Inflow Correction of Hepatic Perfusion MeasurementsUsing T1-Weighted, Fast Gradient-Echo,Contrast-Enhanced MRI

Frank Peeters,* Laurence Annet, Laurent Hermoye, and Bernard E. Van Beers

Inflow effects were studied for T1-weighted, fast gradient-echo,contrast-enhanced MRI. This was done on the basis of realisticsimulations (e.g., taking slice profiles into account) for unsteadyflow. The area under the point spread function (PSF) was usedto estimate the flow-related enhancement. A simple analyticalmodel that accurately describes the inflow effects was derivedand validated. This model was used to correct the experimentalperfusion calibration curves (signal intensity vs. relaxation rate)for inflow effects. Hepatic perfusion measurements, performedon patients, were analyzed in terms of a dual-input, first-orderlinear model. It was shown that inflow causes incorrect perfu-sion input functions. The resulting estimated perfusion param-eters displayed a systematic error of typically 30–40%. By per-forming two extra time-resolved flow measurements during theexamination, one can correct the input functions. Magn Re-son Med 51:710–717, 2004. © 2004 Wiley-Liss, Inc.

Key words: dynamic MRI; perfusion; inflow effects; fast gradi-ent echo; liver

Perfusion is an important determinant of liver function inhealth and disease (1). Previous studies performed withCT and MRI have shown that the hepatic perfusion param-eters are correlated with liver function in patients withchronic liver diseases, including cirrhosis (2,3). In MRI,perfusion can be measured by using a T1-relaxivity con-trast agent (such as Gd-DTPA or -DOTA) in combinationwith a fast gradient-echo sequence (1,2). One can thenmeasure the passage of the bolus at the location of interestby performing a dynamic acquisition. In order to convertthe measured signal intensity vs. time curves into (bolus)concentration vs. time curves, the sequence should becalibrated. Therefore, the exact relationship between sig-nal intensity, relaxation rate R1 � 1/T1, and concentrationshould be accurately known. This relationship is usuallyestimated on the basis of phantom measurements and/ortheoretical models (3–6).

For the estimation of perfusion parameters, the arterialinput function should be known. For the liver, the portalvenous input function should also be measured. There-fore, the signal intensity vs. time curves should be mea-sured in the artery (and vein) of interest and converted toconcentration vs. time curves. Unfortunately, gradient-

echo sequences exhibit strong inflow effects. Since thecalibration is performed in the absence of flow, these in-flow effects lead to overestimation of the (concentration)input functions. It is clear that these inflow effects shouldbe corrected for, if accurate perfusion parameters are de-sired.

In this work we present a method to correct the calibra-tion curves for inflow effects. The method is based onphantom measurements (without flow) and an analyticalmodel that is valid for both steady and pulsatile flows.Such an approach allows one to study the importance ofthe hemodynamic and sequence-related parameters. Themethod is validated on a flow phantom and demonstratedfor in vivo hepatic perfusion measurements together withits consequences for the estimated perfusion parametersobtained from a dual-input compartmental model.

MATERIALS AND METHODS

Calibration Without Inflow Effects

Perfusion measurements using T1-relaxivity agents relyupon the linear relationship between the relaxation rate R1

and the concentration C (7):

R1 �1T1

�1

T10� r1C, [1]

where T10 and T1 are the spin-lattice relaxation timesbefore and after injection, respectively, and r1 is the relax-ivity of the contrast agent. To identify this relationship, weconstructed a phantom consisting of 50 tubes filled withsaline and different concentrations of Gd-DOTA (DOT-AREM; Guerbet, Paris, France) in the range of 0–6 mM.The T1-relaxation times of the tubes were obtained fromimages acquired at multiple flip angles (8) with a standardspoiled gradient-echo sequence on a Philips Gyroscan In-tera 1.5 T system. As a result, a simple linear regression onthe (C, R1) data yields the desired parameters.

