118 RESULTS
Figure 5.11: The MD slices in axial view (left), and overlaid with the results
of first registration (middle), and the second round of registration (right).
This figure should be viewed in color.
§ 5.3 Diffusion MRI 119
Figure 5.12: Comparison of corpus callosum bundles reconstructed by using
manual seeding(middle) and our method. The left figure shows the label map
for manual seeding.
Fig.
5.12 com p a r es the corpus callosum constructed by manually seeded
tractography (middle) and by the proposed automatic fi ber-to- DTI registra-
tion method. As shown, the shape of the deformed corpus callosum model
well matches the fibers reconstructed by manually seeded tractography while
the tractography result is in co m p l et e, e.g., in the yellow rectangular region,
due to early term ination. Further, even with a carefully delineated seeding
region, it is still very difficult to avoid outlier fibers in tractogra p hy. A bun-
dle of outlier fibers are highlighted in the red rectangle for example. Since
outlier fibers in our fiber mod el have been removed by experts, the fibers
reconstructed by our method is clean.
120 RESULTS
To evaluate the consistency of this fiber-to-DTI registration among sub-
jects, we warp backward the FA volume of each subject to the fiber model
space and examine the averaged volume. Fig.
5.13 displays the averaged FA
of all the subjects after back-warping. As shown, the averaged FA images
appear rather blurry without u si n g any r e gi st r at i on due to the misalignmen-
t among subjects. The major skeleton of the WM becomes much clearer
after affine regist r at i on which compensates variations of size, position, and
orientation. As expected, the averaged images given by nonrigid fiber-to-
DTI are the sharpest which demonstrated consistent alignment given by our
fiber-to-DTI registration.

We also computed the pixel-wise standard devia t io n of back-warped FA
volumes to quantitatively assess the group alignment. Fig.
5.14 shows the
statistics of such pixel-wise standard deviation wi thin the brain area. By
using our nonri gi d fiber-to-DTI registra t io n , more points ”move” to the left
side indicating the redu ct io n of the standard deviation, i.e., the improve-
ment of group alignments. The mean standard deviations are 0.25, 0.20, and
0.18 respectively for no r egi st r at i on , affine fiber-to-DTI registration and non-
rigid fiber-to-DTI registration. The reduction of mean standard deviation s
demonstrated that our nonrigid fiber- t o- D TI registration method improved
the alignment of the FA volumes and thus indicati ng more accurate i nter-
subject correspondence.
§ 5.3 Diffusion MRI 121
Figure 5.13: The average FA images after back-warping. From top to bottom
shows sagittal, coronal, and axial views. From left to right shows the results
using no registration, affine registration, and non-rigid regi st r at i on .
122 RESULTS
0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5
0
0.5
1
1.5
2
2.5
3
3.5
4
x 10
4
Pixel−wise standard deviation

Noumber of pixels


No Registration
Affine Registration
Nonrgid Registration
Figure 5.14: The histograms of pixel-wise FA standard d e vi at i ons within
the brain area after back-warping all the subjects to th e brain fiber model
domain.
Previous clinical studies (
Nitkunan et al., 2008) suggested that DTI mea-
sures sho u l d have str o n g correlations with cognitive impairment. We there-
fore quantitatively validate our results by assessing the partial correlat i on s
(controlled for a ge, gender, and educat i on ) between the averaged FA and
widely used cognitive scores: the Montreal Cognitive Assessment (MoCA, Nasred-
dine et al.
(2005)); the Mini-Mental State Examination (MMSE , Folstein
et al.
(1975)); and the Color Trails Test 1&2 (CTT1, CTT2, D’Elia et al.
(1996)). The correl a ti o n tests are performed among all the subjects wit h
valid cogn i t i ve scores and ther e are about 45 subjects for each cognitive s-
core. Table
5.3 shows correl at i on s for the average FA along fi bers, amon g
the whole brain volumes and the average skeletonised FA by TBSS(
Smith
et al.
, 2006). ‘Corr.’ r ep r e sents the correlation i n absolute value, and ‘Sig.’
stands for the t-test significance level. Compared with the skeletonished FA
§ 5.3 Diffusion MRI 123
value of TBSS, our along-fiber FA correlates better with the cognitive scores.

