Numerical simulation of a fractional mathematical model for epidermal wound healing

A number of mathematical models investigating certain aspects of the complicated process of wound healing are reported in the literature in recent years. However, effective numerical methods and supporting error analysis for the fractional equations which describe the process of wound healing are still limited. In this paper, we consider numerical simulation of fractional model based on the coupled advection-diffusion equations for cell and chemical concentration in a polar coordinate system. The space fractional derivatives are defined in the Left and Right Riemann-Liouville sense. Fractional orders in advection and diffusion terms belong to the intervals (0; 1) or (1; 2], respectively. Some numerical techniques will be used. Firstly, the coupled advection-diffusion equations are decoupled to a single space fractional advection-diffusion equation in a polar coordinate system. Secondly, we propose a new implicit difference method for simulating this equation by using the equivalent of the Riemann-Liouville and Gr¨unwald-Letnikov fractional derivative definitions. Thirdly, its stability and convergence are discussed, respectively. Finally, some numerical results are given to demonstrate the theoretical analysis.

Integrated vision-based attitude estimation

For many years, computer vision has lured researchers with promises of a low-cost, passive, lightweight and information-rich sensor suitable for navigation purposes. The prime difficulty in vision-based navigation is that the navigation solution will continually drift with time unless external information is available, whether it be cues from the appearance of the scene, a map of features (whether built online or known a priori), or from an externally-referenced sensor. It is not merely position that is of interest in the navigation problem. Attitude (i.e. the angular orientation of a body with respect to a reference frame) is integral to a visionbased navigation solution and is often of interest in its own right (e.g. flight control). This thesis examines vision-based attitude estimation in an aerospace environment, and two methods are proposed for constraining drift in the attitude solution; one through a novel integration of optical flow and the detection of the sky horizon, and the other through a loosely-coupled integration of Visual Odometry and GPS position measurements. In the first method, roll angle, pitch angle and the three aircraft body rates are recovered though a novel method of tracking the horizon over time and integrating the horizonderived attitude information with optical flow. An image processing front-end is used to select several candidate lines in a image that may or may not correspond to the true horizon, and the optical flow is calculated for each candidate line. Using an Extended Kalman Filter (EKF), the previously estimated aircraft state is propagated using a motion model and a candidate horizon line is associated using a statistical test based on the optical flow measurements and location of the horizon in the image. Once associated, the selected horizon line, along with the associated optical flow, is used as a measurement to the EKF. To evaluate the accuracy of the algorithm, two flights were conducted, one using a highly dynamic Uninhabited Airborne Vehicle (UAV) in clear flight conditions and the other in a human-piloted Cessna 172 in conditions where the horizon was partially obscured by terrain, haze and smoke. The UAV flight resulted in pitch and roll error standard deviations of 0.42° and 0.71° respectively when compared with a truth attitude source. The Cessna 172 flight resulted in pitch and roll error standard deviations of 1.79° and 1.75° respectively. In the second method for estimating attitude, a novel integrated GPS/Visual Odometry (GPS/VO) navigation filter is proposed, using a structure similar to a classic looselycoupled GPS/INS error-state navigation filter. Under such an arrangement, the error dynamics of the system are derived and a Kalman Filter is developed for estimating the errors in position and attitude. Through similar analysis to the GPS/INS problem, it is shown that the proposed filter is capable of recovering the complete attitude (i.e. pitch, roll and yaw) of the platform when subjected to acceleration not parallel to velocity for both the monocular and stereo variants of the filter. Furthermore, it is shown that under general straight line motion (e.g. constant velocity), only the component of attitude in the direction of motion is unobservable. Numerical simulations are performed to demonstrate the observability properties of the GPS/VO filter in both the monocular and stereo camera configurations. Furthermore, the proposed filter is tested on imagery collected using a Cessna 172 to demonstrate the observability properties on real-world data. The proposed GPS/VO filter does not require additional restrictions or assumptions such as platform-specific dynamics, map-matching, feature-tracking, visual loop-closing, gravity vector or additional sensors such as an IMU or magnetic compass. Since no platformspecific dynamics are required, the proposed filter is not limited to the aerospace domain and has the potential to be deployed in other platforms such as ground robots or mobile phones.

