A Surgeon Specific Automatic Path Planning

Algorithm for Deep Brain Stimulation

Yuan Liua, Benoit M. Dawant

a, Srivatsan Pallavaram

a, Joseph S. Neimat

b, Peter E. Konrad

b,

Pierre-François D’Haesea, Ryan D. Datteri

a, Bennett A. Landman

a and Jack H. Noble

a

aDept. of Electrical Eng. and Comp. Science, Vanderbilt University, Nashville, TN 37235, USA

bDept. of Neurosurgery, Vanderbilt University, Nashville, TN 37235, USA

ABSTRACT

In deep brain stimulation surgeries, stimulating electrodes are placed at specific targets in the deep brain to treat

neurological disorders. Reaching these targets safely requires avoiding critical structures in the brain. Meticulous

planning is required to find a safe path from the cortical surface to the intended target. Choosing a trajectory

automatically is difficult because there is little consensus among neurosurgeons on what is optimal. Our goals are to

design a path planning system that is able to learn the preferences of individual surgeons and, eventually, to standardize

the surgical approach using this learned information. In this work, we take the first step towards these goals, which is to

develop a trajectory planning approach that is able to effectively mimic individual surgeons and is designed such that

parameters, which potentially can be automatically learned, are used to describe an individual surgeon’s preferences. To

validate the approach, two neurosurgeons were asked to choose between their manual and a computed trajectory, blinded

to their identity. The results of this experiment showed that the neurosurgeons preferred the computed trajectory over

their own in 10 out of 40 cases. The computed trajectory was judged to be equivalent to the manual one or otherwise

acceptable in 27 of the remaining cases. These results demonstrate the potential clinical utility of computer-assisted path

planning.

KEYWORDS: Deep brain stimulation, path planning, computer-assisted surgery

1. INTRODUCTION

Deep brain stimulation (DBS) is widely used to treat patients suffering from neurological disorders such as

Parkinson’s disease, tremor, and dystonia [1]. An electrode is implanted deep in the brain to stimulate specific nuclei

with electrical impulses to control the disease symptoms. Multiple studies have indicated that precise planning of the

trajectory is necessary to avoid negative neuropsychological and motor side effects [2] and complications such as

hemorrhage [3]. In our current planning system [4], the target is automatically predicted [5]. In this study we focus on

finding an optimal entry point. Brunenberg et al. [6] studied the feasibility of planning a DBS trajectory given a selected

target point. They allowed the surgeon to choose a plan from the set of all possible trajectories that satisfied hard

constraints to avoid sensitive anatomical structures such as the vessels and ventricles. Guo et al. [7] found trajectories

that optimized electrophysiology and obeyed hard constraints to avoid sensitive structures. A more comprehensive

framework was presented by Essert et al. [8], where surgical rules were accounted for in a cost function. Recently,

Bériault et al. [9] proposed a framework that use a fuzzy vesselness cost term to account for trajectories that pass close to

a critical structure multiple times along the path. It is difficult to assess the performance of all of these methods because

they lack evaluation of the clinical usability of their results.

It is widely believed in the neurosurgery community that there is disagreement among neurosurgeons about what

characterizes an optimal trajectory. If this lack of consensus is substantial, it poses a fundamental problem to all

trajectory planning methods. Planning software that perfectly mimics one neurosurgeon would likely not be used by

many other neurosurgeons. We propose that a better approach would be to use a planning system that can mimic

individual surgeons by learning their preferential trajectories, and eventually, extract common constraints that would

standardize the surgical approach. In this work, we take the first step towards these goals by developing a parametric

trajectory planning approach. Such a system can potentially be automatically adapted through cost functions to describe

a single surgeon’s preferences. The system we have designed optimizes the entry point by minimizing a cost function

that includes terms corresponding to each planning criterion and weights each term according to its preferred emphasis.

