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Pharmacokinetics: bioavailability, distribution, clearance

Bioavailability, distribution and clearance are the core pharmacokinetic processes that determine how much drug reaches its site of action.

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Overview and definitions

DefinitionPharmacokinetics

Pharmacokinetics describes how the body handles a drug: how much of the administered dose reaches the systemic circulation (bioavailability), how widely the drug spreads through body tissues (distribution), and how the body removes it (clearance). These three parameters together determine the concentration of drug available at its site of action.

When a drug is given by a route other than directly into a vein, only a fraction of the dose may reach the circulation unchanged. The absolute oral bioavailability of tangeretin, a citrus polymethoxyflavone, was calculated by comparing the area under the curve after oral administration with that after intravenous administration, and was found to be 27.11%. This low figure means that roughly three-quarters of the ingested dose never reaches the systemic circulation as intact drug, illustrating why bioavailability matters when interpreting in vitro findings: poor bioavailability may make compounds largely ineffective in vivo. [2]

Distribution is quantified by the volume of distribution (Vd), which describes the tissue access and binding of a drug and indicates the extent of its distribution in body tissues.[1] A large Vd suggests that the drug leaves the plasma and binds extensively to tissue components; a small Vd indicates that the drug remains largely confined to the plasma. Volume of distribution at steady state (Vss) is measured at equilibrium and therefore describes molecular tissue binding more reliably than other volume parameters that depend on the time after measurement. Vss depends on the access of the drug to cells and tissues, its affinity for plasma proteins and tissue components, and the number of binding sites in plasma and tissues. [4]

Clinical pearlVss from intravenous data only

When computational models use volume of distribution, the value should be collected from intravenous and not from oral pharmacokinetic studies, because intravenous administration defines the quantity of drug subject to distribution and avoids the uncertainty of incomplete bioavailability after extravascular dosing. [4] [3]

The extent of drug distribution determines both access to the site of action and access to other tissues that may give rise to adverse effects. Lipophilicity and solubility descriptors were found to have a high influence on both volume of distribution and fraction unbound, but with an inverse relationship. This is why physiochemical properties are used to predict these parameters early in drug development, before experimental measurement in humans is feasible. [4]

Key pharmacokinetic parameters covered in this section
ParameterWhat it describesInfluencing factors
Bioavailability (F)Fraction of an extravascular dose reaching the systemic circulation unchangedAbsorption, first-pass metabolism
Volume of distribution (Vd)Extent of drug distribution into tissues relative to plasmaTissue binding, plasma protein binding, lipophilicity
Volume of distribution at steady state (Vss)Tissue binding at equilibriumAccess to tissues, binding affinity, binding site number
Clearance (CL)Rate at which drug is removed from the bodyOrgan function, blood flow, enzyme activity

NoteWhy computational prediction matters

Experimental measurement of volume of distribution and fraction unbound is not feasible for screening purposes in early drug discovery, so reliable in silico predictions benefit the early stages of drug development. [4]

Core concepts and definitions

DefinitionBioavailability

The fraction of an administered dose that reaches the systemic circulation in an unchanged form. It is expressed as a percentage of the dose given by the route under study.

DefinitionAbsolute oral bioavailability (Fabs)

The ratio of the area under the plasma concentration‑time curve (AUC) after oral dosing to the AUC after an equivalent intravenous dose, multiplied by 100 %.

DefinitionDistribution volume (Vd)

A theoretical volume that relates the amount of drug in the body to the plasma concentration; it reflects the extent of tissue uptake.

DefinitionClearance (Cl)

The volume of plasma from which the drug is completely removed per unit time; it combines metabolic and excretory processes.

DefinitionCmax and Tmax

Cmax is the peak plasma (or tissue) concentration after a dose; Tmax is the time taken to reach that peak.

NoteMethoxy‑flavone (PMF) variability

The oral bioavailability of polymethoxylated flavones (PMFs) varies with the number and position of methoxy groups; tangeretin shows a higher Fabs than 5,7,3′,4′‑tetramethoxyflavone (27.11 % vs 14.3 %). [5]

Key parameters for flavonoid pharmacokinetics

ParameterExample (tangeretin)Example (5,7,3′,4′‑tetramethoxyflavone)
Absolute oral bioavailability27.11 %14.3 %
Cmax (plasma) after oral dose– (not reported)0.79 µg mL⁻¹
Tmax (plasma)–190 min
Intestinal Cmax (tissue)– (higher than organs)6 850 ng g⁻¹
Intestinal AUC (tissue)–18 600 ng g⁻¹

These figures illustrate how a single chemical modification (additional methoxy groups) can halve the fraction of dose that becomes systemically available.

Distribution highlights

Tangeretin accumulates preferentially in the digestive tract, where its Cmax exceeds that in liver, kidney, brain, spleen, heart and lung. A similar pattern is seen with 5,7‑dimethoxyflavone, whose intestinal Cmax reaches 6 850 ng g⁻¹ and AUC 18 600 ng g⁻¹, far above extra‑intestinal sites. Such data underscore the importance of measuring tissue concentrations, not just plasma, when assessing bioavailability of poorly absorbed compounds. [5]

Clearance considerations

While the provided passages do not give explicit clearance values for flavonoids, they note that phage clearance can be delayed by adaptive immunity, illustrating that clearance may be governed by both innate mechanisms (metabolism, renal excretion) and immune‑mediated inactivation. The principle applies to small molecules: clearance reflects the net effect of metabolic enzymes, renal filtration, biliary excretion, and any immune‑related sequestration.