The signal intensity vs. relaxation rate relationship S(R1)is also needed, but this depends on the pulse sequenceused for the perfusion studies. We used a T1-weightedturbo field echo (TFE) sequence (9), i.e., a spoiled turbo-FLASH, synchronized to the cardiac cycle (ECG-triggered)for the in vivo studies. A non-slice-selective 90° prepara-tion pulse was incorporated into the sequence to avoidsignal changes due to variations in the cardiac cycle (10).To calibrate the TFE sequence, we acquired images of thephantom with parameters identical to those used in vivo,and using the same coil (i.e., the body coil). This was donefor three flip angles: 15°, 45°, and 90°. The signal intensi-ties were scaled with the appropriate receiver gain so that

Diagnostic Radiology Unit, Center for Anatomical, Functional and MolecularImaging Research, St-Luc University Hospital, Universite Catholique de Lou-vain (UCL), Brussels, Belgium.*Correspondence to: Frank Peeters, Ph.D., MRI Unit, Diagnostic RadiologyUnit, St-Luc University Hospital, Universite Catholique de Louvain (UCL),Avenue Hippocrate 10, 1200 Brussels, Belgium. E-mail: Frank.Peeters@rdgn.ucl.ac.beReceived 9 December 2002; revised 20 November 2003; accepted 21 No-vember 2003.DOI 10.1002/mrm.20032Published online in Wiley InterScience (www.interscience.wiley.com).

Magnetic Resonance in Medicine 51:710–717 (2004)

© 2004 Wiley-Liss, Inc. 710

the calibration curves S(R1) were compatible with the(scaled) in vivo intensities. In contrast to our earlier work(5), in this study we used another coil and scaled intensi-ties instead of reference (Agar) tubes. It is clear that thecalibration curves are only valid in the absence of infloweffects because the tubes in the phantom are filled withstationary fluid.

Calculation of Inflow Effects

To study the inflow effects for our perfusion sequence, wenumerically solved the Bloch equations under realisticconditions. Then we constructed a simple analyticalmodel that could be used to correct the calibration curves.This model was validated on the basis of the numericalsimulations.

Numerical Simulations

For a T1-weighted (i.e., spoiled) TFE sequence, the evolu-tion of the longitudinal magnetization M(n) just before theexcitation at time tn � nTR can be written in terms of adifference equation (8):

M�n � 1� � cos ��z�E1M�n� � M0�1 � E1�, [2]

with E1 � exp(–TR/T1), where TR is the repetition timeand M0 is the thermal equilibrium magnetization. Hereby,the slice profile is incorporated via the flip angle profile�(z). This will lead to a magnetization profile M(n,z). In thepresence of flow along the z-direction (i.e., perpendicularto the slice), the RF history of the flowing spins should betracked. In a Lagrangian description (11), Eq. [2] is stillvalid, but z now becomes the position of the spins at timetn: zn � z(tn). In order to express the signal from excitationat tN � NTR in terms of the position zN of the spins at thistime, we can use the following relationship:

zn � zN � �nTR

NTR

v�t�dt, [3]

where v(t) is the velocity waveform of the (unsteady) flow.Substituting this in Eq. [2] yields:

M�n � 1, zN� � cos ��zN ��nTR

NTR

v�t�dt�E1M�n, zN�

� M0�1 � E1�. [4]

Here, n can adopt the values 0,1,2,. . .,N – 1. Solution ofthe difference equation (Eq. [4]) leads to the magnetizationprofile M(N,zN) at time tN � NTR in terms of the spinpositions at this time. The initial value M(0,z0) is deter-mined by the preparation pulses. The signal profile com-ing from excitation at tN � NTR (i.e., the (N � 1)-th echo)is then given by:

s�N, zN� � M�N, zN�sin ��zN�exp��TE/T*2� [5]

where TE is the echo delay and T2* is the effective (in-cluding inhomogeneities) spin-spin relaxation time. Weconsidered excitation from sinc-Gaussian RF pulses (12)(as was implemented in the perfusion sequence). We cal-culated the slice (flip angle) profiles �(z) by numericallysolving the Bloch equations in the presence of flow (13).The signal for the (N � 1)-th echo was then obtained afterthe signal profile was integrated: S(N) � �s(N, zN)dzN.Fourier transformation of the signal S(N) yields the pointspread function (PSF) (14).

