Anticipation of Brain Shift in Deep Brain Stimulation

Automatic Planning

Noura Hamze, Alexandre Bilger, Christian Duriez, Stephane Cotin, Caroline

Essert

To cite this version:

Noura Hamze, Alexandre Bilger, Christian Duriez, Stephane Cotin, Caroline Essert. Antici-pation of Brain Shift in Deep Brain Stimulation Automatic Planning. IEEE Engineering inMedicine and Biology Society (EMBC’15), Aug 2015, Milan, Italy. IEEE, pp.3635 - 3638 2015,<10.1109/EMBC.2015.7319180>. <hal-01242851>

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Anticipation of brain shift in Deep Brain Stimulation automaticplanning

Noura Hamze1,4, Alexandre Bilger2, Christian Duriez3, Stephane Cotin3,4 and Caroline Essert1,4

Abstract— Deep Brain Stimulation is a neurosurgery proce-dure consisting in implanting an electrode in a deep structureof the brain. This intervention requires a preoperative planningphase, with a millimetric accuracy, in which surgeons decide thebest placement of the electrode depending on a set of surgicalrules. However, brain tissues may deform during the surgerybecause of the brain shift phenomenon, leading the electrode tomistake the target, or moreover to damage a vital anatomicalstructure. In this paper, we present a patient-specific automaticplanning approach for DBS procedures which accounts forbrain deformation. Our approach couples an optimizationalgorithm with FEM based brain shift simulation. The systemwas tested successfully on a patient-specific 3D model, andwas compared to a planning without considering brain shift.The obtained results point out the importance of performingplanning in dynamic conditions.

I. INTRODUCTION

Deep Brain Stimulation (DBS) is a neurosurgery pro-cedure used to treat a variety of neurological disorders,most commonly Parkinson’s disease, dystonia, or essentialtremors. It consists in implanting an electrode in a precisebrain target, generally the subthalamic nucleus, to stimulateit permanently. The stimulation is done via a neurostimulator,implanted under the patient’s chest skin, that delivers elec-trical impulses through an extension wire to metallic leadslocated at the tip of the electrode.

The success of the intervention and the reduction of thepostoperative symptoms depend on an accurate placement ofthe stimulating leads at the target location.

Moreover, a misplacement of the electrode may lead tothe stimulation of other structures causing side effects, or amassive hemorrhage if the electrode meets a vessel.

Neurosurgeons use MRI and CT images to perform a rig-orous preoperative planning: they identify and locate the tar-get within the brain, and trace the trajectory of the electrode.The trajectory planning is subjected to a set of surgical rulesto ensure both the safety of the patient and the effectivenessof the procedure. In fact, this preoperative planning step istime-consuming since it is still performed manually in mostDBS centers. During the surgery, a burr hole is drilled inthe patient’s skull, and when the skull and the dura mater

*This work was supported by the French National Research Agency(ANR) through the ACouStiC project grant (ANR 2010 BLAN 0209 02)

1Noura Hamze and Caroline Essert are with ICube, University ofStrasbourg, France hamze,essert@unistra.fr

2Alexandre Bilger is with the University of Luxembourg, Luxembourgalexandre.bilger@uni.lu

3Christian Duriez and Stephane Cotin are with INRIA, Francechristian.duriez,stephane.cotin@inria.fr

4Noura Hamze, Caroline Essert and Stephane Cotin are affiliated withthe Institut Hospitalo-Universitaire de Strasbourg, France

are open, cerebrospinal fluid (CSF) may leak through thehole leading to a brain deformation called brain shift. Thisphenomenon, which is hard to accurately anticipate, caneffectively alter the desired results of the intervention. Thisis due to the difference between the preoperative planning instatic condition where no deformation is considered, and theintra-operative dynamic condition where the brain deforms.

In this paper, we address DBS planning in dynamic condi-tions. We present a patient-specific method which proposesautomatically an optimized safe electrode trajectory for DBSprocedures and accounts for brain deformation.

II. RELATED WORKS

Several techniques can be adpoted for modeling the be-haviour of brain tissue. A mass-spring-damper model isused when fast computation is preferred to accuracy, forinstance for real-time interaction. For a precise planning, amore accurate model is a better choice. It means a highercomputational time which can be acceptable, but needs toremain compatible with clinical use.

