Int J CARS (2013) 8:87–97DOI 10.1007/s11548-012-0693-6

ORIGINAL ARTICLE

Toward a preoperative planning tool for brain tumor resectiontherapies

Aaron M. Coffey · Michael I. Miga · Ishita Chen ·Reid C. Thompson

Received: 30 January 2012 / Accepted: 18 April 2012 / Published online: 25 May 2012© CARS 2012

AbstractBackground Neurosurgical procedures involving tumorresection require surgical planning such that the surgical pathto the tumor is determined to minimize the impact on healthytissue and brain function. This work demonstrates a predic-tive tool to aid neurosurgeons in planning tumor resectiontherapies by finding an optimal model-selected patient ori-entation that minimizes lateral brain shift in the field of view.Such orientations may facilitate tumor access and removal,possibly reduce the need for retraction, and could minimizethe impact of brain shift on image-guided procedures.Methods In this study, preoperative magnetic resonanceimages were utilized in conjunction with pre- and post-resec-tion laser range scans of the craniotomy and cortical surfaceto produce patient-specific finite element models of intraop-erative shift for 6 cases. These cases were used to calibratea model (i.e., provide general rules for the application ofpatient positioning parameters) as well as determine the cur-rent model-based framework predictive capabilities. Finally,an objective function is proposed that minimizes shift subjectto patient position parameters. Patient positioning parameterswere then optimized and compared to our neurosurgeon as apreliminary study.

A. M. Coffey · M. I. Miga · I. ChenDepartment of Biomedical Engineering, Vanderbilt University,P.O. 1631, Station B, Nashville, TN 37235, USA

M. I. Miga · R. C. ThompsonDepartment of Neurological Surgery, Vanderbilt UniversityMedical Center, T-4224MCN/VUMC,Nashville, TN 37232 2380, USA

M. I. Miga (B)Department of Radiology and Radiological Sciences,Vanderbilt University Medical Center, CCC-1106MCN/VUMC,Nashville, TN 37232 2675, USAe-mail: michael.miga@vanderbilt.edu; michael.i.miga@vanderbilt.edu

Results The proposed model-driven brain shift minimiza-tion objective function suggests an overall reduction of brainshift by 23 % over experiential methods.Conclusions This work recasts surgical simulation from atrial-and-error process to one where options are presented tothe surgeon arising from an optimization of surgical goals.To our knowledge, this is the first realization of an evaluativetool for surgical planning that attempts to optimize surgicalapproach by means of shift minimization in this manner.

Background

As current standard of care, neurosurgical interventioninvolving tumor resection is performed with the aid of neuro-navigation systems. The basis of these neuronavigation sys-tems consists of the use of a localizer and a computer systemto relate position and orientation of a tracked surgical instru-ment to features of interest in a preoperative tomographicimage, enabling what is known as image-guided surgery(IGS). IGS systems improve spatial orientation during theintraoperative planning phase as well as assist in performingresection. The current commercial IGS systems used in neu-rosurgery make the underlying assumption that the patient’shead and its contents behave as a rigid body. However, studieshave shown [1,2] that this assumption is invalid owing to sig-nificant positional error in the brain between the time of imag-ing and the time of the interventional procedure after openingthe skull. Often referred to as ‘brain shift’, the nonrigid defor-mation of the brain occurring upon performing a craniotomyis due to a variety of mechanisms including hyperosmoticdrugs, edema, gravity-induced sagging, and surgical manip-ulation such as from retraction and tissue resection [1,3,4].

Strategies for the compensation of intraoperative brainshift have fallen into two categories—active intraoperative

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imaging [4–7] and preoperative image updates based uponthe estimated displacements derived from biomechanicalmodels [8–13]. With the latter, many approaches have beenproposed with variations usually dependent on the data usedto constrain the models. For example, the work by Ferrantet al. [10] used intraoperative magnetic resonance imagingdata and biomechanical models to achieve volumetric intra-operative transforms, while the work by Chen et al. [14] wassolely driven by cortical surface deformation data. Typically,data-driven computer models can compensate for 70–80 % ofthe brain shift on average depending on the study [14]. Thisdegree of compensation for intraoperative brain shift sug-gests that a biomechanical simulation environment may beconsidered sufficiently capable of translating complex sur-gical events into accurate estimates of tissue response. Thepotential for using such models in a predictive sense for deter-mining the effects of surgical decisions is intriguing.