As a result, we describe inflow effects for the TFE se-quences in terms of the PSF. However, in practice it iscommon to describe inflow effects in terms of a singlenumber: the flow-related enhancement (FRE). Therefore,we quantify the FRE in terms of the area under the PSF, or,equivalently, the signal obtained when the center of k-space is crossed (15). This approach is certainly suited forperfusion measurements in which the concentration-timecurves are obtained by calculating the image intensity overa region of interest (ROI).

Analytical Model

Instead of working with slice profiles, one can use a sim-pler compartmental model to calculate the inflow effects(16). Here we consider two populations of spins: freshspins flowing into the slice, and spins that remain in theslice (between two excitations). The fraction of fresh spinscan be written as:

f�n� �1L �

nTR

�n�1�TR

v�t�dt, [6]

where L is the slice thickness. These enter the slice at tn �nTR with longitudinal magnetization Mi(n). The fraction 1– f(n) of spins that remains in the slice evolves accordingto Eq. [2]. As a result, the longitudinal magnetization obeysthe linear first-order difference equation:

M�n � 1� � �1 � f�n�cos �E1M�n�

� �1 � f�n�M0�1 � E1� � f�n�Mi�n�, [7]

with a well known closed-form solution (17):

M�n� � �cos �E1�n �

�0

n�1

�1 � f���M�0� � M0�1 � E1�

� ��0

n�1�1 � f��M0�1 � E1� � f��Mi��

�cos �E1��1 ���0

�1 � f��� � . [8]

The initial value M(0) is determined by T1-relaxation dur-ing the preparation (saturation) period and Mi(n) by T1-relaxation between the saturation pulse and tn�1 � (n �1)TR.. The fractions f(n) can be approximated by use of thetrapezium rule: f(n) � [v(n) � v(n � 1)]TR/ 2L. . The MRsignal is then given by:

s�N� � LM�N�sin � exp��TE/T*2�, [9]

Inflow Correction of Perfusion Measurements 711

where N corresponds to the central line of k-space.

Calibration With Inflow Effects

The start point of our calibration procedure is the calibra-tion data obtained from the tubes phantom (see “Calibra-tion Without Inflow Effects” below). In order to correct thecalibration curves S(R1) for inflow effects using the analyt-ical model, the (effective) slice thickness L and flip angle �should be known. These parameters were obtained from atwo-parameter fit of Eq. [9] to the numerical simulationdata (all other parameters fixed) in the absence of flow (v �0). Then Eq. [9] was fitted to the experimental calibrationdata S(R1) with free parameters A (scale factor), B (back-ground: noise), and flip angle �. All other parameters werefixed (including the slice thickness L). The flip angle wasfitted again to take into account experimental imperfec-tions. If the velocity waveform is measured, the inflow-corrected calibration curves can be easily calculated fromthe closed-form solution of the analytical model.

The inflow-corrected calibration procedure was vali-dated on a flow phantom. The flow phantom consisted ofa tube circuit through which tap water was pumped froma reservoir by a cardiovascular pump (Travenol Laborato-ries Inc., Morton Grove, IL). The pump was capable ofgenerating an oscillating flow in the circuit. The reservoirwas filled with water of different known concentrations ofGd-DOTA (0, 1, and 2 mM). For each experiment, wemeasured the velocity waveform using a retrospectivephase contrast sequence. The concentration was then es-timated on the basis of the inflow-corrected calibrationcurve and compared to the known reference value.

