The genetic architecture of most human complex traits is highly polygenic, motivating efforts to detect polygenic selection involving a large number of loci. In contrast to previous work relying on top GWAS loci, we developed a method that uses genome-wide association statistics and linkage disequilibrium patterns to estimate the genome-wide genetic component of population differentiation of a complex trait along a continuous gradient, enabling powerful inference of polygenic selection. We analyzed 43 UK Biobank traits and focused on PC1 and North-South and East-West birth coordinates across 337K unrelated British-ancestry samples, for which our method produced close to unbiased estimates of genetic components of population differentiation and high power to detect polygenic selection in simulations across different trait architectures. For PC1, we identified signals of polygenic selection for height (74.5±16.7% of 9.3% total correlation with PC1 attributable to genome-wide genetic effects; P = 8.4×10-6 ) and red hair pigmentation (95.9±24.7% of total correlation with PC1 attributable to genome-wide genetic effects; P = 1.1×10 -4 ); the bulk of the signal remained when removing genomewide significant loci, even though red hair pigmentation includes loci of large effect. We also detected polygenic selection for height, systolic blood pressure, BMI and basal metabolic rate along North-South birth coordinate, and height and systolic blood pressure along East-West birth coordinate. Our method detects polygenic selection in modern human populations with very subtle population structure and elucidates the relative contributions of genetic and non-genetic components of trait population differences.

Purpose: External tracking systems used for patient positioning and motion monitoring during radiotherapy are now capable of detecting both translations and rotations (6DOF). In this work, we develop a novel technique to evaluate the 6DOF performance of external motion tracking systems. We apply this methodology to an infrared (IR) marker tracking system and two 3D optical surface mapping systems in a common tumor 6DOF workspace. Methods: An in‐house designed and built 6DOF parallel kinematics robotic motion phantom was used to follow input trajectories with sub‐millimeter and sub‐degree accuracy. The 6DOF positions of the robotic system were then tracked and recorded independently by three optical camera systems. A calibration methodology which associates the motion phantom and camera coordinate frames was first employed, followed by a comprehensive 6DOF trajectory evaluation, which spanned a full range of positions and orientations in a 20×20×16 mm and 5×5×5 degree workspace. The intended input motions were compared to the calibrated 6DOF measured points. Results: The technique found the accuracy of the IR marker tracking system to have maximal root mean square error (RMSE) values of 0.25 mm translationally and 0.09 degrees rotationally, in any one axis, comparing intended 6DOF positions to positions measured by the IR camera. The 6DOF RSME discrepancy for the first 3D optical surface tracking unit yielded maximal values of 0.60 mm and 0.11 degrees over the same 6DOF volume. An earlier generation 3D optical surface tracker was observed to have worse tracking capabilities than both the IR camera unit and the newer 3D surface tracking system with maximal RMSE of 0.74 mm and 0.28 degrees within the same 6DOF evaluation space. Conclusion: The proposed technique was effective at evaluating the performance of 6DOF patient tracking systems. All systems examined exhibited tracking capabilities at the sub‐millimeter and sub‐degree level within a 6DOF workspace.

Purpose: High precision patient positioning is critical in stereotactic radiosurgery (SRS). A 6 Degree‐of‐freedom (6D) robotic serial couch has the potential to correct both translational and rotational target motion deviations during image‐guided radiosurgery procedures. An inverse kinematics algorithm based on the structure of the couch is presented, and a feedback control algorithm is discussed. The feasibility of motion compensation with a 6D couch is demonstrated by simulation with prerecorded volunteer head motion data. Methods: The proposed 6D couch motion compensation system included a robotic 6D couch, an image tracking system, and a control computer. For the control, the desired couch top plane was computed based on coordinate frames transformation, and the actuator outputs were calculated by 6D couch inverse kinematics algorithm. During the control, the rotation and translation were coupled, leading to undesired coupling motion of the lesion. Although such coupling was eventually cancelled out, it nonetheless represented unnecessary displacements of the target. An optimal decoupling control algorithm was designed to resolve this problem. The lever effect of the distance of between the target and the pivot of 6D couch roll/pitch were also discussed. Results: The pre‐recorded volunteer head motion data was used in a computer‐based motion compensation simulation, by 6D couch motion compensation, the corrected target was within a 0.3 mm of translational errors and 0.1 degree in the rotational errors about 99.5% of time. Conclusion: We presented an optimal decoupling control algorithm for motion compensation by using a robotic 6D couch. The simulation also showed that reducing the distance between the target and the pivot of roll/pitch of the couch can also improve the accuracy of the compensation. The simulation showed that the 6D robotic system can achieve submillimeter/subdegree position accuracies.

