DMLC leaf-pair optimal control for mobile, deforming target

Existing algorithms of dynamic control of independent pairs of leaves allow optimal DMLC delivery of IMRT to rigid targets translating parallel to leaf trajectories. However, in numerous cases of radiotherapy treatments simplifying assumptions of rigid-like motions of targets and surrounding tissues are clearly not satisfied. Therefore algorithms have to be developed that allow one to control MLC so that predetermined intensities are delivered to various points in targets that experience compression and expansion at the time of irradiation. Moreover, it is desirable for such algorithms to ensure that delivery of modulated intensity map will be done with minimal expense of monitor units. Derivation of the algorithm that optimizes the DMLC IMRT to mobile, deforming target is presented in this paper. [To illustrate the general algorithm two representative examples of DMLC IMRT delivery to deforming targets are presented in full detail.] Finally, similarities and differences between solutions for immobile targets, for moving, rigid targets and for moving, deforming targets are discussed.     

DMLC IMRT delivery to targets moving in 2D in Beam's eye view

The goal of this article is to present the algorithm for DMLC leaf control capable of delivering IMRT to tumors that experience motion in two dimensions in the beams eye view (BEV) plane. The generic, two-dimensional (2D) motion of the projection of the rigid target on BEV plane can be divided into two components. The first component describes the motion of the projection of the target along the x axis (parallel to the MLC leaf motions) and the other describes the motion of the target projection on the y axis (perpendicular to the leaf motion direction). First, time optimal leaf trajectories are calculated independently for each leaf pair of the MLC assembly to compensate the x-axis component of the 2D motion of the target on the BEV. These leaf trajectories are then synchronized following the mid time (MT) synchronization procedure. To compensate for the y-axis component of the motion of the target projection on the BEV plane, the procedure of "switching" leaf pair trajectories in the upward (or downward) direction is executed when the target's BEV projection moves upward (or downward) from its equilibrium position along the y axis. When the intensity function is a 2D histogram, the error between the intended and delivered intensity in 2D DMLC IMRT delivery will depend on the shape of the intensity map and on the MLC physical constraint (leaf width and maximum admissible leaf speed). The MT synchronization of leaf trajectories decreases the impact of above constraints on the error in 2D DMLC IMRT intensity map delivery. The proof is provided, that if hardware constraints in the 2D DMLC IMRT delivery strategy are removed, the errors between planned and delivered 2D intensity maps are entirely eliminated. Examples of 2D DMLC IMRT delivery to rigid targets moving along elliptical orbits on BEV planes are calculated and analyzed for 20 clinical fluence maps. The comparisons between the intensity delivered without motion correction, with motion correction along x axis only, and with motion correction for full 2D motion of the target are calculated and quantitatively evaluated. The fluence maps were normalized to 100 MU and the rms difference between the desired and delivered fluence was 12 MU for no motion compensation, 11.18 MU for 1D compensation, and 4.73 MU for 2D motion compensations. The advantage of correcting for full 2D motion of target projected on the BEV plane is demonstrated.     

Real-time DMLC IMRT delivery for mobile and deforming targets

In numerous cases of radiotherapy delivery to moving targets, simplifying assumptions of identical pattern of motions of tissue for each fraction are not satisfied. Therefore, algorithms capable to respond in real time to motions of target registered at treatment should be developed to improve the precision of radiation intensity delivery. The DMLC delivery of predetermined intensity maps to moving and deforming targets in real time is developed in this paper. Algorithms are constructed so that constraints on maximum admissible speed of leaves are preserved during delivery. A sequence of examples is presented to illustrate behavior of leaf trajectories for representative cases of [dynamic multileaf collimator] (DMLC) [intensity modulated radiation therapy] (IMRT) real-time delivery. The examples presented show real-time deliveries to targets moving as rigid bodies and targets deforming uniformly over their volumes. Examples are admitting random perturbations of predefined target motions that are time dependent only, i.e., target motion perturbations are identical for all target points.     

