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