Most of the physics-based brain deformation models arebased on FEM method, but differ from each other by thechoice of the constitutive equation. [10] use a linear constitu-tive equation, while [12] introduced a non-linear hyperelasticmodel. The law determines the tissue behaviour, but thereis no consensus about a constitutive equation unifying allthe applications, such as simulating deformation during acar crash or a neurosurgery. Brain deformation models havebeen widely used for training systems, registration of medicalimages [10], or compensating brain shift [4], but not for thepreoperative planning of a surgery.

Due to the impossibility to predict CSF loss, [4] pre-computed different brain deformations for possible inputparameters, but the goal was to update the different structuresposition during the surgery which is not our case.

In DBS procedures, surgeons usually plan the interven-tions manually based on MRI and CT images, with theassistance of some interactive medical image visualizationworkstations such as Medtronics StealthStation or Cranial-Vault [6]. Despite their valuable assistance, the planningprocess remains mentally difficult and time-consuming. Inthe last decade, automatic planning solvers were introducedin many works. Some approaches maximize the distancebetween the trajectory and obstacle structures [3], [14],whereas others take into account a larger variety of placementrules classified into hard or soft constraints to optimizethe trajectory [2], [8], [15], and even to perform automatictargeting [6], [11].

To the best of our knowledge, no study investigated DBSautomatic trajectory planning accounting for brain deforma-tion. We propose a hybrid simulation/planning system toaddress this problem.

III. METHODS

A. Brain model and brain shift simulation

1) Brain deformation: The brain is considered as a softbody subject to the laws of continuum mechanics. One ofthe numerical methods to solve the governing equations ofmotion is the Finite Element Method (FEM). In this work,we use P1 Lagrange tetrahedral elements.

As the brain shift process occurs at a very low velocity,we consider the problem as quasi-static and only look for theconfiguration of the brain at that equilibrium, disregardingthe dynamic transient effects. Finally, the discrete equationto solve is

f(x) = 0 (1)

where x and f are respectively the position and the force vec-tors on the nodes of the tetrahedral elements. Here, f is a non-linear function of the position of the nodes x, and representsthe sum of the internal and external forces. To solve this non-linear equation, we use a first-order linearization at each timestep: f(x+dx) = f(x)+K(x)dx, where the Jacobian matrixK(x) = ∂f

∂x depends on the nodes position. This matrix iscalled stiffness matrix for the internal forces. The solutionof Equation 1 is then approximated with the first iteration ofthe Newton-Raphson algorithm. The resulting equation is alinear system solved with a Conjugate Gradient algorithm.This process is applied iteratively until reaching equilibrium.

Regarding the application of the simulation, brain defor-mation can be considered as small. This allows us to useHooke’s law to define the tissue behavior. It defines a linearrelationship between strain and stress. From this law, wecan write the local (relative to an element e) stiffness matrixKe =

∫ve

JeTDeJedV where ve is the volume of element e,

Je denotes a matrix providing strain-displacement relation-ship and De stands for the strain-stress relationship. In ourcase, with Hooke’s law, Je and De are constant. To handlelarge displacements (while maintaining small deformation),we use a co-rotational formulation [9], where the geometricnon-linearities are approximated with the rotation of theelement with respect to its initial configuration. With thisapproach, the stiffness matrix Kr

e of the element e is definedas Kr

e = ReTKeRe where Re is the rotation matrix of

element e. Finally, the global matrix K is assembled fromthe local element stiffness matrices Ke.

2) CSF model and boundary conditions:a) Interaction with bony structures: When the brain

deforms and moves, it may collide the endocranium. Oncethey have been detected, contacts are solved using Signorini’slaw 0 ≤ δ⊥λ ≥ 0. It establishes an orthogonal relationshipbetween the contact response force λ and the interpenetrationdistance δ. We ensure the Signorini’s condition is fulfilled atthe end of each time step by adding a term of constraints inEquation 1: f(x) = HTλ where H is a matrix containing

Fig. 1: Illustration showing the components of the simulation

the constraints directions and λ is Lagrange multiplierscontaining the constraint force intensities. λ is unknownand has to be computed. A linear complementary systemis obtained, and is solved using a Gauss-Seidel algorithm.More details on the overall solving process are given in [7].

