Fabio Mangini^{1}, Laura Maugeri^{1}, Mauro DiNuzzo^{1}, Marta Moraschi^{2}, Daniele Mascali^{2}, Alejandra Sierra^{3}, Alessia Cedola^{4}, Federico Giove^{2}, and Michela Fratini^{1}

The effects of the spinal cord (SC) vessel topology on the blood oxygenation level dependent (BOLD) signal is poorly characterized. We performed numerical simulations on models of vasculature

Numerical simulations on a simplified model of SC vasculature have been performed in order to quantify the effect of the vessel micro and macro distribution in the BOLD contrast. The induced local magnetic field was determined a angular frequency, through several numerical simulations representing the vessels as the so-called Infinite Cylinder Model (ICM, see Figure 1). After that, the diffusion random walk of the water molecule was computed show a Montecarlo simulation implemented in Matlab ^{9}. The induced magnetic field was then integrated over these Brownian paths in order to calculate the accumulated phase for a particular echo time. Thanks to the knowledge of the phase, it was possible to determine the effective transverse relaxation rate constant *R _{2}**and consequently the BOLD signal

We improved the model using the COMSOL Multiphysics ^{12 }software simulator and the SC vascular network extracted from the segmented X-ray tomographic images (Figure 2). The effective transverse relaxation rate constant *R _{2}** was then computed in the same way as described for the simplified model.

**Results**

**Discussion and Conclusion**

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Simplified vessel model, based on the ICM.

Spinal cord ventral horn (left) and Segmented X ray Tomography image from a mouse SC, (right).

Relaxation rate constant *R*_{2}* as a function of the vessel radius. The small-vessels are represented with red line, the large-vessels with green line and the aggregate (all vessels) distribution, which characterize the brain, is represented with blue line.