The effect of intraoperative force on scoliosis correction at the apex : a biomechanical investigation

Adolescent idiopathic scoliosis (AIS) is a complex 3D deformity of the spine, which may require surgical correction in severe cases. Computer models of the spine provide a potentially powerful tool to virtually ‘test’ various surgical scenarios prior to surgery. Using patient-specific computer models of seven AIS patients who had undergone a single rod anterior procedure, we have recently found that the majority of the deformity correction occurs at the apical joint or the joint immediately cephalic to the apex. In the current paper, we investigate the biomechanics of the apical joint for these patients using clinically measured intra-operative compressive forces applied during implant placement. The aim of this study is to determine a relationship between the compressive joint force applied intra-operatively and the achievable deformity correction at the apical joint.

A computer model to simulate scoliosis surgery

Use of patient-specific computer models as a pre-operative planning tool permits predictions of the likely deformity correction and allows a more detailed investigation of the biomechanical influence of different surgical procedures on the scoliotic spinal anatomy. In this paper, patient-specific computer models are used of adolescent idiopathic scoliosis patients who underwent a single rod anterior procedure at the Mater Children’s Hospital in Brisbane, to predict deformity correction and to investigate the change in biomechanics of the scoliotic spine due to surgical compressive forces applied during implant placement.

Polycaprolactone-based scaffold plus recombinant human bone morphogenetic protein (rhBMP-2) in an ovine model of anterior spinal fusion

Synthetic scaffolds combined with growth factors have the potential to replace allograft or autograft as a graft material for spinal interbody fusion. Such tissue engineering approaches may be useful in Adolescent Idiopathic Scoliosis (AIS) surgery, however there are no studies to date examining the use of such biodegradable implants in combination with biologics in a thoracic spine model. This in vivo study examines the use of biodegradable polycaprolactone (PCL) based scaffolds with rhBMP-2 as a bone graft substitute in a sheep thoracic fusion model, where an anterior approach is used to simulate minimally invasive surgical deformity correction in the setting of AIS.

Reversal of acute coagulopathy during hypotensive resuscitation using small-volume 7.5% NaCl adenocaine and Mg2+ in the rat model of severe hemorrhagic shock

OBJECTIVE: : Acute traumatic coagulopathy occurs early in hemorrhagic trauma and is a major contributor to mortality and morbidity. Our aim was to examine the effect of small-volume 7.5% NaCl adenocaine (adenosine and lidocaine, adenocaine) and Mg on hypotensive resuscitation and coagulopathy in the rat model of severe hemorrhagic shock. DESIGN: : Prospective randomized laboratory investigation. SUBJECTS: : A total of 68 male Sprague Dawley Rats. INTERVENTION: : Post-hemorrhagic shock treatment for acute traumatic coagulopathy. MEASUREMENTS AND METHODS: : Nonheparinized male Sprague-Dawley rats (300-450 g, n = 68) were randomly assigned to either: 1) untreated; 2) 7.5% NaCl; 3) 7.5% NaCl adenocaine; 4) 7.5% NaCl Mg; or 5) 7.5% NaCl adenocaine/Mg. Hemorrhagic shock was induced by phlebotomy to mean arterial pressure of 35-40 mm Hg for 20 mins (~40% blood loss), and animals were left in shock for 60 mins. Bolus (0.3 mL) was injected into the femoral vein and hemodynamics monitored. Blood was collected in Na citrate (3.2%) tubes, centrifuged, and the plasma snap frozen in liquid N2 and stored at -80°C. Coagulation was assessed using activated partial thromboplastin times and prothrombin times. RESULTS: : Small-volume 7.5% NaCl adenocaine and 7.5% NaCl adenocaine/Mg were the only two groups that gradually increased mean arterial pressure 1.6-fold from 38-39 mm Hg to 52 and 64 mm Hg, respectively, at 60 mins (p < .05). Baseline plasma activated partial thromboplastin time was 17 ± 0.5 secs and increased to 63 ± 21 secs after bleeding time, and 217 ± 32 secs after 60-min shock. At 60-min resuscitation, activated partial thromboplastin time values for untreated, 7.5% NaCl, 7.5% NaCl/Mg, and 7.5% NaCl adenocaine rats were 269 ± 31 secs, 262 ± 38 secs, 150 ± 43 secs, and 244 ± 38 secs, respectively. In contrast, activated partial thromboplastin time for 7.5% NaCl adenocaine/Mg was 24 ± 2 secs (p < .05). Baseline prothrombin time was 28 ± 0.8 secs (n = 8) and followed a similar pattern of correction. CONCLUSIONS: : Plasma activated partial thromboplastin time and prothrombin time increased over 10-fold during the bleed and shock periods prior to resuscitation, and a small-volume (~1 mL/kg) IV bolus of 7.5% NaCl AL/Mg was the only treatment group that raised mean arterial pressure into the permissive range and returned activated partial thromboplastin time and prothrombin time clotting times to baseline at 60 mins.