Dynamic-MLC leaf control utilizing on-flight intensity calculations: a robust method for real-time IMRT delivery over moving rigid targets

An algorithm is presented that allows for the control of multileaf collimation (MLC) leaves based entirely on real-time calculations of the intensity delivered over the target. The algorithm is capable of efficiently correcting generalized delivery errors without requiring the interruption of delivery (self-correcting trajectories), where a generalized delivery error represents anything that causes a discrepancy between the delivered and intended intensity profiles. The intensity actually delivered over the target is continually compared to its intended value. For each pair of leaves, these comparisons are used to guide the control of the following leaf and keep this discrepancy below a user-specified value. To demonstrate the basic principles of the algorithm, results of corrected delivery are shown for a leading leaf positional error during dynamic-MLC (DMLC) IMRT delivery over a rigid moving target. It is then shown that, with slight modifications, the algorithm can be used to track moving targets in real time. The primary results of this article indicate that the algorithm is capable of accurately delivering DMLC IMRT over a rigid moving target whose motion is (1) completely unknown prior to delivery and (2) not faster than the maximum MLC leaf velocity over extended periods of time. These capabilities are demonstrated for clinically derived intensity profiles and actual tumor motion data, including situations when the target moves in some instances faster than the maximum admissible MLC leaf velocity. The results show that using the algorithm while calculating the delivered intensity every 50 ms will provide a good level of accuracy when delivering IMRT over a rigid moving target translating along the direction of MLC leaf travel. When the maximum velocities of the MLC leaves and target were 4 and 4.2 cm/s, respectively, the resulting error in the two intensity profiles used was 0.1 +/- 3.1% and -0.5 +/- 2.8% relative to the maximum of the intensity profiles. For the same target motion, the error was shown to increase rapidly as (1) the maximum MLC leaf velocity was reduced below 75% of the maximum target velocity and (2) the system response time was increased.     

IMRT delivery to a moving target by dynamic MLC tracking: delivery for targets moving in two dimensions in the beam's eye view

A new modification of the dynamic multileaf collimator (dMLC) delivery technique for intensity-modulated therapy (IMRT) is outlined. This technique enables the tracking of a target moving through rigid-body translations in a 2D trajectory in the beam's eye view. The accuracy of the delivery versus that of deliveries with no tracking and of 1D tracking techniques is quantified with clinically derived intensity-modulated beams (IMBs). Leaf trajectories calculated in the target-reference frame were iteratively synchronized assuming regular target motion. This allowed the leaves defined in the lab-reference frame to simultaneously follow the target motion and to deliver the required IMB without violation of the leaf maximum-velocity constraint. The leaves are synchronized until the gradient of the leaf position at every instant is less than a calculated maximum. The delivered fluence in the target-reference frame was calculated with a simple primary-fluence model. The new 2D tracking technique was compared with the delivered fluence produced by no-tracking deliveries and by 1D tracking deliveries for 33 clinical IMBs. For the clinical IMBs normalized to a maximum fluence of 200 MUs, the rms difference between the desired and the delivered IMB was 15.6 +/- 3.3 MU for the case of a no-tracking delivery, 7.9 +/- 1.6 MU for the case where only the primary component of motion was corrected and 5.1 +/- 1.1 MU for the 2D tracking delivery. The residual error is due to interpolation and sampling effects. The 2D tracking delivery technique requires an increase in the delivery time evaluated as between 0 and 50% of the unsynchronized delivery time for each beam with a mean increase of 13% for the IMBs tested. The 2D tracking dMLC delivery technique allows an optimized IMB to be delivered to moving targets with increased accuracy and with acceptable increases in delivery time. When combined with real-time knowledge of the target motion at delivery time, this technique facilitates improved target conformality relative to no-tracking deliveries and allows PTV margin reduction.     

Synchronized delivery of DMLC intensity modulated radiation therapy for stationary and moving targets

When delivering intensity modulated treatments the "tongue-and-groove" underdosage effect is a concern that should not be ignored. Algorithms aimed at removing the tongue-and-groove underdosage have been investigated in the past for irradiation of stationary targets. This paper is devoted to algorithms that remove tongue and grove effect for stationary and moving targets. To this end this paper develops original mid-time based algorithms for leaf synchronization. These algorithms exhibit a few additional advantageous properties for DMLC IMRT delivery beyond the removal of tongue-and-grove underdosage. In particular, they safeguard the minimization of time of delivery (for mid-time synchronized algorithms). Moreover, they avoid iterative procedures for synchronization of delivery for multiple pairs of leaves.     

Generalized field-splitting algorithms for optimal IMRT delivery efficiency

Intensity-modulated radiation therapy (IMRT) uses radiation beams of varying intensities to deliver varying doses of radiation to different areas of the tissue. The use of IMRT has allowed the delivery of higher doses of radiation to the tumor and lower doses to the surrounding healthy tissue. It is not uncommon for head and neck tumors, for example, to have large treatment widths that are not deliverable using a single field. In such cases, the intensity matrix generated by the optimizer needs to be split into two or three matrices, each of which may be delivered using a single field. Existing field-splitting algorithms used the pre-specified arbitrary split line or region where the intensity matrix is split along a column, i.e., all rows of the matrix are split along the same column (with or without the overlapping of split fields, i.e., feathering). If three fields result, then the two splits are along the same two columns for all rows. In this paper we study the problem of splitting a large field into two or three subfields with the field width as the only constraint, allowing for an arbitrary overlap of the split fields, so that the total MU efficiency of delivering the split fields is maximized. Proof of optimality is provided for the proposed algorithm. An average decrease of 18.8% is found in the total MUs when compared to the split generated by a commercial treatment planning system and that of 10% is found in the total MUs when compared to the split generated by our previously published algorithm.     

