Pulsed arterial spin labeling perfusion imaging at 3 T: estimating thenumber of subjects required in common designs of clinical trials
Kevin Murphya, Ashley D. Harrisa, Ana Diukovaa, C. John Evansa, David J. Lythgoeb,Fernando Zelayab, Richard G. Wisea,⁎
aCardiff University Brain Research Imaging Centre (CUBRIC), School of Psychology, Cardiff University, CF10 3AT Cardiff, UKbKing's College London, Institute of Psychiatry, Centre for Neuroimaging Sciences, DeCrespigny Park, Denmark Hill, SE5 8AF London, UK
Received 8 November 2010; revised 1 February 2011; accepted 20 February 2011
The coupling between neural activity, including synapticand metabolic activity, and cerebral perfusion is the basis ofmost applications of noninvasive functional magnetic reso-nance imaging (FMRI). This is most commonly exploited asblood oxygenation level dependent (BOLD) FMRI in whichimage (T2⁎) contrast is generated from increased capillary andvenous blood oxygenation as a result of perfusion increasesoutstripping the local oxygen utilization. However, recentadvances in MRI hardware and software have made itincreasingly viable to noninvasively measure cerebral perfu-sion or cerebral blood flow (CBF), a parameter that can beexpressed in physical units (typically ml/100 g brain tissue/min) and should be dependent on a single physiological
phenomenon. For this reason, the use of arterial spin labeling(ASL) in functional imaging yields potentially less sensitivityto local imaging conditions than BOLD imaging. It has alsobeen demonstrated at 7 T that high-resolution functionalCBF imaging can provide better localization than functionalBOLD data [1].
Cerebral perfusion is responsible for the delivery ofoxygen and nutrients to the brain parenchyma. The flow ofblood into the capillary bed, or the CBF, has been used as amarker of normal or pathological brain function or brainactivity [2]. Such activity could be vascular in origin: thenormal or pathological increase or decrease of CBF resultingfrom a change in vascular properties, such as in stroke. Inmany neurological conditions, it is the potential alteration inneural (neuronal or astrocytic) activity which is of interestand for which CBF is a marker [3,4].
It is possible to noninvasively measure the bulk flow ofblood in specific arteries supplying a capillary bed using
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transcranial Doppler ultrasound or phase-contrast velocity-encoded MRI. However, perfusion imaging techniquesyielding spatially resolved CBF maps generally require atracer whose kinetics, whether they be intravascular or freelydiffusible, are modeled to estimate CBF within each three-dimensional image element or voxel. Techniques of nuclearmedicine such as single photon emission computed tomog-raphy (SPECT) and positron emission tomography (PET)require radioactive tracers, and a limited number of repeatscans can be performed. This limits their usefulness inclinical trials where longitudinal follow-up may be required.
Magnetic resonance imaging based perfusion measure-ments can overcome some of these drawbacks and fall intotwo main categories: dynamic susceptibility contrast MRIand ASL. Dynamic susceptibility contrast MRI employs aninjected intravascular contrast agent whose bolus through thevasculature is tracked dynamically using a rapid imagingapproach [5]. Arterial spin labeling, while being inherently asomewhat lower signal-to-noise technique [6], has theadvantage of being completely noninvasive as it employs amagnetic label of the water in arterial blood [7,8]. Thepractical implementation requires the magnetic label to beapplied distal to the brain region of interest (ROI) followedby a delay period in which the labeled water flows into thecapillary network and exchanges with tissue water. Theimaging readout then follows. A perfusion-weighted imageis obtained from the subtraction of a labeled image (tagimage) from one which has been acquired without labeling(the control image). Repeated acquisition and averaging oftag–control image pairs are normally needed to build upsufficient signal-to-noise in the measurement.
There exist several different methods for ASL perfusionmeasurement including continuous labeling ASL (CASL) [7]pulsed labeling ASL [8,9] (PASL) and pseudo-continuouslabeling ASL [10,11]. The principal difference between pulsedand continuous labeling lies in the near-instantaneousinversion label for the pulsed approach, while the continuousapproach labels blood for the order of seconds as it flowsthrough an inversion plane. While the CASL approach canyield a signal-to-noise advantage, its implementation is lesswidespread than PASL because of RF hardware requirements.