b) Cerebro-spinal fluid: The main cause of brain shiftis a loss of Cerebro-Spinal Fluid (CSF) surrounding thebrain. The density of CSF is similar to water (ρ = 1007kg/m3). A loss of CSF leads to a change of pressure insidethe skull and causes a deformation of the brain. The actionof CSF on the brain is modeled with a hydrostatic pressure:

fCSF =

∫Se

(ρ g h+ p(z0)

)dS (2)

where Se is the surface of a submerged element belongingto the surface of the brain, g denotes the gravitationalacceleration, h stands for the height from a point to the fluidsurface, and p(z0) is the pressure of the point z0 located onthe fluid surface. Fig.1 illustrates the different componentsinto play in the simulation. The amount of brain shift iscontrolled by the fluid level. With a loss of CSF the fluidlevel, h, and the fluid forces decrease.

B. Trajectory planning

Our preoperative planning approach is based on a ge-ometric constraint solving method in static conditions wepreviously published in [8].

1) static environment: To implement a planning in staticconditions Es, we formalize the surgical rules into twocategories of geometric constraints: Hard constraints HC,and soft constraints SC. While HC express strict ruleswhich must not be violated such as crossing a vessel, SCexpress preferences such as keeping the trajectory as far aspossible from the ventricles. To solve HC, we extract fromthe initial skin surface Ω0 the feasible insertion zone Ωs

which satisfies HC. This is done by eliminating from theskin mesh the triangles that are invisible from the target.Afterwards, we compute an optimal trajectory based on anestimation of its quality in respect to SC. To this end,we assign a cost function fi to each SC, and create amain aggregative objective function f composed from allSC. By minimizing f using a derivative-free optimizationtechnique we obtain an optimal trajectory (insertion pointand direction).

f =

∑ni=1 wi.fi∑ni=1 wi

(3)

In Eq. 3, weights wi reflect the importance of each surgicalrule relatively to the others and are determined by surgeons.

2) dynamic environment: In order to implement a plan-ning in dynamic conditions Ed, we need to anticipate thepotential deformations caused by the brain shift phenomenonϕ. For now, it is not possible to determine preoperativelythe exact magnitude of a brain shift. It may vary from aminimum level ϕ0 (corresponding to no brain shift) to amaximum ϕmax (corresponding to full CFS loss through theentry point). However, we can estimate ϕmax for a givenentry point. For this reason, our objective is to find a safetrajectory whatever the brain shift intensity from ϕ0 to ϕmax

and including all possible intermediate levels ϕi.While in Es the planning is performed on the initial static

model Ms, in Ed it is computed on several deformed modelsMdϕ computed as described in Section III-A using SOFAbiomechanical simulation framework [1]. We precompute arange of simulations corresponding to levels ϕ0 to ϕmax andstore them as a patient-specific deformations database. Weaccess the simulations database during the planning processusing our planning plugin implemented in MITK [16].

Fig. 2: Schematic representation of the entry points (blue)of the initial skin mesh Ω0 lying at the same height h andlikely to lead to the same possible maximal brain shift ϕmax.

Our method consists in two phases:• Compute the feasible insertion zone in dynamic condi-

tions Ωd.• Compute the optimized trajectory in Ωd.To obtain Ωd we assign a height level h to each entry point

pi ∈ Ω0 (as illustrated in Fig.2). For each height h, we buildits corresponding deformed model Mdh by summing up allthe deformable models Mdϕ0

to Mdϕmaxresulting from ϕ0

to ϕmax. After that, we check whether pi satisfies HC onMdh to add it to Ωd, otherwise we exclude it.

In a second step, we apply the Nelder-Mead optimizationmethod [13] over Ωd to find the best trajectory. At eachiteration, we propose a candidate trajectory τ , get the modelMdh depending on the candidate entry point’s height h, andevaluate f(τ) on Mdh. The iterations are stopped when theimprovement of f falls under a threshold ε, then τ is storedas the optimal trajectory.

Fig. 3: Ω0 is the large rectangular patch, Ωs is a subset ofΩ0 and is the union of red and green shapes, and Ωd is asubset of Ωs and is the green mesh.

