A dosimetrically motivated pathfinding approach for non-isocentric dynamic trajectory radiotherapy.

Objective.Non-isocentric dynamic trajectory radiotherapy (DTRT) involves dynamic table translations in synchrony with intensity modulation and dynamic gantry, table, and/or collimator rotation. This work aims to develop and evaluate a novel dosimetrically motivated path determination technique for non-isocentric DTRT.Approach.The path determination considers all available beam directions, given on a user-specified grid of gantry angle, table angle, and longitudinal, vertical, and lateral table position. Additionally, the source-to-target distance of all beam directions can be extended by moving the table away from the gantry along the central beam axis to increase the collision-free space. The path determination uses a column generation algorithm to iteratively add beam directions to paths until a user-defined total path length is reached. A subsequent direct aperture optimization of the intensity modulation along the paths creates deliverable plans. Non-isocentric DTRT plans using the path determination and using a manual path setup were created for a craniospinal and a spinal irradiation case. Furthermore, VMAT, isocentric DTRT, and non-isocentric DTRT plans are created for a breast, head and neck (H&N), and esophagus case. Additionally, a HyperArc plan is created for the H&N case. The plans are compared in terms of the dosimetric treatment plan quality and estimated delivery time.Main results.For the craniospinal and spinal irradiation case, using path determination results in dose distributions with improved conformity but a slightly worse target homogeneity compared to manual path setup. The non-isocentric DTRT plans maintained target coverage while reducing the mean dose to organs-at-risk on average by 1.7 Gy (breast), 1.0 Gy (H&N), and 1.6 Gy (esophagus) compared to the VMAT plans and by 0.8 Gy (breast), 0.6 Gy (H&N), and 0.8 Gy (esophagus) compared to the isocentric DTRT plans.Significance.A general dosimetrically motivated path determination applicable to non-isocentric DTRT plans is successfully developed, further advancing the treatment planning for non-isocentric DTRT.

Dosimetrically motivated beam-angle optimization for non-coplanar arc radiotherapy with and without dynamic collimator rotation.

BACKGROUND: Non-coplanar techniques have shown to improve the achievable dose distribution compared to standard coplanar techniques for multiple treatment sites but finding optimal beam directions is challenging. Dynamic collimator trajectory radiotherapy (colli-DTRT) is a new intensity modulated radiotherapy technique that uses non-coplanar partial arcs and dynamic collimator rotation. PURPOSE: To solve the beam angle optimization (BAO) problem for colli-DTRT and non-coplanar VMAT (NC-VMAT) by determining the table-angle and the gantry-angle ranges of the partial arcs through iterative 4π fluence map optimization (FMO) and beam direction elimination. METHODS: BAO considers all available beam directions sampled on a gantry-table map with the collimator angle aligned to the superior-inferior axis (colli-DTRT) or static (NC-VMAT). First, FMO is performed, and beam directions are scored based on their contributions to the objective function. The map is thresholded to remove the least contributing beam directions, and arc candidates are formed by adjacent beam directions with the same table angle. Next, FMO and arc candidate trimming, based on objective function penalty score, is performed iteratively until a desired total gantry angle range is reached. Direct aperture optimization on the final set of colli-DTRT or NC-VMAT arcs generates deliverable plans. colli-DTRT and NC-VMAT plans were created for seven clinically-motivated cases with targets in the head and neck (two cases), brain, esophagus, lung, breast, and prostate. colli-DTRT and NC-VMAT were compared to coplanar VMAT plans as well as to class-solution non-coplanar VMAT plans for the brain and head and neck cases. Dosimetric validation was performed for one colli-DTRT (head and neck) and one NC-VMAT (breast) plan using film measurements. RESULTS: Target coverage and conformity was similar for all techniques. colli-DTRT and NC-VMAT plans had improved dosimetric performance compared to coplanar VMAT for all treatment sites except prostate where all techniques were equivalent. For the head and neck and brain cases, mean dose reduction-in percentage of the prescription dose-to parallel organs was on average 0.7% (colli-DTRT), 0.8% (NC-VMAT) and 0.4% (class-solution) compared to VMAT. The reduction in D2% for the serial organs was on average 1.7% (colli-DTRT), 2.0% (NC-VMAT) and 0.9% (class-solution). For the esophagus, lung, and breast cases, mean dose reduction to parallel organs was on average 0.2% (colli-DTRT) and 0.3% (NC-VMAT) compared to VMAT. The reduction in D2% for the serial organs was on average 1.3% (colli-DTRT) and 0.9% (NC-VMAT). Estimated delivery times for colli-DTRT and NC-VMAT were below 4 min for a full gantry angle range of 720°, including transitions between arcs, except for the brain case where multiple arcs covered the whole table angle range. These times are in the same order as the class-solution for the head and neck and brain cases. Total optimization times were 25%-107% longer for colli-DTRT, including BAO, compared to VMAT. CONCLUSIONS: We successfully developed dosimetrically motivated BAO for colli-DTRT and NC-VMAT treatment planning. colli-DTRT and NC-VMAT are applicable to multiple treatment sites, including body sites, with beneficial or equivalent dosimetric performances compared to coplanar VMAT and reasonable delivery times.