Sufficiently informative measurements for stability of approximate conditional mean estimates

This paper establishes sufficient conditions to bound the error in perturbed conditional mean estimates derived from a perturbed model (only the scalar case is shown in this paper but a similar result is expected to hold for the vector case). The results established here extend recent stability results on approximating information state filter recursions to stability results on the approximate conditional mean estimates. The presented filter stability results provide bounds for a wide variety of model error situations.

Spatial mapping of city-wide PBDE levels using an exponential decay model

Passive air samplers (PAS) consisting of polyurethane foam (PUF) disks were deployed at 6 outdoor air monitoring stations in different land use categories (commercial, industrial, residential and semi-rural) to assess the spatial distribution of polybrominated diphenyl ethers (PBDEs) in the Brisbane airshed. Air monitoring sites covered an area of 1143 km2 and PAS were allowed to accumulate PBDEs in the city's airshed over three consecutive seasons commencing in the winter of 2008. The average sum of five (∑5) PBDEs (BDEs 28, 47, 99, 100 and 209) levels were highest at the commercial and industrial sites (12.7 ± 5.2 ng PUF−1), which were relatively close to the city center and were a factor of 8 times higher than residential and semi-rural sites located in outer Brisbane. To estimate the magnitude of the urban ‘plume’ an empirical exponential decay model was used to fit PAS data vs. distance from the CBD, with the best correlation observed when the particulate bound BDE-209 was not included (∑5-209) (r2 = 0.99), rather than ∑5 (r2 = 0.84). At 95% confidence intervals the model predicts that regardless of site characterization, ∑5-209 concentrations in a PAS sample taken between 4–10 km from the city centre would be half that from a sample taken from the city centre and reach a baseline or plateau (0.6 to 1.3 ng PUF−1), approximately 30 km from the CBD. The observed exponential decay in ∑5-209 levels over distance corresponded with Brisbane's decreasing population density (persons/km2) from the city center. The residual error associated with the model increased significantly when including BDE-209 levels, primarily due to the highest level (11.4 ± 1.8 ng PUF−1) being consistently detected at the industrial site, indicating a potential primary source at this site. Active air samples collected alongside the PAS at the industrial air monitoring site (B) indicated BDE-209 dominated congener composition and was entirely associated with the particulate phase. This study demonstrates that PAS are effective tools for monitoring citywide regional differences however, interpretation of spatial trends for POPs which are predominantly associated with the particulate phase such as BDE-209, may be restricted to identifying ‘hotspots’ rather than broad spatial trends.

