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We present a finite component based simulation and analysis method to depict the spacial extent of stimulation and the effects of electrode-tissue interactions in subretinal prosthetic devices. In peculiar, we estimate the threshold stimulation current needed to depolarize and arouse action potencies in the ganglion cells to be stimulated at a peculiar distance from the electrode.

This is achieved through the application of a threshold electric field to a inactive point nerve cell theoretical account of a ganglion cell under consideration. Threshold stimulation currents and the sidelong extent of the stimulation zone were computed for microelectrode stimulation in subretinal manner. Recent grounds indicates a lessening in threshold charge with clip following subretinal nidation. Consequently, to explicate the fluctuation in threshold stimulation currents, we propose a hypothesis based on an electrode-tissue spread.

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Threshold stimulation currents and electric resistances for different electrode-tissue spreads were computed. We validate the hypothesis with our simulation consequences that the alterations in electric resistance observed with clip in vivo can be chiefly attributed to the changing distance of the ganglion cells from electrodes due to alterations in electrode-tissue spread. Our simulation model proposes a convenient and practical method applicable for analyzing different electrode geometries used for retinal stimulation.Keywords: Biomedical microdevices, electrical subretinal stimulation, electrode-tissue interface, finite component method, implant declaration, retinal implant, ocular prosthetic deviceIntroductionElectronic retinal prosthetic devices aimed at reconstructing sight by exciting interior retinal nerve cells in human topics enduring from retinitis pigmentosa ( RP ) and age-related macular devolution ( AMD ) is a major focal point of biomedical research. When the outer retina is significantly degenerated, the interior beds undergo anatomical reorganization. A elaborate survey of patients with RP and AMD, every bit good as of carnal theoretical accounts of degenerative retinal diseases have demonstrated that significant figure of interior retinal cells can last and that ganglion cells remain functional even at the late phases of devolution. This has motivated many research groups to look into efficaciousness of extracellular electrical stimulation as a agency to reconstruct some ocular map by epiretinal, or subretinal microelectrode array attacks. Most prosthetic devices designed to interface with the retina rely on the hypothesis that a direct stimulation applied either to the outer beds of the retina or to the ganglion cell bed could reconstruct sight to the patients.

Ganglion cells form the inmost retinal cell bed, relaying the transformed ocular input to the encephalon, connoting that they are the marks in either subretinal or epiretinal stimulation strategies. They can be excited either by direct or indirect electric stimulation applied through the intermediate retinal web. Indirect stimulation of ganglion cells is by experimentation observed through activation of bipolar and amacrine cells and besides predicted theoretically by patterning bipolar cell stimulation. Based on the consequence that “ short stimulation pulsations are preferred for safety and efficaciousness considerations in subretinal prosthetic devices and that direct activation of ganglion cells will be necessary for dependable activation during high-frequency stimulation ” ; in this survey, we are patterning direct activation of ganglion cells by extracellular stimulation. A simple inactive theoretical account of extracellular stimulation of the haoma of a ganglion cell has been considered before for analytical surveies. We consider a ganglion cell as a point nerve cell and speculate its activation by delegating a cross-membrane depolarization status.

Spot clinch and extracellular multi-electrode recordings have been used to mensurate the threshold currents required to trip ganglion cells in both subretinal and epiretinal attacks. The threshold stimulation current applied on electrodes is one of the cardinal elements in finding the public presentation of a retinal prosthetic device. Palanker and colleagues approximated a threshold electric field of 3000V/m to execute analytical computations and draw anticipations on assorted parametric quantities affected during stimulation. In the present survey, we define a typical threshold as the minimal stimulation current required to obtain an electric field of 3000V/m at a certain distance between the stimulating electrode and the retinal ganglion cell.A recent psychophysical survey in unsighted human voluntaries demonstrated a strong lessening in threshold charge delivered by the electrodes as a map of clip after nidation. We hypothesize that this lessening is linked to the discharge form of the current above the electrode as a consequence of altering measured electric resistance. Impedance fluctuations may happen owing to alterations in electrode electric resistances due to assorted factors like physical and chemical alterations in electrodes, mechanical changes, retinal tissue remodelling in the procedure of devolution, etc. Under ideal nidation conditions and presuming that electrode corrosion does non happen, the electric resistance fluctuation can be explained by two chief theories:Gliosis theory – a proliferation of glial cells at the site of a tissue hurt or neural loss caused by surgical intercession and interpolation of the implant.

