1. \({C}_{{t}}={C}_{{0}}\) - \({k}_{{0}}t\)    \({k}_{{0}}: \text{zero order rate constant}\)
2. \({C}_{{t}}={C}_{{0}}\) \({e}^{{-kt}}\)    \(\text{Log }{C}_{{t}}\)=\(\text{log }{C}_{{0}}\) - \({kt}/{2.3}\)
3. \({AUC}_{{0-\infty}}={AUC}_{{0-t}}\) + \({C}_{{last/k}}\)
• \({AUC}_{{0-t}}=\frac{C1+C2}{2}\times\left(t2-t1\right)+....+....\text{etc}\)
• \({AUC}_{{0-\infty}}=\frac{{C}_{0}}{k}\)
4. \(\text{CL}=\frac{\text{F*Dose}}{{AUC}_{0-\infty}}\)
5. \({k}_{ei}=\frac{CL}{{V}_{d}}\)
• \({t}_{\frac{1}{2}}=\frac{0.693}{{k}_{el}}\)
6. \({V}_{{d}}=\frac{\text{Dose}}{{C}_{0}}\)
7. \({C}_{{t}}=Ae^{-\alpha\text{t}}+Be^{-\beta\text{t}}\text{    }\left(\text{biexponential}\right)\)
• \({V}_{{d\beta}}=\frac{CL}{\beta}\text{; }{V}_{c}=\frac{\text{Dose}}{A+B}\)
• \({k}_{ei}=\frac{\alpha\beta}{{k}_{21}}\)
• \({t}_{\frac{1}{2}\alpha}=\frac{0.693}{\alpha}\)
• \({t}_{\frac{1}{2}\beta}=\frac{0.693}{\beta}\)
• \(\text{Cl}=\frac{\text{Dose}}{{AUC}_{0-\infty}}\)
• \({AUC}_{0-\infty}=\frac{A}{\alpha}+\frac{B}{\beta}\)
8. \(\text{IV Infusion}\)
• \({C}_{p}=\frac{{R}_{0}}{CL\left(1-e^{-\text{kel t}}\right)}\)
• \({C}_{p}\left(t\right)={C}_{ss}\left(1-e^{-\text{kel t}}\right)\text{        }\left(\text{ at steady state }\right)\)
• \({C}_{p}\left(\text{ post inf }\right)={C}_{stop}e^{-\text{kel t}}\)
9. \(\text{Multiple Dosing}\)
• \(\text{F*Dose Rate}={CL}*{C}_{ss}\)
• \(r=\frac{{A}_{ss}\text{ min }}{{A}_{ss}\text{ max }}=e^{-kelt}\)
• \({D}_{M}=\left(1-r\right){A}_{ss}\text{ max }\)
• \({D}_{L}=\frac{{D}_{M}}{\left(1-r\right)}=2{D}_{M}\)
10. \(\text{Oral Dosing}\left(\text{single dose}\right)\)
• \({C}_{p}=\frac{\text{F * Dose ka }}{{V}_{d}*\left({k}_{el}-{k}_{a}\right)}\left(e^{-ka.t}-e^{-kel.t}\right)\)
11. \(\text{Non-Linear Metabolsim}\left(\text{Michaelis-Menten}\right)\)
• \(\text{ Oral Dose Rate }=\frac{{V}_{m}*{C}_{ss}}{{K}_{m}+{C}_{ss}}\)
•  \(\text{re-arranged}\)
• \({C}_{ss}=\frac{{K}_{m}*F*\text{ Dose Rate }}{{V}_{m}-F*\text{ Dose Rate }}\)
• \(\text{half-life}=\frac{\text{ln }2\text{ V}}{{V}_{m}}\left({K}_{m}+{C}_{ss}\right)\)
• \(CL=\frac{{V}_{m}}{{K}_{m}+{C}_{ss}}\)
• \(\text{I.V. Infusion}\)
• \(\text{Infusion Rate}\left({R}_{0}\right)\)
• \({R}_{0}=\frac{{V}_{max}{C}_{ss}}{{K}_{m}+{C}_{ss}}\)
• \(\text{ i.e. }\)
• \({R}_{0}={V}_{max}-\frac{\left({K}_{m}*{R}_{0}\right)}{{C}_{ss}}\)
