# Linear 1-compartment

Linear 1-compartment, bolus
Parameters
$$CL$$ Clearance. Ratio of the drug’s elimination rate from the body over its circulating concentration, [L/h]
$$V$$ Volume of distribution. Ratio of the drug’s amount present in the body over its circulating concentration, [L]
$$k_e$$ $$=\frac{CL}{V}$$
Equations
Equation: $$\frac{dC}{dt} = -{k_e} C = -\frac{CL}{V} C$$
Initial conditions: $$C(t_0) = C_{residual} + \frac{D}{V}$$

Linear 1-compartment, infusion
Parameters
$$CL$$ Clearance. Ratio of the drug’s elimination rate from the body over its circulating concentration, [L/h]
$$V$$ Volume of distribution. Ratio of the drug’s amount present in the body over its circulating concentration, [L]
$$T_{inf}$$ Infusion time, [h]
$$k_e$$ $$=\frac{CL}{V}$$
$$k_0$$ $$=\frac{D}{T_{inf}}$$
Equations
Equation: \begin{align*} \frac{dC}{dt} &= \begin{cases} \frac{k_0}{V} – k_e C , &\text{for t\leq t_0 + T_{inf}}\\ - k_e C, &\text{for t> t_0 + T_{inf}} \end{cases} \end{align*}
Initial conditions: $$C(t_0) = C_{residual}$$

Linear 1-compartment, extravascular
Parameters
$$CL$$ Clearance. Ratio of the drug’s elimination rate from the body over its circulating concentration, [L/h]
$$V$$ Volume of distribution. Ratio of the drug’s amount present in the body over its circulating concentration, [L]
$$k_a$$ Absorption rate constant. Relative rate constant of the drug’s absorption into the body, [h⁻¹]
$$F$$ Bioavailability. Fraction of the drug’s administered dose that reaches unchanged the systemic circulation, [%]
$$k_e$$ $$=\frac{CL}{V}$$
Equations
Equation: \begin{align*} \frac{dC_1}{dt} &= k_a C_2 – k_e C_1 \\ \frac{dC_2}{dt} &= -k_a C_2 \end{align*}
Initial conditions: \begin{align*} C_1(t_0) &= C_{1residual} \\ C_2(t_0) &= C_{2{residual}} + \frac{F D}{V} \end{align*}