Gap theory – shortly after nidation, the retina may non be in intimate contact with the electrodes giving rise to a spread. This spread is predicted to be really little in the order of a few micrometers. It is likely that a close contact between the retina and electrodes is recovered within a few yearss. Similar post-implantation consequence of an electrode-tissue spread is besides observed between the mark tissue and the stimulation electrodes instantly after a deep encephalon nidation.In the instance of a glial reaction, new cells surround the electrode surface ensuing in retinal ganglion cells traveling further off from the electrode.

The extremely resistive glial cells increase the electric resistance and accordingly raise the threshold stimulation currents. On the contrary, when the retinal cells move nearer to the electrode and make full the electrode-retina spread, it has the same consequence of increasing the electric resistance due to the higher electric resistance of the retinal cells and finally cut downing the threshold of stimulation currents.Numbers of surveies related to the experimental finding of threshold stimulation currents in subretinal stimulation on assorted species in vitro have been reported.

Despite the extent of literature on the stimulation parametric quantities and methods, there is still a deficiency of understanding on the relationship between the electrical belongingss of the retinal tissue and the microelectrode specifications.The electrical belongingss of the retinal tissue influence the electric field generated at different deepnesss in the retina from the surface of the stimulating electrode. The retina is a multi-layered construction composed of different cell types and densenesss. As a effect, the electrical conduction in the retina is nonuniform. This inhomogeneity in the electrical conduction within the retina is represented chiefly by the high electric resistance of the retinal pigment epithelial tissue ( or photoreceptor bed ) and the reduced electric resistance at the ganglion cell bed. Sing the direct activation of a ganglion cell, this abnormality has a considerable impact on retinal stimulation in both epiretinal and subretinal stimulation strategies.

This consequence can be demonstrated by comparing the electric field distributions in a homogenous and superimposed theoretical account of a retina.A simple theoretical account to characterize the electrical belongingss of tissue is utile for imitating electric Fieldss in the retinal tissue. Sing the nonuniform nature of the retina and the convenience offered by computational tools, it is more accurate to utilize a multi-layer alternatively of the homogenous individual bed theoretical account to cipher electric field distributions in the retina. An electric theoretical account of the human retina derived from generalizing electric resistance measurings on an integral macaque retina is assumed for our simulations.

This theoretical account represents the retina by beds of different electrical electric resistances. Earlier numerical patterning surveies alternatively consider the retina as a homogenous medium bearing an electrical electric resistance of a‰¤1I©m.Finite component method ( FEM ) is one of the legion schemes available to analyze electric field magnitudes in the part environing microelectrodes during stimulation. It has been used antecedently in the field of retinal prosthetic devices for basic electrostatic possible distribution computations, applied to neuron theoretical accounts, 3-dimensional distribution of electric field of a planar electrode array and electrostatic interactions between two electrodes in assorted stimulation constellations.The purpose of this work is to foretell the threshold currents for subretinal stimulation of the retina by utilizing a superimposed electric resistance theoretical account of the retinal tissue.

The stimulation of the retina is based on the direct activation of ganglion cells pretermiting the part of the interior beds within the retina. We assume a inactive point nerve cell theoretical account of a ganglion cell with an electric field stimulation standard of 3000V/m. A sidelong extent of the stimulation zone is estimated at the ganglion cell bed deepness in the retina for a given value of stimulation current.

Finally, the consequence of an electrode-tissue spread on the threshold currents and electric resistance is analysed. We demonstrate a simple finite component simulation model aimed at foretelling the activationelectrode ( left ) and when a bed of PF is present between the retina and the electrode ( right ) .The spread is assumed to be filled with PF whose electrical conduction is assigned a value of 2I©m.Electric resistanceElectric resistance is computed as the ratio between the applied stimulation electromotive force and the ensuing current seen at the electrode accounting for the retina with or without an electrode-tissue spread. In all simulations, the electric field lines arising from the stimulation electrode were computed presuming a return ( land ) electrode in far field.The electric resistance can be modelled as parts from the electrode-electrolyte interface and the series complex tissue electric resistance.Animal theoretical account and electric resistance spectrometryElectric resistance recordings were performed on P23H line 1 rats at least 3 months old which were implanted with usage made polyimide-based implants under a well defined surgical intercession protocol.

