Magnetic stimulation is a standard tool in brain research and has found important clinical applications in neurology, psychiatry, and rehabilitation. Whereas coil designs and the spatial field properties have been intensively studied in the literature, the temporal dynamics of the field has received less attention. Typically, the magnetic field waveform is determined by available device circuit topologies rather than by consideration of what is optimal for neural stimulation. This paper analyzes and optimizes the waveform dynamics using a nonlinear model of a mammalian axon. The optimization objective was to minimize the pulse energy loss. The energy loss drives power consumption and heating, which are the dominating limitations of magnetic stimulation. The optimization approach is based on a hybrid global-local method. Different coordinate systems for describing the continuous waveforms in a limited parameter space are defined for numerical stability. The optimization results suggest that there are waveforms with substantially higher efficiency than that of traditional pulse shapes. One class of optimal pulses is analyzed further. Although the coil voltage profile of these waveforms is almost rectangular, the corresponding current shape presents distinctive characteristics, such as a slow low-amplitude first phase which precedes the main pulse and reduces the losses. Representatives of this class of waveforms corresponding to different maximum voltages are linked by a nonlinear transformation. The main phase, however, scales with time only. As with conventional magnetic stimulation pulses, briefer pulses result in lower energy loss but require higher coil voltage than longer pulses. Magnetic stimulation is a standard tool for noninvasive activation of neurons. It can be applied to the brain, where it is known as transcranial magnetic stimulation (TMS) Compared to other stimulation methods, however, magnetic stimulation is extremely energy inefficient. The electrical pulse energy transferred to the stimulation target is less than one percent Furthermore, driving the high currents necessitates voltages up to 4000 V which requires reliable high voltage insulation. Mobile devices with battery-powered pulse sources have been proposed but are at present not practical for repetitive protocols due to the high power consumption.While the efficiency of magnetic stimulation in the spatial domain has been studied extensively with appropriate coil designs In the temporal domain, the induction process, wherein an alternating coil current induces an electric field, is approximately linear. However, the neuron dynamics are complex and nonlinear, resulting in a nontrivial relationship between the pulse waveform and the neural response. Nevertheless, the conventional waveforms are limited by the relatively simple and inflexible stimulator circuit topologies rather than derived from consideration of what is optimal from the perspective of a neuron.Presently, there are two waveforms–monophasic and biphasic–commonly found in magnetic stimulation devices. Standard monophasic stimulators generate an overdamped sine current pulse and dissipate the whole pulse energy as heat The question of the optimal pulse shape for neural activation has been studied in more detail in electrical stimulation. An analytic variational approach with a linear first-order neuron model, also known as leaky integrate-and-fire model In contrast to linear dynamics, nonlinear models cannot be inverted easily and chaotic behavior of the corresponding differential equations renders numerical handling problematic. Therefore, many parameter studies in models as well as in experiments were instead performed with specific predefined waveforms For magnetic stimulation, there are few studies of different waveforms with experiments [15, 16, 18, 30.or numerical models The magnetic stimulation pulse waveform could be optimized with respect to several aspects. In this work, we minimize the energy loss during a pulse, which affects the required power supply and causes coil heating. The device power consumption and heating of the stimulation coil are both approximately proportional to the energy loss and limit the maximum duration of a stimulation session as well as the pulse repetition rate The dominating mechanism of energy loss is Joule heating originating from the intrinsic resistance of all electrical components. For coil current Only two constraints are imposed on the optimization problem. First, the coil current has to successfully elicit a neuron response. Second, the coil voltage It should be noted again that this optimization formulation addresses only the pulse waveform and deliberately disregards specific device circuit implementations. Consequently, additional loss mechanisms that are circuit-dependent and can in principle be avoided or minimized, such as forward bias voltages of semiconductor p-n junctions and capacitive switching losses, are not considered in the optimization. In addition, only temporal aspects of the stimulation system are addressed. The coil design and the spatial characteristics of the induced field are not considered, except for the coil’s inductive and resistive properties which pertain to the time domain. This approach relies on the good separability of space and time in neuronal stimulation and is commonly deployed to decouple the spatial and the temporal domain In summary, the optimization approach identifies a function The functions A peripheral motor axon was used in the neuron model for the following reasons. First, in functional peripheral stimulation, such as neuromuscular stimulation, which targets motoric innervations A pre-evaluation of the optimal current waveforms was performed using the optimization method as an exploration tool in order to provide an approximate map of the solution space. It also acted as a test for the stability of the algorithms. The results are presented in In Notably, the conventional monophasic waveform is insignificantly less efficient than conventional biphasic pulses, despite its relatively long current tail. Thus, conventional monophasic devices are substantially less efficient than biphasic devices not because of the intrinsic waveform properties, but rather because of the inefficient electrical circuit that shapes the pulse with intentional damping by a resistor that dissipates the pulse energy in the form of heat. This observation might call for better circuit topologies since monophasic pulses may be preferable in some applications due to their higher stimulation selectivity and stronger neuromodulatory effect This lower edge of the scatter is smooth and appears to represent the same class of stimuli. For very high device voltages, the current waveforms degenerate to pulses resembling a Dirac delta.After the pre-evaluation of the waveform space, a refined optimization was performed for several voltages in the range of those typical in conventional devices. The number of degrees of freedom reached up to one thousand during these optimization runs. Thus, frequency components up to several hundred kilohertz could be accurately represented. The representative pulses labeled (a)–(c) in The best solutions are very similar to one another. The current always exhibits three relatively distinct phases. A slow first phase precedes a short large-amplitude second phase with triangular shape in the opposite direction. A separate third phase becomes visible after a large number of optimization iterations.The corresponding coil voltage waveform see  is dominThe rectangularly shaped voltage during the second phase is likely a consequence of the second constraint, i.e., the voltage limit. The system uses the maximum allowed voltage level for the total duration of the second phase. This explains the positive swing of the voltage. The subsequent negative swing reduces the current as quickly as possible after the peak. Although this hyperpolarizing field might counteract excitation, a lower current level appears to be more important due to the dependence of the optimization objective on the squared coil current. The negative voltage is maintained at its maximum value until a certain low current level is reached from which the third phase converges to zero in a slow, approximately exponential decay.Such reasoning can also be used to explain the slow negative first current phase. The first phase of the coil current introduces a negative bias for the onset of the second, depolarizing phase. While keeping the rise time constant, the peak current of the second phase is reduced by the magnitude of the shifted baseline at the end of the first phase. Thus, the negative bias created by the first phase decreases the energy loss by lowering the peak current in the second phase without reducing the pulse duration. The first phase contributes to the loss, of course, but its current amplitude is relatively low. Since the loss depends on the squared current, the first phase saves more energy due the reduced current in the second phase than the additional loss it contributes itself.Importantly, the slow first phase of the coil current has a minimal effect on the neural dynamics. Accordingly, it biases the current and reduces the energy loss without significantly disrupting the membrane state. The weak influence of the first current phase on the state of the neuron can be demonstrated by inspecting the state of the modeled ion channels and the membrane potential. By the end of the first phase, the membrane potential has changed by less than It should be noted that such an explanation of the mechanism of single phases is always a simplification. Ascribing certain functions to isolated parts of a pulse could be misleading in the context of nonlinear dynamics. Nevertheless, it is encouraging that the features of the optimal pulse shape are qualitatively consistent with simplified considerations of membrane dynamics in combination with electromagnetic induction.The similarity among the waveforms in The detailed behavior of the optimal initial first phase was analyzed in a separate parameter study. The amplitude of the first phase, i.e., the value of the most negative point in the current profile, was set proportional to the main phase peak amplitude by an adjustable ratio. As a second degree of freedom, the duration of the rising slope of the main phase was varied; the falling slope changes proportionally to the rising slope. The optimal amplitude of the first phase was evaluated for various different main phase durations. The results are presented in The top panel of Despite the substantial ohmic cost of the first phase, this investment is rewarding with respect to the total energy loss at the