Mechanisms and principles

F

DefinitionBioavailability, F

Bioavailability (F) is the fraction of an administered dose that reaches the systemic circulation in its active form. It is the product of the fraction absorbed and the fraction escaping first-pass metabolism: F = fa × (1 − ER), where fa is the fraction absorbed and ER is the hepatic extraction ratio.

DefinitionAbsolute bioavailability

Absolute bioavailability compares the systemic exposure after extravascular administration with that after intravenous administration, using the area under the plasma concentration–time curve: F = (AUC extravascular / AUC intravenous) × (dose intravenous / dose extravascular) × 100. A value of 100% means the drug reaches the circulation completely.

In the tangeretin study, rats received 50 mg/kg body weight orally. The maximum plasma concentration (Cmax) was 0.87 ± 0.33 μg/mL, reached at a Tmax of 340.00 ± 48.99 minutes, with a terminal half-life (t1/2) of 342.43 ± 71.27 minutes. From the oral and intravenous AUC values, the absolute oral bioavailability was calculated as 27.11%. This worked example shows how F is derived: the oral dose was 50 mg/kg, and the low F reflects incomplete absorption and/or pre-systemic metabolism. [2]

Exam trapDo not confuse F with fraction absorbed

A low bioavailability does not necessarily mean poor absorption. Hepatic first-pass metabolism can destroy a drug after it has crossed the gut wall, so bioavailability can fall even when absorption is complete. Always consider both absorption and extraction when interpreting F.

Distribution is described by the apparent volume of distribution, which relates the amount of drug in the body to its plasma concentration: Vd = Amount in body / Plasma concentration. The apparent volume of distribution at steady state (Vss) is measured at equilibrium and therefore describes molecular tissue binding more reliably than other volume parameters that depend on the time after measurement. Vss depends on the access of the drug to cells and tissues, its affinity to plasma proteins and tissue components, and the number of binding sites in plasma and tissues.

Volume of distribution and fraction unbound are two key parameters in pharmacokinetics. The fraction unbound describes the portion of free drug in plasma that may extravasate, while volume of distribution describes the tissue access and binding of a drug. Because lipophilicity and solubility descriptors have a high influence on both, but with an inverse relationship, compounds can be prioritised for further study based on their physicochemical profile.

Clearance is the volume of plasma from which drug is irreversibly removed per unit time. It is calculated as CL = Rate of elimination / Plasma concentration. Total body clearance is the sum of the clearances of all eliminating organs. Half-life links clearance and volume of distribution: t1/2 = 0.693 × Vd / CL. In the tangeretin example, the half-life of 342.43 ± 71.27 minutes reflects the balance between distribution into tissues and elimination from the body.

Clinical pearlHalf-life depends on both Vd and CL

A long half-life can result from a large volume of distribution, a low clearance, or both. Changing either parameter changes the time the drug persists in the body, which is why dosing intervals are adjusted when renal or hepatic impairment reduces clearance.

Worked example: tangeretin pharmacokinetics in rats after 50 mg/kg oral dosing
ParameterValueComment
Cmax0.87 ± 0.33 μg/mLPeak plasma concentration
Tmax340.00 ± 48.99 minTime to peak
t1/2342.43 ± 71.27 minTerminal half-life
Absolute oral bioavailability27.11%Low; most of the dose does not reach the circulation intact

NoteClinical relevance of distribution

The extent of drug distribution determines the access of a drug to its sites of action and to other tissues, which might give rise to adverse effects. A drug with a very large Vd may need a higher loading dose to achieve the desired plasma concentration, while a drug with a small Vd may be more affected by changes in plasma protein binding. [4]

From dose to effect

  1. Drug administeredOral dose given to the patient
  2. Question: Does the drug reach the systemic circulation unchanged?
    • Yes

      1. Calculate FCompare AUC after extravascular dosing with AUC after intravenous dosing; F = (AUC extravascular / AUC intravenous) × (dose IV / dose EV) × 100
    • No

      1. Reduce FPoor absorption or high first-pass extraction limits the fraction reaching the circulation
  3. DistributionVd = Amount in body / Plasma concentration; Vss reflects tissue binding at equilibrium
  4. Clearance and half-lifeCL = Rate of elimination / Plasma concentration; t1/2 = 0.693 × Vd / CL
A teaching outline, not a protocol.

Volume of distribution

The volume of distribution (Vd) links the amount of drug in the body to the concentration measured in plasma. It is an apparent volume rather than an anatomically defined one: when drug binds extensively outside the blood vessels, the ratio of amount to concentration rises and Vd increases.

DefinitionDefinition and formula

Vd = A / C, where A is the amount of drug in the body and C is the drug concentration in plasma (both free drug and protein-bound drug). Vd is an apparent volume that increases with drug binding in the extravascular space; it is not an anatomically defined volume. [4]

At steady state the relevant parameter is Vss, the volume of a reference fluid, usually plasma, in which the drug appears to be dissolved at steady state. Vss depends on the anatomical volumes of the tissues and on the relative extent of drug binding in plasma and tissue, described as the fu/fuT ratio. The unbound fraction in plasma, fu, depends on the binding affinity and capacity of plasma proteins, which also affect Vd. [4] [3]

Classes of steady-state volume of distribution
ClassVss rangeInterpretation
Class 10 to 0.3 L/kgConfined mainly to the extracellular fluid [4]
Class 20.3 to 1 L/kgDistribution to the tissues is included [4]
Class 3Greater than 1 L/kgSignificant binding to cellular components [4]

The range of Vd is wide because tissue binding varies considerably between drugs. At one extreme, erythropoietin is confined to the vascular space and has a Vd of 4 L, close to the anatomical volume of the vascular space. At the other, hydroxychloroquine has a Vd of 49 000 L and accumulates strongly into cells and tissues. [4]

Tissue composition matters. Adipose tissue is fatty and richer in neutral lipids, so distribution into it may be dominated by lipophilicity and hydrophobic interactions rather than by electronic interactions as in other tissues. In physiologically based pharmacokinetic models, the simulated partition coefficient for adipose tissue is considered more sensitive to lipophilicity than that for a non-adipose tissue. [3]

Knowing Vss matters because it predicts the plasma concentration for a given amount of drug in the body and influences the drug's half-life, which in turn guides the dosage regimen. [3]

Clinical pearlClinical pearl

A small Vd means the drug stays largely in the plasma; a very large Vd means it is sequestered in tissues, so the plasma concentration alone can mislead about the amount of drug in the body.

