C-arm fluoroscopy is ubiquitous in contemporary surgery, but it lacks the ability to accurately reconstruct three-dimensional (3D) information. A major obstacle in fluoroscopic reconstruction is discerning the pose of the x-ray image, in 3D space. Optical/magnetic trackers tend to be prohibitively expensive, intrusive and cumbersome in many applications. We present single-image-based fluoroscope tracking (FTRAC) with the use of an external radiographic fiducial consisting of a mathematically optimized set of ellipses, lines, and points. This is an improvement over contemporary fiducials, which use only points. The fiducial encodes six degrees of freedom in a single image by creating a unique view from any direction. A nonlinear optimizer can rapidly compute the pose of the fiducial using this image. The current embodiment has salient attributes: small dimensions (3 x 3 x 5 cm); need not be close to the anatomy of interest; and accurately segmentable. We tested the fiducial and the pose recovery method on synthetic data and also experimentally on a precisely machined mechanical phantom. Pose recovery in phantom experiments had an accuracy of 0.56 mm in translation and 0.33 degrees in orientation. Object reconstruction had a mean error of 0.53 mm with 0.16 mm STD. The method offers accuracies similar to commercial tracking systems, and appears to be sufficiently robust for intraoperative quantitative C-arm fluoroscopy. Simulation experiments indicate that the size can be further reduced to 1 x 1 X 2 cm, with only a marginal drop in accuracy.

Intraoperative dosimetric quality assurance in prostate brachytherapy critically depends on discerning the three-dimensional (3D) locations of implanted seeds. The ability to reconstruct the implanted seeds intraoperatively will allow us to make immediate provisions for dosimetric deviations from the optimal implant plan. A method for seed reconstruction from segmented C-arm fluoroscopy images is proposed. The 3D coordinates of the implanted seeds can be calculated upon resolving the correspondence of seeds in multiple x-ray images. We formalize seed-matching as a combinatorial optimization problem, which has salient features: (a) extensively studied solutions by the computer science community; (b) proof for the nonexistence of any polynomial time exact algorithm; and (c) a practical pseudo-polynomial algorithm that mostly runs in O(N3) time using any number of images. We prove that two images are insufficient to correctly match the seeds, while a third image renders the matching problem to be of nonpolynomial complexity. We utilize the special structure of the problem and propose a pseudopolynomial time algorithm. Using three presegmented images, matching and reconstruction of brachytherapy seeds using the Hungarian algorithm achieved complete matching in simulation experiments; and 98.5% in phantom experiments. 3D reconstruction error for correctly matched seeds has a mean of 0.63 mm, and 0.9 mm for incorrectly matched seeds. The maximum seed reconstruction error in each implant was typically around 1.32 mm. Both on synthetic data and in phantom experiments, matching rate and reconstruction error achieved using presegmented images was found to be sufficient for prostate brachytherapy. The algorithm is extendable to deal with arbitrary number of images without any loss in speed or accuracy. The algorithm is sufficiently generic to provide a practical solution to any correspondence problem, across different imaging modalities and features.

Abstract. Intra-operative guidance in Transrectal Ultrasound (TRUS) guided prostate brachytherapy requires localization of inserted radioactive seeds relative to the prostate. Seeds were reconstructed using a typical C-arm, and exported to a commercial brachytherapy system for dosimetry analysis. Technical obstacles for 3D reconstruction on a nonisocentric C-arm included pose-dependent C-arm calibration; distortion correction; pose estimation of C-arm images; seed reconstruction; and C-arm to TRUS registration. In precision-machined hard phantoms with 40-100 seeds, we correctly reconstructed 99.8% seeds with a mean 3D accuracy of 0.68 mm. In soft tissue phantoms with 45-87 seeds and clinically realistic 15 o C-arm motion, we correctly reconstructed 100% seeds with an accuracy of 1.3 mm. The reconstructed 3D seed positions were then registered to the prostate segmented from TRUS. In a Phase-1 clinical trial, so far on 4 patients with 66-84 seeds, we achieved intra-operative monitoring of seed distribution and dosimetry. We optimized the 100% prescribed iso-dose contour by inserting an average of 3.75 additional seeds, making intra-operative dosimetry possible on a typical C-arm, at negligible additional cost to the existing clinical installation.

