Functional MRI using intravascular contrast agents: detrending of the relative cerebrovascular (rCBV) time course

Functional MRI using intravascular contrast agents: detrending of therelative cerebrovascular (rCBV) time course

Adam J. Schwarz*, Torsten Reese, Alessandro Gozzi, Angelo BifoneDepartment of Neuroimaging, Centre of Excellence for Drug Discovery (Psychiatry), GlaxoSmithKline Medicines Research Centre, Verona, Italy

Received 15 August 2003; received in revised form 22 August 2003; accepted 23 August 2003

Abstract

In pharmacological fMRI experiments in animal models, blood pool contrast agents may be used to map cerebral blood volume changeas a surrogate for neural activation. When the background signal drift due to contrast agent washout is non-negligible over the duration ofthe signal changes of interest, time-course detrending is essential for accurate interpretation of the experiment. Detrending approaches basedon estimation of the background signal from a baseline period of the time course prior to pharmacological (or functional) challenge wereevaluated with the aim of identifying a robust method of estimating the contrast agent washout contribution to the background signal drift.For fMRI studies in the rat, it was found that a constrained fit of a mono-exponential washout model was more accurate than a constantbackground approximation and unconstrained fits for experiments investigating the functional response to rapid pharmacological challengessuch as cocaine and amphetamine. Moreover, the constrained fitting approach allows shorter baseline periods than unconstrainedextrapolation, reducing the required duration of the experiment. © 2003 Elsevier Inc. All rights reserved.

Keywords: Functional MRI (fMRI); Pharmacological MRI; Cerebral blood volume (CBV); Pharmacology; Time series; Detrending

1. Introduction

Functional MRI (fMRI) methods detect the hemody-namic response to changes in the metabolic activity ofneural tissue. These methods may be tailored to be sensitiveto changes in cerebral blood flow (CBF) [1,2], cerebralblood volume (CBV) [3,4], or the oxygenation state ofhemoglobin (BOLD) [5–7]. Changes in CBV may be mea-sured by administration of a superparamagnetic iron oxide(SPIO) contrast agent, which remains in the blood pool witha half-life of several hours in a quasi-steady-state [8,9].Transient changes in vascular volume then cause localchanges in the amount of contrast agent in the image voxels,differentially affecting the relaxivity of local spins andhence the signal in appropriately weighted MR sequences.

Spatial and temporal coupling between BOLD signalsand CBV changes in the rat brain has been demonstrated forsomatosensory and pharmacological stimuli [10], and forCO2 challenge [11]. At field strengths of 4.7T and below,the contrast-to-noise available using contrast agents typi-

cally exceeds that of BOLD [10], and the CBV approach hasbeen applied in preclinical experiments to acute pharmaco-logical stimuli including cocaine [12], amphetamine[13,14], and bicuculline [15], as well as forepaw stimulation[16].

A typical CBV experiment comprises a T2*- or T2-weighted image time series, near the beginning of which thecontrast agent is injected, upon which the signal dropssharply due to the contrast agent-enhanced relaxivity, andreflects the local resting state blood volume [10]. Subse-quently, the functional or pharmacological challenge(s) areapplied. Transient increases (decreases) in blood volume aspart of the hemodynamic response give rise to a furthersignal decreases (increases) which are, in general, thechanges of interest. However, these changes are superim-posed upon background signal changes that include a driftof the signal intensity back to its pre-contrast value, as thecontrast agent is gradually eliminated from the vascularsystem, as well as components due to changes in the ani-mal’s physiological condition and residual high-frequencynoise. The contrast agent washout component, intrinsic tothe CBV method, is a monotonic change amenable to de-trending. The extent to which detrending of the time coursesis needed depends upon the rate of washout relative to the

* Corresponding author. Tel.: �39-045-921-9067; fax: �39-045-921-8047.

E-mail address: [email protected] (A. Schwarz).