Hepatic Perfusion Measurements

Hepatic perfusion measurements without and with inflowcorrection were performed in nine patients (four malesand five females, 42 14 years old). This subgroup ofpatients had participated in a larger clinical study (46patients) comparing the hepatic flow parameters measuredwith MRI and Doppler sonography in cirrhosis and portalhypertension. The results of that study are published else-where (3). The present study was approved by the ethicscommittee of our institution, and the patients gave writteninformed consent to participate in the study. A low dose ofGd-DOTA (0.05 mmol/kg) was injected at the beginning ofthe MR acquisition. The pulse sequence was the (satu-rated) TFE sequence described above, which consisted of120 phases. Some of the relevant parameters were: slicethickness L � 6 mm, flip angle � � 15°, single shot, TE �1.3 ms , TR � 5.4 ms, TFE factor (i.e., number of RFexcitations in one shot) � 88 (four dummies), yielding ashot duration of 516 ms (saturation prepulse included).

An axial slice was taken that included the liver, abdom-inal aorta, and portal vein. We performed time-resolvedflow measurements in slices perpendicular to the aortaand portal vein using standard phase-contrast gradient-echo sequences. The slice angulations were taken intoaccount to determine the (projected) velocity waveformconform to the orientation of the slice used for perfusionanalysis. The mean signal intensity was measured in anROI selected in the liver, aorta, and portal vein. After we

converted the data (using inflow-corrected calibrationcurves) to concentration-time curves, we employed a dual-input compartmental model to analyze the results (18):

dCL

dt� kLCL�t� � kACA�t � �A� � kPCP�t � �P�, [10]

where CL, CA and CP represent the concentrations in theliver, aorta, and portal vein. The inflow rate constants arekA, kP, and kL is the outflow rate constant of the liver.Transit times for the aorta and portal vein are denoted by�A, �P. With the use of the measured concentration-timecurves CL(t), CA(t) and CP(t) the parameters kL, kA, kP

and �A, �P , were fitted from a discrete version of Eq. [10]:

1T

CL�t � T� � �kL �1T�CL�t� � kACA�t � �A�

� kPCP�t � �P� � e�t�, [11]

where T represents the sampling time (time between twoimages in the dynamic series), and t now becomes a dis-crete time. The model in Eq. [11] is called an equationerror model (also known as an autoregressive model withexogeneous variable (ARX)) because the white-noise terme(t) enters as a direct term in the difference equation (19).

RESULTS AND DISCUSSION

Calibration Without Inflow Effects

The (C, R1)-data obtained from the tubes phantom aredisplayed in Fig. 1. A linear regression yielded a relaxationrate R10 � (0.665 0.050)1/s or relaxation time T10 �(1.50 0.11)s for saline and relaxivity r1 � (4.171 0.018)1/(s.mM) for Gd-DOTA in saline.

The calibration curves S(R1) for the perfusion TFE se-quence are shown in Fig. 2 for three different flip angles(all other parameters fixed). These curves were obtainedfrom the tubes phantom using the quadrature body coil astransmitter/receiver (as in the in vivo studies). The signalintensities S are scaled by the receiver gain and expressedin arbitrary units (a.u.). It can be seen that for small relax-ation rates (as expected in vivo), a flip angle of 15° pro-

FIG. 1. Relaxation rate R1 vs. Gd-DOTA concentration C data ob-tained from the tubes phantom.

712 Peeters et al.

vides the highest signal (see range 0 � R1 � 10.1/s in Fig.2). Therefore, this value was used for the hepatic perfusionmeasurements. It should be noted that the S(R1) curve for� � 15° is more susceptible to saturation problems at highrelaxation rates. The plateau should be avoided by the useof a low injection dose of contrast agent. The fact that thecalibration curve is nonlinear does not really pose a prob-lem, because it is strictly monotonic. However, if noise isaccounted for in the analysis, nonlinear noise propagationshould be taken into account.