The success of prostate brachytherapy critically depends on delivering adequate dose to the prostate gland. Intraoperative localization of the implanted seeds provides potential for dose evaluation and optimization during therapy. A reduced-dimensionality matching algorithm for prostate brachytherapy seed reconstruction (REDMAPS) that uses multiple X-ray fluoroscopy images obtained from different poses is proposed. The seed reconstruction problem is formulated as a combinatorial optimization problem, and REDMAPS finds a solution in a clinically acceptable amount of time using dimensionality reduction to create a smaller space of possible solutions. Dimensionality reduction is possible since the optimal solution has approximately zero cost when the poses of the acquired images are known to be within a small error. REDMAPS is also formulated to address the “hidden seed problem” in which seeds overlap on one or more observed images. REDMAPS uses a pruning algorithm to avoid unnecessary computation of cost metrics and the reduced problem is solved using linear programming. REDMAPS was first evaluated and its parameters tuned using simulations. It was then validated using five phantom and 21 patient datasets. REDMAPS was successful in reconstructing the seeds with an overall seed matching rate above 99% and a reconstruction error below 1 mm in less than 5 s.

The registration of preoperative CT to intra-operative reality systems is a crucial step in Computer Assisted Orthopedic Surgery (CAOS). The intra-operative sensors include 3D digitizers, fiducials, X-rays and Ultrasound (US). Although US has many advantages over others, tracked US for Orthopedic Surgery has been researched by only a few authors. An important factor limiting the accuracy of tracked US to CT registration (1-3mm) has been the difficulty in determining the exact location of the bone surfaces in the US images (the response could range from 2-4mm). Thus it is crucial to localize the bone surface accurately from these images. Moreover conventional US imaging systems are known to have certain inherent inaccuracies, mainly due to the fact that the imaging model is assumed planar. This creates the need to develop a bone segmentation framework that can couple information from various post-processed spatially separated US images (of the bone) to enhance the localization of the bone surface.In this paper we discuss the various reasons that cause inherent uncertainties in the bone surface localization (in Bmode US images) and suggest methods to account for these. We also develop a method for automatic bone surface detection. To do so, we account objectively for the high-level understanding of the various bone surface features visible in typical US images. A combination of these features would finally decide the surface position. We use a Bayesian probabilistic framework, which strikes a fair balance between high level understanding from features in an image and the low level number crunching of standard image processing techniques. It also provides us with a mathematical approach that facilitates combining multiple images to augment the bone surface estimate.

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Abstract. In the past decade ultrasound (US) has become the preferred modality for a number of interventional procedures, offering excellent soft tissue visualization. The main limitation however is limited visualization of surgical tools. A new method is proposed for robust 3D tracking and US image enhancement of surgical tools under US guidance. Small US sensors are mounted on existing surgical tools. As the imager emits acoustic energy, the electrical signal from the sensor is analyzed to reconstruct its 3D coordinates. These coordinates can then be used for 3D surgical navigation, similar to current day tracking systems. A system with realtime 3D tool tracking and image enhancement was implemented on a commercial ultrasound scanner and 3D probe. Extensive water tank experiments with a tracked 0.2mm sensor show robust performance in a wide range of imaging conditions and tool position/orientations. The 3D tracking accuracy was 0.36 ± 0.16mm throughout the imaging volume of 55• × 27 • × 150mm. Additionally, the tool was successfully tracked inside a beating heart phantom. This paper proposes an image enhancement and tool tracking technology with sub-mm accuracy for US-guided interventions. The technology is non-disruptive, both in terms of existing clinical workflow and commercial considerations, showing promise for large scale clinical impact.

Deterministic loading of single atoms onto arbitrary two-dimensional lattice points has recently been demonstrated, where by dynamically controlling the optical-dipole potential, atoms from a probabilistically loaded lattice were relocated to target lattice points to form a zero-entropy atomic lattice. In this atom rearrangement, how to pair atoms with the target sites is a combinatorial optimization problem: brute-force methods search all possible combinations so the process is slow, while heuristic methods are time-efficient but optimal solutions are not guaranteed. Here, we use the Hun-garian matching algorithm as a fast and rigorous alternative to this problem of defect-free atomic lattice formation. Our approach utilizes an optimization cost function that restricts collision-free guiding paths so that atom loss due to collision is minimized during rearrangement. Experiments were performed with cold rubidium atoms that were trapped and guided with holographically controlled optical-dipole traps. The result of atom relocation from a partially filled 7-by-7 lattice to a 3-by-3 target lattice strongly agrees with the theoretical analysis: using the Hungarian algorithm minimizes the collisional and trespassing paths and results in improved performance, with over 50% higher success probability than the heuristic shortest-move method.