Magnetic Resonance Imaging 21 (2003) 1191–1200

0730-725X/03/$ – see front matter © 2003 Elsevier Inc. All rights reserved.doi:10.1016/j.mri.2003.08.020

duration and rate-of-change of the signals of interest; aconstant background signal may be assumed only if the driftis sufficiently slow.

The half-life of the widely used superparamegnetic ironoxide contrast agent Endorem (Guerbet, France) in the rathas been measured as 252 min (95% confidence range,193-364 min) [9]. For a contrast agent following an expo-nential elimination curve with half-life 252 min, and assum-ing a 50% signal drop following contrast agent injection, thebackground signal value increases by �11% between 0 and30 min, and by �7% from 60 to 90 min. With half-lives atthe lower and upper values of the range reported above,these changes are �14% and �8% (193 min half-life) and�8% and �6% (364 min half-life). By way of illustration,in acute cocaine challenge experiments such as that illus-trated in Fig. 1, this results in a tangible gradual increase inthe background signal over the duration of the response tothe challenge.

In some of the initial pharmacological fMRI studies, aconstant background signal approximation was used[10,12]. This approach may be reasonable for transientsignals immediately following an acute challenge. How-ever, to better characterize changes over longer time scales,detrending may be essential. In the example of a fast-actingpharmacological study, an estimate of the pharmacokinetictime constants could be adversely affected by signal drift.Moreover, the inter-subject variability of the washout rateprecludes the prescription of a generic value for a givencombination of species and contrast agent. Here, we eval-uate several approaches to estimate the background signalfrom measured values in a pre-challenge baseline period(including the constant baseline approximation) for the caseof Endorem in the rat. Consideration of the effect of param-eters such as signal-to-noise ratio (SNR) and washout rateenables the results to be more generally applicable. The aimis the identification of a robust detrending method for CBVexperiments covering the functional response to fast-actingpharmacological stimuli such as amphetamine and cocaine.

2. Methods

We investigated methods for extrapolating the back-ground signal drift from a baseline period prior to a putativefunctional or pharmacological challenge in each timecourse. This was performed for simulated and in vivo datain which no challenge was actually applied. Thus, the ac-curacy of the background signal estimation could be quan-tified by comparison with the known signal values later inthe time course. Whereas the simulated signals permit eval-uation in the case of ideal signals, the in vivo data includethe effects of physiological noise and differential washoutrates. A number of in vivo cocaine challenge experimentshave also been performed and illustrate some of the detrend-ing issues.

2.1. Simulated data

Each set of phantom data comprised 64 simulated timecourses obeying an exponential contrast agent washout (sig-nal increase) with a known decay time constant Tw of theform

B�t� � SPRE � �SPRE � SPOST�e�t/Tw � ��t�, (1)

where �(t) represents independent identically distributedgaussian noise, SPRE is the signal intensity prior to contrastagent injection (and hence at time infinity when the contrastagent has been completely eliminated), SPOST is the signalintensity immediately following contrast agent injection andequilibration, and Tw is the washout time constant. For thisstudy, Tw was set to 4 h (240 min) for all time courses,SPOST was equal to SPRE/2, and the signal time resolutionwas 10 s (6 frames/min). This approximates our present invivo acquisition protocol. The time courses were generatedwith 512 time points, to enable the evaluation of detrendingefficacy with different baseline period sizes.

Sets of data were generated for different SNR values,namely 20, 60, and 150. SNR � 20 approximates the SNRin a single voxel time course observed in vivo (see Section2.2.). SNR � 60 approximates the situation of improvedSNR in a single voxel after spatial smoothing, or perhaps asmall ROI on the order of 3 � 3 voxels. The SNR � 150case is relevant to larger ROIs or larger anatomic regions onthe order of 60 voxels.

2.2. In vivo data

2.2.1. Baseline estimation experimentsIn vivo data sets were acquired from six male Sprague-

Dawley rats (ca. 250–350 g) (Charles River, Como, Italy).The animals were housed in a temperature- and humidity-controlled environment and had free access to standard ratchow and tap water. All experiments were carried out inaccordance with Italian regulations governing animal wel-fare and protection.

