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Lei Xing

Publications and source records attributed to Lei Xing.

At least 37 records · Page 2Linked to original sources
PubMed2005

Dose-volume based ranking of incident beam direction and its utility in facilitating IMRT beam placement.

PURPOSE: Beam orientation optimization in intensity-modulated radiation therapy (IMRT) is computationally intensive, and various single beam ranking techniques have been proposed to reduce the search space. Up to this point, none of the existing ranking techniques considers the clinically important dose-volume effects of the involved structures, which may lead to clinically irrelevant angular ranking. The purpose of this work is to develop a clinically sensible angular ranking model with incorporation of dose-volume effects and to show its utility for IMRT beam placement. METHODS AND MATERIALS: The general consideration in constructing this angular ranking function is that a beamlet/beam is preferable if it can deliver a higher dose to the target without exceeding the tolerance of the sensitive structures located on the path of the beamlet/beam. In the previously proposed dose-based approach, the beamlets are treated independently and, to compute the maximally deliverable dose to the target volume, the intensity of each beamlet is pushed to its maximum intensity without considering the values of other beamlets. When volumetric structures are involved, the complication arises from the fact that there are numerous dose distributions corresponding to the same dose-volume tolerance. In this situation, the beamlets are not independent and an optimization algorithm is required to find the intensity profile that delivers the maximum target dose while satisfying the volumetric constraints. In this study, the behavior of a volumetric organ was modeled by using the equivalent uniform dose (EUD). A constrained sequential quadratic programming algorithm (CFSQP) was used to find the beam profile that delivers the maximum dose to the target volume without violating the EUD constraint or constraints. To assess the utility of the proposed technique, we planned a head-and-neck and abdominal case with and without the guidance of the angular ranking information. The qualities of the two types of IMRT plans were compared quantitatively. RESULTS: An effective angular ranking model with consideration of volumetric effect has been developed. It is shown that the previously reported dose-based angular ranking represents a special case of the general formalism proposed here. Application of the technique to a abdominal and a head-and-neck IMRT case indicated that the proposed technique is capable of producing clinically sensible angular ranking. In both cases, we found that the IMRT plans obtained under the guidance of EUD-based angular ranking were improved in comparison with that obtained using the conventional uniformly spaced beams. CONCLUSIONS: The EUD-based function is a general approach for angular ranking and allows us to identify the potentially good and bad angles for clinically complicated cases. The ranking can be used either as a guidance to facilitate the manual beam placement or as prior information to speed up the computer search for the optimal beam configuration. Thus the proposed technique should have positive clinical impact in facilitating the IMRT planning process.

Abdominal Neoplasms↗
PubMed2005

Narrow band deformable registration of prostate magnetic resonance imaging, magnetic resonance spectroscopic imaging, and computed tomography studies.

