- Email: [email protected]
MODELING THE CEREBRAL BLOOD FLOW USING A LINEAR SYSTEM APPROACH
Presentation O-276
Mass Transport
S279
MODELING THE CEREBRAL BLOOD FLOW USING A LINEAR SYSTEM APPROACH Johannes Reichold (1), Alfred Buck (2), Bruno Weber (3), Patrick Jenny (1)
1. Institute of Fluid Dynamics, ETH Zurich, Switzerland; 2. Nuclear Medicine,University Hospital Zurich, Switzerland; 3. Institute for Pharmacology & Toxicology, University of Zurich, Switzerland
Introduction
Results
In this work, we aim to model the cerebral blood flow (CBF) in a realistic angioarchitectural setting, by employing a linear systems approach. The ultimate goal is to further our understanding of CBF regulation in general. Imaging modalities such as magnetic resonance imaging measure CBF as a surrogate of neural activity [Logothetis, 2004]. Our model may help to deduce the corresponding point spread function that will allow for a more confident interpretation of CBF visualizations. Other possible biomedical applications include the modeling of drug delivery as well as cerebrovascular impairment [Nishimura, 2006].
Our model can be used to compute pressure and blood flow as well as oxygen transport in the fully resolved cerebral vasculature. The figure below illustrates how local changes in the vasculature effect the flow in the surrounding tissue.
Methods Synchrotron-based computed tomographies (SRCT) of formalin-fixed and barium sulphate perfused brain samples resolve the vascular tree down to capillary level [Weber, 2006]. The complex angioarchitecture in SRCT specimen is reduced to a set of nodes (bifurcation- / end-points) and segments (connections between nodes) in order to construct corresponding computational grids. A transmissibility value is assigned to each segment according to the Hagen-Poisseuille law. Pressure boundary conditions are set at the nodes of the large feeding arteries and draining veins. The introduction of mass balance equations at the node points creates a set of linear equations, which can be solved to yield the pressure at all nodes in the entire domain. In the next step, CBF is computed by multiplying the pressure difference between nodes with the transmissibility of the vessels connecting them. Oxygen transport is implemented by setting source terms at the nodes corresponding to the feeding arteries. Diffusion into the tissue is assumed proportional to the surface area of the vessels and acts as a sink term at the individual nodes. Realistic artificial vascular trees are created on which the above modeling framework is applied in addition. The construction algorithm harnesses a statistical database of the vasculature, comprising branch point density, branching angles, the number of daughter branches, as well as their directions and lengths.
16th ESB Congress, Oral Presentations, Wednesday 9 July 2008
Large change
Small change
Figure 1: CBF in macaque visual cortex. The image on the right depicts computed flow changes due to local vasodilation (circular region). The corresponding SRCT based image is shown left.
Discussion The proposed modeling framework allows to study CBF and its regulation. It has a diverse range of biomedical applications, which will be subject of future work. The limitations of the SRCT data, namely imperfect connectivity and size restrictions, can be overcome by creating realistic artificial vascular trees.
References N. K. Logothetis et al, Annu Rev Physiol, 66:735769, 2004. N. Nishimura et al, Nat Methods, 3:99-108, 2006. B. Weber et al, Quantitative aspects of the microvascular system in macaque visual cortex, Federations of European Neuroscience Societies, Wien, 2006.
Journal of Biomechanics 41(S1)
Mass Transport
S279
MODELING THE CEREBRAL BLOOD FLOW USING A LINEAR SYSTEM APPROACH Johannes Reichold (1), Alfred Buck (2), Bruno Weber (3), Patrick Jenny (1)
1. Institute of Fluid Dynamics, ETH Zurich, Switzerland; 2. Nuclear Medicine,University Hospital Zurich, Switzerland; 3. Institute for Pharmacology & Toxicology, University of Zurich, Switzerland
Introduction
Results
In this work, we aim to model the cerebral blood flow (CBF) in a realistic angioarchitectural setting, by employing a linear systems approach. The ultimate goal is to further our understanding of CBF regulation in general. Imaging modalities such as magnetic resonance imaging measure CBF as a surrogate of neural activity [Logothetis, 2004]. Our model may help to deduce the corresponding point spread function that will allow for a more confident interpretation of CBF visualizations. Other possible biomedical applications include the modeling of drug delivery as well as cerebrovascular impairment [Nishimura, 2006].
Our model can be used to compute pressure and blood flow as well as oxygen transport in the fully resolved cerebral vasculature. The figure below illustrates how local changes in the vasculature effect the flow in the surrounding tissue.
Methods Synchrotron-based computed tomographies (SRCT) of formalin-fixed and barium sulphate perfused brain samples resolve the vascular tree down to capillary level [Weber, 2006]. The complex angioarchitecture in SRCT specimen is reduced to a set of nodes (bifurcation- / end-points) and segments (connections between nodes) in order to construct corresponding computational grids. A transmissibility value is assigned to each segment according to the Hagen-Poisseuille law. Pressure boundary conditions are set at the nodes of the large feeding arteries and draining veins. The introduction of mass balance equations at the node points creates a set of linear equations, which can be solved to yield the pressure at all nodes in the entire domain. In the next step, CBF is computed by multiplying the pressure difference between nodes with the transmissibility of the vessels connecting them. Oxygen transport is implemented by setting source terms at the nodes corresponding to the feeding arteries. Diffusion into the tissue is assumed proportional to the surface area of the vessels and acts as a sink term at the individual nodes. Realistic artificial vascular trees are created on which the above modeling framework is applied in addition. The construction algorithm harnesses a statistical database of the vasculature, comprising branch point density, branching angles, the number of daughter branches, as well as their directions and lengths.
16th ESB Congress, Oral Presentations, Wednesday 9 July 2008
Large change
Small change
Figure 1: CBF in macaque visual cortex. The image on the right depicts computed flow changes due to local vasodilation (circular region). The corresponding SRCT based image is shown left.
Discussion The proposed modeling framework allows to study CBF and its regulation. It has a diverse range of biomedical applications, which will be subject of future work. The limitations of the SRCT data, namely imperfect connectivity and size restrictions, can be overcome by creating realistic artificial vascular trees.
References N. K. Logothetis et al, Annu Rev Physiol, 66:735769, 2004. N. Nishimura et al, Nat Methods, 3:99-108, 2006. B. Weber et al, Quantitative aspects of the microvascular system in macaque visual cortex, Federations of European Neuroscience Societies, Wien, 2006.
Journal of Biomechanics 41(S1)