A Novel Mechanistic Approach to Predict the Steady State Volume of Distribution (Vss) using the Fick-Nernst-Planck Equation
Lu Gaohua, David B. Turner, Ciaran Fisher, Ariane Emami Riedmaier, Helen Musther, Iain Gardner and Masoud Jamei
Simcyp Limited (a Certara Company)
Objectives: The notion that unbound, unionized drug concentrations are in equilibrium between intracellular and extracellular water at steady state is a key assumption of some in silico methods for predicting tissue:plasma ratio (kp) and volume of distribution at steady state (Vss) [1, 2], Mathematically this is expressed as Kpuu,uu = 1. However, there is evidence that ionised drug species can also cross membranes (albeit at a lower rate than unionised drug) and that membrane potential and pH differences across membranes could result in Kpuu,uu having values not equal to 1. The Rodgers and Rowland method (R&R) for predicting Kp and Vss [1, 2] has been extended to account for electrolyte passive permeability across cell membranes.
Methods: Membrane potential is incorporated into the physiologically-based pharmacokinetic (PBPK) model [1-3] to account for the passive permeation of both neutral molecules (Fick’s law) and ionized molecules (Nernst-Planck equation) across the cell membranes. Kpuu,uu is derived from the steady-state Fick-Nernst-Planck equation. The Kp and Vss prediction algorithm in R&R method is revised to use non-unity values of Kpuu,uu. The new method is tested using a library of compounds (n = 71, including 7 neutral compounds, 35 monoprotic bases, 12 monoprotic acids, 6 diprotic bases and 11 ampholytes). The performance of the new method is compared to the predicted Vss from the R&R method as well as the observed Vss.
Results: Assuming a, physiologically reasonable, membrane potential (-10 mV for red blood cells and -41 mV for tissue cells) and passive permeability for electrolytes (2-4 log-unit lower than neutral molecules), Kpuu,uu > 1 was predicted for basic compounds and Kpuu,uu < 1 for acidic compounds. Compared to the R&R method, the new method predicted higher Vss for basic compounds, but lower Vss for acidic compounds. The new method improved Vss prediction for strong bases (pKa > 7; n = 22). Vss was predicted within 2 or 3 -fold of observed values for 16 and 20 compounds, respectively. In contrast, the classic R&R method predicted Vss within 2 or 3 -fold of observed values for 13 and 17 compounds, respectively.
Conclusions: The results show accounting for electrolyte passive permeation has an impact on the prediction of Vss and the predictions for the strongly basic compounds investigated was improved. Further research is required to investigate the model performance for a bigger dataset.
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