Among the four cognitive measures , TBSS correlates best with CTT-2 at
0.671 while the correlation between our along fiber measure and CTT-2 is
0.760 which surpassed TBSS by 13.3%. Besides, b ot h our along fiber measure
and TBSS skeletonised FA remarkably outperform the whole br ai n average.
The correlations with cognitive scores are quite low for brain stem, which is
known to b e responsible for basic life functions like heart-beat i n g and breath-
ing. Fig.
5.15 shows the average measurements over the whole brain and the
fibers reconstructed by our method. As shown, the measurements generated
by our results better separate the healthy subjects and patients.
124 RESULTS
MOCA MMSE CTT-1 CTT-2
Along All Fibers
Corr. 0.601 0.629 0.628 0.760
Sig. 0.000 0.000 0.000 0.000
Corpus Callosum
Corr. 0.569 0.608 0.660 0.762
Sig. 0.000 0.000 0.000 0.000
Corona Radiata
Corr. 0.551 0.548 0.397 0.647
Sig. 0.000 0.000 0.005 0.000
Arcuate Region
Corr. 0.540 0.577 0.452 0.658
Sig. 0.000 0.000 0.001 0.000
Occipito Frontal
Corr. 0.601 0.566 0.532 0.708
Sig. 0.000 0.000 0.000 0.000
Superior Cingulum
Corr. 0.507 0.563 0.533 0.646
Sig. 0.000 0.000 0.000 0.000

Brain Stem
Corr. 0.157 0.065 0.148 0.052
Sig. 0.275 0.654 0.315 0.735
Whole Brain
Corr. 0.387 0.396 0.317 0.559
Sig. 0.006 0.004 0.028 0.000
TBSS
Corr. 0.544 0.582 0.610 0.671
Sig. 0.000 0.000 0.000 0.000
Table 5.3: Correlations between MRI scores and cognitive scores. For all th e
entries except ‘TBSS’ and ‘whole brain ’ , the MRI score is the average FA
value along the fibers obtained by the proposed method. ‘TBSS’ uses the
average of skeletonised FA values (
Smith et al., 2006) as the MRI score. For
‘whole brain’, the MRI score is the average FA for the entire brain region.
Brain masks are produced by 3D Slicer.
§ 5.3 Diffusion MRI 125
0 5 10 15 20 25 30 35
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
subjects
DTI measures



Healthy subjects
Patients
0 5 10 15 20 25 30 35
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
subjects
DTI measures


Healthy subjects
Patients
Figure 5.15: Comparison of MR measurements between healthy subjects and
patients. The top figure shows the resu l ts using mean FA, while the bottom
figure shows measurements along our reconstructed fibers.
126 RESULTS
Chapter 6
Conclusion and Future Work
This chapter concludes the thesis and dis cu sses the limitation of the pre-
sented work and the direction of future work. Section
§ 6.1 summarizes the
research objectives of this thesis and highlights the technical contributions.
The limitations of th e work and the recommendations of future research are