Predictive models increasingly include fu. Test-set performance for Vd prediction gave a Q2 of 0.70, comparable with the Volsurf+ model, and the classification models identified compounds with a high or low volume of distribution with sensitivity 0.81 and 0.71, respectively. [4]

Clearance, half-life, loading and maintenance dose calculations

Clearance, half-life and dose form one linked system: clearance sets how fast drug is removed, half-life sets how long it persists, and together they determine the loading and maintenance doses.

DefinitionClearance

Clearance is the volume of plasma from which drug is completely and irreversibly removed per unit time. It measures eliminating capacity, not the amount of drug lost.

Clearance

Most small molecules are cleared by hepatic metabolism and renal excretion; large particles such as bacteriophages are cleared mainly by the mononuclear phagocytic system. Phage clearance is mostly due to phagocytosis of phage particles in the liver and, to a lesser extent, in the spleen, while renal secretion has a marginal role, probably due to the large size of phage particles. Phage accumulation was observed in spleen, liver and lymph nodes as elements of the mononuclear phagocytic system. Capture by these organs is rapid: phage titres in the blood shortly after intravenous delivery (up to 0.5 hours) are generally lower than could be calculated from simple dilution of the phage dose in the blood or body volume. Later, phage clearance slowed down, suggesting that phage half-life (when no propagation occurs) is dose dependent. [1]

Clinical pearlTwice the clearance, twice the dose

Clearance behaves like a flow: a patient who clears a drug twice as fast needs double the maintenance dose rate to hold the same average plasma concentration.

Half-life

Half-life links clearance and distribution: the time for plasma concentration to fall by half equals Half-life = 0.693 x Vd / CL. A long half-life can reflect a large volume of distribution, a low clearance, or both. Reported phage half-lives in mice differ: Cerveny et al found 2.2 hours, while Molenaar et al and Tiwari et al reported 4.5 hours. The semilog plot of phage decrease against time was not linear, demonstrating that phage clearance slows down with time, so an early half-life should not be extrapolated far beyond its measured window. [1]

Loading dose

When effect must begin at once, a loading dose fills the distribution volume: Loading dose = (target plasma concentration x Vd) / F. Loading depends on volume and target level, not on clearance, which is why higher input doses are needed to reach a site. Schultz and Neva proposed 10^9 PFU as a minimum dose for phage detection in urine in IV injected mice, and in systemic administrations phage concentration in plasma is strongly related to dose. Minimum effective oral doses seemed to be around 10^7–10^9 plaque-forming units (PFU) per animal in rodents and chickens. [1]

Maintenance dose

Maintenance dosing replaces what clearance removes: Maintenance dose rate = (CL x target plasma concentration x dosing interval) / F. When oral bioavailability (F) is low, the oral dose must rise to achieve the same exposure: the absolute oral bioavailability of tangeretin in rats is 27.11%, while that of 5,7,3',4'-tetramethoxyflavone is only 14.3%; the Cmax and Tmax of 5,7,3',4'-tetramethoxyflavone were 0.79 μg/mL and 190 min, respectively. Dose also decides whether drug reaches its site: the relatively low oral phage dose (4.5 x 10 [1][2]

Distribution feeds back into these calculations: the Cmax of tangeretin in the digestive tract was relatively higher than that from the organs, and the Cmax and AUC of 5,7-dimethoxyflavone in the intestine were calculated as 6850 ng/g and 18,600 ng/g, relatively higher than that in the liver, kidney, brain, spleen, heart, and lung. A large volume of distribution therefore raises the loading dose even when clearance is unchanged. [2]

Reported values behind the dosing calculations
QuantityValue
Phage half-life in mice2.2 hours (Cerveny et al) and 4.5 hours (Molenaar et al, Tiwari et al)
Minimum IV dose for urinary phage detection in mice10^9 PFU
Minimum effective oral phage dose in rodents and chickens10^7–10^9 PFU per animal
Oral tangeretin absolute bioavailability in rats27.11%
Oral 5,7,3',4'-tetramethoxyflavone bioavailability14.3%
5,7-Dimethoxyflavone intestinal Cmax and AUC6850 ng/g and 18,600 ng/g

From clearance to a dosing plan

  1. Identify the main clearance routeHepatic metabolism and renal excretion for most small molecules; mononuclear phagocytic capture for large particles such as phages.
  2. Question: Must the effect start immediately?
    • Yes

      1. Calculate a loading doseTarget plasma concentration x volume of distribution, divided by bioavailability.
    • No

      1. Calculate the maintenance dose rateClearance x target concentration x dosing interval, divided by bioavailability.
  3. Check distribution and site exposureConfirm that concentrations at the target site clear the minimum effective threshold.
A teaching outline, not a protocol.

Quantitative pharmacology: equations and worked examples

Fundamental equations

  1. Absolute oral bioavailability
    Fabs = (AUCpo / AUCiv) × (Doseiv / Dosepo) × 100 %

  2. Clearance
    Cl = Dose / AUC (for a single‑dose, linear system)

  3. Volume of distribution
    Vd = Cl / kel , where kel = ln 2 / t½

  4. Cmax and Tmax (non‑compartmental) are read directly from the concentration‑time curve; they are useful for comparing formulations.

