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Atkinson C, Pereira P. Orientational director effects in nematic liquid crystals with small Ericksen number. Proc Math Phys Eng Sci 2006. [DOI: 10.1098/rspa.2005.1638] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/12/2022] Open
Abstract
Orientational director effects in nematic liquid crystals with small Ericksen number are investigated. The director field is disturbed by a semi-infinite plate on
y
=0 and
and moving with a constant velocity
U
. Strong anchoring conditions at the plate are assumed. The resulting equations are a system of nonlinear partial differential equations for a nematic in the one elastic constant approximation. These equations are reduced to a coupled set of nonlinear ordinary differential equations by a suitable transformation. No such transformation seems possible for the many elastic constant case. The resulting equations are solved using analytical methods and strict bounding solutions obtained. These strict analytical solutions are compared with Picard iterated solutions.
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James S, Tyrrell-Price J, Atkinson C, Hunt L, Searle A, Phillips K, Penfold C, Carter J, Ness A. Evaluation of urinary chloride dipsticks for the rapid estimation of hydration status in patients receiving artificial nutrition: Feasibility study. Clin Nutr ESPEN 2021; 42:339-347. [PMID: 33745603 DOI: 10.1016/j.clnesp.2021.01.010] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/08/2020] [Revised: 01/07/2021] [Accepted: 01/11/2021] [Indexed: 10/22/2022]
Abstract
BACKGROUND AND AIMS The home parenteral nutrition (HPN) population face many challenges, especially with respect to fluid balance management. A low urinary sodium concentration of <20 mmol/L is commonly used as an indicator of dehydration that requires clinical assessment in these patients. The Quantab titrator dipstick measures chloride concentration of a solution and correlates with sodium concentration. We assessed whether it would be feasible to use the Quantab dipstick in the HPN population and explored relationships between Quantab dipstick estimated chloride concentration and quality of life (QOL). METHODS Patients on HPN were asked to collect urine samples at 5 specific times points (day 0,7,14, 21 and 28) to send to the laboratory for formal electrolyte analysis. The participant and a member of laboratory staff tested these samples with the Quantab dipstick to estimate urinary chloride concentration. Participants were instructed to complete a QOL questionnaire at each of the 5 time-points in addition to a baseline demographic questionnaire and an end-of-study questionnaire. Six participants completed an interview at the end of the study period. The relationship between participant-derived and laboratory-derived data was assessed using rank correlation coefficients. QOL assessment was correlated with urine dipstick measurements. RESULTS 10 patients on HPN completed the study. Data on chloride concentration as estimated by the dipstick (assessed by participants and by the laboratory) and sodium concentration from the laboratory were available for 47 urine samples. There was a positive relationship between participant dipstick estimated chloride concentration and laboratory sodium (Kendall's τ = 0.45; P < 0.001; Spearman's rs = 0.58 P < 0.001; 47 pairs). There was a strong correlation between chloride concentrations estimated by dipstick in the laboratory and by participants (Kendall 0.58 p < 0.001, Spearman's 0.69 p < 0.001; 47 pairs). In exploratory analyses, there was no relationship between QOL and dipstick estimated chloride concentration. Participants had no issues collecting urine samples but some difficulties were reported with determining the dipstick reading. CONCLUSIONS Patients on HPN are able to collect urine specimens, complete QOL questionnaires, and are capable of using the Quantab dipstick to estimate urinary chloride concentration. The Quantab dipstick correlates with laboratory measured sodium and chloride concentrations. Further work is required to fully establish whether this point-of-care test could be used to guide fluid balance management in the HPN population.
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Cheng Q, Patel K, Zhu P, Rucker L, Allen P, Vasu C, Nadig S, Atkinson C. Donor Organ Pretreatment with a Gap and Tight Junction Stabilizing Peptide Prevents IRI in a Mouse Lung Transplant Model. J Heart Lung Transplant 2017. [DOI: 10.1016/j.healun.2017.01.170] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022] Open
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Patel K, Cheng Q, Allen D, Aliweah A, Knochelmann H, Paulos C, Goddard M, Nadig S, Atkinson C. Recipient Emphysema Differentially Affects Immunologic Responses During Acute Lung Allograft Rejection in a Pre-Clinical Model. J Heart Lung Transplant 2018. [DOI: 10.1016/j.healun.2018.01.512] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/17/2022] Open
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Atkinson C, Gardner M. Open to suggestions. THE HEALTH SERVICE JOURNAL 1991; 101:29. [PMID: 10115395] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Subscribe] [Scholar Register] [Indexed: 04/12/2023]
Abstract
A survey of patients' attitudes to GP opening hours produced strong evidence for extending surgery times for patients' convenience and to meet specific health needs, say Chris Atkinson and Marjorie Gardner.
