Computational Study of Subdural Cortical Stimulation: Effects of Simulating Anisotropic Conductivity on Activation of Cortical Neurons

Subdural cortical stimulation (SuCS) is an appealing method in the treatment of neurological disorders, and computational modeling studies of SuCS have been applied to determine the optimal design for electrotherapy. To achieve a better understanding of computational modeling on the stimulation effects of SuCS, the influence of anisotropic white matter conductivity on the activation of cortical neurons was investigated in a realistic head model. In this paper, we constructed pyramidal neuronal models (layers 3 and 5) that showed primary excitation of the corticospinal tract, and an anatomically realistic head model reflecting complex brain geometry. The anisotropic information was acquired from diffusion tensor magnetic resonance imaging (DT-MRI) and then applied to the white matter at various ratios of anisotropic conductivity. First, we compared the isotropic and anisotropic models; compared to the isotropic model, the anisotropic model showed that neurons were activated in the deeper bank during cathodal stimulation and in the wider crown during anodal stimulation. Second, several popular anisotropic principles were adapted to investigate the effects of variations in anisotropic information. We observed that excitation thresholds varied with anisotropic principles, especially with anodal stimulation. Overall, incorporating anisotropic conductivity into the anatomically realistic head model is critical for accurate estimation of neuronal responses; however, caution should be used in the selection of anisotropic information.     

From Oscillatory Transcranial Current Stimulation to Scalp EEG Changes: A Biophysical and Physiological Modeling Study

Both biophysical and neurophysiological aspects need to be considered to assess the impact of electric fields induced by transcranial current stimulation (tCS) on the cerebral cortex and the subsequent effects occurring on scalp EEG. The objective of this work was to elaborate a global model allowing for the simulation of scalp EEG signals under tCS. In our integrated modeling approach, realistic meshes of the head tissues and of the stimulation electrodes were first built to map the generated electric field distribution on the cortical surface. Secondly, source activities at various cortical macro-regions were generated by means of a computational model of neuronal populations. The model parameters were adjusted so that populations generated an oscillating activity around 10 Hz resembling typical EEG alpha activity. In order to account for tCS effects and following current biophysical models, the calculated component of the electric field normal to the cortex was used to locally influence the activity of neuronal populations. Lastly, EEG under both spontaneous and tACS-stimulated (transcranial sinunoidal tCS from 4 to 16 Hz) brain activity was simulated at the level of scalp electrodes by solving the forward problem in the aforementioned realistic head model. Under the 10 Hz-tACS condition, a significant increase in alpha power occurred in simulated scalp EEG signals as compared to the no-stimulation condition. This increase involved most channels bilaterally, was more pronounced on posterior electrodes and was only significant for tACS frequencies from 8 to 12 Hz. The immediate effects of tACS in the model agreed with the post-tACS results previously reported in real subjects. Moreover, additional information was also brought by the model at other electrode positions or stimulation frequency. This suggests that our modeling approach can be used to compare, interpret and predict changes occurring on EEG with respect to parameters used in specific stimulation configurations.     

Anatomical Targets Associated with Abrupt versus Gradual Washout of Subthalamic Deep Brain Stimulation Effects on Bradykinesia

The subthalamic nucleus (STN) is a common anatomical target for deep brain stimulation (DBS) for the treatment of Parkinson’s disease. However, the effects of stimulation may spread beyond the STN. Ongoing research aims to identify nearby anatomical structures where DBS-induced effects could be associated with therapeutic improvement or side effects. We previously found that DBS lead location determines the rate – abrupt vs. gradual – with which therapeutic effect washes out after stimulation is stopped. Those results suggested that electrical current spreads from the electrodes to two spatially distinct stimulation targets associated with different washout rates. In order to identify these targets we used computational models to predict the volumes of tissue activated during DBS in 14 Parkinson’s patients from that study. We then coregistered each patient with a stereotaxic atlas and generated a probabilistic stimulation atlas to obtain a 3-dimensional representation of regions where stimulation was associated with abrupt vs. gradual washout. We found that the therapeutic effect which washed out gradually was associated with stimulation of the zona incerta and fields of Forel, whereas abruptly-disappearing therapeutic effect was associated with stimulation of STN itself. This supports the idea that multiple DBS targets exist and that current spread from one electrode may activate more than one of them in a given patient, producing a combination of effects which vary according to electrode location and stimulation settings.     

