Drug metabolism is a chemical modification of a drug to another (active or inactive) chemical.
Drug elimination is the removal of drug from the plasma (by distribution or excretion).
Drug excretion is the removal of drug from the body.
$$\text{Rate of excretion} = C_{\text{Plasma}} \sum_{\text{organs}} Cl_{organ}$$
and
$$Cl_H = \frac{Q_H F_{ub} Cl_{int}}{Q_H + F_{ub} Cl_{int}}$$
$$Cl_R = Q_R \cdot \text{GFR} + Cl_{\text{secreted}} - Cl_{\text{reabsorbed}}$$
Occur in hepatocyte endoplasmic reticuluum. All usually increase water solubility. Metabolites may be inactive, active, or more active than the parent molecule. Prodrugs are inactive substances with active metabolites.
Phase 1 reactions: Oxydation, reduction, or hydrolysis.
Phase 2 reactions: conjugation with another, polar, molecule (e.g. sulfyl, glucuronyl, acetyl, methyl group).
$$Cl_H = Q_H \cdot HER$$
The HER is the proportion of drug that is cleared from hepatic blood by the liver:
$$HER = \frac{C_{in} - C_{out}}{C_{in}} = 1 - \frac{C_{out}}{C_{in}}$$
Note that 1 - HER gives the bio-availability.
What determines the HER? From a mass balance:
$$\text{Mass into liver} = \text{mass in hepatic vein}+\text{mass metabolized}$$
$$C_{in} \cdot Q = C_{out} \cdot (Q + CL_{int})$$
$$C_{out} = frac{C_{in} \cdot Q}{Q + CL_{int}}$$
And then from the definition of HER we have
$$HER = 1 - frac{C_{in} \cdot Q}{C_{in}(Q + CL_{int})}$$
$$HER = 1 - frac{Q}{Q + CL_{int}}$$
And a funky algebra move gets us
$$HER = frac{CL_{int}}{Q + CL_{int}}$$
But we're usually dealing with protein bound drugs, so we have to account for the fraction unbound:
$$HER = frac{F_u CL_{int}}{Q + F_u CL_{int}}$$
$$Cl_H = frac{Q F_u CL_{int}}{Q + F_u CL_{int}}$$
When intrinsic clearance is very low, such that it is much smaller than Q,
$$Cl_H = frac{Q F_u CL_{int}}{Q}$$
$$Cl_H = F_u CL_{int}$$
then clearance does not depend on hepatic blood flow, only intrinsic clearance and fraction unbound
When the intrinsic clearance is very high, such that it is much larger than Q,
$$Cl_H \approx frac{Q F_u CL_{int}}{F_u CL_{int}}$$
$$Cl_H \approx Q$$
then clearance is close to hepatic blood flow, and the fraction unbound and intrinsic clearance do not matter.
High intrinsic clearance drugs: GTN, lidocaine, ketamine, propofol, morphine
Low intrinsic clearance drugs: warfarin, diazepam, rocuronium
CYP2D6: Metabolizes codeine \(to\) morphine, oxycodone \(\to\) oxymorphone (potent), metoprolol and flecainide \(to\) inactive. High inter-individual variability (10% poor metabolizers)
CYP2C9: Propofol \(to\) inactive, warfarin \(\to\) inactive, phenytoin \(\to\) inactive. Inducers: carbemazepine, phenytoin, St John's Wort. Inhibitors: Amiodarone, metronidazole, fluconazole, bactrim.
$$Cl_R = F_{ub} \cdot \text{GFR} + Cl_{\text{secreted}} - Cl_{\text{reabsorbed}}$$
At steady state, we have a constant renal excretion and a constant plasma concentration, so:
$$\text{Renal mass excretion} = Cl_{\text{renal}} \cdot C_{\text{plasma}} = C_{\text{urine}} \cdot V_{\text{urine}}$$
or
$$Cl_{\text{renal}} = \frac{C_u \cdot V_u}{C_p}$$
Factors influencing filtration
Drug
Patient
Factors influencing secretion
Multiple drugs compete for the same transporters, which can become saturated:
Weak acid transporters (furosemide, beta-lactams)
Weak base transporters (trimethoprim, creatinine)
p-glycoprotein tranporters (digoxin, verapamil)
Factors influencing reabsorption
Clinically relevant drugs are not actively reabsorbed, so this is via Fick's law
Low urine flow rate and high dose \(\to\) high concerntration gradient
Urine pH, pKa, and whether drug is acid or base contribute to ion trapping.