Synopsis
Diffusion tensor imaging (DTI) is widely employed to
characterize diffusion anisotropy in multi-directional diffusion MR
acquisitions. However, the DTI model has well-known limitations primarily
because it assumes diffusion to be Gaussian. In this talk, DTI’s limitations
will be discussed for three cases: (i) the presence of orientational
complexity, (ii) nonlinearity of the signal decay curves, and (iii) dependence
on the timing parameters of the sequence. Several alternative approaches will
be outlined and it will be argued that a cost-benefit analysis has to be
performed before abandoning the diffusion tensor model.Target Audience
Scientists with elementary physics background
interested in the main approaches taken to model and represent
diffusion-weighted MR data.
Outcome / Objectives
·
The goal is to introduce models that go beyond
diffusion tensor imaging.
·
The need for more sophisticated models will be
justified.
·
The audience will find out about the different
directions in which the diffusion tensor model is generalized.
Purpose
As the first analytical model used to describe
the anisotropic diffusional processes that can be observed via magnetic
resonance methods, diffusion tensor imaging (DTI) [1,2] has attracted
widespread interest from many different fields of investigation. Several new
MRI indices, akin to different “stains” in histological examinations, have been
introduced that exploits the diffusional characteristics of the medium based on
the DTI model [3,4]. Perhaps equally importantly, DTI has made it possible to
map the major neuronal connections between different regions of the central
nervous system. DTI features a relatively simple mathematical structure, and is
practical also from the point of view of data collection. However, there are
some shortcomings of DTI, stemming from its assumption that diffusion is
Gaussian. This assumption may have serious ramifications related to fiber-tract
mapping and microstructure elucidation. Thus, more general representations
applicable to a wider range of diffusional scenarios are commonly employed.
Methods
Models that go beyond DTI can be grouped into
different classes. DTI’s inability to describe diffusion MRI data becomes most
apparent when one considers variations in different parameters of a pulse
sequence.
·
When the dependence of the signal on the
gradient orientation is concerned, DTI assumes a unimodal profile on the
hemisphere. Such a profile is sufficient when there is a single underlying orientation.
However, since there are as many as 100,000 neurons within a voxel, it is not
unusual to encounter orientationally heterogeneous structures. In such
complicated regions, the principal eigenvector of the estimated diffusion
tensor yields only an average direction, which typically does not coincide with
any of the distinct fiber pathways. As such, DTI may lead to erroneous
connections and pathways in anatomical connectivity studies. To overcome this
limitation, numerous methods have been proposed to date. For example, by
increasing the angular resolution of the diffusion measurements [5], one can
infer the distinct orientations along which diffusion is favored [6-12].
For the case of traditional diffusion
measurements performed by applying a pair of gradients [13], the sensitivity of
the signal to diffusion is determined partially by a quantity called the
q-value, which has the dimension of inverse length. When the logarithm of the
signal is plotted against this quantity, one obtains a linear dependence for
the case of Gaussian diffusion. However, real experiments indicate a deviation
from this behavior [14]; this deviation becomes substantial as the q-value is
increased. Therefore, when data with large q-values are to be used, the DTI
model becomes insufficient. Thus, more general representations are commonly
employed [15-16]. Note that this
deviation is not limited to one-dimensional sampling of the q-space. For
characterizing diffusion anisotropy, one typically samples the
three-dimensional q-space. In this case, one could either use a “model-free” approach
to transform the entire data set directly into a meaningful quantity called the
average propagator [17] or employ a generalization of DTI’s signal expression
[18-19] to represent the data.
Another, often overlooked limitation of DTI is
apparent when one considers the dependence of the MR signal on the timing
parameters of the sequence. Gaussian diffusion suggests a particular
dependence, expressed by the Stejskal-Tanner expression [13], which is quite
different than what one obtains for the case of restricted diffusion [20,21].
The difference is quite significant even at small q-values. Thus, referring to
the small diffusion sensitivity regime as the “DTI regime” may be problematic.
Discussion & Conclusion
Depending on the acquisition scheme and the goal
of the study, different models tailored to that problem could be favored if the
diffusion tensor model fails. We note that some of the shortcomings of DTI
could be overcome if the tensor model is employed as the building block of a
composite model. For example, the signal can be expressed as the sum of two
expressions, each having a separate diffusion tensor [22]. Such representation
produces the nonlinearity of the semi-logarithmic signal vs. q-value plot, and
could be employed to resolve two fiber orientations. Similarly, the signal from
the voxel can be envisioned to emerge from a Wishart distribution of diffusion
tensors [23], which yields, remarkably, a power-law decay in the tail of the
signal decay curve.
Last but not least, it should be mentioned that
the more sophisticated models could be costly in terms of their computational
burden and typically require more time-consuming data acquisitions. In certain
cases, it may be necessary to compromise on the spatial resolution in
acquisitions, which could exacerbate the problem of fiber crossings. Thus, when
the cost of employing a more general model outweighs its benefits, DTI may
still be the method of choice.
Acknowledgements
No acknowledgement found.References
1. P.J. Basser, J. Mattiello, D. LeBihan, Estimation of
the effective self-diffusion tensor from the NMR spin echo, J. Magn. Reson., B
103 (3) (1994) 247– 254.
2. P.J. Basser, J. Mattiello, D. LeBihan, MR diffusion
tensor spectroscopy and imaging, Biophys. J. 66 (1), (1994) 259–267.
