2.1 Drug Absorption & Bioavailability

Absorption is the first step in pharmacokinetics: the process by which a drug moves from its site of administration into the systemic circulation. The key quantitative parameter is bioavailability (F), defined as the fraction of the administered dose that reaches the systemic circulation unchanged.

Historical Context

Adolf Fick published his laws of diffusion in 1855, providing the physical basis for membrane transport. The Henderson-Hasselbalch equation (1908-1916) explained pH-dependent ionization of drugs. Brodie and colleagues in the 1950s established the pH-partition hypothesis, demonstrating that the GI absorption of drugs depends on their ionization state at the local pH.

Derivation 1: Fick's First Law of Diffusion

Most drugs cross biological membranes by passive diffusion. Fick's law provides the quantitative framework.

Step 1: The Flux Equation

The rate of drug transport (flux J) across a membrane of thickness h and area A is proportional to the concentration gradient:

\( J = \frac{dM}{dt} = \frac{D \cdot K \cdot A}{h}(C_{lumen} - C_{blood}) \)

where D = diffusion coefficient (cm^2/s), K = partition coefficient (lipid/water), A = membrane surface area, and h = membrane thickness.

Step 2: Define Permeability Coefficient

Combining D, K, and h into a single permeability coefficient P:

\( P = \frac{D \cdot K}{h} \quad (\text{units: cm/s}) \)

The simplified flux equation becomes:

\( J = P \cdot A \cdot (C_{lumen} - C_{blood}) \)

Step 3: Sink Conditions

Under "sink conditions" (C_blood is much less than C_lumen due to rapid blood flow removing absorbed drug):

\( J \approx P \cdot A \cdot C_{lumen} \)

This explains why drugs with higher lipophilicity (larger K), smaller molecular weight (larger D), and thinner membrane barriers (smaller h) are absorbed faster.

Fick's First Law (Pharmacological Form)

\( J = -P \cdot A \cdot \Delta C = -\frac{D \cdot K \cdot A}{h} \cdot (C_{lumen} - C_{blood}) \)

The negative sign indicates flux from high to low concentration. Lipinski's Rule of 5 is a practical extension: MW < 500, logP < 5, HBD < 5, HBA < 10 for good oral absorption.

Derivation 2: Henderson-Hasselbalch & Drug Ionization

Only the unionized (uncharged) form of a drug readily crosses lipid membranes. The Henderson-Hasselbalch equation predicts the ionization state at any given pH.

Step 1: Equilibrium for a Weak Acid (HA)

A weak acid HA dissociates in water:

\( HA \rightleftharpoons H^+ + A^- \)

\( K_a = \frac{[H^+][A^-]}{[HA]} \)

Step 2: Take Logarithms

Taking -log of both sides:

\( -\log K_a = -\log[H^+] - \log\frac{[A^-]}{[HA]} \)

\( pH = pK_a + \log\frac{[A^-]}{[HA]} \)

Step 3: Fraction Unionized

For a weak acid (unionized form = HA):

\( f_{unionized} = \frac{[HA]}{[HA] + [A^-]} = \frac{1}{1 + 10^{(pH - pK_a)}} \)

For a weak base (unionized form = B, ionized form = BH+):

\( f_{unionized} = \frac{[B]}{[B] + [BH^+]} = \frac{1}{1 + 10^{(pK_a - pH)}} \)

Weak Acids

More unionized at low pH (below pK_a). Aspirin (pK_a = 3.5) is 99% unionized in stomach (pH 1.5), favoring gastric absorption.

Weak Bases

More unionized at high pH (above pK_a). Morphine (pK_a = 8.0) is mostly ionized in stomach but better absorbed in intestine (pH 6.8).

Derivation 3: Bioavailability & First-Pass Effect

Bioavailability (F) is the fraction of administered drug reaching systemic circulation in active form.

Step 1: AUC-Based Definition

Absolute bioavailability compares oral to IV administration (IV has F = 1 by definition):

\( F = \frac{AUC_{oral}}{AUC_{IV}} \times \frac{Dose_{IV}}{Dose_{oral}} \)

Step 2: Decompose the First-Pass Effect

After oral dosing, the drug must survive three sequential barriers before reaching systemic circulation:

\( F = f_{abs} \times f_{gut} \times f_{hepatic} \)

f_abs = fraction absorbed from the GI lumen (incomplete dissolution, efflux by P-gp)

f_gut = fraction surviving gut wall metabolism (CYP3A4 in enterocytes)

f_hepatic = fraction surviving hepatic first-pass metabolism = 1 - E_H

Step 3: Hepatic Extraction

The hepatic extraction ratio E_H determines what fraction of drug is removed in a single pass through the liver:

\( E_H = \frac{CL_H}{Q_H} \)

Therefore f_hepatic = 1 - E_H. Drugs with high E_H (e.g., morphine E_H approximately 0.7, lidocaine E_H approximately 0.7) have low oral bioavailability even if completely absorbed.

