Numerical investigations of linear least squares methods for derivative estimation

The results of a numerical investigation into the errors for least squares estimates of function gradients are presented. The underlying algorithm is obtained by constructing a least squares problem using a truncated Taylor expansion. An error bound associated with this method contains in its numerator terms related to the Taylor series remainder, while its denominator contains the smallest singular value of the least squares matrix. Perhaps for this reason the error bounds are often found to be pessimistic by several orders of magnitude. The circumstance under which these poor estimates arise is elucidated and an empirical correction of the theoretical error bounds is conjectured and investigated numerically. This is followed by an indication of how the conjecture is supported by a rigorous argument.

Anterior vertebral stapling for the fusionless correction of scoliosis

Fusionless scoliosis surgery is an emerging treatment for idiopathic scoliosis as it offers theoretical advantages over current forms of treatment. Currently the treatment options for idiopathic scoliosis are observation, bracing and fusion. While brace treatment is non-invasive, and preserves the growth, motion, and function of the spine, it does not correct deformity and is only modestly successful in preventing curve progression. In adolescents who fail brace treatment, surgical treatment with an instrumented spinal fusion usually results in better deformity correction but is associated with substantially greater risk. Furthermore in younger patients requiring surgical treatment, fusion procedures are known to adversely effect the future growth of the chest and spine. Fusionless treatments have been developed to allow effective surgical treatment of patients with idiopathic scoliosis who are too young for fusion procedures. Anterior vertebral stapling is one such fusionless treatment which aims to modulate the growth of vertebra to allow correction of scoliosis whilst maintaining normal spinal motion The Mater Misericordiae Hospital in Brisbane has begun to use anterior vertebral stapling to treat patients with idiopathic scoliosis who are too young for fusion procedures. Currently the only staple approved for clinical use is manufactured by Medtronic Sofamor Danek (Memphis, TN). This thesis explains the biomechanical and anatomical changes that occur following anterior vertebral staple insertion using in vitro experiments performed on an immature bovine model. Currently there is a paucity of published information about anterior vertebral stapling so it is hoped that this project will provide information that will aid in our understanding of the clinical effects of staple insertion. The aims of this experimental study were threefold. The first phase was designed to determine the changes in the bending stiffness of the spine following staple insertion. The second phase was designed to measure the forces experienced by the staple during spinal movements. The third and final phase of testing was designed to describe the structural changes that occur to a vertebra as a consequence of staple insertion. The first phase of testing utilised a displacement controlled testing robot to compare the change in stiffness of a single spinal motion segment following staple insertion for the three basic spinal motions of flexion-extension, lateral bending, and axial rotation. For the second phase of testing strain gauges were attached to staples and used to measure staple forces during spinal movement. In the third and final phase the staples were removed and a testing specimen underwent micro-computed tomography (CT) scanning to describe the anatomical changes that occur following staple insertion. The displacement controlled testing showed that there was a significant decrease in bending stiffness in flexion, extension, lateral bending away from the staple, and axial rotation away from the staple following staple insertion. The strain gauge measurements showed that the greatest staple forces occurred in flexion and the least in extension. In addition, a reduction in the baseline staple compressive force was seen with successive loading cycles. Micro-CT scanning demonstrated that significant damage to the vertebral body and endplate occurred as a consequence of staple insertion. The clinical implications of this study are significant. Based on the findings of this project it is likely that the clinical effect of the anterior vertebral staple evaluated in this project is a consequence of growth plate damage (also called hemiepiphysiodesis) causing a partial growth arrest of the vertebra rather than simply compression of the growth plate. The surgical creation of a unilateral growth arrest is a well established treatment used in the management of congenital scoliosis but has not previously been considered for use in idiopathic scoliosis.

The statistics of refractive error maps : managing wavefront aberration analysis without Zernike polynomials

The refractive error of a human eye varies across the pupil and therefore may be treated as a random variable. The probability distribution of this random variable provides a means for assessing the main refractive properties of the eye without the necessity of traditional functional representation of wavefront aberrations. To demonstrate this approach, the statistical properties of refractive error maps are investigated. Closed-form expressions are derived for the probability density function (PDF) and its statistical moments for the general case of rotationally-symmetric aberrations. A closed-form expression for a PDF for a general non-rotationally symmetric wavefront aberration is difficult to derive. However, for specific cases, such as astigmatism, a closed-form expression of the PDF can be obtained. Further, interpretation of the distribution of the refractive error map as well as its moments is provided for a range of wavefront aberrations measured in real eyes. These are evaluated using a kernel density and sample moments estimators. It is concluded that the refractive error domain allows non-functional analysis of wavefront aberrations based on simple statistics in the form of its sample moments. Clinicians may find this approach to wavefront analysis easier to interpret due to the clinical familiarity and intuitive appeal of refractive error maps.

