Rigid and Non-rigid Point-based Medical Image Registration

The primary goal of this dissertation is to develop point-based rigid and non-rigid image registration methods that have better accuracy than existing methods. We first present point-based PoIRe, which provides the framework for point-based global rigid registrations. It allows a choice of different search strategies including (a) branch-and-bound, (b) probabilistic hill-climbing, and (c) a novel hybrid method that takes advantage of the best characteristics of the other two methods. We use a robust similarity measure that is insensitive to noise, which is often introduced during feature extraction. We show the robustness of PoIRe using it to register images obtained with an electronic portal imaging device (EPID), which have large amounts of scatter and low contrast. To evaluate PoIRe we used (a) simulated images and (b) images with fiducial markers; PoIRe was extensively tested with 2D EPID images and images generated by 3D Computer Tomography (CT) and Magnetic Resonance (MR) images. PoIRe was also evaluated using benchmark data sets from the blind retrospective evaluation project (RIRE). We show that PoIRe is better than existing methods such as Iterative Closest Point (ICP) and methods based on mutual information. We also present a novel point-based local non-rigid shape registration algorithm. We extend the robust similarity measure used in PoIRe to non-rigid registrations adapting it to a free form deformation (FFD) model and making it robust to local minima, which is a drawback common to existing non-rigid point-based methods. For non-rigid registrations we show that it performs better than existing methods and that is less sensitive to starting conditions. We test our non-rigid registration method using available benchmark data sets for shape registration. Finally, we also explore the extraction of features invariant to changes in perspective and illumination, and explore how they can help improve the accuracy of multi-modal registration. For multimodal registration of EPID-DRR images we present a method based on a local descriptor defined by a vector of complex responses to a circular Gabor filter.

Application of Numerical Methods to Study Arrangement and Fracture of Lithium-Ion Microstructure

The focus of this work is to develop and employ numerical methods that provide characterization of granular microstructures, dynamic fragmentation of brittle materials, and dynamic fracture of three-dimensional bodies.

We first propose the fabric tensor formalism to describe the structure and evolution of lithium-ion electrode microstructure during the calendaring process. Fabric tensors are directional measures of particulate assemblies based on inter-particle connectivity, relating to the structural and transport properties of the electrode. Applying this technique to X-ray computed tomography of cathode microstructure, we show that fabric tensors capture the evolution of the inter-particle contact distribution and are therefore good measures for the internal state of and electronic transport within the electrode.

We then shift focus to the development and analysis of fracture models within finite element simulations. A difficult problem to characterize in the realm of fracture modeling is that of fragmentation, wherein brittle materials subjected to a uniform tensile loading break apart into a large number of smaller pieces. We explore the effect of numerical precision in the results of dynamic fragmentation simulations using the cohesive element approach on a one-dimensional domain. By introducing random and non-random field variations, we discern that round-off error plays a significant role in establishing a mesh-convergent solution for uniform fragmentation problems. Further, by using differing magnitudes of randomized material properties and mesh discretizations, we find that employing randomness can improve convergence behavior and provide a computational savings.

The Thick Level-Set model is implemented to describe brittle media undergoing dynamic fragmentation as an alternative to the cohesive element approach. This non-local damage model features a level-set function that defines the extent and severity of degradation and uses a length scale to limit the damage gradient. In terms of energy dissipated by fracture and mean fragment size, we find that the proposed model reproduces the rate-dependent observations of analytical approaches, cohesive element simulations, and experimental studies.

Lastly, the Thick Level-Set model is implemented in three dimensions to describe the dynamic failure of brittle media, such as the active material particles in the battery cathode during manufacturing. The proposed model matches expected behavior from physical experiments, analytical approaches, and numerical models, and mesh convergence is established. We find that the use of an asymmetrical damage model to represent tensile damage is important to producing the expected results for brittle fracture problems.

The impact of this work is that designers of lithium-ion battery components can employ the numerical methods presented herein to analyze the evolving electrode microstructure during manufacturing, operational, and extraordinary loadings. This allows for enhanced designs and manufacturing methods that advance the state of battery technology. Further, these numerical tools have applicability in a broad range of fields, from geotechnical analysis to ice-sheet modeling to armor design to hydraulic fracturing.

