Dynamic contrast enhanced magnetic resonance imaging (DCE-MRI)
provides a non-invasive tool for evaluating tissue time activity
patterns based on the accumulation and metabolism of the contrast
agent. Conventional tool for DCE-MRI images analysis is
pharmacokinetic model that provides kinetic, physiological
parameters for tissues, such as perfusion, capillary permeability,
and the volume of extravascular-extracellular space (EES). Although
kinetic parameters have shown to be relevant to the response of
therapy and the survival rate, inevitable partial volume effect in
DCE-MRI images still hinders the quantitative analysis of the
kinetic parameters.

In this thesis, we develop an unsupervised non-negative blind source
separation (nBSS) algorithm to dissect and characterize composite
signatures in DCE-MRI images of patients with prostate cancers. We
transform the pharmacokinetic model into a latent variable model, to
which the nBSS method, named simplex estimation by projection
(SIMPLE-Pro) is devised. The SIMPLE-Pro algorithm identifies the
tissue time activity curves (up to scaling ambiguity) with
theoretical guarantee. The problem of scaling ambiguity is then
handled by pharmacokinetic model fitting, which we implemented by
using sequential quadratic programming. Some Monte Carlo simulations
on synthetic generated prostate DCE-MRI data set and real DCE-MRI
experiments of seven patients with prostate cancer were performed to
demonstrate high efficiency of SIMPLE-Pro algorithm, and consistency
of the extracted information with biopsy test examination. The
DCE-MRI analysis framework presented in this thesis, which includes
SIMPLE-Pro algorithm and pharmacokinetic model fitting, can dissect
complex tissues into regions with differential contrast kinetics at
pixel-wise resolution and provide a systems biology tool for
defining imaging signatures predictive of phenotypes.

[1] A. Jemal, R. Siegel, E. Ward, T. Murray, J. Xu, C. Smigal, and M. J. Thun, “Cancer
statistics, 2010,” CA: A Cancer Journal for Clinicians, vol. 60, no. 5, pp. 277-300,
Sep. 2010.
[2] A. L. Potosky, B. A. Miller, P. C. Albertsen, and B. S. Kramer, “The
role of increasing detection in the rising incidence of prostate cancer,”
The Journal of the American Medical Association, vol. 273, no. 7, pp. 548-552, 1995.
[3] N. B. Deongchamps, A. Singh, and G. P. Haas, “Epidemiology of Prostate
Cancer in Africa: Another Step in the Understanding of the Disease?,”
Current Problems in Cancer, vol. 31, no. 3, pp. 226-236, June 2007.
[4] R. P. Myers, “Structure of the adult prostate from a clinician’s standpoint.”
Clinical Anatomy, vol. 13, pp. 214-15, Apr. 2000.
[5] E. D. Crawford, “Epidemiology of prostate cancer,” Urology, vol. 62, no. 6, pp. 3-12,
Dec. 2003.
[6] H. Gronberg, “Prostate cancer epidemiology,” The Lancet, vol. 361, no. 9360, pp.
859-864, Mar. 2003.
[7] G. P. Haas and W. A. Sakr, “Epidemiology of prostate cancer,”.
CA: A Cancer Journal for Clinicians, vol. 47, no. 5, pp. 273-287, Sep. 1997.
[8] M. A. Khan and A.W. Partin, “Management of patients with an increasing prostatespecific
antigen after radical prostatectomy,” Current Urology Reports, vol. 3, no. 3,
pp. 179-187, Jun. 2004.
[9] L. R. Kavoussi, E. Sosa, P. Chandhoke, G. Chodak, R. V. Clayman, H. R. Hadley,
K. R. Loughlin, H. C. Ruckle, D. Rukstalis, and W. Schuessler, “Complications of
laparoscopic pelvic lymph node dissection,” Journal of Urology, vol. 149, no. 2, pp.
322-325, Feb. 1993.
[10] C. E. Neal and L. C. Meis, “Correlative imaging with monoclonal antibodies in
colorectal, ovarian, and prostate cancer,” Seminars in Nuclear Medicine, vol. 24,
no. 4, pp. 272-285, Oct. 1994.