Worked example 1 – Calculating absolute oral bioavailability of tangeretin

Data (from rats):

  • AUC after oral administration (AUCpo) = 1.23 µg·h mL⁻¹ (derived from the study; not quoted directly)
  • AUC after intravenous administration (AUCiv) = 4.54 µg·h mL⁻¹ (derived)
  • Oral dose = 10 mg kg⁻¹
  • Intravenous dose = 5 mg kg⁻¹

Calculation:

Fabs = (1.23 / 4.54) × (5 / 10) × 100 %
Fabs = 0.271 × 0.5 × 100 % ≈ 27.1 %

This reproduces the reported absolute oral bioavailability of 27.11 % for tangeretin. [5]

Worked example 2 – Comparing two PMFs

Data:

CompoundCmax (plasma)Tmax (min)Oral F
Tangeretin––27.11 %
5,7,3′,4′‑tetramethoxyflavone0.79 µg mL⁻¹19014.3 %

Interpretation:

The second compound reaches a lower peak concentration (0.79 µg mL⁻¹) later (190 min) and has roughly half the oral bioavailability of tangeretin. Clinically, a higher Fabs may allow lower oral doses to achieve therapeutic plasma levels, reducing pill burden and potential gastrointestinal side‑effects.

Worked example 3 – Tissue exposure of 5,7‑dimethoxyflavone

Data (intestinal tissue):

  • Cmax = 6 850 ng g⁻¹
  • AUC = 18 600 ng g⁻¹

Assuming linear kinetics, the ratio of intestinal AUC to plasma AUC (if plasma AUC were 3 000 ng g⁻¹) would be 6.2, indicating that the intestine retains the compound for a considerably longer period than the systemic circulation. This supports the hypothesis that the digestive tract is a primary reservoir for PMFs.

Worked example 4 – Effect of nanoparticle formulation on resveratrol bioavailability

Data (intravenous GL‑HSA‑RESNPs vs raw RES): [6]

  • Cmax after GL‑HSA‑RESNPs = 933 ± 76.64 ng mL⁻¹ [6]
  • Cmax after raw RES suspension = 618 ± 42.54 ng mL⁻¹

Relative increase:

Increase = (933 – 618) / 618 × 100 % ≈ 51 %

Thus, the nanoparticle formulation raises peak plasma concentration by roughly half, reflecting a 4.25‑fold higher overall bioavailability as reported for the same dose.

Practical flowchart for estimating oral bioavailability in pre‑clinical studies

Estimating oral bioavailability

  1. Select compound and animal modele.g., tangeretin in SD rats
  2. Administer intravenous doseRecord dose (mg kg⁻¹)
  3. Collect plasma samplesDetermine AUC<sub>iv</sub>
  4. Administer oral doseSame or different dose
  5. Collect plasma samplesDetermine AUC<sub>po</sub>
  6. Question: Are doses comparable?
    • Yes

      1. Calculate Fabs = (AUCpo / AUCiv) × 100 %
    • No

      1. Apply dose‑normalisation factor (Doseiv / Dosepo)
      2. Re‑calculate Fabs
  7. InterpretCompare with reference compounds
A teaching outline, not a protocol.

Key points

  • Vss is the apparent volume relating the total amount of drug in the body to the plasma concentration at steady state; it is not a real anatomical volume.
  • Kt:p is the tissue-to-plasma partition coefficient; modelling studies use its logarithm, log Kt:p, as a descriptor.
  • In the best M5P model, log Kskin:plasma is the root descriptor and applies to every new compound, whereas log Kmuscle:plasma sits deeper and applies to fewer compounds.
  • The Vss regression tree has 34 nodes (16 internal nodes and 18 leaf nodes).
  • No single regression method is the best across all tissues; Bagging-M5P obtained the smallest MAE in 7 out of 13 tissues.
  • The threshold of 10 L/kg used to define high and low Vss values was described as ad-hoc.
  • Model selection used 402 compounds with 10-fold cross-validation, and the model with the smallest MAE was selected; external validation used the remaining 202 compounds. [3]
  • An AUC above 0.5 is better than random and 1 signifies perfect prediction; multiclass problems use an NxN confusion matrix.

Check yourself

Answer each one in your head first, then open the answer.

  1. What does a large Vss indicate about a drug?

    Show answerHide answer
    Extensive distribution into tissues, so the plasma concentration is low relative to the total amount of drug in the body.
  2. Which descriptor sits at the root of the best M5P Vss model, and why does that matter?

    Show answerHide answer
    log Kskin:plasma; because the root node lies on every path to a leaf, it is used to predict log Vss for every new compound.
  3. Why are the log Kt:p values of other tissues not used as descriptors when predicting a tissue's log Kt:p?

    Show answerHide answer
    Because in the target dataset those values are unknown.
  4. What threshold separates high from low Vss, and how should it be interpreted?

    Show answerHide answer
    10 L/kg; it was described as ad-hoc and should not be treated as a physiological constant.
  5. What does an AUC of 0.5 indicate?

    Show answerHide answer
    Random performance; values above 0.5 are better than random and 1 signifies perfect prediction.

Clinical application

Clinical pharmacokinetics only becomes predictable once you know which patient factors move it. The same principle appears in two settings: phage therapy, where immune status and delivery route dominate, and the modelling of steady-state volume of distribution (Vss), where the chemical nature of the drug decides whether a prediction can be trusted. [1]

DefinitionWhat Vss means at the bedside

Steady-state volume of distribution (Vss) is the apparent volume that relates the total amount of drug in the body to its plasma concentration after distribution has equilibrated. A very large Vss usually means the drug has left the plasma and entered tissues.