Calculation of Inflow Effects

Numerical Simulations

Simulations were performed for stationary spins andsteady and unsteady flow. An example of the resultinginflow effects in one dynamic is displayed in Fig. 3. Figure3a shows the unsteady (abdominal aorta) flow waveformused in the example (period: RR � 925 ms). Triggeringwith a peripheral pulse unit and a trigger delay of 300 mswere assumed. The evolution of the signal intensity withphase-encoding step (or echo number) is displayed in Fig.3b (84 values). Three curves are shown: one for stationaryspins, one for a steady flow of v � 9 cm/s (representingflow in the portal vein), and one for the pulsatile waveformshown in Fig. 3a (note that this covers the time interval of300–816 ms in Fig. 3a). Fourier transformation of thecurves yields the PSFs (magnitude vs. pixel number)shown in Fig. 3c. Because the tails of PSFs do not giverelevant information, only the central part is shown. Thearea under the PSF represents the FRE (relative to station-ary spins). The obtained FREs were 1 for stationary spins,1.33 for the steady flow, and 1.31 for the unsteady flow.These values can also be obtained from the signal intensi-ties for the central echoes in Fig. 3b.

Note that the FREs for steady and unsteady flow are verysimilar in this case. This agreement is rather accidentaland depends on waveform characteristics. In general, it isimpossible to approximate the FRE for unsteady flow interms of steady flow (e.g., mean velocity). Note that the

waveforms in our patients displayed a strong variability:aortic waveforms with and without retrograde flow, andportal vein waveforms with strong pulsatility were ob-served.

FIG. 3. a: Waveform of the abdominal aorta. b: Simulated evolution ofthe echo signal with phase-encoding step for stationary spins, portalvein (v � 9 cm/s), and abdominal aorta. c: The central part of thecorresponding PSFs. The FREs are 1, 1.33, and 1.31, respectively.

FIG. 2. Signal S vs. relaxation rate R1 data for the perfusion TFEsequence for three different flip angles: FL � 15°, 45° and 90°.

Inflow Correction of Perfusion Measurements 713

Inflow effects influence the calibration curve S(R1), asshown in Fig. 4 for the three cases considered above. It canbe seen that the FRE depends on the relaxation rate R1.Furthermore, inflow leads to an onset of the plateau (sat-uration) at smaller relaxation rates. To avoid saturationdue to inflow, one should choose a good (low) injectiondose. The use of larger flip angles leads to less saturationeffects in the absence of flow. However, it also leads tostronger inflow effects and thus more saturation due toinflow. As a result, the use of larger flip angles does notsolve the saturation issue.

Adjusting the trigger delay so that the acquisition isperformed during diastole can minimize inflow effects.Unfortunately, this is not always possible, depending onthe acquisition time and the heart rate (RR-interval). Nev-ertheless, even in this case, inflow effects are still present.

Analytical Model

The evolution of the signal with the echo number, calcu-lated with the analytical model, is shown in Fig. 5. Thesecurves should be compared with the curves displayed inFig. 3b. It can be seen that the curves are very similar: theirshapes are identical, and only the quantitative values aresomewhat different. This could be expected because thenumerical simulations take into account the slice profiles(flip angle profiles), whereas the analytical model assumesan ideal rectangular slice profile (and, moreover, it is acompartmental model). As a result, the assumed flip angle(� � 15°) and slice thickness (L � 6 mm) have a differentmeaning in both approaches. However, both models can bematched together by the use of an “effective” flip angle andan “effective” slice thickness.

Calibration With Inflow Effects

The result of matching the analytical model to the simu-lation is shown in Fig. 6. It can be seen that a very goodagreement is obtained. The least-squares algorithm yieldedLeff � 1.66L for the effective slice thickness, and �eff

(1) �

10.7� for the effective flip angle. The result of the matchingof the model to the phantom measurements is displayed inFig. 7. Here an effective flip angle �eff

(2) � 19.4� was ob-tained. The effective values Leff, �eff

(2) and scale factors Aand B were used to determine the calibration curve withinflow effects on the basis of the analytical model. Thefractions f(n) were determined from the measured wave-forms.