In addition to the investigation of normal and pathologicalbrain function, CBF measurements show great potential as abiomarker within clinical trials of pharmaceutical com-pounds [12]. It is in this area which we focus the presentinvestigation. BOLD-based FMRI has shed a good deal oflight on systems-level brain activity in humans in the last 15years. This has almost exclusively been based on examiningthe brain's response to explicit tasks and more recentlyfluctuations in activity in the resting state [13] in theapproximate frequency range of 0.01–0.25 Hz. Lower-frequency designs are poorly powered with BOLD FMRIbecause of the low-frequency noise present arising fromscanner drift, head motion and physiological artefacts. Thishas generally restricted the use of BOLD FMRI in humanpharmacological studies to examining the modulation of
task-related activity [14–16] rather than drug-inducedchanges in brain activity itself. ASL perfusion-basedmeasurements are insensitive to these low-frequency signaldrifts and so can be usefully employed in experimentaldesigns with ultra-low frequencies, for example, the activeperiod on one day and the inactive period on another day[17,18]. ASL therefore has potential for studying the in-fluence of single drug doses or chronically orally adminis-tered dosing to measure drug effects on cerebral perfusionover multiple sessions.
ASL CBF measures have been applied in preclinicalpharmacological studies [19,20] and have recently beenutilized in human pharmacological investigations such asthose into caffeine [15], sevoflurane [21], indomethacin [22]and remifentanil [23]. For pharmacological ASL to be viableas a tool in basic neuroscience research, clinical research anddrug development, both financially and practically, it needsto be repeatable enough and sensitive enough to detectperfusion changes in small cohorts. Studies have recentlyexamined ASL measurements [6,24], the reproducibility ofwhich seems comparable to those of techniques such as PETand SPECT. Most have examined cortical grey matter (GM)as a whole or lobar ROIs, while, more recently, finer-scaleexaminations have been performed [17,25].
In the present study, employing a commonly imple-mented form of PASL within a single imaging center, weestimate the number of subjects needed to detect regionaldifferences in CBF in three different placebo-controlledclinical trial designs which may commonly be used indrug development:
1. between groups,2. a two-period crossover (i.e., within subjects) and3. a within-session dosing.
Cerebral blood flow measurements are made at rest in twoseparate cohorts and repeated in one cohort to estimatebetween-group, between-session and within-session vari-ance in CBF. The number of tag–control image pairs neededto provide a stable perfusion estimate is examined. Powercalculations to determine the number of subjects required toreliably detect a change in perfusion are performed for ROIs.These regions are chosen as exemplars of cortical andsubcortical regions distributed across the brain and with arange of sizes but also to reflect the authors' interest in painprocessing and pharmacological analgesia [26]. The use ofROIs is a common approach in FMRI and particularlypharmacological FMRI where there is a strong priorhypothesis about the region in which a drug is expected toalter brain activity [27].
2. Methods
2.1. Subjects and data acquisition
Two groups [NA=15, age 28.3±4.8 (mean±S.D.), 7 maleand NB=14, age 25.7±4, all male] underwent ASL imaging at
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3 T (GE HDx scanner). Participants in the first group(group A) attended a single MR session in which CBFmeasures were acquired. Two separate CBF measurementswere acquired in the second group (group B) on separate daysat least 1 week apart. Whole-brain CBF maps were acquiredusing a pulsed ASL PICORE QUIPSSII [28] sequence withGE-EPI readout [repetition time (TR)=2.2 s, echo time=19.8ms, matrix=64×64, field of view/slice=240/7 mm, flip=80°,16 slices, TI1=700 ms, TI2=1400 ms (at the most proximalslice), reps=160 giving 80 tag–control pairs]. A single-shotEPI (M0) scan was acquired (TR=∞) with the sameparameters to measure the equilibrium brain tissue magne-tization for calibration purposes. A T1-weighted whole-brainstructural scan was also acquired (1×1×1-mm voxels) forpurposes of image registration. This study was approved bythe Cardiff University School of Psychology Ethics Com-mittee, and all volunteers gave written informed consent.