specific threshold. The bottom panel in To explore the robustness of the optima with respect to the neuron model characteristics, we carried out optimization using two simpler models: the Motz-Rattay model Representative optimal current waveforms for the Motz-Rattay and integrate-and-fire models are shown in We implemented numerical optimization of the pulse shape for inductive stimulation of an axon with the objective of minimizing energy loss. The latter was quantified by the integral of the squared coil current. The optimization constraints were reduced to a minimum, comprising only a limit on the maximum coil voltage and the requirement that the axon model generates an action potential. Thus, the optimization was not limited to specific device circuitry or parametrization of predetermined waveforms, but rather was a practically unconstrained search of the pulse shape space.Refined Optimization. Even though intuitive explanations of phenomena involving nonlinear dynamics could be misleading, it is encouraging that the features of the optimal pulse shape are qualitatively consistent with simplified considerations of membrane dynamics in combination with electromagnetic induction.The results were consistent across various initial conditions, voltage constraints, and alternative neuron models see , and 6. The robustness of the solution is furthermore important for the question of generalizability. While the substantial similarity of motor axons with fibers originating from cortical pyramidal neurons in terms of channel expression Especially, the linear model supports a general character of the results. First, this model reduces the dynamics to the common ground which almost all axons in the central and the peripheral nervous system share. Second, it is a regression of the whole black-box system using the coil current as its input The pulse shapes derived in this study cannot be generated by existing magnetic stimulation systems. Commercial devices generate exclusively sinusoidal pulses based on oscillator circuits and provide only limited control over pulse dynamics. Recently, a more flexible device that generates near-triangular current pulses with several degrees of control over the pulse parameters was presented For the optimal pulse shapes, higher coil voltage results in lower energy loss, analogously to conventional magnetic stimulation waveforms see . In stanThere are, however, practical limits to the use of extremely high voltages, even though these are in principle more efficient. These limits are driven by insulation considerations, semiconductor voltage ratings, high-frequency coil losses, and switching losses due to circuit capacitance. Such practical aspects are highly dependent on the implementation. The pulse parameters for specific circuit topologies could be optimized with the described approach by imposing additional constraints on the waveform shape.The results of this study were obtained in a systematic way and show very plausible features. The outcome was not biased by initialization with current or voltage waveforms that anticipate the final results. Instead, the waveforms evolved solely based on the optimization objective and the constraints. The obtained shapes are relatively stable and reemerged in independent runs with random initialization of the parameters. Indeed, these solutions can be global or not far from the global solution.Still, the optimized waveforms are the best found local minima of the problem formulation, which in turn is based on a nonlinear axon model. Each model has limitations and only approximates reality. Especially in the absolute task of minimization, a physiologic optimum could look slightly different, and could even be an individual characteristic of a specific neuron. Nevertheless, given the robustness of the optimum pulse shape features with respect to the neuron model, it is likely that these features would also be present in pulses optimized in vivo. As with any model-based approach, the numerical results should be considered as a starting point for experimental studies.Finally, it should be noted that improving the energy efficiency is critical to functional and portable magnetic stimulation systems. The former can have very high power consumption, whereas the latter have limited battery energy. On the other hand, in some applications of magnetic stimulation, it may be more appropriate to improve the pulse shape to ensure best selectivity of stimulation of specific neural populations and/or to increase a repetitive stimulation protocol’s neuromodulation potency. For instance, the neural selectivity of a pulse could potentially be controlled by the relative amplitude and duration of the various pulse phases The optimization framework has to describe the temporal dynamics of magnetic stimulation including all stages from the coil current to the neural response. The structure of the optimization setup is depicted in Magnetic stimulation induces an electric field that is proportional to the coil current rate of change which, in turn, is proportional to the coil voltage The framework was implemented in C and optimized for maximum speed. For the solution of the differential equations, a standard second-order Runge-Kutta method was used. The allowed maximum time step for the final analysis was set to 500 ns. The whole optimization framework implementation followed a strict parallel design. Every call of the differential-equation solver was executed in a separate thread. The computation was performed on three eight-core Xeon servers for the low-dimensional problems and on a high-performance system of the Leibniz Supercomputing Centre of the Bavarian Academy of Sciences and Humanities.The objective and all constraints were formulated as functionals; the optimization task is a variational problem. For numerical handling, however, this abstract construction has to be translated into a finite set of numbers. Thus, an appropriate parametrization is an essential element, which moreover influences the stability of the optimization system. This mapping from the finite parameter space to a sufficient  subspace of the Banach space of all waveforms allows a stable evaluation of all needed operators, such as derivatives, in an analytical way. Evading the issue of parametrization by taking a large number of sample points which are handed over to an optimization algorithm may risk instabilities in the context of inductive stimulation.Various waveforms that do not share clear common features are able to stimulate a nerve. Thus, the objective function (energy loss) forms a surface in the waveform parameter space that has numerous local minima. Electromagnetic induction with its differentiating behavior further complicates the waveform optimization problem. The selection of an appropriate coordinate system for the waveform description can remarkably improve the solution process, but the problem is nonlinear and has no natural discrete parametrization. Therefore, we used simultaneously three coordinate systems to parametrize the coil current as their combination stabilizes the numerical processing.First, the waveform is described by cubic spline curves; their finite parameters Therefore, parameter description in frequency space was added. A complex-valued parameter vector The optimization algorithm processes only plain one-dimensional floating-point numbers. There are two simple ways for generating the required complex-valued parameter vector from a real-valued vector All of the three proposed methods of parametrization have at least two continuous derivatives. All of them allow a dynamic change of the coordinate system. This comprises a conversion from one parametrization to another, as well as increasing or reducing the degrees of freedom in the same type of description.The dynamic change of coordinate systems addresses instability due to the vast number of local minima. A local minimum in one coordinate space might not be pronounced in another. Many observed local minima showed artifacts typical for one type of description, such as Gibbs phenomena or ringing, which are not stable for the optimizer with another parametrization. Furthermore, a dynamic change of the number of dimensions was used for adaptive control over stability as described below.We implemented a method for multivariate minimization of the parametrized objective. A global method was chosen due to the large number of local minima. For a quick convergence, the global method was combined with a local algorithm in a hybrid approach. Robust local optimization workers converge rapidly on dominant local minima. The global framework in turn combines the information about these local minima.particle denotes a single waveform parameter set in this context. A particle swarm framework with many local workers allows a concurrent design that is well suited for high-performance computing.For the global algorithm, a particle swarm method was selected Two algorithms, a simplex-derived constrained optimization by linear approximation (COBYLA) The global method hands over the parameters to the local workers who detect a nearby valid local minimum that fulfills all constraints. Their results are considered in deciding every particle’s best as well as the total best in each step. In order to avoid oscillations in the attraction field of local minima, the position of a given particle is not changed to the result of the corresponding local worker.The particle swarm algorithm updates the parameters The decision if a pulse elicits an action potential is made by a nonlinear model of a human motor axon. The nominal model is a local axon description incorporating fast sodium, persistent sodium, and dominant slow potassium channels as well as passive leakage. The formulation and parameters of the membrane dynamics are based on the Schwarz model Like other local or single-compartment models common in neurodynamics To check the robustness of the waveform optima with respect to the neuron model parameters, we also optimized the pulse dynamics using two alternative models. We implemented the Motz-Rattay model and a simple leaky integrate-and-fire model. The Motz-Rattay model is based on a modification of the original Hodgkin-Huxley equations to account for mammalian body temperatures and provides a relatively simple and computationally fast approach for studying pulse dynamics, for example, of auditory nerve axons The linear leaky integrate-and-fire model is widely used in computational neuroscience and is commonly deployed as a regression model in magnetic stimulation to fit experimental strength-duration data Appendix S1Details on the used nominal axon model.(PDF)Click here for additional data file.


