Write a note on pH partition theory regarding Absorption. Also discuss carrier mediate absorption in small length
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pH-Partition Theory of Drug Absorption
The pH-partition theory states that a drug crosses a biological lipid membrane mainly in its unionized, lipid-soluble form. Ionized molecules are more water soluble and generally cross lipid membranes poorly by passive diffusion.
Most drugs are weak acids or weak bases, so their degree of ionization depends on:
- pH of the surrounding fluid
- pKa of the drug
- Lipid solubility of the unionized form
Henderson-Hasselbalch relationship
For a weak acid:
[
pH = pKa + \log \frac{Ionized\ form\ (A^-)}{Unionized\ form\ (HA)}
]
- In an acidic medium, weak acids remain mainly unionized (HA) and are theoretically absorbed better.
For a weak base:
[
pH = pKa + \log \frac{Unionized\ form\ (B)}{Ionized\ form\ (BH^+)}
]
- In an alkaline medium, weak bases remain mainly unionized (B) and are theoretically absorbed better.
Examples
| Drug type | Medium favoring unionized form | Theoretical site of better absorption |
|---|---|---|
| Weak acid, e.g., aspirin | Acidic pH | Stomach |
| Weak base, e.g., morphine | Alkaline pH | Small intestine |
Limitations
Although weak acids are more unionized in the stomach, most drugs are absorbed mainly from the small intestine because it has:
- Very large surface area due to folds, villi, and microvilli
- Rich blood supply
- Longer contact time
- Favorable environment for dissolution and transport
Thus, pH-partition theory predicts passive permeability, but does not alone determine the actual site or extent of absorption. Goodman and Gilman notes that the much larger intestinal absorptive surface can outweigh the effect of drug ionization. Goodman & Gilman’s The Pharmacological Basis of Therapeutics, pp. 45-46. A modern review also notes that paracellular transport and other pathways limit the theory's ability to predict absorption on its own (intestinal permeability review).
Carrier-Mediated Absorption
Carrier-mediated absorption is transport of a substance across the intestinal epithelial membrane using a specific carrier protein. It is important for poorly lipid-soluble substances that cannot readily diffuse through the lipid bilayer.
Types
-
Facilitated diffusion
- Carrier-dependent but does not require energy.
- Movement occurs down the concentration gradient.
- Example: fructose enters enterocytes through GLUT5.
-
Active transport
- Requires energy, directly or indirectly.
- Can move a substance against its concentration gradient.
- Example: glucose and galactose enter intestinal cells through SGLT1, coupled to Na⁺ movement.
Characteristics of carrier-mediated transport
- Specificity: A carrier recognizes particular substances or structurally similar molecules.
- Saturability: At high substrate concentrations, all carriers become occupied and transport reaches a maximum, called Tm or transport maximum.
- Competition: Similar substances may compete for the same carrier and reduce each other's absorption.
- Energy dependence: Applies to active transport.
- Inhibition: Carrier function may be inhibited by drugs, toxins, disease, or lack of required ions such as Na⁺.
In the small intestine
Carrier-mediated mechanisms are especially important in absorption of nutrients:
- Glucose and galactose: apical uptake by Na⁺-glucose cotransporter SGLT1; exit to blood through GLUT2.
- Fructose: apical uptake by facilitated diffusion through GLUT5; exit through GLUT2.
- Amino acids, peptides, vitamins, and several minerals also use selective carriers.
The small intestine therefore absorbs carbohydrates through coordinated apical and basolateral carrier systems. Medical Physiology, Ch. 45, “Carbohydrate Absorption.” Carrier-mediated intestinal transport also enables uptake of some lipid-insoluble drugs that resemble endogenous nutrients (Drug Absorption overview).
Define Order of reaction? Discuss Half-life as parameter of First order kinetics in short
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Order of Reaction
Order of a reaction is the sum of the powers to which the concentration terms are raised in the rate equation.
For example:
[
Rate = k[A]^m[B]^n
]
The overall order of reaction is:
[
m+n
]
In pharmacokinetics, it describes how the rate of drug absorption, metabolism, or elimination changes with drug concentration.
Half-life in First-Order Kinetics
Half-life ((t_{1/2})) is the time required for the amount or plasma concentration of a drug to decline by 50%.
In first-order kinetics, the rate of elimination is proportional to the drug concentration. Therefore, a constant fraction of drug is eliminated per unit time.
[
t_{1/2} = \frac{0.693}{k}
]
Where:
- (t_{1/2}) = half-life
- (k) = first-order elimination rate constant
Key points
- Half-life is constant and independent of dose or concentration.
- After one half-life, 50% of drug remains.
- After two half-lives, 25% remains.
- After three half-lives, 12.5% remains.
- About 94%-97% of a drug is eliminated in 4-5 half-lives.
- Half-life helps determine dosing interval, time to reach steady state, and duration of drug action.