As described antecedently, the implants consisted of a 1 millimeter round caput and a 40mm long shaft. The thickness was 22mm. There were four exciting 50A?m disc electrodes on each implant, surrounded by a big return electrode.

The electrode geometry used in this modeling survey is based on the electrode design used in these implants.The electric resistance spectra were acquired utilizing an Agilent 4284A electric resistance analyzer, controlled by proprietary Java package. Electrodes were connected to the electric resistance analyzer via a 150mm 5 pole-cable and a DIP-switch ( Grayhill 90HBW05 ) mounted on a printed circuit board, to which the electric resistance analyzer was connected.

Measurements were carried out utilizing a electromotive force of 50 to 1000mV RMS with each frequence spectrum taken between 100Hz-1MHz, with the expanse starting at the highest frequence. The measurings were made between one of the four 50I?m electrodes and the environing return electrode. The commercial package ZViewTM was used to analyze the electric resistance informations. The single electric elements patterning the electrode-tissue measuring apparatus were extracted utilizing a complex non-linear least square suiting algorithm ( CNLs ) built into ZViewTM.Stimulation amplitude of 50mV was selected for the subsequent electric resistance measurings to understate the hazard of tissue and electrode harm by inordinate current densenesss. Smaller amplitudes nevertheless contributed to noisy measurings. The tissue electric resistance extracted from the electrical tantamount theoretical account was calculated at 10kHz due to two chief grounds:Relevant as the applied stimulation pulsation breadth is about 0.

1ms in high frequence stimulation.This frequence appeared as a via media for the different sample frequence spectra studied, i.e. the largest alteration in electric resistance occurred around 100kHz right after nidation, whereas it occurred closer to 1kHz after a few hebdomads.FEM modeling:In the FEM simulations presented in this work, we have used a monopolar stimulation strategy for which the land electrode is located far off from the stimulation electrode.

The stimulation electrode is placed 10mm off from the surrounded 100I?m-wide land electrode on the same plane. An external bounding box of 18A?12mm drawn from the axis of the stimulation electrode and restricting the implant is used to restrict the calculation infinite. The retinal electric resistance theoretical account presented before is placed in close contact with the electrodes except during the instance surveies on electrode-tissue spread.Simulations were performed with the Comsol MultiphysicsA® finite component patterning environment. An axisymmetric finite component theoretical account of the stimulation and the land electrodes were created with a mesh declaration of 480805 nodes.

By default, the Delaunay engagement algorithm was utilised in Comsol for engaging the simulation volume. Meshing was chosen to be progressive, with the finest elements mensurating 40nm close to the stimulation electrode. The information extracted from the simulations were post-processed in Matlab to bring forth the needed secret plans.The time-varying bio-electric Fieldss, currents and electromotive forces in a biological medium can be examined in the conventional quasistatic bound. Under these fortunes, the electric scalar potency, V in the biological medium is defined by work outing the Laplace ‘s equation:where, I? and Iµr are the conduction and comparative permittivity of the affair severally.

The angular frequence of the drive stimulation is I‰=2Iˆf, Iµ0 is the permittivity of vacuity, and I is the fanciful unit. The current denseness on the electrode, J is related to V given by Ohm ‘s jurisprudence:We computed the threshold current and the electric resistance utilizing both harmonic and DC manners of stand foring the biological medium.In the harmonic manner, frequences of 1kHz and 10kHz were used based on the clip graduated table of normally applied pulsations for stimulation. The biological medium was represented by conduction and permittivity values taking into history the dispersive ( frequency-dependent ) belongingss of the tissue. The electrode-electrolyte interface electric resistance was besides implemented into this manner in the signifier of a thin-layer estimate as described by Cantrell et Al.

. Simulations indicated that above certain electrode potency, the possible bead seen across the electrode, besides known as overpotential, is negligible compared to the possible bead across the tissue electric resistance. Furthermore, an estimation of the capacitive constituent of the tissue electric resistance at the given frequence is more than an order of magnitude higher than the resistive constituent for both the frequences. These observations suggest that the simulation job could be reduced to a simple and computationally less expensive DC theoretical account.Consequently, a frequence independent DC theoretical account sing the biological medium as strictly resistive along with the ignored electrode interface electric resistance was modelled.

