Acceleration of generalized hypergeometric functions through precise remainder asymptotics

We express the asymptotics of the remainders of the partial sums {s_n} of the generalized hypergeometric function q+1_F_q through an inverse power series z^n n^l \sum_k c_k/n^k, where the exponent l and the asymptotic coefficients {c_k} may be recursively computed to any desired order from the hypergeometric parameters and argument. From this we derive a new series acceleration technique that can be applied to any such function, even with complex parameters and at the branch point z=1. For moderate parameters (up to approximately ten) a C implementation at fixed precision is very effective at computing these functions; for larger parameters an implementation in higher than machine precision would be needed. Even for larger parameters, however, our C implementation is able to correctly determine whether or not it has converged; and when it converges, its estimate of its error is accurate.Comment: 36 pages, 6 figures, LaTeX2e. Fixed sign error in Eq. (2.28), added several references, added comparison to other methods, and added discussion of recursion stabilit

Direction of the formation of anterior lumbar vertebral osteophytes

<p>Abstract</p> <p>Background</p> <p>X-ray images of lumbar degenerative diseases often show not only claw osteophytes, but also pairs of osteophytes that form in a direction away from the adjacent disc. We have investigated the direction of the formation of anterior lumbar vertebral osteophytes across the lumbar vertebrae using a sufficient number of lumbar radiographs, because osteophytes images can provide essential information that will contribute to the understanding of the pathology and progress of lumbar spine degeneration.</p> <p>Methods</p> <p>The direction of the formation of 14,250 pairs of anterior lumbar vertebral osteophytes across the adjacent intervertebral discs in 2,850 patients who were all over 60 years old was investigated. Anterior lumbar vertebral osteophytes were distributed into six groups based on the direction of extension of each pair of osteophytes across the intervertebral disc space.</p> <p>Results</p> <p>In L1–L2 and L2–L3, the number of patients classified into groups B (the pair of osteophytes extended in the direction of the adjacent disc) and C (almost complete bone bridge formation by a pair of osteophytes across the intervertebral disc space) was larger than that classified into group D (the pair of osteophytes extended in a direction away from the adjacent disc). In L3–L4, L4–L5 and L5-S1, the number of patients in group D was greater than that of patients belonging to groups B and C.</p> <p>Conclusion</p> <p>Our study showed that pairs of osteophytes frequently formed in the direction of the adjacent disc in the upper lumbar vertebrae (L1–L2 and L2–L3) and in the direction away from the adjacent disc in middle or lower lumbar vertebrae (L3–L4, L4–L5, and L5-S1).</p

Use of conventional and alternative treatment strategies for a case of low back pain in a F/A-18 aviator

BACKGROUND: Low back pain can diminish jet pilot concentration and function during flight and be severe enough to ground pilots or cause decreased flying time. The objective of this case report is to present an example of the integration of chiropractic care with conventional treatments for the management of low back pain in a F/A-18 aviator. CASE PRESENTATION: The patient had insidious severe low back pain without radiation or neurological deficit, resulting in 24 hours of hospitalization. Spinal degeneration was discovered upon imaging. Four months later, it still took up to 10 minutes for him to get out of bed and several minutes to exit the jet due to stiffness and pain. He had discontinued his regular Marine Corps fitness training due to pain avoidance. Pain severity ranged from 1.5–7.1 cm on a visual analog scale. His Roland Morris Disability Questionnaire score was 5 out of 24. The pilot's pain was managed with the coordinated efforts of the flight surgeon, physiatrist, physical therapist, and doctor of chiropractic. Following this regimen he had no pain and no functional disability; he was able to fly multiple training missions per week and exercise to Marine Corps standards. CONCLUSION: A course of care integrating flight medicine, chiropractic, physical therapy, and physiatry appeared to alleviate pain and restore function to this F/A-18 aviator with low back pain

MRI classification of interspinous ligament degeneration of the lumbar spine: intraobserver and interobserver reliability and the frequency of disagreement

