Optimization of radiosurgery treatment planning via mixed integer programming

Automatic Path-Planning Techniques for Minimally Invasive Stereotactic Neurosurgical Procedures-A Systematic Review

This review systematically examines the recent research from the past decade on diverse path-planning algorithms tailored for stereotactic neurosurgery applications. Our comprehensive investigation involved a thorough search of scholarly papers from Google Scholar, PubMed, IEEE Xplore, and Scopus, utilizing stringent inclusion and exclusion criteria. The screening and selection process was meticulously conducted by a multidisciplinary team comprising three medical students, robotic experts with specialized knowledge in path-planning techniques and medical robotics, and a board-certified neurosurgeon. Each selected paper was reviewed in detail, and the findings were synthesized and reported in this review. The paper is organized around three different types of intervention tools: straight needles, steerable needles, and concentric tube robots. We provide an in-depth analysis of various path-planning algorithms applicable to both single and multi-target scenarios. Multi-target planning techniques are only discussed for straight tools as there is no published work on multi-target planning for steerable needles and concentric tube robots. Additionally, we discuss the imaging modalities employed, the critical anatomical structures considered during path planning, and the current status of research regarding its translation to clinical human studies. To the best of our knowledge and as a conclusion from this systematic review, this is the first review paper published in the last decade that reports various path-planning techniques for different types of tools for minimally invasive neurosurgical applications. Furthermore, this review outlines future trends and identifies existing technology gaps within the field. By highlighting these aspects, we aim to provide a comprehensive overview that can guide future research and development in path planning for stereotactic neurosurgery, ultimately contributing to the advancement of safer and more effective neurosurgical procedures.

Redox integration of signaling and metabolism in a head and neck cancer model of radiation resistance using COSMRO

Redox metabolism is increasingly investigated in cancer as driving regulator of tumor progression, response to therapies and long-term patients' quality of life. Well-established cancer therapies, such as radiotherapy, either directly impact redox metabolism or have redox-dependent mechanisms of action defining their clinical efficacy. However, the ability to integrate redox information across signaling and metabolic networks to facilitate discovery and broader investigation of redox-regulated pathways in cancer remains a key unmet need limiting the advancement of new cancer therapies. To overcome this challenge, we developed a new constraint-based computational method (COSMro) and applied it to a Head and Neck Squamous Cell Cancer (HNSCC) model of radiation resistance. This novel integrative approach identified enhanced capacity for H2S production in radiation resistant cells and extracted a key relationship between intracellular redox state and cholesterol metabolism; experimental validation of this relationship highlights the importance of redox state in cellular metabolism and response to radiation.

A linear programming approach to inverse planning in Gamma Knife radiosurgery

PURPOSE

Leksell Gamma Knife® is a stereotactic radiosurgery system that allows fine-grained control of the delivered dose distribution. We describe a new inverse planning approach that both resolves shortcomings of earlier approaches and unlocks new capabilities.

METHODS

We fix the isocenter positions and perform sector-duration optimization using linear programming, and study the effect of beam-on time penalization on the trade-off between beam-on time and plan quality. We also describe two techniques that reduce the problem size and thus further reduce the solution time: dualization and representative subsampling.

RESULTS

The beam-on time penalization reduces the beam-on time by a factor 2-3 compared with the naïve alternative. Dualization and representative subsampling each leads to optimization time-savings by a factor 5-20. Overall, we find in a comparison with 75 clinical plans that we can always find plans with similar coverage and better selectivity and beam-on time. In 44 of these, we can even find a plan that also has better gradient index. On a standard GammaPlan workstation, the optimization times ranged from 2.3 to 26 s with a median time of 5.7 s.

CONCLUSION

We present a combination of techniques that enables sector-duration optimization in a clinically feasible time frame.

A convex optimization approach to radiation treatment planning with dose constraints

We present a method for handling dose constraints as part of a convex programming framework for inverse treatment planning. Our method uniformly handles mean dose, maximum dose, minimum dose, and dose-volume (i.e., percentile) constraints as part of a convex formulation. Since dose-volume constraints are non-convex, we replace them with a convex restriction. This restriction is, by definition, conservative; to mitigate its impact on the clinical objectives, we develop a two-pass planning algorithm that allows each dose-volume constraint to be met exactly on a second pass by the solver if its corresponding restriction is feasible on the first pass. In another variant, we add slack variables to each dose constraint to prevent the problem from becoming infeasible when the user specifies an incompatible set of constraints or when the constraints are made infeasible by our restriction. Finally, we introduce ConRad, a Python-embedded open-source software package for convex radiation treatment planning. ConRad implements the methods described above and allows users to construct and plan cases through a simple interface.

