Assessment of the effects of cellular tissue properties on ADC measurements by numerical simulation of water diffusion

Abstract

The apparent diffusion coefficient (ADC), as measured by diffusion-weighted MRI, has proven useful in the diagnosis and evaluation of ischemic stroke. The ADC of tissue water is reduced by 30-50% following ischemia and provides excellent contrast between normal and affected tissue. Despite its clinical utility, there is no consensus on the biophysical mechanism underlying the reduction in ADC. In this work, a numerical simulation of water diffusion is used to predict the effects of cellular tissue properties on experimentally measured ADC. The model indicates that the biophysical mechanisms responsible for changes in ADC postischemia depend upon the time over which diffusion is measured. At short diffusion times, the ADC is dependent upon the intrinsic intracellular diffusivity, while at longer, clinically relevant diffusion times, the ADC is highly dependent upon the cell volume fraction. The model also predicts that at clinically relevant diffusion times, the 30-50% drop in ADC after ischemia can be accounted for by cell swelling alone when intracellular T 2 is allowed to be shorter than extracellular The idea to use NMR to measure diffusion was introduced by Torrey in 1956 (1). The clinical utility of diffusionweighted MRI (DWMRI) was realized in the early 1990s in the evaluation of ischemic stroke. Within minutes of onset, DWMRI exhibits hyperintensity in regions of the brain affected by acute stroke, while T 2 -weighted images remain unaffected. The apparent diffusion coefficient (ADC), a quantitative measure of the diffusion of water in tissue, decreases 30 -50% in ischemic regions of the brain (2,3). While these results have had significant clinical utility, there remains no consensus on the biophysical mechanisms causing the drop in ADC. Several mechanisms have been proposed, including increases in the intracellular volume fraction (IVF) (3), increased tortuosity of extracellular spaces (4), decreased membrane permeability (P mem ) (4), and decreases in the diffusion of water in the intracellular space (5,6). Because a large number of tissue parameters have been hypothesized to affect the ADC, mathematical models of water diffusion are useful to assess the role of each parameter on the ADC.In free diffusion, the signal from DWMRI decays exponentially with increasing b-value, and is characterized by the intrinsic diffusion coefficient, D. However, the diffusion of water in tissue is not free: water interacts with lipid membranes, macromolecules, and other cellular and extracellular constituents, causing the signal decay to deviate from the monoexponential decay observed in free diffusion (7,8). The ADC lumps all of these interactions into a single "apparent" diffusion coefficient, which is calculated by fitting the DWMRI signal to an exponential decay over a specific range of b-values, typically between 0 and 1000 sec/mm 2 . Therefore, the ADC provides little indication of the specific biophysical mechanisms contributing the DWMRI signal decay. Other analyses of diffusion fit the non-monoexponential signa...

Optimal experimental design for filter exchange imaging: Apparent exchange rate measurements in the healthy brain and in intracranial tumors

“…Second, the AXR has been shown to be uncorrelated with ADC in the human brain in vivo (21). Finally, although the ADC is sensitive to cell permeability, the effect is almost negligible until the permeability becomes very high (48). Interestingly, ADC shows promise as a fast marker of treatment response (49) due to its sensitivity to treatment-induced tumor cell-kill (50).…”

Numerical simulation of diffusion MRI signals using an adaptive time-stepping method

“…The main difference between our approach and those in the previous works is that we use an efficient adaptive time-stepping method, called the Runge-Kutta Chebyshev (RKC) method (Sommeijer et al 1998), that takes time steps commensurate with the desired accuracy of the time integration at any given point in the simulation. In the case of moderate desired accuracy, we show that this approach is preferred to the explicit Forward Euler method used previously in (Hwang et al 2003, Xu et al 2007, Harkins et al 2009, Russell et al 2012 where the time step size is limited by numerical stability.…”

“…This PDE models the water proton magnetization subject to diffusion-encoding magnetic field gradient pulses and the dMRI signal is given as the integral of the solution of the PDE at echo time. The numerical solution of the multiple compartment Bloch-Torrey has been considered in the past (Hwang et al 2003, Xu et al 2007, Harkins et al 2009, Russell et al 2012). The main difference between our approach and those in the previous works is that we use an efficient adaptive time-stepping method, called the Runge-Kutta Chebyshev (RKC) method (Sommeijer et al 1998), that takes time steps commensurate with the desired accuracy of the time integration at any given point in the simulation.…”

An Explanation of Signal Changes in DW-fMRI: Monte Carlo Simulation Study of Restricted Diffusion of Water Molecules Using 3D and Two-Compartment Cortical Cell Models

“…In every simulation, we set 2r to 10 μm to consider the size of the cell and 2l to 11.262 μm to set the volume ratio of the intracellular and the extracellular regions to 70% [14], [15]. Moreover, we assumed that a cell with a length of 10 μm on each side swelled by 1-10% in length, while 2l is fixed to 11.262 μm.…”