Fluid-mechanical compliant actuator for the insertion of a cochlear implant electrode carrier

Mechanism and Machine Theory 142 (2019) 103590

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Review

Fluid-mechanical compliant actuator for the insertion of a cochlear implant electrode carrier Lena Zentner a,∗, Stefan Griebel a, Silke Hügl b a b

Technische Universität Ilmenau, Compliant Systems Group, 98693 Ilmenau, Germany Hannover Medical School, Clinic for Laryngology, Rhinology and Otology, Carl-Neuberg-Str. 1, 30625 Hannover, Germany

a r t i c l e

i n f o

Article history: Received 16 May 2019 Revised 22 July 2019 Accepted 6 August 2019

Keywords: Compliant actuator Cochlear implant Fluidic actuation Silicone structure

a b s t r a c t In this paper an insertion method of electrode carriers of straight and curved form is shown for the use in cochlear implants. The aim of using a fluid-mechanical actuator is to minimise the contact between the electrode carrier and the cochlea and consequently avoiding damage during its insertion. First, the synthesis method used for beam-shaped fluid-mechanical actuators is shown. The model-based scaling of parameters demonstrates that actuators must be geometrically similar to reach the same form by same inner pressure. This fact facilitates the experimental investigations using up-scaled demonstrators. Electrode carriers as fluid-mechanical actuators of straight and curved form are designed by theory of curved rods for large deformations. For these carriers, a gentle insertion used a stylet and fluidic actuation in combination and is described analytically by the above mentioned theory. The results demonstrate that the insertion of a curved electrode carrier requires lower pressure and does not need any inner pressure in the end position. The measurements of the deformation behaviour of carrier demonstrators prove the validity of the analytical model. The maximum value of the differences between calculated and measured results of the inner pressure is about 10%. © 2019 Published by Elsevier Ltd.

1. Introduction Patients suffering from a severe to profound hearing loss, caused by impaired hair cells within the inner ear (cochlea), can be treated with a cochlear implant (CI) system. It consists of an external part, with microphone, speech processor and sender coil, and an internal part, with a receiver coil and the electrode carrier. The electrode carrier has to be implanted into the three-dimensional (3D) spiral-shaped structure of the cochlea and allows for direct electrical stimulation of the spiral ganglion neurons (dendrites or soma), which form the auditory nerve [1–4]. Thereby, the non-functional hair cells are bypassed, resulting in a regained hearing impression for the patients. Clinically used CI electrode carriers are manufactured either in a straight or in a curved form (Fig. 1) [5]. Being implanted into the spiral-shaped cochlea, the initially straight electrode carriers rest along the outer wall of the cochlea and are thereby forced into a bent form, which is called a lateral final position. Initially curved electrode carriers remain closer to the inner wall of the cochlea, called perimodiolar position. A close distance between the stimulating contacts on the electrode carrier and the stimulated neurons leads to decreased threshold and improved frequency selectivity [6–8]. As the stimulated neurons are situated around the spiral axis of the cochlea (modiolus) and as the auditory nerve emanates from ∗

Corresponding authors. E-mail addresses: [email protected] (L. Zentner), [email protected] (S. Hügl).

https://doi.org/10.1016/j.mechmachtheory.2019.103590 0094-114X/© 2019 Published by Elsevier Ltd.

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Fig. 1. Cochlear implant electrode carrier on a milimetre scale.

the modiolus, a perimodiolar final position of the electrode carrier within the cochlea may be beneficial. A perimodiolar final position may be achieved by an initially curved electrode carrier (Fig. 1), which is held straight for the first part of the insertion through an inner stylet or an outer sheath [9,10]. During insertion, the electrode carrier together with stylet or sheath is inserted for the first few millimetres. After that the stylet or the sheath is being held in place while the carrier is advanced further into the cochlea and thereby retains its initially curved shape [9,10]. Apart from those commercial carriers, there are more experimental approaches [11] to achieve a perimodiolar positioning using hydrogels [12], shape memory actuators [13], tubular manipulators [14] or magnetic guiding of the implant during insertion [13,15]. When treating patients with an existing residual hearing, the preservation of all intra-cochlear soft and bony tissue structures is even more important, as damage to these structures and the still intact hair cells may lead to complete deafness after surgery. That risk has to be minimised in order to enable the beneficial simultaneous use of the cochlear implant along with the residual hearing capability (electro-acoustic stimulation or EAS) [16]. In order to refine the insertion process of an electrode carrier, a fluid-mechanical compliant actuator for the use within an electrode carrier is introduced. We use fluid-mechanical actuation in the form of a compliant bending actuator. The advantage over other types of drive is that no electric auxiliary power is required on the electrode carrier itself for generating a bending movement. The pressure generation can be placed remotely or generated by the surgeon independently by, for example, a pressure on a rubber ball (principle like a manual blood pressure monitor). The influence of electromagnetic fields is thus reduced to a minimum. In the majority of cases bending actuators consist of two different materials, which are materially interconnected. Here, the properties are advantageously combined. On the one hand, they consist of a tensile material, which is additionally limp. On the other hand, there is a compliant, elastomeric material over which one or more cavities are formed. If the cavities are subjected to fluid pressure inside, the elastomeric material expands. The second material is used to limit the strain and create a bending. In addition, there are also solutions which have fibre reinforcement in a radial direction and are known as pneumatic muscles or McKibben muscle. Normally, such actuators only lead to an axial shortening, but with geometric or material asymmetry [17] also bends are possible [18–21]. Due to the material-side bond (composite material) it is possible that the final actuator consists of only one part with a special shape. Advantages of these monolithic compliant structures are that they have a large functional integration and partly superior to rigid body systems [22]. The application as an electrode carrier for a cochlear implant system is interesting, because they have a small and smooth surface, which minimizes the risk of infection, like [23]. Also, they must have small dimensions, like [24]. The vast majority of the known bending actuators have a plurality of chambers, which, however, are connected to one another and form a common cavity. For these reasons, they are rugged or ribbed on the outside [25–29]. However, the entire cavity can also be encapsulated ribbed [30–32]. There are also simple cavities possible, which are axially straight [33–35]. The actuators are always manufactured in a straight initial shape and show a circular shape in the actuated state. To achieve other shapes, asymmetries are applied, like sleeve spacings [36], chambers at an angle with the longitudinal axis [37], converging towards the top [38] or multiple cavities that can be controlled separately [39–42]. These solutions are complex for the production and are not flexible adaptable to a given form. In addition, there is no synthesis method that allows individual solutions to be found within a short period of time. The aim of the contribution is to provide the methods for the development of actuators for medical technology. Using the example of a cochlear implant, it is demonstrated that the developed methods are suitable for the design of a fluidmechanical actuator for the use in a cochlear implant electrode carrier. Such bending actuator as electrode carrier with a curved shape enables the surgeon to avoid any contact and thereby possible risk to damage the intra-cochlear soft and bony structures. The thereby achieved structural integrity is a prerequisite for the preservation of residual hearing. A bending straight shaped fluid-mechanical actuator for the use in a cochlear implant electrode carrier was described previously in [43]. In addition to this, the helical/curved target geometry is chosen as the geometry for the unpressurised state and the needed asymmetry for achieving a straight shape under pressure is shown with the synthesis process described in [43]. Additionally, both electrode carriers were shown with a new method of insertion process. Here the combination of a relative movement between stylet and electrode carrier with actuation of the fluid actuator at the same time is shown. After this, the required pressure for both actuators were compared. Supplementary, the production process of the curved

