Validation of a Method for Coregistering Scalp Recording Locations With 3D Structural MR Images

Transcription

1 Human Bain Mapping 29: (2008) Validation of a Method fo Coegisteing Scalp Recoding Locations With 3D Stuctual MR Images Chistophe Whalen, 1 Edwad L. Maclin, 1 Monica Fabiani, 1,2 and Gabiele Gatton 1,2 * 1 Beckman Institute, Univesity of Illinois at Ubana-Champaign, Ubana, Illinois 2 Psychology Depatment, Univesity of Illinois at Ubana-Champaign, Ubana, Illinois Abstact: A common poblem in bain imaging is how to most appopiately coegiste anatomical and functional data sets into a common space. Fo suface-based ecodings such as the event elated optical signal (EROS), nea-infaed spectoscopy (NIRS), event-elated potentials (ERPs), and magnetoencephalogaphy (MEG), alignment is typically done using eithe (1) a landmak-based method involving placement of suface makes that can be detected in both modalities; o (2) suface-fitting alignment that samples many points on the suface of the head in the functional space and aligns those points to the suface of the anatomical image. Hee we compae these two appoaches and advocate a combination of the two in ode to optimize coegistation of EROS and NIRS data with stuctual magnetic esonance images (smri). Digitized 3D senso locations obtained with a Polhemus 1 digitize can be effectively coegisteed with smri using fiducial alignment as an initial guess followed by a Maquadt Levenbeg least-squaes igid-body tansfom (df 5 6) to match the sufaces. Additional scaling paametes (df 5 3) and point-by-point suface constaints can also be employed to futhe impove fitting. These alignment pocedues place the lowe-bound esidual eo at mm (l 6 s) and the uppe-bound taget egistation eo at mm (l 6 s). The dependence of such eos on scalp segmentation, numbe of egistation points, and initial guess is also investigated. By optimizing alignment techniques, anatomical localization of suface ecodings can be impoved in individual subjects. Hum Bain Mapp 29: , VC 2007 Wiley-Liss, Inc. Key wods: coegistation; suface fitting; fiducial points INTRODUCTION Contact gant sponso: NIMH; Contact gant numbe: MH080182; Contact gant sponso: NIA; Contact gant numbe: AG *Coespondence to: G. Gatton, Univesity of Illinois, Beckman Institute, 405 N. Mathews Ave., Ubana, IL gattong@uiuc.edu Received fo publication 7 Febuay 2007; Revised 11 May 2007; Accepted 12 July 2007 DOI: /hbm Published online 25 Septembe 2007 in Wiley InteScience (www. intescience.wiley.com). Accuate anatomical localization of functional bain data is dependent upon the ability to pecisely align, o coegiste, these data with thei coesponding anatomical infomation. In studies whee data ae combined acoss subjects, accuate coegistation of each subject s data can lead to significant impovement in the esolution of activated egions in the combined data sets. The impotance of such pocedues has led to a wealth of multimodal egistation techniques and stategies [Audette et al., 2000; Cum et al., 2004; Hawkes, 1998; Maintz and Viegeve, 1998; West et al., 1999]. Fo techniques utilizing scalp-placed ecoding sensos, such as the event-elated optical signal [EROS; Gatton et al., 1995], the event-elated bain potential (ERP), tanscanial magnetic stimulation (TMS), and magnetoencephalogaphy (MEG), coegistation is complicated by two factos: (1) the two data sets, functional and anatomical (typi- VC 2007 Wiley-Liss, Inc.

2 Coegistation of Functional and Stuctual Data cally stuctual magnetic esonance imaging, MRI, o computeized tomogaphy, CT), ae acquied at diffeent times in diffeent modalities; and (2) infomation available fo alignment becomes esticted to the suface of the scalp. Coegistation effots have theefoe focused on two appoaches: (1) location and identification of anatomical landmaks; and (2) algoithms attempting to minimize the distances between sufaces. A common method to coegiste data sets is to detemine a set of anatomical landmaks, o fiducial points, which can be identified in the two modalities. These points can theoetically be any thee o moe non-colinea points but should ideally numbe seveal and encompass the data egion. Such paametes ae vital because eos of fiducial egistation ae known to incease with distance fom the centoid of the fiducials and oughly follow N 21/2 dependence, with N epesenting the numbe of fiducial makes [Fitzpatick et al., 1998; Hill et al., 1994; Maue et al., 1997]. By histoical convention and fo eliability, the cutaneous fiducial points typically used ae the two peauicula points and the nasion [oiginally used as efeences makes in the system of EEG/ERP electode placement; Jaspe, 1958]. These locations continue to be used ubiquitously fo EEG/ERP puposes and, moe ecently, have also been used as efeence positions fo coegistation of anatomical data sets with MEG [Williamson and Kaufman, 1989; Williamson et al., 1991] and TMS [Hewig et al., 2003]. Although these thee fiducial points ae most common, bite-bas and othe aangements have also been used [Adjamian et al., 2004; Singh et al., 1997]. Moe accuate invasive tanscutaneous makes ae available fo peopeative clinical pocedues and can povide submillimete pecision in some cases [Maue et al., 1996, 1997, 1998]. Hee we limit ou investigation to the fome noninvasive pocedues. Once located, the fiducial points ae digitized in the efeence fame of the functional data. Digitization can be accomplished with electomagnetic systems such as the Polhemus Fastak 1 used hee, but othe devices using mechanical (Micoscibe TM : co.uk/) o optical (3D-PHD: eseach/phd/index.htm) technologies ae available. Fiducial locations ae also identified pio to an anatomical scan, and a make visible in the imaging modality is placed at the fiducial locations. These makes ae subsequently identified in the MRI image and thei coodinates tanscibed manually. Finally, fiducial alignment of the two images is pefomed. Most commonly this is done via an explicit least-squaes minimization algoithm [Aun et al., 1987]. Afte alignment, fiducial, eos seve as an indicato of the accuacy, and thei vaiance seves as a measue of pecision. Fiducial methods have seveal advantages compaed to featue-based egistation but also suffe fom majo dawbacks. Fo instance, an advantage of fiducial pocedues is that they equie negligible computation time fo alignment; yet they equie modeate time to pecisely identify and accuately place makes ove the fiducial points. Additional time is also needed to locate make coodinates on the anatomical image. Fiducial alignments can be elatively accuate, povided that the anatomical locations can be identified eliably and with pecision. Howeve, cutaneous makes may appea shifted in the MR image due to magnetic susceptibility changes when going fom ai to skin/makes and, in addition, chemical fequency shifts can displace