L. Axel, Cerebral blood flow determination by rapid-sequence computed tomography: theoretical analysis., Radiology, vol.137, issue.3, pp.679-686, 1980.
DOI : 10.1148/radiology.137.3.7003648

J. Bassingthwaighte and G. Goresky, The cardiovascular system., in: Handbook of Physiology, pp.549-626, 1984.

P. Batchelor, A. Chiribiri, N. Z. Nooralipour, and Z. Cvetkovic, ARMA regularization of cardiac perfusion modeling, 2010 IEEE International Conference on Acoustics, Speech and Signal Processing, pp.642-645, 2010.
DOI : 10.1109/ICASSP.2010.5495154

A. Bjørnerud and K. E. Emblem, A Fully Automated Method for Quantitative Cerebral Hemodynamic Analysis Using DSC?MRI, Journal of Cerebral Blood Flow & Metabolism, vol.62, issue.1, pp.1066-1078, 2010.
DOI : 10.1002/mrm.10522

T. Boutelier, K. Kudo, F. Pautot, and M. Sasaki, Bayesian Hemodynamic Parameter Estimation by Bolus Tracking Perfusion Weighted Imaging, IEEE Transactions on Medical Imaging, vol.31, issue.7, pp.1381-1395, 2012.
DOI : 10.1109/TMI.2012.2189890

F. Calamante, Bolus dispersion issues related to the quantification of perfusion MRI data, Journal of Magnetic Resonance Imaging, vol.52, issue.6, pp.718-722, 2005.
DOI : 10.1002/jmri.20454

F. Calamante, Arterial input function in perfusion MRI: A comprehensive review, Progress in Nuclear Magnetic Resonance Spectroscopy, vol.74, pp.1-32, 2013.
DOI : 10.1016/j.pnmrs.2013.04.002

F. Calamante, D. Gadian, and A. Connelly, Quantification of Perfusion Using Bolus Tracking Magnetic Resonance Imaging in Stroke: Assumptions, Limitations, and Potential Implications for Clinical Use, Stroke, vol.33, issue.4, pp.1146-1151, 2002.
DOI : 10.1161/01.STR.0000014208.05597.33

F. Calamante, D. G. Gadian, and A. Connelly, Delay and Dispersion Effects in Dynamic Susceptibility Contrast MRI Simulations Using Singular Value Decom- position, 2000.
DOI : 10.1002/1522-2594(200009)44:3<466::aid-mrm18>3.3.co;2-d

F. Calamante, D. G. Gadian, and A. Connelly, Quantification of bolus-tracking MRI: Improved characterization of the tissue residue function using Tikhonov regularization, Magnetic Resonance in Medicine, vol.98, issue.6, pp.1237-1247, 2003.
DOI : 10.1002/mrm.10643

F. Calamante, D. L. Thomas, G. S. Pell, J. Wiersma, and R. Turner, Measuring Cerebral Blood Flow Using Magnetic Resonance Imaging Techniques, Journal of Cerebral Blood Flow & Metabolism, vol.16, pp.701-735, 1999.
DOI : 10.1097/00004647-199907000-00001

F. Calamante, L. Willats, D. G. Gadian, and A. Connelly, Bolus delay and dispersion in perfusion MRI: Implications for tissue predictor models in stroke, Magnetic Resonance in Medicine, vol.52, issue.5, pp.1180-1185, 2006.
DOI : 10.1002/mrm.20873

F. Calamante, P. J. Yim, and J. R. Cebral, Estimation of bolus dispersion effects in perfusion MRI using image-based computational fluid dynamics, NeuroImage, vol.19, issue.2, pp.341-353, 2003.
DOI : 10.1016/S1053-8119(03)00090-9

M. Chappell, A. Groves, B. Whitcher, and M. Woolrich, Variational Bayesian Inference for a Nonlinear Forward Model, IEEE Transactions on Signal Processing, vol.57, issue.1, pp.223-236, 2009.
DOI : 10.1109/TSP.2008.2005752

M. A. Chappell, M. W. Woolrich, S. Kazan, P. Jezzard, S. J. Payne et al., Modeling dispersion in arterial spin labeling: Validation using dynamic angiographic measurements, Magnetic Resonance in Medicine, vol.57, issue.2, pp.563-570, 2013.
DOI : 10.1002/mrm.24260

M. Charter and S. Gull, Maximum entropy and its application to the calculation of drug absorption rates, Journal of Pharmacokinetics and Biopharmaceutics, vol.11, issue.6, pp.645-655, 1987.
DOI : 10.1007/BF01068418

A. Connelly, F. Calamante, and L. Willats, Improved deconvolution of bolus tracking data using wavelet thresholding, Proc. 14th Sci, pp.3563-3563, 2006.

