Mathematical modelling of LiFePO4 cathodes

LiFePO4 is a commercially available battery material with good theoretical discharge capacity, excellent cycle life and increased safety compared with competing Li-ion chemistries. It has been the focus of considerable experimental and theoretical scrutiny in the past decade, resulting in LiFePO4 cathodes that perform well at high discharge rates. This scrutiny has raised several questions about the behaviour of LiFePO4 material during charge and discharge. In contrast to many other battery chemistries that intercalate homogeneously, LiFePO4 can phase-separate into highly and lowly lithiated phases, with intercalation proceeding by advancing an interface between these two phases. The main objective of this thesis is to construct mathematical models of LiFePO4 cathodes that can be validated against experimental discharge curves. This is in an attempt to understand some of the multi-scale dynamics of LiFePO4 cathodes that can be difficult to determine experimentally. The first section of this thesis constructs a three-scale mathematical model of LiFePO4 cathodes that uses a simple Stefan problem (which has been used previously in the literature) to describe the assumed phase-change. LiFePO4 crystals have been observed agglomerating in cathodes to form a porous collection of crystals and this morphology motivates the use of three size-scales in the model. The multi-scale model developed validates well against experimental data and this validated model is then used to examine the role of manufacturing parameters (including the agglomerate radius) on battery performance. The remainder of the thesis is concerned with investigating phase-field models as a replacement for the aforementioned Stefan problem. Phase-field models have recently been used in LiFePO4 and are a far more accurate representation of experimentally observed crystal-scale behaviour. They are based around the Cahn-Hilliard-reaction (CHR) IBVP, a fourth-order PDE with electrochemical (flux) boundary conditions that is very stiff and possesses multiple time and space scales. Numerical solutions to the CHR IBVP can be difficult to compute and hence a least-squares based Finite Volume Method (FVM) is developed for discretising both the full CHR IBVP and the more traditional Cahn-Hilliard IBVP. Phase-field models are subject to two main physicality constraints and the numerical scheme presented performs well under these constraints. This least-squares based FVM is then used to simulate the discharge of individual crystals of LiFePO4 in two dimensions. This discharge is subject to isotropic Li+ diffusion, based on experimental evidence that suggests the normally orthotropic transport of Li+ in LiFePO4 may become more isotropic in the presence of lattice defects. Numerical investigation shows that two-dimensional Li+ transport results in crystals that phase-separate, even at very high discharge rates. This is very different from results shown in the literature, where phase-separation in LiFePO4 crystals is suppressed during discharge with orthotropic Li+ transport. Finally, the three-scale cathodic model used at the beginning of the thesis is modified to simulate modern, high-rate LiFePO4 cathodes. High-rate cathodes typically do not contain (large) agglomerates and therefore a two-scale model is developed. The Stefan problem used previously is also replaced with the phase-field models examined in earlier chapters. The results from this model are then compared with experimental data and fit poorly, though a significant parameter regime could not be investigated numerically. Many-particle effects however, are evident in the simulated discharges, which match the conclusions of recent literature. These effects result in crystals that are subject to local currents very different from the discharge rate applied to the cathode, which impacts the phase-separating behaviour of the crystals and raises questions about the validity of using cathodic-scale experimental measurements in order to determine crystal-scale behaviour.

Defects induced ferromagnetism in plasma-enabled graphene nanopetals

Ferromagnetism in graphene is fascinating, but it is still a big challenge for practical applications due to the weak magnetization. In order to enhance the magnetization, here, we design plasma-enabled graphene nanopetals with ultra-long defective edges of up to 105 m/g, ultra-dense lattice vacancies, and hydrogen chemisorptions. The designed graphene nanopetals display robust ferromagnetism with large saturation magnetization of up to 2 emu/g at 5 K and 1.2 emu/g at room temperatures. This work identifies the plasma-enabled graphene nanopetals as a promising candidate for graphene-based magnetic devices.