fatty makes by 1 3 mm fo common MR field stengths of T. The MR envionment, with paticipants lying supine, weaing headphones, and using goggles and othe devices, can also cause the makes to be mechanically displaced. Lastly, fiducial points ae limited to points that can be epeatedly and accuately located, making the use of a lage numbe of makes intactable. As a consequence, in pactice, fiducials numbe few and ae located in the font of the head, biasing accuacy to fontal lobes at the expense of occipital egions. Suface techniques offe an altenative to fiducial based appoaches. They consist of fitting a epesentation of the head suface obtained though digitized points with one obtained fom stuctual imaging data. This pocedue equies (1) a lage aay of alignment points; (2) scalp segmentation of the anatomical image; and (3) a sophisticated fitting algoithm based on the minimization of distances between the two sufaces. Scalp segmentation outines ae available via aleady-existent softwae packages, some of which ae available fee-wae (FSL, ac.uk/fsl/; Bainstom, o can be witten in house [fo moe opinions and altenatives see Dogdas et al., 2005; Huppetz et al., 1998; Lammet et al., 2001; Schwatz et al., 1996]. When applied to up-to-date anatomical scans, these algoithms typically poduce suface endeings based on tens of thousands to hundeds of thousands points, which is a sufficiently dense aay to pefom alignment. Similaly, having a lage numbe of digitized points coesponding to the functional data set is impotant. In this case, an aay fomed by hundeds o thousands of points is pefeable, since egistation eos decease as the numbe of points inceases [Kozinska et al., 1997, 2001; Maue et al., 1998; Schwatz et al., 1996]. The final citical featue of suface matching is a good fitting algoithm. Appopiate algoithms ae fast, accuate, and obust. To meet these citeia, algoithms use iteative methods that ely on minimizing the least squaes distance between closest points on the two sufaces. Explicit solutions ae not possible due to lack of infomation about coesponding points, and because such solutions would involve lengthy computational times. The sophistication of fitting algoithms fo this pupose has developed consideably ove the ecent past, beginning with implementation of the quadatic Newton-Mulle method [Daisne et al., 2004; Levin et al., 1988; Pelizzai et al., 1989], followed by seveal othes [Huppetz et al., 1998; Kobe et al., 1993; Wang et al., 1994]. The Powell algoithm [Powell, 1964] was late implemented by Schwatz et al. [1996]. Moe 1289

3 Whalen et al. ecently the Maquadt-Levenbeg algoithm [Levenbeg, 1944; Maquadt, 1963] was effectively adapted to the suface egistation poblem of igid bodies by Kozinska [1998] and Kozinska et al. [1997], and has been shown to be much faste than pevious methods while etaining pecision. Bulan and Oztuk [2001] futhe efined this pocedue by adopting a k-dimensional tee to eplace the distance map; this feed up memoy and deceased computation time while poviding compaable eos. This pocedue was implemented into the Matlab 1 code Align2.0 by Oztuk (pesonal communication on Align2.0 and Maquadt-Levenbeg least-squaes fitting, 2004) and is the code used fo the wok pesented hee. Suface-fitting techniques have seveal advantages ove fiducial egistation but also have thei shotcomings. Computationally, suface-fitting pocedues ae much slowe than fiducial pocedues due to the lage numbe of points, but the inceased time (typically of the ode of seconds o less), is acceptable fo most pactical applications. In fact, the slowest computational pat of the coegistation pocedue is the scalp segmentation algoithm (equied to identify the head suface on the anatomical scans) which can take seveal minutes. Additionally, this pocedue is fequently only semiautomated, equiing use input, which inceases segmentation time. Nevetheless, these time demands ae of minimal concen fo most puposes as they add only a few minutes pe subject to the pocessing of bain imaging data. Of fa geate concen is that suface-fitting algoithms may suffe fom the local minimum poblem. This is a common poblem in multiple non-linea egession, wheeby the algoithm can convege on an undesiable solution associated with a local minimum in the eo function, significantly fa fom the coect solution (associated with the global minimum in the eo function). Fo bain imaging, this poblem is paticulaly seious, because the suface of the head is nealy spheical/ellipsoidal in shape, allowing fo a shallow and bumpy eo function fo paticula otations. It is impotant to conside that the local minimum poblem is stongly dependent on the stating point of the iteative multiple egession pocedue, which is commonly labeled the initial guess. If the initial guess is close to the coect solution, it is moe likely that the pocedue will convege on it. If it is fa away, it is likely that a local minimum in the eo function will be found instead. To ceate an initial guess many suface fitting techniques fequently begin with an automated appoach by matching centoids and moments [Goldstein, 1950; Kozinska et al., 2001; Pess et al., 1989], which is pone to lage inaccuacies due to the spheicity of the human head. Moment techniques also do not distinguish diectionality of axes, allowing fo eflective solutions. That is, in cases of elatively symmetic objects such as the human head, this may lead to the swapping of the left-ight dimension (and, occasionally, even of the anteio-posteio dimension). Fiducial alignment entiely avoids all these poblems because the coesponding points ae known. Thus, this method is much moe likely to poduce an initial alignment that is not fa fom the global minimum. It is impotant to note that fiducial and suface-fitting methods ae not necessaily mutually exclusive. It has been demonstated that using a weighted combination of bone-implanted makes along with skin and bone suface fitting leads to supeio egistation than methods elying solely on fiducial fitting [Maue et al., 1998]. Hee we demonstate that using a fiducial egistation as an initial guess followed by a suface fit educes egistation eos while poviding geate eliability and confidence in the esults. Additional efinements such as scaling and scalp focing ae also evaluated. METHODS This section is divided into two pats. Fist, we descibe the vaious methods that wee used in the coegistation pocedue (including initial alignment, suface fitting, scaling, and scalp focing). Second, we descibe methods fo evaluating the effectiveness of these fitting pocedues. Evaluation is based on an analysis of vaious estimates of the coegistation eo obtained at multiple stages of the egistation pocess. These fitting eos wee measued on six voluntees. Initial guess Coegistation Pocedues As mentioned ealie, this step povides an initial stating