With an effective preoperative planning tool based on bio-mechanical modeling, the possibility exists for anticipatingand optimizing the surgical orientation to mitigate guidancedegradation or to enhance access. In this paper, we hypoth-esize that it may be possible to parameterize the planningvariables to minimize the deleterious effects of shift after thesurgeon has selected the approach. In addition, although notpresented in this paper, we also hypothesize that computermodels combined with surgical parameter optimization cangenerate ‘favorable’ brain shifts that facilitate visualizationand presentation of the tumor for resection. To summarize,the goal of this paper is to present a framework that obtainsan ‘optimal’ orientation to minimize shift, and in so doing, apotential tool is created to further investigate surgical therapyplanning.

Methods

As indicated above, the methods to be introduced represent aninitial optimization framework that provides guidance to sur-geon-elected intraoperative presentation variables to achievebest respective outcome. As determining the optimal surgicalorientation is currently a subjective assessment, this was pro-vided by our veteran neurosurgeon [RCT]. To qualify, [RCT]is currently Professor and Chairman of the Department ofNeurological Surgery, Director of Neurosurgical Oncology,Director of the Vanderbilt Brain Tumor Center. [RCT] hasover 20 years of neurosurgical experience and has performedover 3,000 craniotomies—the majority of which are for braintumors. This work reflects the creation of a predictive toolbased upon those experiences and awaits further accrual toconfirm those ‘optimal’ surgical orientations. Prior to relay-ing the optimization framework, the biomechanical modelfor modeling brain deformation must be calibrated such that

it encompasses the widest possible parameter space reflectiveof intraoperative conditions.

Calibrated computational model

Building upon previous work [9], preoperative images wereused to generate computational models for six patients. Thepreoperative MR images were acquired on Philips Achi-eva Dual Nova 1.5T using three-dimensional spoiled gra-dient recalled echo (3D-SPGR) sequences that are typicalfor neurosurgical image-guidance with 1 mm in-plane reso-lution and 1.2 mm slice thickness. Image segmentation wasachieved using an automatic approach that uses an adaptivebasis algorithm [15]. From segmented surfaces, a subject-specific 3D finite element computational model is generated,which has been shown to predict deformations as a resultof various patient head orientations during surgery [16].This model is capable of simulating the effects of hyperos-motic drugs, gravity-induced deformation, retraction, resec-tion, and swelling from edema. The model treats soft tissuesas a poroelastic medium according to Biot’s consolidationequations. The equations associated with mechanical equi-librium and continuity are as follows

∇·G∇u + ∇ G

1 − 2ν(∇·u) − α∇ p = (ρcsf − ρtissue) g (1)

α∂

∂t(∇·u) − ∇·k∇ p = kcapp

(pcapp − p

)(2)

with the details reported extensively in [9,17,18]. Importantto the realization in this paper, kcapp is the capillary perme-ability and pcapp the intracapillary pressure. The right handsides of equations (1) and (2) describe terms used to simulatebrain sag due to gravitational forces, and the volume-reduc-ing tissue contraction associated with hyperosmotic drugssuch as mannitol [9]. The material properties used for clini-cal cases are listed in Table 1.

As part of the process of calibrating a ‘general’ modelsubject for surgical prediction, it was found that varyingcapillary permeability kcapp values (associated with swell-ing and hyperosmotic drugs) produced improved results inmodel-fitting of the surgical parameters to the laser rangescan (LRS) deformation data over a series of clinical cases.To determine a general functional relationship, kcapp calibra-tion curves were fit via manual optimization for six differentclinical cases based on the best shift predictions for eachcase. Table 2 reports the values found in the fitting process.A general model for the best-fit kcapp across cases was found,

kcapp = −5.2236 × 10−12V 2 + 8.6156 × 10−10V, (3)

where V is the volume of the tumor in cm3, and kcapp hasunits of Pa−1 s−1. With respect to the fit to data, the squaredcorrelation coefficient value was R2 = 0.88.

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Table 1 Model material properties

Symbol Description Value Units

G,white and gray Shear modulus 724 N/m2

ν Poisson’s ratio 0.45 Unitless

ρt Tissue density 1,000 kg/m3

ρf CSF density 1,000 kg/m3

g gravity constant 9.81 m/s2

α Saturation constant 1 Unitless

1/S Compressibility constant 0 1/Pa

kwhite Hydraulicconductivity ofwhite matter

1 × 10−10 m3s/kg

kgray Hydraulicconductivity ofgray matter

5 × 10 −12 m3s/kg

kcapp,white and gray Capillary permeability Variable 1/(Pa s)

pcapp,mannitol Intracapillary pressure −3,633 Pa

Table 2 The data points for 6 cases used to establish the kcapp versustumor volume curves