Simulations were performed under electrostatic conditions with an applied DC electromotive force between the stimulation and land electrodes. The FEM was solved utilizing a direct additive convergent thinker known as PARDISO. Appropriate Dirichlet, von Neumann and continuity boundary conditions were used to specify the electrode-retina interfaces, the insulating material-retina interfaces and the boundaries of the simulation jumping box. Material belongingss, in this instance, electrical electric resistances of Platinum ( Pt ) electrode and dielectric ( assumed as Polyimide ) were adjusted parametric quantities.

The current delivered by the electrode was computed by a boundary integrating of the euclidian norm of the current denseness over the land electrode.ConsequencesSpatial extent of the threshold currentFor a given deepness in the retina, the threshold current is increased for the cells located off from the axis of the electrode. In subretinal implants, the spacial extent of the stimulation represented in a cross subdivision of the retina merely above an electrode is shown in. The different curves show the country that is stimulated by the electrode with the 3000V/m standards at different stimulation currents. For case, the secret plan matching to the stimulation current of 3.5I?A applied on the electrode is the venue of electric field strength standard. The threshold current value on the electrode axis is 39mA for GL.

In this instance, theoretically, merely one cell is stimulated right above the electrode at the tallness measured subretinally. Higher values of exciting current correspondingly stimulate cells over a broad infinite above the electrode. This can be seen from the curve matching to the venue of 59mA stimulation current, where the sidelong stimulation zone extends to about 190A?m off-axis from the electrode for GL bed. The simulations show that the excitable cells in the GL part can be stimulated with threshold currents above 39A?A utilizing our subretinal electrodes.

It is besides seen that the ganglion cells can no longer be stimulated at a lower value than the threshold current.Figure: Spatial extent of threshold stimulation standard met for different electrode currents in a subretinal strategy. The points along the horizontal line at GL ( 175I?m ) represent the sidelong extent of stirred cells with two different currents.

The thick black horizontal saloon represents the location of the electrode.shows the development of the threshold currents with the sidelong distance from the axis of the stimulation electrode. The off-axis threshold currents increase about in a quadratic mode with sidelong distance from the electrode axis connoting that larger currents are required to excite broad country of cells off from the axis of the electrode.Figure: Development of the threshold currents ( 3000V/m standard ) in the GL vs.

the sidelong distance from the electrode axis. The thick black horizontal saloon represents the location of the electrode. A 10 % addition in stimulation current from minimal stimulation current consequences in a sidelong extent of 70-75I?m in the GL.A maximum admissible current during stimulation is based on the hypothesis of an electrochemical bound. For an electrode current ~69I?A applied for 0.1ms on a 50I?m diameter phonograph record electrode, the electrochemical bound of ~0.

35mC/cm2 for Platinum is reached. It is seen that the computed minimal threshold stimulation current of ~39I?A required for exciting the GL is about a factor two below the electrode current at the electrochemical bound.Consequence of a spread between the electrode and the retinal tissueThe electrode-tissue spread plays an of import function in the electric possible distribution above the stimulation electrode and accordingly the strength of the threshold currents arising from the electrode. There is besides a important impact on the electric resistance due to the infinite between the electrode and the retinal tissue being bit by bit replaced by a fluid more conductive than the retina itself. We will now analyze both these effects of a spread between the electrode and the tissue by changing the spread between the retina and implant surface in the FEM theoretical account.Consequence on threshold currentsshows the dependance of the on-axis stimulation current required to make the 3000V/m standard in the GL as a map of the spread between the stimulation electrode and the bottom surface of the retina.

It is seen that the threshold current additions quickly in GL as the spread between the electrode and the tissue increases. As a consequence, the electrode electrochemical bound is reached when the spread exceeds 5I?m for GL stimulation.Figure: Dependence of the on-axis threshold current with the electrode-tissue spread at GL in the retina.Consequence on electric resistanceKnowledge of electric resistance can be used as an indirect measuring of the electrode-tissue spread. It is besides good known that Advanced Optical Coherence Tomography ( OCT ) imaging technique can be used to find the distance between an electrode and tissue in in vivo post-implantation.Our simulation model can foretell the spread between an electrode and tissue by associating computed values with existent measurings of electric resistance. shows the computed electric resistance as a map of the spread between the retina and the stimulation electrode.

