Special issue review article
Classic models for dynamic contrast-enhanced MRI
Steven P. Sourbron,
David L. Buckley,
Corresponding Author
Steven P. Sourbron
Division of Medical Physics, University of Leeds, Leeds, UK
Correspondence to: S. P. Sourbron, Division of Medical Physics, University of Leeds, Worsley Building, Level 8, Leeds LS2 9JT, UK.
E-mail: [email protected]
Search for more papers by this authorDavid L. Buckley
Division of Medical Physics, University of Leeds, Leeds, UK
Search for more papers by this authorSteven P. Sourbron,
David L. Buckley,
Corresponding Author
Steven P. Sourbron
Division of Medical Physics, University of Leeds, Leeds, UK
Correspondence to: S. P. Sourbron, Division of Medical Physics, University of Leeds, Worsley Building, Level 8, Leeds LS2 9JT, UK.
E-mail: [email protected]
Search for more papers by this authorDavid L. Buckley
Division of Medical Physics, University of Leeds, Leeds, UK
Search for more papers by this authorAbstract
Dynamic contrast-enhanced MRI (DCE-MRI) is a functional MRI method where T1 -weighted MR images are acquired dynamically after bolus injection of a contrast agent.
The data can be interpreted in terms of physiological tissue characteristics by applying the principles of tracer-kinetic modelling. In the brain, DCE-MRI enables measurement of cerebral blood flow (CBF), cerebral blood volume (CBV), blood–brain barrier (BBB) permeability–surface area product (PS) and the volume of the interstitium (ve). These parameters can be combined to form others such as the volume-transfer constant Ktrans, the extraction fraction E and the contrast-agent mean transit times through the intra- and extravascular spaces.
A first generation of tracer-kinetic models for DCE-MRI was developed in the early 1990s and has become a standard in many applications. Subsequent improvements in DCE-MRI data quality have driven the development of a second generation of more complex models. They are increasingly used, but it is not always clear how they relate to the models of the first generation or to the model-free deconvolution methods for tissues with intact BBB. This lack of understanding is leading to increasing confusion on when to use which model and how to interpret the parameters.
The purpose of this review is to clarify the relation between models of the first and second generations and between model-based and model-free methods. All quantities are defined using a generic terminology to ensure the widest possible scope and to reveal the link between applications in the brain and in other organs. Copyright © 2013 John Wiley & Sons, Ltd.
REFERENCES
- 1
Runge VM,
Clanton JA,
Herzer WA,
Gibbs SJ,
Price AC,
Partain CL,
James AE. Intravascular contrast agents suitable for magnetic resonance imaging. Radiology 1984; 153(1): 171–176.
- 2
Pettigrew RI,
Avruch L,
Dannels W,
Coumans J,
Bernardino ME. Fast-field-echo MR imaging with Gd-DTPA: physiologic evaluation of the kidney and liver. Radiology 1986; 160(2): 561–563.
- 3
Villringer A,
Rosen BR,
Belliveau JW,
Ackerman JL,
Lauffer RB,
Buxton RB,
Chao YS,
Wedeen VJ,
Brady TJ. Dynamic imaging with lanthanide chelates in normal brain: contrast due to magnetic susceptibility effects. Magn. Reson. Med. 1988; 6(2): 164–174.
- 4
Choyke PL,
Frank JA,
Girton ME,
Inscoe SW,
Carvlin MJ,
Black JL,
Austin HA,
Dwyer AJ. Dynamic Gd-DTPA-enhanced MR imaging of the kidney: experimental results. Radiology 1989; 170(3): 713–720.
- 5
Tofts PS,
Kermode AG. Blood brain barrier permeability in multiple sclerosis using labelled DTPA with PET, CT and MRI. J. Neurol. Neurosurg. Psychiatry 1989; 52(8): 1019–1020.
- 6
Sourbron S,
Ingrisch M,
Siefert A,
Reiser M,
Herrmann K. Quantification of cerebral blood flow, cerebral blood volume, and blood–brain-barrier leakage with DCE-MRI. Magn. Reson. Med. 2009; 62(1): 205–217.
- 7
Rosen BR,
Belliveau JW,
Vevea JM,
Brady TJ. Perfusion imaging with NMR contrast agents. Magn. Reson. Med. 1990; 14(2): 249–265.