Runx2 overexpression in bone marrow stromal cells accelerates bone formation in critically-sized femoral defects

The repair of large non-unions in long bones remains a significant clinical problem due to high failure rates and limited tissue availability for auto- and allografts. Many cell-based strategies for healing bone defects deliver bone marrow stromal cells to the defect site to take advantage of the inherent osteogenic capacity of this cell type. However, many factors, including donor age and ex vivo expansion of the cells, cause bone marrow stromal cells to lose their differentiation ability. To overcome these limitations, we have genetically engineered bone marrow stromal cells to constitutively overexpress the osteoblast specific transcription factor Runx2. In the present study, we examined Runx2-modified bone marrow stromal cells, delivered via poly(caprolactone) scaffolds loaded with type I collagen meshes, in critically-sized segmental defects in rats compared to unmodified cells, cell-free scaffolds and empty defects. Runx2 expression in bone marrow stromal cells accelerated healing of critically-sized defects compared to unmodified bone marrow stromal cells and defects receiving cell-free treatments. These findings provide an accelerated method for healing large bone defects which may reduce recovery time and the need for external fixation of critically-sized defects.

Application of autologous periosteal cells for the regeneration of class III furcation defects in Beagle dogs

The aim of this study was to evaluate the healing of class III furcation defects following transplantation of autogenous periosteal cells combined with b-tricalcium phosphate (b-TCP). Periosteal cells obtained from Beagle dogs’ periosteum explant cultures, were inoculated onto the surface of b-TCP. Class III furcation defects were created in the mandibular premolars. Three experimental groups were used to test the defects’ healing: group A, b-TCP seeded with periosteal cells were transplanted into the defects; group B, b-TCP alone was used for defect filling; and group C, the defect was without filling materials. Twelve weeks post surgery, the tissue samples were collected for histology, immunohistology and X-ray examination. It was found that both the length of newly formed periodontal ligament and the area of newly formed alveolar bone in group A, were significantly increased compared with both group B and C. Furthermore, both the proportion of newly formed periodontal ligament and newly formed alveolar bone in group A were much higher than those of group B and C. The quantity of cementum and its percentage in the defects (group A) were also significantly higher than those of group C. These results indicate that autogenous periosteal cells combined with b-TCP application can improve periodontal tissue regeneration in class III furcation defects.

Performance analysis of adaptive lattice filters for FM signals and alpha-stable processes

