Manifolds and Riemannian Geometry

We present a semi-formal build-up of the mathematical structure of a manifold, the more abstract generalization of a surface. Then, we discuss notions of Riemannian geometry on a specific class of manifolds, called Riemann manifolds, and discuss generalizations of concepts from calculus to Riemann manifolds. Finally, we end with a discussion of curvature on 3D surfaces and prove Gauss\u27s Theorema Egregium

Guidelines for the performance of fusion procedures for degenerative disease of the lumbar spine. Part 2: assessment of functional outcome

Journal ArticleStandards. It is recommended that functional outcome be measured in patients treated for low-back pain due to degenerative disease of the lumbar spine by using reliable, valid, and responsive scales. Examples of these scales in the low-back pain population include the following: The Spinal Stenosis Survey of Stucki, Waddell-Main Questionnaire, RMDQ, DPQ, QPDS, SIP, Million Scale, LBPR Scale, ODI, the Short Form-12, the JOA system, the CBSQ, and the North American Spine Society Lumbar Spine Outcome Assessment Instrument. Guidelines. There is insufficient evidence to recommend a guideline for assessment of functional outcome following fusion for lumbar degenerative disease. Options. Patient satisfaction scales are recommended for use as outcome measures in retrospective case series, where better alternatives are not available. Patient satisfaction scales are not reliable for the assessment of outcome following intervention for low-back pain

Guidelines for the performance of fusion procedures for degenerative disease of the lumbar spine. Part 1: introduction and methodology

Journal ArticleAs scientific understanding of the pathophysiology of degenerative disease of the lumbar spine has increased, the possibilities for correcting the underlying problem and the resulting improvement in clinical function have expanded exponentially. Fueled by advances in material technology and surgical technique, treatment of greater numbers of individuals suffering from lumbar spinal disease has proliferated. Using data from the National Hospital Discharge Survey, Deyo and colleagues4 described a 200% increase in the frequency of lumbar fusion procedures in the 1980s. Davis3 observed that the age-adjusted rate of hospitalization for lumbar surgery and lumbar fusion increased greater than 33% and greater than 60%, respectively, from 1979 to 1990. Lumbar fusion has been described as a treatment of symptomatic degenerative disc disease, spinal stenosis, spondylolisthesis, and degenerative scoliosis. Lumbar fusion has been performed to treat acute and chronic lowback pain, radiculopathy, and spinal instability

Guideline update for the performance of fusion procedures for degenerative disease of the lumbar spine. Part 9: Lumbar fusion for stenosis with spondylolisthesis

pre-printPatients presenting with stenosis associated with a spondylolisthesis will often describe signs and symptoms consistent with neurogenic claudication, radiculopathy, and/or low-back pain. The primary objective of surgery, when deemed appropriate, is to decompress the neural elements. As a result of the decompression, the inherent instability associated with the spondylolisthesis may progress and lead to further misalignment that results in pain or recurrence of neurological complaints. Under these circumstances, lumbar fusion is considered appropriate to stabilize the spine and prevent delayed deterioration. Since publication of the original guidelines there have been a significant number of studies published that continue to support the utility of lumbar fusion for patients presenting with stenosis and spondylolisthesis. Several recently published trials, including the Spine Patient Outcomes Research Trial, are among the largest prospective randomized investigations of this issue. Despite limitations of study design or execution, these trials have consistently demonstrated superior outcomes when patients undergo surgery, with the majority undergoing some type of lumbar fusion procedure. There is insufficient evidence, however, to recommend a standard approach to achieve a solid arthrodesis. When formulating the most appropriate surgical strategy, it is recommended that an individualized approach be adopted, one that takes into consideration the patient's unique anatomical constraints and desires, as well as surgeon's experience

Guidelines for the performance of fusion procedures for degenerative disease of the lumbar spine. Part 3: assessment of economic outcome

Journal ArticleStandards. There is insufficient evidence to recommend a standard for assessment of economic outcome following lumbar fusion for degenerative disease. Guidelines. There is insufficient evidence to recommend a guideline for assessment of economic outcome following lumbar fusion for degenerative disease. Options. It is recommended that valid and responsive economic outcome measures be included in the assessment of outcomes following lumbar fusion surgery for degenerative disease. Return-to-work rates and termination of disability compensation are two such measures. It is recommended that cost analyses related to lumbar spinal fusion include perioperative expenses as well as expenses associated with long-term care, including those incurred in both the operative and nonoperative settings