- 8
Kuhl CK,
Bieling H,
Gieseke J,
Ebel T,
Mielcarek P,
Far F,
Folkers P,
Elevelt A,
Schild HH. Breast neoplasms: T2* susceptibility-contrast, first-pass perfusion MR imaging. Radiology 1997; 202(1): 87–95.
- 9
Larsson HB,
Stubgaard M,
Frederiksen JL,
Jensen M,
Henriksen O,
Paulson OB. Quantitation of blood–brain barrier defect by magnetic resonance imaging and gadolinium-DTPA in patients with multiple sclerosis and brain tumors. Magn. Reson. Med. 1990; 16(1): 117–131.
- 10
Tofts PS,
Kermode AG. Measurement of the blood–brain barrier permeability and leakage space using dynamic MR imaging. 1. Fundamental concepts. Magn. Reson. Med. 1991; 17(2): 357–367.
- 11
Brix G,
Semmler W,
Port R,
Schad LR,
Layer G,
Lorenz WJ. Pharmacokinetic parameters in CNS GD-DTPA enhanced MR imaging. J. Comput. Assist. Tomogr. 1991; 15(4): 621–628.
- 12
Materne R,
Smith AM,
Peeters F,
Dehoux JP,
Keyeux A,
Horsmans Y,
Beers BEV. Assessment of hepatic perfusion parameters with dynamic MRI. Magn. Reson. Med. 2002; 47(1): 135–142.
- 13
Choyke P,
Dwyer A,
Knopp M. Functional tumor imaging with dynamic contrast-enhanced magnetic resonance imaging. J. Magn. Reson. Imaging 2003; 17(5): 509–520.
- 14
Jerosch-Herold M,
Seethamraju R,
Swingen C,
Wilke N,
Stillman A. Analysis of myocardial perfusion MRI. J. Magn. Reson. Imaging 2004; 19(6): 758–770.
- 15
Brix G,
Kiessling F,
Lucht R,
Darai S,
Wasser K,
Delorme S,
Griebel J. Microcirculation and microvasculature in breast tumors: pharmacokinetic analysis of dynamic MR image series. Magn. Reson. Med. 2004; 52(2): 420–429.
- 16
Dujardin M,
Sourbron S,
Luypaert R,
Verbeelen D,
Stadnik T. Quantification of renal perfusion and function on a voxel-by-voxel basis: a feasibility study. Magn. Reson. Med. 2005; 54(4): 841–849.
- 17
de Bazelaire C,
Siauve N,
Fournier L,
Frouin F,
Robert P,
Clement O,
de Kerviler E,
Cuenod CA. Comprehensive model for simultaneous MRI determination of perfusion and permeability using a blood-pool agent in rats rhabdomyosarcoma. Eur. Radiol. 2005; 15(12): 2497–2505.
- 18
Leach MO,
Brindle KM,
Evelhoch JL,
Griffiths JR,
Horsman MR,
Jackson A,
Jayson GC,
Judson IR,
Knopp MV,
Maxwell RJ,
McIntyre D,
Padhani AR,
Price P,
Rathbone R,
Rustin GJ,
Tofts PS,
Tozer GM,
Vennart W,
Waterton JC,
Williams SR,
Workman P. The assessment of antiangiogenic and antivascular therapies in early-stage clinical trials using magnetic resonance imaging: issues and recommendations. Br. J. Cancer 2005; 92(9): 1599–1610.
- 19
Pandharipande P,
Krinsky G,
Rusinek H,
Lee V. Perfusion imaging of the liver: current challenges and future goals. Radiology 2005; 234(3): 661–673.
- 20
Kiessling F,
Jugold M,
Woenne E,
Brix G. Non-invasive assessment of vessel morphology and function in tumors by magnetic resonance imaging. Eur. Radiol. 2007; 17(8): 2136–2148.
- 21
Jackson A,
O'Connor J,
Parker G,
Jayson G. Imaging tumor vascular heterogeneity and angiogenesis using dynamic contrast-enhanced magnetic resonance imaging. Clin. Cancer Res. 2007; 13(12): 3449–3459.
- 22
Grenier N,
Mendichovszky I,
de Senneville B,
Roujol S,
Desbarats P,
Pedersen M,
Wells K,
Frokiaer J,
Gordon I. Measurement of glomerular filtration rate with magnetic resonance imaging: principles, limitations, and expectations. Semin. Nucl. Med. 2008; 38(1): 47–55.