Organs-at-risk dose and normal tissue complication probability with dynamic trajectory radiotherapy (DTRT) for head and neck cancer.

We compared dynamic trajectory radiotherapy (DTRT) to state-of-the-art volumetric modulated arc therapy (VMAT) for 46 head and neck cancer cases. DTRT had lower dose to salivary glands and swallowing structure, resulting in lower predicted xerostomia and dysphagia compared to VMAT. DTRT is deliverable on C-arm linacs with high dosimetric accuracy.

Robust optimization and assessment of dynamic trajectory and mixed-beam arc radiotherapy: a preliminary study.

Objective.Dynamic trajectory radiotherapy (DTRT) and dynamic mixed-beam arc therapy (DYMBARC) exploit non-coplanarity and, for DYMBARC, simultaneously optimized photon and electron beams. Margin concepts to account for set-up uncertainties during delivery are ill-defined for electron fields. We develop robust optimization for DTRT&DYMBARC and compare dosimetric plan quality and robustness for both techniques and both optimization strategies for four cases.Approach.Cases for different treatment sites and clinical target volume (CTV) to planning target volume (PTV) margins,m, were investigated. Dynamic gantry-table-collimator photon paths were optimized to minimize PTV/organ-at-risk (OAR) overlap in beam's-eye-view and minimize potential photon multileaf collimator (MLC) travel. For DYMBARC plans, non-isocentric partial electron arcs or static fields with shortened source-to-surface distance (80 cm) were added. Direct aperture optimization (DAO) was used to simultaneously optimize MLC-based intensity modulation for both photon and electron beams yielding deliverable PTV-based DTRT&DYMBARC plans. Robust-optimized plans used the same paths/arcs/fields. DAO with stochastic programming was used for set-up uncertainties with equal weights in all translational directions and magnitudeδsuch thatm= 0.7δ. Robust analysis considered random errors in all directions with or without an additional systematic error in the worst 3D direction for the adjacent OARs.Main results.Electron contribution was 7%-41% of target dose depending on the case and optimization strategy for DYMBARC. All techniques achieved similar CTV coverage in the nominal (no error) scenario. OAR sparing was overall better in the DYMBARC plans than in the DTRT plans and DYMBARC plans were generally more robust to the considered uncertainties. OAR sparing was better in the PTV-based than in robust-optimized plans for OARs abutting or overlapping with the target volume, but more affected by uncertainties.Significance.Better plan robustness can be achieved with robust optimization than with margins. Combining electron arcs/fields with non-coplanar photon trajectories further improves robustness and OAR sparing.

Robustness analysis of dynamic trajectory radiotherapy and volumetric modulated arc therapy plans for head and neck cancer.