The animals were anesthetized with 3% Halothane in a30:70% O2:N2 gas mixture, tracheotomized, and artificiallyventilated with a mechanical respirator. Upon tracheotomyand throughout surgery, the anesthetic level was maintainedat 2%. Left femoral artery and vein were cannulated, and theanimal was then moved into a customised stereotacticholder. Animal paralysis was achieved by continual infu-sion of D-Tubocurarine (0.25 mg/kg/h) through the artery.Ventilation parameters were adjusted in order to keep thearterial blood gases values within physiological range (32 �PCO2 � 43; PO2 80). During the image acquisition, theanesthetic level was set to 0.8%.

Images were acquired using a Bruker Biospec 4.7T sys-tem, a 72-mm birdcage resonator for RF transmit, and a20-mm diameter single-loop receive coil taped to the ani-mal’s head. Both coils are standard components provided by

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the manufacturer. The CBV experiment comprised sequen-tial T2-weighted RARE time series, with matrix 128 � 128,FOV 40 mm, slice thickness 2 mm, 8 contiguous slices,

TEeff � 110 ms, TR � 2700 ms, Tframe � 10s. A first timeseries of 32 time points was acquired, during which a doseof 800 �l of Endorem contrast agent was administered iv.

Fig. 1. Single pixel time course (following in-plane gaussian smoothing, FWHM � 2 pixels) from a rCBV pharmacological fMRI experiment using Endoremin the rat. (A) T2-weighted signal changes due to contrast agent administration and washout, and CBV changes following an acute iv cocaine challenge. (B)Detail of panel A.

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Following a few minutes equilibration, a second time seriesof 256 time points was acquired.

For each animal, pixel time courses from each pixel intwo 8 � 8 regions of interest (ROIs) from the slice atapproximately zbregma were extracted; one in the cortex, theother in the contralateral Caudate Putamen (CPu). This wasperformed both before and after applying in-plane smooth-ing by convolution with a gaussian kernel of FWHM � 2pixels. The unsmoothed pixel SNR (pre-contrast) was typ-ically 30-34 in the cortex and 16-22 in the CPu.

2.2.2. Cocaine challenge experimentsAnimal preparation and MRI acquisition were identical

to those described above, except that a single time series of384 time points (64 min) was acquired. This encompassedcontrast agent administration and initial equilibration, abaseline period, and the response to acute cocaine challengeof 0.5 mg/kg cocaine dissolved in 1 ml of saline injected ivinto the femoral vein over a period of one minute, afterapproximately 30 min of the acquisition.

2.3. The rCBV transform

Given knowledge of the signal intensity S(t) prior to CAadministration (SPRE), and assuming a mono-exponentialsignal decrease with local changes in blood volume [16], thefunctional or pharmacological signal changes of interest canbe converted into fractional changes in CBV (relative CBV,or rCBV) by the transform

rCBV�t� �ln �S�t�/B�t��

ln �B�t�/SPRE�, (2)

where B(t) is the background signal in the absence of tran-sient functional stimuli. Since this background is disruptedby the transient changes of interest, its value must be esti-mated in the application of the rCBV transform.

2.4. Background estimation approaches and parametersstudied

Several approaches to estimating the washout componentto the background signal B(t) from a baseline period wereevaluated: 1) a constant background approximation, with

B(t) set to the mean value of last 15 points (21⁄2 min) of thebaseline period; 2) linear detrending, with B(t) extrapolatedfrom a linear fit to the baseline points; 3) exponential wash-out detrending, with B(t) extrapolated from a fit of Eq. (1) tothe baseline points; and 4) constrained exponential washoutdetrending as per (c) but with SPRE and SPOST set to valuesobtained from the same time course. SPRE was determinedas the mean signal value in four time points prior to contrastagent administration, and SPOST as the mean signal value offour time points following contrast agent administration andequilibration.