PURPOSE: Endorectal (ER) coil-based magnetic resonance imaging (MRI) and magnetic resonance spectroscopic imaging (MRSI) is often used to obtain anatomic and metabolic images of the prostate and to accurately identify and assess the intraprostatic lesions. Recent advancements in high-field (3 Tesla or above) MR techniques affords significantly enhanced signal-to-noise ratio and makes it possible to obtain high-quality MRI data. In reality, the use of rigid or inflatable endorectal probes deforms the shape of the prostate gland, and the images so obtained are not directly usable in radiation therapy planning. The purpose of this work is to apply a narrow band deformable registration model to faithfully map the acquired information from the ER-based MRI/MRSI onto treatment planning computed tomography (CT) images. METHODS AND MATERIALS: A narrow band registration, which is a hybrid method combining the advantages of pixel-based and distance-based registration techniques, was used to directly register ER-based MRI/MRSI with CT. The normalized correlation between the two input images for registration was used as the metric, and the calculation was restricted to those points contained in the narrow bands around the user-delineated structures. The narrow band method is inherently efficient because of the use of a priori information of the meaningful contour data. The registration was performed in two steps. First, the two input images were grossly aligned using a rigid registration. The detailed mapping was then modeled by free form deformations based on B-spline. The limited memory Broyden-Fletcher-Goldfarb-Shanno algorithm (L-BFGS), which is known for its superior performance in dealing with high-dimensionality problems, was implemented to optimize the metric function. The convergence behavior of the algorithm was studied by self-registering an MR image with 100 randomly initiated relative positions. To evaluate the performance of the algorithm, an MR image was intentionally distorted, and an attempt was then made to register the distorted image with the original one. The ability of the algorithm to recover the original image was assessed using a checkerboard graph. The mapping of ER-based MRI onto treatment planning CT images was carried out for two clinical cases, and the performance of the registration was evaluated. RESULTS: A narrow band deformable image registration algorithm has been implemented for direct registration of ER-based prostate MRI/MRSI and CT studies. The convergence of the algorithm was confirmed by starting the registration experiment from more than 100 different initial conditions. It was shown that the technique can restore an MR image from intentionally introduced deformations with an accuracy of approximately 2 mm. Application of the technique to two clinical prostate MRI/CT registrations indicated that it is capable of producing clinically sensible mapping. The whole registration procedure for a complete three-dimensional study (containing 256 x 256 x 64 voxels) took less than 15 min on a standard personal computer, and the convergence was usually achieved in fewer than 100 iterations. CONCLUSIONS: A deformable image registration procedure suitable for mapping ER-based MRI data onto planning CT images was presented. Both hypothetical tests and patient studies have indicated that the registration is reliable and provides a valuable tool to integrate the ER-based MRI/MRSI information to guide prostate radiation therapy treatment.

Algorithms↗
PubMed2005

Quantitation of the a priori dosimetric capabilities of spatial points in inverse planning and its significant implication in defining IMRT solution space.

In inverse planning, the likelihood for the points in a target or sensitive structure to meet their dosimetric goals is generally heterogeneous and represents the a priori knowledge of the system once the patient and beam configuration are chosen. Because of this intrinsic heterogeneity, in some extreme cases, a region in a target may never meet the prescribed dose without seriously deteriorating the doses in other areas. Conversely, the prescription in a region may be easily met without violating the tolerance of any sensitive structure. In this work, we introduce the concept of dosimetric capability to quantify the a priori information and develop a strategy to integrate the data into the inverse planning process. An iterative algorithm is implemented to numerically compute the capability distribution on a case specific basis. A method of incorporating the capability data into inverse planning is developed by heuristically modulating the importance of the individual voxels according to the a priori capability distribution. The formalism is applied to a few specific examples to illustrate the technical details of the new inverse planning technique. Our study indicates that the dosimetric capability is a useful concept to better understand the complex inverse planning problem and an effective use of the information allows us to construct a clinically more meaningful objective function to improve IMRT dose optimization techniques.

Algorithms↗
PubMed2005

SMNDelta7, the major product of the centromeric survival motor neuron (SMN2) gene, extends survival in mice with spinal muscular atrophy and associates with full-length SMN.

Spinal muscular atrophy (SMA) is an autosomal recessive disorder in humans which results in the loss of motor neurons. It is caused by reduced levels of the survival motor neuron (SMN) protein as a result of loss or mutation of the SMN1 gene. SMN is encoded by two genes, SMN1 and SMN2, which essentially differ by a single nucleotide in exon 7. As a result, the majority of the transcript from SMN2 lacks exon 7 (SMNDelta7). SMNDelta7 may be toxic and detrimental in SMA, which, if true, could lead to adverse effects with drugs that stimulate expression of SMN2. To determine the role of SMNDelta7 in SMA, we created transgenic mice expressing SMNDelta7 and crossed them onto a severe SMA background. We found that the SMNDelta7 is not detrimental in that it extends survival of SMA mice from 5.2 to 13.3 days. Unlike mice with selective deletion of SMN exon 7 in muscle, these mice with a small amount of full-length SMN (FL-SMN) did not show a dystrophic phenotype. This indicates that low levels of FL-SMN as found in SMA patients and absence of FL-SMN in muscle tissue have different effects and raises the question of the importance of high SMN levels in muscle in the presentation of SMA. SMN and SMNDelta7 can associate with each other and we suggest that this association stabilizes SMNDelta7 protein turnover and ameliorates the SMA phenotype by increasing the amount of oligomeric SMN. The increased survival of the SMNDelta7 SMA mice we report will facilitate testing of therapies and indicates the importance of considering co-complexes of SMN and SMNDelta7 when analyzing SMN function.

