Reduction in range of cervical motion on serial long-term follow-up in patients undergoing oblique corpectomy for cervical spondylotic myelopathy.

PURPOSE: To determine whether motion preservation following oblique cervical corpectomy (OCC) for cervical spondylotic myelopathy (CSM) persists with serial follow-up. METHODS: We included 28 patients with preoperative and at least two serial follow-up neutral and dynamic cervical spine radiographs who underwent OCC for CSM. Patients with an ossified posterior longitudinal ligament (OPLL) were excluded. Changes in sagittal curvature, segmental and whole spine range of motion (ROM) were measured. Nathan's system graded anterior osteophyte formation. Neurological function was measured by Nurick's grade and modified Japanese Orthopedic Association (JOA) scores. RESULTS: The majority (23 patients) had a single or 2-level corpectomy. The average duration of follow-up was 45 months. The Nurick's grade and the JOA scores showed statistically significant improvements after surgery (p < 0.001). 17% of patients with preoperative lordotic spines had a loss of lordosis at last follow-up, but with no clinical worsening. 77% of the whole spine ROM and 62% of segmental ROM was preserved at last follow-up. The whole spine and segmental ROM decreased by 11.2° and 10.9°, respectively (p ≤ 0.001). Patients with a greater range of segmental movement preoperatively had a statistically greater range of movement at follow-up. The analysis of serial radiographs indicated that the range of movement of the whole spine and the range of movement at the segmental spine levels significantly reduced during the follow-up period. Nathan's grade showed increase in osteophytosis in more than two-thirds of the patients (p ≤ 0.01). The whole spine range of movement at follow-up significantly correlated with Nathan's grade. CONCLUSIONS: Although the OCC preserves segmental and whole spine ROM, serial measurements show a progressive decrease in ROM albeit without clinical worsening. The reduction in this ROM is probably related to degenerative ossification of spinal ligaments.

Quantum wire with periodic serial structure

Electron wave motion in a quantum wire with periodic structure is treated by direct solution of the Schrödinger equation as a mode-matching problem. Our method is particularly useful for a wire consisting of several distinct units, where the total transfer matrix for wave propagation is just the product of those for its basic units. It is generally applicable to any linearly connected serial device, and it can be implemented on a small computer. The one-dimensional mesoscopic crystal recently considered by Ulloa, Castaño, and Kirczenow [Phys. Rev. B 41, 12 350 (1990)] is discussed with our method, and is shown to be a strictly one-dimensional problem. Electron motion in the multiple-stub T-shaped potential well considered by Sols et al. [J. Appl. Phys. 66, 3892 (1989)] is also treated. A structure combining features of both of these is investigated

External dichotomous noise: The problem of the mean-first-passage time

A retarded backward equation for a non-Markovian process induced by dichotomous noise (the random telegraphic signal) is deduced. The mean-first-passage time of this process is exactly obtained. The Gaussian white noise and the white shot noise limits are studied. Explicit physical results in first approximation are evaluated.

Passage times for the decay of an unstable state triggered by colored noise

We study the decay of an unstable state in the presence of colored noise by calculating the moment generating function of the passage-time distribution. The problems of the independence of the initial condition in this non-Markovian process and that of nonlinear effects are addressed. Our results are compared with recent analog simulations.

First-passage time in a bistable potential with colored noise

A precise digital simulation of a bistable system under the effect of colored noise is carried out. A set of data for the mean first-passage time is obtained. The results are interpreted and compared with presently available theories, which are revisited following a new insight. Discrepancies that have been discussed in the literature are understood within our framework.

Insight toward the first-passage time in a bistable potential with highly colored noise

The exponential coefficient in the first-passage-time problem for a bistable potential with highly colored noise is predicted to be (8/27 by all existing theories. On the other hand, we show herein that all existing numerical evidence seems to indicate that the coefficient is actually larger by about (4/3, i.e., that the numerical factor in the exponent is approximately (32/81. Existing data cover values of ¿V0/D up to ~20, where V0 is the barrier height, ¿ the correlation time of the noise, and D the noise intensity. We provide an explanation for the modified coefficinet, the explanation also being based on existing numerical simulations. Whether the value (8/27 predicted by all large-¿ theories is achieved for even larger values of ¿V0/D is unknown but appears questionable (except perhaps for enormously large, experimentally inaccessible values of this factor) in view of currently available results.

Mean first-passage time of continuous non-Markovian processes driven by colored noise

An equation for mean first-passage times of non-Markovian processes driven by colored noise is derived through an appropriate backward integro-differential equation. The equation is solved in a Bourret-like approximation. In a weak-noise bistable situation, non-Markovian effects are taken into account by an effective diffusion coefficient. In this situation, our results compare satisfactorily with other approaches and experimental data.

First-passage times for a marginal state driven by colored noise

The dynamical process through a marginal state (saddle point) driven by colored noise is studied. For small correlation time of the noise, the mean first-passage time and its variance are calculated using standard methods. When the correlation time of the noise is finite or large, an alternative approach, based on simple physical arguments, is proposed. It will allow us to study also the passage times of an unstable state. The theoretical predictions are tested satisfactorily by the use of computer simulations.

Quantum wire with periodic serial structure

Electron wave motion in a quantum wire with periodic structure is treated by direct solution of the Schrödinger equation as a mode-matching problem. Our method is particularly useful for a wire consisting of several distinct units, where the total transfer matrix for wave propagation is just the product of those for its basic units. It is generally applicable to any linearly connected serial device, and it can be implemented on a small computer. The one-dimensional mesoscopic crystal recently considered by Ulloa, Castaño, and Kirczenow [Phys. Rev. B 41, 12 350 (1990)] is discussed with our method, and is shown to be a strictly one-dimensional problem. Electron motion in the multiple-stub T-shaped potential well considered by Sols et al. [J. Appl. Phys. 66, 3892 (1989)] is also treated. A structure combining features of both of these is investigated.