Each of these was performed for baseline periods of 15,

30, 45, 60, 90, 120, and 180 data points, corresponding to2.5-30 min with a time resolution of 10 s.

In all cases, the baseline period was considered to im-mediately precede the time point of the putative functionalchallenge. However, the absolute timing of the latter was setin two ways: 1) with the start of the baseline period fixed(e.g., immediately following contrast agent administrationand equilibration) and the challenge time point moving laterwith increasing length of the baseline period; and 2) withthe challenge time point fixed, and the beginning of thebaseline period moving earlier toward the beginning of thescan with increasing baseline length.

The former provides a minimum experimental durationfor a given baseline length, whereas the latter reflects thepossibility of including a delay before the baseline period toavoid the steepest portion of the washout.

Overall, the effects of the following parameters wereevaluated: SNR, background signal estimation approach,number of baseline points, and the relative position of thechallenge time point.

2.5. Performance metrics

The background estimation performance was measuredby quantifying the deviation of the extrapolated backgroundfrom the known signal. This was performed for two evalu-ation periods of the time course, 6–35 points, and 120–155points following the end of the baseline. With a temporalresolution of 10 s, this corresponds to intervals covering 1-6min and 20–26 min following acute challenge or the begin-ning of a functional paradigm. (For the in vivo data, com-prising only 256 time points, the later evaluation period wasexamined only for baseline period lengths 15, 30, 45, 60,and 90 points, i.e., 2.5–15 min)

The accuracy of the background signal estimation wasquantified using the mean-squared error (mse) between theknown and predicted signals. For the ith time course,

�i �1

N�t�t1

t2

�bi�t� � Si�t��2, (3)

where t1 and t2 delimit the evalution period, bi(t) denotes theextrapolated baseline, and Si(t) the actual signal. For eachtime course, evaluation period, and combination of the ex-perimental parameters defined in Section 2.4., the medianand upper and lower quartiles of �i were calculated.

3. Results

Figs. 2-4 illustrate the mean-squared error in baselineestimation for the simulated data as a function of SNR,background signal estimation approach, number of baselinepoints, and the relative position of the challenge time point.The constrained exponential detrending gave the best over-all performance, and was robust for the shorter baselinelengths; the estimation error was almost independent of

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baseline size, although results for the late evaluation periodindicate that its performance was slightly worse for the

shortest baseline (15 pts) directly following contrast admin-istration. This suggests a longer delay following contrast

Fig. 2. Baseline estimation accuracy, simulated data, SNR � 20. (A) Early evaluation period (1-6 mins), putative challenge point moving with increasingbaseline length. (B) Early evaluation period, putative challenge point fixed at time point 180. (C-D) As in panels A and B, but for the late evaluation period(20-26 mins).

Fig. 3. Baseline estimation accuracy, simulated data, SNR � 60. (A-D) As in Fig. 2.

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injection and the initial equilibration might be beneficial.The two unconstrained fitting methods (Fig. 2B and C)became comparably accurate only for long baselines ap-proaching 120-180 points (Fig. 2C and D) and tend to “blowup” for short baseline periods.

For SNR � 20 (�single pixel) the constant approxima-tion fared no worse than the other methods for the earlyevaluation period. In fact, for the shorter baselines, it wasconsiderably more robust than the unconstrained fitting ap-proaches. However, at the later evaluation period, and withincreasing SNR, its performance becomes systematicallyworse.

Results with the in vivo data obey the same trends assimulated data (Figs. 5 and 6). There was more interanimalvariation, and the trends were sometimes less monotonicwith baseline length than in the simulated data due tophysiological wobbles in time courses. The signal increaseover the washout time courses (43 min) showed substantialintersubject variability, varying from �12% to �32%.Overall, the constrained exponential again gave a robustdetrending performance over a range of baseline lengths andSNR. With the unsmoothed data, it was as robust as theconstant approximation for the early evaluation period, andprovided a significantly better baseline estimation in thelater period. These trends were consistent in both cortex andCPu ROIs.