Robotic path-finding in inverse treatment planning for stereotactic radiosurgery with continuous dose delivery

PURPOSE

Continuous dose delivery in radiation therapy treatments has been shown to decrease total treatment time while improving the dose conformity and distribution homogeneity over the conventional step-and-shoot approach. The authors develop an inverse treatment planning method for Gamma Knife® Perfexion™ that continuously delivers dose along a path in the target.

METHODS

The authors' method is comprised of two steps: find a path within the target, then solve a mixed integer optimization model to find the optimal collimator configurations and durations along the selected path. Robotic path-finding techniques, specifically, simultaneous localization and mapping (SLAM) using an extended Kalman filter, are used to obtain a path that travels sufficiently close to selected isocentre locations. SLAM is novelly extended to explore a 3D, discrete environment, which is the target discretized into voxels. Further novel extensions are incorporated into the steering mechanism to account for target geometry.

RESULTS

The SLAM method was tested on seven clinical cases and compared to clinical, Hamiltonian path continuous delivery, and inverse step-and-shoot treatment plans. The SLAM approach improved dose metrics compared to the clinical plans and Hamiltonian path continuous delivery plans. Beam-on times improved over clinical plans, and had mixed performance compared to Hamiltonian path continuous plans. The SLAM method is also shown to be robust to path selection inaccuracies, isocentre selection, and dose distribution.

CONCLUSIONS

The SLAM method for continuous delivery provides decreased total treatment time and increased treatment quality compared to both clinical and inverse step-and-shoot plans, and outperforms existing path methods in treatment quality. It also accounts for uncertainty in treatment planning by accommodating inaccuracies.

Automated treatment planning for a dedicated multi-source intracranial radiosurgery treatment unit using projected gradient and grassfire algorithms

PURPOSE

The purpose of this work is to develop a framework to the inverse problem for radiosurgery treatment planning on the Gamma Knife(®) Perfexion™ (PFX) for intracranial targets.

METHODS

The approach taken in the present study consists of two parts. First, a hybrid grassfire and sphere-packing algorithm is used to obtain shot positions (isocenters) based on the geometry of the target to be treated. For the selected isocenters, a sector duration optimization (SDO) model is used to optimize the duration of radiation delivery from each collimator size from each individual source bank. The SDO model is solved using a projected gradient algorithm. This approach has been retrospectively tested on seven manually planned clinical cases (comprising 11 lesions) including acoustic neuromas and brain metastases.

RESULTS

In terms of conformity and organ-at-risk (OAR) sparing, the quality of plans achieved with the inverse planning approach were, on average, improved compared to the manually generated plans. The mean difference in conformity index between inverse and forward plans was -0.12 (range: -0.27 to +0.03) and +0.08 (range: 0.00-0.17) for classic and Paddick definitions, respectively, favoring the inverse plans. The mean difference in volume receiving the prescribed dose (V(100)) between forward and inverse plans was 0.2% (range: -2.4% to +2.0%). After plan renormalization for equivalent coverage (i.e., V(100)), the mean difference in dose to 1 mm(3) of brainstem between forward and inverse plans was -0.24 Gy (range: -2.40 to +2.02 Gy) favoring the inverse plans. Beam-on time varied with the number of isocenters but for the most optimal plans was on average 33 min longer than manual plans (range: -17 to +91 min) when normalized to a calibration dose rate of 3.5 Gy/min. In terms of algorithm performance, the isocenter selection for all the presented plans was performed in less than 3 s, while the SDO was performed in an average of 215 min.

CONCLUSIONS

PFX inverse planning can be performed using geometric isocenter selection and mathematical modeling and optimization techniques. The obtained treatment plans all meet or exceed clinical guidelines while displaying high conformity.