Purpose: This work presents a biomechanical model to investigate the complex respiratory motion for the lung tumor tracking in radiosurgery by computer simulation. Methods: The models include networked massspring‐dampers to describe the tumor motion, different types of surrogate signals, and the force generated by the diaphragm. Each mass‐springdamper has the same mechanical structure and each model can have different numbers of mass‐spring‐dampers. Both linear and nonlinear stiffness parameters were considered, and the damping ratio was tuned in a range so that the tumor motion was over‐damped (no natural tumor oscillation occurs without force from the diaphragm). The simulation was run by using ODE45 (ordinary differential equations by Runge‐Kutta method) in MATLAB, and all time courses of motions and inputs (force) were generated and compared. Results: The curvature of the motion time courses around their peaks was sensitive to the damping ratio. Therefore, the damping ratio can be determined based on the clinical data of a high sampling rate. The peak values of different signals and the time the peaks occurred were compared, and it was found that the diaphragm force had a time lead over the tumor motion, and the lead time (0.1–0.4 seconds) depended on the distance between the tumor and the diaphragm. Conclusion: We reported a model based analysis approach for the spatial and temporal relation between the motion of the lung tumor and the surrogate signals. Due to the phase lead of the diaphragm in comparing with the lung tumor motion, the measurement of diaphragm motion (or its electromyography signal) can be used as a beam gating signal in radiosurgery, and it can also be an additional surrogate signal for better tumor motion tracking. The research is funded by the American Cancer Society (ACS) grant. The grant name is: Frameless SRS Based on Robotic Head Motion Cancellation. The grant number is: RSG‐13‐313‐01‐CCE

Purpose: In radiation therapy optimization the constraints can be either hard constraints which must be satisfied or soft constraints which are included but do not need to be satisfied exactly. Currently the voxel dose constraints are viewed as soft constraints and included as a part of the objective function and approximated as an unconstrained problem. However in some treatment planning cases the constraints should be specified as hard constraints and solved by constrained optimization. The goal of this work is to present a computation efficiency graph form alternating direction method of multipliers (ADMM) algorithm for constrained quadratic treatment planning optimization and compare it with several commonly used algorithms/toolbox. Method: ADMM can be viewed as an attempt to blend the benefits of dual decomposition and augmented Lagrangian methods for constrained optimization. Various proximal operators were first constructed as applicable to quadratic IMRT constrained optimization and the problem was formulated in a graph form of ADMM. A pre‐iteration operation for the projection of a point to a graph was also proposed to further accelerate the computation. Result: The graph form ADMM algorithm was tested by the Common Optimization for Radiation Therapy (CORT) dataset including TG119, prostate, liver, and head & neck cases. Both unconstrained and constrained optimization problems were formulated for comparison purposes. All optimizations were solved by LBFGS, IPOPT, Matlab built‐in toolbox, CVX (implementing SeDuMi) and Mosek solvers. For unconstrained optimization, it was found that LBFGS performs the best, and it was 3–5 times faster than graph form ADMM. However, for constrained optimization, graph form ADMM was 8 – 100 times faster than the other solvers. Conclusion: A graph form ADMM can be applied to constrained quadratic IMRT optimization. It is more computationally efficient than several other commercial and noncommercial optimizers and it also used significantly less computer memory.