point fo the suface fitting pocedue. A fiducial-based initial guess is expected to geatly limit the pobability of goss inaccuacies due to local-minima o eflection poblems. In the cuent study thee fiducial points wee used fo this pupose (see also Placement of Makes): the left and ight peauicula points (LPA and RPA, espectively) and the nasion (Na). We evaluated two methods of using the fiducial data to povide an initial guess: a momentmatching technique (the unweighted method descibed by Kozinska et al. [2001], and a least-squaes fiducial appoach deived by Aun [1987]). Suface alignment and scalp segmentation The initial guess pocedues descibed above wee evaluated and futhe used as the stating point fo a igid body (df 5 6) suface alignment (Align2.0; Oztuk, 2004). Suface alignment equies a desciption of the set of points that compose the head suface, which can be deived fom an anatomical image (in this case a smri scan), though a pocess of scalp segmentation. Scalp segmentation was pefomed with a Matlab pogam, which includes the following steps: 1. Gaussian smoothing kenel (SD mm) and a 2D median filte (3 3 3 neighbohood) ae applied to the MR image to educe gain and atifacts. 1290

4 Coegistation of Functional and Stuctual Data Figue 1. Effects of using diffeent thesholds on suface scalp endeing obtained fom MR images fo one subject. (a) theshold , TRE mm; (b) theshold , TRE mm; (c) theshold , TRE mm. Segmentation (b) shows a moe appopiate suface endition than the othe two. 2. A theshold value (defined as a faction of the lagest voxel intensity) is chosen. Left-ight, anteio-posteio, and supeio scans ae pefomed fom the outside-in until the theshold is eached. The union of the points fom all scanning diections is taken to define the scalp suface. 3. A endeed scalp image is displayed and the use is allowed to adjust the theshold, in ode to contol the segmentation pocess. If needed, steps (2) and (3) ae epeated until a satisfactoy scalp image is obtained (i.e., the suface is smooth and deep stuctues ae not visible). Examples of endeed scalp images ae pesented in Figue 1. This method takes oughly 1 min and was chosen ove available egiongowing algoithms because such algoithms extact a scalp-endition with a thickness of seveal mm, which can lead to a shallow eo function and hence longe alignment times and local minima concens. Convesely, ou in-house algoithm povides a thinne (1 mm) scalp-endition, thus cicumventing these poblems. Segmentation done in this fashion poduced 65,000 95,000 scalp points. The MR-deived scalp points ae egisteed to the digitized points ecoded in the functional coodinate space using the method descibed by Kozinska et al. [1997] 1. The fitting algoithm uses a Maquadt Levenbeg optimization outine [Levenbeg, 1944; Maquadt, 1963] applied to the case of a 3D igid body. In bief, the algoithm minimizes the sum of squaes of the distances between the two data sets. It is impotant to note that the distance minimized is fom the data set to be tansfomed (i.e., the digitized points) to the closest point in the efeence data set (i.e., the MR-deived scalp suface). This may not be the 1 In ou implementation we used a k-dimensional tee using a modified appoximate-neaest-neighbo libay athe than a distance map, because this method has been shown to povide impoved accuacy with faste convegence [Bulan and Oztuk, 2001]. actual coesponding point. Nevetheless, the algoithm offes oughly second-ode convegence by using a Taylo expansion and an iteative appoach, with a vaying weighted combination of an exact gadient fo the fist ode tem and an appoximation to the Jacobian matix of the patial deivatives, called the Hessian matix, seving as the second ode tem. This adaptive method can help minimize the local minima poblem and allows fo apid convegence, as the descent tajectoy on the eo function becomes less gadient-like and moe Newton Raphson-like nea the minimum. The algoithm iteates until peset conditions ae obtained (such as a pedetemined numbe of iteations o an acceptance citeion fo mean distance eo) o once distance eos fail to decease by a pespecified amount. All data pesented hee used the following paametes: a 0.01-adian angula theshold, a 0.1-mm tanslational theshold, 50 maximum iteations, a weighting paamete of 2, a weighting paamete diviso of 2, and 20 maximum loop seaches befoe the step is adjusted and a new seach is stated. Paametes in this ange have been shown to poduce good and apid convegence fo this application [Kozinska et al., 2001]. Scaling Although the 6-paamete igid-body fit educed the bulk of the egistation eo, it is known that MRI gadient inhomogeneities, even in the most caefully monitoed envionments, can poduce scaled gadient inaccuacies in the ange of 1 2% (1 2 mm eo on the scalp) in both the left-ight and anteio-posteio dimensions [Bednaz et al., 1999; Maue et al., 1996]. Similaly, the Polhemus 1 digitize s estimates can deviate fom the tue value in a fashion that is in pat dependent on the distance fom the tansmitte and in pat on the pesence of local magnetic field gadients ( Consequently, we evaluated the use of independent linea scaling factos fo each of the 3 spatial dimensions (df 5 3) to 1291

5 Whalen et al. educe egistation eos. We applied the scaling facto afte the igid body egistation, as this pocedue was peviously shown to esults in a decease in egistation eo anging between 0.5 and 2.0 mm [Maue et al., 1996; Schwatz et al., 1996]. Specifically, we adopted a seial appoach, in which the scaling factos wee estimated by pefoming thee sepaate linea egessions (one fo each spatial dimension) between the positions of digitized points and thei closest anatomical point. This method, being based on a least-squae technique, is insensitive to the poblem of local minima. In all cases the scaling facto anged between 0.97 and Scaling paametes could also be estimated simultaneously with the 6-paametes igid body suface fitting [Koikkalainen and Lotjonen, 2004]. Howeve, this could lead to an incease in the numbe of local minima (associated with the incease in the numbe of fee paametes to be estimated) and educe the pobability that the fitting algoithm will convege on the tue solution [Maue et al., 1996; Schwatz et al., 1996]. A futhe consideation is that pevious studies suppot the idea that a seial appoach, while yielding oveall compaable fit to the oiginal data as the simultaneous appoach, povides moe obust esults when tested using coss-validation methods [Maue et al., 1996; Schwatz et al., 1996]. Scalp focing The scalp locations wee digitized using a Polhemus 1 digitize stylus. Howeve, the stylus depession on the skin of the scalp may vay fom 1 to 3 mm [Schwatz et al., 1996]. In an attempt to account fo the adial digitization eo thus geneated, we constained the digitized points to lie on the suface of the