Generalized Differential Quadrature Finite Element Method applied to Advanced Structural Mechanics

Over the years the Differential Quadrature (DQ) method has distinguished because of its high accuracy, straightforward implementation and general ap- plication to a variety of problems. There has been an increase in this topic by several researchers who experienced significant development in the last years. DQ is essentially a generalization of the popular Gaussian Quadrature (GQ) used for numerical integration functions. GQ approximates a finite in- tegral as a weighted sum of integrand values at selected points in a problem domain whereas DQ approximate the derivatives of a smooth function at a point as a weighted sum of function values at selected nodes. A direct appli- cation of this elegant methodology is to solve ordinary and partial differential equations. Furthermore in recent years the DQ formulation has been gener- alized in the weighting coefficients computations to let the approach to be more flexible and accurate. As a result it has been indicated as Generalized Differential Quadrature (GDQ) method. However the applicability of GDQ in its original form is still limited. It has been proven to fail for problems with strong material discontinuities as well as problems involving singularities and irregularities. On the other hand the very well-known Finite Element (FE) method could overcome these issues because it subdivides the computational domain into a certain number of elements in which the solution is calculated. Recently, some researchers have been studying a numerical technique which could use the advantages of the GDQ method and the advantages of FE method. This methodology has got different names among each research group, it will be indicated here as Generalized Differential Quadrature Finite Element Method (GDQFEM).

Reduced-order modelling, circuit-level design and SOI fabrication of microelectromechanical resonators

This thesis deals with two important research aspects concerning radio frequency (RF) microresonators and switches. First, a new approach for compact modeling and simulation of these devices is presented. Then, a combined process flow for their simultaneous fabrication on a SOI substrate is proposed. Compact models for microresonators and switches are extracted by applying mathematical model order reduction (MOR) to the devices finite element (FE) description in ANSYS c° . The behaviour of these devices includes forms of nonlinearities. However, an approximation in the creation of the FE model is introduced, which enables the use of linear model order reduction. Microresonators are modeled with the introduction of transducer elements, which allow for direct coupling of the electrical and mechanical domain. The coupled system element matrices are linearized around an operating point and reduced. The resulting macromodel is valid for small signal analysis around the bias point, such as harmonic pre-stressed analysis. This is extremely useful for characterizing the frequency response of resonators. Compact modelling of switches preserves the nonlinearity of the device behaviour. Nonlinear reduced order models are obtained by reducing the number of nonlinearities in the system and handling them as input to the system. In this way, the system can be reduced using linear MOR techniques and nonlinearities are introduced directly in the reduced order model. The reduction of the number of system nonlinearities implies the approximation of all distributed forces in the model with lumped forces. Both for microresonators and switches, a procedure for matrices extraction has been developed so that reduced order models include the effects of electrical and mechanical pre-stress. The extraction process is fast and can be done automatically from ANSYS binary files. The method has been applied for the simulation of several devices both at devices and circuit level. Simulation results have been compared with full model simulations, and, when available, experimental data. Reduced order models have proven to conserve the accuracy of finite element method and to give a good description of the overall device behaviour, despite the introduced approximations. In addition, simulation is very fast, both at device and circuit level. A combined process-flow for the integrated fabrication of microresonators and switches has been defined. For this purpose, two processes that are optimized for the independent fabrication of these devices are merged. The major advantage of this process is the possibility to create on-chip circuit blocks that include both microresonators and switches. An application is, for example, aswitched filter bank for wireless transceiver. The process for microresonators fabrication is characterized by the use of silicon on insulator (SOI) wafers and on a deep reactive ion etching (DRIE) step for the creation of the vibrating structures in single-crystal silicon and the use of a sacrificial oxide layer for the definition of resonator to electrode distance. The fabrication of switches is characterized by the use of two different conductive layers for the definition of the actuation electrodes and by the use of a photoresist as a sacrificial layer for the creation of the suspended structure. Both processes have a gold electroplating step, for the creation of the resonators electrodes, transmission lines and suspended structures. The combined process flow is designed such that it conserves the basic properties of the original processes. Neither the performance of the resonators nor the performance of the switches results affected by the simultaneous fabrication. Moreover, common fabrication steps are shared, which allows for cheaper and faster fabrication.

