Intravoxel incoherent motion (IVIM) imaging is a concept and a method initially introduced and developed by Le Bihan et al. to quantitatively assess all the microscopic translational motions that could contribute to the signal acquired with diffusion MRI. In this model, biological tissue contains two distinct environments: molecular diffusion of water in the tissue (sometimes referred to as 'true diffusion'), and microcirculation of blood in the capillary network (perfusion). The concept introduced by D. Le Bihan is that water flowing in capillaries (at the voxel level) mimics a random walk (“pseudo-diffusion” ) (Fig.1), as long as the assumption that all directions are represented in the capillaries (i.e. there is no net coherent flow in any direction) is satisfied. It is responsible for a signal attenuation in diffusion MRI, which depends on the velocity of the flowing blood and the vascular architecture. Similarly to molecular diffusion, the effect of pseudodiffusion on the signal attenuation depends on the b value. However, the rate of signal attenuation resulting from pseudodiffusion is typically an order of magnitude greater than molecular diffusion in tissues, so its relative contribution to the diffusion-weighted MRI signal becomes significant only at very low b values, allowing diffusion and perfusion effects to be separated.
Model In the presence of the magnetic field gradient pulses of a diffusion MRI sequence, the MRI signal gets attenuated due to diffusion and perfusion effects. In a simple model, this signal attenuation, S/So, can be written as:
S S 0 = f I V I M F perf + ( 1 − f I V I M ) F diff {\displaystyle {\frac {S}{S_{0}}}=f_{\mathrm {IVIM} }F_{\text{perf}}+(1-f_{\mathrm {IVIM} })F_{\text{diff}}\,} [1] where f I V I M {\displaystyle f_{\mathrm {IVIM} }} is the volume fraction of incoherently flowing blood in the tissue (“flowing vascular volume”), F perf {\displaystyle F_{\text{perf}}} the signal attenuation from the IVIM effect and F diff {\displaystyle F_{\text{diff}}} is the signal attenuation from molecular diffusion in the tissue. Assuming blood water flowing in the randomly oriented vasculature changes several times direction (at least 2) during the measurement time (model 1), one has for F perf {\displaystyle F_{\text{perf}}} :
F perf = exp ( − b . D ∗ ) {\displaystyle F_{\text{perf}}=\exp(-b.D^{*})\,} [2] where b {\displaystyle b} is the diffusion-sensitization of the MRI sequence, D ∗ {\displaystyle D^{*}} is the sum of the pseudo-diffusion coefficient associated to the IVIM effect and D blood {\displaystyle D_{\text{blood}}} , the diffusion coefficient of water in blood:
D ∗ = L . v blood / 6 + D blood {\displaystyle D^{*}=L.v_{\text{blood}}/6+D_{\text{blood}}\,} [3] where L {\displaystyle L} is the mean capillary segment length and v blood {\displaystyle v_{\text{blood}}} is the blood velocity. If blood water flows without changing direction (either because flow is slow or measurement time is short) while capillary segments are randomly and isotropically oriented (model 2), F perf {\displaystyle F_{\text{perf}}} becomes:
F perf = sinc ( v blood c / π ) ≈ ( 1 − v blood c / 6 ) {\displaystyle F_{\text{perf}}=\operatorname {sinc} (v_{\text{blood}}c/\pi )\approx (1-v_{\text{blood}}c/6)\,} [4] where c {\displaystyle c} is a parameter linked to the gradient pulse amplitude and time course (similar to the b value).
In both cases, the perfusion effect results in a curvature of the diffusion attenuation plot towards b=0 (Fig.2). In a simple approach and under some approximations, the ADC calculated from 2 diffusion-weighted images acquired with b0=0 and b1, as ADC = ln(S(b0)/S (b1)), is:
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