Optimization of beam angles for intensity modulated radiation therapy treatment planning using genetic algorithm on a distributed computing platform

Planning intensity modulated radiation therapy (IMRT) treatment involves selection of several angle parameters as well as specification of structures and constraints employed in the optimization process. Including these parameters in the combinatorial search space vastly increases the computational burden, and therefore the parameter selection is normally performed manually by a clinician, based on clinical experience. We have investigated the use of a genetic algorithm (GA) and distributed-computing platform to optimize the gantry angle parameters and provide insight into additional structures, which may be necessary, in the dose optimization process to produce optimal IMRT treatment plans. For an IMRT prostate patient, we produced the first generation of 40 samples, each of five gantry angles, by selecting from a uniform random distribution, subject to certain adjacency and opposition constraints. Dose optimization was performed by distributing the 40-plan workload over several machines running a commercial treatment planning system. A score was assigned to each resulting plan, based on how well it satisfied clinically-relevant constraints. The second generation of 40 samples was produced by combining the highest-scoring samples using techniques of crossover and mutation. The process was repeated until the sixth generation, and the results compared with a clinical (equally-spaced) gantry angle configuration. In the sixth generation, 34 of the 40 GA samples achieved better scores than the clinical plan, with the best plan showing an improvement of 84%. Moreover, the resulting configuration of beam angles tended to cluster toward the patient's sides, indicating where the inclusion of additional structures in the dose optimization process may avoid dose hot spots. Additional parameter selection in IMRT leads to a large-scale computational problem. We have demonstrated that the GA combined with a distributed-computing platform can be applied to optimize gantry angle selection within a reasonable amount of time.

Accounting for the tongue-and-groove effect using a robust direct aperture optimization approach

PURPOSE

Traditionally, the tongue-and-groove effect due to the multileaf collimator architecture in intensity-modulated radiation therapy (IMRT) has typically been deferred to the leaf sequencing stage. The authors propose a new direct aperture optimization method for IMRT treatment planning that explicitly incorporates dose calculation inaccuracies due to the tongue-and-groove effect into the treatment plan optimization stage.

METHODS

The authors avoid having to accurately estimate the dosimetric effects of the tongue-and-groove architecture by using lower and upper bounds on the dose distribution delivered to the patient. They then develop a model that yields a treatment plan that is robust with respect to the corresponding dose calculation inaccuracies.

RESULTS

Tests on a set of ten clinical head-and-neck cancer cases demonstrate the effectiveness of the new method in developing robust treatment plans with tight dose distributions in targets and critical structures. This is contrasted with the very loose bounds on the dose distribution that are obtained by solving a traditional treatment plan optimization model that ignores tongue-and-groove effects in the treatment planning stage.

CONCLUSIONS

A robust direct aperture optimization approach is proposed to account for the dosimetric inaccuracies caused by the tongue-and-groove effect. The experiments validate the ability of the proposed approach in designing robust treatment plans regardless of the exact consequences of the tongue-and-groove architecture.

On Linear Infeasibility Arising in Intensity-Modulated Radiation Therapy Inverse Planning

Intensity-modulated radiation therapy (IMRT) gives rise to systems of linear inequalities, representing the effects of radiation on the irradiated body. These systems are often infeasible, in which case one settles for an approximate solution, such as an {α, β}-relaxation, meaning that no more than α percent of the inequalities are violated by no more than β percent. For real-world IMRT problems, there is a feasible {α, β}-relaxation for sufficiently large α, β > 0, however large values of these parameters may be unacceptable medically.The {α, β}-relaxation problem is combinatorial, and for given values of the parameters can be solved exactly by Mixed Integer Programming (MIP), but this may be impractical because of problem size, and the need for repeated solutions as the treatment progresses.As a practical alternative to the MIP approach we present a heuristic non-combinatorial method for finding an approximate relaxation. The method solves a Linear Program (LP) for each pair of values of the parameters {α, β} and progresses through successively increasing values until an acceptable solution is found, or is determined non-existent. The method is fast and reliable, since it consists of solving a sequence of LP's.