We introduce the notion of Electric Field Encephalography (EFEG) based on measuring electric fields of the brain and demonstrate, using computer modeling, that given the appropriate electric field sensors this technique may have significant advantages over the current EEG technique. Unlike EEG, EFEG can be used to measure brain activity in a contactless and reference-free manner at significant distances from the head surface. Principal component analysis using simulated cortical sources demonstrated that electric field sensors positioned 3 cm away from the scalp and characterized by the same signal-to-noise ratio as EEG sensors provided the same number of uncorrelated signals as scalp EEG. When positioned on the scalp, EFEG sensors provided 2–3 times more uncorrelated signals. This significant increase in the number of uncorrelated signals can be used for more accurate assessment of brain states for non-invasive brain-computer interfaces and neurofeedback applications. It also may lead to major improvements in source localization precision. Source localization simulations for the spherical and Boundary Element Method (BEM) head models demonstrated that the localization errors are reduced two-fold when using electric fields instead of electric potentials. We have identified several techniques that could be adapted for the measurement of the electric field vector required for EFEG and anticipate that this study will stimulate new experimental approaches to utilize this new tool for functional brain research. Electro-encephalography (EEG) and magneto-encephalography (MEG) are well-established modalities of studying brain signals. EEG samples electric potential across the scalp, while MEG samples magnetic field  several centimeters from the head's surface. High-density implementations of these methods typically use 64–256 sensors covering the top half of the head. Several recent studies compared the two experimental techniques in terms of their spatial resolution and the amount of information they offer about the underlying brain activity. EEG and MEG were found similar in these respects EEG and MEG provide somewhat different information on the brain's activity: MEG is sensitive to only tangential sources , while EEG is sensitive to both radial and (less so) tangential sources Unlike electric potential, electric fields associated with brain activity are not generally studied because of the difficulty of measuring these weak signals. Furthermore, considering that the electric field is given by the negative gradient of the electric potential measured by EEG, one might wonder whether measuring the electric field instead of its potential could provide any new information at all. It has been shown that a potential defined on a surface has a unique continuation to another surface as long as one surface encloses the other and the volume bound by the two surfaces is source-free Although theoretically possible, such a calculation is difficult to implement for several practical reasons. First, in order to calculate gradients of the scalp potential, one needs a dense measurement of the potential distribution, which calls for an unconventionally large number of small-diameter electrodes separated by distances of 1 cm or less. The high-density EEG caps or nets currently in use have at most 256 electrodes. The electrodes are, typically, 1 cm in diameter and are separated from each other by 3 cm or more. This makes gradient calculation using EEG relatively imprecise. Furthermore, a common data processing step in high-density EEG is to discount one or more 'bad' electrodes due to the amount of noise. The resulting data gaps at the locations of the discounted electrodes further undermine the electric field calculation. Finally, measuring scalp potentials is not feasible in many situations due to poor quality of electric contacts between the electrodes and the scalp, e.g., for subjects with very thick hair or, conversely, lack of hair . Apart from this, the quality of the electric contacts quickly deteriorates during physical activity due to sweating, and the lightest movement of the electrodes on the scalp produces overwhelming amounts of noise.It is, thus, likely that dedicated electric field sensors could improve current EEG techniques. The sensors could be used by themselves or in combination with conventional EEG sensors. However, prior to investing time and money into research and development of adequate field sensors, one needs to estimate the promise of the new technique. This defines the rationale of the presented study. Herein, we model the distribution of electric fields near the scalp and evaluate the use of these fields for functional brain research, a method we term Electric Field Encephalography (EFEG). We demonstrate that electric fields generated by cortical sources are more focused than their associated potentials. This makes EFEG a more local measure of brain activity and offers significantly more uncorrelated signals than EEG, provided that sensors are located either on the scalp or close to it and are characterized by signal-to-noise ratio comparable to EEG sensors. This, in turn, results in major improvement to source localization precision.Two head models were used to simulate electric fields of the brain in this study: an anisotropic 4-shell spherical head model and a 3-shell boundary element method (BEM) model . The purpose of using these two models is to compare EFEG and EEG as realistically as possible. Either model has its own inherent limitations. The BEM model omits the highly conductive cerebro-spinal fluid (CSF) layer, because this layer is too thin at many locations to model it with sufficient precision. It also cannot model the radial-tangential anisotropy of the skull's conductivity due to the nature of the BEM method. The 4-shell spherical model, on the other hand, models the latter two head properties, but cannot be applied to a more realistic head shape. Taken together, the results for these two models provide stronger support for the EFEG and EEG comparisons made in our study than would either model alone.We first discuss electric fields produced by a single current dipole positioned inside the brain shell of the spherical model. Then, the number of uncorrelated signals provided by electric field measurements (EFEG) and potential measurements (EEG) is evaluated by principal component analysis (PCA) for spherical and BEM head models. Finally, the quality of source localization is compared between EEG and EFEG methods.Electric fields produced by a current dipole can be calculated analytically for an anisotropic spherical shell model The electric field was also calculated for the anatomically more realistically shaped BEM head model as described in the Materials and Methods section. Scalp electric fields for two representative cortical sources are shown in Given that electric field patterns are more focused than potential patterns, and that there are 3 times more electric field measurements than potential measurements , one might expect that, in the practical case of a limited number of noisy sensors, the electric field would provide more information about brain sources than electric potential. The number of uncorrelated signals present in a set of data is one possible metric of this information. This metric can be calculated by modeling a multitude of realistic cortical sources, with signals measured by sensors located on the scalp or around the head, and then evaluating the degree of correlation among the resulting sensor signals. We simulated 5,124 source patches distributed evenly over the surface of left and right cortices . The resulting potentials and electric fields were sampled by potential and field sensors positioned as discussed in the Materials and Methods section. Electric field components To determine the number of uncorrelated signals the principal component analysis (PCA) was performed as described in the Materials and Methods section. The PCA eigenvalues normalized by the largest eigenvalue for each set are plotted in To better illustrate the increase in the number of detectable signals, the ratio of the two curves for various noise-to-signal levels  was plotted in the inset to The increase in the number of uncorrelated signals did not occur simply because there were 3 times more field sensors than potential sensors. To show this, we simulated a 4-fold increase of the number of potential sensors by refining the 128-sensor mesh used for the rest of the simulations into 485-sensor mesh covering the same area of the head. The corresponding PCA results are plotted by the dashed orange curve. There was no significant increase in the number of usable signals except for unrealistically low noise levels , while Harmony, in addition, seeks a smooth solution. The rationale of the Harmony approach is that the high spatial frequency components of the solution cannot be reliably inferred from scalp data due to strong low-pass spatial filtering of the skull and high spatial frequency sensor noise.Harmony BEM model source reconstructions for two representative source patches are shown in To quantify the localization error for all simulated sources the BEM head model results are shown in the right panel, where In this study we introduced the notion of Electric Field Encephalography (EFEG) and used computer modeling to argue that measuring the electric field vector generated by brain activity has some significant differences from and advantages over, EEG. Electric field measurements can be conducted in a contact-free manner and, unlike EEG, where even the best choice of the reference point can contribute up to 15% of non-local signal The PCA carried out in the present study for spherical and BEM head models demonstrated that high-density measurements of electric field on or near the head surface can provide 2–3 times more uncorrelated signals of cortical activity than EEG measurements at the same locations . This caThe largest increase in the number of uncorrelated signals between the potential and field measurements was observed for the BEM head model. There are several possible reasons for this: the BEM model fitted the brain more closely and, therefore, it had smaller dipole – sensor distances compared to the spherical model. The BEM head model produced less cortical current diffusion because it did not include the large gradient of conductance at the CSF – skull boundary. It also did not model the skull's anisotropy, which spreads currents still further within the skull The increased number of detectable signals agrees with higher spatial resolution of bipolar EEG electrodes compared to conventional EEG electrodes The increased number of uncorrelated signals in the electric field measurements makes the EFEG approach potentially attractive whenever changes in brain state need to be interpreted based on real-time changes to its electric activity. Possible applications include noninvasive brain-computer interfaces, brain performance monitors, and neurofeedback. The increased number of uncorrelated signals should also improve source localization accuracy. Indeed, reconstructions of the simulated cortical sources were significantly improved when electric field measurements were used instead of electric potential measurements , 4. LocaIn principle, EFEG makes it possible to measure brain activity without making a physical contact with the scalp, once such electric field sensors become available. The contactless measurement has several advantages. It eliminates variability in electrode impedance , which is typical for EEG measurements, where electrodes have to be applied to the scalp and therefore such factors as hair, sweat, and skin state play a decisive role especially when electrodes cannot be readjusted during the measurement. Generally, EEG is very noisy for bald subjects due to cornification of the scalp, and also is very difficult to measure for subjects with thick curly hair. Electrode movement is another major factor impacting the quality of the signals measured with contact electrodes. This makes it very difficult to obtain high-quality EEG data for subjects performing tasks involving head movement.We have identified several techniques that could be adapted for the measurement of the electric field vector required for EFEG, and anticipate that our study will stimulate new experimental approaches to utilize this novel mode of functional brain imaging. Several approaches to fiber optic sensors for electric fields have been demonstrated which could be used for EFEG Modeling of electric fields of the brain in this study was based on the electric field produced by a dipole current source positioned inside either a set of concentric spherical shells with homogenous anisotropic conductivity inside each shell , or inside a set of non-spherical shells with homogeneous isotropic conductivity . The electric fields for the spherical head model were calculated in A 4-shell spherical model was used for simulations. The shells were (from innermost to outermost): brain (white and gray matter), cerebro-spinal fluid (CSF), skull (tables and diploë layers), and scalp . We used spherical model parameters typical for human head tissue simulation. The outer radii of the brain, CSF, skull, and scalp shells were 9.1, 9.2, 9.7, and 10.2 cm respectively . The braThe boundary element method (BEM) head model was constructed based on high-resolution MRI data averaged over 40 subjects, the data were distributed as a part of the FreeSurfer toolbox ectively . The radThe cortical surface of the group-averaged data (provided with the FreeSurfer toolbox) was used to place current dipoles in simulations. 10,242 current dipoles were positioned at the nodes of a triangular mesh  for left and right cortices. The neurologist's ''rule of thumb'' is that at least 6 The dipole orientations were fixed to be orthogonal to the cortical surface, reflective of the common assumption that EEG and MEG are due to synaptic currents produced by activity of cortical pyramidal cells. These currents flow along the pyramidal cells' axons, which are primarily perpendicular to the cortex. The magnitude of the source dipoles was equal among the 37 dipoles constituting a source patch and was such as to produce the maximum scalp potentials  at about 10 Realistic sensor locations were obtained by averaging a 128-channel HydroCell GSN net's (EGI Inc.) electrode locations, as they were applied to 34 subjects used for another study. The electrode locations were measured for each subject using a Polhemus FASTRACK digitizer. The locations were projected onto the spherical scalp for the spherical head model and slightly stretched and shifted by an affine transformation to better fit the scalp for the BEM head model. The resulting sensor locations are shown in To determine the number of uncorrelated signals, the principal component analysis (PCA) was performed. First, a covariance matrix Two source localization algorithms, MNE The localization error was calculated as follows: first, the location of the true source was calculated by averaging the locations of its