2.2. Preprocessing
The ASL time series were motion corrected using rigidbody translation/rotation (6 degrees of freedom) with themidpoint volume as a reference using 3dvolreg from AFNI(http://afni.nimh.nih.gov/afni) [29]. The group B ASL datasets were then registered to each other using a similarprocedure. Quantified CBF maps were generated using in-house software. The tag and control time series wereinterpolated to the TR [18]. A subtraction time series wascalculated and averaged to give a CBFmap. These maps werequantified using the standard single-compartment QUIPSSIICBF model [28,30]. TheM0 of blood was estimated from thewhite matter signal assuming a ratio of the proton density ofblood to that in white matter R=1.06 [28]. Other parametersused in the model were T1 blood=1.7 s [31], T⁎2 blood=0.1 s[32], T⁎2 white-matter=0.047 s [33] and q=1 [28]. White matterM0 was calculated by converting the white matter mask fromthe Harvard–Oxford Cortical Structural Atlas to the individ-ual subject space using FLIRT within the FMRIB SoftwareLibrary (FSL; http://www.fmrib.ox.ac.uk/fsl) [34] and aver-aging over the M0 calibration scan within this mask. The M0
of blood was estimated assuming standard T1 values for whitematter and blood, and quantified CBF maps were calculated.These quantified CBF maps were registered to eachindividual's structural scan using transformations calculatedfrom the original EPI data set and converted to MNI spaceusing FLIRT.
2.3. Regions of interest
To assess CBF differences between conditions andsessions, ROIs were prepared in MNI space. Regions oftenimplicated in pain processing were chosen as examples: theanterior cingulate cortex (ACC), the posterior cingulatecortex (PCC), the precuneus cortex, right/left insula, right/left somatosensory cortex (SI+SII) and right/left thalamus[12,35]. Grey matter and visual cortex masks were alsochosen for comparison. These ROIs were defined from the
Harvard–Oxford Cortical and Subcortical StructuralAtlases and the Juelich Histological Atlas that are packagedwith FSL.
2.4. CBF values
Mean CBF values were calculated on a subject-by-subjectbasis in each ROI for each of the scans. Repeatabilitybetween sessions for group B was computed for each ROIusing an intraclass correlation coefficient (ICC) originallyproposed by Shrout and Fleiss [36]. The equations and use ofthis measure in relation to CBF repeatability have beendescribed by Jahng et al. [37]. For the case of repeatabilitybetween two sessions, the ICC is similar to a standardinterclass (Pearson's) correlation in which the data from bothsessions are pooled to estimate the mean and variance ratherthan treated separately.
2.5. Stability of CBF measures
To determine whether CBF measures have reachedstability with 80 tag–control image pairs, quantified CBFvalues were calculated for various lengths of time series withthe group A data. The time series were split into the first 4, 6,8, … tag–control pairs, and quantified CBF maps werecalculated from the resulting data sets. Plots comparing thenumber of tag/control pairs vs. the calculated CBF values, aswell as their corresponding across-subject standard de-viations, were made for each ROI. To aid comparison, thesevalues were also plotted as a ratio relative to the 80 tag/control pairs' CBF value.
2.6. Power calculations
Based on the variability in quantified CBF measures ineach ROI, power calculations were performed to determinethe number of subjects (N) required to detect a given effectsize. The following equation was used [38]:
N =2r2 Z1−a =2 + Z1−b
� �2
eff 2ð1Þ
where σ2 is the variance of the data, Z1−α/2 is Z-valuerelated to the significance level, Z1−β is the Z-valuecorresponding to the detection power and eff is the size ofthe effect. For all calculations, the level of significancewas chosen as .05 (on the basis of a one-tailed test inwhich we have a hypothesis about the direction ofperfusion change) with a detection power of 80%. Threetypes of comparisons were investigated: between groups, atwo-period crossover (i.e., within subjects between ses-sions) and a within-subject within-session dosing. Thevariance, σ2, for the between-group calculations wasestimated using the group A and group B session 1 data.For the within-session variance, each subject's ASL data ingroup A was split into two (40 tag–control pairs each) toyield two CBF measures from within a single scan session.The variance of the difference between these CBF values
For group B, session 1 and session 2 values are shown separately. Therepeatability of these values was investigated using ICCs, with an ICC of 0.6corresponding to P=.05. PCC: posterior cingulate cortex, SI+SII: primaryand secondary sensory cortices.
Fig. 1. The behavior of the CBF measurement is shown as the number of tagsubjects for each ROI, and the graphs on the bottom show the associated stshown, whereas on the right-hand side, the ratio of CBF value to the final CBvalues are within 5% of the final value in all ROIs. The standard deviation
1385K. Murphy et al. / Magnetic Resonance Imaging 29 (2011) 1382–1389
was used in Eq. (1). The variance for the crossover designwas estimated from the subject-by-subject differencebetween session 1 and session 2 in group B. For eachROI, curves were calculated that compared the percentageflow change, ranging from 1% to 50%, to the number ofsubjects required to detect the effect at the chosensignificance and detection power.