Major ion chemistry of snow cores along a transect in central Dronning Maud Land, Antarctica

Among the large variety of particulates in the atmosphere, calcic mineral dust particles have highly reactive surfaces that undergo heterogeneous reactions with nitrogen oxides contiguously. The association between Ca2+, an important proxy indicator of mineral dust and NO3-, a dominant anion in the Antarctic snow pack was analysed. A total of 41 snow cores (~ 1 m each) that represent snow deposited during 2008-2009 were studied along coastal-inland transects from two different regions - the Princess Elizabeth Land (PEL) and central Dronning Maud Land (cDML) in East Antarctica. Correlation statistics showed a strong association (at 99 % significance level) between NO3- and Ca2+ at the near-coastal sections of both PEL (r = 0.72) and cDML (r = 0.76) transects. Similarly, a strong association between these ions was also observed in snow deposits at the inland sections of PEL (r = 0.8) and cDML (r = 0.85). Such systematic associations between Ca2+ and NO3- is attributed to the interaction between calcic mineral dust and nitrogen oxides in the atmosphere, leading to the possible formation of calcium nitrate (Ca(NO3)2). Forward and back trajectory analyses using HYSPLIT model v. 4 revealed that Southern South America (SSA) was an important dust emitting source to the study region, aided by the westerlies. Particle size distribution showed that over 90 % of the dust was in the range < 4 µm, indicating that these dust particles reached the Antarctic region via long range transport from the SSA region. We propose that the association between Ca2+ and NO3- occurs during the long range transport due to the formation of Ca(NO3)2. The Ca(NO3)2 thus formed in the atmosphere undergo deposition over Antarctica under the influence of anticyclonic polar easterlies. However, influence of local dust sources from the nunataks in cDML evidently mask such association in the mountainous region. The study indicates that the input of dust-bound NO3- may contribute a significant fraction of the total NO3- deposited in Antarctic snow.

Performance Evaluation of a Statistical and a Neural Network Model for Nonrigid Shape-Based Registration

Shape-based registration methods frequently encounters in the domains of computer vision, image processing and medical imaging. The registration problem is to find an optimal transformation/mapping between sets of rigid or nonrigid objects and to automatically solve for correspondences. In this paper we present a comparison of two different probabilistic methods, the entropy and the growing neural gas network (GNG), as general feature-based registration algorithms. Using entropy shape modelling is performed by connecting the point sets with the highest probability of curvature information, while with GNG the points sets are connected using nearest-neighbour relationships derived from competitive hebbian learning. In order to compare performances we use different levels of shape deformation starting with a simple shape 2D MRI brain ventricles and moving to more complicated shapes like hands. Results both quantitatively and qualitatively are given for both sets.

Improved Real-time State-of-Charge Estimation of LiFePO4 Battery Based on a Novel Thermoelectric Model

Li-ion batteries have been widely used in electric vehicles, and battery internal state estimation plays an important role in the battery management system. However, it is technically challenging, in particular, for the estimation of the battery internal temperature and state-ofcharge (SOC), which are two key state variables affecting the battery performance. In this paper, a novel method is proposed for realtime simultaneous estimation of these two internal states, thus leading to a significantly improved battery model for realtime SOC estimation. To achieve this, a simplified battery thermoelectric model is firstly built, which couples a thermal submodel and an electrical submodel. The interactions between the battery thermal and electrical behaviours are captured, thus offering a comprehensive description of the battery thermal and electrical behaviour. To achieve more accurate internal state estimations, the model is trained by the simulation error minimization method, and model parameters are optimized by a hybrid optimization method combining a meta-heuristic algorithm and the least square approach. Further, timevarying model parameters under different heat dissipation conditions are considered, and a joint extended Kalman filter is used to simultaneously estimate both the battery internal states and time-varying model parameters in realtime. Experimental results based on the testing data of LiFePO4 batteries confirm the efficacy of the proposed method.

New Method Based on the UNIFAC–VISCO Model for the Estimation of Ionic Liquids Viscosity Using the Experimental Data Recommended by Mathematical Gnostics

The viscosity of ionic liquids (ILs) has been modeled as a function of temperature and at atmospheric pressure using a new method based on the UNIFAC–VISCO method. This model extends the calculations previously reported by our group (see Zhao et al. J. Chem. Eng. Data 2016, 61, 2160–2169) which used 154 experimental viscosity data points of 25 ionic liquids for regression of a set of binary interaction parameters and ion Vogel–Fulcher–Tammann (VFT) parameters. Discrepancies in the experimental data of the same IL affect the quality of the correlation and thus the development of the predictive method. In this work, mathematical gnostics was used to analyze the experimental data from different sources and recommend one set of reliable data for each IL. These recommended data (totally 819 data points) for 70 ILs were correlated using this model to obtain an extended set of binary interaction parameters and ion VFT parameters, with a regression accuracy of 1.4%. In addition, 966 experimental viscosity data points for 11 binary mixtures of ILs were collected from literature to establish this model. All the binary data consist of 128 training data points used for the optimization of binary interaction parameters and 838 test data points used for the comparison of the pure evaluated values. The relative average absolute deviation (RAAD) for training and test is 2.9% and 3.9%, respectively.