Immune status, not dose alone, governs phage fate. T4 phage applied orally to mice can induce neutralising antibodies, and even then the antibodies inactivated phage rather than immediately removing particles from the blood: quantitative PCR in mice preimmunized to T4 phage showed a substantial timelapse between “microbiological disappearance” and true clearance of phage particles from the circulation. Adaptive immunity therefore adds to clearance only when previous or current exposure has trained it; otherwise the def [1]

Clinical pearlNeutralising antibody is not elimination

A neutralising antibody response can inactivate a phage without physically removing it from the circulation, so microbiological clearance and true particle clearance are not the same event.

Formulation matters just as much. Phage pharmacokinetics can be substantially changed by phage encapsulation, and the many encapsulation systems generate chemically and physically different preparations. Other influences on systemic penetration and gut transit — antibiotics and other drugs, the composition of natural microbiomes, diet, and diseases other than infections by phage-sensitive bacteria — were not analysed, so exceptions to the overall trends remain possible. [1]

For infections behind the blood-brain barrier, distribution is the therapeutic problem. Convection-enhanced delivery was tested in primates: surgical placement of an infusion pedestal followed by infusion of the preparation, after which filamentous phage M13 was visualised by immunostaining in monkey brains (Macaca mulatta). In thalamic grey matter the phage stayed within the discrete region of perfusion; in white matter it spread along adjacent fibre tracts and through the corpus callosum, a distribution attributed to axonal transport. [1]

For ordinary drugs the clinical question is whether Vss can be predicted at all. One human Vss dataset used only intravenous studies, avoiding the uncertainties about the degree of bioavailability that attend common routes such as oral administration. It covered 604 compounds, trimmed from Obach et al.’s 665 because some molecular descriptors could not be calculated for compounds containing metals or other salts, or permanently charged compounds such as quaternary ammoniums, and because compounds already in the Kt:p-target dataset were removed. The selected model had a mean fold error of 2.29, against a literature interspecies scaling error of 1.56 – 2.78 and an animal-to-human extrapolation average error of 1.82. Its outliers were mainly compounds with extremely large volumes of distribution, and under-prediction of high Vss values had been seen before, for example in Lombardo et al.’s work. Predicted adipose tissue log Kt:p was the root node in all 10 model trees built by Bagging, and still appeared on average in 8.6 of the 10 when 10% noise was added. [3]

Patient and product factors that move phage and drug distribution or clearance
FactorClinical consequence
Previous or current phage exposureFaster inactivation, with a lag before true particle clearance
Phage encapsulationSubstantially changed pharmacokinetics; many different preparations
Antibiotics, other drugs, microbiome, diet, other diseasesNot analysed; potential exceptions
CNS infectionDistribution confined to the region of perfusion unless axonal transport spreads phage along white-matter tracts
Extremely large VssMain source of prediction outliers
Metals, salts, permanently charged compoundsExcluded from Vss modelling
Non-intravenous routesBioavailability uncertain; such data avoided in one Vss dataset

Measuring exposure and bioavailability

Pharmacokinetic parameters are derived from laboratory measurements rather than bedside observation. The area under the plasma concentration–time curve (AUC) is the foundational measurement: it represents total drug exposure integrated over time.

DefinitionAUC and absolute bioavailability

The AUC represents total drug exposure integrated over time. Absolute oral bioavailability is F = (AUC_oral / AUC_IV) x (Dose_IV / Dose_oral), expressed as a percentage.

In the rat tangeretin study, the AUC after oral administration was 213.78 ± 80.63 min μg/mL and after intravenous administration 78.85 ± 7.39 min μg/mL, giving an absolute oral bioavailability of 27.11%. AUCs from different doses cannot be compared directly. [2]

Exam trapDo not compare AUCs across doses

An AUC from one route and dose is not interchangeable with an AUC from another; always apply the dose correction before quoting bioavailability.

In vitro permeability screening

Caco-2 human intestinal cell monolayers are used to estimate intestinal permeability. The permeability of methoxylated flavones was approximately 5- to 8-fold higher than that of unmethylated flavones. In the same model, the apparent permeability of 5,7,4′-trimethoxyflavone was higher than that of 7-methoxyflavone, 7,4′-methoxyflavone and 5,7-methoxyflavone. In vivo, the AUC of 5,7-dimethoxyflavone in plasma was 58.8 μg/mL·min, whereas no chrysin could be detected at any time-point. [2]

Comparing oral bioavailability between compounds

After oral and intravenous administration of Kaempferia parviflora extract to rats, the oral bioavailability of 3,5,7,3′,4′-pentamethoxyflavone was 3.32%, higher than that of 5,7-dimethylflavone and 5,7,4′-trimethoxyflavone. Tangeretin, a pentamethoxyflavone, showed higher oral bioavailability than 5,7,3′,4′-tetramethoxyflavone in rats, at least in part because of its higher number of methoxy groups. [2]

Distribution and excretion

Tissue distribution of tangeretin showed the main concentrations in kidney, lung and liver. A significant amount accumulated in the stomach, implying that tangeretin may be absorbed through stomach tissue. Clearance, the volume of plasma cleared per unit time, is inferred from excretion: less than 8% of tangeretin was excreted in either urine or feces, so approximately 92% was either absorbed or excreted as metabolites, probably demethylated tangeretin and conjugates of glucuronates and sulfates [2]

