The IVIM signal: a combination of two vascular pools
Gabrielle Fournet1,2, Luisa Ciobanu1, Jing Rebecca Li2, Alex Cerjanic3, Brad Sutton3, and Denis Le Bihan1

1CEA Saclay/Neurospin, Gif-sur-Yvette, France, 2INRIA Saclay, Palaiseau, France, 3Beckman Institute of Advanced Science and Technology, Urbana, IL, United States

Synopsis

IntraVoxel Incoherent Motion (IVIM) imaging allows to extract perfusion parameters from a series of diffusion weighted images. We show that the standard mono-exponential model used to describe the IVIM signal can be improved by switching to a bi-exponential model. Multiple diffusion time rat brain images were acquired at 7T and compared to numerical simulations of blood flow through the microvascular network. Our results demonstrate that the bi-exponential model better describes the data especially at short diffusion times and suggest that the IVIM signal comprises the contributions from two different vascular pools: small vessels (capillaries) and medium sized-vessels.

Introduction

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.

Methods

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 (AICc) 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.

Results

Fig.1 shows experimental data fitted with the two models for the two ROIs for Δ=24ms. The AICc was significantly smaller for the bi-exponential model than the mono-exponential model (Wilcoxon signed rank test, p-value<0.0001). The difference in AICc 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).

Discussion and conclusion

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 vessels5,6. 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.

Acknowledgements

The authors wish to thank Boucif Djemai and Erwan Selingue for their excellent technical assistance. The research was supported by the ANR/NIH Grant ANR-13-NEUC-0002-01.

References

1. Le Bihan D., Breton E., Lallemand D. et al. Separation of diffusion and perfusion in intravoxel incoherent motion MR imaging. Radiology. 1988;168(2):497-505.

2. Akaike H. Information theory and an extension of the maximum likelihood principle. Second international symposium on information theory 1973; 267-281.

3. R Core Team (2015). R: A language and environment for statistical computing. R Foundation for Statistical Computing, Vienna, Austria. URL https://www.R-project.org/.

4. Unekawa M., Tomita M., Osada T. et al. Frequency distribution function of red blood cell velocities in single capillaries of the rat cerebral cortex using intravital laser-scanning confocal microscopy with high-speed camera. Asian Biomedicine. 2008;2:203–218.

5. Ivanov K.P., Kalinina M.K., Levkovich Y.I. Blood flow velocity in capillaries of brain and muscles and its physiological significance. Microvascular Research. 1981;22:143-155.

6. Kobari M., Gotoh F., Fukuuchi Y. et al. Blood Flow Velocity in the Pial Arteries of Cats, with Particular Reference to the Vessel Diameter. Journal of Cerebral Blood Flow and Metabolism. 1984;4:110-114.

Figures

Fig.1. Example of IVIM signal vs b-value for Δ=24ms in two ROIs: (A) LC, (B) LT. The black circles denote the experimental data whereas the lines represent the fits corresponding to the bi- and mono-exponential models. Error bars represent standard deviations from the averaging step; Upper right corners: ROI masks.

Fig.2. (A) Box-and-whisker plots of AICc mono-AICc bi against Δ for both ROIs; Error bars represent standard deviations (N=12). (B) Results of the statistical tests for the AICc in both ROIs; Groups 1 to 3 correspond to Δ=14ms, 24ms and 34ms, respectively.

Fig.3. (A-B) Box-and-whisker plots of D*slow and D*fast against Δ for the ROIs in Fig.1; Error bars represent standard deviations (N=12). (C) Results of the statistical tests for the two parameters. Groups 1 to 3 correspond to Δ=14ms, 24ms and 34ms, respectively.

Fig.4. Examples of IVIM signal vs b-value for the three diffusion times in the LT (A-C). The black circles stand for the experimental data and the blue solid line for the simulated signals best matching the data. Error bars represent standard deviations from the averaging step.



Proc. Intl. Soc. Mag. Reson. Med. 24 (2016)
3330