• \(\text{Thus}\)
• \({C}_{ss}=\frac{\left({K}_{m}{R}_{0}\right)}{\left({V}_{max}-{R}_{0}\right)}\)
12. \(\text{Distribution}\)
• \(\text{Tissue Distribution Rate Constant}\left({K}_{T}\right)\)
• \({K}_{T}=\frac{{Q}_{T}}{{V}_{T}*{K}_{p}}\)
• \(\text{Extent of Tissue Distribution}\)
• \({V}_{d}={V}_{p}+{V}_{T}*\frac{{f}_{u}}{{f}_{u,T}}\)
• \(\text{Distribution into breast milk}\)
• \({\text{Dose}}_{\text{infant}}={C}_{maternal}*\frac{M}{P}*\text{Vol. Consumed}\)
13. \(\text{Elimination}\)
• \({CL}_{total}={CL}_{hepatic}+{CL}_{renal}+{CL}_{other}\)
• \({CL}_{filtration}={f}_{u}*GFR\)
• \({CL}_{H}={Q}_{H}*{E}_{H}\)
• \({E}_{H}=\frac{\left({C}_{in}-{C}_{out}\right)}{{C}_{in}}\)
• \({E}_{H}=\frac{{f}_{u}*{CL}_{int}}{{Q}_{H}+{f}_{u}*{CL}_{int}}\)
• \({CL}_{H}=\frac{{Q}_{H}*{f}_{u}*{CL}_{int}}{{Q}_{H}+{f}_{u}*{CL}_{int}}\)
• \({CL}_{R}={f}_{e}*CL\)
• \({f}_{e}=\frac{{Ae}^{\left(0-\infty\right)}}{\text{DOSE}}\text{ after iv administration}\)
• \({CL}=\frac{\text{DOSE}}{{AUC}_{\left(0-\infty\right)}}\text{after iv administration}\)
• \({L}_{R}=\frac{Ae^{\left(0-\infty\right)}}{{AUC}_{\left(0-\infty\right)}}=\frac{{Ae^{\left(0-t\right)}}}{{AUC}_{\left(0-t\right)}}\)
• \({CL}_{R}=\frac{\text{Urinary Excretion Rate}}{{C}_{p}\text{ mid of collection interval}}\)
• \({CL}_{R}=\frac{\text{Urinary flow }\times\text{Urine concentration}}{\text{ plasma concentration}}\)
14. \(\text{Pharmacodynamics}\)
• \(E=\text{m log C + e}\)
• \(E={E}_{0}-\frac{kmt}{2.3}\)
• \(R=\frac{km}{2.3}\)
• \({T}_{d}=\frac{2.3\left(log{C}_{0}-log{C}_{min}\right)}{k}\)
• \({T}_{d}=\frac{2.3\left(log{D}_{0}-log{D}_{min}\right)}{k}\)
• \(E=\frac{\left({E}_{max}C\right)}{\left({EC}_{50}^{N}+C\right)}\)
• \(E=\frac{\left({E}_{max}C^N\right)}{\left({EC}_{50}^{N}+C^N\right)}\)
15. \(\text{Metabolic Kinetics}\)
• \({AUC}_{0-\infty\text{md}}=\frac{{\text{Dose}}_{m}}{{CL}_{mel}}\)
• \({AUC}_{0-\infty\text{mf}}=\frac{\text{fm Dose}}{{CL}_{mel}}\)
• \(\frac{{AUC}_{\text{m, f}}}{\left(\text{AUC drug}\right)}={f}_{m}\frac{CL}{{CL}_{mel}}\)
• \(\frac{{AUC}_{0-\infty\text{mf}}}{{AUC}_{0-\infty\text{md}}}=\frac{\frac{\left({f}_{m}\text{Dose}\right)}{\left({CL}_{mel}\right)}}{\frac{\left({\text{Dose}}_{m}\right)}{\left({CL}_{mel}\right)}}\)

Link to Maths enrichment Appendix - MSSC