Animals↗
PubMed2005

Measurement of ionizing radiation using carbon nanotube field effect transistor.

Single-walled carbon nanotubes (SWNTs) are a new class of highly promising nanomaterials for future nano-electronics. Here, we present an initial investigation of the feasibility of using SWNT field effect transistors (SWNT-FETs) formed on silicon-oxide substrates and suspended FETs for radiation dosimetry applications. Electrical measurements and atomic force microscopy (AFM) revealed the intactness of SWNT-FET devices after exposure to over 1 Gy of 6 MV therapeutic x-rays. The sensitivity of SWNT-FET devices to x-ray irradiation is elucidated by real-time dose monitoring experiments and accumulated dose reading based on threshold voltage shift. SWNT-FET devices exhibit sensitivities to x-rays that are at least comparable to or orders of magnitude higher than commercial MOSFET (metal-oxide semiconductor field effect transistor) dosimeters and could find applications as miniature dosimeters for microbeam profiling and implantation.

Electrons↗
PubMed2005

In vivo prostate magnetic resonance spectroscopic imaging using two-dimensional J-resolved PRESS at 3 T.

In vivo magnetic resonance spectroscopic imaging of the prostate using single-voxel and multivoxel two-dimensional (2D) J-resolved sequences is investigated at a main magnetic field strength of 3 T. Citrate, an important metabolite often used to aid the detection of prostate cancer in magnetic resonance spectroscopic exams, can be reliably detected along with the other metabolites using this method. We show simulations and measurements of the citrate metabolite using 2D J-resolved spectroscopy to characterize the spectral pattern. Furthermore, using spiral readout gradients, the single-voxel 2D J-resolved method is extended to provide the spatial distribution information as well all within a reasonable scan time (17 min). Phantom and in vivo data are presented to illustrate the multivoxel 2D J-resolved spiral chemical shift imaging sequence.

Choline↗
PubMed2005

cDNA cloning, sequence analysis of the porcine LIM and cysteine-rich domain 1 gene.

LIM domain proteins are important regulators in cell growth, cell fate determination, cell differentiation and remodeling of the cell cytoskeleton by their interaction with various structural proteins, kinases and transcriptional regulators. Using molecular biology combined with in silico cloning, we have cloned the complete coding sequence of pig LIM and the cysteine-rich domain 1 gene (LMCD1) which encodes a 363 amino acid protein. The estimated molecular weight of the LMCD1 protein is 40,788 Da with a pI of 8.39. It was found to be highly expressed in both skeletal muscle and cardiac muscle. Alignment analysis revealed that the deduced protein sequence shares 86%, 91% and 93% homology with that of its human, mouse and rat counterparts, respectively. The LMCD1 protein was predicted by bioinformatics software to contain a novel cysteine-rich domain in the N-terminal region, two LIM domains in the C-terminal region, nine potential protein kinase C phosphorylation sites, seven casein kinase II phosphorylation sites, a tyrosine kinase phosphorylation site, seven N-glycosylation and N-myristoylation sites and a single potential N-glycosylation site, which is similar to the protein's human counterpart. Phylogenetic tree was constructed by aligning the amino acid sequences of the LIM domain from different species. In addition, four base mutations were detected by comparing the sequences of Large White pigs with those of Chinese Meishan pigs. The G294A mutation site was confirmed by polymerase chain reaction-single-strand conformation polymorphism analysis. Its allele frequencies were studied in five pig breeds.

Amino Acid Sequence↗
PubMed2005

Investigation of using a power function as a cost function in inverse planning optimization.