Predicting Novel Features of Toll-Like Receptor 3 Signaling in Macrophages

The Toll-like receptor (TLR) 3 plays a critical role in mammalian innate immune response against viral attacks by recognizing double-stranded RNA (dsRNA) or its synthetic analog polyinosinic-polycytidylic acid (poly (I∶C)). This leads to the activation of MAP kinases and NF-κB which results in the induction of type I interferons and proinflammatory cytokines to combat the viral infection. To understand the complex interplay of the various intracellular signaling molecules in the regulation of NF-κB and MAP kinases, we developed a computational TLR3 model based upon perturbation-response approach. We curated literature and databases to determine the TLR3 signaling topology specifically for murine macrophages. For initial model creation, we used wildtype temporal activation profiles of MAP kinases and NF-κB and, for model testing, used TRAF6 KO and TRADD KO data. From dynamic simulations we predict i) the existence of missing intermediary steps between extracellular poly (I∶C) stimulation and intracellular TLR3 binding, and ii) the presence of a novel pathway which is essential for JNK and p38, but not NF-κB, activation. Our work shows activation dynamics of signaling molecules can be used in conjunction with perturbation-response models to decipher novel signaling features of complicated immune pathways.     

Detection of motor unit action potentials with surface electrodes: influence of electrode size and spacing

A model of the motor unit action potential was developed to investigate the amplitude and frequency spectrum contributions of motor units, located at various depths within muscle, to the surface detected electromyographic (EMG) signal. A dipole representation of the transmembrane current in a three-dimensional muscle volume was used to estimate detected individual muscle fiber action potentials. The effects of anisotropic muscle conductance, innervation zone location, propagation velocity, fiber length, electrode area, and electrode configuration were included in the fiber action potential model. A motor unit action potential was assumed to be the sum of the individual muscle fiber action potentials. A computational procedure, based on the notion of isopotential layers, was developed which substantially reduced the calculation time required to estimate motor unit action potentials. The simulations indicated that: 1) only those motor units with muscle fibers located within 10–12 mm of the electrodes would contribute significant signal energy to the surface EMG, 2) variation in surface area of electrodes has little effect on the detection depth of motor unit action potentials, 3) increased interelectrode spacing moderately increases detection depth, and 4) the frequency content of action potentials decreases steeply with increased electrode-motor unit territory distance.     

Cardiac dynamics: a simplified model for action potential propagation

This paper analyzes a new semiphysiological ionic model, used recently to study reexitations and reentry in cardiac tissue [I.R. Cantalapiedra et al, PRE 82 011907 (2010)]. The aim of the model is to reproduce action potencial morphologies and restitution curves obtained, either from experimental data, or from more complex electrophysiological models. The model divides all ion currents into four groups according to their function, thus resulting into fast-slow and inward-outward currents. We show that this simplified model is flexible enough as to accurately capture the electrical properties of cardiac myocytes, having the advantage of being less computational demanding than detailed electrophysiological models. Under some conditions, it has been shown to be amenable to mathematical analysis. The model reproduces the action potential (AP) change with stimulation rate observed both experimentally and in realistic models of healthy human and guinea pig myocytes (TNNP and LRd models, respectively). When simulated in a cable it also gives the right dependence of the conduction velocity (CV) with stimulation rate. Besides reproducing correctly these restitution properties, it also gives a good fit for the morphology of the AP, including the notch typical of phase 1. Finally, we perform simulations in a realistic geometric model of the rabbit’s ventricles, finding a good qualitative agreement in AP propagation and the ECG. Thus, this simplified model represents an alternative to more complex models when studying instabilities in wave propagation.     

