Week 2

• Drug distribution


  Drug is carried by blood and reversibly transferred to tissues
• Drug distribution


  • We are interested in both rate and extent of distribution
  • Rate - how quickly
  • Extent - how much in tissue and how much in blood
• Transfer of drug


  1. The transfer of drug between blood and tissue takes place largely in the capillary bed

  2. Lipid-soluble drugs can enter the interstitial space and are also able to cross the lipophilic cell wall and enter the intracellular space

  3. Fat-soluble drugs tend to concentrate in fatty tissues within the body

  4. Some drugs may concentrate mainly in only one small part of the body

  5. For a drug within the circulation to get into the interstitial fluid, the drug must permeate the barrier of the capillary wall

  6. To move from the interstitial flued to the intracellular fluid a drug must permeate the barrier of the cell wall

  7. As most drug receptors are located on the cell surface, it is not always necessary for drugs to enter cells in order for them to be effective

  8. As drug in the plasma is exposed to the eliminating organs and removed, drug in the tissue and fluid spaces will move back to the bloodstream to maintain equilibrium

  9. In certain cases the tissue may slowly release the drug. This keeps plasma concentrations of the drug from rapidly decreasing and thereby prolongs the effect of the drug

  10. Some drugs such as those that accumulate in the fatty tissues, may leave the tissues so slowly that the drug continues to circulate in the bloodstream for days after a person has stopped taking medication
• Factors affecting drug distribution


  • Tissue blood flow
  • Physiochemical properties
  • Membrane transports
  • Plasma and tissue protein binding
• Tissue blood flow


  • Blood flow to different organs of the body is not equal. The most vitally important organs received the greatest supply of blood, meaning that they will have medications delivered quicker. These organs include the heart, kidney, liver, lung and brain
  • Distribution to less perfused tissues occurs more slowly, these tissues include skeletal muscle, bone, fat and skin
  • Adipose tissue receives the least amount of blood
• Water solubility / lipophilicity


  • Lipid soluble drugs can more readily move across the intracellular membranes and enter the intracellular space and tend to concentrate in fatty tissues
  • Water soluble drugs are less capable of diffusing across lipophilic membranes and tend to stay in the extracellular sides such as in the plasma and interstitial water
• Molecular weight


  Drugs with a very large molecular size may not be able to penetrate across the capillary wall and may be confined to systemic circulation
• pKa and acid/base balance


  • Drugs that are weak acids and weak bases will exist in an equilibrium mixture of the ionised and unionised form
  • The position of the equilibrium depends on the pH of the fluid they are in
  • Intracellular fluids are typically more acidic (pH ~7.2) than extracellular fluids (pH~7.4)
  • Weak acids tend to be more ionised in extracellular fluids (less acidic) and tend to remain more within these spaces
  • Weak bases are more ionised in intracellular fluids (more acidic) and may concentrate here because of an ion-trapping effect
• Membrane transports


  • There are a number of membrane transports located at different tissue barriers within the body such as the blood brain barrier, the gastrointestinal tract, the renal tubules, the biliary tract and the placenta
  • These transports can carry drugs that are substrates for that particular membrane transporter across biological membranes in the body and can effect drug entry and exit from various sites within the body
• Volume of distribution


  • An important pharmacokinetic parameter
  • All the places a drug distributes to have a volume and we need to take these volumes into account when determining what drug dose to achieve a particular plasma drug concentration
  • The major determinants of a drugs volume of distribution is the relative strength of its binding to tissue components in the body as compared with plasma proteins and blood cells
  • If a drug is very tightly bound by tissues and very little is in the blood, the drug will appear to be dissolved in a large volume and volume of distribution will be large
  • If the drug is tightly bound to plasma proteins or blood cells and/or predominately remains in the blood rather than distributes out to the tissues, volume of distribution will be small and may be close to blood volume
• 1st definition of volume of distribution


  • Volume of distribution is the apparent volume into which a drug distributes with a concentration equal to that of plasma
  • We tend to measure drug in plasma, as plasma tends to be easier to handle for analytical purposes
• Calculating volume of distribution (V)


  Volume = amount in container/concentration
• 2nd definition of volume of distribution


  • Volume of distribution is a constant that describes the ratio of the amount of drug in the body (A) to the concentration in the plasma (C)
  • V = amount/concentration
• Volume of distribution does not have to have a physiological meaning, it can be bigger than the total volume of an individual
• Volume of distribution has physiological meaning for certain drugs, but not others
• How do we estimate volume of distribution?