Background and purpose: Dynamic trajectory radiotherapy (DTRT) has been shown to improve healthy tissue sparing compared to volumetric arc therapy (VMAT). This study aimed to assess and compare the robustness of DTRT and VMAT treatment-plans for head and neck (H&N) cancer to patient-setup (PS) and machine-positioning uncertainties. Materials and methods: The robustness of DTRT and VMAT plans previously created for 46 H&N cases, prescribed 50-70 Gy to 95 % of the planning-target-volume, was assessed. For this purpose, dose distributions were recalculated using Monte Carlo, including uncertainties in PS (translation and rotation) and machine-positioning (gantry-, table-, collimator-rotation and multi-leaf collimator (MLC)). Plan robustness was evaluated by the uncertainties' impact on normal tissue complication probabilities (NTCP) for xerostomia and dysphagia and on dose-volume endpoints. Differences between DTRT and VMAT plan robustness were compared using Wilcoxon matched-pair signed-rank test (α = 5 %). Results: Average NTCP for moderate-to-severe xerostomia and grade ≥ II dysphagia was lower for DTRT than VMAT in the nominal scenario (0.5 %, p = 0.01; 2.1 %, p < 0.01) and for all investigated uncertainties, except MLC positioning, where the difference was not significant. Average differences compared to the nominal scenario were ≤ 3.5 Gy for rotational PS (≤ 3°) and machine-positioning (≤ 2°) uncertainties, <7 Gy for translational PS uncertainties (≤ 5 mm) and < 20 Gy for MLC-positioning uncertainties (≤ 5 mm). Conclusions: DTRT and VMAT plan robustness to the investigated uncertainties depended on uncertainty direction and location of the structure-of-interest to the target. NTCP remained on average lower for DTRT than VMAT even when considering uncertainties.

Technical note: Feasibility of gating for dynamic trajectory radiotherapy - Mechanical accuracy and dosimetric performance.

BACKGROUND: Dynamic trajectory radiotherapy (DTRT) extends state-of-the-art volumetric modulated arc therapy (VMAT) by dynamic table and collimator rotations during beam-on. The effects of intrafraction motion during DTRT delivery are unknown, especially regarding the possible interplay between patient and machine motion with additional dynamic axes. PURPOSE: To experimentally assess the technical feasibility and quantify the mechanical and dosimetric accuracy of respiratory gating during DTRT delivery. METHODS: A DTRT and VMAT plan are created for a clinically motivated lung cancer case and delivered to a dosimetric motion phantom (MP) placed on the table of a TrueBeam system using Developer Mode. The MP reproduces four different 3D motion traces. Gating is triggered using an external marker block, placed on the MP. Mechanical accuracy and delivery time of the VMAT and DTRT deliveries with and without gating are extracted from the logfiles. Dosimetric performance is assessed by means of gamma evaluation (3% global/2 mm, 10% threshold). RESULTS: The DTRT and VMAT plans are successfully delivered with and without gating for all motion traces. Mechanical accuracy is similar for all experiments with deviations <0.14° (gantry angle), <0.15° (table angle), <0.09° (collimator angle) and <0.08 mm (MLC leaf positions). For DTRT (VMAT), delivery times are 1.6-2.3 (1.6- 2.5) times longer with than without gating for all motion traces except one, where DTRT (VMAT) delivery is 5.0 (3.6) times longer due to a substantial uncorrected baseline drift affecting only DTRT delivery. Gamma passing rates with (without) gating for DTRT/VMAT were ≥96.7%/98.5% (≤88.3%/84.8%). For one VMAT arc without gating it was 99.6%. CONCLUSION: Gating is successfully applied during DTRT delivery on a TrueBeam system for the first time. Mechanical accuracy is similar for VMAT and DTRT deliveries with and without gating. Gating substantially improved dosimetric performance for DTRT and VMAT.

Impact of the gradient in gantry-table rotation on dynamic trajectory radiotherapy plan quality.