Application of a digital elevation model for flood modeling for the Pagsangaan River in Leyte

Flood related scientific and community-based data are rarely systematically collected and analysed in the Philippines. Over the last decades the Pagsangaan River Basin, Leyte, has experienced several flood events. However, documentation describing flood characteristics such as extent, duration or height of these floods are close to non-existing. To address this issue, computerized flood modelling was used to reproduce past events where there was data available for at least partial calibration and validation. The model was also used to provide scenario-based predictions based on A1B climate change assumptions for the area. The most important input for flood modelling is a Digital Elevation Model (DEM) of the river basin. No accurate topographic maps or Light Detection And Ranging (LIDAR)-generated data are available for the Pagsangaan River. Therefore, the Advanced Spaceborne Thermal Emission and Reflection Radiometer (ASTER) Global Digital Elevation Map (GDEM), Version 1, was chosen as the DEM. Although the horizontal spatial resolution of 30 m is rather desirable, it contains substantial vertical errors. These were identified, different correction methods were tested and the resulting DEM was used for flood modelling. The above mentioned data were combined with cross-sections at various strategic locations of the river network, meteorological records, river water level, and current velocity to develop the 1D-2D flood model. SOBEK was used as modelling software to create different rainfall scenarios, including historic flooding events. Due to the lack of scientific data for the verification of the model quality, interviews with local stakeholders served as the gauge to judge the quality of the generated flood maps. According to interviewees, the model reflects reality more accurately than previously available flood maps. The resulting flood maps are now used by the operations centre of a local flood early warning system for warnings and evacuation alerts. Furthermore these maps can serve as a basis to identify flood hazard areas for spatial land use planning purposes.

Polycaprolactone-based scaffold plus recombinant human bone morphogenic protein rhBMP-2) in a sheep thoracic spine fusion model

Adolescent idiopathic scoliosis is a complex three dimensional deformity affecting 2-3% of the general population. The resulting spinal deformity consists of coronal curvature, hypokyphosis of the thoracic spine and vertebral rotation in the axial plane with posterior elements turned into the curve concavity. The potential for curve progression is heightened during the adolescent growth spurt. Success of scoliosis deformity correction depends on solid bony fusion between adjacent vertebrae after the intervertebral (IV) discs have been surgically cleared and the disc spaces filled with graft material. Recently a bioactive and resorbable scaffold fabricated from medical grade polycaprolactone has been developed for bone regeneration at load bearing sites. Combined with rhBMP-2, this has been shown to be successful in acting as a bone graft substitute in a porcine lumbar interbody fusion model when compared to autologous bone graft alone. The study aimed to establish a large animal thoracic spine interbody fusion model, develop spine biodegradable scaffolds (PCL) in combination with biologics (rhBMP-2) and to establish a platform for research into spine tissue engineering constructs. Preliminary results demonstrate higher grades of radiologically evident bony fusion across all levels when comparing fusion scores between the 3 and 6 month postop groups at the PCL CaP coated scaffold level, which is observed to be a similar grade to autograft, while no fusion is seen at the scaffold only level. Results to date suggest that the combination of rhBMP-2 and scaffold engineering actively promotes bone formation, laying the basis of a viable tissue engineered constructs.

Biomechanical performance of polycaprolactone (PCL)-based scaffold with rhBMP-2 in a sheep thoracic spine fusion model

Adolescent idiopathic scoliosis is a complex three dimensional deformity affecting 2-3% of the general population. Resulting spine deformities include progressive coronal curvature, hypokyphosis, or frank lordosis in the thoracic spine and vertebral rotation in the axial plane with posterior elements turned into the curve concavity. The potential for curve progression is heightened during the adolescent growth spurt. Success of scoliosis deformity correction depends on solid bony fusion between adjacent vertebrae after the intervertebral discs have been surgically cleared and the disc spaces filled with graft material. Problems with bone graft harvest site morbidity as well as limited bone availability have led to the search for bone graft substitutes. Recently, a bioactive and resorbable scaffold fabricated from medical grade polycaprolactone (PCL) has been developed for bone regeneration at load bearing sites. Combined with recombinant human bone morphogenic protein–2 (rhBMP-2), this has been shown to be successful in acting as a bone graft substitute in acting as a bone graft substitute in a porcine lumbar interbody fusion model when compared to autologous bone graft. This in vivo sheep study intends to evaluate the suitability of a custom designed medical grade PCL scaffold in combination with rhBMP-2 as a bone graft substitute in the setting of mini–thoracotomy surgery as a platform for ongoing research to benefit patients with adolescent idiopathic scoliosis.