Simulation of soft tissue failure using the material point method

Understanding the factors that control the extent of tissue damage as a result of material failure in soft tissues may provide means to improve diagnosis and treatment of soft tissue injuries. The objective of this research was to develop and test a computational framework for the study of the failure of anisotropic soft tissues subjected to finite deformation. An anisotropic constitutive model incorporating strain-based failure criteria was implemented in an existing computational solid mechanics software based on the material point method (MPM), a quasi-meshless particle method for simulations in computational mechanics. The constitutive model and the strain-based failure formulations were tested using simulations of simple shear and tensile mechanical tests. The model was then applied to investigate a scenario of a penetrating injury: a low-speed projectile was released through a myocardial material slab. Sensitivity studies were performed to establish the necessary grid resolution and time-step size. Results of the simple shear and tensile test simulations demonstrated the correct implementation of the constitutive model and the influence of both fiber family and matrix failure on predictions of overall tissue failure. The slab penetration simulations produced physically realistic wound tracts, exhibiting diameter increase from entrance to exit. Simulations examining the effect of bullet initial velocity showed that the anisotropy influenced the shape and size of the exit wound more at lower velocities. Furthermore, the size and taper of the wound cavity was smaller for the higher bullet velocity. It was concluded that these effects were due to the amount of momentum transfer. The results demonstrate the feasibility of using MPM and the associated failure model for large-scale numerical simulations of soft tissue failure.     

Dynamic Impedance Model of the Skin-Electrode Interface for Transcutaneous Electrical Stimulation

Transcutaneous electrical stimulation can depolarize nerve or muscle cells applying impulses through electrodes attached on the skin. For these applications, the electrode-skin impedance is an important factor which influences effectiveness. Various models describe the interface using constant or current-depending resistive-capacitive equivalent circuit. Here, we develop a dynamic impedance model valid for a wide range stimulation intensities. The model considers electroporation and charge-dependent effects to describe the impedance variation, which allows to describe high-charge pulses. The parameters were adjusted based on rectangular, biphasic stimulation pulses generated by a stimulator, providing optionally current or voltage-controlled impulses, and applied through electrodes of different sizes. Both control methods deliver a different electrical field to the tissue, which is constant throughout the impulse duration for current-controlled mode or have a very current peak for voltage-controlled. The results show a predominant dependence in the current intensity in the case of both stimulation techniques that allows to keep a simple model. A verification simulation using the proposed dynamic model shows coefficient of determination of around 0.99 in both stimulation types. The presented method for fitting electrode-skin impedance can be simple extended to other stimulation waveforms and electrode configuration. Therefore, it can be embedded in optimization algorithms for designing electrical stimulation applications even for pulses with high charges and high current spikes.     

A new approach to the determination of cardiac potential distributions: application to the analysis of electrode configurations

This paper presents a mathematical model and new solution technique for studying the electric potential in a slab of cardiac tissue. The model is based on the bidomain representation of cardiac tissue and also allows for the effects of fibre rotation between the epicardium and the endocardium. A detailed solution method, based on Fourier Series and a simple one-dimensional finite difference scheme, for the governing equations for electric potential in the tissue and the blood, is also presented. This method has the advantage that the potential can be calculated only at points where it is required, such as the measuring electrodes. The model is then used to study various electrode configurations which have been proposed to determine cardiac tissue conductivity parameters. Three electrode configurations are analysed in terms of electrode spacing, placement position and the effect of including fibre rotation: the usual surface four-electrode configuration; a single vertical analogue of this and a two probe configuration, which has the current electrodes on one probe and the measuring electrodes on the other, a fixed distance away. It is found that including fibre rotation has no effect on the potentials measured in the first two cases; however, in the two probe case, non-zero fibre rotation causes a significant drop in the voltage measured. This leads to the conclusion that it is necessary to include the effects of fibre rotation in any model which involves the use of multiple plunge electrodes.     