Comparison between analytical and numerical methods for the assessment of masonry arch bridges: Case study of Clemente Bridge on Savio river

This research has focused on the study of the behavior and of the collapse of masonry arch bridges. The latest decades have seen an increasing interest in this structural type, that is still present and in use, despite the passage of time and the variation of the transport means. Several strategies have been developed during the time to simulate the response of this type of structures, although even today there is no generally accepted standard one for assessment of masonry arch bridges. The aim of this thesis is to compare the principal analytical and numerical methods existing in literature on case studies, trying to highlight values and weaknesses. The methods taken in exam are mainly three: i) the Thrust Line Analysis Method; ii) the Mechanism Method; iii) the Finite Element Methods. The Thrust Line Analysis Method and the Mechanism Method are analytical methods and derived from two of the fundamental theorems of the Plastic Analysis, while the Finite Element Method is a numerical method, that uses different strategies of discretization to analyze the structure. Every method is applied to the case study through computer-based representations, that allow a friendly-use application of the principles explained. A particular closed-form approach based on an elasto-plastic material model and developed by some Belgian researchers is also studied. To compare the three methods, two different case study have been analyzed: i) a generic masonry arch bridge with a single span; ii) a real masonry arch bridge, the Clemente Bridge, built on Savio River in Cesena. In the analyses performed, all the models are two-dimensional in order to have results comparable between the different methods taken in exam. The different methods have been compared with each other in terms of collapse load and of hinge positions.

Fluid-structure interaction by a coupled lattice Boltzmann-finite element approach

In this thesis, a strategy to model the behavior of fluids and their interaction with deformable bodies is proposed. The fluid domain is modeled by using the lattice Boltzmann method, thus analyzing the fluid dynamics by a mesoscopic point of view. It has been proved that the solution provided by this method is equivalent to solve the Navier-Stokes equations for an incompressible flow with a second-order accuracy. Slender elastic structures idealized through beam finite elements are used. Large displacements are accounted for by using the corotational formulation. Structural dynamics is computed by using the Time Discontinuous Galerkin method. Therefore, two different solution procedures are used, one for the fluid domain and the other for the structural part, respectively. These two solvers need to communicate and to transfer each other several information, i.e. stresses, velocities, displacements. In order to guarantee a continuous, effective, and mutual exchange of information, a coupling strategy, consisting of three different algorithms, has been developed and numerically tested. In particular, the effectiveness of the three algorithms is shown in terms of interface energy artificially produced by the approximate fulfilling of compatibility and equilibrium conditions at the fluid-structure interface. The proposed coupled approach is used in order to solve different fluid-structure interaction problems, i.e. cantilever beams immersed in a viscous fluid, the impact of the hull of the ship on the marine free-surface, blood flow in a deformable vessels, and even flapping wings simulating the take-off of a butterfly. The good results achieved in each application highlight the effectiveness of the proposed methodology and of the C++ developed software to successfully approach several two-dimensional fluid-structure interaction problems.

Finite element models of coseismic deformation due to the 2009 L'Aquila (Italy) and 2008 Wenchuan(China) earthquakes

The topic of my Ph.D. thesis is the finite element modeling of coseismic deformation imaged by DInSAR and GPS data. I developed a method to calculate synthetic Green functions with finite element models (FEMs) and then use linear inversion methods to determine the slip distribution on the fault plane. The method is applied to the 2009 L’Aquila Earthquake (Italy) and to the 2008 Wenchuan earthquake (China). I focus on the influence of rheological features of the earth's crust by implementing seismic tomographic data and the influence of topography by implementing Digital Elevation Models (DEM) layers on the FEMs. Results for the L’Aquila earthquake highlight the non-negligible influence of the medium structure: homogeneous and heterogeneous models show discrepancies up to 20% in the fault slip distribution values. Furthermore, in the heterogeneous models a new area of slip appears above the hypocenter. Regarding the 2008 Wenchuan earthquake, the very steep topographic relief of Longmen Shan Range is implemented in my FE model. A large number of DEM layers corresponding to East China is used to achieve the complete coverage of the FE model. My objective was to explore the influence of the topography on the retrieved coseismic slip distribution. The inversion results reveals significant differences between the flat and topographic model. Thus, the flat models frequently adopted are inappropriate to represent the earth surface topographic features and especially in the case of the 2008 Wenchuan earthquake.

