A novel method for quantifying in-vivo regional left ventricular myocardial contractility in the border zone of a myocardial infarction

Abstract

Homogeneous contractility is usually assigned to the remote region, border zone (BZ), and the infarct in existing infarcted left ventricle (LV) mathematical models. Within the LV, the contractile function is therefore discontinuous. Here, we hypothesize that the BZ may in fact define a smooth linear transition in contractility between the remote region and the infarct. To test this hypothesis, we developed a mathematical model of a sheep LV having an anteroapical infarct with linearly-varying BZ contractility. Using an existing optimization method (Sun et al., 2009, "A Computationally Efficient Formal Optimization of Regional Myocardial Contractility in a Sheep With Left Ventricular Aneurysm," J. Biomech. Eng., 131(11), pp. 111001), we use that model to extract active material parameter T(max) and BZ width d(n) that "best" predict in-vivo systolic strain fields measured from tagged magnetic resonance images (MRI). We confirm our hypothesis by showing that our model, compared to one that has homogeneous contractility assigned in each region, reduces the mean square errors between the predicted and the measured strain fields. Because the peak fiber stress differs significantly (~15%) between these two models, our result suggests that future mathematical LV models, particularly those used to analyze myocardial infarction treatment, should account for a smooth linear transition in contractility within the BZ.

Fig. 1

Sheep LV with anteroapical aneurysm. (a) Finite element mesh and (b) contractility T_max in BZ. Dotted line: homogeneous T_max in BZ. Solid line: linearly–varying T_max with distance d in BZ.

Fig. 2

Optimization results: (a) convergence with BZ width d_n as a parameter and (b) converged value of OBJ versus d_n

Fig. 3

Contractility in the border zone. d_n = 3 cm. T_{max- R} = 186.3 kPa

Fig. 4

Comparison of stress in myofiber direction at ES. (a) Linearly–varying T_{max- BZ} with d_n = 3 cm and T_{max- R} = 186.3 kPa. (b) Homogeneous T_{max- BZ} with T_{max- R} = 190.1 kPa and T_max- BZ = 60.3 kPa. Unit of fringe levels in kPa.