Stereotactic arrhythmia radioablation (STAR) therapy is a novel treatment for ventricular tachycardia that delivers a high radiation dose to a target volume in the myocardium. Recent publications have recommended the use of cardiorespiratory motion management strategies to prevent damage to nearby critical structures in addition to the commonly applied 5 mm margin of delivery uncertainty in radiation planning. Motion capture in 3D cardiac ultrasound (US) could be utilized for passive and active motion management due to its capability of capturing cardiac motion in 3D with a sufficient frame rate, and due to its advantages like small hardware components as well as real time capability. The transfer of patient-specific cardiorespiratory motion trajectories from US to computed tomography (CT) coordinates for the purpose of radiation plan adaptation presents a novel use-case that necessitates the combination of multiple image processing methods. In this work, we present a framework for motion capture in US developed for the evaluation of a clinical study. 3D/3D registrations of Cartesian and anatomic representations based on a spherical harmonics shape model are evaluated utilizing a human phantom dataset as well as seven patient datasets. Overall numeric results indicate accuracies of less than 5 mm error, and the use of the anatomic shape modelling increases tracking precision. Integration of patient-specific trajectories of the target or critical structures in CT could already be used for passive motion management in STAR therapy. The implemented framework has the potential to increase precision and safety of the therapy and to be further developed into an active motion management system in the future.

We present a novel framework for rigid point cloud registration. Our approach is based on the principles of mechanics and thermodynamics. We solve the registration problem by assuming point clouds as rigid bodies consisting of particles. Forces can be applied between both particle systems so that they attract or repel each other. These forces are used to cause rigid-body motion of one particle system toward the other, until both are aligned. The framework supports physics-based registration processes with arbitrary driving forces, depending on the desired behaviour. Additionally, the approach handles feature-enhanced point clouds, e.g., by colours or intensity values. Our framework is freely accessible for download. In contrast to already existing algorithms, our contribution is to precisely register high-resolution point clouds with nearly constant computational effort and without the need for pre-processing, sub-sampling or pre-alignment. At the same time, the quality is up to 28 percent higher than for state-of-the-art algorithms and up to 49 percent higher when considering feature-enhanced point clouds. Even in the presence of noise, our registration approach is one of the most robust, on par with state-of-the-art implementations.

In cranial radiotherapy highly accurate tumor localization is required to spare healthy tissue while delivering sufficient dose to the target. Here, marker-less optical tracking can support immobilization devices and monitor head motion. However, recent studies have shown that the spatial registration of the optically generated point cloud to a reference is not robust enough. It may suffer from misalignments due to local similarities and changes along the deformable surface geometry. Irrespective from the registration algorithm, we propose to support the spatial information by tissue thickness patterns across the surface. These patterns are predicted by Gaussian Processes which process near infrared optical backscatter from the skin. We first demonstrate for a cohort of 30 volunteers that the tissue thickness can be determined with errors of less than 0.22mm on average. We found high prediction accuracy irrespective of gender, age or skin type. Second, we show that the robustness of a standard iterative closest point (ICP) algorithm can be improved when exploiting cutaneous patterns to identify point-to-point correspondences. On average, tissue thickness support outperformed the standard procedure for every subject and was capable of pushing 90% of all misalignments exceeding a registration error of 1mm below that threshold.

Marker-less tracking provides a non-invasive as well as comfortable approach to compensate for head motion in high precision radiotherapy. However, it suffers from a lack of point-to-point correspondences, typically requiring characteristic spatial landmarks to match point clouds. In this study, we show that cutaneous and subcutaneous structures can be uncovered using an 850 nm laser setup. For three subjects, we compare features extracted from camera images with MR scans serving as an anatomical ground truth. The results confirm the validity of the optically detected structures. The negative correlation between skin thickness and reflected light energy is likewise predicted by Monte-Carlo simulations and can be used to improve spatial point cloud matching. Tissue thickness and its facial structure can be predicted with submillimeter accuracy using a Support Vector regression machine. In addition, the optical measurements reveal the location of vessels that are not immediately visible in the MR scan. These promising findings highly encourage its application for a marker-less tracking system.