- 23
Kershaw L,
Hutchinson C,
Buckley D. Benign prostatic hyperplasia: evaluation of T1, T2, and microvascular characteristics with T1-weighted dynamic contrast-enhanced MRI. J. Magn. Reson. Imaging 2009; 29(3): 641–648.
- 24
Sorensen A,
Reimer P. Cerebral MR Perfusion Imaging. Georg Thieme Verlag: Stuttgart, Germany, 2000.
- 25
Covarrubias D,
Rosen B,
Lev M. Dynamic magnetic resonance perfusion imaging of brain tumors. Oncologist 2004; 9(5): 528–537.
- 26
Waldman A,
Jackson A,
Price S,
Clark C,
Booth T,
Auer D,
Tofts P,
Collins D,
Leach M,
Rees J. Quantitative imaging biomarkers in neuro-oncology. Nat. Rev. Clin. Oncol. 2009; 6(8): 445–454.
- 27
Moody AR,
Martel A,
Kenton A,
Allder S,
Horsfield MA,
Delay G,
Morgan P. Contrast-reduced imaging of tissue concentration and arterial level (CRITICAL) for assessment of cerebral hemodynamics in acute stroke by magnetic resonance. Invest. Radiol. 2000; 35(7): 401–411.
- 28
Martel AL,
Allder SJ,
Delay GS,
Morgan PS,
Moody AA. Perfusion MRI of infarcted and noninfarcted brain tissue in stroke: a comparison of conventional hemodynamic imaging and factor analysis of dynamic studies. Invest. Radiol. 2001; 36(7): 378–385.
- 29
Singh A,
Haris M,
Rathore D,
Purwar A,
Sarma M,
Bayu G,
Husain N,
Rathore R,
Gupta R. Quantification of physiological and hemodynamic indices using T(1) dynamic contrast-enhanced MRI in intracranial mass lesions. J. Magn. Reson. Imaging 2007; 26(4): 871–880.
- 30
Larsson H,
Hansen A,
Berg H,
Rostrup E,
Haraldseth O. Dynamic contrast-enhanced quantitative perfusion measurement of the brain using T1-weighted MRI at 3T. J. Magn. Reson. Imaging 2008; 27(4): 754–762.
- 31
Johnson G,
Wetzel SG,
Cha S,
Babb J,
Tofts PS. Measuring blood volume and vascular transfer constant from dynamic, t(2)*-weighted contrast-enhanced MRI. Magn. Reson. Med. 2004; 51(5): 961–968.
- 32
Kiselev VG. Transverse relaxation effect of MRI contrast agents: a crucial issue for quantitative measurements of cerebral perfusion. J. Magn. Reson. Imaging 2005; 22(6): 693–696.
- 33
Sorensen AG. Perfusion MR imaging: moving forward. Radiology 2008; 249(2): 416–417.
- 34
Calamante F. Clinical MR Neuroimaging, Chapter11. Cambridge University Press: Cambridge, 2009.
- 35
Sourbron S,
Heilmann M,
Biffar A,
Walczak C,
Vautier J,
Volk A,
Peller M. Bolus-tracking MRI with a simultaneous T1- and T2*-measurement. Magn. Reson. Med. 2009; 62(3): 672–681.
- 36
Boxerman JL,
Schmainda KM,
Weisskoff RM. Relative cerebral blood volume maps corrected for contrast agent extravasation significantly correlate with glioma tumor grade, whereas uncorrected maps do not. Am. J. Neuroradiol. 2006; 27(4): 859–867.
- 37
Rohrer M,
Bauer H,
Mintorovitch J,
Requardt M,
Weinmann HJ. Comparison of magnetic properties of MRI contrast media solutions at different magnetic field strengths. Invest. Radiol. 2005; 40(11): 715–724.
- 38
Donahue KM,
Burstein D,
Manning WJ,
Gray ML. Studies of Gd-DTPA relaxivity and proton exchange rates in tissue. Magn. Reson. Med. 1994; 32(1): 66–76.
- 39
Pintaske J,
Martirosian P,
Graf H,
Erb G,
Lodemann KP,
Claussen C,
Schick F. Relaxivity of gadopentetate dimeglumine (Magnevist), gadobutrol (Gadovist), and gadobenate dimeglumine (Multihance) in human blood plasma at 0.2, 1.5, and 3 Tesla. Invest. Radiol. 2006; 41(3): 213–221.