BACKGROUND: To improve organ at risk (OAR) sparing, dynamic trajectory radiotherapy (DTRT) extends VMAT by dynamic table and collimator rotation during beam-on. However, comprehensive investigations regarding the impact of the gantry-table (GT) rotation gradient on the DTRT plan quality have not been conducted. PURPOSE: To investigate the impact of a user-defined GT rotation gradient on plan quality of DTRT plans in terms of dosimetric plan quality, dosimetric robustness, deliverability, and delivery time. METHODS: The dynamic trajectories of DTRT are described by GT and gantry-collimator paths. The GT path is determined by minimizing the overlap of OARs with planning target volume (PTV). This approach is extended to consider a GT rotation gradient by means of a maximum gradient of the path ( G m a x ${G}_{max}$ ) between two adjacent control points ( G = | Δ table angle / Δ gantry angle | $G = | \Delta {{\mathrm{table\ angle}}/\Delta {\mathrm{gantry\ angle}}} |$ ) and maximum absolute change of G ( Δ G m a x ${{\Delta}}{G}_{max}$ ). Four DTRT plans are created with different maximum G&∆G: G m a x ${G}_{max}$ & Δ G m a x ${{\Delta}}{G}_{max}$  = 0.5&0.125 (DTRT-1), 1&0.125 (DTRT-2), 3&0.125 (DTRT-3) and 3&1|(DTRT-4), including 3-4 dynamic trajectories, for three clinically motivated cases in the head and neck and brain region (A, B, and C). A reference VMAT plan for each case is created. For all plans, plan quality is assessed and compared. Dosimetric plan quality is evaluated by target coverage, conformity, and OAR sparing. Dosimetric robustness is evaluated against systematic and random patient-setup uncertainties between ± 3 mm $ \pm 3\ {\mathrm{mm}}$ in the lateral, longitudinal, and vertical directions, and machine uncertainties between ± 4 ∘ $ \pm 4^\circ \ $ in the dynamically rotating machine components (gantry, table, collimator rotation). Delivery time is recorded. Deliverability and delivery accuracy on a TrueBeam are assessed by logfile analysis for all plans and additionally verified by film measurements for one case. All dose calculations are Monte Carlo based. RESULTS: The extension of the DTRT planning process with user-defined G m a x & Δ G m a x ${G}_{max}\& {{\Delta}}{G}_{max}$ to investigate the impact of the GT rotation gradient on plan quality is successfully demonstrated. With increasing G m a x & Δ G m a x ${G}_{max}\& {{\Delta}}{G}_{max}$ , slight (case C, D m e a n , p a r o t i d l . ${D}_{mean,\ parotid\ l.}$ : up to|-1|Gy) and substantial (case A, D 0.03 c m 3 , o p t i c n e r v e r . ${D}_{0.03c{m}^3,\ optic\ nerve\ r.}$ : up to -9.3 Gy, case|B, D m e a n , b r a i n $\ {D}_{mean,\ brain}$ : up to -4.7|Gy) improvements in OAR sparing are observed compared to VMAT, while maintaining similar target coverage. All plans are delivered on the TrueBeam. Expected and actual machine position values recorded in the logfiles deviated by <0.2° for gantry, table and collimator rotation. The film measurements agreed by >96% (2%|global/2 mm Gamma passing rate) with the dose calculation. With increasing G m a x & Δ G m a x ${G}_{max}\& {{\Delta}}{G}_{max}$ , delivery time is prolonged by <2 min/trajectory (DTRT-4) compared to VMAT and DTRT-1. The DTRT plans for case A and B and the VMAT plan for case C plan reveal the best dosimetric robustness for the considered uncertainties. CONCLUSION: The impact of the GT rotation gradient on DTRT plan quality is comprehensively investigated for three cases in the head and neck and brain region. Increasing freedom in this gradient improves dosimetric plan quality at the cost of increased delivery time for the investigated cases. No clear dependency of GT rotation gradient on dosimetric robustness is observed.

Dynamic Trajectory of a Patient-Reported Outcome and Its Associated Factors for Patients with Chronic Heart Failure: A Growth Mixture Model Approach.