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Fig. 2. Demonstration of the principle of fluidic actuation. a: straight-shaped electrode carrier, which takes on a curved shape as interior pressure rises (p > 0). b: curved-shaped electrode carrier, as interior pressure p rises, the curvature becomes smaller including becoming completely straight.

shape demonstrators and the comparison of deformation behaviour for the largest “free length” of the demonstrator to the analytical model are shown. 2. Actuation of the electrode carrier The compliant carrier needs to be designed in such a way that its curvature can be changed during insertion to correspond to the natural curvature of the scala tympani, which is one of three fluid filled chambers within the cochlea. In order to achieve the desired deformation behaviour of the electrode carrier, the body of the carrier contains a cavity to which pressure can be applied fluidically. In the carrier side wall a fibre is embedded, which has a very low section modulus against bending, and is nearly non-stretching. There are two possibilities for the initial form of the carrier: straight or curved form. The pressure increase inside the carrier causes expansion of one side of the silicone wall, whereas expansion of the other side is prevented by the embedded fibre (previously described in [44,45]). This causes the straight electrode carrier to curve as shown schematically in Fig. 2a. The curved electrode carrier changes its shape to a straight form, if the pressure increases (Fig. 2b). By increasing of pressure inside the carrier, the stiffness of the carrier is rising. At the beginning of the insertion, the initially straight-shaped carrier has a low stiffness, which rises during the continuation of the insertion and the carrier’s increasing curvature. This variant is easier to manufacture. The corresponding synthesis and manufacturing process was shown in detail in [45], and [43]. In contrast thereto, the stiffness of the curved electrode carrier becomes lower with continuous insertion. This form has the advantage that the CI electrode carrier retains in its desired curved state after insertion without requiring that internal pressure be maintained and therefore has the least stiffness. To facilitate the manufacturing of the demonstrators, the form of the carrier inner wall (cross section of the cavity along the length of the electrode carrier) and outer wall (cross section of the silicone body along the length) will be designed in a conical and/or cylindrical shape. There are four options to form the electrode carrier by combination of conical or cylindrical shape for inner or outer wall. Two of these possibilities with a fibre laying parallel to the carriers´ longitudinal axis are expedient and shown in Fig. 3a,b for an initial straight-shaped electrode carrier. Due to softer insertion and the decreasing cross-sectional area of the scala tympani from base to apex, the conical outer form of carrier will be chosen. Its cylindrical inner form allows simpler manufacturing. Therefore, the version shown in Fig. 3b will be considered as the suitable shape of the carrier in the following description. Other work of the present authors in [44] has previously described ideas regarding the principle of electrode carrier curvature changes as well as the suitability of the theory of curved rods. The possibility and advantages of combining the finite element method (FEM) with analytical methods for the synthesis of hollow compliant rods were shown in [43]. The authors presented the experimental determination of material parameters for a conically shaped electrode carrier in [43]. This allowed the more exact calculation of elastic modulus, yielding better results for the synthesis of a carrier. Additionally, synthesis of an individualised shape was described along with the conical shape with the aim of improved adaptation to the two-dimensional (2D) representation of the individual 3D spiral of the cochlear turns [46]. In this contribution, the authors first give an overview of the synthesis method used for the electrode carriers. Then, the model-based scaling of parameters, analytically and in general form, is carried out. In order to demonstrate the design of

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Fig. 3. Two possibilities (out of the four options) to form the electrode carrier by combination of conical or cylindrical shape for inner or outer geometry: a – conical inner geometry and cylindrical outer geometry, b - cylindrical inner geometry and conical outer geometry; in both cases the embedded fibre has a constant distance to the rod axis.

electrode carriers using the above mentioned synthesis method, carriers of straight and curved form are considered with the aim of adapting to the shape of the cochlea. For a gentle insertion, a relative movement between stylet and electrode carrier and fluidic actuation is used in combination at the same time, as patented in [47] by the authors. The insertion process is shown for carriers of straight and curved form in comparison. The electrode carrier will be considered without contact electrodes. The described methods may be used also for carriers with electrodes (the sections with electrodes must be modelled as straight parts) and for any other actively-deformable, hydraulically-actuated medical instrument. The measurements of the deformation behaviour of carrier demonstrators prove the validity of the analytical model. The methods have been generally derived and can therefore be applied for all compliant beam-formed actuators with a cavity, an embedded thread or strip and any stylet position. 3. Modelling and synthesis of the electrode carrier The aim is to be able to cause a specifically defined curvature change of the newly designed electrode carrier with respect to the cochlear shape. In order to achieve that, the geometry of the carrier needs to be developed in such a way that its final shape corresponds to the shape of the cochlea given a specific internal pressure. Model-based synthesis is carried out with this aim, combining FEM with analytical modelling. The analytical modelling is based on the theory of curved thin rods for large deformations. On the one hand, the non-linear material properties of the compliant electrode carrier can be represented very well with FEM, whereas synthesis is more complicated to execute using FEM. On the other hand, the analytical modelling method utilised is immensely suitable for synthesis but only linear material parameters can be described. The strain of the electrode carrier is almost evenly distributed along the rod axis during curvature changes under internal pressure, meaning a single elastic modulus and the corresponding linear material properties can be approximated for the particular pressure ranges in the analytical model. First the hyperelastic material properties of the carrier are determined by uniaxial, equibiaxial and pure shear load cases. Then a cylinder-shaped test geometry closed on one side is selected along with a similarly cylindrical cavity. The test geometry will be simulated using FEM for various internal pressures and the resulting curvatures calculated. The curvatures will then be fed into the analytical model, allowing the elastic moduli to be determined for the individual internal pressures. After that, a sought-after new carrier geometry will be found, also based on the analytical model. The model-based synthesis method is summarised in short: 1) FE-model simulation of cylindrical test geometry with given material and geometrical properties, output: curvature depending on pressure; 2) Analytical model of test geometry with curvature from 1), output: Young’s modulus depending on pressure; 3) Analytical model with Young’s modulus from 2) for electrode carrier to reach the desired curvature of cochlear inner wall, output: geometry of the new electrode carrier. Two different types of the electrode carriers, the initially straight and the initially curved form, were designed by the above described method [43,47]. In order to facilitate the manufacturing, the inner radius of the cavity is designed to be constant along the rod axis. Likewise, the embedded fibre has a constant distance from the rod axis, while the outer form is conical (see Fig. 4). These carriers will be described in Section 3.2 in a straight and a curved form. For the same reason of simplify the manufacturing, the analytical models and physical demonstrators will be operated with larger dimensions compared to the real cochlear implants. In the next section the analytical evidence of the scalability is given, which applies to both of the above mentioned forms (straight and curved). 3.1. Parameter scaling The geometry under consideration is a hollow rod of the length L, with an either straight or curved form with initial curvature κ 0 . It possesses the outer radius r, which is proportionate to coordinate of the fibre s, and inner radius ri of the cylindrical inner cavity (see Fig. 4). The fibre runs parallel to the axis of the rod and is embedded at a distance h therefrom. According to the theory of curved rods for large deformations [22,48], the internal bending moment M can be written

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Fig. 4. The geometry of carrier, straight form or curved form, with a conical outer form (radius r2 to r1 ), a cylindrical inner cavity and an embedded fibre.