4. Discussion

These results suggest that estimation of the washoutcomponent of the background signal B(t) in the rCBV trans-

form (Eq. (2)) by a constrained exponential fit to a baselineperiod is a robust detrending method for time scales typicalof the primary functional response to fast-acting pharmaco-logical stimuli. The use of prior knowledge in the form ofmeasured values of SPRE and SPOST from each time courseappears particularly useful in enabling accurate estimationwith short baseline periods, thus maintaining a short exper-iment time. (Minimizing experimental duration is importantin terms of maximizing throughput, but also in maintainingthe physiological condition in pre-clinical experimentswhere changes could produce confounding effects.) How-ever, if only the first �10 min post-challenge are of interest,a constant background approximation remains a reasonableoption for pixel-wise processing, with the SNR and contrastagent elimination characteristics considered here, particu-larly after a delay following contrast administration to avoidthe steepest part of the washout.

In this study, for the constrained exponential detrending,SPOST was estimated as the average of four time pointsfollowing contrast agent administration and equilibration,thus in some instances giving a delay before the formalbaseline period used for the curve fit. Due to the self-similarity of the exponential function, SPOST could alterna-tively be determined from the beginning of the time periodused for the background signal estimation, which wouldexclude influence from baseline signal changes of physio-logical origin unrelated to the washout or functional exper-iment. In either case, it is important to wait for the initialcontrast agent equilibration before applying the detrendingmethod presented here; we have found that a delay ofapproximately 5 min is sufficient to ensure that subsequent

Fig. 4. Baseline estimation accuracy, simulated data, SNR � 150. As in Fig. 2.

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background signal changes are well modeled by the expo-nential washout described in Eq. (1). Similarly, the value of

SPRE could also be determined from data points in the tail ofthe acquired time course, more tightly constraining the

Fig. 5. Baseline estimation accuracy, in vivo data from an ROI in the cortex in one animal (unsmoothed). (A) Early evaluation period (1-6 min), putativechallenge point moving with increasing baseline length. (B) Early evaluation period, putative challenge point fixed at time point 90. (C-D) As in panels Aand B, but for the late evaluation period (20-26 mins).

Fig. 6. Baseline estimation accuracy, in vivo data from an ROI in the cortex in one animal (following gaussian in-plane smoothing, FWHM � 2 pixels). (A-D)As in Fig. 5.

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predicted background signal, provided that foreground sig-nal activity can be assumed to have ceased. Moreover, in thecase of experiments that can be performed with a periodicstimulus (e.g., forepaw stimulation) with intervals in whichthe signal can be considered to return to the backgroundvalue, further intermediate data points may be used, provid-ing additional interpolation points.

The fitting-based approaches require a (non-)linear re-gression to be performed on each time course, which can becomputationally demanding if applied on a pixel-wise basisfor image-based analyses. The computation time can bereduced by the use of shorter baselines permitted by theconstrained exponential approach, and/or the baseline datacan be rebinned into a smaller number of points. The base-line extrapolation method investigated here is local to eachtime course, and thus applicable to signals from eitherindividual pixels or ROIs, without requiring assumptionsabout the relationship between the signal behavior in dif-ferent brain regions or different tissues.

The success of the constrained exponential approach wasdue primarily to the prior knowledge utilized rather than thefunctional form per se; the unconstrained exponential didnot perform nearly as well. One might consider imposingsimilar constraints to a linear baseline regression. This isalso likely to be more stable with short baselines than itsunconstrained version, and with washout rates similar toEndorem or longer, the non-linear portion of the signalchange over periods up to �30 min, as targeted in thisstudy, will typically be small. An approach such as this mayprovide a decreased computation time, but its validity mustbe considered in the case of longer experiments, or contrast

agents or species with faster washout rates, where the use ofa more realistic model of the washout drift becomes moreimportant. Application of this method to substantiallylonger experiments remains to be validated.