- 40
Bruening R,
Kwong KK,
Vevea MJ,
Hochberg FH,
Cher L,
Harsh GR,
Niemi PT,
Weisskoff RM,
Rosen BR. Echo-planar MR determination of relative cerebral blood volume in human brain tumors: T1 versus T2 weighting. Am. J. Neuroradiol. 1996; 17(5): 831–840.
- 41
Haroon HA,
Patankar TF,
Zhu XP,
Li KL,
Thacker NA,
Scott MJ,
Jackson A. Comparison of cerebral blood volume maps generated from t2* and t1 weighted MRI data in intra-axial cerebral tumours. Br. J. Radiol. 2007; 80(951): 161–168.
- 42
Ingrisch M,
Sourbron S,
Morhard D,
Ertl-Wagner B,
Kümpfel T,
Hohlfeld R,
Reiser M,
Glaser C. Quantification of perfusion and permeability in multiple sclerosis: Dynamic contrast-enhanced MRI in 3D at 3T. Invest. Radiol. 2012; 47(4): 252–258.
- 43
Dean BL,
Lee C,
Kirsch JE,
Runge VM,
Dempsey RM,
Pettigrew LC. Cerebral hemodynamics and cerebral blood volume: MR assessment using gadolinium contrast agents and t1-weighted turbo-flash imaging. Am. J. Neuroradiol. 1992; 13(1): 39–48.
- 44
Hackländer T,
Hofer M,
Reichenbach JR,
Rascher K,
Fürst G,
Mödder U. Cerebral blood volume maps with dynamic contrast-enhanced t1-weighted flash imaging: normal values and preliminary clinical results. J. Comput. Assist. Tomogr. 1996; 20(4): 532–539.
- 45
Hackländer T,
Reichenbach JR,
Hofer M,
Mödder U. Measurement of cerebral blood volume via the relaxing effect of low-dose gadopentetate dimeglumine during bolus transit. Am. J. Neuroradiol. 1996; 17(5): 821–830.
- 46
Hackländer T,
Reichenbach JR,
Mödder U. Comparison of cerebral blood volume measurements using the t1 and t2* methods in normal human brains and brain tumors. J. Comput. Assist. Tomogr. 1997; 21(6): 857–866.
- 47
Roberts HC,
Roberts TP,
Brasch RC,
Dillon WP. Quantitative measurement of microvascular permeability in human brain tumors achieved using dynamic contrast-enhanced MR imaging: correlation with histologic grade. Am. J. Neuroradiol. 2000; 21(5): 891–899.
- 48
Ewing JR,
Knight RA,
Nagaraja TN,
Yee JS,
Nagesh V,
Whitton PA,
Li L,
Fenstermacher JD. Patlak plots of GD-DTPA MRI data yield blood–brain transfer constants concordant with those of 14c-sucrose in areas of blood–brain opening. Magn. Reson. Med. 2003; 50(2): 283–292.
- 49
Haroon H,
Buckley D,
Patankar T,
Dow G,
Rutherford S,
Balériaux D,
Jackson A. A comparison of Ktrans measurements obtained with conventional and first pass pharmacokinetic models in human gliomas. J. Magn. Reson. Imaging 2004; 19(5): 527–536.
- 50
Kassner A,
Roberts T,
Taylor K,
Silver F,
Mikulis D. Prediction of hemorrhage in acute ischemic stroke using permeability MR imaging. Am. J. Neuroradiol. 2005; 26(9): 2213–2217.
- 51
Martel AL,
Moody AR,
Allder SJ,
Delay GS,
Morgan PS. Extracting parametric images from dynamic contrast-enhanced MRI studies of the brain using factor analysis. Med. Image Anal. 2001; 5(1): 29–39.
- 52
Pauliah M,
Saxena V,
Haris M,
Husain N,
Rathore RKS,
Gupta RK. Improved t(1)-weighted dynamic contrast-enhanced MRI to probe microvascularity and heterogeneity of human glioma. Magn. Reson. Imaging 2007; 25(9): 1292–1299.
- 53
Larsson HBW,
Courivaud F,
Rostrup E,
Hansen AE. Measurement of brain perfusion, blood volume, and blood–brain barrier permeability, using dynamic contrast-enhanced T(1)-weighted MRI at 3 tesla. Magn. Reson. Med. 2009; 62(5): 1270–1281.
- 54
Tofts PS. Modeling tracer kinetics in dynamic Gd-DTPA MR imaging. J. Magn. Reson. Imaging 1997; 7(1): 91–101.