The performance of an adaptive filter may be studied through the behaviour of the optimal and adaptive coefficients in a given environment. This thesis investigates the performance of finite impulse response adaptive lattice filters for two classes of input signals: (a) frequency modulated signals with polynomial phases of order p in complex Gaussian white noise (as nonstationary signals), and (b) the impulsive autoregressive processes with alpha-stable distributions (as non-Gaussian signals). Initially, an overview is given for linear prediction and adaptive filtering. The convergence and tracking properties of the stochastic gradient algorithms are discussed for stationary and nonstationary input signals. It is explained that the stochastic gradient lattice algorithm has many advantages over the least-mean square algorithm. Some of these advantages are having a modular structure, easy-guaranteed stability, less sensitivity to the eigenvalue spread of the input autocorrelation matrix, and easy quantization of filter coefficients (normally called reflection coefficients). We then characterize the performance of the stochastic gradient lattice algorithm for the frequency modulated signals through the optimal and adaptive lattice reflection coefficients. This is a difficult task due to the nonlinear dependence of the adaptive reflection coefficients on the preceding stages and the input signal. To ease the derivations, we assume that reflection coefficients of each stage are independent of the inputs to that stage. Then the optimal lattice filter is derived for the frequency modulated signals. This is performed by computing the optimal values of residual errors, reflection coefficients, and recovery errors. Next, we show the tracking behaviour of adaptive reflection coefficients for frequency modulated signals. This is carried out by computing the tracking model of these coefficients for the stochastic gradient lattice algorithm in average. The second-order convergence of the adaptive coefficients is investigated by modeling the theoretical asymptotic variance of the gradient noise at each stage. The accuracy of the analytical results is verified by computer simulations. Using the previous analytical results, we show a new property, the polynomial order reducing property of adaptive lattice filters. This property may be used to reduce the order of the polynomial phase of input frequency modulated signals. Considering two examples, we show how this property may be used in processing frequency modulated signals. In the first example, a detection procedure in carried out on a frequency modulated signal with a second-order polynomial phase in complex Gaussian white noise. We showed that using this technique a better probability of detection is obtained for the reduced-order phase signals compared to that of the traditional energy detector. Also, it is empirically shown that the distribution of the gradient noise in the first adaptive reflection coefficients approximates the Gaussian law. In the second example, the instantaneous frequency of the same observed signal is estimated. We show that by using this technique a lower mean square error is achieved for the estimated frequencies at high signal-to-noise ratios in comparison to that of the adaptive line enhancer. The performance of adaptive lattice filters is then investigated for the second type of input signals, i.e., impulsive autoregressive processes with alpha-stable distributions . The concept of alpha-stable distributions is first introduced. We discuss that the stochastic gradient algorithm which performs desirable results for finite variance input signals (like frequency modulated signals in noise) does not perform a fast convergence for infinite variance stable processes (due to using the minimum mean-square error criterion). To deal with such problems, the concept of minimum dispersion criterion, fractional lower order moments, and recently-developed algorithms for stable processes are introduced. We then study the possibility of using the lattice structure for impulsive stable processes. Accordingly, two new algorithms including the least-mean P-norm lattice algorithm and its normalized version are proposed for lattice filters based on the fractional lower order moments. Simulation results show that using the proposed algorithms, faster convergence speeds are achieved for parameters estimation of autoregressive stable processes with low to moderate degrees of impulsiveness in comparison to many other algorithms. Also, we discuss the effect of impulsiveness of stable processes on generating some misalignment between the estimated parameters and the true values. Due to the infinite variance of stable processes, the performance of the proposed algorithms is only investigated using extensive computer simulations.

Vision-based classification of solder joint defects

Inspection of solder joints has been a critical process in the electronic manufacturing industry to reduce manufacturing cost, improve yield, and ensure product quality and reliability. The solder joint inspection problem is more challenging than many other visual inspections because of the variability in the appearance of solder joints. Although many research works and various techniques have been developed to classify defect in solder joints, these methods have complex systems of illumination for image acquisition and complicated classification algorithms. An important stage of the analysis is to select the right method for the classification. Better inspection technologies are needed to fill the gap between available inspection capabilities and industry systems. This dissertation aims to provide a solution that can overcome some of the limitations of current inspection techniques. This research proposes two inspection steps for automatic solder joint classification system. The “front-end” inspection system includes illumination normalisation, localization and segmentation. The illumination normalisation approach can effectively and efficiently eliminate the effect of uneven illumination while keeping the properties of the processed image. The “back-end” inspection involves the classification of solder joints by using Log Gabor filter and classifier fusion. Five different levels of solder quality with respect to the amount of solder paste have been defined. Log Gabor filter has been demonstrated to achieve high recognition rates and is resistant to misalignment. Further testing demonstrates the advantage of Log Gabor filter over both Discrete Wavelet Transform and Discrete Cosine Transform. Classifier score fusion is analysed for improving recognition rate. Experimental results demonstrate that the proposed system improves performance and robustness in terms of classification rates. This proposed system does not need any special illumination system, and the images are acquired by an ordinary digital camera. In fact, the choice of suitable features allows one to overcome the problem given by the use of non complex illumination systems. The new system proposed in this research can be incorporated in the development of an automated non-contact, non-destructive and low cost solder joint quality inspection system.

