Figure 4.

Adaptive IL-2 Dosing Strategy

The kinetics of (A) Tconvs, (B) Tregs, (C) IL-2, and (D) IL-2 dose is shown for fixed (black) and adaptive dose IL-2 therapy (red), each applied at every time unit ($\delta =1$) and combined with adoptive Treg transfer ($R(t=0)=0.5$). The physiological range was $\mathcal{X}=\{\left(\mathrm{0,0,0}\right)<(T,R,I)<\left(\mathrm{40,30,2}\right)\}$ and the therapeutic target window was ${\mathcal{X}}^{Tar}=\{\left(\mathrm{0,19,0}\right)<(T,R,I)<\left(\mathrm{1,22,1}\right)\}$. IL-2 doses were constrained to $\mathcal{U}=\{0<d_{IL-2}<0.7\}$. For the fixed-dose therapy, the maximum allowed dose (i.e., 0.7) was administered. The calculated adaptive doses successfully enforced variables to the therapeutic target window (horizontal dashed lines).

The kinetics of (E) Tconvs, (F) Tregs, (G) IL-2, and (H) IL-2 dose is shown for different IL-2 injection frequencies δ of 1, 2, and 5 time units, corresponding to high, medium, and low frequency, respectively. The control unit selects the corresponding suitable doses in each case. The value of Tconvs, Tregs, and IL-2 is normalized to its maximum value for the uncontrolled case (without IL-2 therapy, Figure 2, black curves). For low frequencies, higher doses are required. Therefore, the maximum allowed IL-2 dose was increased to 2.5 to make the optimization problem feasible. The IL-2 dose is normalized to the dose in (D) fixed-dose value and (H) maximum dose value in low frequency.