- 55
Tofts PS,
Brix G,
Buckley DL,
Evelhoch JL,
Henderson E,
Knopp MV,
Larsson HB,
Lee TY,
Mayr NA,
Parker GJ,
Port RE,
Taylor J,
Weisskoff RM. Estimating kinetic parameters from dynamic contrast-enhanced T(1)-weighted MRI of a diffusable tracer: standardized quantities and symbols. J. Magn. Reson. Imaging 1999; 10(3): 223–232.
- 56
Evelhoch J,
Garwood M,
Vigneron D,
Knopp M,
Sullivan D,
Menkens A,
Clarke L,
Liu G. Expanding the use of magnetic resonance in the assessment of tumor response to therapy: workshop report. Cancer Res.. 2005; 65(16): 7041–7044.
- 57
O'Connor JPB,
Jackson A,
Parker GJM,
Jayson GC. DCE-MRI biomarkers in the clinical evaluation of antiangiogenic and vascular disrupting agents. Br. J. Cancer 2007; 96(2): 189–195.
- 58
Brix G,
Zwick S,
Kiessling F,
Griebel J. Pharmacokinetic analysis of tissue microcirculation using nested models: multimodel inference and parameter identifiability. Med. Phys. 2009; 36(7): 2923–2933.
- 59
Donaldson SB,
Buckley DL,
O'Connor JP,
Davidson SE,
Carrington BM,
Jones AP,
West CML. Enhancing fraction measured using dynamic contrast-enhanced MRI predicts disease-free survival in patients with carcinoma of the cervix. Br. J. Cancer 2010; 102(1): 23–26.
- 60
Henderson E,
Sykes J,
Drost D,
Weinmann HJ,
Rutt BK,
Lee TY. Simultaneous MRI measurement of blood flow, blood volume, and capillary permeability in mammary tumors using two different contrast agents. J. Magn. Reson. Imaging 2000; 12(6): 991–1003.
- 61
Pradel C,
Siauve N,
Bruneteau G,
Clement O,
de Bazelaire C,
Frouin F,
Wedge SR,
Tessier JL,
Robert PH,
Frija G,
Cuenod CA. Reduced capillary perfusion and permeability in human tumour xenografts treated with the VEGF signalling inhibitor zd4190: an in vivo assessment using dynamic MR imaging and macromolecular contrast media. Magn. Reson. Imaging 2003; 21(8): 845–851.
- 62
Jacquez J. Compartmental Analysis in Biology and Medicine, 2nd edn. University of Michigan Press: Michigan, 1985.
- 63
Bassingthwaighte J,
Goresky C. Handbook of Physiology. Section 2: The Cardiovascular System. American Physiological Society: Bethesda, MD, 1984; 549–626.
- 64
Kuikka JT,
Bassingthwaighte JB,
Henrich MM,
Feinendegen LE. Mathematical modelling in nuclear medicine. Eur. J. Nucl. Med. 1991; 18(5): 351–362.
- 65
Larson KB,
Markham J,
Raichle ME. Tracer-kinetic models for measuring cerebral blood flow using externally detected radiotracers. J. Cereb. Blood Flow Metab. 1987; 7(4): 443–463.
- 66
Sawada Y,
Patlak CS,
Blasberg RG. Kinetic analysis of cerebrovascular transport based on indicator diffusion technique. Am. J. Physiol. 1989; 256(3): H794–H812.
- 67
Brix G,
Bahner ML,
Hoffmann U,
Horvath A,
Schreiber W. Regional blood flow, capillary permeability, and compartmental volumes: measurement with dynamic CT–initial experience. Radiology 1999; 210(1): 269–276.
- 68
Cenic A,
Nabavi DG,
Craen RA,
Gelb AW,
Lee TY. A CT method to measure hemodynamics in brain tumors: validation and application of cerebral blood flow maps. Am. J. Neuroradiol. 2000; 21(3): 462–470.
- 69
Koh TS,
Cheong LH,
Hou Z,
Soh YC. A physiologic model of capillary-tissue exchange for dynamic contrast-enhanced imaging of tumor microcirculation. IEEE Trans. Biomed. Eng. 2003; 50(2): 159–167.
- 70
Rempp KA,
Brix G,
Wenz F,
Becker CR,
Gückel F,
Lorenz WJ. Quantification of regional cerebral blood flow and volume with dynamic susceptibility contrast-enhanced MR imaging. Radiology 1994; 193(3): 637–641.