Since generic drugs have the same therapeutic effect as the original formulation but at generally lower costs, their use should be more heavily promoted. However, a considerable number of barriers to their wider use have been observed in many countries. The present study examines the influence of patients, physicians and certain characteristics of the generics' market on generic substitution in Switzerland.We used reimbursement claims' data submitted to a large health insurer by insured individuals living in one of Switzerland's three linguistic regions during 2003. All dispensed drugs studied here were substitutable. The outcome (use of a generic or not) was modelled by logistic regression, adjusted for patients' characteristics  and with several variables describing reimbursement incentives  and the generics' market .The overall generics' substitution rate for 173,212 dispensed prescriptions was 31%, though this varied considerably across cantons. Poor health status  was associated with lower generic use. Higher rates were associated with higher out-of-pocket costs, greater price differences between the original and the generic, and with the number of generics on the market, while reformulation and repackaging were associated with lower rates. The substitution rate was 13% lower among hospital physicians. The adoption of the prescribing practices of the canton with the highest substitution rate would increase substitution in other cantons to as much as 26%.Patient health status explained a part of the reluctance to substitute an original formulation by a generic. Economic incentives were efficient, but with a moderate global effect. The huge interregional differences indicated that prescribing behaviours and beliefs are probably the main determinant of generic substitution. Generic substitution has been associated with notable monetary savings for society in several settings  and reprThere are, however, different barriers to the wider use of generic drugs. The first is the concern of patients. About one third of patients expressed worries after generic substitution and some reported either a reduced effect or new or increased side-effects ,7. ChronFurthermore, generic substitution is generally met with skepticism by health professionals despite a lack of proven differences in the clinical outcomes of generics and original formulations ,14. PhysFinally, economic and regulatory conditions play a major role on the drugs market, with financial incentives for all parties  being an important factor . PatientThe aim of this study was to explore the relationship between the use of generic drugs and its main determinants, i.e. patients, physicians, and certain characteristics of the generics' market to adapt if necessary policies on this area.We used reimbursement claims data from a Swiss health insurer for the year 2003. This period was chosen specifically because it came two years after the introduction of new generic substitution rules in Switzerland and preceded a reform imposing a minimum price difference between original formulations and generics. In addition, drug prices were relatively stable during that year. In the interests of identifying factors that could lead to more efficient prescribing, three cantons were selected, one from each linguistic region of Switzerland.Until 2005 Switzerland had the second smallest market share of generic drugs in Europe and, until recently, the generic substitution rate was well below the average [It is compulsory for all Swiss residents to purchase a health insurance contract. All health insurance funds offer the same package, as set down by the federal authorities, which features a list of reimbursable prescription drugs. Swiss patients contribute to the cost of care through the payment of an annual deductible. They are free to choose the level of their deductible, but the higher the deductible the lower the premium they pay. In 2003, there was no mandatory deductible for children under 18, and a minimum deductible of 230 Swiss francs for adults. The highest was 375 Swiss francs for children and 1,500 Swiss francs for adults. Furthermore, once this is reached, the insured is subject to a co-payment of 10% of the cost of any care service he has received. Co-payments are capped at an annual ceiling depending on the deductible . This means that insurance contracts only differ in terms of the financial incentives associated with the deductible levels, and not in the types of care or drugs that are covered. All patients therefore face the same choice of branded or generic drugs for a given indication.Since January 2001, pharmacists have been authorized to substitute original drugs with generics provided that they have the agreement of the patient and have informed the prescribing physician. Since July of the same year pharmacists have received a fixed fee when dispensing a generic drug, independent of the price of the dispensed drug, which avoids financial penalization. There is no reference pricing scheme that requires the patient to pay the difference between the actual price of the medicine and the reference price. However, since 2006, patient copayments for brand drugs have been raised from 10% to 20%. To be admitted to the reimbursed drugs list, generics need to be priced lower than the branded drug. This means a minimal saving in comparison with the originator being requested since 2005 . Switzerland has no other mechanisms in place like mandatory guidelines and expenditure targets to regulate physicians' generic prescription practices.The data used in this study were on the drugs' reimbursement claims submitted by the entire population of insured of one of Switzerland's largest health insurers (CSS), who lived in one of three cantons - Aargau, Ticino and Vaud - during 2003. In Switzerland, most drugs are delivered through medical prescriptions, but some over-the-counter (OTC) drugs are also reimbursed if prescribed by a physician.This source population of 169,837 subjects represented 15.6%, 10.4%, 7.6% of the population of these cantons respectively. Each canton reflects one of Switzerland's three main linguistic regions , and none allows physicians to dispense drugs . Those iThe studied population consisted of all observations relating to substitutable drugs. To be considered substitutable, a drug must have had at least one generic and one brand-name counterpart sold in Switzerland and was reimbursable by the compulsory basic health insurance system in 2003. Counterpart here means the same active substance, pharmaceutical form , dosage, administration route , similar packaging size (differences in number of doses lower than 30%) and intended use as defined in the Swiss Medicines Compendium . Each suThe study outcome was to ascertain whether the patient had received a generic drug or not.Theoretically, there are at least three main promoting (+) or hindering (-) determinants of the use of generics: patients, physicians and the drugs' market, Figure .th level  of Anatomical Therapeutic Chemical (ATC) codes of dispensed drugs , by whether they had chosen an optional health insurance deductible over the standard minimum deductible, by out-of-pocket participation , and by the canton of residence . Treatment complexity can be measured by the ATC drug classification system because dispensed drugs are a direct measure of treated morbidity and have already been used as a risk adjustment tool, particularly when diagnostic information is not available [As mentioned in the background section, patients with poor health status  tend to be reluctant to use generic drugs. However, in a co-payment setting (high deductible and out-of-pocket participation), patients tend to prefer saving money, and are likely to choose a generic over a branded drug, especially if the price of the latter is much higher than that of the former. Patients were characterized by demographic variables , by treatment complexity which was represented by the number  of the 4vailable . A simplGiven that physicians write prescriptions, they heavily influence the choice of medication. Since our study focused on three cantons which did not have significant drug dispensation by physicians, the latter had no financial interest in the choice of drugs and were assumed to be "loyal agents" acting in the interests of their patients. It was therefore difficult to formulate a priori hypotheses about their influence. Prescribing physicians' variables were their practice status , and the canton where they worked.The only information on pharmacies was the canton where they were located. This lack of information should not compromise the study, because Swiss pharmacists had no significant financial disincentives to dispense generics. Since we excluded out-of-canton drug dispensation, the canton variable was the same for patients, physicians and pharmacies, and was thus included as a separate category and only once.There is no evidence to support the assumption that the size of the generic market has a bearing on generics' substitution. On the contrary, launching new galenic and packaging forms were found to be effective mechanisms for maintaining consumption of brand name drugs.The substitution groups were characterized by the number of different generic drugs available in Switzerland in 2003 , the number of patients treated , the unit price of the original (expressed in quintiles), the relative price difference , the administration mode , whether there were multiple packaging sizes, whether there was an additional galenic form for a branded drug , whether the group had at least one co-branded original . Repackaging and reformulating a brand-name drug is a common technique used to maintain the attractiveness of the originals product. To avoid a collinear association with the price of the medication, we used the number of patients treated in each substitution group rather than the total amount of sales as an indicator of the size of the market.Finally, we introduced the 298 substitution groups as dummy variables to identify the possible influence of other aspects of the treatments.The aim of the analysis was to separate the factors related to the dispensing procedure (such as patient or physician characteristics) from the characteristics of the substitution groups depicting the drugs market. We used three logistic models. The simpler model (Model A) comprised only the patient and physician variables and the cantons. However, we did include some first-order interactions between the variables.We then added dummy indicators of the substitution groups, which take the value 1 if the observation (the drug) belongs to the substitution group and 0 if not (Model B). Finally, the third model (Model C) includes all the variables of Model A and all the variables describing the substitution groups.The area under the receiver operating characteristic (ROC) curve (C-statistics) was used to assess the discriminatory power of the predictive model and the Hosmer-Lemeshow table to test its calibration. Akaike's information criterion (AIC) and Schwarz's Bayesian information criterion (BIC) were used to compare the competing models .To estimate how different policies could influence generic drug use, we computed the marginal effects of all the variables from Model C (the most complete model). They were computed as discrete differences from the reference category . For example, the marginal effect of the variable is the difference between the probability of generic drug use when everyone is considered to be between 0 and 19 years old, and the probability when everyone is considered as to be between 60 and 79 years old, while all other variables hold constant. The computation was not possible for the administration mode and the three character ATC code due to missing cells, caused by the fact that not all administration modes are compatible with all ATC codes.All statistical analyses were performed using Stata 11.0 .The source population included 1,341,197 drug dispensations, among which 273,797 were eligible for generic prescription. This population fell to 186,569 after aggregating multiple deliveries and to 173,212 once out-of-canton prescriptions  were excluded.Descriptive statistics and the results of the univariate analysis (logit model with only one variable and a constant as explanatory variables) are given in Table The results of the multivariate analysis are given in Table A multivariate logistic regression with only the patients' variables and cantons gave results similar to the univariate analysis, except for the "deductible" variable Table , Model AModel A passed the Hosmer and Lemeshow  goodnessTaking the heterogeneity of the substitution groups into account did not change the observed trends significantly, but improved the discriminatory power of the model. The C-statistics moved from less than 70% to over 81% Table , Model BThe replacement of substitution groups by all their measurable characteristics provide a model of comparable predictive performance with a 79% C-statistics Table , model CThe Hosmer and Lemeshow tests for Models B and C indicated a lack of fit. This was due mainly to missing interaction effects between the cantons and the group identifiers in Model B and the market variables in Model C. We excluded these effects in order to keep the models tractable. Moreover, for very large samples like ours, the Hosmer-Lemeshow test is often oversensitive to detect lack of fit .The marginal effects of each factor are reported in Table Prescribing practices, which were measured across hospital physicians, specialist physicians and cantons, had the strongest impact on generic substitution. The substitution rate in the canton of Ticino was much lower (-26%) than in Aargau. The rate difference between hospital physicians and specialists was -13% and -3% between hospital and general physicians.th percentile of substitution odds (rather low).Among substitutable drugs, only one was included in the list of narrow therapeutic index published by the US Food and Drug Administration : carbameAccording to our data, generics' prescriptions in 2003 accounted for only 20% of the overall prescription volume. In contrast, generics accounted for more than 40-60% in some OECD countries , even thWe found that the variations in substitution rates across the cantons were similar to those observed across European countries  during the same period. Adjusting for potential disparities in health status, prescriptions