Beam orientation optimization for intensity-modulated radiation therapy using mixed integer programming

The purpose of this study is to extend an algorithm proposed for beam orientation optimization in classical conformal radiotherapy to intensity-modulated radiation therapy (IMRT) and to evaluate the algorithm's performance in IMRT scenarios. In addition, the effect of the candidate pool of beam orientations, in terms of beam orientation resolution and starting orientation, on the optimized beam configuration, plan quality and optimization time is also explored. The algorithm is based on the technique of mixed integer linear programming in which binary and positive float variables are employed to represent candidates for beam orientation and beamlet weights in beam intensity maps. Both beam orientations and beam intensity maps are simultaneously optimized in the algorithm with a deterministic method. Several different clinical cases were used to test the algorithm and the results show that both target coverage and critical structures sparing were significantly improved for the plans with optimized beam orientations compared to those with equi-spaced beam orientations. The calculation time was less than an hour for the cases with 36 binary variables on a PC with a Pentium IV 2.66 GHz processor. It is also found that decreasing beam orientation resolution to 10 degrees greatly reduced the size of the candidate pool of beam orientations without significant influence on the optimized beam configuration and plan quality, while selecting different starting orientations had large influence. Our study demonstrates that the algorithm can be applied to IMRT scenarios, and better beam orientation configurations can be obtained using this algorithm. Furthermore, the optimization efficiency can be greatly increased through proper selection of beam orientation resolution and starting beam orientation while guaranteeing the optimized beam configurations and plan quality.

Simultaneous beam geometry and intensity map optimization in intensity-modulated radiation therapy

PURPOSE

In current intensity-modulated radiation therapy (IMRT) plan optimization, the focus is on either finding optimal beam angles (or other beam delivery parameters such as field segments, couch angles, gantry angles) or optimal beam intensities. In this article we offer a mixed integer programming (MIP) approach for simultaneously determining an optimal intensity map and optimal beam angles for IMRT delivery. Using this approach, we pursue an experimental study designed to (a) gauge differences in plan quality metrics with respect to different tumor sites and different MIP treatment planning models, and (b) test the concept of critical-normal-tissue-ring--a tissue ring of 5 mm thickness drawn around the planning target volume (PTV)--and its use for designing conformal plans.

METHODS AND MATERIALS

Our treatment planning models use two classes of decision variables to capture the beam configuration and intensities simultaneously. Binary (0/1) variables are used to capture "on" or "off" or "yes" or "no" decisions for each field, and nonnegative continuous variables are used to represent intensities of beamlets. Binary and continuous variables are also used for each voxel to capture dose level and dose deviation from target bounds. Treatment planning models were designed to explicitly incorporate the following planning constraints: (a) upper/lower/mean dose-based constraints, (b) dose-volume and equivalent-uniform-dose (EUD) constraints for critical structures, (c) homogeneity constraints (underdose/overdose) for PTV, (d) coverage constraints for PTV, and (e) maximum number of beams allowed. Within this constrained solution space, five optimization strategies involving clinical objectives were analyzed: optimize total intensity to PTV, optimize total intensity and then optimize conformity, optimize total intensity and then optimize homogeneity, minimize total dose to critical structures, minimize total dose to critical structures and optimize conformity simultaneously. We emphasize that the objectives that include optimizing conformity make use of the critical-normal-tissue-ring. Three tumor sites: head-and-neck, pediatric brain, and prostate are used for comparison.

RESULTS

The critical-normal-tissue-ring acts as a good device for enforcing conformity. Trends in the characteristics and quality of plans resulting from each model were observed. Attempts to reduce dose to critical structures tend to worsen PTV conformity (1.542 to 3.092) and homogeneity (1.223 to 1.984), depending on the relative size and spatial distance of the critical structures to the PTV. When the critical structures are relatively small compared with the PTV (as in the case for the pediatric brain tumor, where each is less than 15% in volume), dose reduction to critical structures is accompanied by much worse scores in conformity (2.482) and homogeneity (1.984). When the critical structures are larger, as in the case of head-and-neck (approximately 50%), the conformity and homogeneity deterioration is less significant (1.542 and 1.239, respectively). There is a clear tradeoff between homogeneity, conformity, and minimum dose to organs at risk (OARs). For head-and-neck and pediatric brain tumor, the model that minimizes total dose to critical structures and optimizes conformity simultaneously offers a compromise among these factors, resulting in reduced critical structure dose with conformal and homogeneous plans. In the prostate case, the tumor is smaller than the two large nearby critical structures, and all models provide very homogeneous PTV dose distribution. However, minimizing dose to critical structures worsens conformity, as it spreads the radiation to the area surrounding the PTV. The maximum dose to the critical structures also increases slightly. Compared with plans used in the clinic which generally have uniformly spaced beam angles, the optimal clinically acceptable plans obtained via the methods herein do not have equispaced beams. The optimal beam angles returned appear to be nonintuitive, and depend on PTV size and geometry and the spatial relationship between the tumor and critical structures.