Case Tumor volume (cm3) Tumor radius (m) kcapp, forces

1 63.6103 0.024756 3.00E-08

2 60.2338 0.025640 3.75E-08

3 10.7679 0.014384 7.00E-09

4 22.9275 0.017897 2.10E-08

5 5.2989 0.012820 8.00E-09

6 27.6589 0.018485 1.50E-08

The last aspect to define a predictive computational biome-chanical model is to prescribe boundary conditions. In pre-vious work, Dumpuri et al. in [16] developed a frameworkto automatically deploy boundary conditions as a functionof the head orientation. Briefly, once the head was oriented,boundaries at high elevations relative to gravity were free todeform, boundaries at lower elevations were allowed to slidealong the cranial wall but not allowed to move normal to thewall (i.e., a slip condition), and boundaries near the brainstem were fixed. With respect to interstitial pressure, bound-aries above cerebrospinal fluid drainage levels were opento atmosphere, while boundaries below were prescribed nodrainage conditions. An example boundary condition set isshown in Fig. 1 (boundary conditions reflect a head rotationabout the cranial-caudal axis with some rotation about theventral-dorsal axis).

Objective function and optimization

With the model prescribed, a general platform for the pre-diction of brain deformations during tumor resection isprovided. With respect to our participating neurosurgeon,(RCT), it was common practice to select head orientations

Z, m

X, m

Z, m

X, m

Pressure BCs: Blue = Atmosphere, Red = Flux

Displacement BCs: G = Stress-Free, K = Slip/Falx, B = Fixed

Fig. 1 Example boundary conditions, Example boundary conditionsof an orientation within an atlas set where (top) green crosses are stress-free (free to deform in x-, y-, and z-), black stars are slip nodes (nomovement in the normal direction), and blue circles are fixed nodes.(bottom) The CSF drainage level for the example set is shown wherered stars indicate submersion of the mesh element and blue crossesindicate atmospheric pressure

minimizing the impact of brain shift. More specifically,(RCT) would often choose alignments using the falx mem-brane to provide support and reduce anterior–posterior shiftinduced by gravity. This shift minimization strategy suggeststhe establishment of displacement-based metrics of the corti-cal surface as a primary component within our optimizationframework. Two such metrics were found useful: (1) min-imization of the lateral shift of the tumor center as viewedalong the line of sight established by the surgical ‘approach’vector to the tumor and (2) an area-based measure consist-ing of minimization of the change to the field of view in the

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craniotomy proved relevant. Quantification of the change inthe field of view was achieved by the classification of the cor-tical area within the craniotomy. The cortical area map beforeintervention was established based on the proposed site of thecraniotomy and estimated radius as prescribed by (RCT) inpreoperative planning. Using model predictions within thecontext of our optimization framework, the area in the crani-otomy was reassessed to determine regions common beforeand after deformation.

Based on this, an objective function was created for leastsquared error minimization of brain shift metrics. These met-rics varied with respect to the spherical angles phi and theta(see Appendix for further coordinate system details) associ-ated with changing patient orientation. The objective func-tion combining the metrics is written as

G(ϕ, θ) = min

{λ1 ‖A − Ao‖2 + λ2

∥∥∥�δ − �δ · �v

∥∥∥

2}

(4)

where A is the area of the craniotomy, and Ao is the areathat remains visually the same in the field of view such thatA–Ao is the area leaving the craniotomy, �v is the surgical‘approach’ vector, and �δ = [δx, δy, δz] are the tumor cen-ter x-, y-, and z-displacement components. The expression�δ − �δ·�v represents the lateral component of the tumor dis-placement as viewed along the line of sight of the ‘approach’vector. Owing to the difference in the measures associatedwith each brain shift metric, each metric required parameterscaling to prevent one measure from being unduly empha-sized in the optimization method. Additionally, the measurescould be further weighted for relative importance. Conse-quently, the scalars λi in Eq. (4) were empirically weightedfactors that were scaled with the inverse of variance associ-ated with each factor over a range of solutions. The optimiza-tion method used to find the minimum was the secant method(SM). The derivatives for the Jacobian matrix were con-structed using backward finite difference approximations.The optimization terminated when the absolute differencebetween objective function evaluations for successive orien-tations achieved a tolerance.

Experimental testing

LRS data of the cortical surface before and after deforma-tion were acquired for six clinical cases. All data acquiredfor patients were done so under an approved protocol bythe Vanderbilt University Institutional Review Board (IRB#010520). Prior to any acquisition and analysis, a signedinformed consent was obtained from the participant by(RCT). Texture-mapped LRS point clouds taken pre- andpost-resection of the operative field and transformed to thesame physical space were fit with radial basis function (RBF)surfaces. For each case, these RBF surfaces were segmentedto produce cortical surfaces and were used to define the cra-