S. A. Drabycz, R. A. Brown, A. G. Law, and J. R. Mitchell, Maximum entropy deconvolution for dynamic susceptibility contrast magnetic resonance imaging, Visualization, Imaging, And Image Processing: Fifth IASTED International Conference Proceedings, 2005.

R. Fang, S. Zhang, T. Chen, and P. C. Sanelli, Robust Low-Dose CT Perfusion Deconvolution via Tensor Total-Variation Regularization, IEEE Transactions on Medical Imaging, vol.34, issue.7, pp.1533-1548, 2015.
DOI : 10.1109/TMI.2015.2405015

URL : http://www.ncbi.nlm.nih.gov/pmc/articles/PMC4779066

W. F. Hamilton, J. W. Moore, J. Kinsman, and R. Spurling, Studies on the circulation, American Journal of Physiology?Legacy Content, vol.99, pp.534-551, 1932.

J. A. Jacquez, Compartmental analysis in biology and medicine, 1972.

S. L. Keeling, T. Kogler, and R. Stollberger, Deconvolution for DCE-MRI using an exponential approximation basis, Medical Image Analysis, vol.13, issue.1, pp.80-90, 2009.
DOI : 10.1016/j.media.2008.06.011

V. G. Kiselev, Transverse relaxation effect of MRI contrast agents: A crucial issue for quantitative measurements of cerebral perfusion, Journal of Magnetic Resonance Imaging, vol.34, issue.6, pp.693-696, 2005.
DOI : 10.1002/jmri.20452

V. G. Kiselev and S. Posse, Analytical model of susceptibility-induced MR signal dephasing: effect of diffusion in a microvascular network Magnetic resonance in medicine 41, pp.499-509, 1999.

L. Knutsson, F. Ståhlberg, and R. Wirestam, Absolute quantification of perfusion using dynamic susceptibility contrast MRI: pitfalls and possibilities, Magnetic Resonance Materials in Physics, Biology and Medicine, vol.16, issue.2, pp.1-21, 2010.
DOI : 10.1007/s10334-009-0190-2

L. Ko, M. Salluzzi, R. Frayne, and M. Smith, Reexamining the quantification of perfusion MRI data in the presence of bolus dispersion, Journal of Magnetic Resonance Imaging, vol.51, issue.3, pp.639-643, 2007.
DOI : 10.1002/jmri.20781

N. A. Lassen, A. R. Andersen, L. Friberg, and O. B. Paulson, -HM-PAO in the Human Brain after Intracarotid Bolus Injection: A Kinetic Analysis, Journal of Cerebral Blood Flow & Metabolism, vol.8, issue.1_suppl, pp.13-22, 1988.
DOI : 10.1038/jcbfm.1988.28

URL : https://hal.archives-ouvertes.fr/in2p3-00164743

A. Mehndiratta, F. Calamante, B. J. Macintosh, D. E. Crane, S. J. Payne et al., Modeling and correction of bolus dispersion effects in dynamic susceptibility contrast MRI, Magnetic Resonance in Medicine, vol.27, issue.Suppl 7, pp.1762-1774, 2014.
DOI : 10.1002/mrm.25077

A. Mehndiratta, F. Calamante, B. J. Macintosh, D. E. Crane, S. J. Payne et al., Modeling the residue function in DSC-MRI simulations: Analytical approximation to in vivo data, Magnetic Resonance in Medicine, vol.22, issue.5, pp.1486-1491, 2014.
DOI : 10.1002/mrm.25056

A. Mehndiratta, B. J. Macintosh, D. E. Crane, S. J. Payne, and M. A. Chappell, A control point interpolation method for the non-parametric quantification of cerebral haemodynamics from dynamic susceptibility contrast MRI, NeuroImage, vol.64, pp.560-570, 2013.
DOI : 10.1016/j.neuroimage.2012.08.083

P. Meier and K. L. Zierler, On the theory of the indicator-dilution method for measurement of blood flow and volume, Journal of applied physiology, vol.6, pp.731-744, 1954.