CONCLUSIONS

The MIP model described allows simultaneous optimization over the space of beamlet fluence weights and beam and couch angles. Based on experiments with tumor data, this approach can return good plans that are clinically acceptable and practical. This work distinguishes itself from recent IMRT research in several ways. First, in previous methods beam angles are selected before intensity map optimization. Herein, we employ 0/1 variables to model the set of candidate beams, and thereby allow the optimization process itself to select optimal beams. Second, instead of incorporating dose-volume criteria within the objective function as in previous work, herein, a combination of discrete and continuous variables associated with each voxel provides a mechanism to strictly enforce dose-volume criteria within the constraints. Third, using the construct of critical-normal-tissue-ring within the objective function can enhance the achievement of conformal plans. Based on the three tumor sites considered, it appears that volume and spatial geometry with respect to the PTV are important factors to consider when selecting objectives to optimize, and in estimating how well suited a particular model is for achieving a specified goal.

Clinical knowledge-based inverse treatment planning

Clinical IMRT treatment plans are currently made using dose-based optimization algorithms, which do not consider the nonlinear dose-volume effects for tumours and normal structures. The choice of structure specific importance factors represents an additional degree of freedom of the system and makes rigorous optimization intractable. The purpose of this work is to circumvent the two problems by developing a biologically more sensible yet clinically practical inverse planning framework. To implement this, the dose-volume status of a structure was characterized by using the effective volume in the voxel domain. A new objective function was constructed with the incorporation of the volumetric information of the system so that the figure of merit of a given IMRT plan depends not only on the dose deviation from the desired distribution but also the dose-volume status of the involved organs. The conventional importance factor of an organ was written into a product of two components: (i) a generic importance that parametrizes the relative importance of the organs in the ideal situation when the goals for all the organs are met; (ii) a dose-dependent factor that quantifies our level of clinical/dosimetric satisfaction for a given plan. The generic importance can be determined a priori, and in most circumstances, does not need adjustment, whereas the second one, which is responsible for the intractable behaviour of the trade-off seen in conventional inverse planning, was determined automatically. An inverse planning module based on the proposed formalism was implemented and applied to a prostate case and a head-neck case. A comparison with the conventional inverse planning technique indicated that, for the same target dose coverage, the critical structure sparing was substantially improved for both cases. The incorporation of clinical knowledge allows us to obtain better IMRT plans and makes it possible to auto-select the importance factors, greatly facilitating the inverse planning process. The new formalism proposed also reveals the relationship between different inverse planning schemes and gives important insight into the problem of therapeutic plan optimization. In particular, we show that the EUD-based optimization is a special case of the general inverse planning formalism described in this paper.

Speed and convergence properties of gradient algorithms for optimization of IMRT

Gradient algorithms are the most commonly employed search methods in the routine optimization of IMRT plans. It is well known that local minima can exist for dose-volume-based and biology-based objective functions. The purpose of this paper is to compare the relative speed of different gradient algorithms, to investigate the strategies for accelerating the optimization process, to assess the validity of these strategies, and to study the convergence properties of these algorithms for dose-volume and biological objective functions. With these aims in mind, we implemented Newton's, conjugate gradient (CG), and the steepest decent (SD) algorithms for dose-volume- and EUD-based objective functions. Our implementation of Newton's algorithm approximates the second derivative matrix (Hessian) by its diagonal. The standard SD algorithm and the CG algorithm with "line minimization" were also implemented. In addition, we investigated the use of a variation of the CG algorithm, called the "scaled conjugate gradient" (SCG) algorithm. To accelerate the optimization process, we investigated the validity of the use of a "hybrid optimization" strategy, in which approximations to calculated dose distributions are used during most of the iterations. Published studies have indicated that getting trapped in local minima is not a significant problem. To investigate this issue further, we first obtained, by trial and error, and starting with uniform intensity distributions, the parameters of the dose-volume- or EUD-based objective functions which produced IMRT plans that satisfied the clinical requirements. Using the resulting optimized intensity distributions as the initial guess, we investigated the possibility of getting trapped in a local minimum. For most of the results presented, we used a lung cancer case. To illustrate the generality of our methods, the results for a prostate case are also presented. For both dose-volume and EUD based objective functions, Newton's method far outperforms other algorithms in terms of speed. The SCG algorithm, which avoids expensive "line minimization," can speed up the standard CG algorithm by at least a factor of 2. For the same initial conditions, all algorithms converge essentially to the same plan. However, we demonstrate that for any of the algorithms studied, starting with previously optimized intensity distributions as the initial guess but for different objective function parameters, the solution frequently gets trapped in local minima. We found that the initial intensity distribution obtained from IMRT optimization utilizing objective function parameters, which favor a specific anatomic structure, would lead to a local minimum corresponding to that structure. Our results indicate that from among the gradient algorithms tested, Newton's method appears to be the fastest by far. Different gradient algorithms have the same convergence properties for dose-volume- and EUD-based objective functions. The hybrid dose calculation strategy is valid and can significantly accelerate the optimization process. The degree of acceleration achieved depends on the type of optimization problem being addressed (e.g., IMRT optimization, intensity modulated beam configuration optimization, or objective function parameter optimization). Under special conditions, gradient algorithms will get trapped in local minima, and reoptimization, starting with the results of previous optimization, will lead to solutions that are generally not significantly different from the local minimum.