The purpose of this paper is to investigate the use of a power function as a cost function in inverse planning optimization. The cost function for each structure is implemented as an exponential power function of the deviation between the resultant dose and prescribed or constrained dose. The total cost function for all structures is a summation of the cost function of every structure. When the exponents of all terms in the cost function are set to 2, the cost function becomes a classical quadratic cost function. An independent optimization module was developed and interfaced with a research treatment planning system from the University of North Carolina for dose calculation and display of results. Three clinical cases were tested for this study with various exponents set for tumor targets and sensitive structures. Treatment plans with these exponent settings were compared, using dose volume histograms. The results of our study demonstrated that using an exponent higher than 2 in the cost function for the target achieved better dose homogeneity than using an exponent of 2. An exponent higher than 2 for serial sensitive structures can effectively reduce the maximum dose. Varying the exponent from 2 to 4 resulted in the most effective changes in dose volume histograms while the change from 4 to 8 is less drastic, indicating a situation of saturation. In conclusion, using a power function with exponent greater than 2 as a cost function can effectively achieve homogeneous dose inside the target and/or minimize maximum dose to the critical structures.

Algorithms↗
PubMed2005

Towards biologically conformal radiation therapy (BCRT): selective IMRT dose escalation under the guidance of spatial biology distribution.

It is well known that the spatial biology distribution (e.g., clonogen density, radiosensitivity, tumor proliferation rate, functional importance) in most tumors and sensitive structures is heterogeneous. Recent progress in biological imaging is making the mapping of this distribution increasingly possible. The purpose of this work is to establish a theoretical framework to quantitatively incorporate the spatial biology data into intensity modulated radiation therapy (IMRT) inverse planning. In order to implement this, we first derive a general formula for determining the desired dose to each tumor voxel for a known biology distribution of the tumor based on a linear-quadratic model. The desired target dose distribution is then used as the prescription for inverse planning. An objective function with the voxel-dependent prescription is constructed with incorporation of the nonuniform dose prescription. The functional unit density distribution in a sensitive structure is also considered phenomenologically when constructing the objective function. Two cases with different hypothetical biology distributions are used to illustrate the new inverse planning formalism. For comparison, treatments with a few uniform dose prescriptions and a simultaneous integrated boost are also planned. The biological indices, tumor control probability (TCP) and normal tissue complication probability (NTCP), are calculated for both types of plans and the superiority of the proposed technique over the conventional dose escalation scheme is demonstrated. Our calculations revealed that it is technically feasible to produce deliberately nonuniform dose distributions with consideration of biological information. Compared with the conventional dose escalation schemes, the new technique is capable of generating biologically conformal IMRT plans that significantly improve the TCP while reducing or keeping the NTCPs at their current levels. Biologically conformal radiation therapy (BCRT) incorporates patient-specific biological information and provides an outstanding opportunity for us to truly individualize radiation treatment. The proposed formalism lays a technical foundation for BCRT and allows us to maximally exploit the technical capacity of IMRT to more intelligently escalate the radiation dose.

Dose-Response Relationship, Radiation↗
PubMed2005

Optimization of radiotherapy dose-time fractionation with consideration of tumor specific biology.

The "four Rs" of radiobiology play an important role in the design of radiation therapy treatment protocol. The purpose of this work is to explore their influence on external beam radiotherapy for fast and slowly proliferating tumors and develop an optimization framework for tumor-biology specific dose-time-fractionation scheme. The linear quadratic model is used to describe radiation response of tumor, in which the time dependence of sublethal damage repair and the redistribution and reoxygenation effects are included. The optimum radiotherapeutic strategy is defined as the treatment scheme that maximizes tumor biologically effective dose (BED) while keeping normal tissue BED constant. The influence of different model parameters on total dose, overall treatment time, fraction size, and intervals is also studied. The results showed that, for fast proliferating tumors, the optimum overall time is similar to the assumed kickoff time T(k) and almost independent of interval patterns. Significant increase in tumor control can be achieved using accelerated schemes for the tumors with doubling time smaller than 3 days, but little is gained for those with doubling time greater than 5 days. The incomplete repair of normal tissues between two consecutive fractions in standard fractionation has almost no influence on the fractional doses, even for the hyperfractionation with an interval time of 8 h. However, when the resensitization effect is included, the fractional doses at the beginning and end of each irradiated week become obviously higher than others in the optimum scheme and the hyperfractionation scheme has little advantage over the standard or hypofractionation one. For slowly proliferating tumors, provided that the alpha/beta ratio of the tumor is comparable to that of the normal tissues, a hypofractionation is more favorable. The overall treatment time should be larger than a minimum, which is predominantly determined by the resensitization time. The proposed technique provides a useful tool to systematically optimize radiotherapy for fast and slow proliferating tumors and sheds important insight into the complex problem of dose-time fractionation.