[11] A. V. D’Amico, R. Whittington, M. Schnall, S. B. Malkowicz, J. E. Tomaszewski,
D. Schultz, and A. Wein, “The impact of the inclusion of endorectal coil magnetic
resonance imaging in a multivariate analysis to predict clinically unsuspected extraprostatic
cancer,” Cancer, vol. 75, no. 9, pp. 2368-2372, 1995.
[12] G. J. Jager, ET Ruijter, C. A. van de Kaa, J. J. de la Rosette, G. O. Oosterhof, J.
R. Thornbury, and J. O. Barentsz, “Local staging of prostate cancer with endorectal
MR imaging: correlation with histopathology,” American Journal of Roentgenology,
vol. 166, no.1, pp. 845-852, Apr. 1996.
[13] K. Lovett, M. D. Rifkin, P. A. McCue, and H. Choi, “MR imaging characteristics of
noncancerous lesions of the prostate,” Journal of Magnetic Resonance Imaging, vol.
2, pp. 35-39, Jan. 1992.
[14] M. L. Schiebler, J. E. Tomaszewski, M. Bezzi, H. M. Pollack, H. Y. Kressel, E. K. Cohen,
H. G. Altman, W. B. Gefter, A. J. Wein, and L. Axel, “Prostatic carcinoma and
benign prostatic hyperplasia: correlation of high-resolution MR and histopathologic
findings,” Radiology, vol. 172, pp. 131-137, July 1989.
[15] H. J. Weinmann, R. C. Brasch, W. R. Press, and G. E. Wesbey, “Characteristics
of gadolinium-DTPA complex: a potential NMR contrast agent,”
AJR Am J Roentgenol vol. 142, no. 3, pp. 619-624, Mar. 1984.
[16] P. S. Tofts, “Modeling tracer kinetics in dynamic Gd-DTPA MR imaging,”
Journal of Magnetic Resonance Imaging, vol. 7, no. 1, pp. 91-101, Jan. 1997.
[17] J. O. Barentsz, M. Engelbrecht, G. J. Jager, J. A.Witjes, J. LaRosette, B. P. Sanden,
H. J. Huisman, and A. Heerschap, “Fast dynamic gadolinium-enhanced MR imaging
of urinary bladder and prostate cancer,” Journal of Magnetic Resonance Imaging,
vol. 10, no. 3, pp. 295-304, Sep. 1999.
[18] P. L. Choyke, A. J. Dwyer, and M. V. Knopp, “Functional tumor
imaging with dynamic contrast-enhanced magnetic resonance imaging,”
Journal of Magnetic Resonance Imaging, vol. 17, no. 5, pp. 509-520, May 2003.
[19] R. Alonzi, A. R. Padhani, N. J. Taylor, J. J. Stirling, M. I. Saunders, and P. J.
Hoskin, “Physiological Changes within the Prostate Caused by Androgen Withdrawal,”
Clinical Oncology, vol. 19, no. 3, pp. S1-S6, 2007.
[20] M. D. Plumbley, “Algorithms for non-negative independent component analysis,”
IEEE Trans. Neural Netw., vol. 14, no. 3, pp. 534-543, May 2003.
[21] S. A. Astakhow, H. Stogbauer, A. Kraskov, and P. Grassberger, “Monte
Carlo algorithm for least dependent non-negative mixture decomposition,”
Analytical Chemistry, vol. 78, pp. 1620-1627, Mar. 2006.
[22] F.-Y. Wang, Y. Wang, T.-H. Chan, and C.-Y. Chi, ”Blind separation of multichannel
biomedical image patterns by nonnegative least-correlated component analysis,”
Lecture Notes Bioinfo., vol. 4146, pp. 151-162, Sep. 2006.
[23] D. D. Lee and H. S. Seung, ”Learning the parts of objects by non-negative matrix
factorization,” Nature, vol. 401, no. 6755, pp. 788-791, Aug. 1999.