or prescribers' characteristics did not alter these variations, which suggests that the impact of cultural aspects such as prescribing behaviours or beliefs about generic substitution may be as important as national policies. This interpretation is confirmed by the finding that hospital physicians substituted less, and should therefore be a focus of any future initiatives encouraging more effective outpatient prescribing practices.As shown in previous studies, poorer health status, captured in the present study by age and treatment complexity, was associated with lower generic use. Older people are less willing to substitute when offered the choice . This rePricing and reimbursement regulations thus appear to be of utmost importance when it comes to increasing generic use. Consumers facing high out-of-pocket costs bought more generics. They were more likely to substitute generics when the savings relative to brand name price would be high. However, the marginal effects of financial incentives related to insurance coverage were rather weak in our study. This could be explained by the annual ceiling of patients' co-payments that protect people against high out-of-pocket expenses. Another reason could be the relatively low proportion of pharmaceutical costs in Switzerland , high patent protection and the small market size may thus explain the low generic market share.Second, measures to protect brand name exclusivity such as reformulations and repackaging were also effective in curbing generic distribution. Although these minor changes may confer benefits on some patients, it is also possible that others may be switched inappropriately to these reformulated drugs, whose prices are higher than the generics. For instance, a recent meta-analysis on cardiovascular drugs found no evidence to support the claim that these peripheral differences between brand name and generic drugs  constitute a significant clinical advantage .Our study has limitations. The source population was limited to a single, large insurance company and it is therefore possible that the population was not totally representative of the Swiss population. Another issue is related to the non-reimbursement of dispensed drugs for patients who have not asked for reimbursement. The actual substitution rate on the Swiss generics market therefore could be slightly higher than observed. Furthermore, our results could not reflect the behaviour of patients in relatively good health who did not reach the deductible. After adjustment of measurable factors, there remained large differences in mean substitution rates among patients, physicians and pharmacies. Further qualitative research would be useful to identify modifiable behavioral determinants.Nevertheless, our findings highlight that policies on pricing and reimbursement are important as an impetus for the generic medicines market but not sufficient for a sustained generic market share. The opposite effects of stimulating the substitution market or protecting brand products provide some evidence that generic substitution is more than a simple question of time.The policy measures recently introduced in Switzerland - 20% co-payment for brand drugs, minimal savings between originals and generics - should be effective since the relative price difference and out-of-pocket participation variables were both significantly associated with a higher rate of generic use. However, if all existing incentives under the control of health policies were fully applied, i.e. maximizing patients' contribution to the costs of care through deductibles and out-of-pocket payments and increasing the number of generics on the market, they would provide an additional potential switch towards generics of about 10%  explain a part of the reluctance to substitute an original formulation by a generic, but this uncontrollable determinant is responsible for only a tiny part of substitution rate variations. The economic incentives  were efficient, but with a moderate global effect. In contrast, adopting the practices of the canton with the highest generic use would itself increase the substitution rate from up to 26%. There was also evidence that an abundant supply of generics would also provide strong incentives to shift towards generics.AIC: Akaike's information criterion; ATC: Anatomical Therapeutic Chemical; BIC: Schwarz's Bayesian information criterion; CI: Confidence interval; NTI: Narrow therapeutic index; OECD: Organisation for Economic Co-operation and Development; OTC: Over-the-counter; USA: United States of AmericaThe authors declare that they have no competing interests.All the four authors participated to the design of the study, to the statistical analysis, interpretation of results, to the writing of the paper and approved the final manuscript.The pre-publication history for this paper can be accessed here:http://www.biomedcentral.com/1472-6963/11/17/prepub


One striking feature of chromatin organization is that chromosomes are compartmentalized into distinct territories during interphase, the degree of intermingling being much smaller than expected for linear chains. A growing body of evidence indicates that the formation of loops plays a dominant role in transcriptional regulation as well as the entropic organization of interphase chromosomes. Using a recently proposed model, we quantitatively determine the entropic forces between chromosomes. This Dynamic Loop Model assumes that loops form solely on the basis of diffusional motion without invoking other long-range interactions. We find that introducing loops into the structure of chromatin results in a multi-fold higher repulsion between chromosomes compared to linear chains. Strong effects are observed for the tendency of a non-random alignment; the overlap volume between chromosomes decays fast with increasing loop number. Our results suggest that the formation of chromatin loops imposes both compartmentalization as well as order on the system without requiring additional energy-consuming processes. Chromatin in higher eukaryotes is compacted and folded on several scales. While the folding mechanisms on the scale of the chromatin fiber are rather well understood Nowadays however, there is an ever growing body of evidence that chromatin is not organized as a simple linear polymer. Rather functional loops seem to play a pivotal role in transcriptional regulation of higher eukaryotes. Several experimental techniques have allowed the determination of specific intra- as well as interchromosomal contacts et al.Recently, several computational studies have been put forward investigating the entropic effects of looping. It was shown that ring polymers in proximity show less intermingling than corresponding linear systems The scope of this paper is to extend the study of effective interactions between ring polymers to the more complex system of looping chromosomes. Chromsomes are simulated using the Dynamic Loop (DL) model To obtain information about the repulsive interactions between chromosomes, we use the recently developed Dynamic Loop (DL) model. This model initally assumes chromatin to consist of a coarse-grained linear polymer chain. Loop formation is achieved using diffusional motion of the monomers in the following way: Whenever two segments co-localize by diffusional motion, a chromatin loop is formed with a certain probability The stochastic nature of loop formation provides a method to effectively incorporate protein-chromatin and chromatin-chromatin interactions. Probabilistic looping, which is often thought to be mediated by DNA-binding factors A typical human chromosome has a length of about 100 mega basepairs (Mb), rendering a detailed description on the molecular level computationally impossible. Coarse-graining approaches, where a long stretch of chromatin is modeled as an effective monomer, are well justified on a scale above the persistence length What happens, when two polymeric coils are brought close together? Clearly, in the absence of other interactions than excluded volume forces, polymers repell each other due to the constrained conformational space available. Such a behaviour has been found both for linear self-avoiding walks Evidently, the effective potential increases when approaching the two chromosomes, i.e. lowering the center-of-mass distance To demonstrate how the data can be mapped onto physical units, we use model polymers of chain length lifetime .The quantitative increase in the effective potential of looping polymers over linear chains  is shown in Chromosomes, when brought in close proximity, not only reveal a strong repulsion between their centers of mass; besides this, their structural properties undergo significant changes. Here, we investigate how size and shape of a model chromosome changes in presence of a second one. Such effects play an important role inside the cell nucleus, as chromosomes are located in a complex environment being typically separated by only a few While linear chains and ring polymers only show a mild swelling in the presence of a second chain, we find that model chromosomes swell enormously. cf. also . In factThe swelling of the chromosomes might suggest that they open up to create space for the monomers of the other chromosome, i.e. allow for intermingling. In the following, we will show that this is not the case, rather the contrary is observed. To achieve this, we investigate how the shape of the chromosomes changes when being close together. The asphericity The changes in shape and dimension are visualized in These findings indicate that chromosomes, similar to ring polymers, do not swell in order to create space for the second chromosome. On the contrary, they swell to avoid each other by elongating in such a way that the overlapping is minimized. This is achieved by aligning the highly aspherical gyration tensors in a parallel way when close together.To answer the question whether chromosomes swell to create space for each other or if they rather try to avoid each other, the mutual alignment of the polymers is studied. An established measure for the mutual alignment is given by the average angle These findings might be explained by a tendency of the chromosomes to minimize the overlap area. When the distance between chromosomes is lowered to values in the order of the size of the chromosome, they start to feel the presence of the second chromosome. Thus, the space of accessible conformations is reduced and the chromosome stretches in a direction perpendicular to the center-of-mass axis. However, when the chromosomes are forced even closer together, nearly overlapping completely, the observed perpendicular alignment together with the strong elongation minimizes the volume shared by both chains .To quantitatively assess the amount of intermingling between the model chromosomes in dependency of the average number of loops, we project the monomer positions to the line connecting the centers of mass of both chromosomes. Thus, a density distribution can be obtained as shown in In this paper, we have analyzed the effect of loops on the repulsive interactions between polymers. As a measure for these interactions we applied the theory of effective potentials, where monomeric degrees of freedom in the partition sum are traced out. The resulting effective potential The major finding of this study is that introducing dynamic loops in the structure of chromatin results in a strong increase of the repulsive interactions by about one order of magnitude . Using aerritory . These oMoreover, we found that the existence of loops introduces strong changes in the size and shape properties of the chromosomes. Indeed, when being brought close together, looping polymers swell and become pronouncedly aspherical, the observed effect being multi-fold larger than for linear chains or ring polymers. Chromosomes in proximity display a highly non-random orientation of their gyration ellipsoids. Increasing the number of loops leads to a significant decrease in the overlap fraction.Clearly, the modelling approach pursued here is simplified with regard to the cellular system. In reality, we have a dense system of chromosomes with a chromatin content of about 10%. It remains to be studied in further publications, whether bringing multiple chromosomes together leads to even stronger effects. Here, for ease of simplicity, we focussed on a two-chromosome-system because it allows best to highlight pairwise interactions between chromosomes and the effect of loops while keeping simulational effort reasonable. Studying the impact of multiple chromosome in a dynamic system the future might also shed light on the question whether the proximity between chromosomes reversly might affect looping probabilty. This, however, is not possible in the framework of the Dynamic Loop Model as presented here because it takes the looping probability as an input parameter.Our findings indicate that chromatin loops not only play an important role in transcriptional regulation. Rather, they help to impose a certain state of order and segregation. Thus, loops seem to constitute a highly efficient regulatory mechanism concerning gene regulation as well as chromatin compartmentalization. The Dynamic Loop model used in this study refrains from assuming active driving mechanisms for loop formation, rather loops form by diffusional motion, minimizing the energy cost.Model chromosomes are simulated using the Dynamic Loop model introduced in Ref. We perform simulations of isolated chromosomes with coarse-grained lengths ranging from Since subsequent conformations in the Markov chain created by the Monte Carlo algorithm are highly correlated, one has to perform a certain number of Monte Carlo steps to obtain two independent conformations. For each set of parameters U between the centers of mass of looping polymers. Simulations have been conducted using the DL model for different chain lengths N and different looping probabilities p. The average number of loops per monomer resulting from the parameter p is indicated by the color bar. Data is scaled with the radius of gyration of isolated polymer chains to allow comparison between different parameters sets. The effective potential increases strongly with looping probability p, but is basically independent of the level of coarse-graining  used.The effective potential (0.14 MB PDF)Click here for additional data file.Figure S2N = 256 using different looping probabilities. Experimental data shows results from FISH measurements on human chromosomes 1 and 11. The chain is mapped to chromosome 11 by assuming one bead to comprise a 400-kb stretch of chromatin. Consistent with the experimental data, this is set equal to 480nm. Different symbols indicate different looping lifetimes Click here for additional data file.