Example - Nitroglycerin: E_H > 0.99, so oral F is less than 1%. Administered sublingually (F approximately 40%) to bypass hepatic first pass.

Derivation 4: pH-Partition Hypothesis

The pH-partition hypothesis states that the rate and extent of drug absorption depend on the fraction unionized at the local pH, which is in turn determined by the Henderson-Hasselbalch equation.

Step 1: Combine Fick's Law with Ionization

Only the unionized fraction can permeate the membrane, so effective permeation rate:

\( J_{eff} = P \cdot A \cdot f_{unionized} \cdot C_{total} \)

where f_unionized depends on local pH and the drug's pK_a.

Step 2: Stomach vs Intestine

Comparing absorption environments:

Parameter	Stomach	Small Intestine
pH	1.0-3.0	5.0-7.0
Surface area	~0.1 m^2	~200 m^2 (villi)
Blood flow	Moderate	High (splanchnic)
Residence time	1-3 h	3-5 h
Weak acid absorption	Favored (ionization)	Also significant (surface area)

Step 3: The Paradox

Despite weak acids being more unionized in the stomach, most drugs (even weak acids) are primarily absorbed in the small intestine. The enormous surface area of the intestinal villi (approximately 200 m^2 vs approximately 0.1 m^2) dominates the product P * A * f_unionized, making the intestine the primary absorption site regardless of pH considerations.

Derivation 5: First-Order Absorption Kinetics

Oral absorption is typically modeled as a first-order process, where the rate of absorption is proportional to the amount of drug remaining at the absorption site.

Step 1: First-Order Absorption

The amount of drug at the GI absorption site declines exponentially:

\( X_{GI}(t) = F \cdot Dose \cdot e^{-k_a t} \)

where k_a is the first-order absorption rate constant.

Step 2: Wagner-Nelson Method

The fraction absorbed at time t can be calculated from plasma concentration data without knowing k_a a priori:

\( \frac{A_t}{A_{\infty}} = \frac{C_t + k_{el} \int_0^t C \, dt}{k_{el} \int_0^{\infty} C \, dt} \)

Plotting -ln(1 - A_t/A_infinity) vs t gives a straight line with slope k_a, allowing estimation of the absorption rate constant from plasma data alone.

Drug Absorption Pathway

Python Simulation: Absorption & Bioavailability

Drug Absorption — Fick Diffusion, Henderson-Hasselbalch, Bioavailability & pH-Partition

Python

script.py87 lines

import numpy as np

# ── Panel 1: Fick's Law — Flux vs Partition Coefficient ──
K_values = np.linspace(0.01, 10, 200)
D = 1e-6   # cm^2/s
h = 50e-4  # 50 um membrane
A_mem = 1.0  # cm^2
C_diff = 1.0  # mg/mL concentration gradient
J = D * K_values * A_mem * C_diff / h

print("CHART1_TITLE: Fick Law: Flux vs Partition Coefficient")
print("CHART1_XLABEL: Partition Coefficient (K)")
print("CHART1_YLABEL: Flux J (mg/s)")
for i in range(0, len(K_values), 5):
    print(f"K={K_values[i]:.3f} J={J[i]:.6f}")

# ── Panel 2: Henderson-Hasselbalch — Fraction Unionized vs pH ──
pH_range = np.linspace(0, 14, 200)
drugs_acid = [("Aspirin", 3.5), ("Ibuprofen", 4.4), ("Phenobarbital", 7.4)]
drugs_base = [("Morphine", 8.0), ("Diazepam", 3.3), ("Chloroquine", 10.2)]

print("\nCHART2_TITLE: Weak Acids: Fraction Unionized vs pH")
print("CHART2_XLABEL: pH")
print("CHART2_YLABEL: Fraction Unionized")
for i in range(0, len(pH_range), 5):
    vals = []
    for name, pka in drugs_acid:
        fu = 1.0 / (1.0 + 10**(pH_range[i] - pka))
        vals.append(f"{name}={fu:.4f}")
    print(f"pH={pH_range[i]:.2f} " + " ".join(vals))

print("\nCHART3_TITLE: Weak Bases: Fraction Unionized vs pH")
print("CHART3_XLABEL: pH")
print("CHART3_YLABEL: Fraction Unionized")
for i in range(0, len(pH_range), 5):
    vals = []
    for name, pka in drugs_base:
        fu = 1.0 / (1.0 + 10**(pka - pH_range[i]))
        vals.append(f"{name}={fu:.4f}")
    print(f"pH={pH_range[i]:.2f} " + " ".join(vals))