Figure 8 shows the oscillating velocity waveform mea-sured during the validation experiment. To mimic thesituation in vivo during the perfusion measurement, atrigger delay of 178 ms was used in the perfusion sequence(to obtain forward flow first and reverse flow afterwards).The estimated Gd-DOTA concentrations (with and with-out inflow correction) are compared with the referencevalues in Table 1. It can be seen that the estimated valuesagree very well (within the uncertainty) with the referencevalues.

FIG. 4. Calibration curves with inflow effects. The three curvesrepresent the calibration curves for the three cases considered inFig. 3. FIG. 5. Evolution of the echo signal with phase-encoding step for

stationary spins, portal vein (v � 9 cm/s), and abdominal aortaaccording to the analytical model.

FIG. 6. Model matched to simulation: shown are the simulated andfitted analytical calibration curves (for details see text).

714 Peeters et al.

Hepatic Perfusion Measurements

Figure 9 shows one image from a perfusion series (axialslice through the liver, abdominal aorta, and portal vein)for a patient. The measured velocity waveforms in theabdominal aorta and portal vein are shown in Fig. 10a.Note that the flow in the portal vein is not steady for thispatient (although respiration effects were minimized bythe use of a navigator, they were not completely compen-sated for because a navigator only detects motion along itsdirection). As mentioned above, these waveforms wereobtained by the use of standard phase contrast sequencessynchronized to the cardiac cycle. The measured (mean)pulsation period was RRa � 882 ms during the arterialflow measurement and RRv � 857 ms during the venousflow measurement. In each case, the imaging slice waspositioned perpendicular to the vessel of interest. Becausethe imaging slice was not perfectly perpendicular to thevessels during the perfusion measurement, projected ve-locity waveforms compatible with the perfusion measure-ment were calculated on the basis of the slice angulations.For this patient, the projection factors were 1 (aorta) and0.883 (portal vein).

The calibration curves (signal intensity vs. relaxationrate) obtained from these waveforms are shown in Fig. 10b.Shown is a calibration curve without inflow correction (as

needed for the liver) and two inflow-corrected curves.Both curves were calculated with Eqs. [8] and [9] becauseof the unsteadiness of the flow. The raw perfusion curves(i.e., signal intensity vs. time for the three ROIs) are dis-played in Fig. 10c. A comparison with Fig. 10b reveals thatsaturation is not a problem in our measurements (note thesignal intensity at the peak of the aortic perfusion curve).The temporal resolution of the curves is T � 0.82 s.Figure 11 shows a comparison of inflow-corrected and-noncorrected perfusion, but in this case as concentrationvs. time curves. It can clearly be seen that without correc-tion, the arterial and venous input functions are overesti-mated.

We estimated the perfusion parameters in Eqs. [10] and[11] both with and without inflow correction, using a linearleast-squares regression for different delays. The retaineddelays were those leading to a minimal cost function. Theresults for the patient discussed above are shown in Table 2.The perfusion values are in accordance with those reportedin previous human studies performed with dye clearance(20), single photon emission computed tomography (21),and CT (2). The total hepatic perfusion values (arterial plusportal) were in same range (roughly 100–200 ml/min.ml).It can be seen that inflow correction significantly changesthe estimated perfusion parameters. In this case, it leads toa relative increase of 24% for kA, 31% for kp, and 2% for kL.The estimated delays and mean squared fit (MSF), MSF� ¥i � 1

N (CLi(measured) � CLi(estimated))2/N), didnot change. When all nine patients were considered, wefound the following relative increases in the perfusionparameters due to inflow: m(�kA/kA) � 33%, �(�kA/kA)� 14%, min(�kA/kA) � 10%, max(�kA/kA) � 54% for the

FIG. 9. Axial slice through the liver, aorta, and portal vein.

Table 1Validation Measurements

Cref (mM) Not corrected Inflow corrected

0 0.00874 0.002990.998 0.083 0.985 0.9191.99 0.17 2.55 2.26

FIG. 7. Model matched to calibration measurements: shown are thecalibration data and fitted analytical calibration curve (for details seetext).