/controandardF valueacross
3. Results
Mean and standard deviation of CBF across subjects foreach ROI are shown in Table 1. There is large variability inmean CBF values across the ROIs in each of the sessions,suggesting between-region differences in perfusion. How-ever, the relative differences between ROIs are relativelyconsistent across sessions. Repeatability between sessions ingroup B is demonstrated by ICC values close to 1 in most ofthe ROIs.
Stability of the CBF measure is shown in Fig. 1. Themean CBF across the subjects in each ROI is shown forincreasing numbers of tag/control pairs. To aid compari-sons, the CBF measures are also shown expressed as aratio of the final (80 tag/control pairs) CBF measure. Afteronly 40 tag/control pairs, the mean CBF values across thesubjects are within 5% of their final value for all ROIs.The variance across the subjects is important in detectingdifferences in perfusion, and the bottom panels in Fig. 1demonstrate that the standard deviation across subjects hasalso stabilized after 40 tag/control pairs. This suggests thatrepeatable CBF measures could have been obtained ingroup A if the ASL scans were acquired for only half aslong as they actually were. To estimate the within-sessionvariance for the power calculations, the differences
l pairs is increased. The graphs in the top row show the mean CBF across thedeviation across the group. On the left-hand side, the actual CBF values areafter 80 tag/control pairs is shown. After 40 tag/control pairs, the mean CBFsubjects has also stabilized after 40 tag/control pairs.
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between CBF measures derived from the first and secondhalf of the experiment were used.
Sample sizes for the three types of study designs wereestimated: between groups, a two-period crossover (i.e.,within subjects between sessions) and a within-subjectwithin-session dosing. Fig. 2 demonstrates that the numberof subjects required to detect a given effect size is highlydependent on the type of design. To detect a 15% increase(or decrease) in CBF between groups on a per-ROI basis,approximately 20 to 40 subjects are needed in each group. Ifa within-session design is used in which subjects arescanned, as a drug is infused or intervention is performed,between 5 and 10 subjects are needed in total to detect asimilar 15% increase in CBF. The number of subjects neededto detect a 15% increase in CBF in the case of a within-subjects crossover is between 4 and 15. The number for eachindividual ROI is displayed in Fig. 2. Detecting an overallincrease in CBF of 15% across all of GM requires only foursubjects. There is large variability in the number of subjectsrequired across the ROIs, but less than 15 are needed todetect a change of 15% for the within-subjects crossover.
Fig. 2. The sample size required to detect a given effect size in each ROI is plotted foof subjects. To estimate the values for between-group designs, the variance was estiwithin-session calculations was estimated by splitting group A data sets into twoestimated using the within-subject difference between group B, sessions 1 and 2. Tdisplayed in the circles (red: between groups, green: crossover, blue: within session)the dashed vertical and horizontal lines.
For comparison, for a 10% CBF change, at least 34 subjectswould be required to detect this effect in all regions with acrossover design.
4. Discussion
Our implementation of a pulsed ASL technique appears tobe sufficiently sensitive in small cohorts to detect regionaldifferences in CBF such as may be expected in studies oftask- or disease-related brain activity or pharmacologicalintervention [25]. Wang and colleagues have demonstratedthat such PASL measures were also reproducible on aregional basis [39]. In that study, multiple measures wereused to probe reproducibility, such as the within-subjectstandard deviation, a repeatability index and ICC. SimilarICC measures are seen between sessions in group B of ourstudy compared to those reported by Wang and colleagues.This suggests that intersession reproducibility of CBFmeasures across different imaging centers and vendors(Siemens in the case of Wang and colleagues) is similar.