Most drugs, at therapeutic concentrations, follow first-order elimination kinetics. NCBI pharmacokinetics reference
Define Order of reaction? Discuss Half-life as parameter of First order kinetics
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Order of Reaction
The order of reaction is the sum of the powers of the concentration terms in the rate equation. It indicates how the reaction rate depends on the concentration of reactant or drug.
If:
[
\text{Rate} = k[A]^m[B]^n
]
then the overall order is:
[
m+n
]
Where (k) is the rate constant.
In pharmacokinetics, the order describes the relationship between drug concentration and the rate of absorption, metabolism, or elimination.
- Zero-order kinetics: A constant amount of drug is eliminated per unit time.
- First-order kinetics: A constant fraction of drug is eliminated per unit time. Most drugs at therapeutic concentrations follow this pattern.
Half-life as a Parameter of First-Order Kinetics
Definition
The biological half-life, denoted (t_{1/2}), is the time needed for the amount of drug in the body or its plasma concentration to decrease by 50%.
For a first-order process:
[
t_{1/2} = \frac{0.693}{k}
]
Where:
- (t_{1/2}) = half-life
- (k) = first-order elimination rate constant
It may also be expressed as:
[
t_{1/2} = \frac{0.693 \times V_d}{CL}
]
Where (V_d) is volume of distribution and (CL) is clearance.
Characteristics in first-order kinetics
-
Half-life is constant.
It does not change with dose or plasma drug concentration, as long as elimination pathways are not saturated. -
A fixed fraction is eliminated in a fixed time.
For example, if the half-life is 6 hours, 50% of the remaining drug is eliminated every 6 hours.
| Number of half-lives | Drug remaining |
|---|---|
| 0 | 100% |
| 1 | 50% |
| 2 | 25% |
| 3 | 12.5% |
| 4 | 6.25% |
| 5 | About 3% |
Thus, approximately 94% of a drug is eliminated after 4 half-lives and about 97% after 5 half-lives.
Importance
Half-life is useful for determining:
- Dosing interval
- Duration of drug action
- Time needed to reach steady-state concentration during repeated dosing
- Time required for drug removal after treatment is stopped
For most first-order drugs, steady state is reached in about 4-5 half-lives. Harrison’s Principles of Internal Medicine, Plasma Half-life, p. 2406.
Write a detailed note on volume of distribution as parameter for one compartment model
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Volume of Distribution as a Parameter of the One-Compartment Model
Definition
Volume of distribution (Vd) is the apparent or hypothetical volume of body fluid that would be required to contain the total amount of drug in the body at the same concentration as that measured in plasma.
[
V_d = \frac{\text{Amount of drug in the body}}{\text{Plasma drug concentration}}
]
It is expressed in litres (L) or litres per kilogram (L/kg).
Vd is not necessarily an actual anatomical volume. It is a pharmacokinetic proportionality constant that indicates the extent to which a drug leaves the bloodstream and distributes into tissues.
One-Compartment Open Model
In the one-compartment model, the entire body is considered to be one homogeneous, well-stirred compartment.
Assumptions
- Drug is administered directly into the central compartment, usually plasma.
- Distribution throughout the body is assumed to be instantaneous.
- At every time point, plasma concentration is assumed to represent the drug concentration throughout the compartment.
- Drug is eliminated from the same compartment, usually by renal excretion and/or hepatic metabolism.
- Elimination commonly follows first-order kinetics.
The model is called open because drug can leave the body by elimination.
[
\text{Drug dose} \rightarrow \boxed{\text{Single well-stirred body compartment}} \rightarrow \text{Elimination}
]
Although the model simplifies actual body physiology, it is useful for describing the relation among volume of distribution, clearance, and half-life.
Calculation of Vd in a One-Compartment Model
Following an intravenous bolus dose:
[
V_d = \frac{Dose}{C_0}
]
Where:
- (Dose) = amount of drug injected intravenously
- (C_0) = theoretical plasma drug concentration at time zero
Since a blood sample cannot usually be obtained at the exact moment of injection, (C_0) is obtained by extrapolating the log plasma concentration-time curve back to time zero.
For first-order elimination:
[
C_t = C_0e^{-kt}
]
Taking logarithms:
[
\log C_t = \log C_0 - \frac{kt}{2.303}
]
The intercept at time zero gives (C_0), after which Vd can be calculated.
Example
If 500 mg of a drug is administered intravenously and the extrapolated initial plasma concentration is 10 mg/L:
[
V_d = \frac{500\ mg}{10\ mg/L} = 50\ L
]
Thus, the apparent volume of distribution is 50 L.