Fig. 5. Parameter scaling for a cylinder-shaped rod: a – cross-section of the rod, b, c – geometrically similar cylinder-shaped rods with embedded fibres and cavity, made of identical material and at the same internal pressure, attain a geometrically similar shape.

depended of the curvature κ in the rod coordinate system with the basis vectors {e1 , e2 , e3 }:

dM = 0, ds

M (L ) = hpπ ri 2 ,

M = E I3 (κ − κ0 ).

(1)

From that, Eq. (2) follows for the dependency of the curvature κ on geometric parameters, internal pressure and elastic modulus E.

κ=

hpπ ri 2 + κ0 E I3

(2)

Previously it was proven that geometrically similar cylinder-shaped rods with an embedded fibre and a cavity closed on one side attain a geometrically similar shape for the same material and the same internal pressure (Fig. 5b,c) [43]. This result can be used for further investigations for straight and curved rods, as the knowledge gained from the analysis of enlarged models can be transferred to models of any arbitrary size. Therefore, 9.5:1-scaled systems will be used for further theoretical and experimental investigations. The described method for scaling can also be used for carriers with electrodes. The sections with electrodes must be modelled as straight parts embedded in the carrier. Such structures can also be scaled. According to the analytical theory, the straight parts should be scaled with the same coefficient as the carrier. The analysis and synthesis methods described in this contribution are feasible to be used for any other compliant hydraulically-actuated actuator with hollow and thread and with or without electrodes. 3.2. Designed electrode carriers In the following, the design of the initially curved-shaped electrode carrier on a scale of 9.5:1 is described, to be consistent with later mentioned demonstrators (see chapter 4.), which were fabricated in order to verify experimentally the

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Fig. 6. Cochlear walls and derived form of fibre for electrode carrier which suits the cochlear shape under 6 bar, both on a scale of 9.5:1.

analytical findings. The executions correspond to those made for 3:1 scaled straight electrode carriers in [43]. Because the fabrication of an initially curved-shaped functional demonstrator in laboratory conditions is more ambitious than the fabrication process of straight ones, the specific scaling factor had to be increased to 9.5:1. Additionally, and in contrast to [10], the 2D curvature of cochlea inner wall κ C in the basal turn is described using a polynomial approach depended of s:

κC (s ) = 1.16 · 10−1 +1.09 · 10−2 s+6.27 · 10−4 s2 +2.04 · 10−5 s3 .

(3)

This way allows the design of the carrier with high accuracy, because unlimitedly high polynomial degrees could be selected to achieve the specified accuracy. In this case, the maximal difference of for example 0.1 mm between the given inner wall geometry and the curve (3) was set as criterion. Additionally, the polynomial form of the curvature facilitates further analytical calculations. The distance between the cochlear inner wall and the embedded fibre of the carrier is a = 5.7 mm (Fig. 6). That value is chosen in consideration of the approximate dimensions of the clamped end of the carrier derived from the dimensions of the straight electrode carrier by using the upscaling. The initial curvature of this desired position of the curved carrier is κ 0D :

κ0D (s ) =

κC (s ) . 1 + a κC (s )

(4)

The coordinates x and y of the curved fibre of the carrier, which suits the cochlear inner wall, can be achieved by Eqs. (5).

d θ0 D = κ0D , ds

θ0 D ( 0 ) = 0 ,

d x0D = cosθ0D , ds

x0D ( 0 ) = 0,

d y0D = sinθ0D , ds

y0D ( 0 ) = 0

(5)

The parameters of the curved carrier are set to be h = 1.65 mm and ri = 0.95 mm. The length of such fibre is L = 126 mm. The outer radius of the carrier r = r(s) is to be calculated. Thereby, the aim is to achieve the straight form by inner pressure of 6 bar. The outer radius here can be calculated analogous to Eq. (1):



r (s ) =

4hpri 2 ri (ri +4h ) + 4h − κ0D E 2

2

2

4

0 . 5

0.5 − 2h

2

(6)

The determination of the elastic modulus E is shown in [43] with the result of E = 0.826 MPa. The outer radius of the carrier calculated by (6) and shown in Fig. 7 is very unfavourable for production due to its non-linear course. Therefore, it will be approximated by a straight line, yielding a proportionality to coordinate of the fibre s. Following parameters were obtained: r1 = 2 mm, r2 = 2.7 mm. The approximation curve at inner pressure of 6 bar does not necessarily have to be a strict straight line (Fig. 8). Both carriers, straight and curved, can be developed independently of each other. Only the fibre with the length L has to be embedded at different sides of the carrier wall for straight and curved carriers. 3.3. Methods of implementation and simulation of the insertion The anatomical variation of the cochlea geometry has already been widely investigated. Studies investigated corrosion casts of the cochlea [49] as well as micro-computed tomography scans [50] and found anatomical variations in the total

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Fig. 7. Graph of the resulting outer radius along the rod axis of the 9.5:1-scaled electrode carrier for r: 1 – using Eq. (6) and 2 – a regression line for a conically shaped carrier.

Fig. 8. Curved electrode carrier, which suits the cochlear shape in its non-pressurised state and is nearly straight under 6 bar.

length of the cochlea (metric and angular length) [51,52], in the distance from the round window to the lateral wall on the opposite side (A-value) and the thereto perpendicular distance through the modiolus (B-value) [53] and in the vertical path along the cochlear length [50]. Recently, approaches to estimate the cochlear length prior to surgery have been investigated to support the choice of a suitable cochlear implant for individual patients [54,55]. In order to address these anatomical variations a patient-specific insertion process, which enables the surgeon to adapt both, the insertion depth and the curvature of the implant independently form each other, is evaluated in this section. To reach a successful insertion, only a part of electrode carrier, which is inserted into the curved section of cochlea, should be actuated. The other part of the electrode carrier, that reaches only into the first part of the cochlear basal turn, which can the approximated to be linear, must be kept in a straight form. In order to achieve this, a stylet will be used in combination with hydraulic actuation (Fig. 9a–c). At the beginning of the insertion and to overcome the nearly linear part of the basal turn, the stylet is kept completely inside the carrier to hold it straight. After that it is gradually moved out of the electrode carrier (relative movement between stylet and carrier), by insertions movement of the carrier further into the cochlea, enabling the stylet-free part of the carrier (which signed with Lf ) to be curved. This part is curved by hydraulic actuation. A duct in the centre of the stylet enables the entry of the fluid and therefore the actuation of the free part of carrier. Such a solution requires a seal between the stylet and the holder for the electrode carrier. Also, a technical solution is possible in which the electrode carrier is used simultaneously as a seal. Of course, at the same time a relative movement between stylet and electrode carrier and a tightness up to 6 bar must be made possible. Another design version of the stylet is an outer stylet, such as a sheath, with or without gap (Fig. 9c). Then, the carrier will be inserted into the stylet and is pushed out of it during insertion to facilitate the actuation of the free part of carrier. This method of insertion can be used for straight as well as curved carriers. However, the initially curved carrier is beneficial for future clinical application, as there is no need for applying pressure after the immediate process of insertion. The length of the stylet-free part of the carrier is Lf and only this length can be curved. For this part, the equations for large deformations of curved rods can be written:

dM = 0, ds

M (L f ) = hpπ ri 2 ,

M = E I3 (κ − κ0 ).

