Faculty Bibliography

The mathematical basis for the Gaussian entanglement is discussed in detail, as well as its implications in the internal space-time structure of relativistic extended particles. It is shown that the Gaussian entanglement shares the same set of mathematical formulas with the harmonic oscillator in the Lorentz-covariant world. It is thus possible to transfer the concept of entanglement to the Lorentz-covariant picture of the bound state, which requires both space and time separations between two constituent particles. These space and time variables become entangled as the bound state moves with a relativistic speed. It is shown also that our inability to measure the time-separation variable leads to an entanglement entropy together with a rise in the temperature of the bound state. As was noted by Paul A. M. Dirac in 1963, the system of two oscillators contains the symmetries of the O (3, 2) de Sitter group containing two O (3, 1) Lorentz groups as its subgroups. Dirac noted also that the system contains the symmetry of the Sp (4) group, which serves as the basic language for two-mode squeezed states. Since the Sp (4) symmetry contains both rotations and squeezes, one interesting case is the combination of rotation and squeeze, resulting in a shear. While the current literature is mostly on the entanglement based on squeeze along the normal coordinates, the shear transformation is an interesting future possibility. The mathematical issues on this problem are clarified.

Background and Purpose. The gold standard for detection of implant wear and migration is currently radiostereometry (RSA). The purpose of this study is to compare a three-dimensional computed tomography technique (3D CT) to standard RSA as an alternative technique for measuring migration of acetabular cups in total hip arthroplasty. Materials and Methods. With tantalum beads, we marked one cemented and one uncemented cup and mounted these on a similarly marked pelvic model. A comparison was made between 3D CT and standard RSA for measuring migration. Twelve repeated stereoradiographs and CT scans with double examinations in each position and gradual migration of the implants were made. Precision and accuracy of the 3D CT were calculated. Results. The accuracy of the 3D CT ranged between 0.07 and 0.32 mm for translations and 0.21 and 0.82 degrees for rotation. The precision ranged between 0.01 and 0.09 mm for translations and 0.06 and 0.29 degrees for rotations, respectively. For standard RSA, the precision ranged between 0.04 and 0.09 mm for translations and 0.08 and 0.32 degrees for rotations, respectively. There was no significant difference in precision between 3D CT and standard RSA. The effective radiation dose of the 3D CT method, comparable to RSA, was estimated to be 0.33 mSv. Interpretation. Low dose 3D CT is a comparable method to standard RSA in an experimental setting.

BACKGROUND: Radiostereometric analysis (RSA) is often used for evaluating implanted devices over time. Following patients who have had tantalum beads implanted as markers in conjunction with joint replacements is important for longitudinal evaluation of these patients and for those with similar implants. As doing traditional RSA imaging is exacting and limited to specialized centers, it is important to consider alternative techniques for this ongoing evaluation. This paper studies the use of computed tomography (CT) to evaluate over time tantalum beads which have been implanted as markers. METHODS: The project uses both a hip model implanted with tantalum beads, acquired in several orientations, at two different CT energy levels, and a cohort of seven patients. The model was evaluated twice by the same observer with a 1-week interval. All CT volumes were analyzed using a semi-automated 3D volume fusion (spatial registration) tool which provides landmark-based fusion of two volumes, registering a target volume with a reference volume using a rigid body 3D algorithm. The mean registration errors as well as the accuracy and repeatability of the method were evaluated. RESULTS: The mean registration error, maximum value of repeatability, and accuracy for the relative movement in the model were 0.16 mm, 0.02 degrees and 0.1 mm, and 0.36 degrees and 0.13 mm for 120 kVp and 0.21 mm, 0.04 degrees and 0.01 mm, and 0.39 degrees and 0.12 mm for 100 kVp. For the patients, the mean registration errors per patient ranged from 0.08 to 0.35 mm. These results are comparable to those in typical clinical RSA trials. This technique successfully evaluated two patients who would have been lost from the cohort if only RSA were used. CONCLUSIONS: The proposed technique can be used to evaluate patients with tantalum beads over time without the need for stereoradiographs. Further, the effective dose associated with CT is decreasing.