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Goddard MJ, Atkinson C, Horsley J, Dunning JJ, Wallwork J. Systemic vasculitis complicating pig to primate xenotransplantation. J Heart Lung Transplant 2001; 20:215-216. [PMID: 11250397 DOI: 10.1016/s1053-2498(00)00470-8] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/18/2022] Open
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Li C, Patel K, Allen P, TU Z, Kilkenny J, Wallace C, Nadig S, Tomlinson S, Atkinson C. A Novel Injury Site-Targeted Complement Inhibitor Which Protects against Lung Transplant Ischemia Reperfusion Injury. J Heart Lung Transplant 2019. [DOI: 10.1016/j.healun.2019.01.016] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/27/2022] Open
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85
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Atkinson C. A large swimming pool. Physiotherapy 1965; 51:320-1. [PMID: 5831383] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [MESH Headings] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/16/2023]
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Koughan N, Atkinson C. Nutrition Screening Initiative and the Louisiana Food for Seniors experience. THE JOURNAL OF THE LOUISIANA STATE MEDICAL SOCIETY : OFFICIAL ORGAN OF THE LOUISIANA STATE MEDICAL SOCIETY 1993; 145:447-449. [PMID: 8263374] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Subscribe] [Scholar Register] [Indexed: 05/22/2023]
Abstract
The Nutrition Screening Initiative (NSI), an interdisciplinary agency, has developed three levels of nutritional screening for the elderly. Nutritionists from the Office of Public Health and the Orleans Parish Nutrition Commodity Service screened 104 Commodity Supplemental Food Program--Food for Seniors (CSFP) participants utilizing the NSI's checklist. Anthropometric measures were also obtained and the Body Mass Index (BMI), a measure of total body fat, was calculated. Eighty percent of the participants were at moderate or high nutritional risk. Fifty percent of the obese participants (BMI > 30) were at high nutritional risk; whereas 83% of underweight participants (BMI < 21) were at high nutritional risk. Results suggest the need for further evaluation and nutritional intervention among low-income seniors.
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Bowen AP, O'Brien MD, Welsh S, Atkinson C. The New England Pediatric Trauma Nurse Consortium. J Emerg Nurs 1998; 24:604-6. [PMID: 9836826 DOI: 10.1016/s0099-1767(98)70053-4] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/17/2022]
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Atkinson C. A comparative study of job satisfaction in a state institution. HOSPITAL & COMMUNITY PSYCHIATRY 1979; 30:850-1. [PMID: 500023 DOI: 10.1176/ps.30.12.850] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 12/15/2022]
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Chen C, Atkinson C. The stress analysis of thin contact layers: a singular perturbation method for integral equations. Proc Math Phys Eng Sci 2008. [DOI: 10.1098/rspa.2007.0298] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/12/2022] Open
Abstract
In this paper, a contact problem is considered with a circular indenter pressed normally against a semi-infinite elastic composite that consists of a contact layer with uniform thickness welded together with another dissimilar medium. The indentation is modelled by means of a real continuous function
g
(
t
), and an integral equation representation for the displacement is derived in terms of
g
(
t
) on the contact boundary. The integral equation is evaluated numerically for
g
(
t
) when the contact layer is finite. In the case when the thickness of the contact layer becomes small compared with the radius of the contact region, a singular perturbation technique is used to derive an asymptotic expansion for
g
(
t
). This leads to a Wiener–Hopf equation formulation for the semi-infinite geometry in the Fourier-transformed domain of the inner coordinates. Subsequently, Van Dyke's matching principle is used to match the inner with the outer solution of
g
(
t
). The results are illustrated and verified with a simple limit solution derived using an
integral argument.