Interpretation of Vd Values
The Vd gives an idea of the relative distribution of a drug between plasma and tissues.
| Approximate Vd | Interpretation | Typical distribution |
|---|---|---|
| 3-5 L | Mainly confined to plasma | Large molecules, highly plasma protein-bound drugs |
| 10-20 L | Mainly distributed in extracellular fluid | Hydrophilic drugs that do not enter cells well |
| About 40 L | Distributed in total body water | Drugs entering both extracellular and intracellular fluid |
| Much greater than 40 L | Extensive tissue binding or sequestration | Lipid-soluble drugs, drugs binding strongly to tissues |
A Vd larger than total body water does not mean the drug is present in a real fluid volume greater than the body. It means plasma drug concentration is very low because much of the drug has moved into tissues.
Factors Affecting Volume of Distribution
1. Lipid solubility
Lipid-soluble drugs readily cross cell membranes and enter tissues, especially adipose tissue. Therefore, they generally have a high Vd.
- Example: diazepam has a large Vd because of extensive tissue distribution.
Hydrophilic drugs remain more in plasma and extracellular fluid and generally have a smaller Vd.
2. Plasma-protein binding
Drugs bound to albumin or other plasma proteins remain in the vascular compartment.
- High plasma-protein binding leads to a low Vd.
- Low plasma-protein binding permits more free drug to leave plasma and may increase Vd.
3. Tissue binding
Binding of a drug to tissue proteins, fat, bone, or intracellular components reduces its plasma concentration and increases Vd.
- Strong tissue binding causes a high Vd.
- Digoxin, for example, distributes extensively into tissues.
4. Molecular size and capillary permeability
Large molecules, such as plasma proteins and some biologics, cross capillary membranes poorly and tend to remain in plasma. They have a low Vd.
Small molecules cross capillaries more easily and may distribute into extracellular or intracellular fluid.
5. Physiological and pathological factors
Vd may change with:
- Age
- Body weight and obesity
- Pregnancy
- Dehydration
- Edema and ascites
- Burns
- Hypoalbuminemia
- Renal, hepatic, or cardiac disease
For example, edema or ascites can increase the Vd of water-soluble drugs because extracellular fluid volume is increased.
Relation of Vd to Elimination Rate Constant, Clearance, and Half-Life
In the one-compartment model:
[
CL = k_e \times V_d
]
Where:
- (CL) = clearance
- (k_e) = elimination rate constant
- (V_d) = volume of distribution
Therefore:
[
k_e = \frac{CL}{V_d}
]
The elimination half-life is:
[
t_{1/2} = \frac{0.693}{k_e}
]
Substituting for (k_e):
[
t_{1/2} = \frac{0.693 \times V_d}{CL}
]
Significance
- If clearance remains constant, a larger Vd produces a longer half-life.
- If Vd remains constant, increased clearance produces a shorter half-life.
- Thus, a prolonged half-life can result from increased Vd, decreased clearance, or both.
Clinical Importance of Vd
1. Calculation of loading dose
The main practical use of Vd is calculating the dose required to promptly achieve a target plasma concentration.
[
\text{Loading dose} = \frac{V_d \times \text{Target plasma concentration}}{F}
]
Where (F) is bioavailability.
For intravenous administration, (F = 1), so:
[
\text{Loading dose} = V_d \times \text{Target plasma concentration}
]
A drug with a large Vd requires a larger loading dose to achieve the same target plasma concentration.
2. Prediction of tissue distribution
Vd helps predict whether a drug remains mainly in blood or distributes extensively to tissues.
- Low Vd: predominantly intravascular distribution
- High Vd: extensive tissue distribution
3. Usefulness in poisoning and dialysis
Drugs with a low Vd are more likely to remain in plasma and may be removed by hemodialysis.
Drugs with a very high Vd are extensively tissue-bound and are usually poorly removed by dialysis.
4. Helps estimate half-life
Because half-life depends directly on Vd, knowledge of Vd helps in selecting dosage intervals and anticipating how long a drug remains in the body.
Limitations of the One-Compartment Vd
The one-compartment model is an approximation. Many drugs first distribute rapidly into highly perfused organs and then more slowly into muscle, fat, or other tissues. Such drugs may be better described by multi-compartment models.
Therefore, in a true multicompartment situation, the apparent Vd calculated early after injection may differ from the Vd estimated later in the elimination phase.
Summary
Volume of distribution is an apparent volume relating the amount of drug in the body to its plasma concentration. In the one-compartment model, the body behaves as one homogeneous compartment with instantaneous drug distribution.
[
V_d = \frac{Dose}{C_0}
]
Vd is influenced by lipid solubility, plasma-protein binding, tissue binding, body composition, and disease states. It is important for estimating loading dose and is related to clearance and half-life by:
[
CL = k_eV_d
]
[
t_{1/2} = \frac{0.693V_d}{CL}
]
A larger Vd generally indicates greater tissue distribution and, when clearance is unchanged, a longer elimination half-life. This agrees with the one-compartment pharmacokinetic description in NCBI's Vd overview.
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