Ion-acoustic envelope modes in a degenerate relativistic electron-ion plasma

A self-consistent relativistic two-fluid model is proposed for one-dimensional electron-ion plasma dynamics. A multiple scales perturbation technique is employed, leading to an evolution equation for the wave envelope, in the form of a nonlinear Schrödinger type equation (NLSE). The inclusion of relativistic effects is shown to introduce density-dependent factors, not present in the non-relativistic case - in the conditions for modulational instability. The role of relativistic effects on the linear dispersion laws and on envelope soliton solutions of the NLSE is discussed.

Os efeitos nucleares em processos de produ¸c˜ao de quarkonium no Relativistic Heavy Ion Collider (RHIC) e no Large Hadron Collider (LHC)

Neste trabalho de disserta¸c˜ao, investigamos os efeitos nucleares em processos de produ¸c˜ao de quarkonium no Relativistic Heavy Ion Collider (RHIC) e no Large Hadron Collider (LHC). Para tanto, consideramos o Modelo de Evapora¸c˜ao de Cor (CEM), baseado em processos partˆonicos calculados mediante a QCD perturbativa e em intera¸c˜oes n˜ao perturbativas via troca de gl´uons suaves para a forma¸c˜ao do quarkonium. Supress˜ao de quarkonium ´e um dos sinais de forma¸c˜ao do assim chamado Plasma de Quarks e Gl´uons (QGP) em colis˜oes ultrarelativ´ısticas de ´ıons pesados. No entanto, a supress˜ao n˜ao ´e somente causada em colis˜oes n´ucleo-n´ucleo (AA) devido `a forma¸c˜ao do QGP. De fato, a supress˜ao de quarkonium tamb´em foi observada em colis˜oes pr´oton-n´ucleo (pA). A fim de separar os efeitos da mat´eria quente (devidos ao QGP) e fria (efeitos n˜ao devidos ao QGP), pode-se olhar primeiro para colis˜oes pA, onde somente efeitos de mat´eria fria desempenham um papel fundamental, e depois aplicar esses efeitos em colis˜oes AA, uma vez que parte da supress˜ao ´e devido a efeitos de mat´eria fria. No regime de altas energias, a produ¸c˜ao do quarkonium ´e fortemente dependente da distribui¸c˜ao de gl´uons nuclear, o que viabiliza uma oportunidade ´unica de estudar o comportamento de pequeno x dos gl´uons dentro do n´ucleo e, consequentemente, restringir os efeitos nucleares. Estudamos os processos nucleares utilizando distintas parametriza¸c˜oes para as distribui¸c˜oes partˆonicas nucleares. Calculamos a raz˜ao nuclear para processos pA e AA em fun¸c˜ao da vari´avel rapidez para a produ¸c˜ao de quarkonium, o que permite estimar os efeitos nucleares. Al´em disso, apresentamos uma compara¸c˜ao com os dados do RHIC para a produ¸c˜ao do m´eson J/Ψ em colis˜oes pA, demonstrando que a an´alise deste observ´avel ´e uma quest˜ao em aberto na literatura. Adicionalmente, estimamos a produ¸c˜ao de quarks pesados e quarkonium na etapa inicial e durante a fase termal de uma colis˜ao ultrarelativ´ıstica de ´ıons pesados. O objetivo deste estudo ´e estimar as distintas contribui¸c˜oes para a produ¸c˜ao e de alguns efeitos do meio nuclear.