(7)

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Fig. 9. Implementation of insertion by combination of stylet relative movement and hydraulic actuation; a – straight-shaped electrode carrier, ps is the pressure, which causes the shown bending, b – curved-shaped electrode carrier, pc is the pressure to achieve the straight form for the free length Lf , c – cross section of three different versions of the stylet.

The area moment of inertia with respect to e3 is given by following equation:

I3 =

π 4







r 4 − ri4 + π r 2 − ri2 h2 ,





Lf s with r = r1 + (r2 − r1 ) − . L L

(8)

When the curvature κ is calculated, then the coordinates of the carrier fibre can be found:

dθ = κ, ds

θ ( 0 ) = 0,

dx = cos θ , ds

x ( 0 ) = 0,

(9)

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Fig. 10. Insertion of straight electrode carrier with stylet is shown in ten steps with different lengths Lf in equal steps: Lf = 0.1 i L, i = 1,…,10; electrode carrier has 3:1-scaled shape.

dy = sin θ , ds

y ( 0 ) = 0.

(10)

θ is the angle between the x-axis and the tangent to the neutral axis (the embedded fibre) of the rod (Fig. 5). The initial curvature κ 0 is equal 0 for the straight carrier and characterises the initial shape of the curved carrier. To find the right pressure for each length Lf , the pressure is changed until the minimal distance between the cochlear inner wall and the carrier wall remains nearly 1% of the length L of the carrier. The pressure is changed (increased) in steps of 0.05 bar. Ten different lengths Lf are chosen in equal steps. The calculation method is valid also for both straight and curved carriers and returns analytical results for the curvature κ by Eq. (2) with I3 from (8) and angle θ by (9) of the carrier with i = 1,…,10:

κ=

4hri2 p     + κ0 , E r 4 − r 4 + 4 r 2 − r 2 h2 i

θ=

i

4 phri2





E (r2 − r1 )(2 + ri2 ) 4 + ri2 +





4 + ri2 arctanh

r 4 + ri2

− arctan

r1 − ( r2 − r1 ) r − arctanh ri ri



with

arctan 

r = r1 + ( r2 − r1 )

Lf L

r1 − ( r2 − r1 )





Lf L

4 + ri2

+ κ0 s



Lf s − . L L

(11)

By the curvature the shape of the carrier is uniquely determined. The calculated values for θ are applied for the establishment of the suitable carrier shapes for different lengths of Lf . The positions of the deformed carrier with the length Lf in the Cartesian coordinate system are calculated numerically according to (10). 3.4. Results of the insertion simulation The insertion is illustrated for a straight carrier in Fig. 10 and for a curved carrier in Fig. 11. In the process of insertion, while the relative movement between stylet and electrode carrier is executed, the free length Lf is increased. The suitable pressure for each Lf is found by increasing it in steps of 0.05 bar by model equation in Section 3.3. The considered condition is that the carrier does not yet touch the inner wall of the cochlea. At first contact, the calculation is stopped and the pressure from the previous step is taken. With this method, the steps can be chosen with varying degrees of fineness. The accuracy, with which the pressure can be adjusted during experimental investigations, must be taken into account.

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Fig. 11. Insertion of curved electrode carrier with stylet is shown in ten steps with different lengths Lf in equal steps: Lf = 0.1 i L, i = 1,…,10; curved electrode carrier has 9.5:1-scaled shape.

Fig. 12. Required pressure for the insertion of the straight carrier with stylet shown in Fig. 10; the pressure is shown in ten steps with different lengths Lf in equal steps: Lf = 0.1 i L, i = 1,…,10.

The dependence between length Lf and pressure p for the straight carrier is shown in Fig. 12. For the length of Lf = 0.1 L, the pressure of 3.9 bar is already needed. The pressure increases up to 6 bar with increasing length Lf to L. Lower pressure is needed to insert the initially curved electrode carrier (Fig. 13). The top pressure of only 2 bar is required for the smallest length Lf = 0.1 L, where the strongest deformation of the carrier compared to its manufactured curved shape is needed. In contrast to the insertion of the straight carrier, the pressure decreases when increasing the inserted length of the curved carrier into the cochlea. In addition, in this case, the application of inner pressure is needed for only half of the insertion process. For the length from Lf = 0.6 L onwards, the pressure is so small (p = 0.05 bar) that it can be omitted. For this insertion process, the cochlear outer wall is not affected by carrier and the minimal distance between the cochlear inner wall and the carrier wall is still more than 0.5% of the length L. The indication of such relative geometrical values is indispensable due to the scaled forms of the electrode carriers. However, the pressure values shown in Figs. 12 and 13 remain the same for differently scaled shapes, due to the above proved geometrical scalability of the system. 4. Experimental investigations In order to allow the metrological evaluation of the calculated deformation behaviour for straight and curved forms of demonstrators, a suitable production method was being established. With the help of injection moulding curved-shaped CI demonstrators with functional fluidic actuation were manufactured in 9.5:1-scaled dimensions using silicone Elastosil® M4644 (Wacker Chemie AG, Munich, Germany).

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Fig. 13. Required pressure for the insertion of the curved carrier with stylet shown in Fig. 11; the pressure is shown in ten steps with different lengths Lf in equal steps: Lf = 0.1 i L, i = 1,…,10.

Fig. 14. Manufacturing steps I to XI: 1 SMA wire, 2 Kapton® film, 3 silicone skins, 4 spacers, 5 carbon fibre bundles, 6 twisted thread, 7 sleeve.

4.1. Development of molding tools and manufacturing process The mold halves (see in Fig. 14 No.II and V) were fabricated by rapid prototyping in the stereolithography process (Form 1+, Formlabs Inc., Somerville, USA). For a better tightness, the mold halves were then sanded step by step with standard 300 grit abrasive paper up to 40 0 0 grit. As soon as all plan exterior surfaces are finish by that grindindg method the view into the mold is allowed. Of course the use of a transparent resin/photopolymer (Formlabs. Inc., Somerville, USA) is a prerequisite therefore. In order to generate the cavity inside the silicone structure, an SMA (shape-memory alloy) wire (NiTi SM495, EUROFLEX GmbH, Pforzheim, Germany) with a diameter of 1.90 mm was used. It was placed in an aluminium plate with a correspondingly milled negative mold to impart the desired initial shape to the wire (see No.1 in Fig. 14). Subsequently, the aluminium mold with wire was annealed at 500°C for one hour. The SMA wire was chosen because the wire can be straightened, thereby losing its original curved shape, in order to be able to easily pull offthe silicone structure after curing. Heating the wire to temperatures above 70°C, for example by means of a commercial hot air blower, the initial curved shape can be restored for reuse of the wire. In order to introduce the thread at a distance h from the longitudinal axis, a Kapton® film (see No. 2 in Fig. 14) with a thickness of 0.18 mm was glued on one mold half within each mold. This leads during the injection molding to a slot-shaped recess in the annular cross-sectional area along the silicone body. All contours of the film were cut using a multifunction laser (MUFU 100, LPKF Laser & Electronics AG, Garbsen, Germany). The exact position of the mold halves to each other and the film was achieved via two dowel pins. Compared to silicone, the roving, which has a tensile Young’s modulus of 230 GPa, guarantees tensile strength. Since the individual filaments/carbon