# ── Panel 4: Bioavailability — AUC comparison ──
t = np.linspace(0, 24, 200)
Dose = 100
Vd = 50
kel = 0.2
ka = 1.5
C_iv = (Dose / Vd) * np.exp(-kel * t)
F_values = [1.0, 0.8, 0.5, 0.2]
print("\nCHART4_TITLE: Oral Concentration Profiles (varying F)")
print("CHART4_XLABEL: Time (h)")
print("CHART4_YLABEL: Concentration (mg/L)")
for i in range(0, len(t), 5):
    vals = []
    for fv in F_values:
        c_oral = (fv * Dose * ka) / (Vd * (ka - kel)) * (np.exp(-kel * t[i]) - np.exp(-ka * t[i]))
        vals.append(f"F_{fv:.1f}={max(0, c_oral):.3f}")
    print(f"t={t[i]:.2f} IV={C_iv[i]:.3f} " + " ".join(vals))

# ── Panel 5: pH-Partition — Effective permeation at different pH ──
print("\nCHART5_TITLE: pH-Partition: Effective Permeation (Aspirin, pKa=3.5)")
print("CHART5_XLABEL: pH")
print("CHART5_YLABEL: Relative Permeation Rate")
pka_asp = 3.5
P_unionized = 1.0
for i in range(0, len(pH_range), 5):
    fu = 1.0 / (1.0 + 10**(pH_range[i] - pka_asp))
    perm = P_unionized * fu
    print(f"pH={pH_range[i]:.2f} permeation={perm:.4f}")

# ── Panel 6: First-Pass Effect Components ──
print("\nCHART6_TITLE: Bioavailability Decomposition (First-Pass)")
print("CHART6_XLABEL: Drug")
print("CHART6_YLABEL: Fraction")
drugs_fp = [
    ("Morphine", 0.95, 0.90, 0.30),
    ("Lidocaine", 0.90, 0.85, 0.35),
    ("Propranolol", 0.90, 0.85, 0.40),
    ("Nitroglycerin", 0.80, 0.70, 0.01),
    ("Metoprolol", 0.95, 0.90, 0.55),
    ("Diazepam", 0.95, 0.95, 0.98),
]
for name, fabs, fgut, fhep in drugs_fp:
    F_total = fabs * fgut * fhep
    print(f"drug={name} f_abs={fabs:.2f} f_gut={fgut:.2f} f_hepatic={fhep:.2f} F_total={F_total:.3f}")

print("\nSimulation complete: 6 panels generated")

Click Run to execute the Python code

Code will be executed with Python 3 on the server

Clinical Applications

Antacid Drug Interactions

Raising gastric pH with antacids or PPIs can reduce absorption of weak acids (ketoconazole requires acidic pH for dissolution) and enhance absorption of some weak bases. Always check pH-dependent absorption.

Bioequivalence Studies

Generic drugs must demonstrate bioequivalence: AUC and C_max within 80-125% of the reference product (90% CI). This ensures equivalent rate and extent of absorption despite different formulations.

Sublingual Nitroglycerin

Hepatic extraction ratio > 99% makes oral nitroglycerin impractical. Sublingual administration delivers drug directly to systemic circulation via sublingual veins, bypassing the portal system entirely.

Ion Trapping in Overdose

Alkalinizing urine (pH 7-8) with sodium bicarbonate traps weak acids (aspirin, phenobarbital) in ionized form in the renal tubule, preventing reabsorption and enhancing elimination.

Key Takeaways

1.
Fick's law: J = P * A * (C_lumen - C_blood), where P = D*K/h. Lipophilicity (K) and surface area (A) are key determinants.
2.
Henderson-Hasselbalch predicts ionization: weak acids are unionized (absorbable) at pH below pK_a; weak bases at pH above pK_a.
3.
Bioavailability F = f_abs * f_gut * f_hepatic. The first-pass effect through the gut wall and liver is the primary cause of reduced oral bioavailability.
4.
The pH-partition hypothesis predicts that unionized drug is absorbed faster, but intestinal surface area (200 m^2) usually dominates over pH effects.
5.
First-order absorption kinetics (k_a) can be estimated from plasma data using the Wagner-Nelson method.

← Part 2 Overview 2.2 Distribution →

Share:X Reddit LinkedIn