Guideline update for the performance of fusion procedures for degenerative disease of the lumbar spine. Part 10: Lumbar fusion for stenosis without spondylolisthesis

pre-printLumbar stenosis is one of the more common radiographic manifestations of the aging process, leading to narrowing of the spinal canal and foramen. When stenosis is clinically relevant, patients often describe activity-related low-back or lower-extremity pain, known as neurogenic claudication. For those patients who do not improve with conservative care, surgery is considered an appropriate treatment alternative. The primary objective of surgery is to reconstitute the spinal canal. The role of fusion, in the absence of a degenerative deformity, is uncertain. The previous guideline recommended against the inclusion of lumbar fusion in the absence of spinal instability or a likelihood of iatrogenic instability. Since the publication of the original guidelines, numerous studies have demonstrated the role of surgical decompression in this patient population; however, few have investigated the utility of fusion in patients without underlying instability. The majority of studies contain a heterogeneous cohort of subjects, often combining patients with and without spondylolisthesis who received various surgical interventions, limiting fusions to those patients with instability. It is difficult if not impossible, therefore, to formulate valid conclusions regarding the utility of fusion for patients with uncomplicated stenosis. Lower-level evidence exists, however, that does not demonstrate an added benefit of fusion for these patients; therefore, in the absence of deformity or instability, the inclusion of a fusion is not recommended

Guidelines for the performance of fusion procedures for degenerative disease of the lumbar spine. Part 4: radiographic assessment of fusion

Journal ArticleStandards. Static lumbar radiographs are not recommended as a stand-alone means to assess fusion status following lumbar arthrodesis surgery. Guidelines. 1) Lateral flexion and extension radiography is recommended as an adjunct to determine the presence of lumbar fusion postoperatively. The lack of motion between vertebrae, in the absence of rigid instrumentation, is highly suggestive of successful fusion. 2) Technetium-99 bone scanning is not recommended as a means to assess lumbar fusion. Options. Several radiographic techniques, including static radiography, lateral flexion-extension radiography, and/ or CT scanning, often in combination, are recommended as assessment modality options for the noninvasive evaluation of symptomatic patients in whom failed lumbar fusion is suspected

Guidelines for the performance of fusion procedures for degenerative disease of the lumbar spine. Part 6: magnetic resonance imaging and discography for patient selection for lumbar fusion

Journal ArticleStandards. There is insufficient evidence to recommend a treatment standard. Guidelines. 1) It is recommended that MR imaging be used as a diagnostic test instead of discography for the initial evaluation of patients with chronic low-back pain. 2) It is recommended that MR imaging-documented disc spaces that appear to be normal not be considered for treatment as a source of low-back pain. 3) It is recommended that lumbar discography not be used as a stand-alone test on which treatment decisions are based for patients with low-back pain. 4) If discography is performed as a diagnostic tool to identify the source of a patient's low-back pain, it is recommended that both a concordant pain response and morphological abnormalities be present at the pathological level prior to initiating any treatment directed at that level. Options. 1) It is recommended that discography be reserved for use in patients with equivocal MR imaging findings, especially at levels adjacent to clearly pathological levels. 2) It is recommended that patients in whom discography is positive but in whom MR imaging evidence of disc degeneration is absent not be considered candidates for operative intervention

Guidelines for the performance of fusion procedures for degenerative disease of the lumbar spine. Part 5: correlation between radiographic and functional outcome

Journal ArticleStandards. There is insufficient evidence to recommend a treatment standard. Guidelines. There is insufficient evidence to recommend a treatment guideline. Options. It is recommended that when performing lumbar arthrodesis for degenerative lumbar disease, strategies to achieve successful radiographic fusion should be considered. There appears to be a correlation between successful fusion and improved clinical outcomes; however, it should be noted that the correlation between fusion status and clinical outcome is not strong, and in a given patient fusion status may be unrelated to clinical outcome. between fusion status and clinical outcome after lumbar arthrodesis procedures performed in the treatment of lumbar spinal degenerative disease

Guidelines for the performance of fusion procedures for degenerative disease of the lumbar spine. Part 12: pedicle screw fixation as an adjunct to posterolateral fusion for low-back pain

Journal ArticleStandard. There is insufficient evidence to recommend a treatment standard. Guidelines. There is insufficient evidence to recommend a treatment guideline. Options. 1) Pedicle screw fixation is recommended as a treatment option for patients with low-back pain treated with PLF who are at high risk for fusion failure because the use of pedicle screw fixation improves fusion success rates. 2) Pedicle screw fixation as a routine adjunct to PLF in the treatment of patients with chronic low-back pain due to DDD is not recommended because there is conflicting evidence regarding a beneficial effect of pedicle screw fixation on functional outcome, and there is consistent evidence that the use of pedicle screw fixation is associated with higher costs and complications