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fibres have a diameter of less than 10 μm, these are also limp as a bundle. When gluing the bundle, care was taken to ensure that the silicone structure was not brought under pretension, which influences the initial curvature of the silicone body. In preliminary tests, it was found that a simple storage of the wire at its two ends, in each case via a cylinder/cylinder pairing, does not lead to the desired centric position of the SMA wire over the entire cross section within the molding tool. For this reason, nine silicon spacers (see No. 4 in Fig. 14) were cast onto the wire in an intermediate step in the first mold. The shape of the spacers was chosen so that the cross section within the second mold was not completely closed and the flow of material and air could be ensured. In order to connect the functional demonstrators airtight to the experimental setup, these were attached to plastic hoses. For this purpose, radial notches were introduced into the plastic hoses and the functional demonstrators were fixed thereon by means of a twist thread (compare No. 6 in Fig. 14). In order to ensure a firm clamping of the functional patterns even at higher internal pressure, these were additionally pressed into a sleeve (see No. 7 in Fig. 14). 4.2. Manufacturing steps for the production of functional demonstrators To produce the functional demonstrators, the 2-component silicone (Elastosil® M4644, Wacker Chemie AG, Munich, Germany) was used. This silicone has a Shore hardness A of 40. Comparative scientific works for cochlear implants use often Sylgard 184 (Dow Chemical Company, Midland, United States). This silicone has a Shore hardness A of 43 and is similar to the silicone used for manufacturing cochlear implants [56]. In general, the Shore hardness primarily affects the stiffness of the actuator. This means: A larger Shore hardness leads to a higher pressure required. The Deformation behaviour however, changes only slightly. Because of this fact, for a proof of principle examination, which we do, the silicone used in current clinical devices does not necessarily have to be used for modelling. Furthermore, an adaption of the insertions model to other silicones is possible with just a few steps [43]. The components of Elastosil were mixed, then deaerated in vacuo and after that injected into the mold. After a vulcanization time of 12 h, the component can then be removed from the respective mold. The individual production steps for producing the functional demonstrators are listed below (see Fig. 14 Steps I to XI): • • • • • • •

•

Imprinting the desired shape into the SMA wire (mold core) by annealing with an aluminum mold (I) Injection molding with mold No. 1 (II) Demolding and removal of sprues and silicone skins (III-IV) Injection molding with mold No. 2 (V) Demolding and removal of sprues and silicone skins (VI-VII) Pre-strain-free gluing of the carbon fibre bundle into the slot-shaped recess of the silicone body (VIII) Shortening of the carbon fibre bundle to silicone body length and one-sided closure of the silicone body at the relieved end (IX) Fixing the functional demonstrator on a plastic tube and attaching a sleeve to its end (X and XI)

4.3. Measurements In order to compare the deformation states of the manufactured functional demonstrators with the analytically calculated shapes of the carriers Eqs. (7)–(10), the measurement device shown in Fig. 15 was used. The pressure provided by the compressed air supply (No. 1) was adjusted via a manual pressure reducer (No. 2). The pressure pm was determined and displayed by means of a pressure sensor (No. 3) with digital display (DMU4 0–10 bar, Kalinsky Sensor Elektronik GmbH & Co.KG, Erfurt, Germany). A demonstrator holder (No. 4) ensured the fixed clamping and positioning of the curved demonstrator (No. 5) in relation to a template (No. 6). On the template, seven deformation states of the curved electrode carrier for increased internal pressures p in the range from 0 to 6 bar were shown in the form of lines, calculated by the analytical model Eqs. (7)–(10). The deformation lines represented the position of the fibre (simultaneously representing the neutral axis) calculated with the analytical model using the pressures 0, 3, 4, 4.6, 5.1, 5.6 and 6 bar. The selection of the deformation states on the stencil, which allows the above-mentioned pressure values to be derived, was based on an optical evaluation of the distance between the deformation lines. Since the analytical model showed a larger deformation change compared to its responsible pressure change in the higher pressure range, the pressure differences between the selected deformation states decrease further for higher pressures. During the experiment, the real deformation state including the pressure display was recorded by means of a photo when each analytically calculated deformation state was reached. For this purpose a camera (No. 8) (Olympus OM-D E-10 Mark II, Olympus Europa SE & Co. KG, Hamburg, Germany) was used, which was mounted on a tripod for a constant image section and triggered remotely by means of a smartphone (No. 7) and an associated app. Two additional artificial light sources (No. 9) (Multiled LT V6, GS Vitec GmbH, Bad Soden Salmünster, Germany) were used to provide constant illumination of the experimental setup, producing a diffuse front light in the direction of the camera view and a diffuse side light at an angle of 90° Furthermore a black background was chosen for a high contrast. An evaluation of the real curvature behaviour of the demonstrators was carried out by optical comparison between the real form of the demonstrator and the form calculated by the analytical model. For this purpose, the images, which

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Fig. 15. Experimental setup for the measurement of the pressure pm needed to stepwise straighten the curved demonstrators; detail of the measurement and schematic representation of the measurement device: 1 air supply, 2 manual pressure reducer, 3 pressure sensor, 4 functional demonstrator holder, 5 functional demonstrator, 6 template with analytically derived curvature states, 7 smartphone with associated app, 8 camera, 9 artificial light sources.

Fig. 16. The demonstrator forms for different internal pressures are shown for one demontrator exemplarily. The model values p and the corresponding measured average pressure values pm including its standard deviation σ p are shown for 11 demonstrators.

provided the greatest possible coverage of the demonstrator with the individual curvature lines of the template (cf. Fig. 15), were selected. The points at the demonstrator with the greatest deviations did not exceed 4% of its length. A total of 11 demonstrators were measured. The values p derived by the analytical model, the measured averaged pressure values pm , and the standard deviation σ p of pm are given in Fig. 16. The difference between the mean measured pressures and the analytically calculated values has a maximum value of 0.61 bar, whereby the standard deviation is 0.18 bar, occurring for the analytically identified pressure of 5.6 bar. These results