Selection of beam orientations in intensity-modulated radiation therapy using single-beam indices and integer programming

While the process of IMRT planning involves optimization of the dose distribution, the procedure for selecting the beam inputs for this process continues to be largely trial-and-error. We have developed an integer programming (IP) optimization method to optimize beam orientation using mean organ-at-risk (MOD) data from single-beam plans. Two test cases were selected in which one organ-at-risk (OAR) and four OARs were simulated, respectively, along with a PTV. Beam orientation space was discretized in 10 degrees increments. For each beam orientation, a single-beam plan without intensity modulation and without constraints on OAR dose was generated and normalized to yield a mean PTV dose of 2 Gy and the corresponding MOD was calculated. The degree of OAR sparing was related to the average OAR MODs resulting from the beam orientations utilized with improvements of up to 10% at some dose levels. On the other hand, OAR DVHs in the IMRT plans were insensitive to beam numbers (in the 6-9 range) for similar average single-beam MODs. These MOD data were input to an IP optimization process, which then selected specified numbers of beam angles as inputs to a treatment planning system. Our results show that sets of beam angles with lower average single-beam MODs produce IMRT plans with better OAR sparing than manually selected beam angles. To optimize beam orientations, weights were assigned to each OAR following MOD input to the IP which was subsequently solved using the branch-and-cut algorithm. Seven-beam orientations obtained from solving the IP were applied to the test case with four OARs and the resulting plan with a dose prescription of 63 Gy was compared with an equi-spaced beam plan. The IP selected beams produced dose-volume improvements of up to 40% for OARs proximal to the PTV. Further improvement in the DVH can be obtained by increasing the weights assigned to these OARs but at the expense of the remaining OARs.

Plug pattern optimization for gamma knife radiosurgery treatment planning

PURPOSE

To develop a novel dose optimization algorithm for improving the sparing of critical structures during gamma knife radiosurgery by shaping the plug pattern of each individual shot.

METHOD AND MATERIALS

We first use a geometric information (medial axis) aided guided evolutionary simulated annealing (GESA) optimization algorithm to determine the number of shots and isocenter location, size, and weight of each shot. Then we create a plug quality score system that checks the dose contribution to the volume of interest by each plug in the treatment plan. A positive score implies that the corresponding source could be open to improve tumor coverage, whereas a negative score means the source could be blocked for the purpose of sparing normal and critical structures. The plug pattern is then optimized via the GESA algorithm that is integrated with this score system. Weight and position of each shot are also tuned in this procedure.

RESULTS

An acoustic tumor case is used to evaluate our algorithm. Compared to the treatment plan generated without plug patterns, adding an optimized plug pattern into the treatment planning process boosts tumor coverage index from 95.1% to 97.2%, reduces RTOG conformity index from 1.279 to 1.167, lowers Paddick's index from 1.34 to 1.20, and trims the critical structure receiving more than 30% maximum dose from 16 mm(3) to 6 mm(3).

CONCLUSIONS

Automated GESA-based plug pattern optimization of gamma knife radiosurgery frees the treatment planning team from the manual forward planning procedure and provides an optimal treatment plan.