PK Basics

VOLUME OF DISTRIBUTION

https://www.acs.org/content/dam/acsorg/events/drug-discovery/slides/2015-10-29-ddds10-pharmacokinetics.pdf
  • The process of distribution refers to the movement of a drug between the intravascular (blood/plasma) and extravascular (intracellular & extracellular) compartments of the body.
  • Within each compartment of the body, a drug exists in equilibrium between a protein bound or free form.
  • A drug with high Vd tends to leave the plasma and enter the extravascular compartments of the body, requiring a higher dose of that drug to achieve a given plasma concentration.
  • However, Vd and Clearance are not affected by the dose of drug.
  • Clearance is only PK parameter that inversely affects both t1/2 and AUC.
  • Change in Vd leads to proportional change in t1/2 but no change in AUC.
https://www.acs.org/content/dam/acsorg/events/drug-discovery/slides/2015-10-29-ddds10-pharmacokinetics.pdf

Single vs. Multi-compartment models of Distribution

  • Single compartment model:
    • Because these drugs distribute “instantaneously”, the initial plasma concentration of drug at time = 0 (Co) is difficult to measure and is therefore estimated via extrapolation to time =0 on a plasma concentration vs. time curve.
    • any measured decline in drug plasma concentration is a result of drug elimination from the body only.
    • Vd of these drugs can be represented by a single value, which is Vd of the central compartment (Vc).
  • Multi-compartment model:
  • Single drug have multiple Vd values, which are each time-dependent depending on where we are in the Cp vs t profile.
  • Only the drug located in the central compartment can be eliminated from the body because the process of elimination is primarily carried out by the liver and kidneys, highly perfused organs contained in central copmartment.
  • At a constant rate of clearance, a drug with high Vd will have a longer elimination half-life.

Volume of distribution terms in Two Compartment Model

  • Vp or Vc or initial volume of distribution
  • In two-compartment model, Vp may also be considered a mass balance factor governed by the mass balance between dose and concentration At time = 0, no drug is eliminated, D0 = VpCp
  • The apparent volume of the tissue compartment (Vt) is a conceptual volume only and does not represent true anatomic volumes. The Vt may be calculated from knowledge of the transfer rate constants (k12 and k21 )and Vp.
  • (Vd)ss
  • Steady state is reached at a time greater by at least five elimination half-lives of the drug.
  • The total amount of drug in the body at is equal to the sum of amount of drug in the tissue compartment, Dt, and amount of drug in the central compartment, Dp. Therefore, the apparent volume of drug at steady state (Vd)ss may be calculated by dividing the total amount of drug in the body by the concentration of drug in the central compartment at steady state.
  • (Vd)ss, is possible in multiple dosing or infusion. (Vd)ss is much larger than Vp; it approximates (Vd)β but differs somewhat in value, depending on the transfer constants.
  • (Vd)β or (Vd)area or Volume of Distribution by Area
  • Afer the drug is distributed, the total amount of drug in the body ( not the drug amount in tissue) during the elimination of β phase is calculated using (Vd)β. This volume represents a proportionality factor between plasma concentrations and total amount of drug in body during terminal β phase of disposition.
  • (Vd)β, is obtained through calculations similar to those used to find Vp, except that the rate constant β is used instead of k. Hence, (Vd)β is affected by changes in the overall elimination rate (ie, change in k).
  • (Vd)β is often calculated from total body clearance divided by β . This volume is considered a time-dependent and clearance-dependent volume of distribution parameter.
  • The value of (VD)β is affected by elimination, and it changes as clearance is altered. Reduced drug clearance from the body may increase AUC (area under the curve), such that (Vd)β is either reduced or unchanged depending on the value of β.
  • (Vd)exp or Extrapolated Volume of Distribution
  • The extrapolated volume of distribution (Vd)exp is calculated by using B which is the y intercept obtained by extrapolation of the β phase of the plasma level curve to the y axis.

CLEARANCE

https://www.acs.org/content/dam/acsorg/events/drug-discovery/slides/2015-10-29-ddds10-pharmacokinetics.pdf
https://www.acs.org/content/dam/acsorg/events/drug-discovery/slides/2015-10-29-ddds10-pharmacokinetics.pdf