The approach is similar to Essert et al. [8], however, a fundamental difference is that we place unique weightings on the

importance of each surgical constraint and these weighting parameters are tuned in order to account for surgeon specific

preferences. The allowable entry points are bounded to lie within the entry region typically chosen by the surgeon

instead of searching over the entire head. Moreover, as opposed to other approaches, we perform a direct evaluation of

the clinical usability of our approach. This validation study consists of asking neurosurgeons to choose between their

manual and a computed trajectory, blinded to their identity, in a set of volumes. The results of such a study are used to

indicate how often our system produces clinically acceptable trajectories. We also conduct an experiment in which we

study the disagreement between neurosurgeons by asking the surgeons to choose between their manual and a trajectory

computed based on another surgeon’s preferences in a set of volumes. As will be shown, the results of that experiment

indicate that lack of consensus may not be significant after all.

2. METHODS

In this section of the paper, we present our methods for computing a trajectory that optimizes a set of constraints

defined by a surgeon. First, we discuss the data we use. In the following sub-sections we detail our methods for

formulating the surgical constraints, for optimizing the trajectory with respect to the designed cost function, and for

validating the results.

2.1 Input Data

For each patient in our experiments, our dataset includes an MR T1-weighted image without contrast agent (MR

T1), an MR T1 with contrast agent (MR T1-C), and the planned target points for the left and right trajectories. The MRIs

(TR 7.9 ms, TE 3.65 ms, 256×256×170 voxels, with typical voxel resolution of 1×1×1 mm³) were acquired using the

SENSE parallel imaging technique (T1W/3D/TFE) from Philips on a 3T scanner. Prior to trajectory optimization, the

MR T1-C is rigidly registered to the MR T1 so that the vessels can be readily identified. The target points, all chosen for

subthalamic nucleus (STN) stimulation, are automatically predicted and, when necessary, are manually adjusted by the

neurosurgeons.

2.2 Surgical Constraints Analysis

Based on extensive consultation with two neurosurgeons experienced in DBS planning, the following constraints

governing the insertion procedure were defined:

1. The entry point of the electrode should be within certain bounds. It should be posterior to the hairline for cosmetic

reasons and anterior to the motor cortex to avoid side effects. We define a hard constraint that the entry point of the

trajectory must lie within these bounds.

2. To minimize the risk of hemorrhaging, the trajectory should not be close to the vessels. We use a cost term that

penalizes trajectories that lie closer than 3 mm to a vessel with cost values that increase with closer distance.

3. The ventricles are sensitive structures that should not be intersected by the trajectory. However, it is also desirable

to be close to the ventricles so that the trajectory is not too lateral. Thus, we define a hard constraint that the trajectory

can be no closer than 2 mm to the ventricles and define a cost term that penalizes trajectories relative to their distance

from the ventricles above this 2 mm lower bound.

4. The cortical surface of the brain is populated with numerous gyri and sulci that could be intersected multiple

times by a surgical trajectory. It is dangerous to cross sulci because often there are small vessels at the base of the sulci

that are not visible on preoperative imaging. Thus, we have designed a cost term that penalizes trajectories that intersect

with cortical surface on the base of the sulci.

5. Some neurosurgeons prefer the entry point to be near the coronal suture. The suture lies approximately in the

middle of the entry region we have defined. Thus, we define a cost term that is higher for entry points that lie further

posterior or anterior to the middle of our allowable entry region.

6. When targeting STN, some surgeons prefer to intersect the lateral edge of the thalamus. Thus, we have included a

cost term that penalizes trajectories that do not pass a distance of at least 1 mm through the thalamus.

2.3 Path Planning

In this section, we will present the methods that we use to perform path planning. First, we will describe our approach

for generating a set of candidate trajectories. Next, we will present the cost function that we use to choose the optimal

trajectory from the set of candidates. The cost function is dependent on segmentations of critical structures. Thus, finally,

we discuss how these segmentations are obtained. An overview of the method is shown in Figure 1.