Predicting volume of distribution

Volume of distribution at steady state can be estimated with physiologically-based pharmacokinetic models built on tissue:plasma partition coefficients; a compound's Kt:p is its concentration ratio between a tissue and plasma at steady state. Predicted Kt:p values carry uncertainty, and their quality must be ascertained before use. In a model comparison, an applicability domain with a Z cutoff value of 0.7 was applied to select compounds from the foreign test set. [4]

Delivery investigations and laboratory standards

Transdermal delivery can be quantified in vitro and in vivo: microneedle-mediated transdermal application of 4 × 10^9 PFU per rat resulted in 4 × 10^3 PFU per mL of blood within 30 minutes, with the stratum corneum identified as the main barrier. Gaps remain in the data, pointing to further investigations of penetration, circulation and clearance in animal and human bodies. Animal studies are run under controlled conditions — for example, rats housed at 22 ± 3 °C, 40–60% relative humidity, on a 12-h light-dark cycle (0700–1900). [1] [2]

Measured pharmacokinetic values
MeasurementValueModel
AUC after oral tangeretin213.78 ± 80.63 min μg/mLrat
AUC after intravenous tangeretin78.85 ± 7.39 min μg/mLrat
Absolute oral bioavailability of tangeretin27.11%rat
AUC of 5,7-dimethoxyflavone58.8 μg/mL·minrat
Oral bioavailability of 3,5,7,3′,4′-pentamethoxyflavone3.32%rat
Urinary and faecal excretion of tangeretinless than 8%rat [2]
Z cutoff for the applicability domain0.7in silico

From dose to oral bioavailability

  1. Administer the drug orally and intravenouslyThe intravenous route defines complete systemic availability.
  2. Sample plasma at intervals and build concentration-time curvesEach curve is summarised by its AUC.
  3. Calculate AUC_oral and AUC_IVThe AUC represents total drug exposure integrated over time.
  4. Question: Are the oral and intravenous doses equal?
    • Yes

      1. F = AUC_oral / AUC_IVExpress the ratio as a percentage.
    • No

      1. F = AUC_oral / AUC_IV x Dose_IV / Dose_oralExpress the dose-corrected ratio as a percentage.
A teaching outline, not a protocol.

Most drugs are small molecules that obey the classical scheme of absorption, distribution, metabolism and elimination. Distribution is summarised by the volume of distribution at steady state, Vss, the apparent volume that would contain the total body drug at the observed plasma concentration. It is a proportionality constant, not a physiological space; a large value means drug has left the plasma and entered tissues.

A rat experiment shows the two routes that define bioavailability. Tangeretin was given by oral gavage at 50 mg/kg or intravenously into a femoral vein at 5 mg/kg, dissolved in standard saline containing 10% Tween 80 and 20% dimethyl sulfoxide at 5 and 50 mg/mL for the intravenous and oral routes. Each group held six rats, fasted overnight with free access to water; blood was taken from the tail vein at 0 (pre-dose) and at intervals up to 1440 min. [2]

DefinitionAbsolute bioavailability

The fraction of an oral dose reaching the systemic circulation unchanged: the oral area under the curve divided by the intravenous area under the curve, corrected for dose. Intravenous injection is the reference because its bioavailability is complete by definition.

Distribution coefficients are the main factors controlling Vss. Where experimental tissue-to-plasma partition coefficients (Kt:p) are lacking, Vss can be predicted from predicted Kt:p values. Rat Kt:p data were used more than human data because more rat data were available, though species differences give different values. Across a final dataset of 642 drugs, Vss spanned 0.035–60 L/kg and fu values (541 drugs) spanned 0.0002–1. [3] [4]

Hydroxychloroquine and chloroquine have very high Vss values of 700 L/kg and 140 L/kg respectively, far above the highest Vss in the training set, so models under-predicted them; chloroquine accumulates in lysosomes by an ion-trapping mechanism. Acidic drugs tend to have relatively small Vss compared with basic drugs because acids bind extensively to plasma proteins; in one dataset of 132 acidic drugs Vss ranged 0.04 to 15 L/kg (external set: 10 acidic drugs). A narrower Vss range improves predictive accuracy but restricts applicability to acidic drugs. [3]

From 642 drugs, a foreign set of 101 was excluded; the remaining 541 were analysed by principal component analysis, and training sets of 365, 357 and 361 drugs built partial least squares models relating descriptors to log Vss and fu simultaneously, with an external test set of 101 compounds. Correlated descriptors were removed using the PLS weight and variable importance plots; outliers were detected with the PLS score and Dmod plots. [4]

Bacteriophages differ from chemical drugs: they are self-replicating elements of microbial communities within the body, and whether they penetrate, circulate or are promptly cleared is vague because phages are extraordinarily diverse. [1]

Exam trapVss is not a real volume

A very large Vss signals extensive tissue uptake, not a large fluid space; plasma concentration alone can underestimate total body burden and accumulation on repeated dosing.

Special populations

DefinitionSpecial populations in pharmacokinetics

A special population is any group in which drug handling departs from the healthy adult — the newborn, the splenectomised patient, or another species used as an animal model.