Toxoplasmic retinochoroiditis is deemed a local event, which may fail to evoke a detectable systemic immune response. A correct diagnosis of the disease is a necessary basis for estimating its clinical burden. This is not so difficult in a typical clinical picture. In atypical cases, further diagnostic efforts are to be installed. Although the aqueous humor may be analyzed for specific antibodies or the presence of parasitic DNA, the DNA burden therein is low, and in rare instances a confirmation would necessitate vitreous sampling. A laboratory confirmation of the diagnosis is frustrated by individual differences in the time elapsing between clinical symptoms and activation of specific antibody production, which may result in false negatives. In congenital ocular toxoplasmosis, a delay in the onset of specific local antibody production could reflect immune tolerance. Herein, the authors attempt to provide a simple and practicable algorithm for a clinically tailored diagnostic approach in atypical instances. Toxoplasma gondii range in an age-dependent manner from 22.5% to more than 80% .–40.37–40us humor . Howeverividuals .Toxoplasma antibodies within the serum and aqueous humor of Swiss patients—who were presumed to have been infected congenitally—with those of individuals living in the southern Brazilian region of Erechim—who were presumed to have acquired the disease postnatally—revealed higher levels in the latter than in the former group. Although the concentration of total  IgG in the serum did not differ significantly between the two groups, the level of total IgG in the aqueous humor was markedly higher in the Brazilian than in the Swiss patients [A comparison of the levels of anti-patients . This phpatients , 43. Accpatients , 32. Falpatients , 44–46. Toxoplasma infection and its reactivation is so much poorer than that of the host's humoral immune response to the parasite. In a clinical setting, the analysis of cytokine- and cell-mediated immune responses has yielded no information that could be usefully applied to routine practice [It must be borne in mind that the immune control of the parasite is mediated by the Thl-lymphocyte and not by a humoral response. This circumstance accounts for the increased risk of reactivation in patients who have undergone immunosuppressive therapy and in individuals who are suffering from a cellular immune deficiency. Against this background, it is somewhat surprising that our understanding of the cellular control of primary practice –52.Toxoplasma gondii and the local activation of specific antibody production may be up to 2 weeks. And even after marked infiltration of the vitreous, the interval is still 10 days. However, in a lapine model of secondary ocular toxoplasmosis, a delay of up to 3 weeks after the onset of symptoms can be expected. On the other hand, intraocular production of antibodies has been detected within the first 2 weeks of disease activity both in patients with primary ocular toxoplasmosis and in those with a recurrent manifestation of the disease. These findings indicate that the Goldmann-Witmer coefficient may still be a useful parameter in the early diagnosis of ocular toxoplasmosis [In a significant proportion of patients (21%), a clinically relevant time lapse has to be expected between the onset of clinical symptoms and the activation of local antibody production, and this circumstance has been confirmed in a lapine model of ocular toxoplasmosis [lasmosis .Toxocara has been described to cause Toxoplasma-like lesions [Toxoplasma-like lesions [Several aspects relating to the laboratory diagnosis of ocular toxoplasmosis are poorly understood. Local antibody production cannot be confirmed in one-third of clinically diagnosed cases. This circumstance may reflect individual differences in the diagnostic window between the onset of symptoms and an activation of the local humoral immune response, the immune status of the patient, or a congenital immunotolerance, for which there is some theoretical support. Discrepancies also exist in the confirmation of local antibody production according to the ELISA and the immunoblotting techniques. Theoretically, the results of the two analyses should completely coincide. Consequently, the discrepancies are hardly explainable if not by infection with another agent, which has always to be considered in the differential diagnosis.  lesions . And als lesions , 56. Fur lesions , 57.Toxoplasma gondii has a bearing on the detection of local antibody production has not been determined. However, the highly virulent type I strains are typically associated with ocular toxoplasmosis in healthy Brazilian individuals [Toxoplasma strains and the outcome of laboratory analyses.Whether the strain of ividuals , whereasividuals . It is cividuals , 61. FurToxoplasma-specific IgG and negative for Toxoplflsma-specific IgM, and if the patient responds to appropriate anti-Toxoplasma therapy, most authorities will agree that the individual is suffering from a reactivated form of ocular toxoplasmosis. If serum samples are positive for Toxoplasma-specific IgM, additional laboratory testing is recommended to establish whether ocular involvement is the consequence of a recently acquired infection. Sampling of the intraocular fluids is not required in either instance. However, if there is clinical doubt about the diagnosis, paired samples of aqueous humor and serum should be collected and analyzed in parallel.On the basis of the available information, we have developed an algorithm for the laboratory confirmation of clinically suspected cases of ocular toxoplasmosis . If the Investigation of these samples may face technical difficulties since none of the commercially available ELISA, PCR, and immunoblotting tests are standardized for testing ocular fluid samples, nor are they routinely applied in most commercial laboratories. Since the number of cases per center requiring the aforementioned diagnostics are few, a cooperation with one of the specialized diagnostic centers should be considered. In these centers a support in the clinical interpretation of outcomes may also be available.If local IgG production is detected using the ELISA technique (Goldmann-Witmer coefficient), then the clinical diagnosis can be considered confirmed. If no local specific IgG production is detected, or if the blood–retinal barrier is severely compromised, we recommend an immunoblotting analysis of the serum and aqueous humor , and a PCR analysis of the latter to detect parasitic DNA. Using this strategy, a laboratory confirmation of the diagnosis can be achieved in 85% of cases . If a laToxoplasma therapy. Even so, a laboratory confirmation of the clinical diagnosis is not achieved in 15–40% of cases.In conclusion, the clinical diagnosis of ocular toxoplasmosis may be supported by laboratory tests in 60–85% of cases, depending on the time of sampling. Analysis of the aqueous humor is particularly helpful in patients with atypical lesions or in individuals who are irresponsive to anti-Several aspects of humoral immunity are still poorly understood. These include (1) unclariries with regard to the diagnostic window of false-negative results; (2) the discordance in samples registering positive for antibodies that are detected by the immunoblotting and ELISA techniques; (3) the mechanism underlying the persistence of antibody production after the cessation of disease activity; and (4) the question as to whether an unspecific stimulator of the humoral immune response is capable of inducing the local production of specific antibodies. Although little is known of the role that is played by the parasitic strain in the evolution of the disease, sufficient evidence has accumulated to indicate that this factor has been hitherto underestimated. To further our understanding of the pathophysiology of ocular toxoplasmosis, these issues must be addressed and clarified.