This contribution reports the development of a novel robotic manipulator for stereotactic surgery on small animals, the spherical assistant for stereotactic surgery (SAS- SU). A kinematic design is deduced based on the surgical task requirements. Forward and inverse kinematics are derived analytically. As the system is required to position medical probes of varying size and shape, details on the calibration for different probe configurations are provided. The kinematic design of the novel manipulator is compared to an existing stereotactic instrument in terms of kinematic accuracy. Results show that the SASSU systems is less sensitive to translational positioning errors induced by changes in the joint variables.

We present an exact and practical incremental method for general translational assembly planning. In practical cases, an exact and complete representation of the relevant free regions in the high-dimensional assembly configuration space becomes amenable by incrementally computing an arrangement of cells in d-dimensional space. Here we introduce a novel reduction scheme, D-node reduction, that allows for online defragmentation of the computed cell decomposition and thus significant speedup and reduction of storage requirements. Experimental results for both two- and three-dimensional assemblies show the practicality of the proposed approach and illustrate the impact of the new reduction scheme.

We address the problem of efficiently determining if the intersection of a given set of d-dimensional halfspaces is unbounded. It is shown that detecting unboundedness can be reduced to a single linear range computation followed by a single linear feasibility test. In contrast, detecting unboundedness is at least as hard as linear feasibility testing and maximization. Our analysis suggests that algorithms for establishing linear unboundedness can be used as a basis of simple and practical algorithms in motion planning, insertability analysis and assembly planning. We show that m-handed assembly planning can be reduced to testing for unboundedness. A valid motion sequence can be computed in polynomial time, if the parts are not already separated in their initial placement. No polynomial algorithms were previously known for this problem. We present experimental results obtained with an implementation of our algorithms.

Radiosurgery is a treatment for brain tumours and other lesions which employs a moving beam of photon radiation. In robotic radiosurgery, the radiation source is moved by a six degree-of-freedom robotic arm. A treatment planning system for robotic radiosurgery was developed. This planning system combines collision avoidance techniques and geometric algorithms for finding appropriate robot paths and beam activation profiles. The following design goals characterize our application: 1) ability to generate conformal 3D dose distributions; 2) transparency of the planning process; and 3) full use of the motion flexibility provided by the robotic arm. The new planning system is in clinical use in several leading medical institutions. Results obtained from the studies suggest that highly conformal distributions can be generated in a very effective way.

An exact and practical method for translational motion planning with many degrees of freedom is derived. It it shown that certain D-dimensional arrangements of hyperplanes can be searched in the following way: only a single connected component is traversed during the search, and the arrangement is searched as an arrangement of surface patches rather than full hyperplanes. This reduction in search effort allows for polynomial time bounds in appropriate cases. Heuristic and randomized planners cannot return an information about infeasibility of planning problems. The new method is exact and complete. Experiments obtained with an implementation suggest that it is capable of reaching the performance of the most advanced random planning schemes. In addition, insolvability can be established in practical cases.

In radiosurgery a beam of radiation is used as an ablative surgical instrument to destroy brain tumors. Treatment planning consists of computing a sequence of beam configurations for delivering a necrotic dose to the tumor, without damaging healthy tissue or particularly critical structures. In current systems, kinematic limitations severely constrain beam motion. This often results in inappropriate dose distributions. A new radiosurgical system has been implemented to overcome this disadvantage. In this system, a compact radiation source of high energy is moved by a 6-dof robotic arm. We describe algorithms for computing a motion with specified characteristics for this new system. Treatment plans used at test sites with earlier systems are compared to plans computed with the described algorithms. The experience reported shows that full kinematic flexibility combined with treatment planning algorithms allows for better protection of healthy tissue and higher dosage in tumors.>