presented in Section
§ 6.2.
§ 6.1 Conclusion and Discussion
Perfusion MRI and diffusion MRI are important tools for early detection of
myocardial and cerebr a l ischemia respectively. Due to p a t i ent respiration
and arrhythmia, nonrigid registration is important for pixel-wise perfusion
signal analysis which is likely to great l y improve early myocardial ischemia
diagnosis. In brain diffusion MRI analysis, reconstructing brain fibers from
DTI is challenging due to the large amount of fiber tracts and the p r esen ce
of WM lesions. This thesis introduced a nonrigid regist r at i on m et h od for
perfusion MRI sequence calibration and a nonrigid fiber-to-D TI registration
127
128 CONCLUSION AND FUTURE WORK
method for full brain fiber rec on st r u c t io n .
§ 6.1.1 Cardiac Perfusion MRI
The proposed n onrigid perfusion sequence registration meth od compensates
for the elastic deformation of perfusion sequences by imposing spatiotempo-
ral smoothness constraints. In contrast to traditional registration approaches
that obtain the deformation field by pairwise registration of t he observed im-
ages in different perfusion phases, our method seeks the global op t i m al defor-
mation for the entire sequence by introduci ng the pseudo ground truth. As
the intensity variations of the pseudo ground truth and the observed sequence
are almost identical, it becomes not necessary to use multi-modality regis-
tration algorithms (such as NMI-based methods) that are computationally
expensive in general. Consequently, it enables us to apply existing intensity
based registration algorithms that are more computationall y effici ent.
The temporal smoothness constraint essentially uses the temporal neigh-
borhood of a frame to linearly estimate its counterpart in the pseudo ground
truth. Note that the contrast variations for pre- and post-bolus arrival frames
are not linear, which i n dicates that the perfusion signal is piece-wise linear.

Accordingly, there are minor intensity differences between the pseudo ground
truth and the observed sign al s for those frames due to smoothing. Such a s-
cenario is similar to the re gu l ar i zat i on in the registration approach where th e
first order or second order derivative penal ty is com m o n l y used although the
optimal deformation is n ei t h er constant nor linear for all t he pixels. In fact,
the pseudo ground truth here is only used to faci l it a t e nonrigid registration
§ 6.1 Conclusion and Discussion 129
rather than perfusion signal extraction. We assume that most registration
methods can tolerate such min or intensity differences, and ou r experimental
results reveal that the demons algorithm satisfies this assumpt io n .
By incor poratin g the spatial smoothness constraint, the pseudo ground
truth fitting for a pixel uses the major signal of the region to resol ve the ambi-
guity caused by deformation (Section § 3.3.3). This m ay lead to slight texture
difference between the ps eu d o ground truth sequence and the observed se-
quence, and we use an edge-emphasized demons method to overcome this
texture mismatch. In order to maintain the sharpness of strong edges, l ike
myocardium boundaries, we incorporate heart ventricle segmentation to en-
sure that pixels from different regions are not smoothed at all.
Compared with previous research using artificial sequence to facilitat e
registration in (
Buonaccorsi et al., 2005; Adluru et al., 2006; Melbourne et al.,
2007; Milles et al., 2008), the advantage of our method is threefold:
a) Our r egi st r at i on method utilizes spatiot em poral sm oothness constraints
in generati n g the ar ti fi c ia l sequence, i.e., the pseudo ground t r u t h.
It is more genera li zed than pharmacokinetic model based approach-
es (
Buonaccorsi et al., 2005; Adluru et al., 2006).
b) Instead of analyzing the intensity-time curves independ ently, we i ntro-
duce the spatial smoothness constraint in pseudo ground truth fitting,
so that the estim a t ed signal for a pixel depends on not only its own

intensity-time curve, but also its n ei ghbors’. This helps avoid blurred
boundaries in the artificial sequence, and consequently prevents the
method from incorrectly converging to local optima.
c) The m et h od has proven to be capable of compensating for nonrigid
130 CONCLUSION AND FUTURE WORK
deformation which is common in cardiac perfusion studies, while most
of the existing ar t i fi ci al sequence based methods focus only on rigid
registration. Although
Melbourne et al. (2007) addressed nonrigid mo-
tion, their method requires that there is no periodic motion present in
the sequence, despite that periodic motion is quite common in perfu-
sion stud i es due to pati ent breathing. Our method does not have this
limitation.
Our experimental results on 20 real perfusion MRI sequences have both
quantitatively and qualitatively shown that our method is able to effectively
compensate for the elastic deformation of the heart. The variation of the
pixel-wise perfusion signals was greatly reduced after applying our nonrigid
sequence registration approach, which is attributed to the successful com-
pensation of nonrigid h ea r t motion. This improvement on perfusion signal
extraction implies that pixel-wise perfusi on parameter is feasible and the
proposed method wi l l benefit early myocardial i schemia d ia gn o si s.
§ 6.1.2 Cerebral Diffusion MRI
Our fiber-to-tensor registration scheme, i.e., the FFFs model, deforms an
expert-annotated fiber m odel to diffusion tensor images of new subjects.
Fiber trajectories and anatomically meaningful fiber bundles are automat-
ically obtained by this registration. The free-form deformation s are used
to regularize the transformations at the whole brain level and across fib er
bundles. Fiber curvatures are penalized as the intra-fiber regularization to
encourage the smoothness of transformed fibers.
§ 6.1 Conclusion and Discussion 131

