Mathematical modelling of magnesium corrosion for orthopaedic implants

Magnesium (Mg) has grasped the attention of biomaterial researchers due to its desirable properties for orthopaedic implants. It is a biodegradable, lightweight structured metal with mechanical properties more comparable to the human bone than frequently used implant materials like titanium and stainless steel. However, the element corrodes rapidly in aqueous environments, which prevents its direct use as an implant material. In this thesis, novel mathematical models are presented to address the problem of Mg corrosion. In aqueous environments, a Mg implant reacts to form magnesium hydroxide (\ce{Mg(OH)2}), which can react further with bicarbonate ions to form magnesium carbonate (\ce{MgCO3}); these reactions are considered in the corrosion models developed in this work, and this is the first study to consider \ce{MgCO3}. A simple mass action model was derived first, which predicted the amount of Mg and its corrosion products over time, where an exponential decay of Mg was perceived. The backbone of this thesis is a PDE model for Mg corrosion, which considers distinct porous layers of \ce{Mg(OH)2} and \ce{MgCO3} surrounding a block of Mg with the advection and diffusion of \ce{H2O} and \ce{CO2} through porous media; this porous media assumption is a novel feature in comparison to other metal corrosion models. The model was derived and analysed in one spatial dimension for Cartesian, radically symmetric spherical and cylindrical geometries. Singularities resulting from the model at small time were handled using asymptotic analysis. The effect of the model parameters on key timescales was investigated, whereby porosity of the layers and reaction rates of \ce{H2O} and Mg were shown to have a significant effect. Furthermore, the porous media assumption on the Mg compound layers led to the prediction of a slightly faster corrosion of the original Mg block compared to that with different rates of advection. In addition to the above, corrosion from inside a single Mg pore was considered using the same modelling approach. The timescale for pore closure and the size of Mg corrosion at pore closure were of particular interest, and were affected by changes in the parameters. The pore closure time was found to be rapid in comparison to the degradation time of the implant. The final model in this work is a physiologically based pharmacokinetic (PBPK) model, which is used to explore the effects of a corroding Mg implant on blood serum levels; a high amount of Mg in the blood can cause complications. Values for the implant release rate of Mg and urine excretion rates were refined in the model, where it was highlighted that an Mg implantation must be carefully considered for patients, particularly those with reduced renal function

Numerical modelling of effects of biphasic layers of corrosion products to the degradation of magnesium metal in vitro

© 2017 by the authors. Magnesium (Mg) is becoming increasingly popular for orthopaedic implant materials. Its mechanical properties are closer to bone than other implant materials, allowing for more natural healing under stresses experienced during recovery. Being biodegradable, it also eliminates the requirement of further surgery to remove the hardware. However, Mg rapidly corrodes in clinically relevant aqueous environments, compromising its use. This problem can be addressed by alloying the Mg, but challenges remain at optimising the properties of the material for clinical use. In this paper, we present a mathematical model to provide a systematic means of quantitatively predicting Mg corrosion in aqueous environments, providing a means of informing standardisation of in vitro investigation of Mg alloy corrosion to determine implant design parameters. The model describes corrosion through reactions with water, to produce magnesium hydroxide Mg(OH) 2 , and subsequently with carbon dioxide to form magnesium carbonate MgCO 3 . The corrosion products produce distinct protective layers around the magnesium block that are modelled as porous media. The resulting model of advection-diffusion equations with multiple moving boundaries was solved numerically using asymptotic expansions to deal with singular cases. The model has few free parameters, and it is shown that these can be tuned to predict a full range of corrosion rates, reflecting differences between pure magnesium or magnesium alloys. Data from practicable in vitro experiments can be used to calibrate the model's free parameters, from which model simulations using in vivo relevant geometries provide a cheap first step in optimising Mg-based implant materials

INFLUENCE OF SUPPLYING SOME SAFE NATURAL HONEY BEE PRODUCTS ON FENNEL PLANTS GROWTH, SEEDS YIELD, OIL PRODUCTION AND ITS COMPONENTS