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Jones H, Donovan T, Goddard M, McNeil K, Atkinson C, Clark J, White J, Chilvers E. Pet imaging of [18]-FDG as a non-invasive indicator of infection versus rejection in lung transplant recipients. J Heart Lung Transplant 2003. [DOI: 10.1016/s1053-2498(02)01059-8] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/01/2022] Open
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Patel K, Cheng Q, Finnegan R, Ballish Z, Rucker L, Nadig S, Atkinson C. Augmentation of UW Solution with a Gap and Tight Junction Stabilizing Peptide, αCT1, Ameliorates Ischemia Reperfusion Injury, Facilitates Prolonged Graft Storage, and Protects Against the Development of Allograft Vasculopathy. J Heart Lung Transplant 2017. [DOI: 10.1016/j.healun.2017.01.1074] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022] Open
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92
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Atkinson C, Pitman R, Phillpotts C, Charman S, Wallwork J, Goddard M. Distribution of collagen subtypes and matrix metalloproteinases in coronary artery vasculopathy. J Heart Lung Transplant 2003. [DOI: 10.1016/s1053-2498(02)00749-0] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022] Open
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93
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Palermo R, Atkinson C, Willis M, De Lissa P, Sewell C, McArthur G. Implicit and explicit processing of facial expression in childhood, adolescence and adulthood: An ERP study. J Vis 2010. [DOI: 10.1167/8.6.704] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/24/2022] Open
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Touma Z, Hoskin B, Atkinson C, Bell D, Massey O, Lofland JH, Berry P, Karyekar C, Costenbader K. SAT0213 IMPACT OF FLARES ON HEALTHCARE RESOURCE USAGE AND PROS IN SYSTEMIC LUPUS ERYTHEMATOSUS PATIENTS. Ann Rheum Dis 2020. [DOI: 10.1136/annrheumdis-2020-eular.6010] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/04/2022]
Abstract
Background:The effect of flares on healthcare resource usage and patient-reported outcome scores in SLE patients is not well quantified.Objectives:To understand how flares impact healthcare resource utilization (HCRU) and patient-reported outcomes amongst an international real-world dataset of SLE patients.Methods:The Adelphi Real World 2015 Lupus Disease Specific Programme (DSP) is a cross-sectional study of 263 rheumatologists in the US and EU5. Rheumatologists were asked to complete patient record forms (PRFs) for the next 5 prospectively consulting SLE patients; the same patients were asked to complete patient self-completion (PSC) forms describing how SLE affected them. PRFs collected data pertaining to the patient’s diagnosis, disease history, current clinical outcomes, treatment and management history. PSCs collected similar data and included patient-reported outcome measures (PROs) to assess humanistic burden. Propensity score matching was used to assess differences in HCRU and health status between SLE patients who had flared (physician defined) in the last 12 months and those who had not. Matching variables were patient ethnicity, time since diagnosis, and severity at diagnosis. Data were extracted from 1278 PRFs, and 591 PSCs. Propensity score matching was carried out on two matched groups of 408 patients.Results:Demographic data are reported in Table 1. Propensity score matching showed patients who flared in the last 12 months experienced significantly greater hospitalizations, visits to the ER, and total HCP consults in the last 12 months. Significantly greater drug burden lower physician and patient satisfaction, lower EQ-5D score (worse health status), lower FACIT Fatigue score (greater fatigue), and greater overall work impairment (Table 2) were also observed.Table 1.Demographic dataVariableFlared in last 12 monthsNot flared in the last 12 monthsMean age (years)41.842.4% Female86.087.0% White/Caucasian66.276.3Mean years diagnosed5.95.4Table 2.Propensity score matching resultsOutcome variableFlared meanNot flared meanCoefficient95% CIp-valueHospitalisations in last 12 months24.267.630.17[0.12 – 0.21]<0.001Emergency department visits in last 12 months20.834.190.17[0.12 – 0.21]<0.001Number of tests in last 12 months46.4938.907.59[3.74 – 11.44]<0.001Number of current medications2.762.190.57[0.43 – 0.72]<0.001Physician satisfied64.4686.63-0.22[-0.28 – -0.17]<0.001Patient satisfied69.2985.09-0.16[-0.24 – -0.08]<0.001EQ-5D-3L0.720.83-0.11[-0.15 – -0.07]<0.001FACIT Fatigue30.0636.48-6.42[-8.5 – -4.3]<0.001WPAI overall percentage work impairment42.7430.2312.5[7.51 – 17.50]<0.001Conclusion:The analysis of international real-world data confirmed that SLE patients who flared in the last year represent a greater burden on healthcare resource and demonstrate significantly worse health status, greater fatigue, lower patient and physician satisfaction and greater overall work impairment compared with non-flaring patients. There is a need for more effective treatments in this patient population to reduce patient and healthcare burden.Study funded by Johnson and Johnson.Disclosure of Interests:Zahi Touma Consultant of: Consultant for Janssen, Ben Hoskin Consultant of: Consultant for Janssen, Christian Atkinson Consultant of: Consultant for Janssen, David Bell Consultant of: Janssen, Olivia Massey Consultant of: Janssen, Jennifer H. Lofland Employee of: Janssen, Pamela Berry Employee of: Janssen, Chetan Karyekar Shareholder of: Johnson & Johnson, Consultant of: Janssen, Employee of: Janssen Global Services, LLC. Previously, Novartis, Bristol-Myers Squibb, and Abbott Labs., Karen Costenbader Grant/research support from: Merck, Consultant of: Astra-Zeneca
