The development of drugs targeting the brain still faces a high failure rate. One of the reasons is a lack of quantitative understanding of the complex processes that govern the pharmacokinetics ... Show moreThe development of drugs targeting the brain still faces a high failure rate. One of the reasons is a lack of quantitative understanding of the complex processes that govern the pharmacokinetics (PK) of a drug within the brain. While a number of models on drug distribution into and within the brain is available, none of these addresses the combination of factors that affect local drug concentrations in brain extracellular fluid (brain ECF). Here, we develop a 3D brain unit model, which builds on our previous proof-of-concept 2D brain unit model, to understand the factors that govern local unbound and bound drug PK within the brain. The 3D brain unit is a cube, in which the brain capillaries surround the brain ECF. Drug concentration-time profiles are described in both a blood-plasma-domain and a brain-ECF-domain by a set of differential equations. The model includes descriptions of blood plasma PK, transport through the blood-brain barrier (BBB), by passive transport via paracellular and transcellular routes, and by active transport, and drug binding kinetics. The impact of all these factors on ultimate local brain ECF unbound and bound drug concentrations is assessed. In this article we show that all the above mentioned factors affect brain ECF PK in an interdependent manner. This indicates that for a quantitative understanding of local drug concentrations within the brain ECF, interdependencies of all transport and binding processes should be understood. To that end, the 3D brain unit model is an excellent tool, and can be used to build a larger network of 3D brain units, in which the properties for each unit can be defined independently to reflect local differences in characteristics of the brain. Show less
Vendel, E.; Rottschäfer, V.; Lange, E.C.M. de 2020
PURPOSE\nMETHODS\nRESULTS\nCONCLUSIONS\nWe have developed a 3D brain unit network model to understand the spatial-temporal distribution of a drug within the brain under different (normal and... Show morePURPOSE\nMETHODS\nRESULTS\nCONCLUSIONS\nWe have developed a 3D brain unit network model to understand the spatial-temporal distribution of a drug within the brain under different (normal and disease) conditions. Our main aim is to study the impact of disease-induced changes in drug transport processes on spatial drug distribution within the brain extracellular fluid (ECF).\nThe 3D brain unit network consists of multiple connected single 3D brain units in which the brain capillaries surround the brain ECF. The model includes the distribution of unbound drug within blood plasma, coupled with the distribution of drug within brain ECF and incorporates brain capillaryblood flow, passive paracellular and transcellular BBB transport, active BBB transport, brain ECF diffusion, brain ECF bulk flow, and specific and nonspecific brain tissue binding. All of these processes may change under disease conditions.\nWe show that the simulated disease-induced changes in brain tissue characteristics significantly affect drug concentrations within the brain ECF.\nWe demonstrate that the 3D brain unit network model is an excellent tool to gain understanding in the interdependencies of the factors governing spatial-temporal drug concentrations within the brain ECF. Additionally, the model helps in predicting the spatial-temporal brain ECF concentrations of existing drugs, under both normal and disease conditions. Show less
A novel mathematical model describes spatial-temporal drug distribution within one or more brain units, which are cubic representations of a piece of brain tissue with brain capillaries at the... Show moreA novel mathematical model describes spatial-temporal drug distribution within one or more brain units, which are cubic representations of a piece of brain tissue with brain capillaries at the edges. The brain unit can be considered a highly representative building block of the brain in terms of drug distribution. While the focus of the model is on drug distribution within the brain ECF, the model includes descriptions of drug concentrations within the blood plasma, drug distribution via brain capillary blood flow, drug transport across the blood-brain barrier (BBB) by passive paracellular and transcellular transport as well as active transport, brain ECF diffusion, brain ECF bulk flow, non-specific binding of the drug to brain tissue, and drug target binding kinetics. We study the model with analytical methods and numerical simulations. This allows us to examine the integrated effect of the individual processes important to drug distribution and effect on the local concentration-time profiles of free and (non-)specifically bound drug. Moreover, the model allows us to generate a local distribution profile of a drug within the brain. In addition, the impact of disease-induced changes in brain-specific properties on the concentrations of drug within the brain ECF is assessed. Show less
Vendel, E.; Rottschäfer, V.; Lange, E.C.M. de 2019
The blood brain barrier (BBB) is the main barrier that separates the blood from the brain. Because of the BBB, the drug concentration-time profile in the brain may be substantially different from... Show moreThe blood brain barrier (BBB) is the main barrier that separates the blood from the brain. Because of the BBB, the drug concentration-time profile in the brain may be substantially different from that in the blood. Within the brain, the drug is subject to distributional and elimination processes: diffusion, bulk flow of the brain extracellular fluid (ECF), extra-intracellular exchange, bulk flow of the cerebrospinal fluid (CSF), binding and metabolism. Drug effects are driven by the concentration of a drug at the site of its target and by drug-target interactions. Therefore, a quantitative understanding is needed of the distribution of a drug within the brain in order to predict its effect. Mathematical models can help in the understanding of drug distribution within the brain. The aim of this review is to provide a comprehensive overview of system-specific and drug-specific properties that affect the local distribution of drugs in the brain and of currently existing mathematical models that describe local drug distribution within the brain. Furthermore, we provide an overview on which processes have been addressed in these models and which have not. Altogether, we conclude that there is a need for a more comprehensive and integrated model that fills the current gaps in predicting the local drug distribution within the brain. Show less
Vendel, E.; Rottschäfer, V.; Lange, E.C.M. de 2018
The development of drugs that target the brain is very challenging. A quantitative understanding is needed of the complex processes that govern the concentration-time profile of a drug ... Show moreThe development of drugs that target the brain is very challenging. A quantitative understanding is needed of the complex processes that govern the concentration-time profile of a drug (pharmacokinetics) within the brain. So far, there are no studies on predicting the drug concentration within the brain that focus not only on the transport of drugs to the brain through the blood-brain barrier (BBB), but also on drug transport and binding within the brain. Here, we develop a new model for a 2D square brain tissue unit, consisting of brain extracellular fluid (ECF) that is surrounded by the brain capillaries. We describe the change in free drug concentration within the brain ECF, by a partial differential equation (PDE). To include drug binding, we couple this PDE to two ordinary differential equations that describe the concentration-time profile of drug bound to specific as well as non-specific binding sites that we assume to be evenly distributed over the brain ECF. The model boundary conditions reflect how free drug enters and leaves the brain ECF by passing the BBB, located at the level of the brain capillaries. We study the influence of parameter values for BBB permeability, brain ECF bulk flow, drug diffusion through the brain ECF and drug binding kinetics, on the concentration-time profiles of free and bound drug. Show less