- 71
Ostergaard L,
Sorensen AG,
Kwong KK,
Weisskoff RM,
Gyldensted C,
Rosen BR. High resolution measurement of cerebral blood flow using intravascular tracer bolus passages. part ii: Experimental comparison and preliminary results. Magn. Reson. Med. 1996; 36(5): 726–736.
- 72
Aumann S,
Schoenberg S,
Just A,
Briley-Saebo K,
Bjornerud AB,
Bock M,
Brix G. Quantification of renal perfusion using an intravascular contrast agent (Part 1): Results in a canine model. Magn. Reson. Med. 2003; 49(2): 276–287.
- 73
Delille JP,
Slanetz PJ,
Yeh ED,
Kopans DB,
Garrido L. Breast cancer: regional blood flow and blood volume measured with magnetic susceptibility-based MR imaging – initial results. Radiology 2002; 223(2): 558–565.
- 74
Vallée JP,
Lazeyras F,
Khan HG,
Terrier F. Absolute renal blood flow quantification by dynamic MRI and Gd-DTPA. Eur. Radiol. 2000; 10(8): 1245–1252.
- 75
Jerosch-Herold M,
Swingen C,
Seethamraju R. Myocardial blood flow quantification with MRI by model-independent deconvolution. Med. Phys. 2002; 29(5): 886–897.
- 76
Makkat S,
Luypaert R,
Stadnik T,
Bourgain C,
Sourbron S,
Dujardin M,
Greve JD,
Mey JD. Deconvolution-based dynamic contrast-enhanced MR imaging of breast tumors: correlation of tumor blood flow with human epidermal growth factor receptor 2 status and clinicopathologic findings–preliminary results. Radiology 2008; 249(2): 471–482.
- 77
Sourbron SP,
Buckley DL. Tracer kinetic modelling in MRI: estimating perfusion and capillary permeability. Phys. Med. Biol. 2012; 57(2): R1–33.
- 78
Landis CS,
Li X,
Telang FW,
Coderre JA,
Micca PL,
Rooney WD,
Latour LL,
Vtek G,
Plyka I,
Springer CS. Determination of the MRI contrast agent concentration time course in vivo following bolus injection: effect of equilibrium transcytolemmal water exchange. Magn. Reson. Med. 2000; 44(4): 563–574.
- 79
Buckley D,
Kershaw L,
Stanisz G. Cellular-interstitial water exchange and its effect on the determination of contrast agent concentration in vivo: dynamic contrast-enhanced MRI of human internal obturator muscle. Magn. Reson. Med. 2008; 60(5): 1011–1019.
- 80
Bains LJ,
McGrath DM,
Naish JH,
Cheung S,
Watson Y,
Taylor MB,
Logue JP,
Parker GJM,
Waterton JC,
Buckley DL. Tracer kinetic analysis of dynamic contrast-enhanced MRI and CT bladder cancer data: A preliminary comparison to assess the magnitude of water exchange effects. Magn. Reson. Med. 2010; 64(2): 595–603.
- 81
Peeters F,
Annet L,
Hermoye L,
Beers BV. Inflow correction of hepatic perfusion measurements using T1-weighted, fast gradient-echo, contrast-enhanced MRI. Magn. Reson. Med. 2004; 51(4): 710–717.
- 82
Garpebring A,
Wirestam R,
Ostlund N,
Karlsson M. Effects of inflow and radiofrequency spoiling on the arterial input function in dynamic contrast-enhanced MRI: a combined phantom and simulation study. Magn. Reson. Med. 2011; 65(6): 1670–1679.
- 83
Schabel MC,
Parker DL. Uncertainty and bias in contrast concentration measurements using spoiled gradient echo pulse sequences. Phys. Med. Biol. 2008; 53(9): 2345–2373.
- 84
Roberts C,
Little R,
Watson Y,
Zhao S,
Buckley DL,
Parker GJM. The effect of blood inflow and b(1)-field inhomogeneity on measurement of the arterial input function in axial 3D spoiled gradient echo dynamic contrast-enhanced MRI. Magn. Reson. Med. 2011; 65(1): 108–119.
- 85
Perl W,
Lassen NA,
Effros RM. Matrix proof of flow, volume and mean transit time theorems for regional and compartmental systems. Bull. Math. Biol. 1975; 37(6): 573–588.
- 86
Lassen N,
Perl W. Tracer Kinetic Methods in Medical Physiology. Raven Press: New York, 1979.