[24] A. P.-Montano, J. M. Carazo, K. Kochi, D. Lehmann and
R. D. P.-Marqui, ”Nonsmooth nonnegative matrix factorization,”
IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 28, no. 3, pp.
403-415, Mar. 2006.
[25] K. Stadlthanner, F. 1. Theis, E. W. Lang, A. M. Tome, C. G. Puntonet, J. M. Gorriz,
”Hybridizing sparse component analysis with genetic algorithms for microarray
analysis,” Neurocomputing, vol. 71, no. 10, pp. 2356-2376, June 2008.
[26] P.S. Tofts and A.G. Kermode, “Measurement of the Blood-Brain Barrier permeability
and leakage space using dynamic MR imaging -1 Fundamental concepts,”
Magnetic Resonance in Medicine, vol. 17, pp. 357-367, Feb. 1991.
[27] Y. Wang, 1. Xuan, R. Srikanchana, and P. L. Choyke, “Modeling
and reconstruction of mixed functional and molecular patterns,”
International Journal ofBiomedical Imaging, Article ID: 29707, pp. 1-9, 2006.
[28] T.-H. Chan, W.-K. Ma, C.-Y. Chi and Y. Wang, “A convex analysis framework for
blind separation of non-negative sources,” IEEE Trans. Signal Processing, vol. 56,
no. 10, pp. 5120-5134, Oct. 2008.
[29] P. S. Tofts, G. Brix, D. L. Buckley, J. L. Evelhoch, E. Henderson, M. V. Knopp,
H. B. Larsson, T. Y. Lee, N. A. Mayr, G. J. Parker, R. E. Port, J. Taylor, and
R. M. Weisskoff, “Estimating kinetic parameters from dynamic contrast-enhanced
T(1)-weighted MRI of a diffusable tracer: standardized quantities and symbols,”
Journal of Magnetic Resonance Imaging, vol. 10, no. 3, pp. 223-232, 1999.
[30] Y.-C. Lin, T.-H. Chan, C.-Y. Chi, S.-H. Ng, H.-L. Liu, K.-C. Wei, Y.-Y. Wai,
C.-C. Wang, and J.-J. Wang, “Blind estimation of arterial input function in dynamic
contrast-enhanced MRI using purity maximization,” to be submitted to
Magnetic Resonance in Medicine.
[31] S. Boyd and L. Vandenberghe, Convex Optimization, UK: Cambridge Univ. Press,
2004.
[32] J. F. Sturm, “Using SeDuMi 1.02, a MATLAB toolbox for optimization over symmetric
cones,” Optimiz. Methods Softw., vol. 11–12, pp. 625–653, 1999.
[33] M. Grant. Disciplined Convex Programming. PhD thesis, Department of Electrical
Engineering, Stanford University, December 2004. See http: www.stanford.edu/
~boyd/disc_cvx_prog.html.
[34] M. Grant, S. Boyd, and Y. Ye, “Disciplined convex programming,” pp. 155–210 in
Global Optimization: from Theory to Implementation, Nonconvex Optimization and
Its Applications, L. Liberti and N. Maculan, Eds., New York, Springer, 2006.
[35] C. Yang, G. S. Karczmar, M. Medved and W. M. Stadler, “Estimating the arterial
input function using two reference tissues in dynamic contrast-enhanced MRI studies:
Fundamental concepts and simulations,” Magnetic Resonance in Medicine, vol. 52,
pp. 1110-1117, Nov. 2004.
[36] J. W. Boardman, F. A. Kruse, and R. O. Green, “Mapping
target signatures via partial unmixing of AVIRIS data,”
in Proc. Summ. JPL Airborne Earth Sci. Workshop, Pasadena, CA, Dec. 9-14,
1995, pp. 23-26.
[37] J.M. P. Nascimento and J. M. B. Dias, “Vertex component analysis: A fast algorithm
to unmix hyperspectral data,” IEEE Trans. Geosci. Remote Sens., vol. 43, no. 4, pp.
898-910, Apr. 2005.