The advantages of this FFFs approach are threefold:
a) This free-form fibers system simultaneously achieves tr a ct ogr a p hy and
tractography segmentation after registration. The fiber cor r es pon-
dence among different subjects is also ob t ai n ed. It enforces the in-
tegrity of fibers and is robust to DTI defects by using inter- and intra-
fiber regularization (Fig.
1.2) and thus overcomes the early termination
problem.
b) Our whole brain fiber model is m er ged from fiber tracts of 10 brains,
and thus it is more representative than each individual model. In
this merged fiber model, the common fiber bundles are much denser
than bundles corresponding to individual difference and thus the local
deformations mainly rely on the common fiber bundles.
c) This FFFs system can au t om at i cal l y rectify the regist r at i on through
group analysis. Robust P CA is used to identify outlier fiber segments
which are deformed into non-WM regions or WM lesion regions. Then
a novel statistical context prior is introduced t o guide the registration
of these fiber segments.
To demonstrate the feasibility of whole brain fiber-to- DTI registration, we
did not incorporate the DTI-to-DTI registration in this approach. However,
the fiber-to-DTI registrat i on is not to compete with DTI-to-DTI registra-
tion. On the co ntrary, the well developed DTI-to-DTI registration methods
are likely to provide a robust initialization of this fiber-to-DTI r eg is tr a t io n
approach when an a tl a s, i.e., aligned fiber model and DTI, is available. In
addition, based on our regional prior term § 4.3.2, it is easy to incorporate
the DTI-to- DTI similarity in our system. The fiber-to-DTI registration com-
132 CONCLUSION AND FUTURE WORK
plements DTI-to-DTI method in two ways: a) Our fiber- t en sor - fi t measure is
directly defined on the fibers and it can rectify the error in the atlas. Due to
individual differences amon g subjects, it i s better to generate the atlas from

multiple subjects, which however cannot ensure a perfect alignment between
the reference fiber model and the reference DTI. Using DTI-to-DTI registra-
tion t o indirectly deform atlas fibers, these misalignments in the atlas will
be inherited in the resultant fibers. On the contrary, as we directly perform
registration from the fiber model t o DTI, small errors in the atlas can be cor-
rected. b) Thanks to the intra-fiber reg u l ar i ty, our fiber-to-DTI registration
can maintain reasonable fiber structures. However, the DTI-to-DTI regis-
tration met h od is blind to fiber structures and may result in unreasonable
shapes of fi bers, unless a strong regulari zat i on i s used .
We observed successful registration on 64 br ai n DTI studies, inclu ding
both heal thy control subjects and SVD patients. The DTI measures com-
puted from registered anatomical fiber bundles exhibit significant correlation
with cognitive functions, an d are likely to lead to a reliable SVD assessment
measure.
§ 6.2 Future Work
§ 6.2.1 Cardiac Perfusion MRI
First, one limitation of the proposed perfusion MRI registrat io n method lies
in the increased computational com plexity associated with the PGT esti-
mation. Introducing the pseudo ground tr u t h successfully overcomes the
§ 6.2 Future Work 133
intensity var i at i on problem. It however increases the number of unknown
variables and therefor e requires iterative optimization. Although empirical-
ly three iterations give satisfactory results, the absolute convergence of the
algorithm may require more iterations. An alternative s ol u t i on circumvent-
ing iterative optimization is to directly define the s p at i ot em poral smoothness
constraints on the deformed sequence as the energy functional, which could
be solved by gradient descent method. However, it is import ant to note that
due to the high order derivatives in our energy functional, the computation
of partial differential equation is complex, and the solut i on space may con-
tain many local op t i m a. Thus an advanced optimization approach may be

