model to an existing strongly coupled electromechanical model of the heart.

Volume loading of the cardiac ventricles is known to slow electrical conduction in the rabbit heart, but the mech- anisms remain unclear. Previous experimental and modeling studies have investigated some of these mechanisms, including stretch-activated membrane currents, reduced gap junctional conductance, and altered cell membrane capacitance. In order to quantify the relative contributions of these mechanisms, we combined a monomain model of rabbit ventricular electrophysiology with a hyperelastic model of passive ventricular mechanics. After a simplied geometric model with prescribed homogeneous deformation had been used to t model parameters and charcterize individual MEF mechanisms, a 3D model of the rabbit left and right ventricles was compared with experimental measurements from optical electrical mapping studies in the isolated rabbit heart. The model was in ated to an end-diastolic pressure of 30 mmHg, resulting in epicardial strains comparable to those measured in the anterior left ventricular free wall. While the e ects of stretch activated channels did alter epicardial conduction velocity, an increase in cellular capacitance was required to explain previously reported experimental results. The new results suggest that for large strains, various mechanisms can combine and produce a biphasic relationship between strain and conduction velocity. However, at the moderate strains generated by high end-diastolic pressure, a stretch- induced increase in myocyte membrane capacitance is the dominant driver of conduction slowing during ventricular volume loading.

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This paper describes an extension of the so-called Rush-Larsen scheme, which is a widely used numerical method for solving dynamic models of cardiac cell electrophysiology. The proposed method applies a local linearization of non-linear terms in combination with the analytical solution of linear ordinary differential equations, to obtain a second order accurate numerical scheme. We compare the error and computational load of the second order scheme to the original Rush-Larsen method. For a given error tolerance, the second order method is from nine to 500 times faster than the original scheme, depending on the choice of model and tolerance.