Repair of calvarial defects with customized tissue-engineered bone grafts - I. Evaluation of osteogenesis in a three-dimensional culture system

Bone generation by autogenous cell transplantation in combination with a biodegradable scaffold is one of the most promising techniques being developed in craniofacial surgery. The objective of this combined in vitro and in vivo study was to evaluate the morphology and osteogenic differentiation of bone marrow derived mesenchymal progenitor cells and calvarial osteoblasts in a two-dimensional (2-D) and three-dimensional (3-D) culture environment (Part I of this study) and their potential in combination with a biodegradable scaffold to reconstruct critical-size calvarial defects in an autologous animal model [Part II of this study; see Schantz, J.T., et al. Tissue Eng. 2003;9(Suppl. 1):S-127-S-139; this issue]. New Zealand White rabbits were used to isolate osteoblasts from calvarial bone chips and bone marrow stromal cells from iliac crest bone marrow aspirates. Multilineage differentiation potential was evaluated in a 2-D culture setting. After amplification, the cells were seeded within a fibrin matrix into a 3-D polycaprolactone (PCL) scaffold system. The constructs were cultured for up to 3 weeks in vitro and assayed for cell attachment and proliferation using phase-contrast light, confocal laser, and scanning electron microscopy and the MTS cell metabolic assay. Osteogenic differentiation was analyzed by determining the expression of alkaline phosphatase (ALP) and osteocalcin. The bone marrow-derived progenitor cells demonstrated the potential to be induced to the osteogenic, adipogenic, and chondrogenic pathways. In a 3-D environment, cell-seeded PCL scaffolds evaluated by confocal laser microscopy revealed continuous cell proliferation and homogeneous cell distribution within the PCL scaffolds. On osteogenic induction mesenchymal progenitor cells (12 U/L) produce significantly higher (p < 0.05) ALP activity than do osteoblasts (2 U/L); however, no significant differences were found in osteocalcin expression. In conclusion, this study showed that the combination of a mechanically stable synthetic framework (PCL scaffolds) and a biomimetic hydrogel (fibrin glue) provides a potential matrix for bone tissue-engineering applications. Comparison of osteogenic differentiation between the two mesenchymal cell sources revealed a similar pattern.

An electrospun polycaprolactone–collagen membrane for the resurfacing of cartilage defects

A polycaprolactone (PCL)–collagen electrospun mesh is proposed as a novel alternative to the conventional periosteal graft in autologous chondrocyte implantation. This is the first known attempt in designing a cartilage resurfacing membrane using a mechanically resilient PCL mesh with a weight-average molecular weight of 139 300 that is enhanced with bioactive collagen. PCL–collagen 10, 20 and 40% electrospun meshes (Coll-10, Coll-20 and Coll-40) were evaluated and it was discovered that the retention of surface collagen could only be achieved in Coll-20 and Coll-40. Furthermore Coll-20 was stiffer and stronger than Coll-40 and it satisfied the mechanical demands at the cartilage implant site. When seeded with mesenchymal stem cells (MSCs), the cells adhered on the surface of the Coll-20 mesh and they remained viable over a period of 28 days; however, they were unable to infiltrate through the dense meshwork. Cell compatibility was also noted in the chondrogenic environment as the MSCs differentiated into chondrocytes with the expression of Sox9, aggrecan and collagen II. More importantly, the mesh did not induce a hypertrophic response from the cells. The current findings support the use of Coll-20 as a cartilage patch, and future implantation studies are anticipated.

An alginate-based hybrid system for growth factor delivery in the functional repair of large bone defects

The treatment of challenging fractures and large osseous defects presents a formidable problem for orthopaedic surgeons. Tissue engineering/regenerative medicine approaches seek to solve this problem by delivering osteogenic signals within scaffolding biomaterials. In this study, we introduce a hybrid growth factor delivery system that consists of an electrospun nanofiber mesh tube for guiding bone regeneration combined with peptide-modified alginate hydrogel injected inside the tube for sustained growth factor release. We tested the ability of this system to deliver recombinant bone morphogenetic protein-2 (rhBMP-2) for the repair of critically-sized segmental bone defects in a rat model. Longitudinal [mu]-CT analysis and torsional testing provided quantitative assessment of bone regeneration. Our results indicate that the hybrid delivery system resulted in consistent bony bridging of the challenging bone defects. However, in the absence of rhBMP-2, the use of nanofiber mesh tube and alginate did not result in substantial bone formation. Perforations in the nanofiber mesh accelerated the rhBMP-2 mediated bone repair, and resulted in functional restoration of the regenerated bone. [mu]-CT based angiography indicated that perforations did not significantly affect the revascularization of defects, suggesting that some other interaction with the tissue surrounding the defect such as improved infiltration of osteoprogenitor cells contributed to the observed differences in repair. Overall, our results indicate that the hybrid alginate/nanofiber mesh system is a promising growth factor delivery strategy for the repair of challenging bone injuries.

