public class AlgorithmSM2
extends AlgorithmBase

Based on the document provided by Daniel Reich: Notes on DCE with SM2 (standard model, aka Tofts model, 2-compartment) 3 model parameters are fit for each voxel in 3D: 1) K_trans in [1.0E-5, 5.0] in /min On input ktrans is converted from /min to /sec and on output ktrans is converted from /sec to /min. 2) ve in [1.0E-5, 0.99] 3) f_vp in [0, 0.99] srcImage is a dynamic "4D volume" of MRI signal (3D over time). The equation used here is virtually identical to equation 10.3 in T1-w DCE-MRI. Ct(t) = vpCp(t) + ktrans*integral from 0 to t of Cp(t') * exp[-ktrans*(t - t')/ve]dt' (10.3) Cp is the concentration of agent in the vascular plasma space, vp. ve is the volume of the extravascular extracellular space per unit volume of tissue. ktrans is the volume transfer constant between vp and ve. Ct is the tracer concentration in the tissue as a whole. Our equation is: R1(t) - R10 = (vp * [R1,p(t) - R10,p] + ktrans*integral from 0 to t of [R1,p(tau) - R10,p]*exp[-ktrans*(t - tau)/ve]d(tau))/(1 - h) where R10 is the tissue R1 map in the absence of contrast material, a 3D volume R1(tj) is the tissue R1 map during contrast infusion, a 4D data set. h = hematocrit with a default value of 0.4. With the sagittal sinus VOI: Average over this VOI to extract the constant R10,p from the R10 map. Average over this VOI to extract the time series R1,p(tj) from the R1(tj) 4D data set. tj is a vector of the center times for each volume, where j = 1,...,n and n is the number of post-contrast volumes. Solve the equation numerically assuming piecewise linearity and using the trapezoid rule. The pre-injection volumes are actually averaged together to generate the R10 map. So you're right, they wouldn't provide any additional information, and we don't need to fit them. After injection (t=t1), the first volume usually has no contrast in it. That's because the contrast has to circulate to the brain. So R1,p(t1) should be the same as R10,p, but in our scheme R1,p(t1) wasn't used to generate the R10 map. Any differences should be due to noise. Does that help explain things? For monomeric gadolinium chelates, Ktrans for the normal blood brain barrier is approximately 10^-4 min^-1 (from the legend to Fig 5 of Li, Rooney, and Springer (MRM, 2005)). So a lower bound of 10^-5 should be ok. If R1,p(t1) = R10,p except for noise, then R1,p(t1) - R10,p is purely noise and contains no useful information References: 1.) "A Unified Magnetic Resonance Imaging Pharmacokinetic Theory: Intravascular and Extracellular Contrast Reagents" by Xin Li, William D. Rooney, and Charles S. Springer, Jr., Magnetic Resonance in Medicine, Vol. 54, 2005, pp. 1351-1359. 2.) Erratum: Magnetic Resonance in Medicine, Vol. 55, 2006, p.1217. 3.) Quantitative MRI of the Brain, Edited by Paul Tofts, 2003, John Wiley & Sons, Ltd., ISBN: 0-47084721-2, Chapter 10, T1-w DCE-MRI: T1-weighted Dynamic Contrast-enhanced MRI by Geoff J. M. Parker and Anwar R. Padhani, pp. 341-364. 4.) Larsson HBW, Courivaud F, Rostrup E, Hansen AE. Measurement of brain perfusion, blood volume, and blood-brain barrier permeability, using dynamic contrast-enhanced T1-weighted MRI at 3 tesla. Magnetic Resonance in Medicine 2009; 62(5):1270-1281. 5.) Li X, Rooney WD, Springer CS. A unified magnetic resonance imaging pharmacokinetic theory: intravascular and extracellular contrast reagents. Magnetic Resonance in Medicine 2005 Dec; 54(6): 1351-1359. 6.) Tofts PS, Modeling tracer kinetics in dynamic Gd-DPTA MR imaging. Journal of Magnetic Resonance Imaging, 1997, 7(1), pp. 91-101. 7.) Tofts PS, Brix G, Buckley DL, Evelhoch JL, Henderson E, Knopp MV, Larsson HB, 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 quantitites and symbols. J. Magn. Reson Imaging 1999 Sep; 10(3), pp. 223-232.