Introduction

Peripheral arterial disease (PAD) affects around 8.5 million adults in the USA and 230 million worldwide.^1,2 Early diagnosis is crucial for personalized management and therapy planning. Intravoxel incoherent motion (IVIM)^3,4 is an MRI method that assesses tissue perfusion and diffusion simultaneously, providing information about tissue viability and wound healing potential. IVIM can potentially detect subtle perfusion abnormalities in the microcirculation, indicating PAD before significant arterial stenosis is observed. Early detection is essential for timely intervention and disease prevention. Here, we present a novel method based on mixture prior to calculating the IVIM’s pseudo-diffusion coefficient (D*) and the flowing blood-fraction (f), which are both connected to the microcirculation in the tissues.

Methods

The IVIM model suggests perfusion parameters can be estimated from low b-values, but DWI data is noisy due to scanner gradient imperfections. A mixture prior can improve parameter estimates.^5,6 We explain the approach using Figure 1 and the following mathematical description. The IVIM model^3,4 states that the signal $$$S(b)=S_0 ( (1-f) e^{(-bD)}+fe^{(-b(D+D^* ) ) } )+n$$$, where $$$S_0$$$ is the noise-free signal at $$$b=0, f $$$ is the fraction of the signal due to perfusion, $$$D$$$ is the diffusion coefficient, $$$D^*$$$ is the pseudo-diffusion coefficient due to perfusion, and $$$n$$$ is measurement noise, which may be taken to have a Normal or a Rician distribution. Suppose $$$S_x=\left\{S(b)|b∈\left\{b_1,⋯,b_n\right\}\right\}$$$ is the set of measured $$$S(b)$$$ values at voxel $$$x$$$. Then, assuming Gaussian noise, the parameters at voxel x can be estimated by the algorithm outlined in Figure 1. In brief, this algorithm assumes a mixture of Gaussians prior for IVIM parameters. The algorithm iterates between updating the IVIM parameters and the prior. Data from all voxels contribute to updating the prior, affecting the parameter estimate at every voxel. The mixture-of-Gaussians prior models different perfusion-diffusion classes in the image.
Experiments:
A healthy volunteer was scanned using a 3T MRI scanner (MAGNETOM Prisma^fit; Siemens Healthcare, Erlangen, Germany) using a PA-Matrix Coil. High-resolution T₁W images were acquired with a turbo spin echo sequence (TSE) at 0.8×0.8×2.0 mm³ resolution, TR=819ms, TE=10ms, flip-angle=150°, 196mm field-of-view,10 slices. The experiment test the effect of post-ischemic calf reactive-hyperemia on IVIM-parameters assessed before and after 5ms thigh cuff-occlusion. IVIM datasets in the right calf were acquired using two identical scans in a healthy volunteer, expecting greater differences with greater ischemia induced by high cuff pressures. Both datasets were acquired using a resolve sequence, TE=70ms, and TR=1080ms,196mm field of view, 10 slices, isotropic resolution of 2mm. The diffusion scheme included nine-shell b-values:50,100,150,200,250,300,400,600,800s/mm², each with six directions and five non-diffusion weighted volumes. Another experiment was conducted using an established porcine-model of hindlimb ischemia induced by injection of embolization beads (Embozene® Microspheres, 14 ml, 250 µm) into the distal external iliac to mimic MVD followed by surgical occlusion at the same location. The IVIM scanning scheme is the same one used in the volunteer.
Data Processing:
The algorithm in Figure 1 was used to estimate IVIM parameters.

Results

Figure 2 displays four results comparing IVIM parameters without priors and using the algorithm. The parameter estimates are not robust due to noise, and the algorithm shows vastly improved estimates and a plausible range of estimated f and D* values. The mean value of f values in the Soleus muscle with no prior is 55% at baseline and 47% after cuff release, while the D* values are 9.5x10^-3mm²/s and 8.8x10^-3mm²/s. The mean value of f in the Soleus muscle using the proposed method was 34% at the baseline and 49% after cuff-release. The mean value of D* in the Soleus muscle was 7.3x10^-3mm²/s and 8.5x10^-3 mm²/s. This is consistent with the physiological expectation that the perfusion after cuff-release is higher than baseline. Finally, note that D is unchanged by cuff-release, which follows physiologic expectations. Figure 3 shows the histograms of f and D* in the Soleus of the baseline and after cuff-release using no-prior and the proposed method. Welch’s t-test was applied on f and D* in baseline versus after cuff release, rejecting the null hypothesis of equal means at the default significance level of 5% in f and D* with f t-statstic=-17.3, p-value=1.7e-52, and D* t-statistic=-18.4, p-value=4e-38. While for D the t-test does not reject the null hypothesis, tstatistic= -0.8277 p-value=0.04.
Figures 4,5 illustrate the porcine results of the proposed algorithm with a mean value of 50.8% for f and 3.8x10-4 mm²/s for D*. The mean water diffusion D was 4x10^-5mm²/s.

Discussion and Conclusion

Using the proposed mixture prior method, we observed improved estimates of the IVIM parameters and a plausible range of estimated $$$f$$$ and $$$D^*$$$ values in the expected tissue locations.

Acknowledgements

No acknowledgement found.