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Distribution

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Volume of distribution

The volume of distribution (Vd) is a pharmacokinetic parameter that describes the apparent space in the body available to contain a drug. It is not a physical volume but rather a mathematical concept used to characterize the distribution of a drug between the bloodstream and the rest of the body tissues.
The formula for calculating the volume of distribution is:


Vd = Amount of drug in the body / Concentration of drug in the plasma[ 1 ]

Vd helps to estimate how extensively a drug distributes into tissues after administration. A high volume of distribution suggests that the drug is extensively distributed into tissues, while a low volume of distribution indicates that the drug remains primarily in the bloodstream.

The volume of distribution can be influenced by various factors, including the drug's physicochemical properties, tissue binding, and lipid solubility. It is an important parameter in pharmacokinetics as it provides insights into the distribution characteristics of a drug within the body, which, in turn, can impact its therapeutic effectiveness and potential for side effects.

Tissue-to-plasma ratios

The tissue-to-plasma ratio, also known as the partition coefficient, is a pharmacokinetic parameter that quantifies the distribution of a drug between tissues and plasma. It represents the ratio of drug concentration in a specific tissue to its concentration in the plasma at a given point in time.

This ratio provides insights into the extent of a drug's distribution into tissues relative to its concentration in the bloodstream. A tissue-to-plasma ratio greater than 1 indicates that the drug has a higher concentration in the tissue compared to the plasma, suggesting good tissue penetration. Conversely, a ratio less than 1 implies that the drug is more concentrated in the plasma than in the tissue.

The tissue-to-plasma ratio is a valuable parameter for understanding the pharmacokinetics of a drug, especially regarding its distribution into specific target tissues or organs. Different tissues may have varying affinities for a drug, and the tissue-to-plasma ratio helps assess the drug's propensity to accumulate in certain areas of the body.

It's important to note that the tissue-to-plasma ratio is influenced by factors such as the drug's physicochemical properties, lipid solubility, tissue binding, and the presence of transporters. Additionally, this ratio is often measured at specific time points after drug administration to capture the dynamic distribution process.

Vd Calculator

There are various Vd methods in the literature to compute the TP ratios and only three methods are currently available on Teoreler:

  1. Poulin and Theil1
  2. Berezhkovskiy7
  3. Rodgers & Rowland2-4
  4. Schmitt et al. 20205

Validation of methods

The above methods from literature have been validated using provided equations and datasets from respective articles. The comparison between observed and predicted volume of distribution (L/kg) for various drugs is presented below, highlighting the effectiveness of different methods to predict TP ratios and steady state volume of distribution.

Interactive comparison

The following plots show a visual comparison of the calculated volume of distribution and tissue-to-plasma ratios using various methods against observed data for various drugs. The observed volume of distribution and tissue-to-plasma ratio values were obtained from Poulin and Theil1, Berezhkovskiy7, Rodgers & Rowland2-4 and Schmitt et al. 20205 manuscripts and compared using various methods. The data can be filtered using available Vd methods, property of the drug, log P and tissue.

Observed vs. Calculated Vd

Observed vs. Calculated Kpu

Poulin and Theil

Poulin and Theil are one of the earliest to develop a method to describe the TP ratios and volume of distribution based on drug physicochemical properties that had a significant improvement over previously reported methods and works for a wide variety of drugs. In 2001, they have validated their method for 148 drugs in total (both human and rat). This method works well for Neutral compounds and also for compounds with a higher LogP (> 3).
The following plots show the prediction outcome of using Teoreler in both humans and rats against the predicted value reported by Poulin and Theil, 2001. The dotted lines indicate a 3-fold window.

Further validation was done against observed data and a comparison against Teoreler predicted and Poulin predicted published against observed data demonstrates acceptable AFE values.

Berezhkovskiy

Leonid M. Berezhkovskiy7 modified Poulin and Theil's equation to eliminate the assumption that tissue partition between tissue lipids, water and extracellular water space is mainly governed by passive distribution. Since Berezhkovskiy method has not reported any predicted Kpus and Vu,ss values, the validation of this method was done against available Vu,ss and experimental Kpus from Poulin and Theil1 and Rodgers and Rowland2-4 manuscripts.

