Time-Dependent Diffusion MRI in Cancer: Tissue Modeling and Applications

Olivier Reynaud

doi:10.3389/fphy.2017.00058

Abstract

In diffusion weighted imaging (DWI), the apparent diffusion coefficient has been recognized as a useful and sensitive surrogate for cell density, paving the way for non-invasive tumor staging, and characterization of treatment efficacy in cancer. However, microstructural parameters, such as cell size, density and/or compartmental diffusivities affect diffusion in various fashions, making of conventional DWI a sensitive but non-specific probe into changes happening at cellular level. Alternatively, tissue complexity can be probed and quantified using the time dependence of diffusion metrics, sometimes also referred to as temporal diffusion spectroscopy when only using oscillating diffusion gradients. Time-dependent diffusion (TDD) is emerging as a strong candidate for specific and non-invasive tumor characterization. Despite the lack of a general analytical solution for all diffusion times / frequencies, TDD can be probed in various regimes where systems simplify in order to extract relevant information about tissue microstructure. The fundamentals of TDD are first reviewed (a) in the short time regime, disentangling structural and diffusive tissue properties, and (b) near the tortuosity limit, assuming weakly heterogeneous media near infinitely long diffusion times. Focusing on cell bodies (as opposed to neuronal tracts), a simple but realistic model for intracellular diffusion can offer precious insight on diffusion inside biological systems, at all times. Based on this approach, the main three geometrical models implemented so far (IMPULSED, POMACE, VERDICT) are reviewed. Their suitability to quantify cell size, intra- and extracellular spaces (ICS and ECS) and diffusivities are assessed. The proper modeling of tissue membrane permeability – hardly a newcomer in the field, but lacking applications - and its impact on microstructural estimates are also considered. After discussing general issues with tissue modeling and microstructural parameter estimation (i.e. fitting), potential solutions are detailed. The in vivo applications of this new, non-invasive, specific approach in cancer are reviewed, ranging from the characterization of gliomas in rodent brains and observation of time-dependence in breast tissue lesions and prostate cancer, to the recent preclinical evaluation of new treatments efficacy. It is expected that clinical applications of TDD will strongly benefit the community in terms of non-invasive cancer screening.

Highlights

In diffusion weighted imaging (DWI), the apparent diffusion coefficient (ADC) has been recognized as a useful and sensitive surrogate for cell density, paving the way for non-invasive tumor staging, and characterization of treatment efficacy in cancer
This review focuses on time-dependent diffusion (TDD), i.e., the manifestation of tissue complexity through the dependence of the metrics previously introduced with diffusion time t: D = D(t) (and K = K(t)), sometimes referred to as temporal diffusion spectroscopy [9]
Results differed from the previous experiment in that the treated tumor ADC decreased for high frequencies, but still increased for pulsed gradient spin echo (PGSE) and low-frequency oscillating gradient spin echo (OGSE)

Summary

INTRODUCTION

Infinitely short time regime is well defined for any system, and disentangle geometric from purely diffusive tissue properties [10]. A perturbative solution to the time-dependence of diffusion exists near the tortuosity limit [11, 31] In this regime, Novikov et al [11] demonstrated that the diffusion depends on large scale structural fluctuations via the power law: DPGSE (t) = D∞ + A · t −θ δ. In addition to the unrealistic case of infinite impermeable membranes already described by Tanner and Stejskal [41], similar expressions were derived for diffusion inside spherical shells [42] and infinite cylinders [43] The former, in order to represent cellular nuclei and cytoplasm, adds two extra degrees of freedom to a problem already prone to overfitting [15]. The latter was shown successful in estimating the size of small cylinders in the absence of an extracellular medium [44] and could be promising for axonal size estimation but is of little use for MR in cancer

A Simple Model for Intracellular Diffusion

Conclusion

CONCLUSION

24. Hürlimann