- 87
Sourbron S,
Luypaert R,
Schuerbeek PV,
Dujardin M,
Stadnik T. Choice of the regularization parameter for perfusion quantification with MRI. Phys. Med. Biol. 2004; 49(14): 3307–3324.
- 88
Zierler KL. Theory of the use of arteriovenous concentration differences for measuring metabolism in steady and non-steady states. J. Clin. Invest. 1961; 40(12): 2111–2125.
- 89
Sourbron S,
Michaely H,
Reiser M,
Schoenberg S. MRI-measurement of perfusion and glomerular filtration in the human kidney with a separable compartment model. Invest. Radiol. 2008; 43(1): 40–48.
- 90
Calamante F,
Gadian DG,
Connelly A. Delay and dispersion effects in dynamic susceptibility contrast MRI: simulations using singular value decomposition. Magn. Reson. Med. 2000; 44(3): 466–473.
- 91
Calamante F,
Gadian D,
Connelly A. Quantification of bolus-tracking MRI: Improved characterization of the tissue residue function using Tikhonov regularization. Magn. Reson. Med. 2003; 50(6): 1237–1247.
- 92
Wu O,
Østergaard L,
Weisskoff RM,
Benner T,
Rosen BR,
Sorensen AG. Tracer arrival timing-insensitive technique for estimating flow in MR perfusion-weighted imaging using singular value decomposition with a block-circulant deconvolution matrix. Magn. Reson. Med. 2003; 50(1): 164–174.
- 93
Sourbron S,
Luypaert R,
Morhard D,
Seelos K,
Reiser M,
Peller M. Deconvolution of bolus-tracking data: a comparison of discretization methods. Phys. Med. Biol. 2007; 52(22): 6761–6778.
- 94
Michoux N,
Huwart L,
Abarca-Quinones J,
Dorvillius M,
Annet L,
Peeters F,
Beers BEV. Transvascular and interstitial transport in rat hepatocellular carcinomas: dynamic contrast-enhanced MRI assessment with low- and high-molecular weight agents. J. Magn. Reson. Imaging 2008; 28(4): 906–914.
- 95
Renkin EM. Transport of potassium-42 from blood to tissue in isolated mammalian skeletal muscles. Am. J. Physiol. 1959; 197: 1205–1210.
- 96
Guyton A. Textbook of Medical Physiology. WB Saunders Company: Philadelphia, 1991.
- 97
Sangren WC,
Sheppard CW. A mathematical derivation of the exchange of a labeled substance between a liquid flowing in a vessel and an external compartment. Bull. Math. Biophys. 1953; 15: 387–394.
- 98
Thomassin-Naggara I,
Balvay D,
Cuenod C,
Dara E,
Marsault C,
Bazot M. Dynamic contrast-enhanced MR imaging to assess physiologic variations of myometrial perfusion. Eur Radiol. 2010; 20(4): 984–994.
- 99
Donaldson SB,
Betts G,
Bonington SC,
Homer JJ,
Slevin NJ,
Kershaw LE,
Valentine H,
West CML,
Buckley DL. Perfusion estimated with rapid dynamic contrast-enhanced magnetic resonance imaging correlates inversely with vascular endothelial growth factor expression and pimonidazole staining in head-and-neck cancer: a pilot study. Int. J. Radiat. Oncol. Biol. Phys. 2011; 81(4): 1176–1183.
- 100
Johnson JA,
Wilson TA. A model for capillary exchange. Am. J. Physiol. 1966; 210(6): 1299–1303.
- 101
Garpebring A,
Ostlund N,
Karlsson M. A novel estimation method for physiological parameters in dynamic contrast-enhanced MRI: application of a distributed parameter model using Fourier-domain calculations. IEEE Trans. Med. Imaging 2009; 28(9): 1375–1383.
- 102
Lawrence KSS,
Lee TY. An adiabatic approximation to the tissue homogeneity model for water exchange in the brain: II. Experimental validation. J. Cereb. Blood Flow Metab. 1998; 18(12): 1378–1385.
- 103
Kershaw LE,
Buckley DL. Precision in measurements of perfusion and microvascular permeability with t1-weighted dynamic contrast-enhanced MRI. Magn. Reson. Med. 2006; 56(5): 986–992.