  1. To estimate volume of distribution requires knowledge of both A and C

  2. The only time that A is known exactly is at time zero after an iv-bolus injection

  3. A0 = dose

  4. Therefore V = dose / C0
• V as a scale factor


  • The amount of drug in the body A is a function of dose and elimination
  • We can use volume as a factor that allows is to scale from amount of drug in the body to concentration of drug in the plasma
  • The amount of drug in the plasma C is a function of dose and time and V
  • Concentration of drug in the plasma at any given time after an iv bolus dose is a function of the dose, drug volume of distribution, drug elimination rate constant and time post-dose of interest
  • Volume of distribution is a scale factor, it is a constant that describes the ratio of drug in the body (A) to the concentration in the plasma (C)
• How do we estimate V


  1. V can be estimated by non-compartmental methods

  2. The further use of these methods assume a specific underlying compartmental model

  3. AUC is the area under plasma-concentration time curve

  4. AUMC is the area under moment curve
• Why do we need to know about V?


  • Because it forms the basis for determination of the loading dose
  • This initial dose represents the loading dose (LD) and C represents the concentration you would like to target on initial delivery of that dose
  • This can also be referred to as the target concentration
  • Giving a LD will help achieve the target concentration quicker
• When should a loading dose be given?


  • For drugs that are given as a single dose only, then the dose is a loading dose by definition
  • Yes for drugs that require rapid attainment of therapeutic concentrations such as antibiotics
  • No - loading doses should not be used for drugs that may cause toxicity associated with higher Cmax concentrations (e.g., antidepressants, carbamazepine)
  • The pharmacology if the drug and the patients clinical condition will dictate the need for a loading dose
• Non-compartmental analysis (NCA)


  A method used to describe and summarise concentration measurement without making any assumptions about how the data arose (i.e. it does not assume any underlying model of drug disposition)
• NCA


  An alternative to compartmental analysis
• Compartmental analysis


  Approach that assumes there is some underlying compartmental model that describes the concentration-time curve, dividing and lumping the body into different compartments depending on their physiological similarity with respect to the PK of the drug
• NCA

  • Makes (almost) no assumptions about the distribution or elimination of the drug from the body
  • Does not require that a mathematical model is derived to describe the concentration-time curve
  • Does not require dividing or lumping of tissues
  • Makes less assumptions about the data (and also less 'powerful' because of this)
• Why NCA is used


  Because these approaches make less assumptions about the data, they are often used by pharmaceutical manufacturers, regulatory authorities, and researchers when describing data
• What NCA can tell us about PK


  • Because NCA does not assume a model, it can only be used to describe the data, not for prediction
  • Typically summary "metrics" of the data include - Cmax, Tmax, 1/2 AUC, MRT (mean residence time) and MAT (mean absorption time)
  • These summary measures can be converted into CL and V - which does provide predictive ability (but in doing so may need to assume an underlying compartmental model)
• Cmax


  • The maximum observed concentration in the matrix of interest, typically the plasma
  • The accuracy of Cmax is dependent on the assay and the presence of intensive sampling times around the time at which the Cmax is likely to occur
• Tmax


  • The time that the maximum concentration is observed
  • The accuracy of Tmax is dependant on the presence of intensive sampling times around the time at which the Cmax is likely to occur
• Cmax and Tmax


  Cmax and Tmax are inversely correlated, the larger the Tmax (the further post dose it is) the small the Cmax will be, if dose and form remain the same
• Tz 1/2 - terminal phase half-life


  • Half-life of the terminal slope of the curve
  • A linear regression of the log-transformed data for the linear 'last part' of the curve provides an estimate of the half-life of the drug
  • This method is dependant on the number if samples taken in the final decay part of the curve and the accuracy of the assay
• AUC0-t


  • AUC is the area under the concentration-time curve
  • It is estimate by integrating the concentration time curve between two times, either mathematically (assuming the compartmental model is known) or numerically e.g. by using the trapezoidal rule
• AUC does not imply a shape
• AUC0-t at steady state = AUCo-x after the same single dose
• How to estimate AUC0-infinity when the data doesn't go for long enough


  • AUC12-infintiy can be estimated by dividing the last measured concentration by k (the elimination rate constant) giving you the area between the last concentration measurement and the time infinity
  • AUC0-infinity can be estimated as AUC0-12 + AUC12-infintiy
  • If AUC0-infinity more than 20% larger than AUC0-12 then the extrapolation is risky
• AUMC


  • The area-under-the-concentration-time first moment curve, based on the theory if statistical movements
  • AUMC will always be larger than AUC
  • The greater the AUMC the greater the concentration-time curve is skewed to the right
• MRT - mean residence time


  • The average time that a drug molecule will remain in the body, a measurement of persistence of drug in the body
  • MRT can be calculated as AUMC divided by AUC
  • MRT will be longer for a slow-release product -although the elimination will be the same. Therefore MRT is affected by both absorption and elimination processes
• MAT - mean absorption time


  • The average period of time it takes for a molecule to reach the systemic circulation, depending on dissolution and absorption processes
  • MAT is calculated by determining the MRT associated with an extravascular dose (i.e. an oral dose) minus the MRT associated with an IV bolus dose
• Useful relationships can be derived from non-compartmental summaries
• Non-compartmental analyses are commonly performed, but they may not be truly non-compartmental
• Useful PK relationships can be derived from non-compartmental data without the need for modelling