scalp. This scalp focing was accomplished by eplacing the digitized coodinates of each point (obtained afte fiducial alignment, suface fitting, and scaling) with those of the closest segmented MR scalp point. Eo Estimation In ode to evaluate the vaious alignment methods, a measue of egistation eo must be used. Note that the coegistation pocedue involves optimizing the fit between diffeent data sets. As fo many othe optimization pocedues, we need to distinguish between two ways of evaluating the goodness of the fit: (a) intenal tests (in which the paamete used to estimate the eo is the same used to optimize the pocedue), and (b) coss-validation tests (in which independent estimates of the eo ae obtained). The eo estimate obtained using coss-validation is typically consideed a bette estimate of the tue eo than that obtained using intenal tests. In ou case, the tue eo is the map eo the eo between coesponding points obseved in the two modalities. Howeve, this pocedue is pactically unfeasible, because it equies knowledge of which MR point coesponds to each digitized point. Of couse, if this infomation wee eadily available, the coegistation pocedue would consist of a simple and explicit easily-deteminable solution. Theefoe, given the pactical constaints outlined above, the map eo is typically eseved fo theoetical calculations and simulations [Fitzpatick et al., 1998; Koikkalainen and Lotjonen, 2004; Kozinska et al., 2001; Maue et al., 1998; Singh et al., 1997]. Howeve, an appoximate estimate of the map eo can be obtained using a cossvalidation appoach. In the cuent case, this means computing the distance between estimates of the locations of coesponding points on the suface of the head obtained with digitization and MR data (afte coegistation) when these points ae not used to deive the coegistation paametes. This implies using makes to make the points visible on the MR scans. We will hee label this eo assessment the taget egistation eo (TRE). The TRE includes not only the map eo but also othe foms of eo such as make shifts between digitization and MR scanning. Theefoe the TRE may be consideed an uppe limit fo the map eo. In addition to the TRE, we will also discuss two othe types of eo estimates that can be (and commonly ae) used to evaluate coegistation methods. The fist is the fiducial egistation eo (FRE), defined as the distance between coesponding locations fo each fiducial make obtained afte coegistation. This estimate, howeve, may be biased and unde-epesent the map eo, because fiducial infomation is explicitly used fo coegistation. Futhe, it suffes fom the poblem of being based on a vey small numbe of points, and theefoe being potentially unstable. The second type of eo is the esidual eo (RE), that is, the distance between the digitized points and the closest suface points deived fom the anatomical image. As minimization of this paamete is the pupose of the suface-fitting pocedue, the RE can also be biased. In fact, it is typically smalle than the map eo, which may lead to oveestimation of the accuacy of the coegistation pocedue. A small RE does not necessaily imply a small map eo. An exteme example of this occus when the sufaces defined by the digitization and stuctual imaging methods ae both sphees. In this case, any otation of one of the sphees with espect to the othe will poduce a esidual eo of zeo (if scaling is allowed), wheeas the tue assessment of eo, the map eo, could be as lage as the diamete of the sphee. Howeve, since the RE epesents the best possible fit between the two sufaces, it does epesent a lowe-bound estimate of the map eo, povided that the scalp data set is accuate, complete, and continuous. It is theefoe essential, if we wish to have a complete epesentation of the eo, that we not only estimate the RE and the FRE, but also the moe meaningful TRE. Having infomation fom all thee types of eos also affods the ability to compae them and fom an undestanding of 1292

6 Coegistation of Functional and Stuctual Data the eliability and limitations of each an impotant aea fo which little infomation is cuently available. Expeimental estimation of the eo To detemine egistation eos and hence the efficacy of vaious egistation stategies, 32 (16 in one case) IZI 1 makes wee placed on the scalps of six male paticipants whose heads wee eithe completely bald o shaved. Although much wok on the efficacy of coegistation has been done via simulations, we conside the use of human subjects as essential to epoduce actual expeimental (o clinical) conditions. Each paticipant povided witten infomed consent and the pocedues used in the study wee appoved by the Institutional Review Boad of the Univesity of Illinois. The makes wee eadily visible and could be accuately located in both spaces (anatomical and functional) and seved as coesponding points fom which to assess the TRE and FRE. Thee of the makes wee on the fiducial points and wee used fo coegistation, wheeas the emainde seved solely to assess the TRE. The use of bald paticipants allowed fo makes to be affixed diectly to the scalp, theeby educing displacement eos that wee evident in peliminay wok in which the makes wee affixed to swim caps. Placement of makes Fiducial makes wee placed on each paticipant s LPA, RPA, and nasion. The nasion was located though visual and manual inspection. The LPA and RPA wee maked by means of a T-boad device ceated in ou lab (see Fig. 2). This device is essentially a stencil fitted on the ea and aligned with the oute canthus of the eye. Once the device is placed, the LPA and RPA ae maked in the notch of the T-section of the boad (as illustated in Fig. 2) and ae placed vey nea the peauicula points commonly used fo EEGs/ERPs [Jaspe, 1958]. The use of the T-boad has poved to be moe effective than visual/tactile localization of the peauicula points, which can be subject to inta- and inte-expeimente eo. To show the Figue 2. T-boad stencil used to quickly and accuately locate ight (shown by white aow) and left peauicula fiducial points. effectiveness of the T-boad, we compaed the accuacy of fiducial estimations obtained on 81 subjects fo whom the T-boad was used fo identifying the fiducial locations with that of 147 subjects fo whom the T-boad was not used. Fo each of these subjects we measued the FRE (fiducial egistation eo, see above) as a combined measue of accuacy and eliability of fiducial identification. As a eminde, this measue is based on fitting the location of the fiducial as detemined using the Polhemus 1 digitize to those obtained fom MR ecodings. In the case of these 228 subjects, these measuements wee obtained in sepaate sessions, and theefoe involved sepaate localizations of fiducials on the head. The FRE was, on aveage, 0.6 mm smalle (t(226) , P < 0.05 one-tailed) fo the subjects fo whom the T-boad was used, thus showing a