Analysis of optimal control problems for the incompressible MHD equations and implementation in a finite element multiphysics code

This thesis deals with the study of optimal control problems for the incompressible Magnetohydrodynamics (MHD) equations. Particular attention to these problems arises from several applications in science and engineering, such as fission nuclear reactors with liquid metal coolant and aluminum casting in metallurgy. In such applications it is of great interest to achieve the control on the fluid state variables through the action of the magnetic Lorentz force. In this thesis we investigate a class of boundary optimal control problems, in which the flow is controlled through the boundary conditions of the magnetic field. Due to their complexity, these problems present various challenges in the definition of an adequate solution approach, both from a theoretical and from a computational point of view. In this thesis we propose a new boundary control approach, based on lifting functions of the boundary conditions, which yields both theoretical and numerical advantages. With the introduction of lifting functions, boundary control problems can be formulated as extended distributed problems. We consider a systematic mathematical formulation of these problems in terms of the minimization of a cost functional constrained by the MHD equations. The existence of a solution to the flow equations and to the optimal control problem are shown. The Lagrange multiplier technique is used to derive an optimality system from which candidate solutions for the control problem can be obtained. In order to achieve the numerical solution of this system, a finite element approximation is considered for the discretization together with an appropriate gradient-type algorithm. A finite element object-oriented library has been developed to obtain a parallel and multigrid computational implementation of the optimality system based on a multiphysics approach. Numerical results of two- and three-dimensional computations show that a possible minimum for the control problem can be computed in a robust and accurate manner.

A Trans-dimensional inversion algorithm to model deformation sources with unconstrained shape in finite element domains

Ground deformation provides valuable insights on subsurface processes with pattens reflecting the characteristics of the source at depth. In active volcanic sites displacements can be observed in unrest phases; therefore, a correct interpretation is essential to assess the hazard potential. Inverse modeling is employed to obtain quantitative estimates of parameters describing the source. However, despite the robustness of the available approaches, a realistic imaging of these reservoirs is still challenging. While analytical models return quick but simplistic results, assuming an isotropic and elastic crust, more sophisticated numerical models, accounting for the effects of topographic loads, crust inelasticity and structural discontinuities, require much higher computational effort and information about the crust rheology may be challenging to infer. All these approaches are based on a-priori source shape constraints, influencing the solution reliability. In this thesis, we present a new approach aimed at overcoming the aforementioned limitations, modeling sources free of a-priori shape constraints with the advantages of FEM simulations, but with a cost-efficient procedure. The source is represented as an assembly of elementary units, consisting in cubic elements of a regular FE mesh loaded with a unitary stress tensors. The surface response due to each of the six stress tensor components is computed and linearly combined to obtain the total displacement field. In this way, the source can assume potentially any shape. Our tests prove the equivalence of the deformation fields due to our assembly and that of corresponding cavities with uniform boundary pressure. Our ability to simulate pressurized cavities in a continuum domain permits to pre-compute surface responses, avoiding remeshing. A Bayesian trans-dimensional inversion algorithm implementing this strategy is developed. 3D Voronoi cells are used to sample the model domain, selecting the elementary units contributing to the source solution and those remaining inactive as part of the crust.

Numerical and analytical vibro-acoustic modelling of porous materials: the Cell Method for poroelasticity and the case of inclusions

