Table 3.

Summary algorithms for constructing two-parameter $(T,D_0)$ equi-dosing regimen regions

Analytical approach (one- and two-compartment models)

Numerical approach for TCM (construct $f_{\mathit{lo}}(T)$ and $f_{\mathit{hi}}(T)$ numerically)

Find expression for max and min values of $a_c^{\infty }$, namely $a_{c,\text{max}}^{\infty }$ and $a_{c,\text{min}}^{\infty }$, in terms of dosing regimen parameters $D_0$ and T, as in (5.2) and (5.5) Set therapeutic range constraints $D_{\mathit{me}}<a_{c,\text{min}}^{\infty }$ and $a_{c,\text{max}}^{\infty }<D_{\mathit{MS}}$ Rearrange constraints into form $f_{\mathit{lo}}(T)<D_0<f_{\mathit{hi}}(T)$, as in (5.3) and (5.6) Plot curves $D_0=f_{\mathit{lo}}(T)$ and $D_0=f_{\mathit{hi}}(T)$. Region bounded by these two curves is the EDRR

Discretise the $(T,D_0)$ parameter space, i.e. lay down a grid of points $(T_i,D_{0,j})$ For each $T_i$:    For each $D_{0,j}$:       Use expression for $a_c^{\infty }(t^{\infty })$ (3.28) to compute $a_{c,\text{max}}^{\infty }$ and $a_{c,\text{min}}^{\infty }$ numerically    End    $f_{\mathit{lo}}(T_i)=D_{0,j}$ such that $|a_{c,\text{min}}^{\infty }-D_{\mathit{me}}|$ is minimised    $f_{\mathit{hi}}(T_i)=D_{0,j}$ such that $|a_{c,\text{max}}^{\infty }-D_{\mathit{MS}}|$ is minimised End Plot curves $D_0=f_{\mathit{lo}}(T)$ and $D_0=f_{\mathit{hi}}(T)$. Region bounded by these two curves is the EDRR