The Virtual Ventricular Wall: A Tool for Exploring Cardiac Propagation and Arrhythmogenesis

Methods for the experimental and clinical investigation of cardiac arrhythmias are limited to inferring propagation within the myocardium, from surface measurements, or from electrodes at a few sites within the cardiac wall. Biophysically and anatomically detailed computational models of cardiac tissues offer a powerful way for studying the electrical propagation processes and arrhythmias within the virtual heart. We use virtual tissues to study and visualise the effects of patho- and physiological conditions, and pharmacological interventions on transmural propagation in the virtual ventricular walls. Class III drug actions are quantitatively explained by changes induced in the transmural dispersion of action potential duration. We illustrate the automated construction of a virtual anisotropic ventricle from Diffusion Tensor MRI for individual hearts, and use it to explore mechanisms leading to ventricular fibrillation. The virtual ventricular wall provides an effective tool for exploring, evaluating and visualising processes during the initiation and maintenance of ventricular arrhythmias.     

Quasi-Monopolar Stimulation: A Novel Electrode Design Configuration for Performance Optimization of a Retinal Neuroprosthesis

In retinal neuroprostheses, spatial interaction between electric fields from various electrodes – electric crosstalk – may occur in multielectrode arrays during simultaneous stimulation of the retina. Depending on the electrode design and placement, this crosstalk can either enhance or degrade the functional characteristics of a visual prosthesis. To optimize the device performance, a balance must be satisfied between the constructive interference of crosstalk on dynamic range and power consumption and its negative effect on artificial visual acuity. In the present computational modeling study, we have examined the trade-off in these positive and negative effects using a range of currently available electrode array configurations, compared to a recently proposed stimulation strategy – the quasi monopolar (QMP) configuration – in which the return current is shared between local bipolar guards and a distant monopolar electrode. We evaluate the performance of the QMP configuration with respect to the implantation site and electrode geometry parameters. Our simulation results demonstrate that the beneficial effects of QMP are only significant at electrode-to-cell distances greater than the electrode dimensions. Possessing a relatively lower activation threshold, QMP was found to be superior to the bipolar configuration in terms of providing a relatively higher visual acuity. However, the threshold for QMP was more sensitive to the topological location of the electrode in the array, which may need to be considered when programming the manner in which electrode are simultaneously activated. This drawback can be offset with a wider dynamic range and lower power consumption of QMP. Furthermore, the ratio of monopolar return current to total return can be used to adjust the functional performance of QMP for a given implantation site and electrode parameters. We conclude that the QMP configuration can be used to improve visual information-to-stimulation mapping in a visual prosthesis, while maintaining low power consumption.     

On the effect of parent-aneurysm angle on flow patterns in basilar tip aneurysms: towards a surrogate geometric marker of intra-aneurismal hemodynamics

As a part of previous computational fluid dynamic (CFD) validation studies, particle image velocimetry (PIV) of two anatomically realistic basilar artery tip aneurysm models revealed two distinct types of flow (one of which has yet to be reported in the literature), characterized by the location and strength of the intra-aneurismal vortex. We hypothesized that these distinct "hemodynamic phenotypes" could be anticipated by a simple geometric parameter: the angle of the aneurysm bulb relative to the parent artery. An idealized basilar tip aneurysm model was constructed to allow independent control of this angle, and CFD simulations were carried out for angles ranging from 2 degrees to 30 degrees , these extremes corresponding to the angles measured from the two anatomically realistic models. The gross hemodynamics predicted by the idealized model for 2 degrees and 30 degrees were consistent with those seen in the corresponding anatomically realistic models. For the idealized model, the flow type switched at an angle between 8 degrees and 12 degrees . Sensitivity studies suggested that, near these angles, the hemodynamic phenotype was sensitive to inflow momentum. Outside this range, however, the parent-bulb angle appeared to be a robust predictor of hemodynamic phenotype. Our findings suggest that blood flow dynamics in basilar artery tip aneurysms fall into one of the two broad phenotypes, each subject to distinct hemodynamic forces. That the general features of these flow types may be anticipated by a relatively simple-to-measure geometric parameter could help ease the introduction of hemodynamic information into routine clinical decision-making.     

