Mathematical Modelling of Intravenous Thrombolysis in Acute Ischaemic stroke: Effects of Dose Regimens on Levels of Fibrinolytic Proteins and Clot Lysis Time

Figures

• 

  Figure 1. Overview of the full mathematical model. (a) Two-compartment model for pharmacokinetics and pharmacodynamics (PKPD) of tissue plasminogen activator (tPA) in the body (or the “systemic PKPD model”), (b) one-dimensional (1D) blood flow and species transport in an occluded artery, and (c) fibrinolysis described by binding of fibrinolytic proteins with fibrin fibres and the cleavage of fibrin network by bound plasmin. Coupled 1D blood flow and transport and fibrinolysis are referred to as the “local PD model”.

• 

  Figure 2. Schematic of 1D blood flow and species transport model. The entrance of the blocked artery corresponds to the bifurcating point where flow splits into two branches. The shaded area represents the clot with a porosity of εclot and the open area is clot-free with ε = 1.

• 

  Figure 3. Flow chart of the solution procedure for the systemic and local models. Input information required for solving each model is specified in the green boxes.

• 

  Figure 4. Changes in systemic concentrations of fibrinolytic proteins over time with different drug doses: 0.6 (Regimen 2), 0.9 (Regimen 1), and 1.2 (Regimen 3) mg/kg of patient weight, as low (solid line), medium (dashed line) and high (dotted line) doses, respectively. (a) tPA concentration in the central (blue lines) and peripheral (orange lines) compartments, (b) systemic concentrations of fibrinogen (FBG), (c) α2-macroglobulin (MG), and (d) plasminogen activator inhibitor type 1 (PAI) (shown for 1 min only).

• 

  Figure 5. Effects of bolus-continuous IV infusion delay on the concentrations of (a) tPA and (b) FBG. Simulated Regimens 4–6 correspond to delays of 5, 10, and 30 min, respectively. The reference regimen with no delay (Regimen 1) is also included for comparison.

• 

  Figure 6. Effects of bolus to infusion ratios at a fixed dose of 0.9 mg/kg, on the concentration of (a) tPA, and (b) FBG. The amount of bolus is varied from 0% (Regimen 7) to 50% (Regimen 9) of the total dose. Regimen 1 has a bolus to infusion ratio of 1:9, while Regimens 8 and 9 have a ratio of 1:4 and 1:1, respectively.

• 

  Figure 7. Concentrations of tPA (a) and FBG (b)over time for the new regimens simulated in this study.

• 

  Figure 8. Predicted recanalisation times for the simulated dosage regimens. The black bar and dashed line are the reference regimen. Different colour bars indicate the therapeutic parameters that are varied: tPA dose (blue bars), bolus-infusion delay (orange), bolus-infusion ratio (yellow), and new regimens (green).

• 

  Figure 9. Temporal and spatial concentrations of free phase tPA, PLG, and FBG, and the total concentration of binding sites (ntot) in the clot for the standard dosage regimen. Each map shows variations of concentration in time (vertical axis) and space (horizontal axis). (a) The total binding site and (b) free phase tPA, (c) PLG, and (d) FBG.