r three types of experimental design. Eq. (1) was used to calculate the numbermated with group A and group B session 1 CBF values. The variance for theto give two CBF measures for each subject. Crossover design variance washe number of subjects required to detect a 15% CBF change in each ROI is. The sample sizes for a 15% CBF change are also indicated on the graphs by
1387K. Murphy et al. / Magnetic Resonance Imaging 29 (2011) 1382–1389
In addition to establishing the number of subjects neededto detect a given effect, it is important for efficient clinicaltrial design to be able to collect the required data within theminimum time possible. Large variability in data sets willreduce the power of a trial. For this reason, the stability ofthe CBF measures was investigated with respect to theduration of scanning for each subject, namely, the numberof tag–control perfusion-weighted image pairs that werecollected. Both the CBF measure itself and the standarddeviation of CBF between subjects for a given region werestable after acquisition of approximately 40 tag–controlpairs (Fig. 1). This gives confidence that the between-subject standard deviations in Table 1 are related to trueCBF differences between subjects rather than noiseintroduced by unstable CBF measures caused by insuffi-cient signal-to-noise ratio (SNR). Furthermore, for our MRsetup and SNR, 80 tag–control pairs took approximately 6min to acquire. In practice, this could be reduced to 3 minwith little impact on the sensitivity of the study. It isrecommended that individual laboratories determine, in asimilar fashion, the length of ASL scan required to produceaccurate and reliable quantified CBF values with MR setupand SNR available. This is important information as rapidacquisition of CBF data allows it to be more easilycombined with other functional MRI and structural MRImeasures within the same scan session. More rapidacquisition is also valuable in reducing the opportunity forcomplications, such as head motion and change of the stateof arousal, during clinical studies.
Our power calculations are based on estimating meansand variances in CBF within a cohort of volunteers at rest.Naturally, the sample sizes depend on the desired effectsize, which at the outset is normally unknown. Owen andcolleagues, performing a within-subject within-scan com-parison, have demonstrated approximately a 10% increasein CBF in pain-responsive regions such as the insularcortex arising from a tonic muscular pain stimulus in 11healthy volunteers [40]. This is consistent with our samplesize estimates (Fig. 2). Were one to extend such a study toone of pharmacological analgesia in which pain responsesare effectively abolished within scan [16], one mayestimate that a similar group size would be required.Chen and Parrish [15] observed percentage reductions inCBF of between 22% and 32% for intravenous doses ofcaffeine ranging from 1 to 5 mg/kg and based on ananalysis of all GM and using a similar PASL technique toourselves in 13 subjects. Low-dose anesthetic (sevoflurane)has been shown recently to reduce CBF by 11% and 5%,respectively, in visual and auditory regions again usingPASL [21] in 16 subjects. Macintosh and colleagues [23]recently demonstrated 35% CBF increases related to theintravenous administration of an opioid in 10 volunteersusing a PASL technique, albeit with a GRASE readout.These caffeine, anesthetic and opioid studies were allconducted principally within the same scanning session,removing the influence of intersession variance. Fewer
pharmacological studies have been performed betweensessions as a crossover or between groups, i.e., patientsand controls. Between-groups comparisons using ASLhave principally focused on examining pathologicalconditions or those at risk of disease in comparison tohealthy controls. Fleisher and colleagues [41] recentlydemonstrated a 25% higher resting hippocampal perfusionin subjects at higher risk of developing Alzheimer'sdementia compared to low-risk controls (25 and 13subjects, respectively) using a PASL technique. A recentrandomized controlled experiment examining CBF changesin healthy older adults with a course of cognitive training(27 and 31 subjects in the treatment and control groups,respectively) revealed 36% CBF increases in rightprefrontal cortex after a whole-brain analysis [42].Additional examples of clinical studies employing ASLtechniques can be found in the review by Brown andcolleagues [43]. Naturally, the articles quoted are those inwhich statistically significant CBF changes have beenfound with ASL techniques. Published articles couldtherefore show a bias towards larger effect sizes onCBF. In our sample size estimates, we have therefore triedto represent effect sizes spanning the expected range.