On the accuracy of a moving average algorithm for target tracking during radiation therapy treatment delivery

Real-time tumor targeting involves the continuous realignment of the radiation beam with the tumor. Real-time tumor targeting offers several advantages such as improved accuracy of tumor treatment and reduced dose to surrounding tissue. Current limitations to this technique include mechanical motion constraints. The purpose of this study was to investigate an alternative treatment scenario using a moving average algorithm. The algorithm, using a suitable averaging period, accounts for variations in the average tumor position, but respiratory induced target position variations about this average are ignored during delivery and can be treated as a random error during planning. In order to test the method a comparison between five different treatment techniques was performed: (1) moving average algorithm, (2) real-time motion tracking, (3) respiration motion gating (at both inhale and exhale), (4) moving average gating (at both inhale and exhale) and (5) static beam delivery. Two data sets were used for the purpose of this analysis: (a) external respiratory-motion traces using different coaching techniques included 331 respiration motion traces from 24 lung-cancer patients acquired using three different breathing types [free breathing (FB), audio coaching (A) and audio-visual biofeedback (AV)]; (b) 3D tumor motion included implanted fiducial motion data for over 160 treatment fractions for 46 thoracic and abdominal cancer patients obtained from the Cyberknife Synchrony. The metrics used for comparison were the group systematic error (M), the standard deviation (SD) of the systematic error (sigma) and the root mean square of the random error (sigma). Margins were calculated using the formula by Stroom et al. [Int. J. Radiat. Oncol., Biol., Phys. 43(4), 905-919 (1999)]: 2sigma + 0.7sigma. The resultant calculations for implanted fiducial motion traces (all values in cm) show that M and sigma are negligible for moving average algorithm, moving average gating, and real-time tracking (i.e., M and sigma = 0 cm) compared to static beam (M = 0.02 cm and sigma = 0.16 cm) or gated beam delivery (M = -0.05 and 0.16 cm at both exhale and inhale, respectively, and sigma = 0.17 and 0.26 cm at both exhale and inhale, respectively). Moving average algorithm sigma = 0.22 cm has a slightly lower random error than static beam delivery sigma = 0.24 cm, though gating, moving average gating, and real-time tracking have much lower random error values for implanted fiducial motion. Similar trends were also observed for the results using the external respiratory motion data. Moving average algorithm delivery significantly reduces M and sigma compared with static beam delivery. The moving average algorithm removes the nonstationary part of the respiration motion which is also achieved by AV, and thus the addition of the moving average algorithm shows little improvement with AV. Overall, a moving average algorithm shows margin reduction compared with gating and static beam delivery, and may have some mechanical advantages over real-time tracking when the beam is aligned with the target and patient compliance advantages over real-time tracking when the target is aligned to the beam.     

IMRT delivery verification using a spiral phantom

In this paper we report on the testing and verification of a system for IMRT delivery quality assurance that uses a cylindrical solid water phantom with a spiral trajectory for radiographic film placement. This spiral film technique provides more complete dosimetric verification of the entire IMRT treatment than perpendicular film methods, since it samples a three-dimensional dose subspace rather than using measurements at only one or two depths. As an example, the complete analysis of the predicted and measured spiral films is described for an intracranial IMRT treatment case. The results of this analysis are compared to those of a single field perpendicular film technique that is typically used for IMRT QA. The comparison demonstrates that both methods result in a dosimetric error within a clinical tolerance of 5%, however the spiral phantom QA technique provides a more complete dosimetric verification while being less time consuming. To independently verify the dosimetry obtained with the spiral film, the same IMRT treatment was delivered to a similar phantom in which LiF thermoluminescent dosimeters were arranged along the spiral trajectory. The maximum difference between the predicted and measured TLD data for the 1.8 Gy fraction was 0.06 Gy for a TLD located in a high dose gradient region. This further validates the ability of the spiral phantom QA process to accurately verify delivery of an IMRT plan.     