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make it possible to use the presented analytical model for the design of carriers with a predefined straightening or bending process under pressurisation and for describing the insertion process. 5. Discussion and summary With the aim of minimising or avoiding damage of the intra-cochlear bony and soft tissue structures during the insertion of a cochlear implant electrode carrier, a fluid-mechanical compliant actuator is analytically modelled, designed and the process of its insertion is described. Because the demonstrated method is the focus of the presented paper, the electrode carrier was described without embedded electrodes. The electrodes can be considered by the same theory as straight and rigid parts or parts with higher stiffness then the other material of the carrier. It was shown that model-based synthesis of these systems by theory of curved rods for large deformations and analytical simulation of the insertion process including both, stylet and fluidic actuation, is possible. The model-based investigation of the scaling of geometrical parameters demonstrates that geometrically similar models of identical material and identical inner pressure show a geometrically similar curved form. These results have a general character and can be used for similar fluid-mechanical, beam-formed, compliant actuators with a cavity and an embedded thread. Therefore, scaled models can be used for theoretical and experimental investigations. The designed straight electrode carrier on a scale of 3:1 was shown and a curved-shaped electrode carrier on a scale of 9.5:1 was designed using the theory of curved rods for large deformations. Using the polynomial approach for the curvature of the carrier allows the design of the carrier with high accuracy for a given cochlear form. With the help of the analytical method, synthesis of the electrode carrier requires a few seconds, saving time compared to FEM. Therefore, this method is especially suitable for synthesising individually fitted electrode carriers. It is easily and quickly possible to form an individual carrier geometry based on a patient’s segmented anatomical shape of the cochlea. In order to ensure insertion of the carrier with minimal contact to the cochlear wall, a new method of insertion was suggested. Due to the combination of relative movement between the hollow stylet and the electrode carrier and the additional fluidic actuation of the carrier at the same time, its form can be partially bent specifically at the tip of the carrier (see part 3.3 and 3.4). In addition, experimental investigations with fluidic actuation were added for the largest free length position of the scaled electrode carrier. The use of an internal (but solid) stylet is already known in commercial CI electrode carriers [9]. However, if the electrode carrier is advanced off the stylet or pushed out of an outer sheath [10] the tip of electrode carrier directly curls into its final shape with a tight curvature. That tight curvature does not fit to the local curvature of the cochlea at that insertion depth. The fluid-mechanical actuator equipped with a hollow stylet, in turn, allows for the intermediate adaption of the curvature of the carrier to the local curvature of the cochlea. This is enabled by the independently adaptable insertion depth of the carrier, the stylet and the pressure to reach a certain curvature. Furthermore an already achieved tight curvature can be untightened in the case of an unexpected event during insertion, due to the fluid-mechanical actuator while the system still being held inside the cochlea. This is not possible with neither commercially available perimodiolar systems [9,10] nor experimental approaches like an actively or passively by body temperature provoked shape memory actuator inside the carrier [13] or the application of swelling of hydrogels [3]. For the analysis of the insertion process, the model-based simulation was carried out. The results show that three times smaller pressure (reduced to 2 bar) is needed to insert the curved electrode carrier in comparison to the insertion of the straight-shaped carrier. The clinical application of the presented system needs secure utilization of pressure up (to 2 bar) within the electrode carrier. It can be seen that there are already widely used systems in different disciplines of clinical routine to work with applied pressure: 3–12.2 bar during balloon angioplasty in children and adults for congenital and acquired obstructions of vessels and heart valves [57], 2.4–3.5 bar during balloon dilation in patients with intestinal stenosis [58], 6.1–8.1 bar in the dilatation of the Eustachian tube [59], 10.1 bar for balloon dilatation of subglottic stenosis [60] and up to 20.7 bar for balloon dilatation applied during kyphoplasty to restore the form and height of a deformed vertebral body [61]. Comparing the already achieved clinical routine with those systems and the applied pressure value, the implementation of a similar system for the application with the presented fluid-mechanical actuator for electrode carrier seems feasible, although not solved yet. The deformation of curved demonstrators was qualitatively and quantitatively evaluated while inner pressure was increased, enabling the confirmation of the results from the analytical model. There, the deviations between the mean measured pressures and the analytically calculated values reached a maximum of 0.61 bar. The greatest deviation between the calculated and measured form was no more than 4% of its length. It is conceivable that the wires can be used as threads to act for the bending of the actuator. Thereby the wires fulfil two functions and serve as the mechanical part (thread) and as wires for electricity transmission. Then the stiffness of the structure is different and should be measured. The result is that we need to determine a new system parameter. This fact leads to a higher complexity. However, the theory and methods remain unchanged. The aim of this contribution is to prove and to provide the methods for the analysis and synthesis of such actuators. The next step for further research on the demonstrated systems is the model-based description and detection of the forces occurring during the insertion due to a contact between the carrier and the intra-cochlear structures. Also, the manufacturing challenge for a 1:1 scaling must be solved. Furthermore the handling of the electrode carrier equipped with the fluid-mechanical actuator and its hollow stylet has to be analysed with respect to a manually or automated insertion procedure.