This paper describes a system that assists in the planning and the performing of a surgical action, namely the corrective osteotomy of the thigh bone (femur). The corrective osteotomy of the thigh bone is used for changing the posture of the hip joint. During surgery, a small cross-sectional slice is cut out of the thigh bone by the use of a sawing device. Our system supports the planning phase of this surgery by allowing interactive visualizations of the cutting planes using a 3D surface-oriented model of the thigh bone derived from computer tomography (CT). It also supports the actual surgery, in which a robot hand is steered towards the predetermined cutting planes, a process that is guided and monitored by a vision system.>

In radiosurgery a moving beam of radiation is used as an ablative surgical instrument to destroy brain tumors. A new camera-guided system capable of tracking patient motion during treatment has been built. The radiation source is moved by a six degree-of-freedom robotic arm. In addition to offering a more cost effective, less invasive, and less painful treatment, the robotic gantry allows for arbitrary spatial motion of the radiation source. Based on this feature we can treat non-spherical lesions with accuracies unachievable with classical radiosurgical systems. The system introduces a new class of radiosurgical procedures, called non-stereotactic, or image-guided radiosurgery. At the heart of these procedures are algorithms for planning both a treatment and the corresponding beam motion, given the geometric description of the tumor shape and relative locations in the particular case.>

Stereotaxic radiosurgery is a procedure that uses a beam of radiation as an ablative surgical instrument to destroy brain tumors (or more generally, brain lesions). The beam is produced by a linear accelerator that is moved by a mechanical gantry. Radiation is concentrated by crossfiring at the tumor from multiple directions, to reduce the amount of energy deposited in healthy tissues. Because access to and exit from the tumor is obstructed along some directions by critical structures (e.g., brain stem, optic nerves), planning the path of the beam is often difficult and time-consuming. This paper describes a computer-based planner developed to interactively assist the surgeon generate a satisfactory treatment, given the spatial distribution of the brain tissues obtained with medical imaging. This planner has been experimented on using 11 cases previously processed at the Stanford Medical Center. A dosimetric comparison with the manually generated plans for these cases was carried but. Although still limited, results indicate that automatic planning can significantly improve energy deposition. It can also shorten the overall treatment, hence reducing the patient's pain and allowing the radiosurgery equipment to be used for more patients. Stereotaxic radiosurgery is an example of so-called "bloodless surgery." Computer-based planning techniques are expected to facilitate further development of this safer, less painful, and more cost effective type of surgery.>

The problem of partitioning an assembly of polyhedral objects into two subassemblies that can be separated arises in assembly planning. The authors describe an algorithm to compute the set of all translations separating two polyhedra with n vertices in O(n/sup 4/) steps and show that this is optimal. Given an assembly of k polyhedra with a total of n vertices, an extension of this algorithm identifies a valid translation and removable subassembly in O(k/sup 2/n/sup 4/) steps if one exists. Based on the second algorithm, a polynomial time method for finding a complete assembly sequence consisting of single translations is derived. An implementation incorporates several changes to achieve better average-case performances. Experimental results obtained for composite objects consisting of isothetic polyhedra are described.>

An exact and practical method for determining the number, location, and multiplicity of all real zeros of the trigonometric polynomials is described. All computations can be performed without loss of accuracy. lThe method is based on zero isolation techniques for algebraic polynomials. An efficient method for the calculation of the coefficients of a corresponding algebraic polynomial is stated. The complexity of trigonometric zero isolation depending on the degree and the coefficient size of the given trigonometric polynomial is analyzed. In an experimental evaluation, the performance of the method is compared to the performance of recently developed numeric techniques for the approximate determination of all roots of trigonometric polynomials. The case of exponential or hyperbolic polynomials is treated in an appendix.

An exact collision detection algorithm is described and analyzed. The time bound considers the complexity of the solids, the number of joints, and the number of distinct collision configurations. A bound for the number of collision configurations can be taken directly from the input data. The algorithm is based on an exact treatment of trigonometric expressions. The representation of trigonometric constants is discussed. Since all computations are exact, the distances between objects can be arbitrarily small. It is shown that collision detection can be performed in polynomial time. Other measures for the complexity of a motion with respect to collision detection could be based on minimal distances between objects. In this case smaller distances lead to increased computing time.>