M. Meijs, S. Christensen, M. G. Lansberg, G. W. Albers, and F. Calamante, Analysis of perfusion mri in stroke: To deconvolve, or not to deconvolve Magnetic resonance in medicine, 2015.

J. J. Mouannes-srour, W. Shin, S. A. Ansari, M. C. Hurley, P. Vakil et al., Correction for arterial-tissue delay and dispersion in absolute quantitative cerebral perfusion DSC MR imaging, Magnetic Resonance in Medicine, vol.22, issue.2, pp.495-506, 2012.
DOI : 10.1002/mrm.23257

URL : http://www.ncbi.nlm.nih.gov/pmc/articles/PMC3310307

K. Mouridsen, K. Friston, N. Hjort, L. Gyldensted, L. Østergaard et al., Bayesian estimation of cerebral perfusion using a physiological model of microvasculature, NeuroImage, vol.33, issue.2, pp.570-579, 2006.
DOI : 10.1016/j.neuroimage.2006.06.015

L. Østergaard, D. A. Chesler, R. M. Weisskoff, A. G. Sorensen, and B. R. Rosen, Modeling cerebral blood flow and flow heterogeneity from magnetic resonance residue data, Journal of Cerebral Blood Flow & Metabolism, vol.19, pp.690-699, 1999.

L. Østergaard, P. Johannsen, P. Høst-poulsen, P. Vestergaard-poulsen, H. Asboe et al., Cerebral blood flow measurements by magnetic resonance imaging bolus tracking: comparison with [15o] h2o positron emission tomography in humans, Journal of Cerebral Blood Flow & Metabolism, vol.18, pp.935-940, 1998.

L. Østergaard, R. M. Weisskoff, D. A. Chesler, C. Gyldensted, and B. R. Rosen, High resolution measurement of cerebral blood flow using intravascular tracer bolus passages. part i: Mathematical approach and statistical analysis. Magnetic resonance in medicine 36, pp.715-725, 1996.

C. S. Park and S. J. Payne, A generalized mathematical framework for estimating the residue function for arbitrary vascular networks. Interface focus 3, 2013.

K. A. Rempp, G. Brix, F. Wenz, C. R. Becker, F. Gückel et al., Quantification of regional cerebral blood flow and volume with dynamic susceptibility contrast-enhanced MR imaging., Radiology, vol.193, issue.3, pp.637-641, 1994.
DOI : 10.1148/radiology.193.3.7972800

M. Rohrer, H. Bauer, J. Mintorovitch, M. Requardt, and H. J. Weinmann, Comparison of Magnetic Properties of MRI Contrast Media Solutions at Different Magnetic Field Strengths, Investigative Radiology, vol.40, issue.11, pp.715-724, 2005.
DOI : 10.1097/01.rli.0000184756.66360.d3

B. R. Rosen, J. W. Belliveau, B. R. Buchbinder, R. C. Mckinstry, L. M. Porkka et al., Contrast agents and cerebral hemodynamics, Contrast agents and cerebral hemodynamics, pp.285-292, 1991.
DOI : 10.1002/mrm.1910190216

B. R. Rosen, J. W. Belliveau, J. M. Vevea, and T. J. Brady, Perfusion imaging with nmr contrast agents. Magnetic resonance in medicine 14, pp.249-265, 1990.
DOI : 10.1002/mrm.1910140211

M. S. Shiroishi, G. Castellazzi, J. L. Boxerman, F. D-'amore, M. Essig et al., *-weighted dynamic susceptibility contrast MRI technique in brain tumor imaging, Journal of Magnetic Resonance Imaging, vol.36, issue.2, pp.296-313, 2015.
DOI : 10.1002/jmri.24648

M. Smith, H. Lu, S. Trochet, and R. Frayne, Removing the effect of svd algorithmic artifacts present in quantitative mr perfusion studies. Magnetic resonance in medicine 51, pp.631-634, 2004.

O. Speck, L. Chang, N. M. Desilva, and T. Ernst, Perfusion MRI of the human brain with dynamic susceptibility contrast: Gradient-echo versus spin-echo techniques, Journal of Magnetic Resonance Imaging, vol.16, issue.3, pp.381-387, 2000.
DOI : 10.1002/1522-2586(200009)12:3<381::AID-JMRI2>3.0.CO;2-Y

C. Starmer and D. O. Clark, Computer computations of cardiac output using the gamma function, Journal of applied physiology, vol.28, pp.219-220, 1970.