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The systems described in this work not only change their curvature in response to a pressure increase, but also their stiffness because of applied inner pressure or used stylet. Depending on the chosen variant (a straight or curved form in the initial state) the stiffness of the system rises or falls with increasing curvature. These properties of the fluid-mechanical actuator and the described insertion method can also be used for other surgical instruments in medical technology or for technical applications. Acknowledgements The authors wish to thank the German Research Foundation (DFG) for its financial support (ZE 714/92). References [1] S. Biedron, M. Westhofen, J. Ilgner, On the number of turns in human cochleae, Otol. Neurotol. 30 (3) (2009). [2] E. Erixon, H. Högstorp, K. Wadinanf, H. Rask-Andersen, Variational anatomy of the human cochlea; implications for cochlear implantation, Otol. Neurotol. 30 (1) (2009) 14–22. [3] L.A. Cartee, C.A. Miller, C. van den Honert, Spiral ganglion cell site of excitation I: comparison of scala tympani and intrameatal electrode responses, Hear. Res. 215 (1–2) (2006) 10–21. [4] A. Kral, M. Dorman, B.S. Wilson, Neuronal development of hearing and language: cochlear implants and critical periods, Annu. Rev. Neurosci. 42 (2019) 47–65. [5] A. Dhanasingh, C. Jolly, An overview of cochlear implant electrode array designs, Hear. Res. 356 (2017) 93–103. [6] R.K. Shepherd, S. Hatsushika, G.M. Clark, Electrical stimulation of the auditory nerve: the effect of electrode position on neural excitation, Hear. Res. 66 (1) (1993) 108–120. [7] M.L. Hughes, P.J. Abbas, Electrophysiologic channel interaction, electrode pitch ranking, and behavioral threshold in straight versus perimodiolar cochlear implant electrode arrays, J. Acoust. Soc. Am. 119 (3) (2006) 1538–1547. [8] F. Risi, Considerations and rationale for cochlear implant electrode design-past, present and future, J. Int. Adv. Otol. 14 (3) (2018) 382. [9] O.F. Adunka, H.C. Pillsbury, J. Kiefer, Combining perimodiolar electrode placement and atraumatic insertion properties in cochlear implantation–fact or fantasy? Acta Otolaryngol. 126 (5) (2006) 475–482. [10] A. Aschendorff, R. Briggs, G. Brademann, S. Helbig, J. Hornung, T. Lenarz, M. Marx, A. Ramos, T. Stöver, B. Escudé, C.J. James, Clinical investigation of the nucleus slim modiolar electrode, Audiol. Neurotol. 22 (3) (2017) 169–179. [11] T.S. Rau, S. Hügl, T. Lenarz, O. Majdani, Toward steerable electrodes. An overview of concepts and current research, Curr. Dir. Biomed. Eng. 3 (2) (2017) 765–769. [12] H.L. Seldon, M.C. Dahm, G.M. Clark, S. Crowe, Silastic with polyacrylic acid filler: swelling properties, biocompatibility and potential use in cochlear implants, Biomaterials 15 (14) (1994) 1161–1169 1994 Nov. [13] O. Majdani, T. Lenarz, N. Pawsey, F. Risi, G. Sedlmayr, Th.S. Rau, First results with a prototype of a new cochlear implant electrode featuring shape memory effect, Biomed. Tech. 2013 (58) (2013), doi:10.1515/bmt- 2013- 4002. [14] T.S. Rau, J. Granna, T. Lenarz, O. Majdani, J. Burgner-Kahrs, Tubular manipulators: a new concept for intracochlear positioning of an auditory prosthesis, Curr. Dir. Biomed. Eng. 1 (1) (2015) 515–518. [15] J.R. Clark, L. Leon, F.M. Warren, J.J. Abbott, Magnetic guidance of cochlear implants: proof-of-Concept and initial feasibility study, J. Med. Devices 6 (3) (2012) 035002. [16] K.N. Talbot, D.E.H. Hartley, Combined electro-acoustic stimulation: a beneficial union? Clin. Otolaryngol. 33 (6) (2008) 536–545. [17] S. Dilibal, H. Sahin, Y. Celik, Experimental and numerical analysis on the bending response of the geometrically gradient soft robotics actuator, Arch. Mech. 70 (5) (2018) 391–404. Warszawa, doi:10.24423/aom.2903. [18] I.S. Godage, Y. Chen, K.C. Galloway, E. Templeton, B. Rife, I.D. Walker, Real-time dynamic models for soft bending actuators, in: IEEE ROBIO 2018: IEEE International Conference on Robotics and Biomimetics December 12–15, 2018, Kuala Lumpur, Malaysia, Kuala Lumpur, Malaysia, Piscataway, New Jersey, IEEE, 2018, pp. 1310–1315. [19] G. Miron, B. Bédard, J.-S. Plante, Sleeved bending actuators for soft grippers: a durable solution for high force-to-weight applications, Actuators 7 (2018) 40, doi:10.3390/act7030040. [20] H. Ru, J. Huang, W. Chen, C. Xiong, J. Wang, Design and control of a soft bending pneumatic actuator based on visual feedback, WCICA 2018: The 2018 13th World Congress on Intelligent Control and Automation July 4–8, 2018, Changsha, China, IEEE, 2018. [21] H. Al-Fahaam, S. Davis, S. Nefti-Meziani, T. Theodoridis, Novel soft bending actuator-based power augmentation hand exoskeleton controlled by human intention, Intel. Serv. Robot. 11 (2018) 247–268, doi:10.1007/s11370- 018- 0250- 4. [22] L. Zentner, S. Linß, Compliant Systems: Mechanics of Elastically Deformable Mechanisms, Actuators and Sensors, DE GRUYTER, 2019 ISBN 978-3-11-047731-3. [23] B. Zhang, C. Hu, P. Yang, Z. Liao, H. Liao, Design and modularization of multi-dof soft robotic actuators, Ieee robot, Autom. Lett. 4 (2019) 2645–2652, doi:10.1109/LRA.2019.2911823. [24] S. Wakimoto, K. Suzumori, K. Ogura, Miniature pneumatic curling rubber actuator generating bidirectional motion with one air-supply tube, Adv. Robot. 25 (2012) 1311–1330, doi:10.1163/016918611X574731. [25] T. Rehman, A.A.M. Faudzi, D.E.O. Dewi, M.S.M. Ali, Design, characterization, and manufacturing of circular bellows pneumatic soft actuator, Int. J. Adv. Manuf. Techn. 93 (2017) 4295–4304, doi:10.10 07/s0 0170-017- 0891- z. [26] T. Wang, Y. Zhang, Z. Chen, S. Zhu, Parameter identification and model-based nonlinear robust control of fluidic soft bending actuators„ IEEE/ASME Trans. Mechatron. 24 (2019) 1346–1355, doi:10.1109/TMECH.2019.2909099. [27] G. Alici, T. Canty, R. Mutlu, W. Hu, V. Sencadas, Modeling and experimental evaluation of bending behavior of soft pneumatic actuators made of discrete actuation chambers, Soft Roboti. 5 (2018) 24–35, doi:10.1089/soro.2016.0052. [28] M. Ariyanto, J.D. Setiawan, R. Ismail, I. Haryanto, T. Febrina, D.R. Saksono, Design and characterization of low-cost soft pneumatic bending actuator for hand rehabilitation, in: M. Facta (Ed.), 2018 5th International Conference on Information Technology, Computer, and Electrical Engineering (ICITACEE): September 26–28th, 2018, Semarang, Indonesia proceedings, IEEE, 2018. [29] B. Mosadegh, P. Polygerinos, C. Keplinger, S. Wennstedt, R.F. Shepherd, U. Gupta, J. Shim, K. Bertoldi, C.J. Walsh, G.M. Whitesides, Pneumatic networks for soft robotics that actuate rapidly, adv, Funct. Mater. 24 (2014) 2163–2170, doi:10.1002/adfm.201303288. [30] K. Elgeneidy, N. Lohse, M. Jackson, Bending angle prediction and control of soft pneumatic actuators with embedded flex sensors – A data-driven approach, Mechatronics 50 (2018) 234–247, doi:10.1016/j.mechatronics.2017.10.005. [31] F. Ilievski, A.D. Mazzeo, R.F. Shepherd, X. Chen, G.M. Whitesides, Soft robotics for chemists, Angew. Chem. (Int. Ed. Engl.) 50 (2011) 1890–1895, doi:10. 1002/anie.201006464. [32] R.F. Shepherd, F. Ilievski, W. Choi, S.A. Morin, A.A. Stokes, A.D. Mazzeo, X. Chen, M. Wang, G.M. Whitesides, Multigait soft robot, in: Proceedings of the National Academy of Sciences of the United States of America, 108, 2011, pp. 20400–20403, doi:10.1073/pnas.1116564108. [33] P. Polygerinos, Z. Wang, J.T.B. Overvelde, K.C. Galloway, R.J. Wood, K. Bertoldi, C.J. Walsh, Modeling of soft fiber-reinforced bending actuators„ IEEE Trans. Robot. 31 (2015) 778–789, doi:10.1109/TRO.2015.2428504.