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Troy A, Davidson P, Atkinson C, Hart D. Phenotypic characterisation of the dendritic cell infiltrate in prostate cancer. J Urol 1998; 160:214-9. [PMID: 9628653] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/07/2023]
Abstract
PURPOSE To investigate whether dendritic cells (DC), which as professional antigen presenting cells have the capacity to stimulate immune responses against tumour associated antigens, are recruited into and activated within prostate cancer. MATERIALS AND METHODS Immunoenzyme and immunofluorescence labelling was used to identify leucocyte and DC subsets within 15 cases of prostate cancer. Cell numbers were compared with numbers in adjacent normal prostatic tissue. Total DC numbers were identified as CD45+ leucocytes not coexpressing any lineage specific markers. The Langerhans cell (LC) subset was detected using anti CD1a staining and activated DC were identified by their expression of either CD83, CD86 or CMRF44. RESULTS DC were found to represent a small subset of leucocytes present in both benign and malignant prostatic tissue. Statistically there were significantly less DC and LC in prostate cancer compared with normal prostatic tissue. While only a small subset of DC expressed markers of activation in prostate cancer, this was significantly more than the virtual absence of activated DC in normal prostatic tissue. CONCLUSIONS This is the first time that DC have been studied in prostate cancer using the relatively new DC specific monoclonal antibodies CD83 and CMRF-44. These findings suggest that there is no active recruitment of DC into prostate cancer and those DC present are only minimally activated.
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Mitchell A, England C, Atkinson C. A survey of dietary advice for people with an ileostomy. Clin Nutr ESPEN 2020. [DOI: 10.1016/j.clnesp.2020.09.561] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/23/2022]
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Atkinson C. Primary team nursing: a new ITU method. Nurs Stand 1991; 6:25-8. [PMID: 1954087 DOI: 10.7748/ns.6.3.25.s43] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/29/2022]
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Moseley RL, Atkinson C, Surman R, Greville-Harris M, May L, Vuillier L. Sex-specific mechanisms for eating disorder risk in men and women with autistic traits: the role of alexithymia. J Eat Disord 2023; 11:18. [PMID: 36765413 PMCID: PMC9912205 DOI: 10.1186/s40337-023-00746-7] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Figures] [Journal Information] [Submit a Manuscript] [Subscribe] [Scholar Register] [Received: 06/29/2022] [Accepted: 02/02/2023] [Indexed: 02/12/2023] Open
Abstract
BACKGROUND A poorly understood relationship exists between eating disorders (ED) and autism spectrum conditions (ASC: henceforth 'autism'). ED are more prevalent in autistic people and people with high autistic traits, and autistic features are prognostic of longer illness. Aiming to understand what increases the risk of ED in relation to autism and autistic traits, previous research has implicated alexithymia as a causal mechanism in this relationship. These studies could not, however, disentangle whether alexithymia explains the relationship between ED pathology and autistic traits directly or through its impact on anxious/depressive symptoms, which in turn result in higher ED symptomatology. Moreover, despite evidence for sex differences in the aetiology of ED, little research has examined the impact of sex on these relationships. METHODS Focusing on the association between autistic traits and ED psychopathology, we examined independent mediating effects of alexithymia and anxious/depressive symptoms, as well as sequential mediation effects where alexithymia affects ED psychopathology via its impact on anxious/depressive symptoms. Participants were 198 men and 265 women with formally diagnosed and suspected ED, who completed an online survey of standardised scales. RESULTS In men, higher autistic traits were associated with ED psychopathology sequentially via greater alexithymia and through that, greater depressive/anxious symptoms. In women, alexithymia mediated the relationship between autistic traits and ED psychopathology both directly and sequentially through its impact on anxious/depressive symptoms. Interestingly, depressive/anxious symptoms also mediated that relationship independently from alexithymia. CONCLUSIONS While cross-sectional, these findings suggest that the relationship between autistic traits and ED symptomatology is mediated by other variables. In support of its proposed role in the aetiology of ED, alexithymia was directly associated with ED symptoms in women. It also affected ED symptoms indirectly, in all participants, via its effect on depressive/anxious symptoms. Interventions focusing on alexithymia may facilitate recovery not only via their effect on ED, but via their effect on other forms of state psychopathology which contribute to the maintenance and development of ED. Sex differences, however, reflect that alternative therapeutic targets for men and women may be beneficial.