2.3.1 Path Generation

The trajectory planning algorithm consists of generating all candidate trajectories and computing the cost for each

trajectory using a cost function based on the above surgical constraints to find the optimal one. Each trajectory shares a

common target point and can be uniquely represented by its entry point on the skin-air interface. A surface representing

the skin-air interface is obtained by isosurfacing the patient’s MR T1 after smoothing using the marching cubes

algorithm [10] and then filtering the results to remove extraneous components. The allowable entry region as described

in Constraint 1 is obtained by first (a) having a neurosurgeon define the search region once in an atlas by choosing four

points defining a tetrahedron that bounds the region, then (b) mapping these points to the patient’s MR T1 image using

registration-based techniques, and finally (c) defining the set of candidate entry points as the set of vertices in the skin

interface mesh that correspond to a trajectory that passes through the tetrahedron defined by those points.

2.3.2 Path Optimization

Constraints 2-6 on the trajectory listed in Section 2.2 will be accounted for using a cost function. The cost function,

which will be defined below, is a weighted sum of individual cost terms associated with each of the constraints we have

defined. The cost term for Constraint i will be referred to as . These cost terms are defined as:

Figure 1. Overview of the path planning algorithm.

{

,

{

,

,

,

and

{

,

where is the respective “distance quantity” that we compute associated with each ith constraint, and are

the maximum and minimum values of over the set of all candidate trajectories, and the constants in the equations are

chosen to match those discussed in the constraints analysis. The set of distance quantities { } are the distance from

the trajectory to the vessels, distance to the ventricles, a sulci distance quantity that will be presented below, distance

from the entry point to the suture, and the distance that the trajectory passes through the thalamus, respectively. It can be

seen that each cost term is formulated as a piecewise linear function. The terms are designed to scale and shift the input

distance quantity to produce a cost value ranging from 0 to 1. The techniques described in [11] are used to efficiently

compute these distance values. The method requires distance map representations of the structures, which were

computed using fast marching methods [12].

, the sulci distance quantity, is a number used to characterize how close a trajectory is to crossing a sulcus. It is

computed, as indicated in Figure 2 by a 2D example, by (i) finding the deepest intersection point of the trajectory with

cortical surface (indicated by a purple dot), (ii) identifying all vertices in the cortical surface mesh that fall within n

neighbor edge connections from this point (n=2 in this figure, and these vertices are indicated by black dots), where

, (iii) projecting those neighborhood points onto the given trajectory (indicated by black, dashed lines), (iv)

computing the signed distance from the projected points to the closest intersection point, (v) and computing the weighted

average of those distance values. As can be seen in the figure, is positive when the intersection point lies in a valley

of the coronal surface like a sulcus, is around zero when intersecting neither a peak nor valley, and is negative when

intersecting a peak like a gyrus. Thus, is minimized when a trajectory intersects the cortical surface once through the

top of a gyrus.

The overall cost function is defined by combining all of the individual cost terms as:

{∑

∑

,

where { } are values used to weight the relative importance of each cost term. Since { } are normalized by scale,

forcing { } to be positive and sum to 1 results in an with a range from 0 to 1. The piecewise definition of is

designed so that if the trajectory hits a vessel, i.e., when , or if the trajectory is closer than 2 mm to the ventricles,

i.e., when , is set to its maximum cost value. Otherwise, is equal to the weighted sum of the cost

terms. The optimization is completed when we have calculated the cost for all candidate trajectories and found the entry

point that minimizes .

2.3.2 Anatomical Structure Segmentation

The cost function we have defined relies on segmentations of several critical structures (see Figure 3). To segment

the vessels, the MR T1 is subtracted from the MR T1-C to highlight the contrast enhanced regions of the brain. Vessel

labels are identified as the brightest 0.65% of the image voxels. The ventricles and thalamus were identified by

combining atlas-based segmentations from four atlases using STAPLE [13]. All non-rigid registrations were performed

with the Adaptive Bases Algorithm [14]. The cortical surface was extracted using the LongCruise method [15].

2.4 Path Validation

The validation study consists of asking neurosurgeons to choose between their manual and a computed trajectory,

blinded to their identity, in a set of volumes. For both surgeons used in this study, we have selected a unique set of cost

function parameters { }. To do this, we relied on a training set of left and right trajectories in 10 volumes for each

surgeon. We started with initial weighting factors suggested by the surgeon and manually adjusted them until the

surgeon judged all 20 computed trajectories to be satisfactory (see left panel of Figure 4). Only once these parameters

were fixed did we move onto the testing set. In future studies, parameter tuning methods could be developed to automate

this process.

