Original Research Microstructural Changes in Ischemic Cortical Gray Matter Predicted by a Model of Diffusion-Weighted MRI Peter Vestergaard-Poulsen, PhD, 1 * Brian Hansen, MS, 1,2 Leif Østergaard, PhD, 1 and Rikke Jakobsen, MS 1 Purpose: To understand the diffusion attenuated MR sig- nal from normal and ischemic brain tissue in order to extract structural and physiological information using mathematical modeling, taking into account the transverse relaxation rates in gray matter. Materials and Methods: We fit our diffusion model to the diffusion-weighted MR signal obtained from cortical gray matter in healthy subjects. Our model includes variable volume fractions, intracellular restriction effects, and ex- change between compartments in addition to individual diffusion coefficients and transverse relaxation rates for each compartment. A global optimum was found from a wide range of parameter permutations using cluster com- puting. We also present simulations of cell swelling and changes of exchange rate and intracellular diffusion as possible cellular mechanisms in ischemia. Results: Our model estimates an extracellular volume frac- tion of 0.19 in accordance with the accepted value from histology. The absolute apparent diffusion coefficient ob- tained from the model was similar to that of experiments. The model and the experimental results indicate significant differences in diffusion and transverse relaxation between the tissue compartments and slow water exchange. Our model reproduces the signal changes observed in ischemia via physiologically credible mechanisms. Conclusion: Our modeling suggests that transverse relax- ation has a profound influence on the diffusion attenuated MR signal. Our simulations indicate cell swelling as the primary cause of the diffusion changes seen in the acute phase of brain ischemia. Key Words: MRI; diffusion; transverse relaxation; brain; ischemia J. Magn. Reson. Imaging 2007;26:529 –540. © 2007 Wiley-Liss, Inc. WATER SELF-DIFFUSION can be measured by diffu- sion-weighted proton magnetic resonance, which pro- duces an average signal from the water diffusion in all cell compartments. Diffusion in tissues is influenced by restriction and hindrance effects of e.g., cell mem- branes, and also the water exchange between the intra- and the extracellular compartment. Thus, water self- diffusion measured by this method depends on the dif- fusion distance within the cells, the tortuosity of the interstitial space, and the transport through cell mem- branes. Currently, there is no experimental in vivo method, which completely separates the superposition of these effects on the average signal. Consequently, the diffusion-weighted signal is not a direct measure of the free diffusion and gives rise to the so-called apparent diffusion coefficient (ADC) (1,2). The ADC does not pro- vide a direct measure of the specific underlying cellular microstructure and modeling of tissue water diffusion is needed to infer microstructure from the compound signal. Successful modeling of tissue water diffusion would provide a tool for estimation of important cellular variables, such as volume fractions and membrane per- meability in normal and pathological states. Of partic- ular interest is an improved understanding of the underlying cellular mechanisms in acute cerebral isch- emia, where the ADC decreases as much as 40% to 50% (3). So far, no model has produced realistic physical volume fractions and absolute ADC values comparable to those measured in brain. Realistic tissue diffusion models of normal tissue is required before applying the model to studies of ischemia. Several mechanisms are thought to be responsible for the reduced ADC in isch- emia: reduced water mobility in the extra- and intracel- lular compartments (4), water moving from the extra- to the intracellular compartment, changes in membrane permeability, and increased tortuosity of the extracel- lular space due to cell swelling (5). The effects on the diffusion-weighted MR signal of these mechanisms 1 Center of Functionally Integrative Neuroscience/Department of Neu- roradiology, Aarhus University Hospital, Aarhus University, Aarhus, Denmark. 2 Institute of Physics and Astronomy, Aarhus University, Aarhus, Den- mark. Contract grant sponsor: Danish National Research Foundation. *Address reprint requests to: P.V-P., Center of Functionally Integrative Neuroscience, Aarhus University Hospital, Nørrebrogade 44, Building 30, DK-8000, Aarhus, Denmark. E-mail: peterv@pet.auh.dk Received September 19, 2006; Accepted May 3, 2007. DOI 10.1002/jmri.21030 Published online in Wiley InterScience (www.interscience.wiley.com). JOURNAL OF MAGNETIC RESONANCE IMAGING 26:529 –540 (2007) © 2007 Wiley-Liss, Inc. 529