G. N. Stewart, Researches on the Circulation Time in Organs and on the Influences which affect it, The Journal of Physiology, vol.15, issue.1-2, pp.1-45, 1894.
DOI : 10.1113/jphysiol.1893.sp000462

A. Villringer, B. R. Rosen, J. W. Belliveau, J. L. Ackerman, R. B. Lauffer et al., Dynamic imaging with lanthanide chelates in normal brain: Contrast due to magnetic susceptibility effects, Magnetic Resonance in Medicine, vol.7, issue.2, pp.164-174, 1988.
DOI : 10.1002/mrm.1910060205

E. J. Vonken, F. J. Beekman, C. J. Bakker, and M. A. Viergever, Maximum likelihood estimation of cerebral blood flow in dynamic susceptibility contrast MRI, Magnetic Resonance in Medicine, vol.7, issue.2, pp.343-350, 1999.
DOI : 10.1002/(SICI)1522-2594(199902)41:2<343::AID-MRM19>3.0.CO;2-T

E. J. Vonken, M. J. Van-osch, C. J. Bakker, and M. A. Viergever, Measurement of cerebral perfusion with dual-echo multi-slice quantitative dynamic susceptibility contrast MRI, Journal of Magnetic Resonance Imaging, vol.14, issue.2, pp.109-117, 1999.
DOI : 10.1002/(SICI)1522-2586(199908)10:2<109::AID-JMRI1>3.0.CO;2-#

R. Weisskoff, C. S. Zuo, J. L. Boxerman, and B. R. Rosen, Microscopic susceptibility variation and transverse relaxation: Theory and experiment, Magnetic Resonance in Medicine, vol.24, issue.6, pp.601-610, 1994.
DOI : 10.1002/mrm.1910310605

L. Willats, A. Connelly, and F. Calamante, Improved deconvolution of perfusion MRI data in the presence of bolus delay and dispersion, Magnetic Resonance in Medicine, vol.52, issue.1, pp.146-156, 2006.
DOI : 10.1002/mrm.20940

L. Willats, A. Connelly, and F. Calamante, Modelling the bolus dispersion from DSC-MRI data, Proceedings of the International Society for Magnetic Resonance in Medicine (ISMRM), 15th Annual Meeting, pp.1445-1445, 2007.

L. Willats, A. Connelly, and F. Calamante, Minimising the effects of bolus dispersion in bolus-tracking MRI, NMR in Biomedicine, vol.78, issue.10, pp.1126-1137, 2008.
DOI : 10.1002/nbm.1290

L. Willats, A. Connelly, S. Christensen, G. A. Donnan, S. M. Davis et al., The Role of Bolus Delay and Dispersion in Predictor Models for Stroke, Stroke, vol.43, issue.4, pp.1025-1031, 2012.
DOI : 10.1161/STROKEAHA.111.635888

R. Wirestam and F. Ståhlberg, Wavelet-based noise reduction for improved deconvolution of time-series data in dynamic susceptibility-contrast MRI, Magnetic Resonance Materials in Physics, Biology and Medicine, vol.24, issue.3, pp.113-118, 2005.
DOI : 10.1007/s10334-005-0102-z

O. Wu, L. Østergaard, R. M. Weisskoff, T. Benner, B. R. Rosen et al., Tracer arrival timing-insensitive technique for estimating flow in MR perfusion-weighted imaging using singular value decomposition with a block-circulant deconvolution matrix, Magnetic Resonance in Medicine, vol.32, issue.1, pp.164-174, 2003.
DOI : 10.1002/mrm.10522

F. Zanderigo, A. Bertoldo, G. Pillonetto, and C. Cobelli, Nonlinear Stochastic Regularization to Characterize Tissue Residue Function in Bolus-Tracking MRI: Assessment and Comparison With SVD, Block-Circulant SVD, and Tikhonov, IEEE Transactions on Biomedical Engineering, vol.56, issue.5, pp.1287-1297, 2009.
DOI : 10.1109/TBME.2009.2013820

K. L. Zierler, Theoretical Basis of Indicator-Dilution Methods For Measuring Flow and Volume, Circulation Research, vol.10, issue.3, pp.393-407, 1962.
DOI : 10.1161/01.RES.10.3.393

K. L. Zierler, Equations for Measuring Blood Flow by External Monitoring of Radioisotopes, Circulation Research, vol.16, issue.4, pp.309-321, 1965.
DOI : 10.1161/01.RES.16.4.309