gms | German Medical Science

GMS Current Topics in Computer and Robot Assisted Surgery

Deutsche Gesellschaft für Computer- und Roboterassistierte Chirurgie (CURAC)

ISSN 1863-3153

Incorporating interfractional motion in the treatment planning for motion compensated radiosurgery

Research Article

  • corresponding author Alexander Schlaefer - Institute for Robotics and Cognitive Systems, University of Lübeck, Lübeck, Germany
  • Sonja Dieterich - Department of Radiation Medicine, Georgetown University Hospital, Georgetown, USA
  • Achim Schweikard - Institute for Robotics and Cognitive Systems, University of Lübeck, Lübeck, Germany

GMS CURAC 2006;1:Doc16

The electronic version of this article is the complete one and can be found online at:

Published: November 6, 2006

© 2006 Schlaefer et al.
This is an Open Access article distributed under the terms of the Creative Commons Attribution License ( You are free: to Share – to copy, distribute and transmit the work, provided the original author and source are credited.


In robotic radiosurgery cyclic movements of the target, like respiratory motion, can be compensated by moving the beams accordingly. However, conventionally treatment planning is performed on 3D image data and does not account for organ motion. We propose to discretize the target motion into steps along its spatial dimensions. For each step we compute its fraction of the breathing cycle, calculate the dose coefficient and incorporate this information in the optimization phase of the planning problem.

Simulating planning and dose delivery for a simplified test case we show that the new approach can mitigate potential problems when treating highly mobile targets with motion compensated radiosurgery.

Keywords: motion compensation, radiosurgery, inverse planning, robotics


When applying radiosurgical procedures in the lung and abdomen, the target and the surrounding normal tissue are subject to motion, notably due to respiration [1], [2], [3], [4]. Conventionally this problem is handled by introducing margins around the clinical target volume (CTV) and the organs at risk (OAR) [5], [6]. The enlarged planning target volume (PTV) is constructed to cover the target during all stages of the breathing cycle. However, this leads to a substantial increase in the dose to non target tissue, and a potential overlapping of PTV and OAR [7].

One way to avoid large margins is to manage the breathing motion. Patients can be trained to stop breathing for a prolonged time, and the treatment is only performed during those breath holds [6]. Similarly, gating methods can be employed. Here the patient keeps breathing normally, but the respiration is tracked and used to trigger the treatment beams. The disadvantage of these techniques is a prolonged treatment time, as only a part of the respiratory cycle can be used to deliver the dose. A continuous treatment would be possible if the beams follow the targets motion, and it has been attempted to adjust the leaf motion of a multi-leaf-collimator (MLC) accordingly [8]. However, the MLC-leafs allow only one-dimensional movements and additional problems could result from relative leaf motion.

A more flexible form of motion compensation is enabled by robotic radiosurgery. Using a lightweight linear accelerator mounted on a robot arm with six degrees of freedom, treatment beams can be moved synchronously to virtually any target trajectory [3], [9], [10], [11], [12]. Thus the safety margin can be reduced substantially. While robotic radiosurgery can achieve steep gradients and spare tissue surrounding the CTV, the motion pattern of OAR might differ from the target motion. When treatment planning is done on a single 3D image, the different relative motion in combination with motion compensation could lead to changes in the dose for OAR. Methods incorporating systematic and random organ movements in the treatment planning have been reported for treatment without motion compensation [13], [14], [15], [16].

When motion compensation is employed, the beams effect to the target will be approximately as planned, even with a 3D patient geometry and independently of the breathing state where this geometry was obtained. In Figure 1 [Fig. 1] the beams move synchronously to the target and cover the same target regions, both, for maximum inhalation (left side) and maximum exhalation (right side). However, if the OAR does not move, the relative motion between beams and OAR might lead to differences in the dose delivered to the OAR depending on the state of the breathing cycle. For example, the OAR in Figure 1 [Fig. 1] does not move, and while the beams stay clear of the OAR during maximum inhalation (left side), they intersect the OAR during maximum exhalation (right side).

We implemented a method to incorporate the organ motion in the treatment planning for robotic radiosurgery. Considering a moving target in the proximity of an immobile OAR, we demonstrate that motion compensation could have an impact on the dose to critical structures. In a simulation we compare the new method to planning on a single 3D patient geometry to show that the new method can improve planning.


For normal breathing, motions induced by respiration follow a cyclic pattern (Figure 2 [Fig. 2]). Thus, the path of all positions a volume takes from complete exhalation to complete inhalation and back to complete exhalation can be established. Dividing the path into discrete steps s1, …, sn we can determine the position of the volume and the fraction of the breathing cycle for which the volume is closer to the current step than to any other step. This leads to a set of step weights a1, …, an.