significant advantage in eliability/accuacy. In addition, the use of the T-boad equies less taining and less time (2 5 min faste pe subject). Again, the emphasis on a pope choice of fiducials is not limited to the specific locations descibed hee, but, moe impotantly, on the choice of points that can be epeatedly and eliably located. The scalp makes wee aanged in five symmetically placed swaths of 4 7 makes unning anteio to posteio (see tous-shaped makes in Fig. 3). The makes theefoe spanned most of the head and the TREs epoted hee epesent the aveage ove all make locations. Makes wee howeve omitted fom the fa posteio egions to ensue paticipant s comfot and eliminate posteio make displacement while lying supine in the scanne. Digitization Afte makes wee affixed, paticipants wee digitized with a Polhemus FastTak 1 3D digitize (Colcheste, VT; accuacy mm) using a ecoding stylus and thee head-mounted eceives (which automatically account fo small movements of the head without poducing position eos). The thee fiducial points wee digitized, followed by the scalp makes (the cente of the hole in the tous makes was chosen). An additional 600 points wee digitized: 400 quasi-unifomly distibuted acoss the head and 200 points fom the face. Face points ae consideed extemely impotant fo expedient and accuate suface egistation. In fact, the added contou of the face impoves the fitting outine because it is hee that the head depats most clealy fom spheicity, and theefoe allows the fitting algoithm to quickly convege on unique and appopiate solutions. These points wee used both fo suface egistation and fo computation of the esidual eo. Examples of the digitized points fom one subject, oveplotted ove the coesponding suface stuctual image, ae pesented in Figue 3. MRI acquisition and make identification A stuctual MRI was ecoded fom each paticipant immediately afte digitization. Scans wee acquied sagi- 1293

7 Whalen et al. TABLE I. Mean eos 6 SD fo consecutive stages of the coegistation pocedues using the moment and least-squaes method fo the initial guess a Initial fit Coegistation pocedue Moment Least-squaes Taget egistation eo (TRE) Initial fit Suface Scaling Scalp focing Fiducial egistation eo (FRE) Initial fit Suface Scaling Scalp focing Residual eo (RE) Initial fit Suface Scaling Scalp focing a Thee assessments of eo ae epoted. Figue 3. Example of digitized image coegisteed with a coesponding suface MR endition. The digitized image compised 632 points ecoded with a Polhemus 1 digitize, including thee fiducials (LPA, RPA and nasion IZI 1 makes; ed dots), 29 scalp makes (tous-shaped IZI 1 makes, white dots), and 600 face and scalp points (digitized geen dots). The effects of vaious coegistation pocedues on eos ae summaized in Table I, whee the means and standad deviations of the TRE, FRE, and RE ae epoted fo diffeent coegistation methods acoss the six subjects. The use of all thee types of eo (TRE, FRE, and RE) allows us not only to detemine which egistation technique is the most accuate, but also to evaluate the utility of the thee types of eo assessment. We conside the TRE as the most useful and unbiased estimate of map eo, albeit of its uppe bounday. Fo any given egistation method, RE is in geneal smalle than TRE: fo example, the RE of the fiducial fit was mm compaed with a TRE of mm (Table I). This discepancy in the two eo measues illustates the impotance of not elying too heavily on the RE alone. The thid measue of eo, the FRE, was in between the othe two at tally with a T1 weighted image on a Siemens 3T scanne (TE ms, TR ms, flip angle 5 88) with 144 slices, in-plane esolution of 1.3 mm mm and out-ofplane esolution of 1.2 mm. The IZI 1 makes wee then identified in the MR images and thei coodinates tanscibed manually by the fist autho. To assess the epoducibility of make identification the pocedue was epeated five times on the makes of one paticipant. We then computed the standad deviation of the make position on each space coodinate (x, y, and z). The aveage of these thee standad deviations was found to be 0.74 mm. Thus, make identification contibutes less than 1 mm to the oveall egistation eo. RESULTS Figue 4. Example of misalignment associated with small RE between digitized data set and MR image fom one subject, when using moments-based alignment followed by suface fitting. 1294

8 Coegistation of Functional and Stuctual Data mm. The thee measues of eo fo the explicit fiducial fit all diffeed significantly fom one anothe (F(2,10) , P < ), illustating the impotance of multiple means of eo assessment. Initial Guess Hee we evaluate what is the best pocedue to poduce the initial guess to be used in the fitting pocedue. Two common methods wee evaluated: least-squaes fiducial fit, and moment matching. The aveage TRE vaied widely between these methods, with the moment-matching method yielding eos ( mm) that wee significantly highe than the least-squaes method ( mm), t(5) , P < The lowe pefomance of the moments method is likely due to the difficulty of (1) digitizing points quasi-unifomly ove the scalp such that thei distibution esults in simila centoids and moments compaed with the MRI segmented scalp; and (2) uniquely matching ellipsoidal heads containing two axes of simila lengths (infeiosupeio and left-ight) an effect appaent upon visualization of endeed images, wheeby occasional lage otations about the anteio-posteio axis wee obvious even afte suface alignment (see, fo example Fig. 4). Inteestingly, howeve, the RE fo the moments method was mm, implying a easonably good fit, and consistent with pevious data epoted using this method [Kozinska et al., 2001]. This suggests that the discepancy between the two measues was the esult of the ability to otate an ellipsoidal head about cetain axes without a damatic incease in esidual eo. Suface Fit Using the explicit otation fiducial fit as a stating point fo suface fitting significantly educed the TRE (fom mm to mm; t(5) ; P < 0.01 one-tailed) compaed to pefoming a fiducial fit alone. The RE also deceased fom 2.8 to 1.6 mm (t(5) , P < onetailed). Despite the impoved fitting of the TRE and RE, the FRE wosened significantly fom 3.8 to 6.8 mm (t(5) , P < one-tailed). This futhe illustates that a high FRE does not necessaily indicate poo egistation and vice vesa. When the moments-matching technique was used as an initial guess fo the suface fitting pocedue, we obseved an inteesting phenomenon: fou out of six paticipants conveged, with an eo of mm. Howeve, two out of the six did not, with a mm eo despite having simila initial eos. Futhemoe, the aveage RE fo the non-conveging paticipants was 8.1 mm, which could be easily misintepeted as an acceptable fit and thus is a pime example of the local minimum poblem inheent to esidual-eo algoithms. This again indicates that goodness of fit based solely