Aspergillus nidulans and analyzed transcriptome data. We demonstrate the advantages of our approach by proposing new hypotheses for the functional annotation of specific genes of differentially expressed fungal gene clusters. Our extension of the Ondex framework makes it possible to overcome the separation between data integration and interactive analysis. More specifically, computationally demanding calculations can be performed on selected sub-networks without losing any information from the whole network. Furthermore, our extensions allow for direct access to online biological databases which helps to keep the integrated information up-to-date.Network inference utilizes experimental high-throughput data for the reconstruction of molecular interaction networks where new relationships between the network entities can be predicted. Despite the increasing amount of experimental data, the parameters of each modeling technique cannot be optimized based on the experimental data alone, but needs to be qualitatively assessed if the components of the resulting network describe the experimental setting. Candidate list prioritization and validation builds upon data integration and data visualization. The application of tools supporting this procedure is limited to the exploration of smaller information networks because the display and interpretation of large amounts of information is challenging regarding the computational effort and the users' experience. The Ondex software framework was extended with customizable context-sensitive menus which allow additional integration and data analysis options for a selected set of candidates during interactive data exploration. We provide new functionalities for on-the-fly data integration using InterProScan, PubMed Central literature search, and sequence-based homology search. We applied the Ondex system to the integration of publicly available data for  In our study, we developed and applied customizable context-sensitive menus to the data integration and visualization tool Ondex. This allows for the interactive exploration of experimental data that is integrated into an information network. The introduction starts with a survey of network inference methods and qualitative assessment of inferred networks. Exploratory data analysis looks for new patterns and hypothesis in a dataset and it is thus well suited to qualitatively assess network modeling and experimental results within the context of an information network.Network inference reconstructs molecular interaction networks on the basis of experimental high-throughput data. Nodes in the resulting network usually represent molecular entities , for which concentration or activity has been measured using omics-technology. The edges in the network stand for direct and indirect relationships between the molecular entities, i.e., they symbolize diverse modes of regulation or direct molecular interaction. New molecular relationships may be predicted with the help of network inference modeling techniques. The predictions are new biological hypotheses which result from the given experimental data. A highly diverse variety of network inference modeling techniques have been developed based on differential equation systems or Bayesian networks  is required, which was not included in the training dataset for the network inference. It consists of expert knowledge and data which was predicted with the help of bioinformatic tools, e.g., the software tool SiTAR for transcription factor binding sites predictions . Using ontologies, Ondex automates the integration of heterogeneous data from diverse sources  into a semantically consistent graph representation. The provenance of the data is retained during the integration process. The modular plug-in architecture of Ondex enables the addition of extra functionality, such as parsers for new data sources or complex filtering methods. The Ondex front-end facilitates interactive visualization, searching, and filtering of the datasets. Certain attributes contained in the graph can be associated with the color, glyphs, and visibility of nodes and edges. Ondex is open source, written in platform-independent Java and supports open standards and interfaces. The Ondex data integration framework has already successfully been used for the study of microarray expression data . In order to demonstrate the practical relevance of our approach, the context-sensitive menus and the invocation of external web services were applied to the integrated network for A. nidulans and (2) an extension of the Ondex framework in the form of context-sensitive menus, which are subsequently (3) used to analyze a transcriptome experiment. In this section, the functionality of the menus and generalizable workflows and approaches are presented. Exploration strategies which are based on the specific data, intermediate results, and the research question of the experiment are presented in the results section. The workflow of data integration, the resulting network, and the context-specific menu items are available from http://ondex.rothamsted.ac.uk/anidulans.In this section, we present (1) an information network for A. nidulans using the pre-existing plug-ins from the Ondex integrator. . Additional functional annotation data from the FunCat     were compared under four different induced growth stages—vegetative 14 h, vegetative 20 h, sexual 48 h, asexual 48 h. For each growth stage, two biological replicates each with four technical replicates were measured, summing up to a total of 32 samples. The raw data was downloaded from GEO and the biological replicates were normalized individually with the help of loess and quantile normalization provided by the limma package  files on the local file system using JavaBeans. Each XML-file represents one context menu item which can be restricted to be applicable only to the nodes of particular Ondex concept classes. The context-specific menus can also be organised hierarchically, where the nesting of the sub-menus is represented by the structure of the directories containing the XML-files in the file system.The flexibility and power of the analysis offered by the Ondex system is realized primarily through the notion of customisability, i.e., users are free to build their own application cases from a set of generic re-usable components. Larger integration and analysis tasks are realized as workflow components, whereas the less substantial ones can be completed by calling a set of in-built functions. To that end, the Ondex system incorporates a JavaScript API (based on Mozilla Rhino v1.7) and a rich selection of binding and analysis functions that can be used both to manipulate the graph and to alter its appearance in the Ondex front-end. The binding and functions available via the scripting environment abstract some of the complexity of the Java-based Ondex API and allow for more concise syntax and greater convenience. This additional simplification is made possible by the use of run-time bytecode code generation (powered by the JavaAssist v3.12.0 library) that creates a set of wrappers. This setup allows both easy incorporation of additional external libraries and their seamless integration into the Mozilla Rhino scripting environment by automating the process of creating wrappers that implement additional interface(s) or delegate calls to multiple classes. The Ondex scripting environment can be accessed interactively using a console environment. In this work, we have extended this functionality further by developing a system of context-specific menus that can dispatch calls to the Ondex scripting APIs. The use of temporary sub-graphs also allows users to define their own JavaScript functions to be added as entries on these menus. For this study, we provide new functions for on-the-fly data integration using InterProScan, Blast, and PubMedCentral full-text search (see next section for more details). Using the modular architecture of Ondex, we extended the framework with context-sensitive pop-up menus which allow integration to be performed on the fly, while the network is being explored visually  of the editor provides an easy way to specify concept class restrictions, integration of additional Java libraries and syntax highlighting with help of jEdit. The Ondex framework extension has been integrated into the main Ondex project and is freely available at p-value. Thus, the number of interesting concepts which need to be manually checked were reduced. At the same time, all available information can be reconsidered during the analysis by redisplaying previously filtered data. We independently analyzed each contrast, i.e., the differences in transcript abundance between the ΔcsnE-mutant and the wild-type at different time points , and filtered for either differentially expressed transcripts (DEGs)  or for strongly differentially expressed transcripts . Previously integrated information, i.e., concepts such as gene ontologies and publications, was included in the visualization if it is associated with the resulting gene sets.In Ondex, the precise workflow of exploration depends specifically on the integrated data, the research question, and the preferences of the user. Nevertheless, we performed analyses with a generally applicable workflow that gave us a first overview of the information contained in the data, i.e., filtering down to specific genes, biological processes, and underlying interactions. For our study, we provide new functionalities to Ondex through context-sensitive menus, namely the InterProScan, a sequence-based homology search, and a full-text literature search at PubMed Central. During the procedure described above, the log-fold changes of gene expression data from 32 samples were integrated as attributes to the gene concepts in the information network. This allowed us to significantly reduce the number of concepts  by applying a filter based on the log-fold change and The DEGs were subject to further exploratory analysis and the integrated dataset was used to identify which of the functional categories were predominantly up or down-regulated. For this purpose, only gene concepts which are differentially regulated were made visible and all connected gene ontology concepts have been visualized while retaining their hierarchical network structure   can also be mapped to pathways from the Kyoto Encyclopedia of Genes and Genomes (KEGG)   This implies that most changes caused by the mutant take place before cell differentiation. Specifically, 1161 genes  have a |fold-change| ≥4 during sexual or asexual development in contrast to only 157 DEGs (12.5%) during vegetative growth. A similar proportion holds for higher |fold-changes| ≥8  are comparable to the original publication . The most prominent functional categories are secondary metabolism, stress and defence related genes, cell wall and genes associated with transport processes. In addition to the results published by Nahlik et al.  is immediately identified as being strongly expressed in the vegetative growth phase after 20 h and in both developmental stages at 48 h  and located on chromosome IV  and the prediction of a transmembrane protein domain by InterProScan led us to conjecture that this is a potential sterigmatocystin transporter, which needs to be validated experimentally (data not shown).Gene clusters found in the previous step were explored in greater detail in order to confirm their relevance. At this stage, several context-sensitive menus were used to obtain additional annotations . The InterProScan predicts that this gene contains a serine hydrolase domain and is therefore catalytically active. Additionally, the protein sequence was used to invoke a BLAST web service in order to search for potential similar genes. We found that only the CPSG_01145 gene from the pathogenic fungus Coccidioides posadasii had a high sequence similarity of more than 60%. It is annotated as citrinin biosynthesis oxidoreductase CtnB and therefore is likely to be involved in the secondary metabolism of this fungus. These findings and the chromosomal location of AN7899.4 in the proximity of two secondary metabolite gene clusters has not been reported before and make this gene interesting for further experimental research. The example shows that the added Ondex functionality helps to make new hypotheses which otherwise would not have been recognized.Another example of our exploratory data analysis was the application of the InterProScan for gene AN7899.4, in the region of the predicted NRPS AN7884.4 and the already described NRPS-PKS AN7909.4  which was strongly differentially expressed during the asexual growth stage . By providing these data integration