In pharmacological fMRI studies, neglect of backgroundsignal changes can lead to misinterpretation of the pharma-cological action. For example, acute cocaine challenge (Fig.1) produces a time course that closely follows a first-orderpharmacokinetic profile, but the quantification of the timeconstants of the activation is affected by the baseline esti-mate. Fig. 7 shows the rCBV time courses from a 5 � 5pixel ROI in the cortex from this experiment for each of thedifferent baseline estimation approaches considered above.The constant approximation results in the rCBV time coursereturning to the baseline value after �20 min and thencontinuing to drift below. Both linear and unconstrainedexponential detrending result in an apparent sustained CBVchange following the peak response in the first �15 min.The time constants Tin and Tout governing such responsesmay be estimated via a non-linear regression with the dif-ference-of-exponentials first-order pharmacokinetic equa-tion rCBV (t) � C1 � C2t �C3 (e(t � t0)/Tout � e (t�t0)/Tin) wheret0 is the onset time and Ci (i � 1,2,3) constants. Fits to eachcurve under the assumption of constant baseline (C2 � 0)and allowing a linear residual baseline are also shown inFig. 7, and the resulting time constants summarized in Table1. Under the assumption that the rCBV undershoot andplateau in Fig. 7, A–C are artifacts of inaccurate detrending,the incorporation of a linear term in the fit helps to recovera more accurate description of the response. In some cases,this could be considered an alternative means of dealing

Fig. 7. rCBV time courses from a 5 � 5 pixel ROI in the rat cortex from the acute iv cocaine challenge experiment, following baseline estimation using eachof the four methods examined in this study. Functional fits using a first-order pharmacokinetic equation with (light curve) and without (heavy curve) anadditional linear term (see text) are also shown.

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with the background signal drift; however, it requires a fit tothe signal, which may not be the desired means of quanti-fying the response. Moreover, in the case of pixel-wiseprocessing, inaccurate or failed fits are more likely due tothe lower SNR.

The present study focused on the case of CBV studies inthe rat using the contrast agents with elimination half-livesof around 4 h, but with considerable intersubject variability(e.g., Endorem). This has been a widely used CBV set-up inrecent years, and one in which the signal drift may be anappreciable confound in certain experiments. The same con-trast agents may however have different elimination char-acteristics in other species [17]. Moreover, contrast agentswith longer blood pool lifetimes, or designed for concurrentuse with compounds that extend the lifetime, are currentlyunder development. As these become available, the need fordetrending of the time course data may be less acute. Thebasic underlying consideration remains the rate of back-ground signal change relative to the duration and rate ofchange of the signals of interest.

5. Conclusions

In rCBV experiments in which the background signaldrift is non-negligible over the duration of the signalchanges of interest, time course detrending is essential foraccurate interpretation of the experiment. In the case offMRI studies using Endorem in the rat, it was found that arobust estimation of the background signal used in therCBV transform was obtained by a constrained fit of amono-exponential washout model to a baseline period of thetime course. This enables more accurate rCBV values to beobtained at least for experiments of time scales covering theprimary functional response of rapid pharmacological chal-lenges such as cocaine and amphetamine. Moreover, theconstrained fitting approach allows shorter baseline periodsthan unconstrained extrapolation, thus reducing the requiredduration of the experiment.

Acknowledgments

The authors gratefully acknowledge Simone Bertani andValerio Crestan for animal preparation and experimentalassistance.

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Table 1Time constants determined from fit to rCBV response to acute cocaine challenge

Form of functional fit Fit of difference-of-exponentials Fit of difference-of-exponentials � linear term

Tin (min) Tout (min) Tin (min) Tout (min)

Detrending approach Constant 1.8 4.6 0.5 9.5Linear 0.4 26.8 1.0 8.9Exponential 0.4 25.8 1.0 9.0Constrained exponential 1.3 6.9 0.9 9.4

“Wash-in” and “wash-out” time constants (Tin and Tout, respectively) derived from a functional fit of a first-order pharmacokinetic equation with andwithout the linear term (see text) to the ROI time course illustrated in Fig. 7.

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