Porous materials are widely used in many fields of industrial applications, to achieve the requirements of noise reduction, that nowadays derive from strict regulations. The modeling of porous materials is still a problematic issue. Numerical simulations are often problematic in case of real complex geometries, especially in terms of computational times and convergence. At the same time, analytical models, even if partly limited by restrictive simplificative hypotheses, represent a powerful instrument to capture quickly the physics of the problem and general trends. In this context, a recently developed numerical method, called the Cell Method, is described, is presented in the case of the Biot's theory and applied for representative cases. The peculiarity of the Cell Method is that it allows for a direct algebraic and geometrical discretization of the field equations, without any reduction to a weak integral form. Then, the second part of the thesis presents the case of interaction between two poroelastic materials under the context of double porosity. The idea of using periodically repeated inclusions of a second porous material into a layer composed by an original material is described. In particular, the problem is addressed considering the efficiency of the analytical method. A analytical procedure for the simulation of heterogeneous layers based is described and validated considering both conditions of absorption and transmission; a comparison with the available numerical methods is performed. ---------------- I materiali porosi sono ampiamente utilizzati per diverse applicazioni industriali, al fine di raggiungere gli obiettivi di riduzione del rumore, che sono resi impegnativi da norme al giorno d'oggi sempre più stringenti. La modellazione dei materiali porori per applicazioni vibro-acustiche rapprensenta un aspetto di una certa complessità. Le simulazioni numeriche sono spesso problematiche quando siano coinvolte geometrie di pezzi reali, in particolare riguardo i tempi computazionali e la convergenza. Allo stesso tempo, i modelli analitici, anche se parzialmente limitati a causa di ipotesi semplificative che ne restringono l'ambito di utilizzo, rappresentano uno strumento molto utile per comprendere rapidamente la fisica del problema e individuare tendenze generali. In questo contesto, un metodo numerico recentemente sviluppato, il Metodo delle Celle, viene descritto, implementato nel caso della teoria di Biot per la poroelasticità e applicato a casi rappresentativi. La peculiarità del Metodo delle Celle consiste nella discretizzazione diretta algebrica e geometrica delle equazioni di campo, senza alcuna riduzione a forme integrali deboli. Successivamente, nella seconda parte della tesi viene presentato il caso delle interazioni tra due materiali poroelastici a contatto, nel contesto dei materiali a doppia porosità. Viene descritta l'idea di utilizzare inclusioni periodicamente ripetute di un secondo materiale poroso all'interno di un layer a sua volta poroso. In particolare, il problema è studiando il metodo analitico e la sua efficienza. Una procedura analitica per il calcolo di strati eterogenei di materiale viene descritta e validata considerando sia condizioni di assorbimento, sia di trasmissione; viene effettuata una comparazione con i metodi numerici a disposizione.

Exploring New Material and Analytical Method for Characterization and Conservation of Artifacts

In this dissertation, we focus on developing new green bio-based gel systems and evaluating both the cleaning efficiency and the release of residues on the treated surface, different micro or no destructive techniques, such as optical microscopy, TGA, FTIR spectroscopy, HS-SPME and micro-Spatially Offset Raman spectroscopy (micro-SORS) were tested, proposing advanced analytical protocols. In the first part, a ternary PHB-DMC/BD gel system composed by biodiesel, dimethyl carbonate and poly-3 hydroxybutyrate was developed for cleaning of wax-based coatings applied on indoor bronze. The evaluation of the cleaning efficacy of the gel was carried out on a standard bronze sample which covered a layer of beeswax by restores of Opificio delle Pietre Dure in Florence, and a real case precious indoor bronze sculpture Pulpito della Passione attributed to Donatello. Results obtained by FTIR analysis showed an efficient removal of the wax coating. In the second part, two new kinds of combined gels based on electrospun tissues (PVA and nylon) and PHB-GVL gel were developed for removal of dammar varnish from painting. The electrospun tissue combined gels exhibited good mechanical property, and showed good efficient in cleaning over normal gel. In the third part, green deep eutectic solvent which consists urea and choline chloride was proposed to produce the rigid gel with agar for the removal of proteinaceous coating from oil painting. Rabbit glue and whole egg decorated oil painting mock-ups were selected for evaluating its cleaning efficiency, results obtained by ATR analysis showed the DES-agar gel has good cleaning performance. Furthermore, we proposed micro-SORS as a valuable alternative non-destructive method to explore the DES diffusion on painting mock-up. As a result, the micro-SORS was successful applied for monitoring the liquid diffusion behavior in painting sub-layer, providing a great and useful instrument for noninvasive residues detection in the conservation field.

A comprehensive experimental and numerical approach for assessing the hydro-mechanical behaviour of river embankments

In this doctoral dissertation, a comprehensive methodological approach for the assessment of river embankments safety conditions, based on the integrated use of laboratory testing, physical modelling and finite element (FE) numerical simulations, is proposed, with the aim of contributing to a better understanding of the effect of time-dependent hydraulic boundary conditions on the hydro-mechanical response of river embankments. The case study and materials selected for the present research project are representative for the riverbank systems of Alpine and Apennine tributaries of the main river Po (Northern Italy), which have recently experienced various sudden overall collapses. The outcomes of a centrifuge test carried out under the enhanced gravity field of 50-g, on a riverbank model, made of a compacted silty sand mixture, overlying a homogeneous clayey silt foundation layer and subjected to a simulated flood event, have been considered for the definition of a robust and realistic experimental benchmark. In order to reproduce the observed experimental behaviour, a first set of numerical simulations has been carried out by assuming, for both the embankments and the foundation unit, rigid soil porous media, under partially saturated conditions. Mechanical and hydraulic soil properties adopted in the numerical analyses have been carefully estimated based on standard saturated triaxial, oedometer and constant head permeability tests. Afterwards, advanced suction-controlled laboratory tests, have been carried out to investigate the effect of suction and confining stresses on the shear strength and compressibility characteristics of the filling material and a second set of numerical simulations has been run, taking into account the soil parameters updated based on the most recent tests. The final aim of the study is the quantitative estimation of the predictive capabilities of the calibrated numerical tools, by systematically comparing the results of the FE simulations to the experimental benchmark.