This study describes a 3D-CT method for analyzing facet joint motion and vertebral rotation in the lumbar spine after TDR. Ten patients were examined before and then three years after surgery, each time with two CT scans: provoked flexion and provoked extension. After 3D registration, the facet joint 3D translation and segmental vertebral 3D rotation were analyzed at the operated level (L5-S1) and adjacent level (L4-L5). Pain was evaluated using VAS. The median (+/-SD) 3D movement in the operated level for the left facet joint was 3.2 mm (+/-1.9 mm) before and 3.5 mm (+/-1.7 mm) after surgery and for the right facet joint was 3.0 mm (+/-1.0 mm) before and 3.6 mm (+/-1.4 mm) after surgery. The median vertebral rotation in the sagittal plane at the operated level was 5.4 degrees (+/-2.3 degrees ) before surgery and 6.8 degrees (+/-1.7 degrees ) after surgery and in the adjacent level was 7.7 degrees (+/-4.0 degrees ) before and 9.2 degrees (+/-2.7 degrees ) after surgery. The median VAS was reduced from 6 (range 5-8) to 3 (range 2-8) in extension and from 4 (range 2-6) to 2 (range 1-3) in flexion.

Eighteen consecutive patients, treated with a Taylor Spatial Frame for complex tibia conditions, gave their informed consent to undergo Na(18)F(-) PET/CT bone scans. We present a Patlak-like analysis utilizing an approximated blood time-activity curve eliminating the need for blood aliquots. Additionally, standardized uptake values (SUV) derived from dynamic acquisitions were compared to this Patlak-like approach. Spherical volumes of interest (VOIs) were drawn to include broken bone, other (normal) bone, and muscle. The SUV m (t) (m = max, mean) and a series of slopes were computed as (SUV m (t i ) - SUV m (t j ))/(t i - t j ), for pairs of time values t i and t j . A Patlak-like analysis was performed for the same time values by computing ((VOI p (t i )/VOI e (t i ))-(VOI p (t j )/VOI e (t j )))/(t i - t j ), where p = broken bone, other bone, and muscle and e = expected activity in a VOI. Paired comparisons between Patlak-like and SUV m slopes showed good agreement by both linear regression and correlation coefficient analysis (r = 84%, r s = 78%-SUVmax, r = 92%, and r s = 91%-SUVmean), suggesting static scans could substitute for dynamic studies. Patlak-like slope differences of 0.1 min(-1) or greater between examinations and SUVmax differences of ~5 usually indicated good remodeling progress, while negative Patlak-like slope differences of -0.06 min(-1) usually indicated poor remodeling progress in this cohort.

OBJECT Artificial disc replacement (ADR) devices are unlike implants used in cervical fusion in that they are continuously exposed to stress not only within the implant site but also at their site of attachment to the adjacent vertebra. An imaging technique with higher accuracy than plain radiography and with the possibility of 3D visualization would provide more detailed information about the motion quality and stability of the implant in relation to the vertebrae. Such high-accuracy studies have previously been conducted with radiostereometric analysis (RSA), which requires implantation of tantalum markers in the adjacent vertebrae. The aim of this study was to evaluate in vivo motion and stability of implanted artificial discs. A noninvasive analysis was performed with CT, with an accuracy higher than that of plain radiographs and almost as high as RSA in cervical spine. METHODS Twenty-eight patients with ADR were included from a larger cohort of a randomized controlled trial comparing treatment of cervical radiculopathy with ADR or anterior cervical decompression and fusion. Surgical levels included C4-7; 18 patients had 1-level surgery and 10 patients had 2-level surgery. Follow-up time ranged from 19 to 50 months, with an average of 40 months. Two CT volumes of the cervical spine, 1 in flexion and 1 in extension, were obtained in each patient and then spatially registered using a customized imaging tool, previously used and validated for the cervical spine. Motion between the components in the artificial disc, as well as motion between the components and adjacent vertebrae, were calculated in 3 planes. Intraclass correlation (ICC) between independent observers and repeatability of the method were also calculated. RESULTS Intrinsic motion, expressed as degrees in rotation and millimeters in translation, was detectable in a majority of the ADRs. In the sagittal plane, in which the flexion/extension was performed, sagittal rotation ranged between 0.2 degrees and 15.8 degrees and translation between 0.0 and 5.5 mm. Eight percent of the ADRs were classified as unstable, as motion between at least 1 of the components and the adjacent vertebra was detected. Five percent were classified as ankylotic, with no detectable motion, and another 8% showed very limited motion due to heterotopic ossification. Repeatability for the motion in the sagittal plane was calculated to be 1.30 degrees for rotation and 1.29 mm for translation (95% confidence level), ICC 0.99 and 0.84, respectively. All 3 patients with unstable devices had undergone 1-level ADRs at C5-6. They all underwent revision surgery due to increased neck pain, and instability was established during the surgery. CONCLUSIONS The majority of the artificial discs in this study showed intrinsic mobility several years after implantation and were also shown to be properly attached. Implant instability was detected in 8% of patients and, as all of these patients underwent revision surgery due to increasing neck pain, this might be a more serious problem than heterotopic bone formation.