required.
Second, in our current implementation, the myocard i al segmentation re-
quires the user to input two clicks for initialization purpose. Despite this
interaction is minor, it is desirable to automate the initialization step. In
our future work, we will develop a fully automatic system for myocardial
perfusion MRI registration.
Third, it has been proven that temporal dynamics provide rich informa-
tion for segmentation. After p e rfo r m ing nonrigid registration, we are ab le to
obtain more accurate perfusion dynamics an d hence more accurate myocar-
dial segmentation, which is desirable in myocardial image analysis and car-
diac disease diagnosis. In Section § 3.3.2 we have introduced a segmentation
framework that incorp or at es the temporal information. In addition, we have
also demonstra t ed that nonrigid regis t ra t io n can benefit from segmentation.
Consequently, it would be interesting to explore a hybrid registration and
segmentation system such that the two com ponents will be jointly improved.
134 CONCLUSION AND FUTURE WORK
§ 6.2.2 Cerebral Diffusion MRI
Since the brain fiber tracts are of highly compl ex topology, the inter-subject
variation is not n e gl ig ible. In our current approach, we merge brain fibers
from multiple instances to allow common fiber bundles lead t h e local deforma-
tion. Accordingly, the registered fiber model is “over-complete”. Alt hough
the redundant fibers are unlikely to bias the along-fiber DTI measurements
as they are minor in population an d are randomly distrib u t ed , removing
those redu n dant fibers has the potential to improve the reliability of the
along-fiber measurements. Future work on this fiber-to-DTI study includes
exploring a proper DTI measure to assess the reliability of the regi st er ed
fiber. Fu r t h er m o r e, a statistic tool like robust PCA will be used to remove
the redundancy.
Bibliography
Adluru, G., DiBella, E., Schabel, M., Nov 2006. Model-based registration for

dynamic cardiac perfusion MRI. J Magn Reson Imaging 24 (5), 1062–1070.
Al-Saadi, N., Nagel, E., Gross, M., Bornstedt, A., Schnackenburg, B., Klein,
C., Klimek, W. , Oswald, H., Fleck, E., Mar 2000. Noninvasive detection of
myocardial ischemia from perfusion reserve based on cardiovascular mag-
netic resonance. Circulation 101 (12), 1379–1383.
Arsigny, V., Commowick, O., Pennec, X., Ayache, N., 2006. A Log-Euclidean
polyaffine framework for locally rigid or affine registration. In: Biomedical
Image Registration. pp. 120–127.
Arsigny, V., Fillard, P., Pennec, X., Ayache, N., AUG 2006. Log-euclidean
metrics for fast and simple calculus on di ffusion tensors. Magn Reson Med
56 (2), 411–421.
Ashburner, J., OCT 15 2007. A fast diffeomo r p h i c imag e re gi st r at i on a lg o-
rithm. NeuroImage 38 (1), 95–113.
Ashburner, J., Friston, K., JUN 2000. Voxel-based morphometry - The meth-
ods. NeuroImage 11 (6, Part 1), 805–821.
135
136 BIBLIOGRAPHY
Avants, B. B., Epstein, C. L., Grossman, M., Gee, J. C., FEB 2008. Sym-
metric diffeomorphic im ag e registration with cross-correlation: Evaluating
automated labeling of elderly and neurodege n er at i ve brain. Med Image
Anal 12 (1), 26–41, Special Issue on the 3rd International Workshop on
Biomedical Image R egi st r at i on, Utrecht Univ, Utr echt, NETHERLANDS,
JUL 09-11, 2006.
Bajcsy, R., Kovacic, S., APR 1989. Multiresolution elastic matching. Comput
Vis Graph Image Process 46 (1) , 1–21.
Bertschinger, K., Nanz, D. , Buechi, M., Luescher, T., Marincek, B., von
Schulthess, G., Schwitter, J., Nov 2001. Magnetic resonance myocardial
first-pass perfusion imaging: parameter optimization for signal response
and cardiac coverage. J Magn Reson Imaging 14 (5), 556–562.
Bookstein, F. L., 1989. Principal warps- thin plate splines and the decompo-