3. P.J. Basser, Inferring microstructural features and
the physiological state of tissue from diffusion weighted images, NMR Biomed. 8 (1995) 333-344.
4. C. Pierpaoli, P.J. Basser, Toward a quantitative
assessment of diffusion anisotropy. Magn.
Reson. Med. 36 (1996) 893-906.
5. D.S. Tuch, T.G. Reese, M.R. Wiegell, N. Makris, J.W.
Belliveau, V.J. Wedeen, High angular resolution diffusion imaging reveals
intravoxel white matter fiber heterogeneity, Magn. Reson. Med. 48 (4) (2002)
577–582.
6. D.S. Tuch, Q-ball imaging, Magn. Reson. Med. 52 (2004)
1358–1372.
7. E. Özarslan, T.H. Mareci, Generalized diffusion tensor
imaging and analytical relationships between diffusion tensor imaging and high
angular resolution diffusion imaging, Magn. Reson. Med. 50 (5) (2003), 955–965.
8. J.D. Tournier, F. Calamante, D.G. Gadian, A. Connelly,
Direct estimation of the fiber orientation density function from
diffusion-weighted MRI data using spherical deconvolution, Neuroimage 23,
(2004), 1176–1185.
9. E. Özarslan, T.M. Shepherd, B.C. Vemuri, S.J.
Blackband, T.H. Mareci, Resolution of complex tissue microarchitecture using
the diffusion orientation transform (DOT), Neuroimage 31 (3) (2006) 1086–1103.
10. M. Descoteaux, E. Angelino, S. Fitzgibbons, R.
Deriche, Regularized, fast, and robust analytical q-ball imaging, Magn. Reson.
Med. 58 (3) (2007) 497–510.
11. I. Aganj, C. Lenglet, G. Sapiro, E. Yacoub, K.
Ugurbil, N. Harel, Reconstruction of the orientation distribution function in
single- and multiple-shell q-ball imaging within constant solid angle, Magn.
Reson. Med. 64 (2) (2010) 554–566.
12. F. Dell'Acqua, P. Scifo, G. Rizzo, M. Catani, A.
Simmons, G. Scotti, F. Fazio, A modified damped Richardson–Lucy algorithm to
reduce isotropic background effects in spherical deconvolution, Neuroimage 49
(2) (2010) 1446–1458.
13.
E.O. Stejskal, J.E. Tanner, Spin diffusion measurements:
Spin echoes in the presence of a time-dependent field gradient, J. Chem. Phys.
42 (1) (1965) 288–292.
14. R.V. Mulkern, H. Gudbjartsson, C.-F. Westin, H.P.
Zengingönül, W. Gartner, C.R. Guttmann, R.L. Robertson, W. Kyriakos, R.
Schwartz, D. Holtzman, F.A. Jolesz, S.E. Maier, Multi-component apparent
diffusion coefficients in human brain, NMR Biomed. 12 (1) (1999) 51–62.
15. J.H. Jensen, J.A. Helpern, A. Ramani, H. Lu, K.
Kaczynski, Diffusional kurtosis imaging: the quantification of non-gaussian water
diffusion by means of magnetic resonance imaging, Magn. Reson. Med. 53 (2005)
1432–1440.
16. E. Özarslan, C.G. Koay, P.J. Basser, Simple harmonic
oscillator based estimation and reconstruction for one-dimensional q-space MR,
in Proc. Intl. Soc. Mag. Reson. Med. 16 (2008) p. 35.
17. V.J. Wedeen, P. Hagmann, W.-Y.I. Tseng, T.G. Reese,
R.M. Weisskoff, Mapping complex tissue architecture with diffusion spectrum
magnetic resonance imaging, Magn. Reson. Med. 54 (6) (2005) 1377–1386.
18. C.L. Liu, R. Bammer, M.E. Moseley, Generalized
diffusion tensor imaging (GDTI): a method for characterizing and imaging
diffusion anisotropy caused by non-Gaussian diffusion, Isr. J. Chem. 43 (1–2)
(2003) 145–154.
19. E. Özarslan, C.G. Koay, T.M. Shepherd, M.E. Komlosh,
M.O. Irfanoglu, C. Pierpaoli, P.J. Basser, Mean apparent propagator (MAP) MRI:
a novel diffusion imaging method for mapping tissue microstructure, NeuroImage
78 (2013) 16–32.
20. E. Özarslan, P.J. Basser, Microscopic anisotropy
revealed by NMR double pulsed field gradient experiments with arbitrary timing
parameters, J. Chem. Phys. 128 (15) (2008) 154511.
21. E. Özarslan, C.-F. Westin, T.H. Mareci, Characterizing
magnetic resonance signal decay due to Gaussian diffusion: the path integral
approach and a convenient computational method, Concept. Magn. Reson. A, 44(A)
(2015) 203–213.
22. B.A. Inglis, E.L. Bossart, D.L. Buckley, E.D. Wirth,
T.H. Mareci, Visualization of neural tissue water compartments using
biexponential diffusion tensor MRI, Magn. Reson. Med. 45 (4) (2001) 580–587.
23. B. Jian, B.C. Vemuri, E. Özarslan, P.R. Carney,
T.H. Mareci, A novel tensor distribution model for the diffusion-weighted MR
signal, Neuroimage 37 (1) (2007) 164–176.