- 104
Naish J,
Kershaw L,
Buckley D,
Jackson A,
Waterton J,
Parker G. Modeling of contrast agent kinetics in the lung using T1-weighted dynamic contrast-enhanced MRI. Magn. Reson. Med. 2009; 61(6): 1507–1514.
- 105
Korporaal JG,
van Vulpen M,
van den Berg CAT,
van der Heide UA. Tracer kinetic model selection for dynamic contrast-enhanced computed tomography imaging of prostate cancer. Invest. Radiol. 2012; 47(1): 41–48.
- 106
Bisdas S,
Konstantinou G,
Surlan-Popovic K,
Khoshneviszadeh A,
Baghi M,
Vogl TJ,
Koh TS,
Mack MG. Dynamic contrast-enhanced CT of head and neck tumors: comparison of first-pass and permeability perfusion measurements using two different commercially available tracer kinetics models. Acad. Radiol. 2008; 15(12): 1580–1589.
- 107
Koh TS,
Thng CH,
Hartono S,
Kwek JW,
Khoo JBK,
Miyazaki K,
Collins DJ,
Orton MR,
Leach MO,
Lewington V,
Koh DM. Dynamic contrast-enhanced MRI of neuroendocrine hepatic metastases: A feasibility study using a dual-input two-compartment model. Magn. Reson. Med. 2011; 65(1): 250–260.
- 108
Sourbron SP,
Buckley DL. On the scope and interpretation of the Tofts models for DCE-MRI. Magn. Reson. Med. 2011; 66(3): 735–745.
- 109
Buckley D,
Shurrab A,
Cheung C,
Jones A,
Mamtora H,
Kalra P. Measurement of single kidney function using dynamic contrast-enhanced MRI: comparison of two models in human subjects. J. Magn. Reson. Imaging 2006; 24(5): 1117–1123.
- 110
Luypaert R,
Sourbron S,
de Mey J. Validity of perfusion parameters obtained using the modified Tofts model: a simulation study. Magn. Reson. Med. 2011; 65(5): 1491–1497.
- 111
Michaely H,
Sourbron S,
Buettner C,
Lodemann KP,
Reiser M,
Schoenberg S. Temporal constraints in renal perfusion imaging with a 2-compartment model. Invest. Radiol. 2008; 43(2): 120–128.
- 112
Luypaert R,
Sourbron S,
de Mey J. Validity of perfusion parameters obtained using the modified Tofts model: A simulation study. Magn Reson. Med. 2011; 65(5): 1491–1497.
- 113
Ewing JR,
Brown SL,
Lu M,
Panda S,
Ding G,
Knight RA,
Cao Y,
Jiang Q,
Nagaraja TN,
Churchman JL,
Fenstermacher JD. Model selection in magnetic resonance imaging measurements of vascular permeability: Gadomer in a 9L model of rat cerebral tumor. J. Cereb. Blood Flow Metab. 2006; 26(3): 310–320.
- 114
Hackstein N,
Heckrodt J,
Rau WS. Measurement of single-kidney glomerular filtration rate using a contrast-enhanced dynamic gradient-echo sequence and the Rutland–Patlak plot technique. J. Magn. Reson. Imaging 2003; 18(6): 714–725.
- 115
Brix G,
Zwick S,
Griebel J,
Fink C,
Kiessling F. Estimation of tissue perfusion by dynamic contrast-enhanced imaging: simulation-based evaluation of the steepest slope method. Eur Radiol. 2010; 20(9): 2166–2175.
- 116
Peters AM,
Gunasekera RD,
Henderson BL,
Brown J,
Lavender JP,
Souza MD,
Ash JM,
Gilday DL. Noninvasive measurement of blood flow and extraction fraction. Nucl. Med. Commun. 1987; 8(10): 823–837.
- 117
Miles KA. Measurement of tissue perfusion by dynamic computed tomography. Br. J. Radiol. 1991; 64(761): 409–412.
- 118
Cheong LHD,
Lim CCT,
Koh TS. Dynamic contrast-enhanced CT of intracranial meningioma: comparison of distributed and compartmental tracer kinetic models–initial results. Radiology 2004; 232(3): 921–930.
- 119
Wirestam R,
Andersson L,
Ostergaard L,
Bolling M,
Aunola JP,
Lindgren A,
Geijer B,
Holtås S,
Ståhlberg F. Assessment of regional cerebral blood flow by dynamic susceptibility contrast MRI using different deconvolution techniques. Magn. Reson. Med. 2000; 43(5): 691–700.
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