The success and usefulness of lumped cardiovascular models are directly dependent on the physiological fidelity of their formulation. In most existing lumped formulations for the heart, the compliance of the chamber is modeled based on its electrical analog, the capacitor. This has traditionally resulted in the use of a pre-described time-varying stiffness modulus for simulating the cardiac contractions. Unfortunately, such a time-varying stiffness does not include any physiological contractile machinery and thus no dependency on fiber sarcomere length and intracellular calcium concentrations, key mechanisms responsible for proper cardiac function. In this paper a lumped cardiovascular model is presented that is based on the incorporation of detailed myofilament activation for simulating the ventricular calcium binding and cross-bridging mechanism. Upon validation against experimental data, it is shown that the new myofilament activation-based model considerably increases the physiological validity and internal consistency of the cardiovascular simulations in comparison to the traditional variable compliance-based models. It is also shown, through specific case studies, that the present model can serve as a quick response tool for testing various hypotheses concerning the impact of the calcium binding and crossbridge kinetics on the overall performance of the cardiovascular system.