Biophysical Phenomena↗
PubMed2005

Optical detection of tumors in vivo by visible light tissue oximetry.

Endoscopy is a standard procedure for identifying tumors in patients suspected of having gastrointestinal (G.I.) cancer. The early detection of G.I. neoplasms during endoscopy is currently made by a subjective visual inspection that relies to a high degree on the experience of the examiner. This process can be difficult and unreliable, as tumor lesions may be visually indistinguishable from benign inflammatory conditions and the surrounding mucosa. In this study, we evaluated the ability of local ischemia detection using visible light spectroscopy (VLS) to differentiate neoplastic from normal tissue based on capillary tissue oxygenation during endoscopy. Real-time data were collected (i) from human subjects (N = 34) monitored at various sites during endoscopy (enteric mucosa, malignant, and abnormal tissue such as polyps) and (ii) murine animal subjects with human tumor xenografts. Tissue oximetry in human subjects during endoscopy revealed a tissue oxygenation (StO2%, mean +/- SD) of 46 +/- 22% in tumors, which was significantly lower than for normal mucosal oxygenation (72 +/- 4%; P < or = 0.0001). No difference in tissue oxygenation was observed between normal and non-tumor abnormal tissues (P = N.S.). Similarly, VLS tissue oximetry for murine tumors revealed a mean local tumor oxygenation of 45% in LNCaP, 50% in M21, and 24% in SCCVII tumors, all significantly lower than normal muscle tissue (74%, P < 0.001). These results were further substantiated by positive controls, where a rapid real-time drop in tumor oxygenation was measured during local ischemia induced by clamping or epinephrine. We conclude that VLS tissue oximetry can distinguish neoplastic tissue from normal tissue with a high specificity (though a low sensitivity), potentially aiding the endoscopic detection of gastrointestinal tumors.

Adult↗
PubMed2004

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.

Algorithms↗
PubMed2004

Quantitative measurement of MLC leaf displacements using an electronic portal image device.

The success of an IMRT treatment relies on the positioning accuracy of the MLC (multileaf collimator) leaves for both step-and-shoot and dynamic deliveries. In practice, however, there exists no effective and quantitative means for routine MLC QA and this has become one of the bottleneck problems in IMRT implementation. In this work we present an electronic portal image device (EPID) based method for fast and accurate measurement of MLC leaf positions at arbitrary locations within the 40 cm x 40 cm radiation field. The new technique utilizes the fact that the integral signal in a small region of interest (ROI) is a sensitive and reliable indicator of the leaf displacement. In this approach, the integral signal at a ROI was expressed as a weighted sum of the contributions from the displacements of the leaf above the point and the adjacent leaves. The weighting factors or linear coefficients of the system equations were determined by fitting the integral signal data for a group of pre-designed MLC leaf sequences to the known leaf displacements that were intentionally introduced during the creation of the leaf sequences. Once the calibration is done, the system can be used for routine MLC leaf positioning QA to detect possible leaf errors. A series of tests was carried out to examine the functionality and accuracy of the technique. Our results show that the proposed technique is potentially superior to the conventional edge-detecting approach in two aspects: (i) it deals with the problem in a systematic approach and allows us to take into account the influence of the adjacent MLC leaves effectively; and (ii) it may improve the signal-to-noise ratio and is thus capable of quantitatively measuring extremely small leaf positional displacements. Our results indicate that the technique can detect a leaf positional error as small as 0.1 mm at an arbitrary point within the field in the absence of EPID set-up error and 0.3 mm when the uncertainty is considered. Given its simplicity, efficiency and accuracy, we believe that the technique is ideally suitable for routine MLC leaf positioning QA.