sition of deformations. IEEE Trans Pattern Anal Mach Intell 11, 567–585.
Breeuwer, M., Spreeuwers, L., Quist, M., Feb 2001. Automatic quantitative
analysis of card i ac MR per fu si on images. In: Proc Soc Photo Opt Instrum
Eng. pp. 733–742.
Brox, T., Weickert, J., Oct 2006. Level set segmentation wi t h multiple re-
gions. IEEE Trans Image Process 15 (10), 3213–3218.
Buonaccorsi, G., Roberts, C., Cheung, S., Watson, Y., Jayson, K. D. A. J. G.,
Parker, G., Oct 2005. Tracer kinetic model-driven registration for dynamic
contrast enhanced MRI time series. In: Med Image Comput Comp u t Assist
Interv.
BIBLIOGRAPHY 137
Calamante, F., Tournier, J D., Jackson, G. D., Connelly, A., DEC 2010.
Track-density imag ing (TDI): Super-resolution white matter imaging using
whole-brain track-density mapping. NeuroIm a ge 53 (4), 1233–1243.
Candes, E. J., Li, X., Ma, Y., Wright, J., MAY 2011. Robust Principal
Component Analysis? J ACM 58 (3).
Cercignani, M., Bammer, R., Sormani , M., Fazekas, F., Filippi, M., APR
2003. Inter-sequence and inter-imaging unit variability of diffusion tensor
MR imaging hi st o gr am - d er i ved metrics of t h e brain in healthy volunteers.
AJNR Am J Neur or adiol 24 (4), 638–643.
Cercignani, M., Inglese, M., Pagani, E., Comi, G., Filippi, M., MAY 2001.
Mean diffusivity and fractional anisotropy histograms of patients with mul-
tiple sclerosis. AJNR Am J Neuroradiol 22 (5), 952–958.
Chan, T., Vese, L., Feb. 2001a. Active contours without ed g es. IEEE Trans
Image Process 10 (2), 266 – 277.
Chan, T., Vese, L., Dec. 2001b. A multiphase level set fr am e work for image
segmentation using the mumford and shah model. Int J Comput Vis 50 (3),
271–293.
Chan, T., Zhu, W., 2005. Level set based shape prior segmentation. In: Proc
IEEE Com p u t Soc Conf Comput Vis Pattern Recognit. Vol. 2. IEEE, pp.