FIG. 8. Velocity waveform during the validation experiment.

Inflow Correction of Perfusion Measurements 715

abdominal aorta, m(�kP/kP) � 50%, �(�kP/kP) � 10%,min(�kP/kP) � 33%, max(�kP/kP) � 67% for the portalvein and m(�kL/kL) � 1.3%, �(�kL/kL) � 0.8%, min(�kL/kL) � �0.2%, max(�kL/kL) � 2.6% for the liver. Herem(�k/k) represents the mean value, �(�k/k) the standarddeviation (SD), and min/max the minimum/maximumvalues.

It can be seen that an increase in the perfusion parame-ters kA, kP is always observed. Because the inflow correc-tion leads to lower concentrations for the input functions,higher rate constants are found. On the other hand, theoutput function is not corrected; therefore, kL does notchange significantly. The fact that �kP/kP � �kA/kA canbe explained on the basis of the inflow effect of the cali-bration curves. Although for the calibration curves S(R1)(inflow-corrected or not) the signal S increases with R1, therelative inflow correction (Sflow � S)/S (where Sflow is thesignal with inflow correction, and S is the signal withoutinflow correction at a certain R1) decreases with R1. As aresult, the inflow correction has more effect at small con-centrations (R1). Because the venous input function haslower concentrations than the arterial input function, thisleads to �kP/kP � �kA/kA.

It was found for all of the patients that the quality of thefit did not change due to inflow correction (see MSF inTable 2, and Fig. 12). In addition, the relative uncertainties

FIG. 10. a: Velocity waveforms for the abdominal aorta and portalvein. b: Calibration curves: inflow-corrected on the basis of themeasured waveforms in a, and not corrected (as needed for theliver). c: Raw perfusion curves for the three ROIs.

FIG. 11. Comparison of the perfusion curves when corrected andnot corrected for inflow.

Table 2Perfusion Parameters

Quantity Inflow corrected Not corrected

kA (ml/100 ml.min) 38.2 5.8 30.9 5.8kP (ml/100 ml.min) 138 21 105 16kL (ml/100 ml.min) 433 18 426 19�A (s) 4.92 4.92�P (s) 4.92 4.92MSF (mM) 0.013 0.013

716 Peeters et al.

of the estimates did not change significantly. This is be-cause our inflow correction does not change the noiseproperties (we did not measure the image noise). If thenonlinear noise propagation due to the nonlinear calibra-tion curve were taken into account, the inflow correctionwould have an effect.

It should be noted that the first-order model we used toanalyze the data is very simple. A more complicatedmodel could be expected to describe the data more accu-rately. Nevertheless, inflow correction will always have asignificant impact on the estimated parameters, indepen-dently of the model used.

Measuring the hepatic perfusion parameters with MRImay have an important clinical impact, as alluded to in theIntroduction. Perfusion is not only altered in liver isch-emia (which can occur, for example, after transplantation),but also in cirrhosis and hepatic metastases. We havepreviously shown that portal and total hepatic perfusionincreases in cirrhosis, whereas arterial perfusion de-creases. These perfusion changes correlate with the sever-ity of cirrhosis and portal hypertension (3). Therefore,perfusion MRI has a potential role in assessing the prog-nosis of liver cirrhosis and the response to medical treat-ments that modify the hepatic microcirculation (22).

CONCLUSIONS

Inflow effects lead to incorrect perfusion curves and esti-mated parameters that are obtained on the basis of T1-weighted TFE sequences. Fortunately, this can be cor-rected if extra flow measurements are performed duringthe examination in order to correct the calibration curveson the basis of an analytical model. This model shouldtake the unsteadiness of the flow into account.

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FIG. 12. Comparison of the measured concentration in the liver(output) with that predicted by the model when using inflow-cor-rected and noncorrected inputs (concentrations in the aorta andportal vein).

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