Convection-enhanced drug delivery is a technique where a therapeutic agent is infused under positive pressure directly into the brain tissue. For predicting the final concentration distribution and optimizing infusion rate and catheter placement, numerical models can be of great help. However, despite advances in modeling this process, often the infused agent does not reach the targeted region prescribed in the modeling phase. In this study, patient-specific brain structure and parameters, obtained from diffusion tensor imaging (DTI), are implemented in a numerical model which describes the flow and transport in an elastic deformable matrix. To our knowledge, this is the first time that information from DTI is used in a numerical model which includes both transport of a therapeutic agent and tissue deformation. Fractional anisotropy (FA) is used to distinguish between gray and white matter and tortuosity to differentiate between inside and outside the brain tissue. One voxel in the DT-image is represented by one element of the numerical grid. The DT-images were in addition used to determine the orientation of the white matter fiber tracts and calibrate permeability and diffusion coefficients found in the literature. Values chosen for the porosity and Lamé parameters are also based on those found in the literature. Given realistic literature values, the calibration of the permeability and diffusion tensors are shown to be successful. Our result shows that preferential flow occur in direction of the white matter fiber tracts. The current model assumes linear deformation, corresponding to small porosity changes.

Syringomyelia, fluid-filled cavities within the spinal cord, occurs frequently in association with a Chiari I malformation and produces some of its most severe neurological symptoms. The exact mechanism causing syringomyelia remains unknown. Since syringomyelia occurs frequently in association with obstructed cerebrospinal fluid (CSF) flow, it has been hypothesized that syrinx formation is mechanically driven. In this study we model the spinal cord tissue either as a poro-elastic medium or as a solid linear elastic medium, and simulate the propagation of pressure waves through an anatomically plausible 3D geometry, with boundary conditions based on in vivo CSF pressure measurements. Then various anatomic and tissue properties are modified, resulting in a total of 11 variations of the model that are compared. The results show that an open segment of the central canal and a stiff pia (relative to the cord) both increase the radial pressure gradients and enhance interstitial fluid flow in the central canal. The anterior median fissure, anisotropic permeability of the white matter, and Poisson ratio play minor roles.

No abstract

We hypothesize that a collapse of the optic nerve subarachnoid space (ONSAS) in the upright posture may protect the eyes from large translamina cribrosa pressure differences (TLCPD) believed to play a role in various optic nerve diseases (e.g., glaucoma). In this study, we combined magnetic resonance imaging (MRI) and mathematical modeling to investigate this potential ONSAS collapse and its effects on the TLCPD. METHODS.First, we performed MRI on six healthy volunteers in 6°head-down tilt (HDT) and 13°head-up tilt (HUT) to assess changes in ONSAS volume (measured from the eye to the optic canal) with changes in posture. The volume change reflects optic nerve sheath (ONS) distensibility. Second, we used the MRI data and mathematical modeling to simulate ONSAS pressure and the potential ONSAS collapse in a 90°upright posture. RESULTS.The MRI showed a 33% decrease in ONSAS volume from the HDT to HUT (P < 0.001). In the upright posture, the simulations predicted an ONSAS collapse 25 mm behind lamina cribrosa, disrupting the pressure communication between the ONSAS and the intracranial subarachnoid space. The collapse reduced the simulated postural increase in TLCPD by roughly 1 mm Hg, although this reduction was highly sensitive to ONS distensibility, varying between 0 and 4.8 mm Hg when varying the distensibility by ± 1 SD. CONCLUSIONS.The ONSAS volume along the optic nerve is posture dependent. The simulations supported the hypothesized ONSAS collapse in the upright posture and showed that even small changes in ONS stiffness/distensibility may affect the TLCPD.