Physiologic Pharmacokinetic Models, Mean Residence Time and Statistical Moment Theory


Physiologic pharmacokinetic models 

- It is mathematical model describing drug movement and disposition in the body based on organ blood flow and the organ spaces penetrated by the drug. 

- In its simplest form, a physiologic pharmacokinetic model considers the drug to be blood flow limited.  

- Drugs are carried to organs by arterial blood and leave organs by venous blood .  

- In such a model, transmembrane movement of drug is rapid, and the capillary membrane does not offer any resistance to drug permeation. 
- Uptake of drug into the tissues is rapid, and a constant ratio of drug concentrations between the organ and the venous blood is quickly established.

Physiologic pharmacokinetic model
Physiologic pharmacokinetic model

Elimination of Drugs by Each Organs

- The rate of drug carried to a tissue organ and tissue drug uptake depend on the rate of blood flow to the organ and the tissue/blood partition coefficient,

- The rate of blood flow to the tissue is expressed as Q t  (mL/min), and the rate of change in the drug concentration with respect to time within a given tissue organ is expressed as

rate of change in the drug concentration with respect to time formula

- Removal of drug from any organ is described by drug clearance (Cl ) from the organ. 
- The rate of drug elimination is the product of the drug concentration in the organ and the organ clearance.

Rate of drug elimination formula

The mass balance for the rate of change in drug concentration in the blood pool is  

mass balance for the rate of change in drug concentration in the blood pool

Application of Physiologic Pharmacokinetic Model

- The effect of a change in blood flow on the drug concentration in a given tissue may be estimated once the model is characterized. 

- The effect of a change in mass size of different tissue organs on the redistribution of drug may also be evaluated using the system of physiologic model differential equations generated. 

- When several species are involved, the physiologic model may predict the pharmacokinetics of a drug in humans when only animal data are available. 

- Changes in drug protein binding, tissue organ drug partition ratios, and intrinsic hepatic clearance may be inserted into the physiologic pharmacokinetic model.

Interspecies Scaling

- Interspecies scaling is a method used in toxicokinetics and the extrapolation of therapeutic drug doses in humans from nonclinical animal drug studies. 

- Toxicokinetics is the application of pharmacokinetics to toxicology and pharmacokinetics for interpolation and extrapolation based on anatomic, physiologic, and biochemical similarities.

- The basic assumption in interspecies scaling is that physiologic variables, such as clearance, heart rate, organ weight, and biochemical processes, are related to the weight or body surface area of the animal species (including humans). 

- Interspecies scaling uses a physiologic variable, y, that is graphed against the body weight of the species on log axes to transform the data into a linear relationship

Interspecies Scaling for Methotrexate and Caffein


Interspecies correlation between methotrexate volume of distribution V and body weight. Linear regression analysis was performed on logarithmically transformed data.


Caffeine Cl int (free drug) in mammalian species as a function of body weight. Line does not utilize man and monkey points.

Physiologic versus Compartment Approach

  1. Compartmental models represent a simplified kinetic approach to describe drug absorption, distribution, and elimination.
  2. The major advantage of compartment models is that the time course of drug in the body may be monitored quantitatively with a limited amount of data.
  3. Compartmental models have been applied successfully to prediction of the pharmacokinetics of the drug and the development of dosage regimens.
  4. Moreover, compartmental models are very useful in relating plasma drug levels to pharmacodynamic and toxic effects in the body.
  5. The simplicity and flexibility of the compartment model is the principal reason for its wide application.
  6. Compartment models account accurately for the mass balance of the drug in the body and the amount of drug eliminated. For this the compartment model is particularly useful for comparing the pharmacokinetics of related therapeutic agents.
In spite of these advantages, the compartmental model is generally regarded as somewhat empirical and lacking physiologic relevance. Many disease-related changes in pharmacokinetics are the result of physiologic changes, such as impairment of blood flow or a change in organ mass. These pathophysiologic changes are better evaluated using a physiologic-based pharmacokinetic model.

The physiologic pharmacokinetic model may also be modified to include a specific feature of a drug. For example, for an antitumor agent that penetrates into the cell, both the drug level in the interstitial water and the intracellular water may be considered in the model. Blood flow and tumor size may even be included in the model to study any change in the drug uptake at that site.

Mean Residence Time

Mean Residence time formula

AUMC: Area under the first moment time curve from time 0 to infinity. The plasma concentration equation multiplied by time  gives AUMC.

Mean Absorption Time and Mean Dissolution Time

Mean Absorption Time and Mean Dissolution Time equation

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