This study mitigated the challenge of head and neck CT angiography by IPA-based time-resolved imaging of contrast kinetics. To this end, 627 cerebral hemorrhage patients with dizziness, brain aneurysm, stroke, or hemorrhagic stroke diagnosis were randomly categorized into three groups, namely, the original dataset (450), verification group (112), and in vivo testified group (65), in the Affiliated BenQ Hospital of Nanjing Medical University. In the first stage, seven risk factors were assigned: age, CTA tube voltage, body surface area, heart rate per minute, cardiac output blood per minute, the actual injected amount of contrast media, and CTA delayed trigger timing. The expectation value of the semi-empirical formula was the CTA number of the patient’s left artery (LA). Accordingly, 29 items of the first-order nonlinear equation were calculated via the inverse problem analysis (IPA) technique run in the STATISTICA 7.0 program, yielding a loss function and variance of 3.1837 and 0.8892, respectively. A dimensionless AT was proposed to imply the coincidence, with a lower AT indicating a smaller deviation between theoretical and practical values. The derived formula was confirmed for the verification group of 112 patients, reaching high coincidence, with average ATavg and standard deviation values of 3.57% and 3.06%, respectively. In the second stage, the formula was refined to find the optimal amount of contrast media for the CTA number of LA approaching 400. Finally, the above procedure was applied to head and neck CTA images of the third group of 65 patients, reaching an average CTA number of LA of 407.8 ± 16.2 and finding no significant fluctuations.