Algorithms↗
PubMed2004

Multiobjective evolutionary optimization of the number of beams, their orientations and weights for intensity-modulated radiation therapy.

We propose a hybrid multiobjective (MO) evolutionary optimization algorithm (MOEA) for intensity-modulated radiotherapy inverse planning and apply it to optimize the number of incident beams, their orientations and intensity profiles. The algorithm produces a set of efficient solutions, which represent different clinical trade-offs and contains information such as variety of dose distributions and dose-volume histograms. No importance factors are required and solutions can be obtained in regions not accessible by conventional weighted sum approaches. The application of the algorithm using a test case, a prostate and a head and neck tumour case is shown. The results are compared with MO inverse planning using a gradient-based optimization algorithm.

Algorithms↗
PubMed2004

Incorporating model parameter uncertainty into inverse treatment planning.

Radiobiological treatment planning depends not only on the accuracy of the models describing the dose-response relation of different tumors and normal tissues but also on the accuracy of tissue specific radiobiological parameters in these models. Whereas the general formalism remains the same, different sets of model parameters lead to different solutions and thus critically determine the final plan. Here we describe an inverse planning formalism with inclusion of model parameter uncertainties. This is made possible by using a statistical analysis-based frameset developed by our group. In this formalism, the uncertainties of model parameters, such as the parameter a that describes tissue-specific effect in the equivalent uniform dose (EUD) model, are expressed by probability density function and are included in the dose optimization process. We found that the final solution strongly depends on distribution functions of the model parameters. Considering that currently available models for computing biological effects of radiation are simplistic, and the clinical data used to derive the models are sparse and of questionable quality, the proposed technique provides us with an effective tool to minimize the effect caused by the uncertainties in a statistical sense. With the incorporation of the uncertainties, the technique has potential for us to maximally utilize the available radiobiology knowledge for better IMRT treatment.

Algorithms↗
PubMed2004

Feasibility study of beam orientation class-solutions for prostate IMRT.

IMRT is being increasingly used for treatment of prostate cancer. In practice, however, the beam orientations used for the treatments are still selected empirically, without any guideline. The purpose of this work was to investigate interpatient variation of the optimal beam configuration and to facilitate intensity modulated radiation therapy (IMRT) prostate treatment planning by proposing a set of beam orientation class-solutions for a range of numbers of incident beams. We used fifteen prostate cases to generate the beam orientation class-solutions. For each patient and a given number of incident beams, a multiobjective optimization engine was employed to provide optimal beam directions. For the fifteen cases considered, the gantry angle of any of the optimized plans were all distributed within a certain range The angular distributions of the optimal beams were analyzed and the most selected directions are identified as optimal directions. The optimal directions for all patients are averaged to obtain the class-solution. The class-solution gantry angles for prostate IMRT were found to be: three beams (0 degrees, 120 degrees, 240 degrees), five beams (35 degrees, 110 degrees, 180 degrees, 250 degrees, 325 degrees), six beams (0 degrees, 60 degrees, 120 degrees, 180 degrees, 240 degrees, 300 degrees), seven beams (25 degrees, 75 degrees, 130 degrees, 180 degrees, 230 degrees, 285 degrees, 335 degrees), eight beams (20 degrees, 70 degrees, 110 degrees, 150 degrees, 200 degrees, 250 degrees, 290 degrees, 340 degrees), and nine beams (20 degrees, 60 degrees, 100 degrees, 140 degrees, 180 degrees, 220 degrees, 260 degrees, 300 degrees, 340 degrees). The level of validity of the class-solutions was tested using an additional clinical prostate case by comparing with the individually optimized beam configurations. The difference between the plans obtained with class-solutions and patient-specific optimizations was found to be clinically insignificant.

Algorithms↗