The validation study is designed to assess the degree to which the weighting factors effectively capture the

neurosurgeon’s preferences. The testing set is composed of left and right trajectories in 10 volumes. The validation study

relies on a path evaluation process (see Figure 4). For path evaluation, a four level rating of trajectory quality is

measured. The neurosurgeon is presented with both the computed trajectory and the trajectory that was chosen manually

for clinical use, blinded to their identity, and is asked to decide which trajectory is preferred. If the computed one is

chosen, the algorithm found a trajectory that better matched the surgeon’s preferences than the one originally planned

manually, and we classify it as type 4: excellent. If the surgeon is not able to determine which one is superior, e.g., if

they are too close to each other; it is rated as type 3: equivalent. If the computed trajectory can otherwise still be used

Figure 3. Segmentations of anatomical structures.

From top to bottom, left to right, the blood vessels,

ventricles, thalamus, cortical surface, and a coronal

view of these structures can be seen.

Figure 2. 2D Illustration of 𝑑 . The curve

represents the cortical surface and the lines

represent candidate trajectories, all color coded by

this sulci distance, 𝑑 , where blue and red

indicating lower and higher values respectively.

The intersection points are indicated in purple.

Neighbor points are shown in black. From left to

right, the average projection distance for each

trajectory is positive, nearly zero, and negative,

respectively.

clinically, it is classified as type 2: acceptable. If modification is necessary, it is classified as type 1: rejected. The

computed trajectory is considered to be successful if a rating of 2 or better is achieved. The validation study consists of

performing this path evaluation process for each side of each testing volume and recording the results.

We also wish to study the lack of consensus between neurosurgeons. We do this by repeating the validation study

process with the exception that for path evaluation, the surgeon is instead asked to choose between their manual and a

trajectory computed based on another surgeon’s preferences in the set of testing volumes.

3. RESULTS

Two experienced neurosurgeons participated in this study and will be referred to as A and B. For Surgeon A,

weighting parameters were chosen through the training process to be 0.18 for constraint 2, 0.18 for constraint 3, 0.35 for

constraint 4, 0.24 for constraint 5, 0.05 for constraint 6. For Surgeon B, weighting parameters were chosen to be 0.20 for

constraint 2, 0.27 for constraint 3, 0.40 for constraint 4, 0.13 for constraint 5, 0.00 for constraint 6. Results for the first

study in which we assess the degree to which these weighting factors effectively capture the neurosurgeon’s preferences

are illustrated in Figure 5. For Surgeon A, 5 cases are rated as excellent, 10 equivalent, 3 acceptable, and 2 rejected out

of the overall 20 cases. For Surgeon B, 5 cases are rated as excellent, 2 equivalent, 10 acceptable, and 3 rejected out of

the overall 20 cases. Success rates of 90% and 85% for Surgeons A and B suggest that the tuned weighting parameters

reflect the surgeons’ preferences reasonably well.

Figure 6 shows the computed trajectory for one case using Surgeon A’s weighting parameters. The left panel is a

projection of the structures to the plane normal to the trajectory (black dot), indicating it does not cross vessels (red) or

the ventricles (yellow), but does pass through the thalamus (green). The right panel is a partial view of cortical surface

(magenta) intersected by the computed trajectory (black line), indicating the entry point (black dot) is on a gyrus.

Colormaps representing the individual cost terms are shown in Figure 7, where blue and red indicate lower and higher

cost, respectively.

