The effects of intravoxel contrast agent diffusion on the analysis of DCE-MRI data in realistic tissue domains

Fig. S1. (a) Simulated time-course for a necrotic voxel (see Fig. 2a), with contrast agent diffusivity, D = 1 × 10⁻⁴ mm² s⁻¹. Error for this simulation is −31.8% in K^trans, −23.7% in v_e, and 11.3% in v_p. (b) The time-course for the same voxel, where D = 4 × 10⁻⁴ mm² s⁻¹. Error for this simulation is −15.5% in K^trans, −0.2% in v_e, and −26.8% in v_p. Note that as D increases, the voxel equilibrates sooner and is associated with reduced error in parameter estimation. Higher diffusivity results in higher accuracy in K^trans and v_e. Underestimation of v_p is because of the true value being < < 0.01 (v_p = 0.003).

Fig. S2. (a) depicts the simulated time-course for a well-perfused voxel (see Fig. 3a), with contrast agent diffusivity, D = 1 × 10⁻⁴ mm² s⁻¹. Error for this simulation is −30.3% in K^trans, −5.7% in v_e, and 49.9% in v_p. (b) The time-course for the same voxel, where D = 4 × 10⁻⁴ mm² s⁻¹. Error for this simulation is −11.7% in K^trans, −3.1% in v_e, and 4.3% in v_p. As with the necrotic voxel (Fig. 2 and Supporting Fig. S1), accuracy in K^trans and v_e is positively correlated with increasing D. Higher v_p accuracy in the well-perfused voxel, compared to the poorly perfused voxel, is because of the increased vascularity in the domain (v_p = 0.009).

Fig. S3. Depiction of the parametric error as a function of domain size for parameters v_e and v_p. Error in K^trans can be seen in Figure 6. (a) Corresponds to the domain shown in Figure 6a, while (b) corresponds to the domain shown in Figure 6b. (c) Corresponds to the domain shown in Figure 6c. Similar to K^trans, v_e and v_p are most accurate with higher diffusivity. In general, as the domain is expanded around the vasculature, the accuracy of v_e and v_p decrease. Dashed lines on v_p error plots indicate where true v_p drops below 0.01. There is no dashed line in (c) because v_p is always above 0.01. Spikes in the plot of v_e error (b) are caused by the non-smooth changes in EES and true volume fractions as the domain increases in size. This non-smooth behavior is unavoidable using discretized steps in an irregular domain. The curves are less smooth for real tissue data, shown in (c).

Fig. S4. (a) The error in K^trans for mouse 2. Error in v_e is shown in (b), and error in v_p is shown in (c).

Fig. S5. (a) The error in K^trans for mouse 3. Error in v_e is shown in (b), and error in v_p is shown in (c).

Fig. S6. (a) The error in K^trans for mouse 4. Error in v_e is shown in (b), and error in v_p is shown in (c).

Fig. S7. Comparison of in vivo DCE-MRI data to simulation results, obtained from the same specimen. (a) A fast spin echo image of the central slice of a BT474 tumor, with the tumor boxed in red. (b) Corresponding H&E histology from the same specimen. (c) K^trans map resulting from fitting the measured signal time-course to in vivo DCE-MRI data. (d) Assigned K^trans map resulting from the forward model with D = 2.6 × 10⁻⁴ mm² s⁻¹. Green ROIs correspond to a necrotic region near the center of the tumor, whereas blue ROIs correspond to a well-perfused region near the periphery of the tumor. (e,f) Measured and simulated signal intensity time-courses, respectively, associated with the green ROI from (c) and (d). The solid red lines in (e) and (f) present the fit of each signal intensity curve with the extended Tofts model. Similarly, (g) and (h) depict the measured and simulated signal intensity time-courses, respectively, associated with the blue ROI in (c) and (d). Again, the solid red lines in (g) and (h) depict the fit of each signal intensity curve with the extended Tofts model. Fitting to the curve in (e) resulted in K^trans = 0.009 min⁻¹, v_e = 1105, and v_p = 2.3E−14. The resulting parametric fit for the simulated curve in (f) was K^trans = 0.019 min⁻¹, v_e = 185, and v_p = 2.2E−14. The resulting fit for the curve in (g) was K^trans = 0.0771 min⁻¹, v_e = 0.331, and v_p = 0.039. Finally, the parametric fit for the simulated curve in (h) is K^trans = 0.052 min⁻¹, v_e = 0.164, and v_p = 0.024. The FEM model is able to recapitulate experimentally measured curve shapes in both poorly and well-perfused regions. When the region is poorly perfused (e.g., the green ROI), analysis with the extended Tofts model leads to non-physiological parameter estimations. When the region is well-perfused (e.g., the blue ROI), the extended Tofts model returns reasonable parameter values.