1164 – 1170.
Chiang, M C., Leow, A. D., Klunder, A. D., Dutton, R. A., Barysheva, M.,
Rose, S. E., McMahon, K. L., de Zubicaray, G. I., Toga, A. W., Thomp-
138 BIBLIOGRAPHY
son, P. M., APR 2008. Fluid registrat i on of diffusio n tensor imag es using
information theory. IEEE Trans Med Imaging 27 (4), 442–456.
Cremers, D., Tischh¨auser, F., Weickert, J., Schn¨orr, C., 2002. Diffusion
snakes: Introducing statisti cal shape kn owledge into the mumford-shah
functional. Int J Comput Vis 50, 295–313.
D’Elia, L., Satz, P., Uchiyama, C., White, T., 1996. Color Trails Test. Pro-
fessional manual. Psychological Assessment Resources, Odessa, FL.
Ducreux, D., Huynh, I., Fillard, P., Renoux, J., Petit-Lacour, M., Marsot-
Dupuch, K., Lasjaunias, P., AUG 2005. Brain MR diffusion tensor imaging
and fibre tracking to differentiate between two diffuse axonal injuries. Neu-
roradiology 47 (8), 604–608.
Ebrahimi, M., Martel, A. L., 2009. A general PDE-framework for registra-
tion of contrast enhanced images. In: Med Image Co m p u t Comput Assist
Interv. pp. 811–819.
Eckstein, I., Shattuck, D. W., Stein, J. L., McMahon, K. L., de Zubicaray,
G., Wright, M. J., Thompson, P. M., Toga, A. W., 2009. Active fibers:
Matching deformable tract templates to diffusion tensor images. NeuroIm-
age 47 (Supplement 2), T82 – T89.
Folstein, M. F., Folstein, S. E., McHugh, P. R., 1975. ”Mini-mental state ”. a
practical method for grad i n g the cognit i ve state of patients for the clinician.
J Psychiatr Res.
BIBLIOGRAPHY 139
Gaens, T., Maes, F., Vandermeulen, D., Suetens, P., 1998. Non-rigid multi-
modal im age registration u sing mutual information. In: Wells, WM and
Colchester, A and Delp, S (Ed.), Med Image Comput Comput Assist In-
terv. Vol. 1496. pp. 1099–1106.

Gao, J., Ablitt, N., Elkington, N., Yang, G., 2002. Deformation modelling
based on PLSR for cardiac magnetic resonance perfusion imaging. In: Med
Image Comput Comput Assist Interv. pp. 612–619.
Gupta, S., Solaiyappan, M., Beache, G., Arai, A., Foo, T., Mar 2003. Fast
method for correcting image misregistration due to organ motion in time-
series MRI data. Magn Reson Med 49 (3), 506–514.
Hajnal, J., Hawkes, D., Hill, D., 2001. Medical image registration. Biomedical
engineering series. CRC Press.
Han, X., Xu, C. , Prince, J., 2003. A topology preserving level set method for
geometric deformable models. IEEE Trans Pattern Anal Mach Intell 25,
755– 768.
Hennemuth, A., Seeger, A., Friman, O., Miller, S., Klumpp, B., Oeltze, S. ,
Peitgen, H O., 2 008. A comprehensive approach to the analysis of contrast
enhanced cardiac MR images. IEEE Tran s Med Imaging 27 (3), 1592–1610.
Hestenes, M., Stiefel, E., Dec 1952. Meth ods of conjugate gradients for solv-
ing linear systems. J Res Natl Bur Stand 49, 409–436.
Jolly, M P., Xue, H., Grady, L., Guehring, J., 2009. Combining registration
and minimum surfaces for the segmentation of the left ventricle in cardiac
140 BIBLIOGRAPHY
cine MR images. In: Med Image Comput Compu t Assist Interv. pp. 910–
918.
Joutel, A., Monet-Lepretre, M., Gosele, C., Baron-Menguy, C., Hammes, A.,
Schmidt, S., Lemaire-Carrette, B., Domenga, V., Schedl, A., Lacombe,
P., Hubner, N., FEB 2010. Cerebrovascular dysfunction an d microcircula-
tion rarefaction precede white matter lesions in a mouse genetic m odel of
cerebral ischemic small vessel disease. J Clin Invest 120 (2), 433–445.
Juntu, J., Sijbers, J., Van Dyck, D., Gielen, J., 2005. Bias field correction for
MRI images. In: Kurzynski, M and Pu chala, E and Wozniak, M and Zol-
nierek, A (Ed.), Computer Recognition Systems, Proceedings. Advances
in Soft Computing. pp. 543–551.