upon RE should be intepeted with caution. Even when we esticted the analysis to the paticipants who showed convegence with the moments technique, the eo afte moment and suface fitting was still significantly highe (0.5 mm; t(3) , P < 0.05 one-tailed) than that fo the same paticipants afte fiducial method and suface fitting. This implies both that within cetain boundaies the suface algoithm is able to convege nea the appopiate global minimum and that an advantage is still gained by an appopiate choice of initial fit. To detemine the optimal igid-body tansfom fo the make points, we applied the explicit least-squaes fit [Aun et al., 1987] to align digitized make points to thei coesponding MR make coodinates. The FRE based upon all tous-shaped makes being used as fiducials was mm, thus demonstating that the fiducial fit followed by the suface egistation technique conveges within 1.2 mm of the igid body limit (ange mm). Although significant (t(5) , P < onetailed), this small eo (which is on the ode of make identification pecision, MRI esolution, and digitization pecision) indicates the appopiateness of the Maquadt Levenbeg-based algoithm to convege to the global minimum, given an appopiate initial condition. In sum, poviding an accuate initial stating point followed by a suface fitting pocedue significantly educes egistation eos. Scaling and Scalp Focing To futhe efine the fit, we implemented two non-igid pocedues: scaling and scalp focing. Although each impoved the data ove the igid fit on thei own (scaling: 0.3 mm, t(5) , P one-tailed; focing: 0.4 mm, t(5) , P < 0.05 one-tailed) the combination of the two poduced the smallest eo, with a TRE of mm (0.5 mm, t(5) , P < 0.05 one-tailed). The slight eduction in TREs using these pocedues suggests that we ae nea the limits of esolution using cutaneous fiducials, as mentioned ealie. By contast, the REs ae not as sensitive to slight scalp displacements and theefoe also show impovement upon scaling but do so in a moe consistent manne (0.2 mm, t(5) , P < one-tailed). The RE of the scalp focing is not meaningful hee. In fact, by definition, the RE is zeo because focing to the closest point makes each digitized point have the coodinates of one of the scalp points. Eos attainable using the afoementioned pocedues wee quite small, but they wee, howeve, significantly dependent upon a numbe of paametes. In the next sections we will examine some of these paametes to povide guidelines fo the coegistation method. Scalp Theshold As mentioned peviously, the scalp theshold is a paamete set by the use duing the segmentation pocess, which vaies ove scans and paticipants. As the choice of 1295

9 Whalen et al. The numbe of digitized points and the numbe of scalp points used fo the suface fitting pocedue also have a pofound impact on eos (Fig. 6) as epeatedly demonstated [Kozinska et al., 1997; Maue et al., 1998; Noihomme et al., 2004; Schwatz et al., 1996]. In pinciple, the numbe of digitized head points should be as many as possible. Inceasing the numbe of points naows the uppe- and lowe-bound estimates (TRE and RE espectively) of the eo. In pactice, diminishing etuns exist beyond 300 points, as the TRE function appoaches an asymptote at this level. It is also impotant to note that, wheeas the TRE deceases with the numbe of points (as can be expected), RE actually inceases when few points ae used. This is because when a vey small numbe of points ae used (say, thee), it will almost always be possible to fit a suface though them with little o no eo, independently on whethe the fit is eal o atifical. Only when the numbe of points is sufficiently lage (moe than 80 in ou case), the eal dependence of the fit on the numbe of points can be evaluated. Theefoe, a small numbe of egistation points give a false sense of accuacy by minimizing the RE while, in fact, the best estimate of tue map eo the TRE is quite lage. These findings futhe bolste the claim that RE, when used in isolation, is an uneliable estimate of coegistation eo. Eo Function Figue 5. TRE and RE dependence on scalp theshold value, obtained afte fiducial and igid body egistation. a scalp theshold is made by the investigato, it is useful to know how it may influence the coegistation pocess. In fact, both the TRE and RE ae dependent upon the choice of scalp theshold, as shown in Figue 5. Selection of an appopiate scalp theshold that comes within a couple millimetes of the actual minimum can be done with minimal taining. Fo instance, eight individuals wee given bief (10 min) taining on theshold selection. The mean eo fo optimal scalp theshold selection was 0.08 mm as measued by the diffeence in TRE coesponding to the theshold selected as compaed to the optimal theshold. Numbe of Points A citical featue of the minimization algoithm is its obustness the ange of initial mis-egistations fom which the algoithm conveges to an appopiate solution. To assess this popety we used the following pocedues to geneate an eo function fo one epesentative subject (Subject 6): (1) We aligned the digitized data set to the MRI data set via a fiducial and suface fit and ecoded TRE and RE; (2) We atificially misaligned the data set by a known amount in one dimension of tanslation o otation and ecod TRE and RE; (3) We ealigned the data set and ecoded TRE and RE; (4) We epeated these pocedues (steps 2 3) to systematically assess the effects ove a wide ange of misalignments. The effects of initial tanslation and otation misalignments on TRE and the RE both befoe and afte ealignment ae shown in Figue 7. This figue only includes data fom one axis of tanslation and one angle of otation (the othe two ae not shown but poduced vey simila esults). The figue indicates that the algoithm conveges to within a few millimetes of the global minimum fom a wide ange of displacement values (6100 mm) and otation angles (6508). Also, the functions ae vey smooth, containing only one minimum ove a wide ange of stating values, poviding geate confidence in the convegence. It is impotant to note that wheeas such plots bolste evidence fo the smoothness and obustness of the eo function, they ae not conclusive. To obtain conclusive evidence, eo infomation about the six-dimensional hype- Figue 6. TRE and RE dependence on numbe of digitized points. 1296

