Monte Carlo Simulations
An AIF was simulated using a gamma-variate function, which was shown by previous studies to correlate well with the shape of measured AIFs (3, 6, 9). The analytical expression for the AIF, Ca(t) was:
with a = 3.0 and b = 1.5 s, representative of data from normal adult volunteers (3, 6, 9). Simulations used C0 = 1, t0 = 20 s over a time range of 200 s to avoid truncation for the longest MTT simulated (24 s). To evaluate the techniques' sensitivity to different underlying R(t), similarly to methods used in Refs. 3 and4, three different models were examined: exponential, box-shaped, and linear. In all models, the MTT was calculated as MTT = CBV/CBF from the central volume theorem (20). CBV was either 4% or 2%. These values were also used by other studies as representative for normal gray matter or white matter, respectively (3, 6). For CBV = 4%, flow values were varied between 10–70 ml/100 g/min in 10 ml/100 g/min increments. For CBV = 2%, flows were evaluated from 5 to 35 ml/100 g/min in 5 ml/100 g/min increments in order to maintain the same range of MTT values as for CBV = 4%. Analytical expressions for C(t) were derived by convolving Ca(t) with each R(t) (6).
Signal curves were generated as S(t)=S0e−kC(t)TE, with baseline MR image intensity S0 = 100, and TE = 65 ms. For all simulations, a proportionality factor k was selected that resulted in a 40% peak signal drop at a flow rate of 60 ml/100 g/min and CBV = 4%, corresponding to values typically found in human gray matter (3, 6). The signal enhancement curve for the AIF, Sa(t), was similarly modeled as S(t), except that Ca(t) was substituted for C(t). The proportionality constant, k, in this case, was selected to generate a peak signal drop of 60%, which is a typical measured signal reduction for selected AIFs in our clinical PWI.
Using previously described techniques (21), noise was added to S(t) and Sa(t) to create signals with baseline SNRs of 20 and 100, respectively. To evaluate the sensitivity of flow estimates to differences in tracer arrival times between the AIF and tissue signal, S(t) was shifted up to ±5 s with respect to Sa(t) in increments of 1 s, resulting in a total of 11 shifts. To simulate shifts that are not multiples of the sampling period, signals were created with Δt = 100 ms, shifted after noise was added, and then resampled to TR = 1 or 1.5 s. A TR = 1 s was used primarily in our analysis to avoid confounds due to shifts that are not multiples of TR, and to be consistent with previous studies (3). Simulations were repeated at TR = 1.5 s to investigate the effects of sampling interval on the algorithms' performance.
Using approaches similar to those described in Refs. 3 and6, image data sets were created, resulting in a total of 1024 data points for each TR, SNR, shift, and flow. For sSVD and cSVD, PSVD was varied between 0 and 95%. For oSVD, OI was varied between 0 and 0.5. To determine absolute flow values, the calculated CBF values were rescaled by the k-factors used above for S(t) and Sa(t).
The following steps were repeated for each SNR and TR. For each PSVD and OI, the error at each iteration t (Et) was calculated as Et = 1/Nf Σ|F – F′|, where F is the true flow value, F′ is the calculated flow value, and Nf is the number of simulated flow values (Nf = 7). The optimal Psvd for sSVD and cSVD, and optimal OI for oSVD were determined as the values that minimized simultaneously over all assumed residue functions R(t) and Nt = 1024 iterations the average Et assuming zero time delays. The optimal PSVD and OI thresholds found in this step were then used to assess the performance of the techniques in terms of its mean error Et (Ē(D) = 1/Nt Σ Et) and standard deviation (σE(D)) over all Nt = 1024 iterations, as a function of tracer arrival time differences (D).
Tracer arrival timing differences between tissue and the AIF were estimated as the sample point, m, where the maximum R(t) occurs. For sSVD, the estimated shift D′ = m · TR. For oSVD, D′ = m · TR for m<L/2 and D′ = −(L – m) · TR for L/2 ≤ m < L, where L is the total number of points. The error in estimating tracer arrival time differences for each iteration t was calculated as EDt = 1/ND Σ|D – D′|, where D is the true time difference, D′ is the estimated difference, and ND is the number of simulated applied shifts (ND = 11). The PSVD and OI used for estimating flows at each SNR and TR were used to estimate timing shifts. The mean delay error EDt (ED(F) = 1/Nt ΣEDt) over all Nt = 1024 iterations, as well as the SD (σED(F)), were calculated at each flow rate, F.
Clinical MRI Acquisition
DSC MRI consisted of spin-echo, echo-planar images obtained during the first pass of 0.2 mmol/kg of a gadolinium-based contrast agent injected 10 s after start of imaging, at a rate of 5 ml/s, using an MRI-compatible power injector (Medrad, Pittsburgh, PA). Imaging studies were performed on 1.5 T GE Signa LX systems (GE Medical Systems, Milwaukee, WI). The parameters included TR/TE = 1500/65 ms, field of view (FOV) = 22 × 22 cm2 or 20 × 20 cm2, and acquisition matrix = 128 × 128. All studies consisted of 11 slices with a thickness of 6 mm and gap of 1 mm collected over 46 time points.
All data analysis was performed retrospectively, with approval from our institution's committee for human subject research. Four patients were retrospectively examined. Patient demographics are shown in Table 1. Based on the simulation results, our analysis was limited to sSVD and oSVD. Relative CBF (sCBF and oCBF) and Delay (sDelay and oDelay) maps were calculated using the same techniques as for the simulations. An AIF was selected from the ipsilateral hemisphere and used for analysis for both sSVD and oSVD. Selection of PSVD for sSVD and OI for oSVD were based on the optimal values found in the simulation section for SNR = 20 and TR = 1.5 s, which are typical for clinically acquired PW images at this institution. Relative cerebral blood volume (CBV) was calculated by numerically integrating the ΔR2(t) curves (14, 22). MTT values were calculated as sMTT = CBV/sCBF and oMTT = CBV/oCBF.
Table 1. Patient Demographics, Diagnosis, and Imaging Times
|1||67/F||Transient ischemic attack due to left ICA stenosis||2 weeks||T2 same day as PWI|
|2||56/F||Right MCA stroke||4 hrs||22-day FLAIR|
|3||62/M||Left MCA stroke||7 hrs||4 month FLAIR|
|4||52/F||Right MCA stroke and complete right ICA occlusion||11 hrs||6 day FLAIR|