functionalities through context-sensitive menus in the Ondex framework, the data interpretation procedure is sped up, it is more reproducible, and it helps to direct the researcher's focus on the data interpretation rather than the methodology of retrieving it. Another advantage of the approach to data integration supported by the Ondex framework is that it facilitates tracking of different sources of data and the path of reasoning and exploration. This would not be possible using web resources and their interfaces alone, which work mostly in a sequential, linear manner. All publicly available information about a gene can be consolidated within one graph, making the navigation easier and ensuring the best possible quality of data, as all relevant data can be efficiently collected. If the information about a gene locus is missing, the utility of Ondex to draw conclusions is limited and additional experimental data or bioinformatic methods are necessary to fill the gap. Thus, the completeness of the underlying functional annotation is of particular importance as it has a major impact on the subsequent interpretation of the dataset. In our example, it became apparent that most conclusions about the functional categorization of The standard procedure in Ondex is to integrate available data from different data sources prior to the visualization and data analysis. If a large amount of data is integrated, it results in large datasets which need to be handled and visualized by the Ondex software framework. Currently, the complexity of layout algorithms and the computational limitations, i.e., memory or CPU, make it challenging to manage the vast amount of data in a user-friendly and responsive manner. Additionally, if access to the most recent information is very important and the underlying data changes frequently, the time-consuming step of data integration has to be repeated regularly. If the data originates from user-made, computationally demanding calculations, a frequent data integration becomes computationally infeasible. Our extension of the Ondex framework overcomes these limitations by offering the option to apply these steps to a selected part of the network via the context-sensitive menus. Thus, the required amount of data is reduced, current data can be instantly downloaded from web resources, and intensive calculations need only be performed for subsets of the available data relevant to the current focus of investigation. Hence, the memory and computational load is reduced and access to the most recent data is guaranteed.In this way, the context-sensitive menus make the interactive data analysis more efficient and user-friendly by providing data integration and filtering on-the-fly. The precise workflow of data analysis does not have to be established for the whole data integration process beforehand and the integration can be repeatedly applied and adjusted during the interactive analysis. This extension to the Ondex framework now combines the advantages of two data integration paradigms, i.e., of data warehousing and federated data integration, into one easy-to-use single system. The extensions to Ondex reported here have significantly improved its suitability for its usage for the qualitative assessment of inferred network models.Fabian Horn initiated and led the work presented here, contributed as the main author to this manuscript and carried out the analysis. Martin Rittweger implemented the context-sensitive menus in Ondex and carried out the analysis. Jan Taubert supported the general implementation in Ondex and contributed to conceptualization and writing of the manuscript. Artem Lysenko supported the implementation with respect to Ondex scripting capabilities and provided feedback on the manuscript. Christopher Rawlings and Reinhard Guthke supervised the work at Rothamsted and the HKI, respectively, and provided feedback on the manuscript. All authors have read and acknowledged the manuscript.This study was supported by the International Leibniz Research School for Microbial and Molecular Interactions (ILRS), as part of the excellence graduate school Jena School for Microbial Communication (JSMC), supported by the Deutsche Forschungsgemeinschaft. The work on Ondex has been funded by BBSRC Grants BBS/B/13640 and BB/F006039/1.The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.


The concept of topographic mapping is central to the understanding of the visual system at many levels, from the developmental to the computational. It is important to be able to relate different coordinate systems, e.g. maps of the visual field and maps of the retina. Retinal maps are frequently based on flat-mount preparations. These use dissection and relaxing cuts to render the quasi-spherical retina into a 2D preparation. The variable nature of relaxing cuts and associated tears limits quantitative cross-animal comparisons. We present an algorithm, “Retistruct,” that reconstructs retinal flat-mounts by mapping them into a standard, spherical retinal space. This is achieved by: stitching the marked-up cuts of the flat-mount outline; dividing the stitched outline into a mesh whose vertices then are mapped onto a curtailed sphere; and finally moving the vertices so as to minimise a physically-inspired deformation energy function. Our validation studies indicate that the algorithm can estimate the position of a point on the intact adult retina to within 8° of arc . The coordinates in reconstructed retinae can be transformed to visuotopic coordinates. Retistruct is used to investigate the organisation of the adult mouse visual system. We orient the retina relative to the nictitating membrane and compare this to eye muscle insertions. To align the retinotopic and visuotopic coordinate systems in the mouse, we utilised the geometry of binocular vision. In standard retinal space, the composite decussation line for the uncrossed retinal projection is located 64° away from the retinal pole. Projecting anatomically defined uncrossed retinal projections into visual space gives binocular congruence if the optical axis of the mouse eye is oriented at 64° azimuth and 22° elevation, in concordance with previous results. Moreover, using these coordinates, the dorsoventral boundary for S-opsin expressing cones closely matches the horizontal meridian. PLOS Computational Biology Software ArticleThis is a retinotopic coordinates, examining the mapping of dorsal versus ventral (DV) retina and nasal versus temporal (NT) retina visuotopic mappings: upper versus lower and central versus peripheral visual field The retina projects directly and indirectly to a large number of areas in the central nervous system, such as the mammalian superior colliculus, lateral geniculate nucleus or visual cortex. Understanding the topographic mapping of these projections is a central feature of visual neuroscience Historically, the anatomical organisation of the retina was frequently examined using serial sections, with the emphasis on example sections rather than reconstructions We describe a method to infer where points on a flat-mount retina would lie in a standard, intact retinal space. The standard retina is approximated as a partial sphere, with positions identified using spherical coordinates. Our results show that the method can estimate the location of a point on a flat-mounted retina to within 8° of arc of its original location, or 3.6% of the NT or DV axis. This has allowed us to define a standard retinal space for the adult and for the developing mouse eye. Establishing the orientation of retinal space for the mouse, whose retina contains no intrinsic markers, requires experimental intervention. In the Results, we focus on data from adult mice. We show that a mark based on the centre of the nictitating membrane is reliable and this mark can be related to the insertion of the rectus eye muscles. Furthermore, we transform standard retinal space into visuotopic space and use the geometry of binocular vision, together with anatomical tracing, to address questions about the projection of the optical axis of the mouse eye into visual space Our Retistruct algorithm not only facilitates comparison of differential retinal distributions across animals but also allows analyses of distributions of labelled cells in spherical coordinates, obviating the distortions associated with 2D flat-mounts. Finally, transforming retinal coordinates into visual coordinates gives insights into the functional significance of retinal distributions.In this section we give an overview of the reconstruction algorithm; a more detailed description is contained in the Supplemental Materials and Methods . The staThe locations of mesh points in the flat-mount and their corresponding locations on the sphere define the relation between any point in the flat-mount and a standard spherical space. This relation is used to map the locations of data points and landmarks in the flat retina onto the standard retina. These can be visualised interactively on a 3D rendering of a sphere see , or reprIn order to analyse data points on the standard retina, we used spherical statistics To assess the amount of residual deformation at the end of the energy minimisation procedure, we plotted the length of each edge at mesh  , using tWe used our algorithm on 297 flat-mounted retinae, 288 of which could be reconstructed successfully, 7 of which failed due to, as-yet unresolved, software problems and 2 of which were rejected because of unsatisfactory reconstructions (see below).  measure . The str measure  indicate measure  there arThus the deformation measure as 0.070 , and 27 It should be noted that retinae which have lost tissue due to poor dissection can be forced onto the spherical surface by the algorithm, albeit with high To determine the rim angle of mouse eyes at varying stages of development we measured the distance e retina . We thenAn alternative approach to setting the rim angle is to infer, for each individual retina, the rim angle that minimises the deformation. This was done by repeating the minimisation for rim angles at 1° intervals within a range The deformation measure gives an indication of how easy it is to morph any particular flattened retina onto a partial sphere, but it does not indicate the error involved in the reconstruction, i.e. the difference between the inferred position on the spherical retina and the original position on the spherical retina. The ideal method for estimating the error would be to flatten a retina marked in known locations, and then compare the inferred with the known locations. However, this proved to be technically very difficult and so we tried another method of estimating the error that uses the inferred locations of the optic discs across a number of retinae. In mice, the optic disc is located “rather precisely in the geometric center of the retina” location . If recoWe now describe the first application of the reconstruction algorithm. The relationship between the projections from the mouse retina to the ipsilateral and contralateral dLGN has been studied in retina flat-mounts following injection of retrograde tracer into the dLGN one retina from an animal that had received bilateral injections into the dLGN , MacOS X 10.8 and Microsoft Windows Vista. The user guide, available from the same site, contains details of the two main data formats Retistruct can process. These are either in the form of coordinates of data points and retinal outline from an in-house camera-lucida setup, or in the form of bitmap images with an outline marked up in ImageJ ROI format The reconstruction and transformation methods described here have been implemented in R The program could be applied to flat-mount preparations of retinae from any vertebrate species at any age, provided the globe of the eye is approximately spherical, and it would be possible to add extra analysis routines. When examining retinae with mosaic labelling It should be stressed that the current version is not intended for use on partial retinae. However, it might eventually be possible to locate incomplete retinae in standard retinal space, if there enough markers to orient the partial retina correctly. Similarly, it should be possible to locate sections  of known orientation and hemiretinal origin in standard space.Dataset S1Complete source code for the Retistruct package (version 0.5.7). Includes demonstration data for (ZIP)Click here for additional data file.Text S1Supplemental information including an extended Discussion, and Materials and Methods containing details of experiments and detailed description of the reconstruction algorithm and analysis of reconstructed data.(PDF)Click here for additional data file.