The second-order differential equation for a damped harmonic oscillator can be converted to two coupled first-order equations, with two two-by-two matrices leading to the group Sp(2). It is shown that this oscillator system contains the essential features of Wigner's little groups dictating the internal space-time symmetries of particles in the Lorentz-covariant world. The little groups are the subgroups of the Lorentz group whose transformations leave the four-momentum of a given particle invariant. It is shown that the damping modes of the oscillator correspond to the little groups for massive and imaginary-mass particles respectively. When the system makes the transition from the oscillation to damping mode, it corresponds to the little group for massless particles. Rotations around the momentum leave the four-momentum invariant. This degree of freedom extends the Sp(2) symmetry to that of SL (2, c) corresponding to the Lorentz group applicable to the four-dimensional Minkowski space. The Poincare sphere contains the S L (2, c) symmetry. In addition, it has a non-Lorentzian parameter allowing us to reduce the mass continuously to zero. It is thus possible to construct the little group for massless particles from that of the massive particle by reducing its mass to zero. Spin-1/2 particles and spin-1 particles are discussed in detail.

Monitoring and quantifying bone remodeling are of interest, for example, in correction osteotomies, delayed fracture healing pseudarthrosis, bone lengthening, and other instances. Seven patients who had operations to attach an Ilizarov-derived Taylor Spatial Frame to the tibia gave informed consent. Each patient was examined by Na(18)F PET/CT twice, at approximately six weeks and three months after the operation. A validated software tool was used for the following processing steps. The first and second CT volumes were aligned in 3D and the respective PET volumes were aligned accordingly. In the first PET volume spherical volumes of interest (VOIs) were delineated for the crural fracture and normal bone and transferred to the second PET volume for SUVmax evaluation. This method potentially provides clinical insight into questions such as, when has the bone remodeling progressed well enough to safely remove the TSF? and when is intervention required, in a timelier manner than current methods? For example, in two patients who completed treatment, the SUVmax between the first and second PET/CT examination decreased by 42% and 13%, respectively. Further studies in a larger patient population are needed to verify these preliminary results by correlating regional Na(18)F PET measurements to clinical and radiological findings.

Background - Determination of the amount of wear in a polyethylene liner following total hip arthroplasty (THA) is important for both the clinical care of individual patients and the development of new types of liners. Patients and methods - We measured in vivo wear of the polyethylene liner using computed tomography (CT) (obtained in the course of regular clinical care) and compared it to coordinate-measuring machine (CMM) readings. Also, changes in liner thickness of the same retrieved polyethylene liner were measured using a micrometer, and were compared to CT and CMM measurements. The distance between the centers of the acetabular cup and femoral head component was measured in 3D CT, using a semi-automatic analysis method. CMM readings were performed on each acetabular liner and data were analyzed using 3D computer-aided design software. Micrometer readings compared the thickest and thinnest regions of the liner. We analyzed 10 THA CTs and retrievals that met minimal requirements for CT slice thickness and explanted cup condition. Results - For the 10 cups, the mean difference between the CT readings and the CMM readings was -0.09 (-0.38 to 0.20) mm. This difference was not statistically significant (p = 0.6). Between CT and micrometer, the mean difference was 0.11 (-0.33 to 0.55) mm. This difference was not statistically significant (p = 0.6). Interpretation - Our results show that CT imaging is ready to be used as a tool in clinical wear measurement of polyethylene liners used in THA.

Diagnosis of new bone growth in patients with compound tibia fractures or deformities treated using a Taylor spatial frame is difficult with conventional radiography because the frame obstructs the images and creates artifacts. The use of Na(18)F PET studies may help to eliminate this difficulty. METHODS: Patients were positioned on the pallet of a clinical PET/CT scanner and made as comfortable as possible with their legs immobilized. One bed position covering the site of the fracture, including the Taylor spatial frame, was chosen for the study. A topogram was performed, as well as diagnostic and attenuation correction CT. The patients were given 2 MBq of Na(18)F per kilogram of body weight. A 45-min list-mode acquisition was performed starting at the time of injection, followed by a 5-min static acquisition 60 min after injection. The patients were examined 6 wk after the Taylor spatial frame had been applied and again at 3 mo to assess new bone growth. RESULTS: A list-mode reconstruction sequence of 1 x 1,800 and 1 x 2,700 s, as well as the 5-min static scan, allowed visualization of regional bone turnover. CONCLUSION: With Na(18)F PET/CT, it was possible to confirm regional bone turnover as a means of visualizing bone remodeling without the interference of artifacts from the Taylor spatial frame. Furthermore, dynamic list-mode acquisition allowed different sequences to be performed, enabling, for example, visualization of tracer transport from blood to the fracture site.