niotomy area and shape (Fig. 2). As can be seen in Fig. 3,homologous points at vessel intersections identifiable in boththe pre- and post-resection cortical surfaces could be selectedand used as measurements of brain deformation. These caseswere used as a means to generate our ‘generic’ model pre-dictive framework, for example, the generation of Eq. (3) toaccount for mannitol effects. With each case, an exhaustivesearch of the model parameter space was done to generate thesurgical presentation parameters for the best possible fit of thedeformation data as derived from intraoperative LRS. Thesewould represent a best model-fit of surgical parameters asexecuted by [RCT] in an effort to minimize brain shift basedon surgical experience. While direct measurements of somesurgical parameters, for example, head orientation, would bebetter than that determined by a best model-fit, it should benoted that this is very difficult in practice; that is, often dur-ing the course of a procedure, elevations and head tilts arechanged through manipulations of the surgical bed. In somerespect, the parameters derived in this search represent a bestaverage fit over the range of parameters experienced duringa case. With respect to analysis, from this fit, the shift oftargeted landmarks as predicted by the model could then becompared to the shift of the same landmarks resulting fromuse of the surgical parameters as determined by the optimi-zation framework. This allows us to compare our optimizedsurgical parameter set to that used clinically by [RCT], aswell as to provide a model estimate to the degree an optimizedapproach might be better than [RCT]’s clinical results.

Objective function optimization proceeded with creatinga sampling of patient orientations defining an extent of theparameter space for each metric, that is, an atlas of parameter-ized deformations. The atlas extent included the orientationsby [RCT]. As an initial condition for orientation from whichto begin optimization, the default patient position consistedof gravity directed along the anterior–posterior axis with thepatient lying supine (head neutral) —a presentation that isoften adopted by many practicing neurosurgeons. This supinepatient position also served as the neutral position for rotationangles in a spherical coordinate system defined as ϕ = 0◦ forrotation about the cranial–caudal axis and θ = 0◦ for tiltingthe head about the ventral-dorsal axis (see Appendix for coor-dinate system details). Given Eq. (4), the optimal solution thatminimized shift subject to the surgical parameters of thepatient-specific model geometry solution distribution wasdetermined.

Results

Calibrated model

The clinical case analysis proceeded with patient-specificmodels constructed from the six sets of image tomograms

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Brain surface Falx cerebri Tumor surface Craniotomy

Fig. 2 Patient-specific modeling. Coronal, sagittal, and axial views ofcase 1 (top) and case 3 (bottom) as examples showing the patient-spe-cific model features where brain surface is red, the tumor surface is

blue, falx is green, and the textured preoperative LRS surface indicatesthe craniotomy placement: (left) coronal (middle) sagittal (right) axial

and LRS scan data. Figure 2 illustrates frontal lobe (case 1)and temporal lobe (case 3) descriptions of example models.The coronal, sagittal, and axial views detail the brain sur-face, the extent and shape of the patient-specific falx insertedinto the model, the craniotomy used as the field of view, andthe tumor. The defined craniotomy encompassed the maxi-mum cortical surface area with surface features clearly visi-ble in the LRS data. Figure 3 shows the homologous pointsmentioned previously, for example, cases 1 and 6 and thethin-plate spline fitting of the preresection cortical surfaceto the post-resection cortical surface using those points ascontrols. The point distribution sought to capture the extentof intraoperative brain shift around the edges of the resec-tion cavity and surrounding tissue. This type of data was col-lected for all cases and used in the model calibration process.Observing Table 3, columns 9–13 report the best possible fitusing our model to the LRS data as procedurally executed by[RCT] over the 6 cases. The average overall cortical displace-ment of the best model-fit of the surgical parameters for thecases is 11.2 mm, or 93 % of the measured LRS deformationdata, and the lateral shift component of the cortical surfacelandmarks is 5.5 mm, or 86 % of the LRS values. While thesemagnitudes of shift are representative, the accuracy of pre-diction of the best-fit parameters reflected 74.2 %, which iscomparable to studies reported in the literature.

Optimization characterization and performance

Post-processing of the atlas displacement solutions producedthe fitted parameter space for finding optimal orientation permetric (Fig. 4, case 2 shown). Objective function evalua-tions for the atlas orientations similarly formed a parameterspace (Fig. 5) whose minimum could be found by the secantmethod.

Table 3 also describes the orientations converged upon bySM optimization of the objective function (columns 5, 6, 7,8), which can be directly compared to the best model-fit of thesurgical parameters (columns 9, 10, 12, 13), thus providingdisplacement-based quantification of the optimization frame-work with respect to the intraoperatively measured LRSdeformation data. Figure 6 displays three examples (cases2, 5, and 6 in each column, respectively) of the area classifi-cation mapping produced from the LRS data (top row), thebest model-fit orientations of the surgical parameters (mid-dle row), and the SM optimization orientations minimizingbrain shift (bottom row). Table 4 records the quantificationof the measures displayed in Fig. 6. It was found that the SMoptimization orientations correspond to an overall reductionin brain shift in comparison with the LRS deformation dataon the basis of both change of cortical surface area and lateralshift of the tumor center.