IV. EXPERIMENTAL RESULTS

We implemented our method on a patient-specific 3D brainmodel obtained thanks to pyDBS [5] pipeline. The modelconsists of surface meshes of the sulci, the ventricles, thesubthalamic nucleus, and a skin patch. A volumetric modelis built for the simulation part. Blood vessels being difficultto segment from MR images and knowing that they are em-bedded in the sulci that are more visible, we considered thatthe sulci form with the ventricles the anatomical structuresto be avoided as obstacles. The target of the stimulation isthe center of the subthalamic nucleus, and the initial solutionspace is the skin patch. The number of elements in the modelis 83k, and the number of simulations in the patient-specificdeformations database file is 20. The Lame’s parameterswere set to λ = 1291 Pa and µ = 1034 Pa according to [10].Experiments were performed on an Intel Core i7 running at2.67 GHz with 8GB RAM workstation.

Firstly, we compared both feasible insertion zones Ωs

and Ωd computed in Es and Ed respectively. The obtainedresults are shown on Table I.

TABLE I: Insertion zones: sizes, computation times, andcoverage ratio.

Ω0 Ωs Ωd

# Triangles 67920 17408 7868

Comp. time (s) - 12 36

Ω0 coverage (%) 100 25.6 11.6

The values in Table I show that Ωd is smaller thanΩs which was quite expected due to the larger number ofobstacles in Ed than in Es. The percentage of Ωd to Ωs isequal to 45.2% which means that the feasible insertion zoneis reduced by 54.8%. A visual illustration of the coverageratio is shown on Fig.3. It can be also noticed that therequired time to build Ωd is around 36s which is three timesas much as the time required to build Ωs, but still keeps theapproach compatible with clinical use.

Secondly, we compared the optimization results in bothEs and Ed. Table II shows the performance of Nelder-Mead

(a) Es, Ms: ωs on Ωs (b) Ed, Md: ωs on Ωd

Fig. 4: (a) distance map to the borders of Ωs, and (b) thesame distance map projected onto Ωd. Parts are cut even inthe initially safe (blue) zone.

optimization algorithm in both Es and Ed. We report thevalue of the evaluation of the objective cost function f whichwe are minimizing, the distance between the optimizedcomputed trajectory and the obstacles (ventricles and sulci),the number of iterations, and at last the convergence time.

TABLE II: Nelder-Mead performance in Es and Ed

Nelder-Mead Es Ed

eval(f ) [0, 1] 0.28 0.38

dist. from ventricles (mm) 11.87 7.39

dist. from sulci (mm) 5.13 3.12

# of iterations 31 21

time (s) 0.034 0.258

The values in Table II show that the optimization algorithmused in Es could also converge in Ed, and find a trajectorysufficiently safe for DBS interventions even in case of abrain shift. The optimized trajectory in Ed was closer tothe obstacles than the one in Es but remains far enoughfrom them. Consequently, the best evaluation value in Ed

(0.38) was not as good as the best one in Es (0.28) butcan be considered as acceptable for clinical practice. Theoptimization time is negligible in both cases and compatiblewith a use in clinical routine.

An interesting observation we obtain is that the safestinsertion regions in static conditions shown as blue zones onFig.4a can be withdrawn from the set of safe trajectories incase of brain shift, as shown on Fig.4b where some formerlyblue parts are cropped.

V. CONCLUSION

We presented a novel approach for DBS automatic preop-erative planning coupling physical simulations with geomet-ric optimization to help the surgeon to anticipate a possibledeformation during the planning. We tested our system on apatient-specific 3D model, with very promising results.

The obtained results illustrate the large variation of sizeand shape of the safe insertion zones for DBS interventionsbetween the static and the dynamic conditions, as it wasshrunk of more than 50% when considering a possible brainshift. This variation shows the interest of including the

brain shift prediction during the planning phase to removedangerous entry points that would not be detected otherwise.Although avoiding a sum of deformations from no brain shiftto a maximum possible brain shift to anticipate a wide rangeof possible levels of deformations causes a high restriction ofthe safe insertion zone, we could still find in the remaininginsertion zone an optimized entry point which is safe andefficient in a reasonable computation time.

Further works could be done to improve the system: on thefirst hand, improving the accuracy of the brain shift modelby using more complex deformation and fluid models, andon the other hand different optimization techniques could beinvestigated and compared. Finally, further clinical validationis required to assess the quality of the overall system.

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