Intravoxel incoherent motion (IVIM) theory in magnetic resonance imaging (MRI) was proposed by Le Bihan et al. to account for the effect of vessel/capillary perfusion on the aggregate diffusion weighted MR signal. The fast component of diffusion is related to micro-perfusion, whereas the slow component is linked to water molecular diffusion. Three parameters can be computed. Dslow (or D) is the diffusion coefficient representing the slow “pure” water molecular diffusion (unaffected by perfusion). The perfusion fraction (PF, or f) represents the fraction of the compartment related to (micro)circulation, which can be understood as the proportional “incoherently flowing fluid” (i.e., blood) volume. Dfast (or D*) is the perfusion-related diffusion coefficient representing the incoherent microcirculation within the voxel, which holds information for blood perfusion’s speed. Among IVIM research community, it has been generally assumed that the perfusion component and the diffusion component can be separately determined. We recently reported that, for the liver, IVIM modeling of the perfusion component is constrained by the diffusion component, and a reduced Dslow measure leads to artificially higher PF and Dfast measures (1,2). Two related questions would then follow: Is this phenomenon also observed in organs other than the liver? Can a reduction of PF lead to an artificial elevation of Dslow measure? We argue that the answer is “yes” to both questions. Hereby, we explain this point by using examples in existing brain IVIM literatures with acute PF change being the initiating factor. These examples suggest a lower PF can lead to a higher observed Dslow.
By increasing arterial carbon dioxide pressure (PaCO2), McKinstry et al. (3) induced brain grey matter perfusion increases in three dogs and IVIM imaging of the brain was acquired. PaCO2 was changed according to the order of: low PaCO2, high PaCO2, and normal PaCO2. Their IVIM analysis in Fig-5 shows, among various PaCO2, PF and Dslow changed toward the opposition directions. When PF went up, Dslow went down; when PF went down, Dslow went up. Pavilla et al. (4) studied cerebral hypoperfusion induced by hyperventilation challenge in 10 healthy volunteers. For the IVIM measures, they reported cerebellum grey matter had PF of 0.16±0.07 under normal ventilation and 0.07±0.09 (P=0.03) under hyperventilation, while Dslow was 0.55±0.10 and 0.63±0.13 (×10−3 mm2/s, P=0.05) respectively under normal ventilation and hyperventilation. Thus, hyperventilation included lower PF and higher Dslow measures in cerebellum grey matter. In the study by Xu et al. (5), a middle cerebral artery occlusion model was established in 24 beagle dogs, and IVIM imaging data were acquired at 4.5 hours after model establishment. Serum soluble CD40L level was used as an indicator of microvascular thrombosis after acute ischemic stroke onset, with its higher level associated with more microvascular thrombosis events and thus lower perfusion in the ischemic stroke lesions (5,6). Their Fig-5A (for Dslow) and Fig-5B (for PF) show a potential negative correlation between PF and Dslow. Compared with the contralateral healthy brain hemisphere [PF =0.055±0.008, Dslow =(0.813±0.152)×10−3 mm2/s], the stroke lesions had lower PF and low Dslow. However, the stroke lesions with higher serum soluble CD40L level and lower PF (0.041±0.007) had higher Dslow (0.531±0.153) than Dslow (0.435±0.044, P=0.057) of the stroke lesions with lower serum soluble CD40L level and higher PF (0.051±0.007, P<0.001). With IVIM measures of 20 acute ischemic stroke patients, Zhu et al. (7) reported penumbra zone, ipsilateral non-ischemia region, and contralateral healthy hemisphere had PF of 0.0541±0.0323, 0.0755±0.0454, and 0.0722±0.0293 respectively, while the corresponding Dslow measure was 0.847±0.116, 0.819±0.225, 0.842±0.100 (×10−3 mm2/s) respectively, with the lowest PF associated with highest Dslow and highest PF associated with lowest Dslow.
In interpreting the relationship between PF and Dslow, it should be noted that acute brain ischemia (with a reduction of PF) can indeed induce cytotoxic edema resulting in a reduction of Dslow (8,9). When both PF and Dslow are truly decreased and the decrease of Dslow is of sufficient extent, Dslow can be measured as “decreased” [such as the case for IVIM measure of brain ischemic core (7-9)]; though a possibility remains that, even for such decreased Dslow measures, their observed value is still over-estimated. On the other hand, there likely is a PF change magnitude window which does not induce observed Dslow reduction but instead induce observed Dslow artificial elevation. As time goes on, ischemia induced cytotoxic edema may turn into vasogenic edema which will demonstrate a true Dslow elevation (8,9). In the examples of McKinstry et al. (3), Pavilla et al. (4) and Xu et al. (5), brain changes or lesions would not have had dominant vasogenic edema with overall true Dslow elevation. In the example of Zhu et al. (7), for the retrospective cohort of stroke patients with vessel occlusion, the mean time from onset to treatment was 8.3±5.1 hours and MRI was conducted before the treatment, it is still more likely that there was no sufficient vasogenic edema leading to overall true Dslow elevation.
