Finding optimal blood pressure (BP) target and BP treatment after acute ischemic or hemorrhagic strokes is an area of controversy and a significant unmet need in the critical care of stroke victims. Numerous large prospective clinical trials have been done to address this question but have generated neutral or conflicting results. One major limitation that may have contributed to so many neutral or conflicting clinical trial results is the "one-size fit all" approach to BP targets, while the optimal BP target likely varies between individuals. We address this problem with the Acute Intervention Model of Blood Pressure (AIM-BP) framework: an individualized, human interpretable model of BP and its control in the acute care setting. The framework consists of two components: one, a model of BP homeostasis and the various effects that perturb it; and two, a parameter estimator that can learn clinically important model parameters on a patient by patient basis. By estimating the parameters of the AIM-BP model for a given patient, the effectiveness of antihypertensive medication can be quantified separately from the patient's spontaneous BP trends. We hypothesize that the AIM-BP is a sufficient framework for estimating parameters of a homeostasis perturbation model of a stroke patient's BP time course and the AIM-BP parameter estimator can do so as accurately and consistently as a state-of-the-art maximum likelihood estimation method. We demonstrate that this is the case in a proof of concept of the AIM-BP framework, using simulated clinical scenarios modeled on stroke patients from real world intensive care datasets.