Repair and regeneration of osteochondral defects in the articular joints

People suffering from pain due to osteoarthritic or rheumatoidal changes in the joints are still waiting for a better treatment. Although some studies have achieved success in repairing small cartilage defects, there is no widely accepted method for complete repair of osteochondral defects. Also joint replacements have not yet succeeded in replacing of natural cartilage without complications. Therefore, there is room for a new medical approach, which outperforms currently used methods. The aim of this study is to show potential of using a tissue engineering approach for regeneration of osteochondral defects. The critical review of currently used methods for treatment of osteochondral defects is also provided. In this study, two kinds of hybrid scaffolds developed in Hutmacher's group have been analysed. The first biphasic scaffold consists of fibrin and PCL. The fibrin serves as a cartilage phase while the porous PCL scaffold acts as the subchondral phase. The second system comprises of PCL and PCL-TCP. The scaffolds were fabricated via fused deposition modeling which is a rapid prototyping system. Bone marrow-derived mesenchymal cells were isolated from New Zealand White rabbits, cultured in vitro and seeded into the scaffolds. Bone regenerations of the subchondral phases were quantified via micro CT analysis and the results demonstrated the potential of the porous PCL and PCL-TCP scaffolds in promoting bone healing. Fibrin was found to be lacking in this aspect as it degrades rapidly. On the other hand, the porous PCL scaffold degrades slowly hence it provides an effective mechanical support. This study shows that in the field of cartilage repair or replacement, tissue engineering may have big impact in the future. In vivo bone and cartilage engineering via combining a novel composite, biphasic scaffold technology with a MSC has been shown a high potential in the knee defect regeneration in the animal models. However, the clinical application of tissue engineering requires the future research work due to several problems, such as scaffold design, cellular delivery and implantation strategies.

Evaluation of a hybrid scaffold/cell construct in repair of high-load-bearing osteochondral defects in rabbits

The objective of this study was to evaluate the feasibility and potential of a hybrid scaffold system in large- and high-load-bearing osteochondral defects repair. The implants were made of medical-grade PCL (mPCL) for the bone compartment whereas fibrin glue was used for the cartilage part. Both matrices were seeded with allogenic bone marrow-derived mesenchymal cells (BMSC) and implanted in the defect (4 mm diameter×5 mm depth) on medial femoral condyle of adult New Zealand White rabbits. Empty scaffolds were used at the control side. Cell survival was tracked via fluorescent labeling. The regeneration process was evaluated by several techniques at 3 and 6 months post-implantation. Mature trabecular bone regularly formed in the mPCL scaffold at both 3 and 6 months post-operation. Micro-Computed Tomography showed progression of mineralization from the host–tissue interface towards the inner region of the grafts. At 3 months time point, the specimens showed good cartilage repair. In contrast, the majority of 6 months specimens revealed poor remodeling and fissured integration with host cartilage while other samples could maintain good cartilage appearance. In vivo viability of the transplanted cells was demonstrated for the duration of 5 weeks. The results demonstrated that mPCL scaffold is a potential matrix for osteochondral bone regeneration and that fibrin glue does not inherit the physical properties to allow for cartilage regeneration in a large and high-load-bearing defect site. Keywords: Osteochondral tissue engineering; Scaffold; Bone marrow-derived precursor cells; Fibrin glue