Rodgers and Rowland

Rodgers, Leahy and Rowland published an improvised method in 2005 for moderate-to-strong basic compounds and further elaborated the method for remaining compounds in a manuscript published in 2006.2-4 This Vd method works well for most of the compounds with different properties and having a log P < 3.

Comparison between published observed data for various drugs against Teoreler predicted values using Rodgers and Rowland method2-4 in humans and rats returned an acceptable average fold error (AFE) of 0.9426 and 1.0175 respectively as shown below:

Validation was also done against available unbound tissue-to-plasma ratios (Kpu) of various organs and tissue of various drugs. Below is the comparison of the values predicted using Teoreler against predicted values from Rodgers and Rowland and also against experimental values. The AFE values are presented in the plots below:

Schmitt et al. 2020

Schmitt et al. further elaborated Rogers and Rowland method based on lysosomal entrapment of drug. Earlier work by Schmitt et al. in 2019 provided evidence of lysosomal trapping of basic lipophilic drugs potentially impacting the overall drug distribution.6 Schmitt et al. 2020 have expanded Rogers and Rowland method to include lysosomal trapping for basic drugs. This enhanced version of Vd method is more precise for basic drugs and is identical to Rogers and Rowland for other compounds.

Comparison between Schmitt's validation against Teoreler predicted values using modified Rodgers and Rowland method in rats returned an acceptable average fold error (AFE) of 0.9542 and 1.0492 for tissue-to-plasma ratios and unbound volume of distribution at steady state respectively as shown below:

Complete Validation of methods - Raw data

A detailed validation of the Vd methods is available to download from this link.

PBPK models

For PBPK modelling, a 'Distribution scalar' option is provided for the users, found in the 'Optional Inputs' tab that allows users to input a scalar value. This scalar modifies all predicted tissue-to-plasma (TP) ratios by the entered value. The default factor is 1, indicating no scaling. The volume of distribution in the simulated output table is presented in L/kg.


References

  1. Poulin P, Theil FP. Prediction of pharmacokinetics prior to in vivo studies. 1. Mechanism-based prediction of volume of distribution. J Pharm Sci. 2002 Jan;91(1):129-56. https://doi.org/10.1002/jps.10005
  2. Rodgers T, Rowland M. Physiologically based pharmacokinetic modelling 2: Predicting the tissue distribution of acids, very weak bases, Neutrals and Zwitterions. Journal of Pharmaceutical Sciences. 2006;95(6):1238-57. https://doi.org/10.1002/jps.20502
  3. Rodgers T, Leahy D, Rowland M. Physiologically Based Pharmacokinetic Modeling 1: Predicting the Tissue Distribution of Moderate-to-Strong Bases. Journal of Pharmaceutical Sciences. 2005;94(6):1259-76. https://doi.org/10.1002/jps.20322
  4. Rodgers T, Rowland M. Mechanistic Approaches to Volume of Distribution Predictions: Understanding the Processes. Pharmaceutical Research. 2007;24(5):918-33. https://doi.org/10.1007/s11095-006-9210-3.
  5. Schmitt MV, Reichel A, Liu X, Fricker G, Lienau P. Extension of the mechanistic tissue distribution model of Rodgers & Rowland by systematic incorporation of lysosomal trapping: impact on Kpu and volume of distribution predictions in the rat. Drug Metabolism and Disposition. 2020:DMD-AR-2020-000161. https://doi.org/10.1124/dmd.120.000161.
  6. Schmitt MV, Lienau P, Fricker G, Reichel A. Quantitation of Lysosomal Trapping of Basic Lipophilic Compounds Using In Vitro Assays and In Silico Predictions Based on the Determination of the Full pH Profile of the Endo-/Lysosomal System in Rat Hepatocytes. Drug Metabolism and Disposition. 2019;47(1):49-57. https://doi.org/10.1124/dmd.118.084541.
  7. Berezhkovskiy LM. Volume of distribution at steady state for a linear pharmacokinetic system with peripheral elimination. J Pharm Sci. 2004;93(6):1628-40. https://doi.org/10.1002/jps.20073.