The heart is a dynamic system that adapts to external constraints to fulfill its physiological role. Systemic hypertension hinders blood ejection into the aorta and occurs for example in aortic-valve stenosis, a common heart disease in which the aortic-valve opening is narrowed, impeding blood flow from the left ventricle (LV). This results in an enhanced pressure gradient across the aortic valve during LV ejection to maintain the required blood-flow rate. Increased afterload tends to reduce the ventricular stroke volume, and leads to ventricular hypertrophy, a thickening of the muscular wall that compensates the increased wall stress and allows generation of higher pressures. Over time, however, the short-term benefits of cardiac remodeling give way to decompensatory behaviour and ultimately heart failure. A better understanding of the nature of the transition from compensation to decompensation is essential for developing diagnosis and treatment of heart failure. Aortic banding (AB), a common experimental model, involves artificially constricting the aorta to impede blood flow. After several weeks, AB rats typically display an increased heart mass and reduced LV diameter at diastole and systole, but while demonstrating ejection fractions remarkably similar to control rats, indicative of compensatory tendencies in these early stages. To better understanding the nature of the transition from compensation to decompensation, we sought to identify changes in the balance of compensatory contributions using a computational-modeling approach supported by heart-specific measurements. We investigated the interplay of mechanistic contributions to LV contraction to identify how these might evolve at different stages of compensation. We fitted a finite-element computational model to geometrical, fibre-configuration, electrophysiological, and hemodynamic measurements derived from individual aortic-banded or control rats. The model was simplified so as to allow an objective parameterisation of essential functional parameters based on the experimental data. These heart-specific models provided a testbed for simulating the contraction and comparing the sensitivities of the LV ejection fraction to the different mechanistic parameters and physiological conditions. Our simulation results suggest a significant enhancement of the sensitivity of the ejection fraction to muscle activation in aortic-banded hearts, whereas geometrical features and passive mechanical properties play a more significant role in a control heart. Despite the near-identical ejection fraction displayed in both heart types, this difference in the underlying compensatory balance may reflect a fundamental evolution in the heart’s response to the aortic banding that will eventually lead to heart failure.