First introduced by Le Bihan et al. in 1988¹, IntraVoxel Incoherent Motion (IVIM) imaging is used to measure perfusion via the acquisition of a series of diffusion weighted images. The standard IVIM mono-exponential model assumes that the DWI signal at low b-values is attenuated from blood flowing in a pseudo-random capillary network. However, vessels such as small arterioles or venules might also contribute to the IVIM effect. We have acquired experimental data at 3 different “diffusion” times and performed numerical simulations to check whether the IVIM signal is really mono-exponential (reflecting a single vascular pool) or might reflect the presence of another vascular pool using a bi-exponential IVIM model.

MRI acquisitions

Twelve Dark Agouti rats were imaged under isoflurane on a 7T MRI scanner. Diffusion images were acquired with a PGSE sequence using 30 b-values ([7-2600]s/mm²). The acquisition parameters were set as follows: 3 gradient directions [1,1,1], [0,1,0] and [0,0,1], diffusion gradient duration δ=3ms and separation time ∆=14, 24 or 34ms, in-plane resolution 250x250μm², 1 segment, TE/TR=45/1000ms, 6 averages, 6 repetitions, 2 slices.

Data analysis

For each value of Δ, the raw signal was averaged over the 3 directions (assuming isotropy) and 6 repetitions in two ROIs each encompassing the 2 slices (Fig.1) placed on the left cortex (LC) and left thalamus (LT). The signal was modeled using a IVIM/Kurtosis model (Eq.1).

$$$\frac{S}{S_0} =(1-f_{IVIM} ) F_{Diff}+f_{IVIM} F_{IVIM}$$$ [1.a.]

with $$$F_{Diff}=\exp(-bADC_0+(bADC_0 )^2 \frac{K}{6})$$$ [1.b.]

and $$$F_{IVIM}=\exp(-bD^*)$$$ [1.c.]

or $$$F_{IVIM}= f_{slow} \exp(-bD_{slow}^* )+f_{fast}\exp(-bD_{fast}^* )$$$ [1.d.]

where $$$\frac{S}{S_0}$$$ is the measured MR signal, $$$F_{Diff}$$$ and $$$F_{IVIM}$$$ are the diffusion and IVIM components respectively, b is the b-value of the sequence with diffusion encoding gradients of duration δ and separation ∆, $$$ADC_0$$$ is the tissue apparent diffusion coefficient obtained when b approaches 0, K is the Kurtosis, $$$f_{IVIM}$$$ is the total IVIM blood volume fraction, $$$f_{fast}$$$ and $$$f_{slow}$$$ are the volume fractions of the fast and slow vascular components, respectively, $$$D_{fast}^*$$$ and $$$D_{slow}^*$$$ are the corresponding pseudo-diffusion coefficients and $$$D^*$$$ is the pseudo-diffusion coefficient of the standard IVIM model.

The signal was first fitted for diffusion for b>500s/mm² (Eq.1.b) then the diffusion component was extrapolated for b<500s/mm² and subtracted from the raw signal. The residual IVIM signal was fitted with the mono- and bi-exponential models (Eq.1.c-d).

Numerical simulations

IVIM signals coming from blood flowing through microvascular networks were numerically simulated. The blood vessels were described as segments connected to one another (with no bifurcations) and characterized by Gaussian distributions of lengths, 50±50µm and blood flow velocities, $$$v_{mean}±\sigma_{v}$$$ with $$$v_{mean}$$$=[0.5-12]mm/s and $$$\sigma_{v}$$$=[0.05-1]x$$$v_{mean}$$$. A dictionary of signals was then generated by combining pairs of signals corresponding to two different velocity distributions. This dictionary was used to find the best match with the data keeping the same $$$f_{slow}$$$-value found from fitting with the bi-exponential model and imposing constant $$$v_{mean}$$$ and $$$\sigma_{v}$$$ for all Δ.

$$$F_{IVIM}=f_{slow} S_{Simu/slow} (v_{slow},σ_{v_{slow}})+f_{fast} S_{Simu/fast}( v_{fast},σ_{v_{fast}})$$$ [2]

Statistical analysis

The corrected Akaike information criterion (AIC_c) was calculated for the two models to assess goodness of fit². The statistical analyses were conducted using the R software³. A p-value<0.05 was considered statistically significant.

Fig.1 shows experimental data fitted with the two models for the two ROIs for Δ=24ms. The AIC_c was significantly smaller for the bi-exponential model than the mono-exponential model (Wilcoxon signed rank test, p-value<0.0001). The difference in AIC_c between the 2 models increased when Δ decreased for both ROIs suggesting that the bi-exponential model is especially appropriate for shorter diffusion times (Fig.2). Fig.3, gathering the boxplots of $$$D_{slow}^*$$$ and $$$D_{fast}^*$$$ against Δ reveals a significant increase in $$$D_{slow}^*$$$ with the diffusion time but no clear dependence for $$$D_{fast}^*$$$. The dependence of $$$D_{slow}^*$$$ on the diffusion time was also confirmed by numerical simulations. By matching the simulated signals to experimental data, we obtain $$$v_{slow}$$$ =1.5±0.5mm/s and $$$v_{fast}$$$=4.5±2.8mm/s (Fig.4).

Our study confirms that a bi-exponential IVIM model better describes DWI data at low b-values, especially at short diffusion times, suggesting a contribution from two vascular pools. At long diffusion times, $$$D_{slow}^*$$$ approaches $$$D_{fast}^*$$$ leading to the merging of the two exponentials into the classical IVIM mono-exponential model. This trend is consistent with results obtained from numerical simulations. The blood velocities for the slow and fast pools matching the experimental data with simulated signal dictionaries suggest that those pools correspond, respectively, to capillaries⁴ and small-size arterioles, perhaps between terminal and pial vessels^5,6. In conclusion, the bi-exponential IVIM representation introduced here is coherent with the known microvascular architecture and has the potential to provide a more complete and accurate picture of cerebral blood flow than previous models.