Synopsis

Cell compartments can present non-uniform T2 relaxations, depending on tissue properties. The non-uniform T2 relaxation has been shown to affect measurements of apparent diffusion coefficients (ADC). In additional to ADC, diffusion heterogeneity measured by modeling non-monoexponential decay has been used to characterize water diffusion in tissue microstructure. The purpose of this study is to study the effects of non-uniform T2 relaxations on the diffusion heterogeneity using a Monte Carlo simulation. The results demonstrate that the diffusion heterogeneity may provide more information about water diffusion within microstructure with non-uniform T2 relaxations.

INTRODUCTION

Non-monoexponential decay of diffusion-weighted imaging (DWI) signals can be phenomenologically modeled by assuming multiple diffusion components. The bi-exponential model fits the data well, but it is difficult to accurately estimate the fitted parameters [1]. More generally, the signal decay is assumed to arise from a continuous distribution of diffusion coefficients [2], for example, using stretched exponential model [3] or gamma distribution model [2]. The shape of the distribution, such as mean and standard deviation (STD), may provide information about microstructure, but their relationship is unclear. Previously, we have developed a 3-dimensional (3-D) Monte Carlo simulation to study the relationship between tumor malignancy-related tissue changes and a non-monoexponential model assuming uniform T2 relaxations [4]. Non-uniform T2 relaxations between cell compartments have been shown to affect measurements of apparent diffusion coefficient (ADC) [5-7]. In this study, we investigate how the non-uniform T2 relaxations affect the non-monoexponential decay described by gamma distribution model with b-values up to 6000 s/mm². We evaluate changes in the fitted parameters with simulated microstructural changes and the fitting accuracy.

METHODS

Microstructure:

A 3-D microenviroment was simulated using randomly packed spheres [4]. The baseline microstructural parameters were derived from previous measurements on biological tissues and low-grade tumors. Four independent microstructural changes related to tumor malignancy were simulated as described previously [4] (Fig. 3 and 4), including increased cell density, nuclear volume, extracellular volume fraction (VF_ex), and extracellular tortuosity (λ_ex). Water diffusivities for nuclear (Dnu), cytoplasmic (Dcyto), and extracellular (Dex) compartments were: 1.2, 0.3, and 1.8 × 10^-3 mm²/s, respectively. T2nu, T2cyto, and T2ex were 78, 29.2, and 150 ms [5-7]. Furthermore, two additional values of membrane permeability (P_mem): 2.4 × 10^-3 and 2.4 × 10^-1 mm/s were applied to study the effects of P_mem.

DWI experiment:

DWI signals were simulated using a Monte Carlo simulation of random walkers and pulsed gradient spin-echo sequence as described previously [4]. The b-values ranged from 0 to 6000 s/mm² in increment of 500 s/mm². Each simulation was repeated 5 times. The simulated signals were fitted with gamma distribution model: (S(b) = βα /(β+b)α) using the Levenberg-Marquardt algorithm in Matlab (Mathworks, Inc.). The mean and STD of the gamma distribution (mean_gamma and STD_gamma) were computed. Apparent diffusion coefficient (ADC) was also computed using the simulated signals with b-values of 0 and 1000 s/mm².

Statistics:

The goodness of fit was assessed using the reduced chi-square statistic (χ_ν²) and the Akaike Information Criterion (AIC) with a correction for finite sample sizes [8]. The changes of the fitted parameters (ADC, mean_gamma, and STD_gamma) with simulated microstructural changes were evaluated using Wilcoxon rank-sum test with p-value < 0.05.

RESULTS

Fitting assessment:

The gamma distribution model fit the simulated DWI signals of all experiments using the χ_ν² test; χ_ν² = 0.03-1.33, ν = 9 (Fig. 1). The AIC values were higher for the signal decay with high P_mem and non-uniform T2 relaxations (Fig. 2). The STD of the fitted parameters across five repeated experiments was 1% for ADC and mean_gamma, and was 2% for STD_gamma.

Effects of uniform T2 relaxations:

Compared with the fitted parameters obtain with uniform T2 relaxations (Fig. 4), the non-uniform T2 relaxations resulted in higher ADC, mean_gamma, and STD_gamma (Fig. 3). Changes in the fitted parameters obtained with uniform and non-uniform T2 relaxations were similar in responding to increased cell density, VF_ex and λ_ex. However, ADC and mean_gamma increased with increased nuclear volume with uniform T2 relaxations (Fig. 4), whereas they showed a decrease or no changes with non-uniform T2 relaxations (Fig. 3). STD_gamma increased with nuclear volume with uniform T2 relaxations (Fig. 4) but showed a decrease with non-uniform T2 relaxations (Fig. 3). Furthermore, with increased P_mem, ADC and mean_gamma showed an increase with uniform T2 relaxations but a decrease with non-uniform T2 relaxations. STD_gamma increased with decreased P_mem with both uniform and non-uniform T2 relaxations.

DISCUSSION

Consistent with previous studies on ADC measurements, non-uniform T2 relaxations led to T2 filtering effect and an increase in diffusion coefficients [5,6]. It also caused reduced diffusion coefficients when P_mem was increased [5]. Additionally, we demonstrate that non-uniform T2 relaxations caused increased diffusion heterogeneity measured by STD_gamma. Interestingly, when P_mem was increased, the diffusion heterogeneity decreased in both cases of uniform and non-uniform T2 relaxations. These results suggest that, compared with ADC, the diffusion heterogeneity may provide more information about changes in heterogeneous microstructure with non-uniform T2 relaxations.

Acknowledgements

References

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