Figure 1.
A Representative Voxel Domain.
a.) The simulated compartmental domain. The gray area represents ve, the white voids represent cells (1-ve-vp), and the red spaces indicate vessels (vp). This domain has a ve of 0.39 and a vp of 0.03. Each side of the voxel is 250 micrometers. b.) An example of the triangular mesh (corresponding to the black dashed line in panel a) which fills ve.
Figure 2.
Voxel EES Contrast Agent Concentration Distribution as a Function of the Coefficient of Diffusion.
The concentration distributions and overall voxel EES concentration are shown for the central voxel of interest for the simulation with ve = 0.39, vp = 0.03, and Ktrans = 0.4 min−1. The top figure shows the overall voxel EES concentration for three representative coefficients of diffusion (D). The lower panels demonstrate spatial voxel contrast agent concentration distribution as a function of diffusion (increasing from top to bottom) and time (increasing from left to right). The four time points are indicated by the black vertical lines on the voxel concentration plot. Note that at a high D value (4×10−4 mm2/s), the contrast agent concentration is nearly uniform throughout the domain at each time point. However, at lower (and more physiologically relevant) D, there is substantial heterogeneity within the domain, especially during the early times points during which the vascular concentration is highly dynamic. Additionally, it is important to note that although the peaks become less distinguished with increasing D at the earliest time point, the overall domain EES CA concentration increases with increasing D. This is due to the fact that with increasing D, the CA is able to diffuse away from the vessel periphery and into the domain. Specifically, the median concentration in the ve domain space is 7×10−4 mM, 0.0026 mM, and 0.0047 mM for each D value shown (from lowest to highest).
Figure 3.
Parameterization Error as a Function of Contrast Agent Diffusion, Temporal Resolution, and Ktrans.
Voxel SI was calculated from each concentration distribution for the appropriate combination of parameters, and SI curves were generated using a range of temporal resolutions. The resulting curves were fit using the extended model. The panels show percent error from input value for (from top to bottom) Ktrans, ve, and vp, and goodness of fit as measured by χ2. The columns indicate input Ktrans value, increasing from left to right. The simulation utilized ve = 0.39 and vp = 0.03.
Figure 4.
Parameterization Error as a Function of Contrast Agent Diffusion, Temporal Resolution, and ve.
Voxel SI was calculated from each concentration distribution for the appropriate combination of parameters, and SI curves were generated using a range of temporal resolutions. The resulting curves were fit using the extended model. The panels show percent error from input value for (from top to bottom) Ktrans, ve, and vp, and goodness of fit as measured by χ2. The columns indicate input ve value, increasing from left to right. The simulation utilized Ktrans = 0.4 and vp = 0.03.
Figure 5.
Parameterization Error as a Function of Contrast Agent Diffusion, Temporal Resolution, and vp.
Voxel SI was calculated from each concentration distribution for the appropriate combination of parameters, and SI curves were generated using a range of temporal resolutions. The resulting curves were fit using the extended model. The panels show percent error from input value for (from top to bottom) Ktrans, ve, and vp, and goodness of fit as measured by χ2. The columns indicate input vp value, increasing from left to right. The simulation utilized Ktrans = 0.4 and ve = 0.39.