Voxelized model of interstitial transport in the rat spinal cord following direct infusion into white matter

Abstract

Direct tissue infusion, e.g., convection-enhanced delivery (CED), is a promising local delivery technique for treating diseases of the central nervous system. Predictive models of spatial drug distribution during and following direct tissue infusion are necessary for treatment optimization and planning of surgery. In this study, a 3D interstitial transport modeling approach in which tissue properties and anatomical boundaries are assigned on a voxel-by-voxel basis using tissue alignment data from diffusion tensor imaging (DTI) is presented. The modeling approach is semi-automatic and utilizes porous media transport theory to estimate interstitial transport in isotropic and anisotropic tissue regions. Rat spinal cord studies compared predicted distributions of albumin tracer (for varying DTI resolution) following infusion into the dorsal horn with tracer distributions measured by Wood et al. in a previous study. Tissue distribution volumes compared favorably for small infusion volumes (<4 microl). The presented DTI-based methodology provides a rapid means of estimating interstitial flows and tracer distributions following CED into the spinal cord. Quantification of these transport fields provides an important step toward development of drug-specific transport models of infusion.

Fig. 1

DTI-based segmentation: (a) FA image from a transverse DTI scan of the in vivo spinal cord at level T13 (voxel resolution=150×150×500 µm³) Gray matter tissue is hypo-intense and white matter tissue is hyperintense. (b) Corresponding S₀ image with uniform intensity in gray and white matter, and (c) tissue segmentation image used in the voxelized computational model (dark blue=white matter, light blue=gray matter, yellow=CSF, red = bone, and surrounding tissues). (d) FA image from a transverse DTI scan of excised tissue at L1 (voxel resolution=30×30×150 µm³) and (e) corresponding S₀ image, where gray matter tissue is hyperintense and white matter tissues is hypo-intense. (f) Corresponding high-resolution tissue segmentation image (blue=white matter, green=gray matter, and red = CSF). The yellow box outlines the dorsal tissue region used in the voxelized model. Artifact voxels resulting from the semi-automatic segmentation method are also identified. Please refer to the digital version of this article for full color images.

Fig. 2

Predicted albumin distributions in the spinal cord using voxelized transport models generated from in vivo DTI (low-resolution) data. Distribution contours in transverse and sagittal planes intersecting the infusion site are overlaid on FA images at varying times after the start of infusion (infusion rate =0.1 µl/min). Tracer concentration contours are for normalized tissue concentrations.

Fig. 3

Predicted albumin distributions in the spinal cord using voxelized transport models generated from DTI of excised, fixed tissues (high-resolution). Distribution contours from excised in transverse and sagittal planes intersecting the infusion site are overlaid over S₀ images at varying times after the start of infusion (infusion rate=0.1 µl/min). Tracer concentration contours are for normalized tissue concentrations.

Fig. 4

Predicted concentration profiles for albumin tracer during direct tissue infusion at 0.1 µl /min. Concentration profiles are for three orthogonal lines passing through the infusion site: (a) vertical line in the transverse plane, (b) horizontal line in the transverse plane, and (c) axial line. Normalized tissue concentrations are given and concentration is the averaged value for nine lines passing through the infusion site. All simulations were using the high-resolution voxel transport model generated from excised DTI data.

Fig. 5

Peclet number contour maps in the transverse plane of the spinal cord generated using voxel transport models from (a) in vivo and (b) excised tissue image data. Peclet contours are overlaid on S₀ images in (a) transverse and sagittal planes and (b) transverse and coronal planes intersecting the infusion site. As an approximation, convection-dominated regions correspond to Peclet number>300.

Fig. 6

Comparison of predicted and measured distributions of albumin tracer in the rat spinal cord following direct infusion into the dorsal horn. Tracer tissue volumes calculated from the voxel transport models using in vivo and excised tissue data sets are plotted. Wood et al. [3] measured distribution of ¹⁴C-labeled albumin following CED into a similar region. Bars correspond to ±1 SD. The threshold value used for volume distribution analysis was 15% of the infusate concentration.

Fig. 7

Parameter sensitivity analysis comparing the final distribution volume (Vd) and the total infusion volume (Vi) on a log-log scale for (a) the hydraulic conductivity of CSF and (b) the image-voxel resolution (high-resolution voxel size=30×30×150 µm³, mid-resolution=60×60×300 µm³, and low-resolution=120×120×600 µm³). Vd and Vi were calculated using the excised tissue data set. Vd was calculated for regions within the gray and white matter tissue regions only. Solid lines correspond to the average Vd value ±3% and ±10% for the set of K ratios and voxel resolutions simulated, respectively.