Purpose: This study aimed to identify subgroups of chronic heart failure (CHF) patients with distinct trajectories of quality of life (QOL) and to identify baseline characteristics associated with the trajectories. Patients and methods: Two-year, prospective, cohort study including 315 patients with CHF was conducted from July 2017. Information on QOL assessed by CHF-patient-reported outcomes measure (CHF-PROM) was collected at baseline, 6, 12, 18, and 24 months. Demographic and clinical variables were recorded at baseline. Growth mixture model was used to identify distinct trajectories of CHF-PROM and its physical, psychological, social, and therapeutic domains. Single factor analysis was employed to assess the factors associated with development of CHF-PROM over time. Results: Two classes of overall score of CHF-PROM were identified: poorer (14.0%) and better (86.0%). Poorer class tended to be aged, have low diastolic blood pressure, have concomitant atrial fibrillation, diabetes, chronic obstructive pulmonary disease, cancers, and central nervous system diseases, and used nitrates. Three classes of physical scores were identified: unstable-poorer (5.2%), stable-poorer (29.4%) and better (65.4%). Age, NYHA grade, chronic obstructive pulmonary disease, combined with cancers and central nervous system diseases were related to the grouping. Poorer (8.6%) and better (91.4%) classes of psychological scores were identified. Poorer class tended to be female and had concomitant atrial fibrillation. Degenerate class (34.6%) and meliorate class (65.4%) of therapeutic scores were identified. Degenerate class tended to have concomitant chronic obstructive pulmonary disease and use less angiotensin converting enzyme inhibitors. Conclusion: We identified different classes with distinct trajectories of QOL that may help proper evaluate QOL and further improve its status for patients CHF.

Enabling non-isocentric dynamic trajectory radiotherapy by integration of dynamic table translations.

Objective.The purpose of this study is to develop a treatment planning process (TPP) for non-isocentric dynamic trajectory radiotherapy (DTRT) using dynamic gantry rotation, collimator rotation, table rotation, longitudinal, vertical and lateral table translations and intensity modulation and to validate the dosimetric accuracy.Approach.The TPP consists of two steps. First, a path describing the dynamic gantry rotation, collimator rotation and dynamic table rotation and translations is determined. Second, an optimization of the intensity modulation along the path is performed. We demonstrate the TPP for three use cases. First, a non-isocentric DTRT plan for a brain case is compared to an isocentric DTRT plan in terms of dosimetric plan quality and delivery time. Second, a non-isocentric DTRT plan for a craniospinal irradiation (CSI) case is compared to a multi-isocentric intensity modulated radiotherapy (IMRT) plan. Third, a non-isocentric DTRT plan for a bilateral breast case is compared to a multi-isocentric volumetric modulated arc therapy (VMAT) plan. The non-isocentric DTRT plans are delivered on a TrueBeam in developer mode and their dosimetric accuracy is validated using radiochromic films.Main results.The non-isocentric DTRT plan for the brain case is similar in dosimetric plan quality and delivery time to the isocentric DTRT plan but is expected to reduce the risk of collisions. The DTRT plan for the CSI case shows similar dosimetric plan quality while reducing the delivery time by 45% in comparison with the IMRT plan. The DTRT plan for the breast case showed better treatment plan quality in comparison with the VMAT plan. The gamma passing rates between the measured and calculated dose distributions are higher than 95% for all three plans.Significance.The versatile benefits of non-isocentric DTRT are demonstrated with three use cases, namely reduction of collision risk, reduced setup and delivery time and improved dosimetric plan quality.

Trajectory-based VMAT for cranial targets with delivery at shortened SAD.

