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


Link to Maths enrichment Appendix - MSSC



Last Updated on Wednesday, 02 September 2015 13:33  

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