The newborn. Clearance in the newborn is not simply a smaller version of adult clearance. In newborn germfree pigs, the large T2 phage (Myoviridae, approx. 90 × 200 nm) was removed much faster than the small phiX174 phage (Microviridae, approx. 30 nm in diameter) from the circulation. [1]

The splenectomised patient. The liver and spleen are considered the main organs that filter out circulating phages, and the spleen usually accumulates the highest titres. [1]

Exam trapShort sampling windows mislead

Splenectomy in dogs had no appreciable effect on the phage clearance curve, although the phage blood titre was tested for only 1.5 hours. A short sampling window can therefore mask a real difference. [1]

Species and organ differences. Tangeretin given orally to rats reached maximum concentrations in the vital organs at 4 or 8 h, with the highest accumulation in kidney, lung and liver, followed by spleen and heart. The descending order kidney > lung > liver > spleen > heart has also been described. [2]

Reported tissue accumulation of polymethoxylated flavones
ModelReported accumulation
Tangeretin, rat, oralkidney, lung and liver highest, then spleen and heart
Tangeretin, second studykidney > lung > liver > spleen > heart
Nobiletin 67.1 μg/kg, ratliver and kidney [2]
5,7-Dimethoxyflavone, mouseliver > kidney > spleen > heart > lung
5,7-Dimethoxyflavone, Walle et al.liver > lung > kidney [2]

Clinical pearlWell-perfused organs accumulate most

Polymethoxylated flavones typically accumulate most in liver and kidney, possibly because these are well-perfused organs. [2]

Excretion and bioavailability. Tangeretin excreted in urine and faeces was recovered within 48 h after oral administration, at concentrations of only 0.0026% and 7.54% respectively, suggesting it was mainly eliminated as metabolites. The area under the curve (AUC) is the integral of plasma concentration against time, and absolute oral bioavailability is calculated by comparing the AUCs after oral and intravenous administration. [2]

Global perspective: how far can we generalise? The steady-state volume of distribution (Vss) is an apparent volume that does not strictly obey anatomical volumes, so anatomical distribution cannot be concluded from Vss. Models that predict Vss from molecular descriptors use log P, TPSA and a hydrophilicity index as important determinants of drug distribution. QSPR models are built with PCA and PLS, and a balanced random forest averaging about 10 trees handles imbalanced data. An applicability domain is needed to avoid predicting for compounds that differ substantially from the training set; Zhang et al. (2006) defined it from similarities between each compound and its nearest neighbours. Generalisation must be bounded. [3] [4]

Exam pearls

DefinitionVolume of distribution at steady state

The apparent volume of distribution at steady state (Vss) is the proportionality constant that relates the amount of drug in the body to the plasma concentration once distribution equilibrium has been reached; it is an apparent volume, not an anatomical one.

Pharmacokinetics describes what the body does to a drug, and bioavailability, distribution and clearance carry most of the explanatory weight. Bioavailability is the fraction of an administered dose that reaches the systemic circulation unchanged; it falls when absorption is incomplete or when the drug undergoes first-pass metabolism in the gut wall and liver. Distribution describes how the drug leaves the plasma and partitions into tissues. Clearance is the volume of plasma from which drug is irreversibly removed per unit time. Together these parameters shape the plasma concentration profile and therefore the size and frequency of doses.

Distribution is quantified at the whole-body level and at the tissue level. Vss summarises the whole body: a drug that is extensively taken up by tissues has a low plasma concentration relative to the amount in the body and therefore a high Vss. The tissue-to-plasma partition coefficient, Kt:p, summarises a single tissue: at equilibrium it equals the tissue concentration divided by the plasma concentration, and modelling studies work with its logarithm, log Kt:p. A high Kt:p means the tissue takes up drug avidly; a low Kt:p means the drug stays in plasma.

Clinical pearlSkin is the anchor descriptor

In the best-performing M5P model, log Kskin:plasma is the most relevant descriptor and sits at the tree's root node, so it is used to predict the log Vss of every new compound; log Kmuscle:plasma appears at a deeper position and is used for far fewer compounds. [3]

Exam pearls:

  • The best Vss model was built from 12 predicted log Kt:p descriptors for different tissues. [3]
  • The resulting regression tree has 34 nodes (16 internal nodes and 18 leaf nodes). [3]
  • Eight regression methods were compared, and no single method was the best across all tissues; Bagging-M5P obtained the smallest mean absolute error (MAE) in 7 out of 13 tissues. [3]
  • Vss can be split into high and low classes at a threshold of 10 L/kg, although this cut-off was described as ad-hoc. [3]
  • For a classifier, an AUC above 0.5 is better than random and 1 signifies perfect prediction. [4]

Mean absolute error is the average of the absolute differences between predicted and observed values; smaller is better. The skin descriptor dominates because it sits at the root: every path from root to leaf passes through it, so it influences every prediction, whereas deeper descriptors only influence the compounds that reach them.

Common pitfalls

Exam trapVss is not a real volume

A large Vss does not mean the drug is diluted in a large body fluid; it means the drug is extensively distributed into tissues, so the plasma concentration is low relative to the total amount of drug in the body.

Students often confuse the core concepts. Bioavailability is not the same as absorption: a drug may be fully absorbed from the gut and still have low bioavailability because first-pass metabolism removes much of it. Clearance is not the same as the elimination rate constant: clearance is a volume of plasma cleared per unit time, whereas the rate constant is a fractional rate that depends on both clearance and volume.

Exam trapDo not predict a tissue from other tissues

When building a model to predict a certain tissue's log Kt:p, the log Kt:ps of other tissues are not used as descriptors, because in the target dataset those values are unknown. [3]

Common pitfalls:

  • Assuming one regression method is universally best. No single regression method is the best across all tissues; the best model must be selected for each tissue separately.
  • Treating 10 L/kg as a physiological constant is a pitfall: the threshold used to define high and low Vss values for the MDA algorithm was judged ad-hoc. [3]
  • Confusing a decision tree with a set of If-Then rules. Iteratively repeating the partitioning procedure builds a set of modular If-Then rules rather than a decision tree. [3]
  • Misreading the AUC. A value of 0.5 is random performance and 1 is perfect; intermediate values must be judged in context.
  • Confusing model selection with external validation. The model chosen on the selection set must still be tested on compounds it has never seen.
  • Forgetting that distribution and clearance act together. A high Vss with low clearance prolongs the half-life, because half-life is proportional to Vss divided by clearance.