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Fig. 3 LRS Registration and Area Mapping, (left column) case 1 and(right column) case 6 with (top) examples of homologous control pointselection on the preresection LRS, and (middle) the post-resection LRS

surfaces that result after thin-plate spline image registration using thesecontrol points. Also shown (bottom) are overlays of the deformed pre-LRS surface in blue and the post-surface in red

With respect to the six cases, the average differencesbetween orientation angles (ϕ and θ) determined usingour model-derived SM optimized prediction and the bestmodel-fit of the surgical parameters as determined from theLRS deformation data [and as executed by (RCT)] were8.2◦ ± 3.7◦ and 14.7◦ ± 9.3◦, respectively, for head rotationand tilt. It should be noted that the fitted LRS deformationdata are not necessarily the optimum for intraoperative shiftminimization, but rather the orientation selected by (RCT)as optimum (an experiential orientation thought to minimizeshift).

Discussion

Given the distinctive nature of the cortical surface area withits pattern of blood vessels and sulci that serve as visual land-marks of location, its classification into regions newly visible,shifting out of view, or remaining visible constitutes a logicaland significant metric to qualify shift. Area remaining vis-ible corresponds to maintaining the presence of landmarksconducive to surgical guidance, suggesting its maximization.Proper model area classification of cortical surface visible inthe craniotomy requires fidelity in the LRS deformation data.

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Int J CARS (2013) 8:87–97 93

Tabl

e3

Bes

tsur

gica

land

mod

elor

ient

atio

nsw

ithL

RS

defo

rmat

ion

data

Cas

eT

umor

LR

Ssh

ift

Lat

eral

shif

tSM

Opt

imiz

edM

odel

shif

tL

ater

alsh

ift

Bes

tsur

gica

lM

odel

shif

tL

ater

alsh

ift

Num

ber

Loc

atio

nof

cort

ical

LR

Sco

rtic

alof

cort

ical

mod

elco

rtic

alof

cort

ical

mod

elco

rtic

alSu

rfac

epo

ints

(mm

)

Surf

ace

poin

ts(m

m)

phi,◦

thet

a,◦

Surf

ace

poin

ts(m

m)

Surf

ace

poin

ts(m

m)

phi,◦

thet

a,◦

%sh

ift

pred

ictio

nSu

rfac

epo

ints

(mm

)

Surf

ace

poin

ts(m

m)

1L

F14

.38.

088

.131

.913

.24.

874

.2−1

6.5

66.9

13.2

7.8

2L

F22

.217

.974

.232

10.3

3.3

103.

812

.367

.718

.414

.5

3LT

8.8

3.0

89.7

09.

71.

274

.8−2

2.4

87.4

92.

8

4LT

11.8

1.6

84.9

−89

0.7

75−2

4.4

89.8

12.1

1.6

5R

T8.

61.

8−1

07.1

−16

7.1

0.4

−76.

2−1

4.1

77.7

9.2

1.4

6LT

P6.

95.

890

.718

.36.

51.

196

.1−4

.855

.55.

54.

8

Ave

rage

12.1

6.4

9.3

1.9

74.2

11.2

5.5

The target landmark points used to assess shift prediction aresparse measures and do not represent a comprehensive mea-sure of fidelity. Consequently, it is difficult to use their eval-uation for the sole assessment of optimization performance.Trying to maintain the original area within the craniotomymay not physically be a complete measure but is more com-prehensive. However, further investigation of more clinicalcases toward this end is necessary to determine its robustnessand does serve as an important limitation to this work at thistime. Nevertheless, the results reported here using these shiftmetrics do suggest considerable strength to the framework.

Closer examination of the shift prediction percentagesshowed the temporal lobe cases had better predictionsbecause the homologous points were observed to displaceintraoperatively more uniformly in direction than in the othercases which the model less easily matched. The frontal lobecases had large movements of tissue into the resection cav-ities. Case 6 was unusual in that the tumor lay close to thefalx and considerable contraction of the surrounding corticalsurface into the resection cavity occurred, more so than inany other case. With the recent work intraoperatively, it hasbeen observed that model-predicted displacements providedby our framework do not completely account for contractiontoward the resection cavity, which is caused by the removalof the supportive tumor mass, as well as the stress-relievingtumor debulking process [14]. Visual examination of the cor-tical area distributions in Fig. 3 demonstrates this contractionof tissue. Since collapsing of tissue into a resection cavityappears an inevitable surgical phenomenon upon removal ofthe supportive tumor mass, the addition of debulking stressseems a sound direction to pursue to attain a more accuratemeasure of area remaining visible. Modeling the resectioncavity decompression through application of these debulkingstresses is currently under investigation [19,20], but valida-tion of the shift predictions by the model is still an area offuture work.