Towards a sustainable approach for Cultural Heritage Conservation: developing micro-structured green materials and analytical protocols for their performance assessment

Cleaning is one of the most important and delicate procedures that are part of the restoration process. When developing new systems, it is fundamental to consider its selectivity towards the layer to-be-removed, non-invasiveness towards the one to-be-preserved, its sustainability and non-toxicity. Besides assessing its efficacy, it is important to understand its mechanism by analytical protocols that strike a balance between cost, practicality, and reliable interpretation of results. In this thesis, the development of cleaning systems based on the coupling of electrospun fabrics (ES) and greener organic solvents is proposed. Electrospinning is a versatile technique that allows the production of micro/nanostructured non-woven mats, which have already been used as absorbents in various scientific fields, but to date, not in the restoration field. The systems produced proved to be effective for the removal of dammar varnish from paintings, where the ES not only act as solvent-binding agents but also as adsorbents towards the partially solubilised varnish due to capillary rise, thus enabling a one-step procedure. They have also been successfully applied for the removal of spray varnish from marble substrates and wall paintings. Due to the materials' complexity, the procedure had to be adapted case-by-case and mechanical action was still necessary. According to the spinning solution, three types of ES mats have been produced: polyamide 6,6, pullulan and pullulan with melanin nanoparticles. The latter, under irradiation, allows for a localised temperature increase accelerating and facilitating the removal of less soluble layers (e.g. reticulated alkyd-based paints). All the systems produced, and the mock-ups used were extensively characterised using multi-analytical protocols. Finally, a monitoring protocol and image treatment based on photoluminescence macro-imaging is proposed. This set-up allowed the study of the removal mechanism of dammar varnish and semi-quantify its residues. These initial results form the basis for optimising the acquisition set-up and data processing.

A model for diffusive and displacive phase transitions in steels

Heat treatment of steels is a process of fundamental importance in tailoring the properties of a material to the desired application; developing a model able to describe such process would allow to predict the microstructure obtained from the treatment and the consequent mechanical properties of the material. A steel, during a heat treatment, can undergo two different kinds of phase transitions [p.t.]: diffusive (second order p.t.) and displacive (first order p.t.); in this thesis, an attempt to describe both in a thermodynamically consistent framework is made; a phase field, diffuse interface model accounting for the coupling between thermal, chemical and mechanical effects is developed, and a way to overcome the difficulties arising from the treatment of the non-local effects (gradient terms) is proposed. The governing equations are the balance of linear momentum equation, the Cahn-Hilliard equation and the balance of internal energy equation. The model is completed with a suitable description of the free energy, from which constitutive relations are drawn. The equations are then cast in a variational form and different numerical techniques are used to deal with the principal features of the model: time-dependency, non-linearity and presence of high order spatial derivatives. Simulations are performed using DOLFIN, a C++ library for the automated solution of partial differential equations by means of the finite element method; results are shown for different test-cases. The analysis is reduced to a two dimensional setting, which is simpler than a three dimensional one, but still meaningful.

The bursting behavior of gas slugs: laboratory and analytical insights into Strombolian volcanic eruptions.