The electric resistance decreases with increasing spread values. A spread of 50I?m is sufficient to diminish the electric resistance by a factor of 10 and about achieve a electric resistance equivalent to that of the PF. The line at 36kW corresponds to the computed electric resistance of the PF as seen by the stimulating electrode with regard to the land.

In vivo electric resistance measurings ( ) demonstrate that the electric resistance measured merely after subretinal nidation in rats is appreciably lower than the expected value obtained when there is a close contact between the electrode and retina. This corresponds to the hypothesis of an electrode-tissue spread. Typically, after 20 yearss, the electrode electric resistance additions to a high value.

It is observed from extra measurings after two months that the attained high value remains stable. This state of affairs corresponds to a little electrode-tissue spread in our theoretical account.Figure: Variation of electric resistance with alterations in electrode-tissue spread.Figure Evolution of the in vivo electrical electric resistance of retinal tissue measured at 10 kilohertz in rats during a two-month period. The electric resistance measurings were performed with deep-rooted rats that exhibited low hempen reaction.DiscussionUsing FEM simulations, this study investigated the appraisal of spacial extent of the threshold currents and the development of threshold currents with sidelong distance in the GL for subretinal stimulation. The consequence of electrode-tissue spread on the threshold current and electric resistance was besides studied.

Threshold currentStimulation experiments conducted by independent research groups indicate that the thresholds for triping the ganglion cells vary depending on the mode of activation – direct or indirect, pulse type, time-course, mutual opposition and many other unknown parametric quantities. Based on our premises, the computed thresholds for direct activation were expressed as charge densenesss. The value is in the order of 0.

2mC/cm2 in the GL for a balanced, cathodic-first, rectangular stimulation with a pulse continuance of 0.1ms. These comparison with the threshold charge denseness values obtained from in vitro subretinal stimulation tests by Tsai et Al. . They by experimentation determined that short balanced biphasic pulsations of the order of 0.1ms/phase straight activated retinal ganglion cells with a threshold charge denseness runing between 0.

06mC/cm2 and 0.12mC/cm2.Sing the restrictions of our inactive theoretical account, the computed thresholds were close to the values obtained by Tsai et Al.

Based on the comparing with their measurings, we predict a higher bound for the threshold currents.Spatial extent of stimulationThe spacial declaration of a local electrical stimulation triggered by a monopolar electrode is related to the spacial extent of the evoked retinal response. The retinal response is straight related to the activation of spatially distributed ganglion cells in the GL. We computed a near-quadratic fluctuation of threshold current with increasing sidelong distances from the electrode Centre for the geometry presented. During existent experiments, to guarantee stimulation, there is a inclination to utilize stimulation currents 10-20 % above the pre-determined minimal threshold current.

For a 10 % surplus on the minimal threshold current, it is observed from that a spacial part of 70-75I?m is in the zone of stimulation at GL. Eckhorn et Al. quotation mark in their paper refering in vitro experiments performed by Stett et Al. in normal and degenerated rat retinas that the spacial declaration at retinal degree, subretinally stimulated by multi-electrode arrays, is at least 70I?m. This restricting value is a good starting point to tie in with the spacial declaration computed at the GL in our FEM theoretical account.

Our FEM model predicts a realistic spacial declaration for the fake geometry and retina theoretical account presented. Consequently, these values can be used as a guideline for finding denseness of stimulation electrodes needed to achieve sensible declaration utilizing current and futuristic retinal implants.Consequence of electrode sizeIn this survey, effects of an nonuniform retina and the electrode-retina spread on subretinal stimulation utilizing a 50I?m diameter phonograph record electrode were computed. Increasing electrode size has proven to increase thresholds in epiretinal stimulation. It besides has the consequence of cut downing the spacial declaration for epiretinal stimulation.

In contrary to these consequences, we performed simulations in subretinal manner to foretell the direct ganglion cell stimulation thresholds and the sidelong extents. The sidelong extends for smaller electrodes ( up to 5I?m ) were merely somewhat lesser than with the 50I?m phonograph record. For larger sizes ( up to 200I?m ) , both the stimulation threshold and the sidelong extents increase marginally.shows the computed values for each of the electrode sizes simulated with the simulation model.TableComputed thresholds of stimulation and sidelong extents for different electrode sizesElectrode size ( I?m )Stimulation threshold ( I?A )Lateral extent ( I?m )539.565-701039.565-702539.