Long-Term Low Carbohydrate Diet Leads to Deleterious Metabolic Manifestations in Diabetic Mice

We investigated long-term effects of low carbohydrate diets on wild type mice, streptozotocin-injected and KKAy obese diabetic mice. These mice were pair-fed three different types of diets, standard chow (SC, C∶P∶F = 63∶15∶22), a low carbohydrate (LC, C∶P∶F = 38∶25∶37) diet and a severely carbohydrate restricted (SR, C∶P∶F = 18∶45∶37) diet for 16 weeks. Despite comparable body weights and serum lipid profiles, wild type and diabetic mice fed the low carbohydrate diets exhibited lower insulin sensitivity and this reduction was dependent on the amount of carbohydrate in the diet. When serum fatty acid compositions were investigated, monounsaturation capacity, i.e. C16:1/C16:0 and C18:1/C18:0, was impaired in all murine models fed the low carbohydrate diets, consistent with the decreased expression of hepatic stearoyl-CoA desaturase-1 (SCD1). Interestingly, both the hepatic expressions and serum levels of fibroblast growth factor 21 (FGF21), which might be related to longevity, were markedly decreased in both wild type and KKAy mice fed the SR diet. Taking into consideration that fat compositions did not differ between the LC and SR diets, we conclude that low carbohydrate diets have deleterious metabolic effects in both wild type and diabetic mice, which may explain the association between diets relatively low in carbohydrate and the elevated risk of cardiovascular events observed in clinical studies.     

Motion control of the ankle joint with a multiple contact nerve cuff electrode: a simulation study

The flat interface nerve electrode (FINE) has demonstrated significant capability for fascicular and subfascicular stimulation selectivity. However, due to the inherent complexity of the neuromuscular skeletal systems and nerve–electrode interface, a trajectory tracking motion control algorithm of musculoskeletal systems for functional electrical stimulation using a multiple contact nerve cuff electrode such as FINE has not yet been developed. In our previous study, a control system was developed for multiple-input multiple-output (MIMO) musculoskeletal systems with little prior knowledge of the system. In this study, more realistic computational ankle/subtalar joint model including a finite element model of the sciatic nerve was developed. The control system was tested to control the motion of ankle/subtalar joint angles by modulating the pulse amplitude of each contact of a FINE placed on the sciatic nerve. The simulation results showed that the control strategy based on the separation of steady state and dynamic properties of the system resulted in small output tracking errors for different reference trajectories such as sinusoidal and filtered random signals. The proposed control method also demonstrated robustness against external disturbances and system parameter variations such as muscle fatigue. These simulation results under various circumstances indicate that it is possible to take advantage of multiple contact nerve electrodes with spatial selectivity for the control of limb motion by peripheral nerve stimulation even with limited individual muscle selectivity. This technology could be useful to restore neural function in patients with paralysis.     

Computational Modeling of Open-Irrigated Electrodes for Radiofrequency Cardiac Ablation Including Blood Motion-Saline Flow Interaction

Radiofrequency catheter ablation (RFCA) is a routine treatment for cardiac arrhythmias. During RFCA, the electrode-tissue interface temperature should be kept below 80°C to avoid thrombus formation. Open-irrigated electrodes facilitate power delivery while keeping low temperatures around the catheter. No computational model of an open-irrigated electrode in endocardial RFCA accounting for both the saline irrigation flow and the blood motion in the cardiac chamber has been proposed yet. We present the first computational model including both effects at once. The model has been validated against existing experimental results. Computational results showed that the surface lesion width and blood temperature are affected by both the electrode design and the irrigation flow rate. Smaller surface lesion widths and blood temperatures are obtained with higher irrigation flow rate, while the lesion depth is not affected by changing the irrigation flow rate. Larger lesions are obtained with increasing power and the electrode-tissue contact. Also, larger lesions are obtained when electrode is placed horizontally. Overall, the computational findings are in close agreement with previous experimental results providing an excellent tool for future catheter research.     