Honeybee products as propolis (Pp) and royal jelly (RJ) are natural mixtures and powerful source of safe nutrients that could be safely used in agriculture as substitution of poisonous and dangerous chemical fertilizers. The impact of using them either solely or in combination as foliar application on some fennel morphological traits, fruit and oil yield and its essential components and chemical components was studied. RJ and Pp were foliar sprayed at three rates i.e. 0.0, 0.2, 0.4% and 0, 3, 6 g l-1 respectively in sole and combination treatments. All records assured that the application of both materials (RJ, Pp) have a positive useful impact on all traits studied either used individually or in combination. The moderate concentrations of both materials individually or in combination (0.2 % RJ, 3 g l-1 Pp) gave the highest records of growth and yield characters as well as anethole in the oil compared with other treatments with more superiority of RJ results over those of Pp in sole treatments even though RJ concentration is less than that of Pp especially in oil percentage and umbels number. On the other side, the highest concentration of either RJ (0.4%) or moderate one of Pp (3 g l-1) as sole treatment or in combination gave the highest records of most chemical composition. Also 0.4% RJ with 6 g l-1 Pp produced the highest percentage of estragole. Hence, fennel plants can be safely grown and highly produced by these safe natural materials without the help of the chemical fertilizer

Pragmatic, Prospective Comparative Effectiveness Trial of Carbon Ion Therapy, Surgery, and Proton Therapy for the Management of Pelvic Sarcomas (Soft Tissue/Bone) Involving the Bone: The PROSPER Study Rationale and Design

Surgical treatment of pelvic sarcoma involving the bone is the standard of care but is associated with several sequelae and reduced functional quality of life (QOL). Treatment with photon and proton radiotherapy is associated with relapse. Carbon ion radiotherapy (CIRT) may reduce both relapse rates and treatment sequelae. The PROSPER study is a tricontinental, nonrandomized, prospective, three-arm, pragmatic trial evaluating treatments of pelvic sarcoma involving the bone. Patients aged at least 15 years are eligible for inclusion. Participants must have an Eastern Cooperative Oncology Group Performance Status score of two or less, newly diagnosed disease, and histopathologic confirmation of pelvic chordoma, chondrosarcoma, osteosarcoma, Ewing sarcoma with bone involvement, rhabdomyosarcoma (RMS) with bone involvement, or non-RMS soft tissue sarcoma with bone involvement. Treatment arms include (1) CIRT (n = 30) delivered in Europe and Asia, (2) surgical treatment with or without adjuvant radiotherapy (n = 30), and (3) proton therapy (n = 30). Arms two and three will be conducted at Mayo Clinic campuses in Arizona, Florida, and Minnesota. The primary end point is to compare the 1-year change in functional QOL between CIRT and surgical treatment. Additional comparisons among the three arms will be made between treatment sequelae, local control, and other QOL measures

Pragmatic, Prospective Comparative Effectiveness Trial of Carbon Ion Therapy, Surgery, and Proton Therapy for the Management of Pelvic Sarcomas (Soft Tissue/Bone) Involving the Bone: The PROSPER Study Rationale and Design

Surgical treatment of pelvic sarcoma involving the bone is the standard of care but is associated with several sequelae and reduced functional quality of life (QOL). Treatment with photon and proton radiotherapy is associated with relapse. Carbon ion radiotherapy (CIRT) may reduce both relapse rates and treatment sequelae. The PROSPER study is a tricontinental, nonrandomized, prospective, three-arm, pragmatic trial evaluating treatments of pelvic sarcoma involving the bone. Patients aged at least 15 years are eligible for inclusion. Participants must have an Eastern Cooperative Oncology Group Performance Status score of two or less, newly diagnosed disease, and histopathologic confirmation of pelvic chordoma, chondrosarcoma, osteosarcoma, Ewing sarcoma with bone involvement, rhabdomyosarcoma (RMS) with bone involvement, or non-RMS soft tissue sarcoma with bone involvement. Treatment arms include (1) CIRT

Surgical site infection after gastrointestinal surgery in high-income, middle-income, and low-income countries: a prospective, international, multicentre cohort study