The aim of this thesis is to study how explosive behavior and geophysical signals in a volcanic conduit are related to the development of overpressure in slug-driven eruptions. A first suite of laboratory experiments of gas slugs ascending in analogue conduits was performed. Slugs ascended into a range of analogue liquids and conduit diameters to allow proper scaling to the natural volcanoes. The geometrical variation of the slug in response to the explored variables was parameterised. Volume of gas slug and rheology of the liquid phase revealed the key parameters in controlling slug overpressure at bursting. Founded on these results, a theoretical model to calculate burst overpressure for slug-driven eruptions was developed. The dimensionless approach adopted allowed to apply the model to predict bursting pressure of slugs at Stromboli. Comparison of predicted values with measured data from Stromboli volcano showed that the model can explain the entire spectrum of observed eruptive styles at Stromboli – from low-energy puffing, through normal Strombolian eruptions, up to paroxysmal explosions – as manifestations of a single underlying physical process. Finally, another suite of laboratory experiments was performed to observe oscillatory pressure and forces variations generated during the expansion and bursting of gas slugs ascending in a conduit. Two end-member boundary conditions were imposed at the base of the pipe, simulating slug ascent in closed base (zero magma flux) and open base (constant flux) conduit. At the top of the pipe, a range of boundary conditions that are relevant at a volcanic vent were imposed, going from open to plugged vent. The results obtained illustrate that a change in boundary conditions in the conduit concur to affect the dynamic of slug expansion and burst: an upward flux at the base of the conduit attenuates the magnitude of the pressure transients, while a rheological stiffening in the top-most region of conduit changes dramatically the magnitude of the observed pressure transients, favoring a sudden, and more energetic pressure release into the overlying atmosphere. Finally, a discussion on the implication of changing boundary on the oscillatory processes generated at the volcanic scale is also given.

Locating the source of volcanic tremor at stromboli volcano, italy

We have developed a method for locating sources of volcanic tremor and applied it to a dataset recorded on Stromboli volcano before and after the onset of the February 27th 2007 effusive eruption. Volcanic tremor has attracted considerable attention by seismologists because of its potential value as a tool for forecasting eruptions and for better understanding the physical processes that occur inside active volcanoes. Commonly used methods to locate volcanic tremor sources are: 1) array techniques, 2) semblance based methods, 3) calculation of wave field amplitude. We have choosen the third approach, using a quantitative modeling of the seismic wavefield. For this purpose, we have calculated the Green Functions (GF) in the frequency domain with the Finite Element Method (FEM). We have used this method because it is well suited to solve elliptic problems, as the elastodynamics in the Fourier domain. The volcanic tremor source is located by determining the source function over a regular grid of points. The best fit point is choosen as the tremor source location. The source inversion is performed in the frequency domain, using only the wavefield amplitudes. We illustrate the method and its validation over a synthetic dataset. We show some preliminary results on the Stromboli dataset, evidencing temporal variations of the volcanic tremor sources.

Influence of Electromagnetic Fields On Biological Signalling: An Experimental and Theoretical Approach

The primary goals of this study were to develop a cell-free in vitro assay for the assessment of nonthermal electromagnetic (EMF) bioeffects and to develop theoretical models in accord with current experimental observations. Based upon the hypothesis that EMF effects operate by modulating Ca2+/CaM binding, an in vitro nitric oxide (NO) synthesis assay was developed to assess the effects of a pulsed radiofrequency (PRF) signal used for treatment of postoperative pain and edema. No effects of PRF on NO synthesis were observed. Effects of PRF on Ca2+/CaM binding were also assessed using a Ca2+-selective electrode, also yielding no EMF Ca2+/CaM binding. However, a PRF effect was observed on the interaction of hemoglobin (Hb) with tetrahydrobiopterin, leading to the development of an in vitro Hb deoxygenation assay, showing a reduction in the rate of Hb deoxygenation for exposures to both PRF and a static magnetic field (SMF). Structural studies using pyranine fluorescence, Gd3+ vibronic sideband luminescence and attenuated total reflectance Fourier transform infrared (ATR-FTIR) spectroscopy were conducted in order to ascertain the mechanism of this EMF effect on Hb. Also, the effect of SMF on Hb oxygen saturation (SO2) was assessed under gas-controlled conditions. These studies showed no definitive changes in protein/solvation structure or SO2 under equilibrium conditions, suggesting the need for real-time instrumentation or other means of observing out-of-equilibrium Hb dynamics. Theoretical models were developed for EMF transduction, effects on ion binding, neuronal spike timing, and dynamics of Hb deoxygenation. The EMF sensitivity and simplicity of the Hb deoxygenation assay suggest a new tool to further establish basic biophysical EMF transduction mechanisms. If an EMF-induced increase in the rate of deoxygenation can be demonstrated in vivo, then enhancement of oxygen delivery may be a new therapeutic method by which clinically relevant EMF-mediated enhancement of growth and repair processes can occur.