Driving-related eye and head movements are changed by the type of presbyopic correction

Purpose: To investigate whether wearing different presbyopic vision corrections alters the pattern of eye and head movements when viewing dynamic driving-related traffic scenes. Methods: Participants included 20 presbyopes (mean age: 56±5.7 years) who had no experience of wearing presbyopic vision corrections (i.e. all were single vision wearers). Eye and head movements were recorded while wearing five different vision corrections: single vision lenses (SV), progressive addition spectacle lenses (PALs), bifocal spectacle lenses (BIF), monovision (MV) and multifocal contact lenses (MTF CL) in random order. Videotape recordings of traffic scenes of suburban roads and expressways (with edited targets) were presented as dynamic driving-related stimuli and digital numeric display panels included as near visual stimuli (simulating speedometer and radio). Eye and head movements were recorded using the faceLAB™ system and the accuracy of target identification was also recorded. Results: The magnitude of eye movements while viewing the driving-related traffic scenes was greater when wearing BIF and PALs than MV and MTF CL (p≤0.013). The magnitude of head movements was greater when wearing SV, BIF and PALs than MV and MTF CL (p<0.0001) and the number of saccades was significantly higher for BIF and PALs than MV (p≤0.043). Target recognition accuracy was poorer for all vision corrections when the near stimulus was located at eccentricities inferiorly and to the left, rather than directly below the primary position of gaze (p=0.008), and PALs gave better performance than MTF CL (p=0.043). Conclusions: Different presbyopic vision corrections alter eye and head movement patterns. In particular, the larger magnitude of eye and head movements and greater number of saccades associated with the spectacle presbyopic corrections, may impact on driving performance.

Contact lens correction of presbyopia

The ageing population highlights the need to provide effective optical solutions for presbyopic contact lens wearers. However, data gathered from annual contact lens fitting surveys demonstrate that fewer than 40% of contact lens wearers over 45 years of age (virtually all of whom can be presumed to suffer a partial or complete loss of accommodation) are prescribed a presbyopic correction. Furthermore, monovision is prescribed as frequently as multifocal lenses. These observations suggest that an optimal solution to the contact lens correction of presbyopia remains elusive.

A biomechanical study of top screw pullout in anterior scoliosis correction constructs

Study Design: Biomechanical testing of vertebral body screw pullout resistance with relevance to top screw pullout in endoscopic anterior scoliosis constructs. Objectives: To analyse the effect of screw positioning and angulation on pullout resistance of vertebral body screws, where the pullout takes place along a curved path as occurs in anterior scoliosis constructs. Summary of Background Data: Top screw pullout is a significant clinical problem in endoscopic anterior scoliosis surgery, with rates of up to 18% reported in the literature. Methods: A custom designed biomechanical test rig was used to perform pullout tests of Medtronic anterior vertebral screws where the pullout occurred along an arc of known radius. Using synthetic bone blocks, a range of pullout radii and screw angulations were tested, in order to determine an ‘optimal’ configuration. The optimal configuration was then compared with standard screw positioning using a series of tests on ovine vertebrae (n=29). Results: Screw angulation has a small but significant effect on pullout resistance, with maximum strength being achieved at 10 degree cephalad angulation. Combining 10 degree cephalad angulation with maximal spacing between the top two screws (maximum pullout radius) increased the pullout resistance by 88% compared to ‘standard’ screw positioning (screws inserted perpendicular to rod at mid-body height). Conclusions: The positioning of the top screw in anterior scoliosis constructs can significantly alter its pullout resistance.

The relationship between deformity correction and clinical outcomes after thoracoscopic scoliosis surgery : a prospective series of 100 patients

The relationship between deformity correction and self-reported patient satisfaction after thoracoscopic anterior scoliosis surgery is unknown. Scoliosis Research Society questionnaire scores, radiographic outcomes, and rib hump correction were prospectively assessed for a group of 100 patients pre-operatively and at two years after surgery. Patients with lower post-op major Cobb angles report significantly higher SRS scores than patients with higher post-op Cobb angles.

