Dosing and Body Weights

$$\text{CrCl} = \frac{(140-\text{age})\text{IBW}}{72*\text{SCr}}*0.85\; (\text{if female})\\ \text{IBW}_\text{M} = 50\;(kg)+2.3(Ht\; (in)-60\;(in))\\ \text{IBW}_\text{F} = 45.5\;(kg)+2.3(Ht\; (in)-60\;(in))\\ \text{NBW} = \text{IBW} + 0.25(Wt-\text{IBW})\\ \text{AdjBW} = \text{IBW} + 0.4(Wt-\text{IBW})\\ \text{BSA}\; (m^2) = \sqrt \frac{\text{mass} \; (kg) * \text{height}\; (cm)}{3600}\\ \text{LBW}_\text{M} = \frac{9270\times \text{Wt}}{216\times \text{BMI} + 6680}\\ \text{LBW}_\text{F} = \frac{9270\times \text{Wt}}{244\times \text{BMI} + 8780}$$

For CrCL, use Wt if Wt < IBW, LBW if BMI ≥ 40, IBW or AdjBW otherwise

Acid-Base

$$\text{Anion Gap} = [Na^+]-[Cl^-]-[{HCO}_3 ^-]\\ \text{Delta Gap} = \text{Anion Gap} - \text{Normal Anion Gap}$$

Nitrogen Balance

$$\text{Intake}\; (g) = \frac{\text{24hr Protein Intake}\; (g)}{6.25}\\ \text{Outake}\; (g) = \text{24hr UUN}\; (g) + 4\;(g)$$

Fluids and Electrolytes

$$\text{Osm} = 2[\text{Na}]+\frac{\text{BUN}}{2.8} + \frac{\text{BG}}{18} + \frac{\text{EtOH}\; (md/dL)}{3.7}\\ \text{Corrected}\; [Na^+] = [Na^+] + 1.6 \left[ \frac{BG}{100}-1 \right]\\ \text{TBW}_M = 0.6\; (L/kg) * Wt\\ \text{TBW}_F = 0.5\; (L/kg) * Wt\\ \text{Na Deficit} = TBW \left( [Na^+]_\text{goal}-[Na^+]_\text{plasma} \right)\\ \text{FWD} = \text{TBW} \left( \frac{[Na^+]}{140}-1 \right)\\ \text{Corrected}\; [Ca^{2+}] = [Ca^{2+}] + 0.8(4-\text{Albumin})\\ \Delta [Na] = \frac{[Na^+]_\text{fluid} - [Na^+]_\text{plasma}}{\text{TBW}+1}$$

Anticoagulation

$$\text{INR} = \left( \frac{\text{PT}_\text{test}}{\text{PT}_\text{normal}} \right)^\text{ISI}$$

EKG Interpretation

$$QTc=\frac{QT}{\sqrt{60/HR}}$$

Pharmacokinetics

General PK

$$C_{ss} = \frac{F(D/\tau)}{CL} \text{ (intermittent)}\\ C_{ss} = \frac{\text{Rate}}{CL} \text{ (infusions)}\\ E = \frac{f_\text{unbound}CL_\text{int}}{Q+f_\text{unbound}CL_\text{int}}\\ CL = Q \times E\\ CL = k \times V_d\\ V_d = V_\text{blood} + \frac{f_b}{f_t}V_\text{tissue}\\ F = \frac{\text{AUC}_\text{PO}}{\text{Dose}_\text{PO}} \div \frac{\text{AUC}_\text{IV}}{\text{Dose}_\text{IV}} = \frac{D_\text{IV}\text{AUC}_\text{PO}}{D_\text{PO}\text{AUC}_\text{IV}}$$

1-Compartment Model

$$\tau_\text{est} = \frac{\ln{(C_\text{max}} / C_\text{min})}{k} + t_\text{inf}\\ MD_\text{est} = \frac{C_\text{max} t_\text{inf} V k \left( 1 - e^{-k\tau} \right)}{\left( 1 - e^{-kt_\text{inf}} \right)}\\ V = \frac{MD \left( 1 - e^{-kt_\text{inf}} \right)}{t_\text{inf}k\left( C_\text{max} - C_\text{min}e^{-kt_\text{inf}} \right)} \\ C_\text{max} = \frac{MD \left( 1 - e^{-kt_\text{inf}} \right)}{t_\text{inf} V k \left( 1 - e^{-k\tau} \right)}\\ C_\text{pk} = C_\text{max} e^{-k(t_\text{pk} - t_\text{max})}\\ C_\text{min} = C_\text{max} e^{-k(\tau - t_\text{inf})}\\ C_\text{min} = C_\text{tr} e^{-k(t_\text{min} - t_\text{tr})}\\ C[b] = C[a] e^{-k (a - b)}$$