Thermal analysis during bone drilling using rigid polyurethane foams: numerical and experimental methodologies

Osteotomy or bone cutting is a common procedure in orthopaedic surgery, mainly in the treatment of fractures and reconstructive surgery. However, the excessive heat produced during the bone drilling process is a problem that counters the benefits of this type of surgery, because it can result in thermal osteonecrosis, bone reabsorption and damage the osseointegration of implants. The analysis of different drilling parameters and materials can allow to decrease the temperature during the bone drilling process and contribute to a greater success of this kind of surgical interventions. The main goal of this study was to build a numerical three-dimensional model to simulate the drilling process considering the type of bone, the influence of cooling and the bone density of the different composite materials with similar mechanical properties to the human bone and generally used in experimental biomechanics. The numerical methodology was coupled with an experimental methodology. The use of cooling proved to be essential to decrease the material damage during the drilling process. It was concluded that the materials with less porosity and density present less damage in drilling process. The developed numerical model proved to be a great tool in this kind of analysis. © 2016, The Brazilian Society of Mechanical Sciences and Engineering.

A deformation model of flexible, high area-to-mass ratio debris under perturbations and validation method

A new type of space debris was recently discovered by Schildknecht in near -geosynchronous orbit (GEO). These objects were later identified as exhibiting properties associated with High Area-to-Mass ratio (HAMR) objects. According to their brightness magnitudes (light curve), high rotation rates and composition properties (albedo, amount of specular and diffuse reflection, colour, etc), it is thought that these objects are multilayer insulation (MLI). Observations have shown that this debris type is very sensitive to environmental disturbances, particularly solar radiation pressure, due to the fact that their shapes are easily deformed leading to changes in the Area-to-Mass ratio (AMR) over time. This thesis proposes a simple effective flexible model of the thin, deformable membrane with two different methods. Firstly, this debris is modelled with Finite Element Analysis (FEA) by using Bernoulli-Euler theory called “Bernoulli model”. The Bernoulli model is constructed with beam elements consisting 2 nodes and each node has six degrees of freedom (DoF). The mass of membrane is distributed in beam elements. Secondly, the debris based on multibody dynamics theory call “Multibody model” is modelled as a series of lump masses, connected through flexible joints, representing the flexibility of the membrane itself. The mass of the membrane, albeit low, is taken into account with lump masses in the joints. The dynamic equations for the masses, including the constraints defined by the connecting rigid rod, are derived using fundamental Newtonian mechanics. The physical properties of both flexible models required by the models (membrane density, reflectivity, composition, etc.), are assumed to be those of multilayer insulation. Both flexible membrane models are then propagated together with classical orbital and attitude equations of motion near GEO region to predict the orbital evolution under the perturbations of solar radiation pressure, Earth’s gravity field, luni-solar gravitational fields and self-shadowing effect. These results are then compared to two rigid body models (cannonball and flat rigid plate). In this investigation, when comparing with a rigid model, the evolutions of orbital elements of the flexible models indicate the difference of inclination and secular eccentricity evolutions, rapid irregular attitude motion and unstable cross-section area due to a deformation over time. Then, the Monte Carlo simulations by varying initial attitude dynamics and deformed angle are investigated and compared with rigid models over 100 days. As the results of the simulations, the different initial conditions provide unique orbital motions, which is significantly different in term of orbital motions of both rigid models. Furthermore, this thesis presents a methodology to determine the material dynamic properties of thin membranes and validates the deformation of the multibody model with real MLI materials. Experiments are performed in a high vacuum chamber (10-4 mbar) replicating space environment. A thin membrane is hinged at one end but free at the other. The free motion experiment, the first experiment, is a free vibration test to determine the damping coefficient and natural frequency of the thin membrane. In this test, the membrane is allowed to fall freely in the chamber with the motion tracked and captured through high velocity video frames. A Kalman filter technique is implemented in the tracking algorithm to reduce noise and increase the tracking accuracy of the oscillating motion. The forced motion experiment, the last test, is performed to determine the deformation characteristics of the object. A high power spotlight (500-2000W) is used to illuminate the MLI and the displacements are measured by means of a high resolution laser sensor. Finite Element Analysis (FEA) and multibody dynamics of the experimental setups are used for the validation of the flexible model by comparing with the experimental results of displacements and natural frequencies.

Model Probability in Self-organising Maps

Growing models have been widely used for clustering or topology learning. Traditionally these models work on stationary environments, grow incrementally and adapt their nodes to a given distribution based on global parameters. In this paper, we present an enhanced unsupervised self-organising network for the modelling of visual objects. We first develop a framework for building non-rigid shapes using the growth mechanism of the self-organising maps, and then we define an optimal number of nodes without overfitting or underfitting the network based on the knowledge obtained from information-theoretic considerations. We present experimental results for hands and we quantitatively evaluate the matching capabilities of the proposed method with the topographic product.

