Synopsis

Although IVIM model can provide valuable insight into tissue perfusion and microstructure without the need for contrast, the estimation of model parameters with sufficient accuracy continues to be a challenge. In this work, we propose a analytical segmented (AS) approach for estimating IVIM model parameters describing tissue perfusion (Df, and f), and tissue diffusion (Ds), and compare the performance of this work against conventional approaches using numerical simulations. Results from our work suggest that AS approach can minimize errors in the estimation of metrics characterizing perfusion, i.e., f, and Df compared to conventional approaches (full fitting , segmented and oversegmented methods) even for tissues with low Df/Ds ratios.

INTRODUCTION

IVIM model of tissue diffusion accounts for tissue perfusion and diffusion and can provide valuable insight into various pathological processes^1,2,3. However, due to the vast differences in the diffusivities between the fluid (perfusion) and tissue compartments, determination of IVIM model parameters –particularly the perfusion indices –remains a challenge and methods proposed to-date can have errors of 50% or more⁴.

The purpose of this work is twofold: (a) Propose a new analytical segmented (AS) method, to extract IVIM model perfusion related parameters; and (b) to compare the performance of the AS method to widely used conventional methods using numerical simulations.

METHODS

Theory: IVIM model describes MR signal (S) decay due to diffusion weighting (diffusion sensitivity parameter 'b’ in s·mm^-2), by equation 1⁵ (Figure 1).

AS method: This approach consists of two steps:

(1) Analogous to other segmented approaches, tissue diffusion (D_s) is estimated by fitting the DWI images with b-values (e.g., b > 200 s·mm^-2) large enough to substantially reduce the signal contribution from the high diffusivity perfusion compartment.

(2) By rearranging Equation 1, one obtains Eq. 2a, and we define f(b) (Eq. 2b). Perfusion related parameters (f, D_f) are extracted directly by fitting f(b) to Equation 3, (Figure 1).

The three commonly used approaches for extracting IVIM parameters considered are:

(i) Full Method (F): S(b) is fitted to the Eq. 1 using a Nonlinear Least Squares approach to extract IVIM parameters (f, D_f, and D_s).

(ii) Segmented Method (S): This method exploits the clinical observation that D_f is often one or two orders of magnitude greater than D_s⁷, and therefore the S(b) at high b values are not affected by the perfusion component. In the first step, D_s is extracted by fitting signal acquired at high b values using equation 3, and rest of the parameters (f, D_f) are estimated by fitting Equation 1, with the additional knowledge of D_s.

(iii) Oversegmented Method (OS): The first part of OS approach is similar to that of segmented approach after which the fitted monoexponential is extrapolated to obtain S-intercept and then f is calculated using Equation 4. D_f is estimated by fitting the entire signal into IVIM equation after fixing both f and D_s estimated in previous steps.

Numerical Simulations: MR signal was simulated using Eq. 1 for tissues with a broad range of D_f /D_s ratios ranging from 1 to 50 in increments of 1, f values ranging from 1-50% in increments of 1%, and a D_s value of 0.001, resulting in 2500 numerical tissue samples. Gaussian noise was added to generate MR signal for each sample at SNR levels of 10, 20 and 50. Eight b values(0,10,50,100,150,200,250,400,800 s·mm^-2) were used . Each sample was simulated 200 times.

Data Analysis: Mean average percentage error (MAPE) for each parameter (f, and D_f) was calculated as the ratio of the signal difference between the estimated and true value of the parameter normalized by the true value of the parameter, and expressed as a percentage, for each of four analysis methods considered.

RESULTS

MAPE for the estimation of f and D_f for the range of tissue models and for the four methods is given in Figures 2 and 3 respectively. A brief summary of key results are:

(a) Among the conventional methods (F, S, and OS), the OS method outperforms F and S when the D_f /D_s ratio is >15, for the estimation of both f and D_f at all SNR levels independent of the f-value.

(b) The proposed AS method outperforms the OS method at even lower D_f /D_s ratios (>5) when estimating f.

(c) At all D_f /D_s ratios, AS method outperforms F, S, and OS methods, at all SNR levels in the estimation of D_f.

DISCUSSION AND CONCLUSION

While both S and AS methods simultaneously estimate (f, and D_f), AS method performs better than the S method for estimating both f and D_f, across the range of D_f /D_s at all SNR levels. While the OS method is superior in the estimation of f when D_f /D_s ratio is >15, the proposed AS method outperforms the OS method at even lower D_f /D_s ratios (>5) at all SNR levels. Recent work by Jerome et al and others suggest that IVIM based estimation of f needs to be corrected for T₂ difference between the two compartments⁶. Equation 2 proposed here needs to extended to include the T₂ effect.

The proposed AS approach would be preferred where both f and D_f are of interest as well as when D_f /D_s ratio is expected to be <15 while OS would be preferred where only f is of interest and the expected D_f /D_s ratio is >15.

Acknowledgements

References

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