Understanding QC and EQA : an authentic learning model for undergraduate students (Conference Abstract)

Introduction QC and EQA are integral to good pathology laboratory practice. Medical Laboratory Science students undertake a project exploring internal QC and EQA procedures used in chemical pathology laboratories. Each student represents an individual lab and the class group represents the peer group of labs performing the same assay using the same method. Methods Using a manual BCG assay for serum albumin, normal and abnormal controls are run with a patient sample over 7 weeks. The QC results are assessed each week using calculated z-scores and both 2S & 3S control rules to determine whether a run is ‘in control’. At the end of the 7 weeks a completed LJ chart is assessed using the Westgard Multirules. Students investigate causes of error and the implications for both lab practice and patient care if runs are not ‘in control’. Twice in the 7 weeks two EQA samples (with target values unknown) are assayed alongside the weekly QC and patient samples. Results from each student are collated and form the basis of an EQA program. ALP are provided and students complete a Youden Plot, which is used to analyse the performance of each ‘lab’ and the method to identify bias. Students explore the concept of possible clinical implications of a biased method and address the actions that should be taken if a lab is not in consensus with the peer group. Conclusion This project is a model of ‘real world’ practice in which student demonstrate an understanding of the importance of QC procedures in a pathology laboratory, apply and interpret statistics and QC rules and charts, apply critical thinking and analytical skills to quality performance data to make recommendations for further practice and improve their technical competence and confidence.

Querying a building information model for construction-specific spatial information

The design and construction community has shown increasing interest in adopting building information models (BIMs). The richness of information provided by BIMs has the potential to streamline the design and construction processes by enabling enhanced communication, coordination, automation and analysis. However, there are many challenges in extracting construction-specific information out of BIMs. In most cases, construction practitioners have to manually identify the required information, which is inefficient and prone to error, particularly for complex, large-scale projects. This paper describes the process and methods we have formalized to partially automate the extraction and querying of construction-specific information from a BIM. We describe methods for analyzing a BIM to query for spatial information that is relevant for construction practitioners, and that is typically represented implicitly in a BIM. Our approach integrates ifcXML data and other spatial data to develop a richer model for construction users. We employ custom 2D topological XQuery predicates to answer a variety of spatial queries. The validation results demonstrate that this approach provides a richer representation of construction-specific information compared to existing BIM tools.

Efficient querying of large process model repositories

Recent years have seen an increased uptake of business process management technology in industries. This has resulted in organizations trying to manage large collections of business process models. One of the challenges facing these organizations concerns the retrieval of models from large business process model repositories. For example, in some cases new process models may be derived from existing models, thus finding these models and adapting them may be more effective and less error-prone than developing them from scratch. Since process model repositories may be large, query evaluation may be time consuming. Hence, we investigate the use of indexes to speed up this evaluation process. To make our approach more applicable, we consider the semantic similarity between labels. Experiments are conducted to demonstrate that our approach is efficient.

Numerical techniques for simulating a fractional mathematical model of epidermal wound healing

A number of mathematical models investigating certain aspects of the complicated process of wound healing are reported in the literature in recent years. However, effective numerical methods and supporting error analysis for the fractional equations which describe the process of wound healing are still limited. In this paper, we consider the numerical simulation of a fractional mathematical model of epidermal wound healing (FMM-EWH), which is based on the coupled advection-diffusion equations for cell and chemical concentration in a polar coordinate system. The space fractional derivatives are defined in the Left and Right Riemann-Liouville sense. Fractional orders in the advection and diffusion terms belong to the intervals (0, 1) or (1, 2], respectively. Some numerical techniques will be used. Firstly, the coupled advection-diffusion equations are decoupled to a single space fractional advection-diffusion equation in a polar coordinate system. Secondly, we propose a new implicit difference method for simulating this equation by using the equivalent of Riemann-Liouville and Grünwald-Letnikov fractional derivative definitions. Thirdly, its stability and convergence are discussed, respectively. Finally, some numerical results are given to demonstrate the theoretical analysis.