SOVLENT REACTIVITY AND INTERFACE EVOLUTION AT MODEL ELECTRODES FOR ENERGY APPLICATIONS

The Li-ion rechargeable battery (LIB) is widely used as an energy storage device, but has significant limitations in battery cycle life and safety. During initial charging, decomposition of the ethylene carbonate (EC)-based electrolytes of the LIB leads to the formation of a passivating layer on the anode known as the solid electrolyte interphase (SEI). The formation of an SEI has great impact on the cycle life and safety of LIB, yet mechanistic aspects of SEI formation are not fully understood. In this dissertation, two surface science model systems have been created under ultra-high vacuum (UHV) to probe the very initial stage of SEI formation at the model carbon anode surfaces of LIB. The first model system, Model System I, is an lithium-carbonate electrolyte/graphite C(0001) system. I have developed a temperature programmed desorption/temperature programmed reaction spectroscopy (TPD/TPRS) instrument as part of my dissertation to study Model System I in quantitative detail. The binding strengths and film growth mechanisms of key electrolyte molecules on model carbon anode surfaces with varying extents of lithiation were measured by TPD. TPRS was further used to track the gases evolved from different reduction products in the early-stage SEI formation. The branching ratio of multiple reaction pathways was quantified for the first time and determined to be 70.% organolithium products vs. 30% inorganic lithium product. The obtained branching ratio provides important information on the distribution of lithium salts that form at the very onset of SEI formation. One of the key reduction products formed from EC in early-stage SEI formation is lithium ethylene dicarbonate (LEDC). Despite intensive studies, the LEDC structure in either the bulk or thin-film (SEI) form is unknown. To enable structural study, pure LEDC was synthesized and subject to synchrotron X-ray diffraction measurements (bulk material) and STM measurements (deposited films). To enable studies of LEDC thin films, Model System II, a lithium ethylene dicarbonate (LEDC)-dimethylformamide (DMF)/Ag(111) system was created by a solution microaerosol deposition technique. Produced films were then imaged by ultra-high vacuum scanning tunneling microscopy (UHV-STM). As a control, the dimethylformamide (DMF)-Ag(111) system was first prepared and its complex 2D phase behavior was mapped out as a function of coverage. The evolution of three distinct monolayer phases of DMF was observed with increasing surface pressure — a 2D gas phase, an ordered DMF phase, and an ordered Ag(DMF)2 complex phase. The addition of LEDC to this mixture, seeded the nucleation of the ordered DMF islands at lower surface pressures (DMF coverages), and was interpreted through nucleation theory. A structural model of the nucleation seed was proposed, and the implication of ionic SEI products, such as LEDC, in early-stage SEI formation was discussed.

DEVELOPMENT OF ION EXCHANGE MODELS FOR WATER TREATMENT AND APPLICATION TO THE INTERNATIONAL SPACE STATION WATER PROCESSOR

The International Space Station (ISS) requires a substantial amount of potable water for use by the crew. The economic and logistic limitations of transporting the vast amount of water required onboard the ISS necessitate onboard recovery and reuse of the aqueous waste streams. Various treatment technologies are employed within the ISS water processor to render the waste water potable, including filtration, ion exchange, adsorption, and catalytic wet oxidation. The ion exchange resins and adsorption media are combined in multifiltration beds for removal of ionic and organic compounds. A mathematical model (MFBMODEL™) designed to predict the performance of a multifiltration (MF) bed was developed. MFBMODEL consists of ion exchange models for describing the behavior of the different resin types in a MF bed (e.g., mixed bed, strong acid cation, strong base anion, and weak base anion exchange resins) and an adsorption model capable of predicting the performance of the adsorbents in a MF bed. Multicomponent ion exchange ii equilibrium models that incorporate the water formation reaction, electroneutrality condition, and degree of ionization of weak acids and bases for mixed bed, strong acid cation, strong base anion, and weak base anion exchange resins were developed and verified. The equilibrium models developed use a tanks-inseries approach that allows for consideration of variable influent concentrations. The adsorption modeling approach was developed in related studies and application within the MFBMODEL framework was demonstrated in the Appendix to this study. MFBMODEL consists of a graphical user interface programmed in Visual Basic and Fortran computational routines. This dissertation shows MF bed modeling results in which the model is verified for a surrogate of the ISS waste shower and handwash stream. In addition, a multicomponent ion exchange model that incorporates mass transfer effects was developed, which is capable of describing the performance of strong acid cation (SAC) and strong base anion (SBA) exchange resins, but not including reaction effects. This dissertation presents results showing the mass transfer model's capability to predict the performance of binary and multicomponent column data for SAC and SBA exchange resins. The ion exchange equilibrium and mass transfer models developed in this study are also applicable to terrestrial water treatment systems. They could be applied for removal of cations and anions from groundwater (e.g., hardness, nitrate, perchlorate) and from industrial process waters (e.g. boiler water, ultrapure water in the semiconductor industry).