A multiportal compensator system for IMRT delivery

We have developed a multiportal compensator system for IMRT delivery, comprising a rotational compensator mount for a linac head, cylindrical compensator enclosures positioned in the mount, a vacuum-formed thermoplastic sheet with heavy alloy granules inside the enclosure, and a vacuum thermoforming device. The mount rotates like a revolver by a stepping motor, thus allowing automatic multiportal IMRT without exchanging compensators by human operators during treatment. The thermoforming device has servo-motor-driven 10 x 10 metal rod elements to actualize an arbitrary intensity profile. The thermoplastic sheet is preheated by a built-in biplanar heater and then it is placed over the rod elements. Subsequently, vacuum forming is performed through corner cutouts of the rod elements. After forced cooling down, the heavy alloy granules are fed into the formed sheet. Preliminary experiment using solid water phantoms and an x-ray film has shown that the intensity profile on the film agrees reasonably well with the desired profile.     

Monte Carlo dose calculation of segmental IMRT delivery to a moving phantom using dynamic MLC and gating log files

Respiratory gating is emerging as a tool to limit the effect of motion for liver and lung tumors. In order to study the impact of target motion and gated intensity modulated radiation therapy (IMRT) delivery, a computer program was developed to simulate segmental IMRT delivery to a moving phantom. Two distinct plans were delivered to a rigid-motion phantom with a film insert in place under four conditions: static, sinusoidal motion, gated sinusoidal motion with a duty cycle of 25% and gated sinusoidal motion with duty cycle of 50% under motion conditions of a typical patient (A = 1 cm, T = 4 s). The MLC controller log files and gating log files were retained to perform a retrospective Monte Carlo dose calculation of the plans. Comparison of the 2D planar dose distributions between simulation and measurement demonstrated that our technique had at least 94% of the points passing gamma criteria of 3% for dose difference and 3 mm as the distance to agreement. This note demonstrates that the use of dynamic multi-leaf collimator and respiratory monitoring system log files together with a fast Monte Carlo dose calculation algorithm is an accurate and efficient way to study the dosimetric effect of motion for gated or non-gated IMRT delivery on a rigidly-moving body.     

Glycemic control in critically ill: A moving target

Glycemic control targets in intensive care units (ICUs) have three distinct domains. Firstly, excessive hyperglycemia needs to be avoided. The upper limit of this varies depending on the patient population studied and diabetic status of the patients. Surgical patients particularly cardiac surgery patients tend to benefit from a lower upper limit of glycemic control, which is not evident in medically ill patient. Patient with premorbid diabetic status tends to tolerate higher blood sugar level better than normoglycemics. Secondly, hypoglycemia is clearly detrimental in all groups of critically ill patient and all measures to avoid this catastrophe need to be a part of any glycemic control protocol. Thirdly, glycemic variability has increasingly been shown to be detrimental in this patient population. Glycemic control protocols need to take this into consideration and target to reduce any of the available metrics of glycemic variability. Newer technologies including continuous glucose monitoring techniques will help in titrating all these three domains within a desirable range.     

Leaf transmission reduction using moving jaws for dynamic MLC IMRT

The aim of this work is to investigate to what extent it is possible to use the secondary collimator jaws to reduce the transmitted radiation through the multileaf collimator (MLC) during an intensity modulated radiation therapy (IMRT). A method is developed and introduced where the jaws follow the open window of the MLC dynamically (dJAW method). With the aid of three academic cases (Closed MLC, Sliding-gap, and Chair) and two clinical cases (prostate and head and neck) the feasibility of the dJAW method and the influence of this method on the applied dose distributions are investigated. For this purpose the treatment planning system Eclipse and the Research-Toolbox were used as well as measurements within a solid water phantom were performed. The transmitted radiation through the closed MLC leads to an inhomogeneous dose distribution. In this case, the measured dose within a plane perpendicular to the central axis differs up to 40% (referring to the maximum dose within this plane) for 6 and 15 MV. The calculated dose with Eclipse is clearly more homogeneous. For the Sliding-gap case this difference is still up to 9%. Among other things, these differences depend on the depth of the measurement within the solid water phantom and on the application method. In the Chair case, the dose in regions where no dose is desired is locally reduced by up to 50% using the dJAW method instead of the conventional method. The dose inside the chair-shaped region decreased up to 4% if the same number of monitor units (MU) as for the conventional method was applied. The undesired dose in the volume body minus the planning target volume in the clinical cases prostate and head and neck decreased up to 1.8% and 1.5%, while the number of the applied MU increased up to 3.1% and 2.8%, respectively. The new dJAW method has the potential to enhance the optimization of the conventional IMRT to a further step.     

