Incorporating a vascular term into a reference region model for the analysis of DCE-MRI data: a simulation study

Abstract

A vascular term was incorporated into a reference region (RR) model analysis of DCE-MRI data, and its effect on the accuracy of the model in estimating tissue kinetic parameters in a tissue of interest (TOI) was systematically investigated through computer simulations. Errors in the TOI volume transfer constant (K(trans,TOI)) and TOI extravascular extracellular volume (v(e,TOI)) that result when the fractional plasma volume (v(p)) was included in (1) neither region, (2) TOI only (3) both regions were investigated. For nominal values of tumor kinetic parameters (v(e,TOI) = 0.40 and K(trans,TOI) = 0.25 min(-1)), if the vascular term was included in neither region or the TOI only, K(trans,TOI) error was within 20% for 0.03 < v(p,TOI) < 0.10, and v(e,TOI) error was within 20% for the range of v(p,TOI) studied (0.01-0.10). The effects of temporal resolution were shown to be complex, and in some cases errors increased with increasing temporal resolution.

Figure 1

(a) Contributions of C_p and C_e,RR (each weighted by their respective fractional volumes) to C_t,RR, the reference region tissue concentration. (b) Resulting C_p curves from C_t,RR, excluding (C_pnv_p) or including (C_pv_p) the vascular term (see equations (3) and (4)). Note the large over- and undershoots when the vascular term was excluded. (c) Effect of v_p,TOI on C_t,TOI. Curves are shown for values of v_p,TOI increasing from 0.01 to 0.10.

Figure 2

Effect of SNR and v_p,TOI on kinetic parameter errors, shown in per cent error. Errors were stable for SNR > 40, except for v_p,TOI < 0.04 in the nv_p,RR – v_p,TOI case.

Figure 3

K^trans,TOI per cent error as a function of K^trans,TOI, v_e,TOI and v_p,TOI. The errors intersected zero, indicating that the correct values awere estimated under certain conditions. The K^trans,TOI error decreased with K^trans,TOI and was relatively insensitive to v_e,TOI, although for low values of K^trans,TOI it decreased with v_e,TOI. The error was linearly proportional to v_p,TOI.

Figure 4

v_e,TOI per cent error as a function of K^trans,TOI, v_e,TOI and v_p,TOI. The error intersected zero, indicating that the correct values were estimated under certain conditions. The v_e,TOI error was relatively insensitive to K^trans,TOI decreased nonlinearly with v_e,TOI and increased linearly with v_p,TOI.

Figure 5

v_p,TOI error as a function of K^trans,TOI, v_e,TOI and v_p,TOI. For the nv_p,RR – v_p,TOI case, the error was close to –100%, reflecting the fact that the model set v_p,TOI to close to zero even if it was included in the model. In the v_p,RR – v_p,TOI case, the error increased linearly with K^trans,TOI, was insensitive to v_e,TOI and decreased nonlinearly with v_p,TOI.

Figure 6

r² goodness-of-fit statistic as a function of K^trans,TOI, v_e,TOI and v_p,TOI. For most values, r² > 0.9, except for regions of high K^trans,TOI, low v_p,TOI and low K^trans,TOI, high v_p,TOI.

Figure 7

K^trans,TOI error as a function of sampling interval (Δt) and K^trans,TOI, v_e,TOI and v_p,TOI. For each column, one parameter was varied, with the minimum and maximum parameter values shown in the graph (minimum shown as a dashed line). For the nv_p,RR – nv_p,TOI case, the dependence on the parameter values reached a minimum at Δt = 20 s. For the nv_p,RR – v_p,TOI case, the errors became more negative (sometimes crossing zero) as Δt increased. For the v_p,RR – v_p,TOI case, the errors decreased from zero as Δt increased. The sign of the dependence on v_p,TOI reversed when going from Δt = 10 s to Δt = 20 s.

Figure 8

Error in v_e,TOI as a function of sampling rate (Δt) and K^trans,TOI, v_e,TOI and v_p,TOI. For each column, one parameter was varied, with the minimum and maximum parameter values shown in the graph (minimum shown as a dashed line). For the nv_p,RR – nv_p,TOI case, the errors were fairly insensitive to Δt. For the nv_p,RR – v_p,TOI case, the errors became more negative (sometimes crossing zero) as Δt increased. For the v_p,RR – v_p,TOI case, the errors decreased from zero as Δt increased. The sign of the dependence on v_p,TOI reversed when going from Δt = 10 s to Δt = 20 s.

Figure 9

Error in v_p,TOI as a function of sampling rate (Δt) and K^trans,TOI, v_e,TOI and v_p,TOI. For each column, one parameter was varied, with the minimum and maximum parameter values shown in the graph (minimum shown as a dashed line). For the nv_pRR – v_p,TOI case the dependence on K^trans,TOI increased with Δt, was insensitive to v_e,TOI and decreased with v_p,TOI. For the v_pRR – v_p,TOI case, the dependence on K^trans,TOI and v_p,TOI increased the most in going from Δt = 10 s to Δt = 20 s. The dependency on v_e,TOI peaked at Δt = 10 s.