6705040.5751004310020054.7140We besides deduced that in smaller electrodes up to 50I?m, similar values of threshold currents imply big current densenesss finally giving rise to electrochemical jobs during stimulation. Additionally, cut downing sizes signify larger electric resistance that causes higher electromotive forces on the electrode surface.

This has an impact on the electromotive force presenting capablenesss of the power beginning used for firing up the electrodes.Consequence of electrode-tissue spreadIn chronic retinal nidations, there have been no observations of a fibrotic or gliotic capsule environing the implant country. A reference on the stimulation electrodes unaffected by corrosion besides indicates that they are largely electrochemically stable. To our best cognition, expressed record of electric resistance measurings over a period in clip after subretinal nidation is non available. But, the recent consequences on post-implantation threshold electromotive force measurings with clip along with computed threshold charge suggest a clip fluctuation of electric resistance in conformity with our hypothesis. This may connote that the alteration in electric resistance is chiefly due to the spread between the tissue and the electrode.

Our FEM calculations on the consequence of an electrode-tissue spread on the electric resistance anticipate that it is the spread between the electrode and the retina which contributes chiefly to the addition of electric resistance and non the electric resistance of the encapsulating tissue environing the deep-rooted electrode in retinal nidations.From the simulation consequences it can be concluded that the electric resistance measured instantly after subretinal nidation may match to the electrode-tissue spread filled with PF. The value of the electric resistance reached post-implantation after a certain settling period corresponds to the electric resistance measured at a bantam electrode-tissue distance.

This hypothesis is supported well by the electric resistance fluctuation over clip measured in vivo as demonstrated in. Consequently, the low electric resistance measured instantly after nidation corresponds to a escape of current ensuing from the spread nowadays between the electrodes and the tissue. The addition of electric resistance is a mark of the accomplishment of an familiarity between them.

Figure Relationship between the threshold current and the corresponding electric resistance for increasing electrode-tissue spread values. No spread ( 0mm ) corresponds to an electric resistance of 320kA© as shown in. Higher values of spread consequence in lower electric resistance and higher thresholds.

Interestingly, we can infer a relationship between fluctuations in threshold current with alterations in electric resistance. The association between them is presented in which is basically a combination of and. Similar behavior has been observed in measurings with epiretinal implants on human topics.

We postulate that supervising electric resistance is non merely an effectual and simple method to look into the unity of the implant ; but with an appropriate electrical theoretical account of the retina it can foretell a realistic stimulation current.DecisionUnderstanding electrode-tissue interactions is a cardinal to efficient and successful stimulation by a retinal prosthetic device. Through the current survey, we have shown that it is possible to analyze subretinal stimulation using an electric electric resistance theoretical account of the retina in a finite component simulation model. The undermentioned decisions can be drawn based on our simulation survey:A superimposed electrical theoretical account of a retina is more realistic and accurate in comparing to a homogenous theoretical account.Using the 3000V/m standard on a inactive point nerve cell theoretical account of a ganglion cell consequences in foretelling the maximal bounds of threshold current and sidelong extent of stimulation to which in vivo experiments conducted by assorted research workers can be benchmarked.The consequence of an electrode-tissue spread is to increase the threshold currents and a corresponding lessening in the electric resistance. The increasing electric resistance related to a closer propinquity of retina to the electrodes in our theoretical account is good supported by in vivo tissue electric resistance measurings.

Therefore, the electric resistance can be a tool to supervise electrode-tissue spread and predict stimulation current at the same time.We conclude that the importance of executing electric resistance measurings after engrafting stimulation devices, guaranting the close contact of mark nervous tissue with the stimulation electrodes, is instrumental in successful nervous stimulation. With farther polish and proof, it may be possible to utilize our method to plan and imitate different electrode geometries that optimise stimulation efficiency of the retina, and the techniques used in this method can be expanded to electrodes used in other nervous stimulation devices.Conflict of Interest StatementThe writers declare that the research was conducted in the absence of any commercial or fiscal relationships that could be construed as a possible struggle of involvement.