Behavioral dynamics of intercepting a moving target

From matters of survival like chasing prey, to games like football, the problem of intercepting a target that moves in the horizontal plane is ubiquitous in human and animal locomotion. Recent data show that walking humans turn onto a straight path that leads a moving target by a constant angle, with some transients in the target-heading angle. We test four control strategies against the human data: (1) pursuit, or nulling the target-heading angle beta, (2) computing the required interception angle beta (3) constant target-heading angle, or nulling change in the target-heading angle beta and (4) constant bearing, or nulling change in the bearing direction of the target psi which is equivalent to nulling change in the target-heading angle while factoring out the turning rate (beta - phi) We show that human interception behavior is best accounted for by the constant bearing model, and that it is robust to noise in its input and parameters. The models are also evaluated for their performance with stationary targets, and implications for the informational basis and neural substrate of steering control are considered. The results extend a dynamical systems model of human locomotor behavior from static to changing environments.     

An intercomparison of IMRT delivery techniques: a case study for breast treatment

Intensity-modulated radiotherapy beams can be delivered using a multileaf collimator by one of two methods: either by superposition of a series of multiple-static fields, or by moving the collimators while the beam is on to produce 'dynamically' modulated beams. The leaf trajectories in this dynamic mode are given by a series of linear steps between control points defining each collimator position at known intervals throughout an exposure. The complexity of the resulting modulation is limited in the first case by the number of fields superposed and in the second case by the number of control points defined. Results are presented for an experimental study that investigates the effect of changing both the number of fields for the multiple-static technique, and the number of control points for a dynamic 'close-in' technique. All deliveries studied are clinical intensity-modulated breast fields. The effect of using a universal wedge in conjunction with the multileaf collimator is also studied, together with a comparison of the relative efficiency, time taken and the absolute dosimetric accuracy of the various delivery options. It is shown that all delivery techniques produce equivalent dose distributions when using 15 control points, with 10 control points being sufficient to produce an adequate breast compensator distribution. Except for the case of a four-control-point dynamic delivery, the universal wedge makes no significant difference to the dose distribution. However, it makes the delivery less efficient. The close-in interpreter consistently produces deliveries that are more efficient than the more conventional sliding-window technique and faster than the multiple-static-field technique. Finally the close-in technique is compared to the more 'standard' leaf-sweep technique and shown to be equivalent.     

Quantification of the fluence error in the motion-compensated dynamic MLC (DMLC) technique for delivering intensity-modulated radiotherapy (IMRT)

When a correction for intrafraction organ motion is to be attempted using the dynamic multileaf collimator (DMLC) 'breathing leaves' technique for intensity-modulated radiotherapy (IMRT), there is a finite response time between the measurement of organ motion and the feeding of a corresponding corrective motion to the leaves. Whilst small this is non-zero. This letter presents a computational strategy to assess the error introduced to the delivered fluence by this system latency. The error depends on the functional form of the intended fluence modulation, the variability of the breathing motion and the magnitude of the system latency.     

Enhancement of IMRT delivery through MLC rotation

Multileaf collimator (MLC) based intensity modulated radiation therapy (IMRT) techniques are well established but suffer several physical limitations. Dosimetric spatial resolution is limited by the MLC leaf width; interleaf leakage and tongue-and-groove effects degrade dosimetric accuracy and the range of leaf motion limits the maximum deliverable field size. Collimator rotation is used in standard radiation therapy to improve the conformity of the MLC shape to the target volume. Except for opposed orthogonal fields, collimator rotation has not been exploited in IMRT due to the complexity of deriving the MLC leaf configurations for rotated sub-fields. Here we report on a new way that MLC-based IMRT is delivered which incorporates collimator rotation, providing an extra degree of freedom in deriving leaf sequences for a desired fluence map. Specifically, we have developed a series of unique algorithms that are capable of determining rotated MLC segments. These IMRT fields may be delivered statically (with the collimator rotating to a new position in between sub-fields) or dynamically (with the collimator rotating and leaves moving simultaneously during irradiation). This introductory study provides an analysis of the rotating leaf motion calculation algorithms with focus on radiation efficiency, the range of collimator rotation and number of segments. We then evaluate the technique by characterizing the ability of the algorithms to generate rotating leaf sequences for desired fluence maps. Comparisons are also made between our method and conventional sliding window and step-and-shoot techniques. Results show improvements in spatial resolution, reduced interleaf effects and maximum deliverable field size over conventional techniques. Clinical application of these enhancements can be realized immediately with static rotational delivery although improved dosimetric modelling of the MLC will be required for dynamic delivery.