Arterial spin labeling CBF measurements have not yetbeen used systematically to evaluate novel pharmaceuticalagents in humans in clinical trials of central nervous system(CNS) disorders. However, our sample size estimatessuggest that ASL could be a practical tool for identifyingdrug effects in small cohorts. However, what are wemeasuring and how is this relevant to understandingpharmacological action? As a biological marker of drugeffect, CBF does not have the specificity of a PET ligandable to give binding potential and specific receptoroccupancy information. Global changes in CBF may indicatea systemic effect of the drug, such as may be seen throughrespiratory depression [44], or a global vascular influence oran effect on a ubiquitous receptor system. Regional changesin CBF may occur as a result of alterations in localmetabolism which could be downstream of receptor binding.Cerebral blood flow alterations may indicate changes insynaptic activity nearby the site of action or indeed distantfrom it where changes occur in presynaptic input to a regionreceiving signals modulated by the drug. Such a conceptcould extend to the modulation of signals from peripheralafferents. Finally, CBF changes may indicate a direct localeffect of the drug on vascular tone such as a vasoconstrictionor vasodilatation. While the measurement of regional CBFdoes not offer the same specificity to neurotransmitter actionoffered by ligand-PET experiments, recent work hasdemonstrated that the link between changes in neuronalactivity and increases in arteriole diameter (and thereforeCBF) may be closer and faster than was previouslyanticipated [15].
The measurement of regional CBF as a marker of drugeffect has potentially different utility at each stage of the drugdevelopment process in man [12]. It is increasingly likely
1388 K. Murphy et al. / Magnetic Resonance Imaging 29 (2011) 1382–1389
that noninvasive neuroimaging techniques will find theirway into early-phase clinical trials of drugs with centraltargets [45]. In phase 1, such studies would provideevidence, early in the drug development pipeline andpossibly using a low dose, that the drug is causing afunctional effect in the CNS. More specifically, it may bepossible to use such techniques to provide early evidence tosupport proof of mechanism or to give an early indication ofsafety issues. Such application of ASL would be likely tofollow a within-subject design, following changes in CBFover time resulting from acute single dosing in a very smallcohort e.g., six volunteers. In phase 2, ASL CBFmeasurements could be used to provide an early signal ofefficacy in a small patient study, which would de-riskprogression to a larger proof of concept (POC) study inpatients using conventional efficacy measures. In this case,placebo-controlled crossover designs with 12–18 patientswould be most likely. It is also conceivable that, with furtherdevelopment, CBF measures may be able to provide asurrogate marker of drug efficacy that could be used todeclare POC or even as an outcome measure in later-stageregulatory studies (phase 3).
The ASL acquisition strategy we have taken is a commonone of using a PASL approach with a single inversion delaytime. The calculation of CBF from such data is madepossible by the definition of the temporal duration of thetagged blood. Nevertheless, the quantification requiresassumptions about the arrival of the tag in the image planeand exchange with tissue water [9]. In common with manyother labs, we have assumed a single-compartment “stan-dard” perfusion model [28]. Quantification of CBF isimproved by a more complete sampling of the kineticcurve of the tagged blood, namely, its time-dependent effecton the signal in the imaged slices [46]. While the benefits ofthis more complete sampling may be limited in younghealthy controls, they are likely to be greater in older subjectsor in conditions where the arterial arrival time is altered, suchas stroke, and fewer assumptions may be made about thekinetics of the tagged blood [47]. Pharmacological interven-tion itself may alter vascular behavior enough to require theuse of a more complete sampling of the kinetic curve andmay also change the intersubject variability requiring areestimation of the necessary sample sizes. The present studyhas assumed levels of variability on the basis of resting datain healthy volunteers. We have also assumed some simpleclinical trial designs without modeling additional effectssuch as drug–order interaction effects which may be presentin a crossover study.
It is important to stress that only one ASL modality wasemployed in this study. The recent introduction of moreefficient arterial blood labeling schemes such as pseudo-continuous, flow-driven inversion [10] and fast, non-EPIreadout methods such as single-shot spiral FSE and GRASE[48] may lead to significant enhancements in the contrast-to-noise ratio of CBF maps and therefore improve thereproducibility, reliability and power of detection of this
technique. It is plausible that such methods will allow theobservation of smaller changes in CBF with a similar numberof subjects.
5. Conclusions
This study has demonstrated the feasibility of usingASL CBF measures for detecting changes in brain stateon a regional basis in clinical trials. Power calculationsshow that even in the least powerful trial designs, i.e.between groups, it is feasible to detect CBF changes onthe order of 15% in a cohort of a practicable size. It is theability to draw conclusions from small studies that makesuse of the technique in early-phase trials feasible andpotentially cost-effective.
Acknowledgments
Funded by Pfizer Ltd. (K.M., R.W.), the UK MedicalResearch Council (R.W.) and the Natural Sciences andEngineering Research Council of Canada (A.H.). We thankMr. Fred Wilson (Pfizer Ltd.) for helpful discussions aboutthe manuscript.
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