The Altitudinal Patterns of Leaf C∶N∶P Stoichiometry Are Regulated by Plant Growth Form,Climate and Soil on Changbai Mountain,China

Understanding the geographic patterns and potential drivers of leaf stoichiometry is critical for modelling the nutrient fluxes of ecosystems and to predict the responses of ecosystems to global changes. This study aimed to explore the altitudinal patterns and potential drivers of leaf C∶N∶P stoichiometry. We measured the concentrations of leaf C, N and P in 175 plant species as well as soil nutrient concentrations along an altitudinal transect (500–2300 m) on the northern slope of Changbai Mountain, China to explore the response of leaf C∶N∶P stoichiometry to plant growth form (PGF), climate and soil. Leaf C, N, P and C∶N∶P ratios showed significant altitudinal trends. In general, leaf C and C∶N∶P ratios increased while leaf N and P decreased with elevation. Woody and herbaceous species showed different responses to altitudinal gradients. Trees had the largest variation in leaf C, C∶N and C∶P ratios, while herbs showed the largest variation in leaf N, P and N∶P ratio. PGF, climate and soil jointly regulated leaf stoichiometry, explaining 17.6% to 52.1% of the variation in the six leaf stoichiometric traits. PGF was more important in explaining leaf stoichiometry variation than soil and climate. Our findings will help to elucidate the altitudinal patterns of leaf stoichiometry and to model ecosystem nutrient cycling.     

Which Disposable Chest Electrode?

Chest electrodes are preferred to limb electrodes for cardiac monitoring, as limb movements are not restricted and produce less interference of the E.C.G. trace. Eight types of disposable chest electrodes were investigated to compare their performance, skin reactions, cost, ease of application, size, and skin–electrode impedance.Elema-Schonander electrodes were found to be the most efficient and the most expensive. In their application care was required to avoid severe skin reactions.Dracard electrodes were simple to attach, worked well without severe skin reactions, and were cheap. They are recommended for routine use. Smith and Nephew electrodes, a type of “multipoint electrodes” which do not require electrode jelly, frequently produced severe skin reactions, making them unsuitable for monitoring for periods exceeding 12 hours.     

Evidence of Heterosynaptic LTD in the Human Nociceptive System: Superficial Skin Neuromodulation Using a Matrix Electrode Reduces Deep Pain Sensitivity

Long term depression (LTD) is a neuronal learning mechanism after low frequency stimulation (LFS). This study compares two types of electrodes (concentric vs. matrix) and stimulation frequencies (4 and 30 Hz) to examine homo- and heterosynaptic effects indirectly depicted from the somatosensory profile of healthy subjects. Both electrodes were compared in a prospective, randomized, controlled cross-over study using 4 Hz as the conditioning LFS compared to 30 Hz (intended sham condition). Quantitative sensory testing (QST) was used to examine 13 thermal and mechanical detection and pain thresholds. Sixteen healthy volunteers (10 women, age 31.0±12.7 years) were examined. Depending on the electrodes and frequencies used a divergent pattern of sensory minus signs occurred. Using LFS the concentric electrode increased thermal thresholds, while the matrix electrode rather increased mechanical including deep pain thresholds. Findings after cutaneous neuromodulation using LFS and a matrix electrode are consistent with the concept of heterosynaptic LTD in the human nociceptive system, where deep pain sensitivity was reduced after superficial stimulation of intraepidermal nerve fibres. Cutaneous neuromodulation using LFS and a matrix electrode may be a useful tool to influence deep pain sensitivity in a variety of chronic pain syndromes.     

Influence of human model resolution on computed currents induced in organs by 60-Hz magnetic fields

The effects of human body model resolution on computed electric fields induced by 60 Hz uniform magnetic fields are investigated. A recently-developed scalar potential finite difference code for low-frequency electromagnetic computations is used to model induction in two anatomically realistic human body models. The first model consists of 204 290 cubic voxels with 7.2-mm edges, while the second comprises 1 639 146 cubic voxels with 3.6-mm edges. Calculations on the lower-resolution model using, for example, the finite difference time domain or impedance methods, push the capabilities of workstations. The scalar method, in contrast, can handle the higher-resolution model using comparable resources. The results are given in terms of average and maximum electric field intensities and current density magnitudes in selected tissues and organs. Although the lower-resolution model provides generally acceptable results, there are important differences that make the added computational burden of the higher-resolution calculations worthwhile. In particular, the higher-resolution modelling generally predicts peak electric fields intensities and current density magnitudes that are slightly higher than those computed using the lower-resolution modelling. The differences can be quite large for small organs such as glands. Bioelectromagnetics 18:478–490, 1997. © 1997 Wiley-Liss, Inc.