INTRODUCTION: Trajectory-based volumetric modulated arc therapy (tr-VMAT) treatment plans enable the option for noncoplanar delivery yielding steeper dose gradients and increased sparing of critical structures compared to conventional treatment plans. The addition of translational couch motion to shorten the effective source-to-axis distance (SAD) may result in improved delivery precision and an increased effective dose rate. In this work, tr-VMAT treatment plans using a noncoplanar "baseball stitch" trajectory were implemented, applied to patients presented with cranial targets, and compared to the clinical treatment plans. METHODS: A treatment planning workflow was implemented: (a) beamlet doses were calculated for control points defined along a baseball stitch trajectory using a collapsed-cone convolution-superposition algorithm; (b) VMAT treatment plans were optimized using the column generation approach; (c) a final dose distribution was calculated in Varian Eclipse using the analytical anisotropic algorithm by importing the optimized treatment plan parameters. Tr-VMAT plans were optimized for ten patients presented with cranial targets at both standard and shortened SAD, and compared to the clinical treatment plans through isodose distributions, dose-volume histograms, and dosimetric indices. The control point specifications of the optimized tr-VMAT plans were used to estimate the delivery time. RESULTS: The optimized tr-VMAT plans with both shortened and standard SAD delivery yielded a comparable plan quality to the clinical treatment plans. A statistically significant benefit was observed for dose gradient index and monitor unit efficiency for shortened SAD tr-VMAT plans, while improved target volume conformity was observed for the clinical treatment plan (P ≤ 0.05). A clear dosimetric benefit was not demonstrated between tr-VMAT delivery at shortened SAD compared to standard SAD, but shortened SAD delivery yielded a fraction size-dependent reduction in the estimated delivery time. CONCLUSION: The implementation of "baseball stitch" tr-VMAT treatment plans to patients presented with cranial targets demonstrated comparable plan quality to clinical treatment plans. The delivery at shortened SAD produced a fraction size-dependent decrease in estimated delivery time.

Simultaneous trajectory generation and volumetric modulated arc therapy optimization.

PURPOSE: Trajectory-based treatment planning involves the combination of a gantry-couch trajectory with volumetric modulated arc therapy (VMAT) treatment plan optimization. This work presents the implementation of an optimization methodology that generates a trajectory simultaneous with treatment plan optimization (simTr-VMAT). METHODS: The optimization algorithm is based on the column generation approach, in which a treatment plan is iteratively constructed through the solution of a subproblem called the "pricing problem." The property of the pricing problem to rank candidate apertures based on their associated price is leveraged to select an optimal aperture while simultaneously determining the trajectory path. A progressively increasing gantry-couch grid resolution is used to provide an initial coarse sampling of the angular solution space while maintaining fine control point spacing with the final treatment plan. The trajectory optimization was applied and compared to coplanar VMAT treatment plans for a lung patient, a glioblastoma patient, and a prostate patient. Algorithm validation was performed through the generation of 5000 random trajectories and optimization using column generation VMAT for each patient case, representing the solution space for the trajectory optimization problem. The simTr-VMAT trajectories were compared against these random trajectories based on a quality metric that prefers trajectories with few control points and low objective function value over long, inefficient trajectories. RESULTS: For the lung patient, the simTr-VMAT plan resulted in a decrease of the mean dose of 1.5 and 1.0 Gy to the heart and ipsilateral lung, respectively. For the glioblastoma patient, the simTr-VMAT plan resulted in improved planning target volume coverage with a decrease in mean dose to the eyes, lens, nose, and contralateral temporal lobe between 2 and 7 Gy. The prostate patient showed no clinically relevant dosimetric improvement. The simTr-VMAT treatment plans ranked at the 99.6, 96.3, and 99.4 percentiles compared to the distribution of randomly generated trajectories for the lung, glioblastoma, and prostate patients, respectively. CONCLUSION: The simTr-VMAT optimization methodology resulted in treatment plans with equivalent or improved dosimetric outcomes compared to coplanar VMAT treatment plans, with the trajectories resulting from the optimization ranking among the optimal trajectories for each patient case.

Identifying KDIGO Trajectory Phenotypes Associated with Increased Inpatient Mortality.