Tin Oxide Based Composites Derived Using Electrostatic Spray Deposition Technique as Anodes for Li-Ion Batteries

Recent advances in the electric & hybrid electric vehicles and rapid developments in the electronic devices have increased the demand for high power and high energy density lithium ion batteries. Graphite (theoretical specific capacity: 372 mAh/g) used in commercial anodes cannot meet these demands. Amorphous SnO2 anodes (theoretical specific capacity: 781 mAh/g) have been proposed as alternative anode materials. But these materials have poor conductivity, undergo a large volume change during charging and discharging, large irreversible capacity loss leading to poor cycle performances. To solve the issues related to SnO2 anodes, we propose to synthesize porous SnO2 composites using electrostatic spray deposition technique. First, porous SnO2/CNT composites were fabricated and the effects of the deposition temperature (200,250, 300 oC) & CNT content (10, 20, 30, 40 wt %) on the electrochemical performance of the anodes were studied. Compared to pure SnO2 and pure CNT, the composite materials as anodes showed better discharge capacity and cyclability. 30 wt% CNT content and 250 oC deposition temperature were found to be the optimal conditions with regard to energy capacity whereas the sample with 20% CNT deposited at 250 oC exhibited good capacity retention. This can be ascribed to the porous nature of the anodes and the improvement in the conductivity by the addition of CNT. Electrochemical impedance spectroscopy studies were carried out to study in detail the change in the surface film resistance with cycling. By fitting EIS data to an equivalent circuit model, the values of the circuit components, which represent surface film resistance, were obtained. The higher the CNT content in the composite, lower the change in surface film resistance at certain voltage upon cycling. The surface resistance increased with the depth of discharge and decreased slightly at fully lithiated state. Graphene was also added to improve the performance of pure SnO2 anodes. The composites heated at 280 oC showed better energy capacity and energy density. The specific capacities of as deposited and post heat-treated samples were 534 and 737 mAh/g after 70 cycles. At the 70th cycle, the energy density of the composites at 195 °C and 280 °C were 1240 and 1760 Wh/kg, respectively, which are much higher than the commercially used graphite electrodes (37.2-74.4 Wh/kg). Both SnO2/CNTand SnO2/grapheme based composites with improved energy densities and capacities than pure SnO2 can make a significant impact on the development of new batteries for electric vehicles and portable electronics applications.

A NOVEL MODELING AND STATE OF CHARGE ESTIMATION SCHEME FOR LITHIUM-ION BATTERIES

Lithium Ion (Li-Ion) batteries have got attention in recent decades because of their undisputable advantages over other types of batteries. They are used in so many our devices which we need in our daily life such as cell phones, lap top computers, cameras, and so many electronic devices. They also are being used in smart grids technology, stand-alone wind and solar systems, Hybrid Electric Vehicles (HEV), and Plug in Hybrid Electric Vehicles (PHEV). Despite the rapid increase in the use of Lit-ion batteries, the existence of limited battery models also inadequate and very complex models developed by chemists is the lack of useful models a significant matter. A battery management system (BMS) aims to optimize the use of the battery, making the whole system more reliable, durable and cost effective. Perhaps the most important function of the BMS is to provide an estimate of the State of Charge (SOC). SOC is the ratio of available ampere-hour (Ah) in the battery to the total Ah of a fully charged battery. The Open Circuit Voltage (OCV) of a fully relaxed battery has an approximate one-to-one relationship with the SOC. Therefore, if this voltage is known, the SOC can be found. However, the relaxed OCV can only be measured when the battery is relaxed and the internal battery chemistry has reached equilibrium. This thesis focuses on Li-ion battery cell modelling and SOC estimation. In particular, the thesis, introduces a simple but comprehensive model for the battery and a novel on-line, accurate and fast SOC estimation algorithm for the primary purpose of use in electric and hybrid-electric vehicles, and microgrid systems. The thesis aims to (i) form a baseline characterization for dynamic modeling; (ii) provide a tool for use in state-of-charge estimation. The proposed modelling and SOC estimation schemes are validated through comprehensive simulation and experimental results.