Background: Surgical site infection (SSI) is one of the most common infections associated with health care, but its importance as a global health priority is not fully understood. We quantified the burden of SSI after gastrointestinal surgery in countries in all parts of the world. Methods: This international, prospective, multicentre cohort study included consecutive patients undergoing elective or emergency gastrointestinal resection within 2-week time periods at any health-care facility in any country. Countries with participating centres were stratified into high-income, middle-income, and low-income groups according to the UN's Human Development Index (HDI). Data variables from the GlobalSurg 1 study and other studies that have been found to affect the likelihood of SSI were entered into risk adjustment models. The primary outcome measure was the 30-day SSI incidence (defined by US Centers for Disease Control and Prevention criteria for superficial and deep incisional SSI). Relationships with explanatory variables were examined using Bayesian multilevel logistic regression models. This trial is registered with ClinicalTrials.gov, number NCT02662231. Findings: Between Jan 4, 2016, and July 31, 2016, 13 265 records were submitted for analysis. 12 539 patients from 343 hospitals in 66 countries were included. 7339 (58·5%) patient were from high-HDI countries (193 hospitals in 30 countries), 3918 (31·2%) patients were from middle-HDI countries (82 hospitals in 18 countries), and 1282 (10·2%) patients were from low-HDI countries (68 hospitals in 18 countries). In total, 1538 (12·3%) patients had SSI within 30 days of surgery. The incidence of SSI varied between countries with high (691 [9·4%] of 7339 patients), middle (549 [14·0%] of 3918 patients), and low (298 [23·2%] of 1282) HDI (p < 0·001). The highest SSI incidence in each HDI group was after dirty surgery (102 [17·8%] of 574 patients in high-HDI countries; 74 [31·4%] of 236 patients in middle-HDI countries; 72 [39·8%] of 181 patients in low-HDI countries). Following risk factor adjustment, patients in low-HDI countries were at greatest risk of SSI (adjusted odds ratio 1·60, 95% credible interval 1·05–2·37; p=0·030). 132 (21·6%) of 610 patients with an SSI and a microbiology culture result had an infection that was resistant to the prophylactic antibiotic used. Resistant infections were detected in 49 (16·6%) of 295 patients in high-HDI countries, in 37 (19·8%) of 187 patients in middle-HDI countries, and in 46 (35·9%) of 128 patients in low-HDI countries (p < 0·001). Interpretation: Countries with a low HDI carry a disproportionately greater burden of SSI than countries with a middle or high HDI and might have higher rates of antibiotic resistance. In view of WHO recommendations on SSI prevention that highlight the absence of high-quality interventional research, urgent, pragmatic, randomised trials based in LMICs are needed to assess measures aiming to reduce this preventable complication

Reducing the environmental impact of surgery on a global scale: systematic review and co-prioritization with healthcare workers in 132 countries

Abstract Background Healthcare cannot achieve net-zero carbon without addressing operating theatres. The aim of this study was to prioritize feasible interventions to reduce the environmental impact of operating theatres. Methods This study adopted a four-phase Delphi consensus co-prioritization methodology. In phase 1, a systematic review of published interventions and global consultation of perioperative healthcare professionals were used to longlist interventions. In phase 2, iterative thematic analysis consolidated comparable interventions into a shortlist. In phase 3, the shortlist was co-prioritized based on patient and clinician views on acceptability, feasibility, and safety. In phase 4, ranked lists of interventions were presented by their relevance to high-income countries and low–middle-income countries. Results In phase 1, 43 interventions were identified, which had low uptake in practice according to 3042 professionals globally. In phase 2, a shortlist of 15 intervention domains was generated. In phase 3, interventions were deemed acceptable for more than 90 per cent of patients except for reducing general anaesthesia (84 per cent) and re-sterilization of ‘single-use’ consumables (86 per cent). In phase 4, the top three shortlisted interventions for high-income countries were: introducing recycling; reducing use of anaesthetic gases; and appropriate clinical waste processing. In phase 4, the top three shortlisted interventions for low–middle-income countries were: introducing reusable surgical devices; reducing use of consumables; and reducing the use of general anaesthesia. Conclusion This is a step toward environmentally sustainable operating environments with actionable interventions applicable to both high– and low–middle–income countries