## 96007 Drug Disposition Equation Sheet

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. $\text{Metabolic Kinetics}$
• ${AUC}_{0-\infty\text{md}}=\frac{{\text{Dose}}_{m}}{{CL}_{mel}}$
• ${AUC}_{0-\infty\text{mf}}=\frac{\text{fm Dose}}{{CL}_{mel}}$
• $\frac{{AUC}_{\text{m, f}}}{\left(\text{AUC drug}\right)}={f}_{m}\frac{CL}{{CL}_{mel}}$
• $\frac{{AUC}_{0-\infty\text{mf}}}{{AUC}_{0-\infty\text{md}}}=\frac{\frac{\left({f}_{m}\text{Dose}\right)}{\left({CL}_{mel}\right)}}{\frac{\left({\text{Dose}}_{m}\right)}{\left({CL}_{mel}\right)}}$

Last Updated on Wednesday, 02 September 2015 13:33

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