Posterior spinal ligament pathology is becoming increasingly recognized as a significant cause of low back pain. Despite the growing clinical importance of interspinous ligament degeneration in low back pain patients, formal reliability studies for the magnetic resonance imaging (MRI) evaluation of interspinous ligaments have not been performed. We proposed an MRI classification system for interspinous ligament degeneration and conducted a comprehensive reliability and reproducibility assessment. Fifty patients who had low back pain with or without leg discomfort (26 males and 24 females) with a mean age of 48.8 years (range 23–85 years) were studied. The classification for lumbar interspinous ligament degeneration was developed on the basis of the literature using mid-sagittal T1- and T2-weighted images. Three spine surgeons independently graded a total of 200 interspinous ligament levels. Intraobserver and interobserver reliability were assessed by kappa statistics. The frequency of disagreement was also identified. The intraobserver agreement was excellent in all readers (kappa range 0.840–0.901). The interobserver agreement was lower as expected, and was substantial to excellent (kappa range 0.726–0.818). Overall complete agreement was obtained in 87.8% of all interspinous ligament levels. A difference of 1, 2, and 3 grades occurred in 8.1, 3.0, and 1.1% of readings, respectively. This proposed MRI classification of interspinous ligament degeneration was simple, reliable, and reproducible. Its use as a standardized nomenclature in clinical and radiographic research may be recommended

The correlation between exaggerated fluid in lumbar facet joints and degenerative spondylolisthesis: prospective study of 52 patients

Magnetic resonance imaging (MRI) is often used to evaluate low back pain; however, MRI in the supine position does not always reveal degenerative spondylolisthesis. The existence of a linear correlation between increased fluid in the facet joints seen on the supine axial T2 MRI of the lumbosacral spine and lumbar instability seen on standing lateral flexion-extension lumbosacral radiographs has recently been reported. The objective of this prospective study was to determine the incidence of increased fluid in the lumbar facet joints seen on the supine axial T2 MRI, and to evaluate the correlation of this finding with radiographic evidence of lumbar instability

Attainment rate as a surrogate indicator of the intervertebral neutral zone length in lateral bending: An in vitro proof of concept study

Background Lumbar segmental instability is often considered to be a cause of chronic low back pain. However, defining its measurement has been largely limited to laboratory studies. These have characterised segmental stability as the intrinsic resistance of spine specimens to initial bending moments by quantifying the dynamic neutral zone. However these measurements have been impossible to obtain in vivo without invasive procedures, preventing the assessment of intervertebral stability in patients. Quantitative fluoroscopy (QF), measures the initial velocity of the attainment of intervertebral rotational motion in patients, which may to some extent be representative of the dynamic neutral zone. This study sought to explore the possible relationship between the dynamic neutral zone and intervertebral rotational attainment rate as measured with (QF) in an in vitro preparation. The purpose was to find out if further work into this concept is worth pursuing. Method This study used passive recumbent QF in a multi-segmental porcine model. This assessed the intrinsic intervertebral responses to a minimal coronal plane bending moment as measured with a digital force guage. Bending moments about each intervertebral joint were calculated and correlated with the rate at which global motion was attained at each intervertebral segment in the first 10° of global motion where the intervertebral joint was rotating. Results Unlike previous studies of single segment specimens, a neutral zone was found to exist during lateral bending. The initial attainment rates for left and right lateral flexion were comparable to previously published in vivo values for healthy controls. Substantial and highly significant levels of correlation between initial attainment rate and neutral zone were found for left (Rho = 0.75, P = 0.0002) and combined left-right bending (Rho = 0.72, P = 0.0001) and moderate ones for right alone (Rho = 0.55, P = 0.0012). Conclusions This study found good correlation between the initial intervertebral attainment rate and the dynamic neutral zone, thereby opening the possibility to detect segmental instability from clinical studies. However the results must be treated with caution. Further studies with multiple specimens and adding sagittal plane motion are warranted

Does lumbar spinal degeneration begin with the anterior structures? A study of the observed epidemiology in a community-based population