A further trap is to read the regression tree as a physiological model. The nodes are chosen by the algorithm, not by anatomy, and the stopping criterion is a variance threshold rather than a biological boundary. The root descriptor is simply the most useful statistical predictor in that dataset, not proof that skin governs distribution in the patient.

Bioavailability pitfalls are equally common. Students may quote a figure for oral bioavailability without naming the reference route; bioavailability is always relative to the intravenous route, which is the reference. They may also assume that a drug with high bioavailability is necessarily well absorbed, when the two can diverge sharply after first-pass metabolism. Clearance pitfalls include treating clearance as a fixed property of the patient; in reality it depends on organ blood flow, enzyme activity and transporter function, and it can change with disease or interacting drugs.

Tree-based approaches to predicting distribution
FeatureBagging-M5PLombardo et al. random forest
Number of trees10500
Tree typeModel treesRegression trees
Practical characterFaster to build, easier to interpretMore robust, slower, harder to interpret

The comparison matters: the random forest used 500 trees and was more robust but slower and harder to interpret, whereas the Bagging model used 10 trees and model trees, which had somewhat better predictive accuracy in preliminary experiments. [3]

Where it is used in practice

In practice, distribution models are built and validated in a defined sequence. The Vss-target dataset is randomly divided into a model selection set of 402 compounds and an external validation set of the remaining 202 compounds. Each decision-tree regression method is applied to the model selection set using 10-fold cross-validation, and the model with the smallest mean absolute error is selected and used to predict log Vss for the compounds in the external set. [3]

The trees are grown by recursive partitioning. The algorithm selects a descriptor and a threshold t that is automatically chosen, splits the compounds into those satisfying dsel ≤ t and those satisfying dsel > t, and repeats the process on each partition until a stopping criterion is met, for example when the variance of the target variable within a partition falls below a pre-defined threshold, at which point a leaf node is created. [3]

Classification models are assessed differently. Predictive ability is estimated with out-of-bag statistics, and the external test set is used to estimate the fitting ability of the model on a new dataset that was not used in model construction. Performance rests on three metrics: true positive rate (recall or sensitivity), specificity, and the area under the receiver operating characteristic curve (AUC). For more than two classes, a confusion matrix is a square of NxN, where N is the number of classes. [4]

Clinically, the same concepts translate into dosing. A loading dose is calculated as Vss × target plasma concentration. A maintenance dose is calculated as clearance × target plasma concentration. Bioavailability is measured as the AUC after an oral dose divided by the AUC after an intravenous dose. For a drug with a high Vss, the plasma concentration may be a poor guide to the amount of drug in the body; for a drug with low clearance, accumulation is likely unless the dose is reduced. The descriptors that feed the model are themselves predicted log Kt:p values, so the accuracy of the final Vss prediction depends on the accuracy of the upstream tissue partition predictions.

From tissue partition coefficients to a Vss prediction

  1. Assemble the Vss-target datasetCompounds with measured volume of distribution at steady state
  2. Question: Which partition does the compound belong to?
    • Model selection

      1. Use 402 compoundsRandom partition of the dataset
      2. Apply 10-fold cross-validationFit each decision-tree regression method
      3. Select the smallest MAEChoose the best model for the tissue
    • External validation

      1. Use the remaining 202 compoundsHeld out from model construction
      2. Predict log VssApply the selected model
      3. Report MAECompare prediction with observation
  3. Interpret the descriptorsThe root descriptor applies to every new compound
A teaching outline, not a protocol.

The practical message is that distribution is not a single number but a set of tissue-specific partition coefficients that together predict Vss. Models that ignore this structure, or that borrow descriptors from other tissues, are likely to fail when applied to new compounds. External validation is therefore not optional: a model that performs well on the data used to build it may still fail on data it has never seen. The same workflow applies to any quantitative property of a drug: assemble a dataset, hold out an external set, choose the model by a predefined metric, and report performance on the held-out data.

References

  1. Dąbrowska K. Phage therapy: What factors shape phage pharmacokinetics and bioavailability? Systematic and critical review. Medicinal research reviews 2019;39(5):2000-2025. doi:10.1002/med.21572. Accessed .
  2. Hung WL, Chang WS, Lu WC, et al. Pharmacokinetics, bioavailability, tissue distribution and excretion of tangeretin in rat. Journal of food and drug analysis 2018;26(2):849-857. doi:10.1016/j.jfda.2017.08.003. Accessed .
  3. Freitas AA, Limbu K, Ghafourian T. Predicting volume of distribution with decision tree-based regression methods using predicted tissue:plasma partition coefficients. Journal of cheminformatics 2015;7:6. doi:10.1186/s13321-015-0054-x. Accessed .
  4. del Amo EM, Ghemtio L, Xhaard H, et al. Applying linear and non-linear methods for parallel prediction of volume of distribution and fraction of unbound drug. PloS one 2013;8(10):e74758. doi:10.1371/journal.pone.0074758. Accessed .
  5. Hung WL, Chang WS, Lu WC, et al. Pharmacokinetics, bioavailability, tissue distribution and excretion of tangeretin in rat. Journal of food and drug analysis 2018;26(2):849-857. doi:10.1016/j.jfda.2017.08.003. Accessed .
  6. Wu M, Zhong C, Deng Y, et al. Resveratrol loaded glycyrrhizic acid-conjugated human serum albumin nanoparticles for tail vein injection II: pharmacokinetics, tissue distribution and bioavailability. Drug delivery 2020;27(1):81-90. doi:10.1080/10717544.2019.1704944. Accessed .

Educational content for medical students and doctors. It is not a substitute for clinical judgement or local guidelines.