As reported in the Results, the average model cortical shiftfor each case in Table 3 intriguingly shows high fidelity to theLRS deformation data if the model is allowed to search thesurgical parameter space to achieve the best model-fit of brainshift based on available data. Similarly, the SM optimized ori-entations’ average overall cortical shift of 9.3 mm comparedwith the best surgical match of 12.1 mm in Table 3 sug-gests that optimization of the parameter space could reduceshift procedurally by about 23 % overall. Furthermore, thegeneral lateral shift reduction of the cortical landmarks was63 %. Case 2 demonstrated an 8 mm shift reduction, or 44% overall, with a 77 % reduction in lateral shift. Table 4shows the average reduction in change of cortical area inthe craniotomy amounted to 60 % less change relative to theprocessed LRS deformation data. The average lateral shiftof the tumor center in comparison with the best model-fit ofthe surgical parameters saw a similar reduction of 70 % in

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94 Int J CARS (2013) 8:87–97

68 56 44 32 20 8 -4

-8

0

8

16

24

32

40

48

56

64

-1680

-8

8

16

24

32

40

48

56

64

-1668 56 44 32 20 8 -480

0

Masked Area Leave Masked Tumor Center Lateral Disp Mag

θ, d

egre

es

degrees,degrees,

θ, d

egre

es

Fig. 4 Atlas results for shift metrics. Brain shift metric surfaces derived from masked orientation atlases for case 2 (left) indicating area leaving(m2) and (right) representing tumor center lateral displacement magnitude (m)

68 56 44 32 20 8 -4

-8

0

8

16

24

32

40

48

56

64

-1680

θ, d

egre

es

Masked Objective Function

degrees

Fig. 5 Atlas-derived objective function. Masked objective function forcase 2. (left) is objective function consisting of area and tumor centerlateral shift measures equally weighted. Darker areas are smaller objec-tive function values

shift across cases. The reduction in change of cortical areacan be attributed to the displacements being more downwardalong the surgical ‘approach’ vector than lateral to it. This is

corroborated by the 60–70 % reduction in lateral shift of thecortical surface landmarks and the tumor center.

Comparison of the SM optimized orientations with thebest fit of the surgical parameter space highlights several fea-tures of note. The angular differences reported suggest betteragreement of the optimal orientation with the surgical orien-tation in the rotation angle ϕ than in the tilt angle θ. This sug-gests that minimization of the anterior–posterior (A-P) shiftof the brain on the part of [RCT] may be a higher priority inselecting orientation. Accordingly, [RCT] likely chooses totilt the head to facilitate ease of surgical access and alleviatepatient safety concerns with jugular venous return blood flowrather than to minimize shift per se. The orientation anglesalso suggest an overall trend whereby tumor locations thatvary from frontal to temporal lobe indicate a lateral decubi-tus position on the side contralateral to the tumor hemisphereis desirable from the standpoint of reducing A-P shift. Thisposition uses the support of the falx membrane as a naturalconstraint to prevent displacement across the falx while rotat-ing the head sufficiently perpendicular to gravity to minimizethe A-P shift. Examination of tilt angles for the optimal ori-entations revealed a relationship between the center of thecraniotomy and the volumetric centroid of the brain given alateral decubitus position. For tumors above the level of thebrain centroid (approximately between the two hemispheresat the level superior to the ears), the head should be tilted

Table 4 Quantitative areametrics and the magnitude oftumor center lateraldisplacement

* Change in area�A = (AEnter + ALeave)/A0

Measure Case 1 Case 2 Case 3 Case 4 Case 5 Case 6

Craniotomy area (cm2) 42.3 23.8 10.5 10.6 5.8 15.5

% Change in area* (LRS) 41 % 47 % 16 % 31 % 21 % 32 %

% Change in area* (Best surgical) 44 % 71 % 21 % 20 % 13 % 33 %

% Change in area* (SM optimized) 19 % 19 % 12 % 9 % 3 % 11 %

Lateral shift (mm) (Best surgical) 8.5 13.8 2.4 1.5 0.6 5.0

Lateral shift (mm) (SM optimized) 1.0 1.2 1.6 0.2 0.4 0.8

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,Z

m

X, m

Y, m

,Z

m

X, m Y, m

,Z

m

X, m

Y, m

,Z

m

X, m

Y, m

,Z

m

X, mY, m

,Z

m

X, m

Y, m

,Z

m

X, m

Y, m

,Z

m

X, mY, m

,Z

m

X, m

Y, m

Area: Red = Same, Blue = In, Yellow = Out

Fig. 6 Area classification maps. Area classification maps whereinyellow denotes area leaving the craniotomy, blue shows area enteringthe craniotomy, and red indicates cortical surface area staying visible.Columns correspond to cases 2, 5, and 6, which span the range of tumor

