An ED pressure of 10.85 mmHg and an ES pressure of 99.55 mmHg is applied to the endocardium in the FE model. Displacements at the base are constrained in the longtitudinal direction, with the epicardial–basal edge being constrained in all directions. Because

*V*_{ED} depends only on diastolic material parameters,

*C*_{R}(=

*C*_{BZ} =0.1

*C*_{I}) is calibrated to 0.95 kPa so that the predicted value of

*V*_{ED} equals the measured value

_{ED} = 123.4ml.

To determine the optimal size of the BZ width *d*_{n}, the optimization is carried out with *d*_{n} ranging from 1cm to 7cm by an incremental change of 1cm.

shows the convergence of OBJ with

*d*_{n} as a parameter. In , the value of OBJ converges quickly; within ~ 6 iterations for all cases. shows that, except for the case when

*d*_{n} = 1cm, adopting a linear variation of

*T*_{max_}_{BZ} with distance in the FE model produces a lower value of OBJ upon convergence when compared to that obtained from the FE model having a homogeneous

*T*_{max_}_{BZ} [

1]. In that model, the BZ is defined as the steep transition in wall thickness between the infarct and the remote and has a width

*d*_{n} ~ 2cm. Our result therefore implies that the measured

*in–vivo* systolic strain can be better predicted by modeling

*T*_{max} as a linearly–varying parameter within the BZ. The figure shows that the optimal BZ width for the sheep LV model at 14 weeks postmyocardial infarction is ~ 3cm. Though the change in OBJ is small, we show later that the impact on myofiber stress is substantial.

The resultant optimal distribution of

*T*_{max} in the border zone (i.e for

*d*_{n} = 3cm) is shown in . In the figure,

*T*_{max} varies linearly from

*T*_{max_}_{I} = 0kPa to

*T*_{max_}_{R} = 186.3kPa within the BZ. In comparision, the optimal values found from assuming a homogenous distribution of

*T*_{max} within the BZ are

*T*_{max_}_{R} = 190.1kPa and

*T*_{max_}_{BZ} = 60.3kPa [

1].

shows a comparison of myofiber stress distribution at ES between (a) the optimal linearly–varying

*T*_{max_}_{BZ} FE model and (b) the optimal homogeneous

*T*_{max_}_{BZ} FE model from Sun

*et al.* [

1]. Between them, the myofiber stress distribution

*S*_{f f} is almost identical. Because the stress–strain relation is monotonic and the two models are optimized to have the same strain distribution measured from tagged MRI, we expect the stress distribution of the two models to be similar i.e. regions having high myofiber stresses should correspond to regions where the myofiber undergoes large strain.

By contrast, the peak myofiber stress found in the linearly–varying *T*_{max_}_{BZ} model (92.5kPa) is about 15% higher than that found in the homogeneous *T*_{max_}_{BZ} model (80.1kPa). Thus, despite the small difference in OBJ between these two cases, the magnitude of difference in the myofiber stress is substantial.