Elimination rate Vs Clearance rate

  • Elimination rate and clearance rate can be different.
  • In first order kinetics, elimination rate is proportional to dose. Higher the dose, the greater the rate of elimination. However, clearance rate remains dose-independent.
https://derangedphysiology.com/main/cicm-primary-exam/required-reading/pharmacokinetics/Chapter%203.3.3/clearance
  • Clearance refers to ”Volume” of plasma from which drug would be totally removed per unit time.
  • Clearance is often calculated by a noncompartmental approach, in which the bolus IV dose is divided by the area under the plasma concentration–time curve from zero to infinity.
  • However, in noncompartmental approach, underestimating the area can inflate the calculated value of clearance.
  • Early time points must be collected frequently to observe the rapid decline in drug conc. (distribution phase) for drugs with multicompartment PK.
  • For a drug with linear PK
    • We would expect that a 2-fold increase in dose would result in a 2-fold increase in drug exposure.
  • Nonlinear PK
    • If the dose is doubled and the exposure increases more than 2-fold. The reason for the non-linearity is related to the saturable clearance at high doses(at high doses, exposure increases faster than dose).
  • All drugs exhibit nonlinear PK at high doses.
    • Some drugs exhibit nonlinear PK in the therapeutic range used to treat patients, while other drugs do not exhibit non-linearity until doses exceed the therapeutic window by several orders of magnitude.
  • Clearance can be used to calculate the rate at which drug must be added to the circulation to maintain the steady state plasma concentration or, in other words, the dosage rate. 
  • Clearance is the only parameter that affects both t1/2 and AUC. For example a 5-fold reduction in CL would result in 5-fold increase in t1/2 and AUC.
https://www.acs.org/content/dam/acsorg/events/drug-discovery/slides/2015-10-29-ddds10-pharmacokinetics.pdf
https://www.certara.com/2013/02/17/nonlinear-pk-what-does-that-mean/?ap=&UTM_LeadSource=
https://www.slideshare.net/abahnassi/pharmacokinetics-lecture-three?from_action=save

Renal Clearance

https://slideplayer.com/slide/7646009/
https://slideplayer.com/slide/7646009/
https://www.acs.org/content/dam/acsorg/events/drug-discovery/slides/2015-10-29-ddds10-pharmacokinetics.pdf

Extraction Ratio

  • Extraction ratio is commonly used to triage compounds in discovery. Compounds with ER < 0.3 are preferred.
https://www.acs.org/content/dam/acsorg/events/drug-discovery/slides/2015-10-29-ddds10-pharmacokinetics.pdf
https://slideplayer.com/slide/9396492/
https://slideplayer.com/slide/7646009/

Extraction ratio Vs Fu & F

  • Hepatic clearance is a function of plasma protein binding for low ER drugs.
https://slideplayer.com/slide/7646009/

PLASMA PROTEIN BINDING

  •  Depending on a specific drug’s affinity for plasma protein, a proportion of the drug may become bound to plasma proteins, with the remainder being unbound. If the protein binding is reversible, then a chemical equilibrium will exist between the bound and unbound states.
  • Protein + drug ⇌ Protein-drug complex
  • Notably, it is the unbound fraction which exhibits pharmacologic effects. It is also the fraction that may be metabolized and/or excreted.
  • VOLUME OF DISTRIBUTION (Vd) & PROTEIN BINDING
  • The normal range for protein levels in blood serum is 6 to 8 grams per deciliter (g/dl). Of this, albumin makes up 3.5 to 5.0 g/dl.
  • Representative proteins to which drugs bind in plasma:
  • albumin (50%-60% of plasma protein) (35-50 g/L)
  • α1- acid glycoprotein (AGP) ( only (1-3% plasma protein) (0.4-1 g/L)
  • lipoproteins (variable)
  • In general, basic molecules will leave systemic circulation leading to higher Vd as compared to acidic molecules because they have strong interactions with negatively charged phospholipid membranes. The extent of this binding is also dependent on the overall lipophilicity of the drug.
  • Basic drugs will also bind to acidic alpha-1 acid glycoprotein (also a plasma protein). In addition to ionic interactions between drug and a macromolecules, hydrophobic interactions also play a important role.
  • Acidic and neutral drugs will primarily bind to albumin. If albumin becomes saturated, then these drugs will bind to lipoprotein.
  • Acidic molecules have a higher affinity for albumin molecules at lower lipophilicity than neutral or basic molecules and thus remain in the plasma leading to lower Vd as compared to basic molecules.
  • Lipophilic molecules are more likely to pass through lipid bilayers, leave the bloodstream and distribute to areas with high lipid density (adipose) and therefore have a higher Vd.
  • Hydrophilic molecules are less likely to pass through lipid bilayers and therefore more likely to remain in the bloodstream and therefore have a lower Vd.
https://www.acs.org/content/dam/acsorg/events/drug-discovery/slides/2015-10-29-ddds10-pharmacokinetics.pdf
https://www.acs.org/content/dam/acsorg/events/drug-discovery/slides/2015-10-29-ddds10-pharmacokinetics.pdf