volumes. The 1st row consists of the LRS area mapping, 2nd row thebest model-fit of the surgical parameters, and 3rd row the SM optimizedorientation

down toward the shoulder contralateral to the tumor, and fortumors below that level in general, the head should be tiltedup. Thus, the Table 3 angular data, shown in Fig. 7 for cases2, 4, and 5, suggest a reasonable approximation of the headrotation angle would be to align gravity along the vector fromthe craniotomy center to the brain centroid.

Minimal shift of the tumor center appears to occur whenthe area distribution is located concentrically within the cra-

niotomy. The optimal atlas orientations in Fig. 6 provide sup-port for this idea. The area entering and leaving the field ofview of the craniotomy displays a notable degree of sym-metry about the craniotomy perimeter in their distributionsand quantity. The perimeter of the shape formed by the areaentering and the area remaining the same in the field of viewexhibits an intriguing degree of concentricity with the crani-otomy perimeter. This concentricity is apparent in Fig. 6.

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0.18

0.16

0.14

0.12

0.08

0.10

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Craniotomy SM OptimizedBest Surgical Supine

Fig. 7 Patient orientations, cases 2, 4, and 5 shown with the supine orientation (green), the best model-fit of the surgical parameters as executedby [RCT] (black), and the SM optimized orientation (red) from the angular data in Table 3

Measurement of shift of the tumor center during surgerywould be challenging, whereas movements of the corticalsurface are readily achieved. The coincidence of the occur-rence of minimum lateral shift with a concentric area distribu-tion suggests a possible method of ascertaining how close tooptimum a surgical orientation manages to achieve. With areaentering with a symmetric distribution and little area leavingfor the optimal orientation, the implication is that the optimalorientation likely occurs where there is an increased amountof compression of the tumor surface by the surroundinghealthy tissue. This hypothesis could be tested in future work.

Conclusions

Conceptualizing a framework whereby biomechanical mod-els could suggest orientations to the surgeon to influencethe impact of shift seems promising. Furthermore, the workpresented here addresses the deformation correction prob-lem associated with image-guided neurosurgery from theperspective of preoperative planning. It is intriguing in thatthis work recasts surgical simulation from a trial-and-errorprocess to one where options are presented to the surgeonarising from an optimization of surgical goals (in this case

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minimization of brain shift). In the future, one could possiblyenvision situations where the surgeon may desire brain shiftto help illuminate an approach into the disease focus. Ulti-mately, this represents a very different realization of guid-ance whereby computer models can assist in the delivery oftherapy by providing additional predictable surgical manip-ulations. To our knowledge, this is the first realization of anevaluative tool for surgical planning that attempts to opti-mize surgical approach by means of shift minimization inthis manner. The results presented demonstrate exciting clin-ical potential for aiding surgeons in the delivery of surgicaltherapies for tumors.

Acknowledgments This research was supported by NIH-NationalInstitute for Neurological Disorders and Stroke Grant # R01 NS049251.The authors wish to thank the participating neurosurgeon RCT and theoperating room staff for their time and assistance

Conflict of interest The authors declare that they have no conflict ofinterest

Appendix

Spherical coordinate system reference

For head orientation purposes, a spherical coordinate sys-tem was used. When overlaid on a set of Cartesian axes, thedefault orientation of the patient lying supine correspondsto the gravity vector being aligned along the positive y axiswhile possessing rotation angles in spherical coordinates of[0◦] for phi and theta. For purposes of nomenclature, theangle phi is considered to indicate the degree of rotation ofthe head, whereas theta is considered to specify tilt. A positiverotation in phi of +90◦ for a left hemisphere tumor, therefore,results in the patient lying in a lateral decubitus position onthe side contralateral to the tumor with the gravity normal tothe plane of the falx. From this position, a positive theta tiltsthe head down, and a negative theta tilts the head up.