Fusionless scoliosis correction using shape memory alloy staples

Severe spinal deformity in young children is a formidable challenge for optimal treatment. Standard interventions for adolescents, such as spinal deformity correction and fusion, may not be appropriate for young patients with considerable growth remaining. Alternative surgical options that provide deformity correction and protect the growth remaining in the spine are needed to treat this group of patients 1, 2. One such method is the use of shape memory alloy staples. We report our experience to date using video-assisted thoracoscopic insertion of shape memory alloy staples. A retrospective review was conducted of 13 patients with scoliosis, aged 7 to 13 years, who underwent video-assisted thoracoscopic insertion of shape memory staples. In our experience, video-assisted thoracoscopic insertion of shape memory alloy staples is a safe procedure with no complications noted. It is a reliable method of providing curve stability, however the follow up results to date indicate that the effectiveness of the procedure is greater in younger patients.

3D lung and rib cage reconstruction using low dose CT scans of adolescent idiopathic scoliosis pre and post anterior thoracoscopic correction

Adolescent Idiopathic Scoliosis (AIS) has been associated with reduced pulmonary function believed to be due to a restriction of lung volume by the deformed thoracic cavity. A recent study by our group examined the changes in lung volume pre and post anterior thoracoscopic scoliosis correction using pulmonary function testing (1), however the anatomical changes in ribcage shape and left/right lung volume after thoracoscopic surgery which govern overall respiratory capacity are unknown. The aim of this study was to use 3D rendering from CT scan data to compare lung and ribcage anatomical changes from pre to two years post thoracoscopic anterior scoliosis correction. The study concluded that 3D volumetric reconstruction from CT scans is a powerful means of evaluating changes in pulmonary and thoracic anatomy following surgical AIS correction. Most likely, lung volume changes following thoracoscopic scoliosis correction are multifactorial and affected by changes in height (due to residual growth), ribcage shape, diaphragm positioning, Cobb angle correction in the thoracic spine. Further analysis of the 3D reconstructions will be performed to assess how each of these factors affect lung volume in this patient cohort.

An economic case for systematic student monitoring and intervention in the first year in higher education

Previous work has established the effectiveness of systematically monitoring first year higher education students and intervening with those identified as at-risk of attrition. This nuts-and-bolts paper establishes an economic case for a systematic monitoring and intervention program, identifying the visible costs and benefits of such a program at a major Australian university. The benefit of such a program is measured in savings to the institution which would otherwise be lost revenue, in the form of retained equivalent full-time student load (EFTSL). The session will present an economic model based on a number of assumptions. These assumptions are explored along with the applicability of the model to other institutions.

Development of a Systematic Approach to Assessing Quality within Australian Residential Aged Care Facilities: The Clinical Care Indicators Tool

Recent years have seen the introduction of formalised accreditation processes in both community and residential aged care, but these only partially address quality assessment within this sector. Residential aged care in Australia does not yet have a standardised system of resident assessment related to clinical, rather than administrative, outcomes. This paper describes the development of a quality assessment tool aimed at addressing this gap. Utilising previous research and the results of nominal groups with experts in the field, the 21-item Clinical Care Indicators (CCI) Tool for residential aged care was developed and trialled nationally. The CCI Tool was found to be simple to use and an effective means of collecting data on the state of resident health and care, with potential benefits for resident care planning and continuous quality improvement within facilities and organisations. The CCI Tool was further refined through a small intervention study to assess its utility as a quality improvement instrument and to investigate its relationship with resident quality of life. The current version covers 23 clinical indicators, takes about 30 minutes to complete and is viewed favourably by nursing staff who use it. Current work focuses on psychometric analysis and benchmarking, which should enable the CCI Tool to make a positive contribution to the measurement of quality in aged care in Australia.

A simple and systematic approach to assigning Denavit-Hartenberg Parameters

This paper presents a simple and intuitive approach to determining the kinematic parameters of a serial-link robot in Denavit– Hartenberg (DH) notation. Once a manipulator’s kinematics is parameterized in this form, a large body of standard algorithms and code implementations for kinematics, dynamics, motion planning, and simulation are available. The proposed method has two parts. The first is the “walk through,” a simple procedure that creates a string of elementary translations and rotations, from the user-defined base coordinate to the end-effector. The second step is an algebraic procedure to manipulate this string into a form that can be factorized as link transforms, which can be represented in standard or modified DH notation. The method allows for an arbitrary base and end-effector coordinate system as well as an arbitrary zero joint angle pose. The algebraic procedure is amenable to computer algebra manipulation and a Java program is available as supplementary downloadable material.