10 Coegistation of Functional and Stuctual Data Figue 7. TRE and RE eo functions as a esult of misalignment along one tanslation axis and otation angle, fo one epesentative subject. The eo estimates befoe alignment ae indicated by solid lines; those afte alignment ae indicated by dashed lines. suface would have to be acquied. Highe dimensional eo sufaces may in fact be moe bumpy evealing local toughs and may explain the local minimum entapment we sometimes obseved with the moment-matching technique (see Fig. 4). Howeve, such a mathematical teatment of highe ode space is beyond the scope of this pape. Two-dimensional sufaces (not shown) wee plotted and, as in the unidimensional case, also eveal that the eo function is smooth and contains a unique minimum. DISCUSSION Compaison With Published Registation Eos and Techniques The data and techniques tested in this study delive eos that ae compaable o smalle than othe established non-invasive techniques. Although stictly limited to sugical patient studies, the most eliable and accuate technique involves bone-implanted fiducial egistation, which thus povides gold standad lowe-bound estimates to evaluate the accuacy of suface-based coegistation methods. In fact, with implanted makes and unde the ight conditions, FREs and TREs with submillimete pecision can be achieved [Labadie et al., 2004]. It is impotant to note, howeve, that such accuacy usually involves optical digitization instumentation, head estaints, and algoithms to pecisely locate the centoids of the makes. Futhe, they ae based on CT scans, which do not have the issues of magnetic susceptibility, gadient inhomogeneities, and chemical shift that can distot the images of fatty makes on the scalp by 1 2 mm in MR images. When a diect compaison was made on MR images, Ammiati et al. [2002] found only a small impovement in bone implanted makes as compaed to skin makes (aveage FREs of 2.25 and 2.76 mm wee obtained, espectively). In the case of eseach in functional neuoimaging, we ae esticted to non-invasive pocedues involving cutaneous fiducials and application of suface fitting appoaches. Suface fitting is inheently a multiple non-linea egession case, subject to the poblem of local minima. This, in ou case, tanslates in an inappopiate fitting between the ecoding locations obtained though digitization and the coesponding scalp points (see Fig. 3 fo an example). To minimize the pobability of hitting a local minimum, it is impotant to geneate a good initial guess. In ou study we investigated two methods fo poviding an initial guess: one based on a moment-matching method and the othe based on the use of fiducials. 1297

11 Whalen et al. The moment-matching method povided REs of 13.2 and 3.9 mm befoe and afte suface alignment, espectively, which ae consistent with the mm and mm anges epoted by othes [Kozinska et al., 2001]. Howeve, these values contast with lage TRE in at least some of the subjects: two of the six paticipants had an aveage TRE of 66.5 mm afte alignment, even though thei aveage RE was 8.1 mm, well within the ange commonly epoted fo these values. Fom this we daw two conclusions: (1) moments matching can be inaccuate and uneliable, especially if used in an automated fashion; and (2) RE is not a valid measue of egistation accuacy when used in isolation. The fiducial fit povides a bette initial guess than moment matching in tems of accuacy and eliability, and can be pefomed easonably quickly with no o minimal discomfot fo the paticipant. Most commonly the fiducial fit is accomplished via skin makes o bite-bas. A diect compaison between the two methods has been done [Adjamian et al., 2004; Singh et al., 1997], with the bite-ba methods consistently showing smalle speads in map eo (FRE) upon epeated digitization and alignment. Howeve, such esults ae expected fom a igid fame and would occu even if the bite-ba changed position between ecodings. Although Adjamian et al. [2004] have shown that the bite-ba is displaced vey little (<0.5 mm) when einseted, no functional impovements in dipole confidence volumes fo MEG median neve stimulation wee found. Additionally, bite-bas can be uncomfotable fo the paticipant. Reducing the spead in eos is ultimately impotant fo alignment accuacy and eliability. Instead of accomplishing this via a bite-ba, we chose to manufactue a stencil, the T-boad (Fig. 2), that can quickly and accuately locate LPA and RPA. A compaison of individuals coegisteed with the T-boad and individuals coegisteed with the old manual tactile method evealed a significant decement in aveage FRE and in the standad deviation of the eo. This method theefoe shows pomise as a eliable making technique to educe FRE and FRE vaiance while maintaining a efeence fame that is affixed to the head of the subject. In most instances whee fiducial egistation is used, the only eo infomation available is the FRE. Oveall, ou cutaneous fiducial fit shows FREs compaable to o smalle than those epoted by othes [Noihomme et al., 2004; Sinha et al., 2006]. By using moe infomation than just a handful of fiducial makes, suface alignment can incopoate thousands of points and impove data egistation. The fiducial method followed by a suface fit yielded significant impovements in TRE and RE. The REs epoted wee compaable to o smalle than those epoted by othe eseaches [Huppetz et al., 1998; Kozinska et al., 2001; Lamm et al., 2001; Noihomme et al., 2002, 2004; Schwatz et al., 1996; Wang et al., 1994]. In such studies, TREs ae usually confined to simulations that do not include many of the eos pesent with actual measues taken in a laboatoy envionment. Howeve, one compaable investigation incopoated 5 6 fiducial makes fo coss-validation with suface egistation in a fashion simila to ou design [Binkmann et al., 1998]. They epoted map eos of mm which ae consistent with ou findings. Scaling and scalp focing wee also employed. Scaling has been shown to impove localization by mm [Maue et al., 1996; Schwatz et al., 1996]. Likewise, we obseved a maginally significant impovement of 0.3 mm with scaling. To ou knowledge, the scalp focing technique has not been used by othes. Hee too, we showed a small (0.4 mm) but statistically significant impovement. Within any egistation technique, the ultimate goal is to find the set of paametes and pocedues that educe eo. One such paamete is the numbe of scalp points. Obviously moe points ae bette, but thee is a pactical tadeoff with digitization time. We find that the asymptotic limit is appoached by points (Fig. 6). Simila stability of the eo function past a couple hunded points has also been shown by othes [Bulan and Oztuk, 2001; Kozinska et al., 1997; Maue et al., 1998; Noihomme et al., 2004]. Anothe technique that has been suggested is the deletion of outlies eithe befoe o duing algoithm iteations. Although some have justified its use based on theoetical consideations alone [Kozinska et al., 2001] and othes have shown eductions in RE with simulations that incopoate eoneous points [Schwatz et al., 1996], no evidence on eal data sets o on TRE have been shown. When outlies wee emoved fom ou data, we found a negligible eduction in RE of 0.03 mm, and a non-significant incease in TRE of 0.08 mm. By definition, emoving outlie points as measued by closest-point distance to the scalp suface must educe the RE, as we in fact obseved. Howeve, note that this esult does