Biomechanics and Modeling in Mechanobiology

, Volume 18, Issue 4, pp 1111–1122 | Cite as

A computational fluid dynamics approach to determine white matter permeability

  • Marco VidottoEmail author
  • Daniela Botnariuc
  • Elena De Momi
  • Daniele Dini
Original Paper


Glioblastomas represent a challenging problem with an extremely poor survival rate. Since these tumour cells have a highly invasive character, an effective surgical resection as well as chemotherapy and radiotherapy is very difficult. Convection-enhanced delivery (CED), a technique that consists in the injection of a therapeutic agent directly into the parenchyma, has shown encouraging results. Its efficacy depends on the ability to predict, in the pre-operative phase, the distribution of the drug inside the tumour. This paper proposes a method to compute a fundamental parameter for CED modelling outcomes, the hydraulic permeability, in three brain structures. Therefore, a bidimensional brain-like structure was built out of the main geometrical features of the white matter: axon diameter distribution extrapolated from electron microscopy images, extracellular space (ECS) volume fraction and ECS width. The axons were randomly allocated inside a defined border, and the ECS volume fraction as well as the ECS width maintained in a physiological range. To achieve this result, an outward packing method coupled with a disc shrinking technique was implemented. The fluid flow through the axons was computed by solving Navier–Stokes equations within the computational fluid dynamics solver ANSYS. From the fluid and pressure fields, an homogenisation technique allowed establishing the optimal representative volume element (RVE) size. The hydraulic permeability computed on the RVE was found in good agreement with experimental data from the literature.


Convection-enhanced delivery Hydraulic permeability Representative volume element White matter 



We kindly thank Prof. Dr. Almut Schüz (Max Planck Institute for Biological Cybernetics—Tübingen) for providing the TEM images dataset. Daniele Dini would like to acknowledge the support received from the EPSRC under the Established Career Fellowship Grant No. EP/N025954/1.


This project has received funding from the European Unions Horizon 2020 research and innovation programme under Grant Agreement No. 688279.

Compliance with ethical standards

Conflict of interest

The authors declare that they have no conflict of interest.


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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Department of Electronics, Information and BioengineeringPolitecnico di MilanoMilanItaly
  2. 2.Department of Mechanical EngineeringImperial College LondonLondonUK
  3. 3.Faculty of ScienceUniversity of LisbonLisbonPortugal

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