The point discussed here will have important implications in interpreting IVIM data. For example, in the report by Zhu et al. (7), the penumbra zone had a decreased PF of 0.0541±0.0323 (normal: 0.0722±0.0293, ischemic core: 0.0445±0.0262), while the observed Dslow was (0.847±0.116)×10−3 mm2/s [normal: (0.842±0.100)×10−3 mm2/s, ischemic core: (0.544±0.111)×10−3 mm2/s]. Considering the degree of PF reduction, there could be a possibility that penumbra zone’s true Dslow had decreased, the observed Dslow which was normal (or slightly higher than normal) was masked by an artificial increase of Dslow measure due to true reduction of PF. Moreover, the results of McKinstry et al. (3) and Zhu et al. (7) also suggest the possibility that a truly increased PF can lead to an artificial lowering of Dslow measure. In the study of McKinstry et al. (3), when a PF increase was induced by increasing PaCO2, a lowering of Dslow was noted. In the results of Zhu et al. (7), compared with the contralateral healthy brain, the ipsilateral non-ischemia region had slightly higher PF measure (0.0755±0.0454) than that of the contralateral brain (PF: 0.0722±0.0293) which would have been caused by collateral blood flow compensation (10), resulting in a slightly lower Dslow measure than that of the contralateral brain (0.819±0.225 vs. 0.842±0.100 ×10−3 mm2/s).
Taking together the evidence explained here and our previously discussions (1,2), it can be summarized that, if one component, being perfusion component or diffusion component, changes toward one direction (i.e., increase or decrease), the other component will be constrained to change toward the opposite direction to a certain extent. For this problem, one might expect the cause could be that currently prevalent IVIM modeling does not fully consider the varied noise proportions of diffusion weighted images scanned under different acquisition conditions (11). However, our preliminary further analysis showed noise correction only slightly improved this “constraining”. Moreover, the prevalent IVIM modeling is based on Eq. :
where SI(b) and SI(0) denote the signal intensity of images acquired with the b-factor value of b and b =0 s/mm2, respectively. With higher b-value associated lower image signal of the target tissue, Eq.  is focused on describing the signal decay pattern along increasingly higher b-values by three IVIM parameters (PF, Dslow, Dfast). Signal intensity at each b-value [i.e., SI(b)] is normalised by the signal intensity of b =0 image [i.e., SI(0)]. Applying this approach, for example if we want to compare the IVIM parameters of the normal brain and a brain tumor, we will take SI(0) of the normal brain and SI(0) of the tumor both as 1 (or 100) for the biexponential decay modelling, thus we would be assuming the SI(0) of the normal brain and the SI(0) the tumor are equal. This could be invalid in many scenarios. We demonstrated that an initial lower SI(0) of the target tissue is associated with a lower Dslow and a higher PF (1,2,11,12), regardless of whether we used segmented fitting or full fitting (1). Regardless of whatever methods we use to fit the curve of the diffusion weighted imaging signal decay along increasingly higher b-values, IVIM parameters are determined by this curve’s pattern which is in turn determined by relativity of SI(b) to SI(0). Therefore, target tissues of different compositions, which have different SI(0), may not necessarily be directly compared with the three IVIM parameters. For example, if two living tissues had the same diffusion and perfusion as well as other biological properties but these two tissues had different iron contents, we would expect the tissue with higher iron content would have lower SI(0), lower measured Dslow, and higher measured PF (12). We consider this problem is not easily solvable by a better fitting approach, by high signal-to-noise images, or by an extensive array of b-value images. Further research to better separate diffusion component and perfusion component should be pursued (1,13). Another possible approach would be that, if the reference values of IVIM diffusion and perfusion components are already known with standardised data acquisition, then we may be able to understand how these constrains can be computationally compensated for each target tissue.
The author thanks Mr. Ben-Heng Xiao, at the Chinese University of Hong Kong, Hong Kong, for helpful discussions.
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