References

1. Hartkens T, Hill DLG, Castellano-Smith AD, Hawkes DJ, MaurerCR, Martin AJ, Hall WA, Liu H, Truwit CL (2003) Measurementand analysis of brain deformation during neurosurgery. IEEE TransMed Imaging 22(1):82–92

2. Roberts DW, Hartov A, Kennedy FE, Miga MI, Paulsen KD(1998) Intraoperative brain shift and deformation: a quantita-tive analysis of cortical displacement in 28 cases. Neurosurgery43(4):749–758

3. Hastreiter P, Rezk-Salama C, Soza G, Bauer M, Greiner G,Fahlbusch R, Ganslandt O, Nimsky C (2004) Strategies for brainshift evaluation. Med Image Anal 8(4):447–464

4. Nimsky C, Ganslandt O, Cerny S, Hastreiter P, Greiner G,Fahlbusch R (2000) Quantification of, visualization of, and com-pensation for brain shift using intraoperative magnetic resonanceimaging. Neurosurgery 47(5):1070–1079

5. Butler WE, Piaggio CM, Constantinou C, Niklason L, GonzalezRG, Cosgrove GR, Zervas NT (1998) A mobile computed tomo-graphic scanner with intraoperative and intensive care unit appli-cations. Neurosurgery 42(6):1304–1310

6. Letteboer MMJ, Willems PWA, Viergever MA, NiessenWJ (2005)Brain shift estimation in image-guided neurosurgery using3-D ultrasound. IEEE Trans Biomed Eng 52(2):268–276

7. Ji SB, Wu ZJ, Hartov A, Roberts DW, Paulsen KD (2008) Mutual-information-based image to patient re-registration using intra-operative ultrasound in image-guided neurosurgery. Med Phys35(10):4612–4624

8. Castellano-Smith AD, Hartkens T, Schnabel JA, Hose DR, Liu AK,Hall WA, Truwit CL, Hawkes DJ, Hill DLG (2001) Constructingpatient specific models for correcting intraoperative brain defor-mation. In: Niessen WJ (ed) Medical image computing and com-puter assisted intervention, vol 2208. Springer, Utrecht, pp 1091–1098

9. Dumpuri P, Thompson RC, Cao AZ, Ding SY, Garg I, DawantBM, Miga MI (2010) A fast and efficient method to compensatefor brain shift for tumor resection therapies measured between pre-operative and postoperative tomograms. IEEE Trans Biomed Eng57(6):1285–1296

10. Ferrant M, Nabavi A, Macq B, Black PM, Jolesz FA, KikinisR, Warfield SK (2002) Serial registration of intraoperative MRimages of the brain. Med Image Anal 6(4):337–359

11. Hagemann A, Rohr K, Stiehl HS, Spetzger U, GilsbachJM (1999) Biomechanical modeling of the human head for physi-cally based, nonrigid image registration. IEEE Trans Med Imaging18(10):875–884

12. Skrinjar O, Nabavi A, Duncan J (2002) Model-driven brain shiftcompensation. Med Image Anal 6(4):361–373

13. Lunn KE, Paulsen KD, Liu FH, Kennedy FE, Hartov A,Roberts DW (2006) Data-guided brain deformation modeling:evaluation of a 3-D adjoint inversion method in porcine studies.IEEE Trans Biomed Eng 53(10):1893–1900

14. Chen I, Coffey AM, Ding SY, Dumpuri P, Dawant BM, Thomp-son RC, Miga MI (2011) Intraoperative brain shift compensation:accounting for dural septa. IEEE Trans Biomed Eng 58(3):499–508

15. D’Haese PF, Duay V, Merchant TE, Macq B, Dawant BM (2003)Atlas-based segmentation of the brain for 3-dimensional treatmentplanning in children with infratentorial ependymoma. In: Medi-cal image computing and computer-assisted intervention— Miccai2003, Pt 2, vol 2879. Springer, Berlin, pp 627–634

16. Dumpuri P, Thompson RC, Dawant BM, Cao A, Miga MI(2007) An atlas-based method to compensate for brain shift: pre-liminary results. Med Image Anal 11(2):128–145

17. Miga MI, Paulsen KD, Lemery JM, Eisner SD, Hartov A, Ken-nedy FE, Roberts DW (1999) Model-updated image guidance: ini-tial clinical experiences with gravity-induced brain deformation.IEEE Trans Med Imaging 18(10):866–874

18. Paulsen KD, Miga MI, Kennedy FE, Hoopes PJ, Hartov A, RobertsDW (1999) A computational model for tracking subsurface tissuedeformation during stereotactic neurosurgery. IEEE Trans BiomedEng 46(2):213–225

19. Coffey AM (2010) Prediction of patient orientation with mini-mized lateral shift for brain tumor resection therapies. VanderbiltUniversity, Nashville

20. Coffey AM, Garg I, Miga MI, Thompson RC (2010) An evalu-ative tool for preoperative planning of brain tumor resection. In:Wong KW, Miga MI (eds) SPIE medical imaging 2010: visuali-zation, image-guided procedures, and modeling, vol 7625. SPIE,San Diego, 762531-1–762531-12

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