Results for the second experiment in which we try to detect the differences between neurosurgeons are illustrated in

Figure 8. In the figure are results of the rating experiments for Surgeon A (left) and Surgeon B (right). Blue shows the

rating for the trajectory computed using the same surgeon’s set of weights. Red indicates rating for the trajectory

computed using the other surgeon’s set of weights. Only experiments that resulted in different rating between the two

trajectories are shown. In the right panel, the plot shows that Surgeon B rejected several trajectories computed using

Surgeon A’s weights and in general prefers his or her own set of weights, as we would expect. However, contrary to our

expectations, we see in the left panel that Surgeon A consistently prefers trajectories computed using Surgeon B’s

Figure 4. Demonstration of the training and validation process used for each surgeon.

weights and rated all of those trajectories acceptable or better. This indicates that the set of weighting parameters chosen

for Surgeon B works better for both surgeons. We believe this may have occurred because Surgeon B was stricter in the

training process resulting in better overall parameters. However, it does indicate that the difference of preferences

between neurosurgeons may not be significant after all. From Figures 5 and 8, we can see that, using Surgeon B’s

weights, the combined result from both surgeons is that 37 out of 40 computed trajectories are acceptable or better, i.e., a

92.5% success rate. This suggests that our system for trajectory optimization could provide valuable clinical assistance.

0%

5%

10%

15%

20%

25%

30%

35%

40%

45%

50%

Excellent Equivalent Acceptable Rejected

Figure 5. Rating distribution of the trajectories computed using the surgeon's own set of weights. Dark color:

Surgeon A; light color: Surgeon B.

Figure 6. Computed Trajectory. Left: Projection of sensitive structures (black dot), with red structures representing

vessels, yellow representing ventricles, green representing thalamus. Right: cortical surface intersection, with

magenta structures representing cortical surface, and black line representing the computed trajectory.

Figure 7. Color maps indicating cost for 𝑓 and 𝑓 from top to bottom, left to right.

Figure 8. Pairwise comparison of rating scores. Left: experiment conducted by Surgeon A; right: experiment conducted by Surgeon B.

4. CONCLUSIONS

Traditionally, the surgical trajectory is chosen by a neurosurgeon and requires a substantial amount of expertise. In

this study, we designed an entry point optimization algorithm with a cost function that includes terms that account for

each criterion that the neurosurgeon considers when choosing an entry point. Moreover, the terms in the cost function

are parameterized by weighting values that were effectively tuned to mimic the planning preferences of individual

neurosurgeons. Trajectories were validated by directly evaluating their clinical usability. Our results show that the

system we have designed could be useful for trajectory selection assistance and, for the two surgeons involved in this

study, it has a 92.5% success rate.

Two of the three trajectories that Surgeon B rejected were done so because they were too close to deep sulci.

Although they did not intersect any sulci, they passed too close to be considered safe and our intersection-based

detection approach failed to assign those trajectories a higher cost. In future work, we will modify our detection scheme

to account for this type of trajectory and further improve the performance of our algorithm.

A more quantitative evaluation of trajectories is not possible because there is in general no single correct trajectory

to serve as a gold standard. Thus, we have relied on an imperfect but effective validation approach in which we ask

neurosurgeons to rate individual trajectories based on their expert judgment and draw our conclusions from the results of

a large group of such experiments. It is worth noting that we did see some inconsistency in the rating process. For cases

9 and 10, the trajectories computed using the two sets of weights were identical, but Surgeon A rated them differently as

can be seen in Figure 8. Rating inconsistencies are to be expected since, as long as two different trajectories pose no

detectable danger, selection between the two often comes down to the surgeon’s instincts and other qualitative factors. In

future studies we will study the repeatability of our rating-based trajectory evaluation approach.

It is widely believed in the neurosurgery community that there is a lack of consensus among neurosurgeons about

what characterizes an optimal trajectory. We started this study with the hypothesis that different neurosurgeons have

different preferences, and thus designed a surgeon specific trajectory planning system. However, our results in Figure 8

show that, in this small study, these surgeons tend to agree on one set of parameters. This suggests that any lack of

consensus between neurosurgeons may not be significant. In future experiments, we will study the preferences of more

surgeons so that we can better answer this question. If we find that significant differences do exist among other surgeons,

future work will include automating the parameter tuning process to account for various preferences, and eventually, to

use this information to standardize the surgical technique by computing trajectories representative of consensus criteria.

5. ACKNOWLEDGEMENTS

This work was supported by NIH grant R01-EB006136 from the National Institute of Biomedical Imaging and

Bioengineering. The content is solely the responsibility of the authors and does not necessarily represent the official

views of this institute.

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