Acute kidney injury (AKI) is a complex systemic syndrome associated with high morbidity and mortality and risk for the subsequent development of renal and non-renal complications. Nearly 50% of patients in the ICU experience AKI. AKI severity is a key metric for evaluating patients risk of hospital mortality. Current AKI stratification is based on absolute changes in Serum Creatinine (SCr) and the maximal increase relative to the patients baseline value. However, such measurement does not consider either the progression or duration of AKI, both of which are associated with adverse outcomes post-AKI. In this article, by leveraging a large volume of SCr temporal variabilities, we present a novel model called Trajectory of Acute Kidney Injury (TAKI) for the identification of AKI trajectory subtypes. Experimental results demonstrate that TAKI is better than the existing trajectory subtyping methods on both the inpatient mortality stratification and the post-7-day AKI progression estimation. With TAKI, it is found that the trend of KDIGO trajectory appears to be more highly associated with inpatient mortality rates than the maximum KDIGO score.

Part 2: Dynamic mixed beam radiotherapy (DYMBER): Photon dynamic trajectories combined with modulated electron beams.

PURPOSE: The purpose of this study was to develop a treatment technique for dynamic mixed beam radiotherapy (DYMBER) utilizing increased degrees of freedom (DoF) of a conventional treatment unit including different particle types (photons and electrons), intensity and energy modulation and dynamic gantry, table, and collimator rotations. METHODS: A treatment planning process has been developed to create DYMBER plans combining photon dynamic trajectories (DTs) and step and shoot electron apertures collimated with the photon multileaf collimator (pMLC). A gantry-table path is determined for the photon DTs with minimized overlap of the organs at risk (OARs) with the target. In addition, an associated dynamic collimator rotation is established with minimized area between the pMLC leaves and the target contour. pMLC sequences of photon DTs and electron pMLC apertures are then simultaneously optimized using direct aperture optimization (DAO). Subsequently, the final dose distribution of the electron pMLC apertures is calculated using the Swiss Monte Carlo Plan (SMCP). The pMLC sequences of the photon DTs are then re-optimized with a finer control point resolution and with the final electron dose distribution taken into account. Afterwards, the final photon dose distribution is calculated also using the SMCP and summed together with the one of the electrons. This process is applied for a brain and two head and neck cases. The resulting DYMBER dose distributions are compared to those of dynamic trajectory radiotherapy (DTRT) plans consisting only of photon DTs and clinically applied VMAT plans. Furthermore, the deliverability of the DYMBER plans is verified in terms of dosimetric accuracy, delivery time and collision avoidance. For this purpose, The DYMBER plans are delivered to Gafchromic EBT3 films placed in an anthropomorphic head phantom on a Varian TrueBeam linear accelerator. RESULTS: For each case, the dose homogeneity in the target is similar or better for DYMBER compared to DTRT and VMAT. Averaged over all three cases, the mean dose to the parallel OARs is 16% and 28% lower, D2% to the serial OARs is 17% and 37% lower and V10% to normal tissue is 12% and 4% lower for the DYMBER plans compared to the DTRT and VMAT plans, respectively. The DYMBER plans are delivered without collision and with a 4-5 min longer delivery time than the VMAT plans. The absolute dose measurements are compared to calculation by gamma analysis using 2% (global)/2 mm criteria with passing rates of at least 99%. CONCLUSIONS: A treatment technique for DYMBER has been successfully developed and verified for its deliverability. The dosimetric superiority of DYMBER over DTRT and VMAT indicates utilizing increased DoF to be the key to improve brain and head and neck radiation treatments in future.

Part 1: Optimization and evaluation of dynamic trajectory radiotherapy.