not tanslate to a eduction of the eal mapping eo (TRE). As we have aleady shown when discussing the effects of vaying the numbe of points used fo fitting, RE and TRE ae not necessaily linked. In fact, emoval of the outlies, in ou case, poduced a simila effect as educing the numbe of points used fo the suface fitting. This suggests that outlie emoval may in fact incease capitalization on chance, pehaps because the points deemed to be outlies actually belong to the nomal eo distibution, and should not be eliminated. Futhe, the obustness analysis we epoted (Fig. 7) indicates that these outlies should be of a vey lage magnitude to actually influence the final esults in a significant manne. Thoughout this pape, we have touted the RE as being the lowe-bound estimate of the eo and the TRE as the uppe-bound. Wheeas this is the case in the application descibed hee, thee may be exceptions. Fo instance, in a scenaio in which MRI scalp points ae decimated causing point gaps in the suface, it is possible that the suface fit would convege on the same minimum keeping the TRE constant but causing an incease in RE. This is also theoetically possible duing scalp segmentation; a scalp epesentation that is too deep would cause an incease in RE, 1298

12 Coegistation of Functional and Stuctual Data and yet could still convege upon the tanslational and otational minimum, causing no ill effect on the TRE. In an exteme cause, these situations could cause the RE to become lage than the TRE. We mention these scenaios hee so that the idiosyncasies between the two eo measuements can be moe fully appeciated and undestood when intepeting coegistation accuacy. It is common pactice in studies of coegistation methods to assess egistation eos by eithe RE o FRE. It is less common fo both to be assessed togethe and even ae to include a measue of the TRE. This of couse is due to the pactical difficulty of having multiple assessments and of computing the TRE. Howeve, as shown in this study, only measues of TRE can povide a eal estimate of egistation eo, and RE in paticula can be misleading. Nevetheless, RE and FRE, when used in conjunction with the TRE, can give useful clues to the souces of egistation eo. Utilization of fiducial makes to assess map eo has poven vital in ascetaining ealistic metics of egistation eo [Adjamian et al., 2004; Bednaz et al., 1999; Binkmann et al., 1998; Maue et al., 1997, 1998; Noihomme et al., 2004; Sinha et al., 2006] and futhe pogess hinges upon continued appopiate coss-validation techniques. Limitations Ou eo estimates wee obtained unde conditions which may not mio completely those commonly used in most expeimental ecodings. Because it was ou aim to educe as many souces of eos as possible, fiducial makes wee not eplaced between the digitization and MRI sessions to minimize epositioning eos. As a consequence, the TREs pesented hee ae likely slightly smalle than those moe typically obtainable in a laboatoy setting using the same pocedues. Cutaneous scalp makes placed on bald paticipants wee a convenient method to assess TRE at multiple scalp locations, but such make positions shift and wap on the suface of the head when in the MR scanne even when, as in ou case, attempts wee made to minimize such displacements. This was appaent in displacement peiodicities in the swaths of ows and columns of makes distibuted acoss the head. To pevent discomfot, no makes wee placed in the fa posteio egions of the head. Theefoe, we have no metic of the TRE fo this aea. Additionally, eos epoted hee efe to the suface of the head and do not include possible elative changes between scalp and intacanial location, such as those due to change in decubitus, espiation, pulsation, and so on. It should be noted, though, that as we get close to the centoid of the stuctue we ae measuing fom (in ou case the head), the effects of mis-egistation should diminish, and it is likely that the cente will be coegisteed with a vey good accuacy [Fitzpatick et al., 1998]. Gadient inhomogeneity coections have been shown to impove anatomical localization and egistation [Bednaz et al., 1999; Jovicich et al., 2004; Maue et al., 1996]. A 2D coection was implemented, but no impovement was noted. Compute algoithms fo 3D coection [Jovicich et al., 2004, 2006] wee not able to be customized fo ou scanne and MR image acquisition sequence. It is theefoe possible that such coections could povide additional eduction in eos. Anothe eo comes fom chemical shift in the MR images, which depends in pat on the type of make used, the stength of the magnetic field, and vaious ecoding pocedues. Optimization of these methods may lead to an impoved TRE. Lastly, diffeent scanne stengths may alte the degee of accuacy obtainable using these methods. Weake field stengths may povide a slight disadvantage at pecisely ecoding make locations due to pooe spatial esolution, wheeas highe field stengths may distot make locations via the chemical shift o the lage local field inhomogeneity encounteed nea the bodes of the image (i.e., ai scalp inteface) as a esult of the high field stength and lage magnetic susceptibility diffeences between neighboing voxels. The use of multiple MR detectos may actually help addess both of these issues. CONCLUSION Optimal multimodal image egistation techniques ae essential to accuately compae functional data sets and localize bain function to anatomy. In compaing the theepoint least-squaes fiducial method to moment-matching techniques, the fiducial-based appoach was moe pecise, yielding TREs of mm. Combining a thee-point fiducial egistation method followed by a suface-matching appoach and subsequent scaling and scalp focing yielded a futhe eduction in TREs down to mm with REs of mm (without scalp focing). Many paametes such as the numbe of digitized points, the numbe of scalp points, the selection of scalp thesholds, as well as the initial guess poved to be cucial in obtaining this level of accuacy. Given appopiate choices fo the above paametes, the eo functions wee stable, obust, and smooth poviding eliability and confidence to the pocedues. As we have demonstated above, using eithe FRE o RE can lead to oveconfidence in egistation accuacy. We demonstate multiple instances whee TREs wee not adequately appoximated by the moe commonly used REs o FREs, which aises concens egading the use of these eo estimates in isolation. Fo instance, we showed that the RE can undeestimate the eo by seveal cm s in some subjects, that bette fits can yield lage FREs, and that thee ae a numbe of instances in which these eo estimates dissociate fom each othe. Hence, ou data suggest that in pactice RE and FRE ae fequently uneliable and potentially misleading poxies fo the TRE. We theefoe advise using multiple eo measues when assessing coegistation methods, while always including a measue 1299