The cardiac system compensates for variations in physiological and pathophysiological conditions through a dynamic remodeling at the organ, tissue, and intracellular levels in order to maintain function. However, on longer time scales following the onset of ventricular pressure overload, such remodeling may begin to inhibit physiological function and ultimately lead to heart failure. This progression from compensatory to decompensatory behavior is poorly understood, in particular owing to the absence of a unified perspective of the concomitantly remodeling subsystems. To address this issue, the present study investigates the evolution of compensatory mechanisms, in response to overload, by integrating diffusion-tensor MRI, echocardiography, and intracellular and hemodynamic measurements within consistent computational simulations of aortic-banded rat hearts. This approach allows a comparison of the relative leverage of different cardiac properties (geometry, passive mechanical stiffness, fiber configuration, diastolic and peak calcium concentrations, calcium-binding affinity, and aortic impedance) to affect cardiac contraction. Measurements indicate that, following aortic banding, an ejection fraction (EF) of 75% was maintained, relative to control rats, despite significant remodeling of the left-ventricular wall thickness (increasing by ~90% over 4 weeks). Applying our framework, we identified the left-ventricular wall thickness (concentric hypertrophy) and the intracellular calcium dynamics as playing the dominant roles in preserving EF acutely, whereas the significance of hypertrophy decreased subsequently. This trend suggests an increasing reliance on intracellular mechanisms (average increase ~50%), rather than on anatomical features (average decrease ~60%), to achieve compensation of pump function in the early phase of heart failure.