PURPOSE: Although volumetric modulated arc therapy (VMAT) is a well-accepted treatment technique in radiotherapy using a coplanar delivery approach, VMAT might be further improved by including dynamic table and collimator rotations leading to dynamic trajectory radiotherapy (DTRT). In this work, an optimization procedure for DTRT was developed and the potential benefit of DTRT was investigated for different treatment sites. METHODS: For this purpose, a dedicated optimization framework for DTRT was developed using the Eclipse Scripting Research Application Programming Interface (ESRAPI). The contours of the target and organs at risk (OARs) structures were exported by applying the ESRAPI and were used to determine the fractional volume-overlap of the OARs with the target from several potential beam directions. Thereby, an additional weighting was applied taking into account the relative position of the OAR with respect to the target and radiation beam, that is, penalizing directions where the OAR is proximal to the target. The resulting two-dimensional gantry-table map was used as input for an A* path finding algorithm returning an optimized gantry-table path. Thereby, the process is also taking into account CT scan length and collision restrictions. The A* algorithm was used again to determine the dynamic collimator angle path by optimizing the area between the MLC leaves and the target contour for each gantry-table path leading to gantry-collimator paths. The resulting gantry-table and gantry-collimator paths are combined and serve as input for the intensity modulation optimization using a research VMAT optimizer and the ESRAPI resulting in dynamic trajectories. This procedure was evaluated for five clinically motivated cases: two head and neck, one lung, one esophagus, and one prostate. Final dose calculations were performed using the Swiss Monte Carlo Plan (SMCP). Resulting dose distributions for the DTRT treatment plans and for the standard VMAT plans were compared based on dose distributions and dose volume histogram (DVH) parameters. For this comparison, the dose distribution for the VMAT plans were recalculated using the SMCP. In addition, the suitability of the delivery of a DTRT treatment plan was demonstrated by means of gafchromic film measurements on a TrueBeam linear accelerator. RESULTS: DVHs for the target volumes showed similar or improved coverage and dose homogeneity for DTRT compared with VMAT using equal or less number of dynamic trajectories for DTRT than arcs for VMAT for all cases studied. Depending on the case, improvements in mean and maximum dose for the DTRT plans were achieved for almost all OARs compared with the VMAT plans. Improvements in DTRT treatment plans for mean and maximum dose compared to VMAT plans were up to 16% and 38% relative to the prescribed dose, respectively. The measured and calculated dose values resulted in a passing rate of more than 99.5% for the two-dimensional gamma analysis using 2% and 2 mm criteria and a threshold of 10%. CONCLUSIONS: DTRT plans for different treatment sites were generated and compared with VMAT plans. The delivery is suitable and dose comparisons demonstrate a high potential of DTRT to reduce dose to OARs using less dynamic trajectories than arcs, while target coverage is preserved.

Dynamic trajectory of multiple single-unit activity during working memory task in rats.

Working memory plays an important role in complex cognitive tasks. A popular theoretical view is that transient properties of neuronal dynamics underlie cognitive processing. The question raised here as to how the transient dynamics evolve in working memory. To address this issue, we investigated the multiple single-unit activity dynamics in rat medial prefrontal cortex (mPFC) during a Y-maze working memory task. The approach worked by reconstructing state space from delays of the original single-unit firing rate variables, which were further analyzed using kernel principal component analysis (KPCA). Then the neural trajectories were obtained to visualize the multiple single-unit activity. Furthermore, the maximal Lyapunov exponent (MLE) was calculated to quantitatively evaluate the neural trajectories during the working memory task. The results showed that the neuronal activity produced stable and reproducible neural trajectories in the correct trials while showed irregular trajectories in the incorrect trials, which may establish a link between the neurocognitive process and behavioral performance in working memory. The MLEs significantly increased during working memory in the correctly performed trials, indicating an increased divergence of the neural trajectories. In the incorrect trials, the MLEs were nearly zero and remained unchanged during the task. Taken together, the trial-specific neural trajectory provides an effective way to track the instantaneous state of the neuronal population during the working memory task and offers valuable insights into working memory function. The MLE describes the changes of neural dynamics in working memory and may reflect different neuronal population states in working memory.

CW-EPR Spectral Simulations: Slow-Motion Regime.

This chapter reviews the range of methods currently available for calculating the electron paramagnetic resonance (EPR) spectrum of nitroxide spin-labeled biomolecules undergoing slow motion. The two major approaches include the stochastic Liouville equation (SLE) which represents the spin label motion using diffusion operators, and the dynamic trajectory (DT) approach, which enables the EPR spectrum to be calculated from molecular dynamics simulations. The basic model parameters needed for each approach are described, together with a broad outline of the theoretical approaches underlying the methods, sufficient to allow their comparison for different applications. Hybrid methods utilizing a combination of SLE and DT approaches are briefly discussed.