Thrombolytic therapy is one of the medical procedures in the treatment of acute ischaemic stroke (AIS), whereby the tissue plasminogen activator (tPA) is intravenously administered to dissolve the obstructive blood clot. The treatment of AIS by thrombolysis can sometimes be ineffective and it can cause serious complications, such as intracranial haemorrhage (ICH). In this study, we propose an efficient mathematical modelling approach that can be used to evaluate the therapeutic efficacy and safety of thrombolysis in various clinically relevant scenarios. Our model combines the pharmacokinetics and pharmacodynamics of tPA with local clot lysis dynamics. By varying the drug dose, bolus-infusion delay time, and bolus-infusion ratio, with the F...