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Kingdon J, Aadan H, Husain S, Atkinson C, Thomson C, Braude P. 22 Design and Implementation of A Nutrition Clinical Pathway for Patients with Fractured Neck of Femur. Age Ageing 2020. [DOI: 10.1093/ageing/afz183.22] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
Abstract
Background
Patients with a fractured neck of femur (FNOF) are commonly malnourished pre-admission, have reduced oral intake in hospital and a hypermetabolic state up to three months postoperatively (E Paillaud 2000). Malnutrition is associated with functional deterioration, higher morbidity and mortality.
Evidence suggests nutritional supplementation post-surgery can reduce postoperative complications. As a result, nutritional assessment is included in the National Hip Fracture Database best practice tariff (Avenell, Cochrane Database of Systematic Reviews 2016).
Introduction
Our aim was to design and implement a clinical pathway for patients with FNOF to identify malnutrition and provide appropriate nutritional support.
Intervention
A retrospective audit of 25 patients was completed to understand baseline rates of assessment, prescription of supplements and referral to dietetics. Using these data meetings were arranged to develop a clinical pathway. Key stakeholders included dietetics, orthopaedic surgeons, geriatricians, physiotherapists and nurses. The pathway was evaluated and optimised with two Plan-Do-Study-Act (PDSA) cycles looking at 25 patients each time.
Results
Baseline: 79% received a nutritional assessment, 32% had nutritional supplements prescribed and 36% (n=9) met criteria for referral to a dietician, of which 55%were referred. However, an additional 5 referrals were made to dietetics for patients who did not meet criteria, a 50% inappropriate referral rate.
PDSA cycle 1: increased nutritional assessment (85%), increased nutritional supplements prescribed (92%), decreased inappropriate referrals to dietetics (43%).
PDSA cycle 2: increased nutritional assessment & nutritional supplements prescribed (100%), increased inappropriate referrals to dietetics (80%).
Conclusions
The implementation of a nutrition pathway has led to increased identification and treatment of malnutrition, which has in addition improved accrual of the best practice tariff. However, greater number of inappropriate referrals have been made to dietetics. This is partly attributed to difficulty weighing patients on admission, and where no weight is inputted on the Malnutrition Universal Screening Tool a “High Risk” score is generated triggering a referral. We are now looking at alternative methods to obtaining a weight such a mid-upper arm circumference.
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Atkinson C, Thompson ME. Analysis of two parallel queues by common exit service and infinite queue size. ADV APPL PROBAB 2016. [DOI: 10.2307/1426472] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/10/2022]
Abstract
A system of two parallel queues is considered, where each customer must leave after service through a common gate G. It is assumed that service times at the two stations I and II are independent and identically distributed, and that exit service takes a fixed length of time. A I-customer may be served at station I only if the previous I-customer has completed exit service. Integral equations are formulated from which the distribution of the total service time may be obtained when the two queue sizes are infinite. These equations are solved for exponential and generalized erlangian service times. Extensions to the case of k parallel queues and to the case of Poisson arrivals and finite queue sizes are discussed briefly.
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