<p>Abstract</p> <p>Background-</p> <p>Prior studies that have concluded that disk degeneration uniformly precedes facet degeneration have been based on convenience samples of individuals with low back pain. We conducted a study to examine whether the view that spinal degeneration begins with the anterior spinal structures is supported by epidemiologic observations of degeneration in a community-based population.</p> <p>Methods-</p> <p>361 participants from the Framingham Heart Study were included in this study. The prevalences of anterior vertebral structure degeneration (disk height loss) and posterior vertebral structure degeneration (facet joint osteoarthritis) were characterized by CT imaging. The cohort was divided into the structural subgroups of participants with 1) no degeneration, 2) isolated anterior degeneration (without posterior degeneration), 3) combined anterior and posterior degeneration, and 4) isolated posterior degeneration (without anterior structure degeneration). We determined the prevalence of each degeneration pattern by age group < 45, 45-54, 55-64, ≥65. In multivariate analyses we examined the association between disk height loss and the response variable of facet joint osteoarthritis, while adjusting for age, sex, BMI, and smoking.</p> <p>Results-</p> <p>As the prevalence of the no degeneration and isolated anterior degeneration patterns decreased with increasing age group, the prevalence of the combined anterior/posterior degeneration pattern increased. 22% of individuals demonstrated isolated posterior degeneration, without an increase in prevalence by age group. Isolated posterior degeneration was most common at the L5-S1 and L4-L5 spinal levels. In multivariate analyses, disk height loss was independently associated with facet joint osteoarthritis, as were increased age (years), female sex, and increased BMI (kg/m²), but not smoking.</p> <p>Conclusions-</p> <p>The observed epidemiology of lumbar spinal degeneration in the community-based population is consistent with an ordered progression beginning in the anterior structures, for the majority of individuals. However, some individuals demonstrate atypical patterns of degeneration, beginning in the posterior joints. Increased age and BMI, and female sex may be related to the occurrence of isolated posterior degeneration in these individuals.</p

The role of intradiscal steroids in the treatment of discogenic low back pain

LBP is one of the most common reasons for visiting a doctor and is the most common cause of disability under age 45.Amongst a variety of etiologies, internal disc disruption (IDD) has been postulated as an important cause of low back pain. Treating discogenic low back pain continues to be a challenge to physicians. Inflammation, either from direct chemical irritation or secondary to an autoimmune response to the nucleus pulposus has been implicated as the primary pain source. Both steroids and non-steroidal anti-inflammatory drugs have partial effectiveness in treating pain associated with inflammation. Therefore, the rationale for using intradiscal steroids is to suppress the inflammation within the disc, thereby alleviating the patient’s symptoms. The goal of this article is to review the literature regarding the efficacy of intradiscal steroids to treat low back pain of discogenic origin

Communally breeding bats use physiological and behavioural adjustments to optimise daily energy expenditure

Small endotherms must change roosting and thermoregulatory behaviour in response to changes in ambient conditions if they are to achieve positive energy balance. In social species, for example many bats, energy expenditure is influenced by environmental conditions, such as ambient temperature, and also by social thermoregulation. Direct measurements of daily fluctuations in metabolic rates in response to ambient and behavioural variables in the field have not been technologically feasible until recently. During different reproductive periods, we investigated the relationships between ambient temperature, group size and energy expenditure in wild maternity colonies of Bechstein’s bats (Myotis bechsteinii). Bats used behavioural and physiological adjustments to regulate energy expenditure. Whether bats maintained normothermia or used torpor, the number of bats in the roosts as well changed with reproductive status and ambient temperature. During pregnancy and lactation, bats remained mostly normothermic and daily group sizes were relatively large, presumably to participate in the energetic benefits of social thermoregulation. In contrast, smaller groups were formed on days when bats used torpor, which occurred mostly during the post-lactation period. Thus, we were able to demonstrate on wild animals under natural conditions the significance of behavioural and physiological flexibility for optimal thermoregulatory behaviour in small endotherms