The actual treatment planning can be divided into two phases. First, a set of potential treatment beams is determined. Second, inverse planning is performed to compute the beam weights, i.e. the number of monitor units (MU) per beam. For our approach we rely on a simple heuristics that places a large number of beams through equally spaced points on the targets surface [17]. We compute the beam weights using inverse planning with linear programming as optimization method. The target and all volumes considered for planning are discretized into voxels. For each voxel v and each beam b we calculate the dose coefficient cvb which relates the beam’s weight to the dose in the voxel.

The optimization problem is formulated as finding a set of beam weights w such that for all voxels the delivered dose is within the specified bounds. Thus, the optimization is subject to constraints of the form lbv <= Σb cvbwb <= ubv, where lbv and ubv are the lower and upper dose bound for voxel v and wb is the weight of beam b, respectively. For planning on a single 3D patient geometry, the cvb are calculated using the position of v with respect to b. When taking into account the breathing motion, we have a different position of v and b for each step si, and we can compute the dose coefficient as weighted sum over all steps, i.e. Equation 1.

We used a phantom problem to simulate the planning with (4D planning) and without (3D planning) incorporating the organ motion. An ellipsoidal target region and a cylindrical organ at risk (OAR) were both embedded in a cylinder with an ellipsoidal base forming the ‘body’. Considering the case where only the target is moving and the OAR remains stationary we assumed a target motion of 8 mm in anterior-posterior direction. The motion was then discretized into 9 steps with step weights (0.18, 0.13, 0.09, 0.07, 0.06, 0.07, 0.09, 0.13, 0.18). For the planning, 1200 candidate beams were generated and the target dose was constrained to be within 6000-7000 cGy while the maximum dose for the OAR was set to 1000 cGy. A treatment was simulated for the 3D plan without motion compensation (3D moving), the 3D plan with motion compensation (3D motion compensated), and the 4D plan with motion compensation (4D motion compensated). For comparison we also report results for the 3D plan under the assumption that the there is no organ motion (3D stationary).


Delivering a 3D plan without motion compensation leads to a serious underdosing of the target (25.2% of the volume, up to 22.1% below the planned minimum, Figure 3 [Fig. 3]). Delivering the same plan with motion compensation drastically reduces the underdosing of the target (4.5% of the volume, up to 1% below the planned minimum) but leads to overdosing of the critical structure (up to 33.2% above the planned maximum, Figure 4 [Fig. 4]). The 4D plan with motion compensation fulfills all dose constraints, under the given discretization scheme. Figure 5 and Figure 6 show the 500, 1000, and 1500 cGy iso-doses with respect to the critical volume and the 5500, 6000, and 6500 cGy iso-doses with respect to the target volume on an axial plane through the target center. For 3D planning with motion compensation, the 1000 cGy iso-dose line clearly intersects the OAR (Figure 5 [Fig. 5]), while it stays outside the OAR for 4D planning with motion compensation (Figure 6 [Fig. 6]).


Delivering a plan computed on a stationary patient geometry in the presence of organ motion leads to changes in the dose distribution, which is consistent with the literature and typically handled by extending the volumes [1], [2], [4], [7], [18]. When the beams are moving synchronously to the target, the planned dose is delivered to the target reducing the need for extra margins. However, our simulations showed that a relative motion of the beam with respect to a critical structure may lead to an overdosing of that structure. Incorporating the beam motion in the planning process can mitigate this problem and in our simulation leads to an acceptable dose delivered to both, target and critical structure.

Clearly, the simulations are based on a number of simplifications. But while in general the motion pattern induced by the respiration will be less regularly, it seems to be possible to determine an idealized pattern before starting the treatment planning. Methods for prediction of the respiratory motion have been described in the literature [9], [12], [19], [20], e.g. by correlating the motion of external and internal markers. Thus, the target motion could be monitored for a limited time before treatment planning, and an average motion pattern could be derived.

Moreover, the monitoring could be continued throughout treatment, and whenever the deviation between planned and measured motion pattern becomes too large, the treatment could be interrupted until the patient returns to normal breathing. Further research needs to address the impact of variations in the treatment pattern for real patient data.


Motion compensation with 3D planning leads to improved target coverage but might induce overdosing of critical structures. For the treatment of highly mobile targets with motion compensated radiosurgery, organ motion should be considered during treatment planning to obtain 4D conformal plans.


This work was partially supported by Deutsche Forschungsgemeinschaft (DFG).


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