Kellman, P., Arai, A., 2007. Imaging sequences for first pass perfusion–a
review. J Cardiovasc Magn Reson 9 (3), 525–37.
Kim, B., Boes, J., Frey, K., Meyer, C., JAN 1997. Mutual information for
automated unwarping of rat brain autoradiogr a p h s. NeuroImage 5 (1), 31–
40.
Kishore, S. P., Michelow, M. D. , 2011. The global burden of dissease. In:
Public Health in the 21st Century. Praeger.
Klassen, C., Nguyen, M., Siuciak, A., Wilke, N. M., Mar 2006. Magn et i c
resonance first pass perfusion imagin g for detecting coronary artery disease.
Eur J Radiol 57, 412 – 416.
BIBLIOGRAPHY 141
Kroon, D J., 2011. non-rigid b-spline grid image registration. Available on
MATLAB central, file ID: #20057.
Lancaster, J., Rainey, L., Summ er l in, J., Freitas, C., Fox, P., Evans, A.,
Toga, A., Mazziotta, J., 1997. Automated labeling of the human brain:
A preliminar y report on the development and evaluation of a forward-
transform method. Hum Brain Mapp 5 (4), 238C242.
Lancaster, J., Woldorff, M., Parsons, L., Liotti, M., Freitas, E., Rainey, L.,
Kochunov, P., Nickerson, D., Mikiten, S., Fox, P., JUL 2000. Automated
Talairach Atlas labels for functional brain mapping. Hum Brain Mapp
10 (3), 120–131.
Le Bihan, D., Mangin, J., Poupon, C., Clark, C., Pappata, S., Molko, N.,
Chabriat, H., APR 2001. Diffusion t en so r ima gi n g: Concepts and applica-
tions. J Magn Reson Imaging 13 (4), 534–546.
Liu, D., Nocedal, J., Dec 1989. On the limited memor y BFGS method for
large-scale optimization. Math Program 45 (3), 503–528.
Maes, F., Collignon, A., Vandermeulen, D., Marchal, G., Suetens, P., APR
1997. Multimodality image registration by maximization of mutual infor-
mation. IEEE Trans Med Imaging 16 (2), 187–198.
Melbourne, A., Atkinson, D., White, M. J. , Collins, D., Leach, M., Hawkes,

D., Sep 20 07. Registration of dynamic contrast-enhanced MRI usi n g a pro-
gressive pr i n ci p al component registration (PPCR). Phys Med Biol 52 (17),
5147–5156.
142 BIBLIOGRAPHY
Milles, J., van der Geest, R. J., Jerosch-Herold, M., Reib er , J., Lelieveldt,
B., Nov 2008. Fully automated motion corr ect i on in first-pass myocardi a l
perfusion MR image sequences. IEEE Trans Med Imaging 27 (11), 1611–
1621.
Modersitzki, J., 2004. Numeri ca l methods for image r egi st r a t io n . Numerical
mathematics and scientific computation. Oxford University Pr ess.
Moelich, M., Chan, T., Feb 2003. Joint segmentation and registration using
logic models. Tech. rep., UCLA CAM.
Moseley, M ., Cohen, Y., Mintorovitch, J., Chileuitt, L., Shimizu, H., Kuchar-
czyk, J., Wendland, M., Weinstein, P., MAY 1990. Early Detection of Re-
gional Cereb r al - Ischemia in Cats - Comparison of D i ffu si on-Weighted and
T2-Weighted MRI and Spectroscopy. Magn Reson Med 14 (2), 330–346.
Nasreddine, Z., Phillips, N., B´edirian, V., Charbonneau, S., Whitehead, V.,
Collin, I., Cummings, J., Chertkow, H., 2005. The montreal cognitive a s-
sessment, (moca): a brief screening to ol for mild cognitive impairment. J
Am Geriatr Soc 53 (4), 695–9.
Nitkunan, A. , Barrick, T. R., Charlton, R. A., Clark, C. A., Markus, H. S.,
2008. Multimodal mri in cerebral small vessel disease: Its relationsh i p wi t h
cognition and sensitivity to changes over time. Stroke 39, 1999–2005.
O’Donnell, L. J., Westin, C F., November 2007. Automatic tractography
segmentation using a high- d i m en s io n al white matter atlas. IEEE Trans
Med Imaging 26 (11), 1562–1575.