  • HALF-LIFE (t1/2)& PROTEIN BINDING
  • t1/2 is a hybrid PK parameter and is determined by Vd and CL. It can be predicted from the predicted CL and Vss values in preclinical species.
  • Protein binding can influence the drug’s biological half life. The bound drug portion may act as a reservoir or depot from which the drug is slowly released as the unbound form. Since the unbound form is being metabolized and/or excreted from the body, the bound fraction will be released in order to maintain equilibrium.
https://www.acs.org/content/dam/acsorg/events/drug-discovery/slides/2015-10-29-ddds10-pharmacokinetics.pdf
  • BIOAVAILABILITY (F), EFFICACY & PROTEIN BINDING
  •  For low hepatic extraction ratio drugsbioavailability is not affected by enzyme activity, hepatic blood flow or protein binding (or fraction unbound).
  • For high ER, BA increases with hepatic blood flow and decreases with fraction unbound.
  • Protein binding affects many PK parameters but does not alter unbound AUC (neither efficacy nor toxicity) for drugs administered orally and eliminated by liver.
https://www.acs.org/content/dam/acsorg/events/drug-discovery/slides/2015-10-29-ddds10-pharmacokinetics.pdf
https://www.acs.org/content/dam/acsorg/events/drug-discovery/slides/2015-10-29-ddds10-pharmacokinetics.pdf
https://www.acs.org/content/dam/acsorg/events/drug-discovery/slides/2015-10-29-ddds10-pharmacokinetics.pdf
https://www.acs.org/content/dam/acsorg/events/drug-discovery/slides/2015-10-29-ddds10-pharmacokinetics.pdf

Two Compartment PK Model

  • In one compartment model immediate distribution is assumed and whole body is treated as one unit.
  • If distribution is minimal, the one compartment can be an adequate approximation. However, only very few drugs show immediate distribution and equilibrium through the body.
  • Two-Compartment body Model includes a peripheral compartment into which the drug may distribute.
  • The hybrid constants A, B, α, and ß may be found by “feathering” which allows us to separate distribution and elimination (similar to the way we found ka and ke in oral administration).
  • The initial concentration after an i.v. bolus dose can be given by: C0= A + B
  • Most two-compartment models assume that elimination occurs from the central compartment model, as shown in Fig (model A), unless other information about the drug is known.
  • Distribution phase
  • The slope for ‘distribution phase’ is steeper than elimination phase as the concentration decreases rapidly in distribution phase.
  • Once a drug enters the body, elimination begins. After an i.v. bolus injection to the central compartment, there is distribution into the peripheral compartment and elimination from the central compartment. Although both elimination and distribution occur concurrently during the distribution phase, there is a net flow of drug out of plasma (along the concentration gradient) until steady-state is reached because rate of distribution >> rate of elimination.
  • Steady-sate
  • At maximum tissue concentrations, rate of drug entry into tissue = rate of drug exit from tissue. (ie, at the peak of the tissue curve, where the slope = 0 or not changing).
  • This may be verified by examining at what time (entry & exit rate are equal) Xp. k12 = Xt. k21
  • However, the fraction of drug in the tissue compartment(whose value may be greater or less than the plasma drug concentration) is now in equilibrium (distribution equilibrium) with the fraction of drug in the central compartment , and the drug concentrations in both the central and tissue compartments decline in parallel and more slowly compared to the distribution phase.
  • Post-distibution (elimination) or (β) phase
  • After steady-state, a concentration gradient is again created – this time in the opposite direction -by the continual elimination of drug from the central compartment. In response to this, drug begins to flow back into the central compartment where it is eliminated. Thus, in β-phase, the concentration of drug in the peripheral compartment is greater than that in the central compartment. The concentrations in both compartments decrease proportionally .
  • Since plasma and tissue concentrations decline in parallel, plasma drug concentrations provide some indication of the concentration of drug in the tissue.
  • At this point, drug kinetics appears to follow a one-compartment model in which drug elimination is a first-order process described by β.
  • This may be viewed as a “pseudo steady-state”: the body wants to reach an equilibrium between the amount of drug in each compartment (Xc and Xp for central and peripheral) but cannot due to elimination (k10).
  • The rate constants for the transfer of drug between compartments are referred to Microconstants or transfer constants (k12, k21, and k10). They relate the amount of drug being transferred per unit time from one compartment to the other. The values for these microconstants cannot be determined by direct measurement, but they can be estimated by a graphic method.
  • The constants α and β are Hybrid first-order rate constants for the distribution phase and elimination phase,respectively.

DOSE INDIVIDUALIZATION BASED ON ESTIMATION OF INDIVIDUAL PK PROFILES

  • Random (experimental) error translates into imprecision or variation. 
  • The systematic error translates into poor accuracy or significant deviation from the true value.
https://oacu.oir.nih.gov/sites/default/files/uploads/arac-guidelines/b2_blood_collection_in_mice_and_rats.pdf

REFERENCES