16

L. Zentner, S. Griebel and S. Hügl / Mechanism and Machine Theory 142 (2019) 103590

[34] C. Yang, R. Kang, D.T. Branson, L. Chen, J.S. Dai, Kinematics and statics of eccentric soft bending actuators with external payloads, Mech. Mach. Theory 139 (2019) 526–541, doi:10.1016/j.mechmachtheory.2019.05.015. [35] Y. Shapiro, K. Gabor, A. Wolf, Modeling a hyperflexible planar bending actuator as an inextensible Euler–Bernoulli beam for use in flexible robots, Soft Robot. 2 (2015) 71–79, doi:10.1089/soro.2015.0 0 03. [36] K.C. Galloway, P. Polygerinos, C.J. Walsh, R.J. Wood, Mechanically programmable bend radius for fiber-reinforced soft actuators, 16th International Conference on Advanced Robotics (ICAR), 2013: 25–29 Nov. 2013, Montevideo, Uruguay, IEEE, 2013. [37] L. Rosalia, B.W.-K. Ang, R.C.-H. Yeow, Geometry-Based customization of bending modalities for 3D-Printed soft pneumatic actuators, IEEE Robot. Autom. Lett. 3 (2018) 3489–3496, doi:10.1109/LRA.2018.2853640. [38] G. Sun, Y. Hu, M. Dong, Y. He, M. Yu, L. Zhu, Posture measurement of soft pneumatic bending actuator using optical fibre-based sensing membrane, Ind. Robot 46 (2019) 118–127, doi:10.1108/IR- 08- 2018- 0159. [39] R.V. Martinez, J.L. Branch, C.R. Fish, L. Jin, R.F. Shepherd, R.M.D. Nunes, Z. Suo, G.M. Whitesides, Robotic tentacles with three-dimensional mobility based on flexible elastomers, Adv. Mater. (Deerfield Beach, Fla.) 25 (2013) 205–212, doi:10.10 02/adma.2012030 02. [40] R. Xie, M. Su, Y. Zhang, Y. Guan, 3D-PSA: a 3D pneumatic soft actuator with extending and omnidirectional bending motion, IEEE ROBIO 2018: IEEE International Conference on Robotics and Biomimetics December 12–15, 2018, Kuala Lumpur, Malaysia, Kuala Lumpur, Malaysia, IEEE, 2018. [41] J. Yan, H. Dong, X. Zhang, J. Zhao, A three-chambed soft actuator module with omnidirectional bending motion, IEEE-RCAR 2016: 2016 IEEE International Conference on Real-Time Computing and Robotics June 6–10, 2016, Angkor Wat, Cambodia, IEEE, 2016. [42] R.F. Surakusumah, A.A.M. Faudzi, D.E.O. Dewi, E. Supriyanto, Development of a half sphere bending soft actuator for flexible bronchoscope movement, 2014 IEEE International Symposium on Robotics and Manufacturing Automation (IEEE-ROMA2014): 15-16 December 2014, Kuala Lumpur, Malaysia, IEEE, 2014. [43] L. Zentner, S. Griebel, C. Wystup, S. Hügl, Th.S. Rau, O. Majdani, Synthesis process of a compliant fluidmechanical actuator for use as an adaptive electrode carrier for cochlear implants, Mechanism and Machine Theory, 112, Elsevier Science, Bd., 2017. [44] L. Zentner, Mathematical synthesys of compliant mechanism as cochlear implant, in: G.K. Ananthasurech, B. Corves, V. Petuya (Eds.), Mikromechanics and Microactuators, Springer, 2012 ISBN 978-94-007-2720-5. [45] L. Zentner, M. Issa, S. Hügl, S. Griebel, T.S. Rau, O. Majdani, Compliant mechanism with hydraulic activation used for implants and medical instruments, XII International SAUM Conference on Systems, Automatic Control and Measurements Niš, Serbia, November 12th–14th, 2014. [46] S. Hügl, L. Zentner, S. Griebel, O. Majdani, Th.S. Rau, Analysis of the customized implantation process of a compliant mechanism with fluidic actuation used for cochlear implant electrode carriers, Eng. Chang. World 59 (2017) 6p, https://www.db-thueringen.de/servlets/MCRFileNodeServlet/ dbt_derivate_0 0 039363/ilm1- 2017iwk- 111.pdf. [47] S. Griebel, S. Hügl, T.S. Rau, O. Majdani, C. Wystup, T. Lenarz, L. Zentner, Adaptive electrode carrier. Pub. No.: WO/2017/148903, International Application No.: PCT/EP2017/054578, Publication Date: 08.09.2017, International Filing Date: 28.02.2017. [48] L. Zentner, Nachgiebige mechanismen, DE GRUYTER, 2014 ISBN 978-3-486-76881-7. [49] H. Rask-Andersen, W. Liu, E. Erixon, A. Kinnefors, K. Pfaller, A. Schrott-Fischer, R. Glueckert, Human cochlea: anatomical characteristics and their relevance for cochlear implantation, Anatom. Rec. 295 (11) (2012) 1791–1811. [50] E. Avci, T. Nauwelaers, T. Lenarz, V. Hamacher, A. Kral, Variations in microanatomy of the human cochlea, J. Comp. Neurol. 522 (14) (2014) 3245–3261. [51] W. Würfel, H. Lanfermann, T. Lenarz, O. Majdani, Cochlear length determination using cone beam computed tomography in a clinical setting, Hear. Res. 316 (2014) 65–72. [52] M. Pietsch, L.A. Dávila, P. Erfurt, E. Avci, T. Lenarz, A. Kral, Spiral form of the human cochlea results from spatial constraints, Sci. Rep. 7 (1) (2017) 7500. [53] B. Escudé, C. James, O. Deguine, N. Cochard, E. Eter, B. Fraysse, The size of the cochlea and predictions of insertion depth angles for cochlear implant electrodes, Audiol. Neurotol. 11 (Suppl. 1) (2006) 27–33. [54] A. Rivas, A. Cakir, J. Hunter, R. Labadie, G. Zuniga, G. Wanna, B. Dawant, J. Noble, Automatic cochlear duct length estimation for selection of cochlear implant electrode arrays, Otol. Neurotol. 38 (3) (2017) 339–346. [55] D. Schurzig, M. Timm, C. Batsoulis, R. Salcher, D. Sieber, C. Jolly, Th. Lenarz, M. Zoka-Assadi, A novel method for clinical cochlear duct length estimation toward patient-specific cochlear implant selection, sage and open access pages, OTO Open 2 (4) (2018) Oct 22473974X18800238. [56] S. Balster, G.I. Wenzel, A. Warnecke, S. Steffens, A. Rettenmaier, K. Zhang, T. Lenarz, G. Reuter, Optical cochlear implant:evaluation of insertion dorces of optical fibres in a cochlear model and of traumata in human temporal bones, Biomed. Eng. (2013), doi:10.1515/bmt- 2013- 0038. [57] P.S. Rao, Interventional pediatric cardiology: state of the art and future directions, Pediatr. Cardiol. 19 (1) (1998) 107–124. [58] A. Ferlitsch, W. Reinisch, A. Püspök, C. Dejaco, M. Schillinger, R. Schöfl, R. Pötzi, A. Gangl, H. Vogelsang, Safety and efficacy of endoscopic balloon dilation for treatment of Crohn’s disease strictures, Endoscopy 38 (05) (2006) 483–487 2006. [59] P.J. Catalano, S. Jonnalagadda, M.Y. Vivian, Balloon catheter dilatation of Eustachian tube: a preliminary study, Otol. Neurotol. 33 (9) (2012) 1549–1552. [60] S.D. Sharma, S.L. Gupta, M. Wyatt, D. Albert, B. Hartley, Safe balloon sizing for endoscopic dilatation of subglottic stenosis in children, J. Laryngol. Otol. 131 (3) (2017) 268–272. [61] G. Tsoumakidou, C.W. Too, G. Koch, J. Caudrelier, R.L. Cazzato, J. Garnon, A. Gangi, CIRSE guidelines on percutaneous vertebral augmentation, Cardiovasc. Interv. Radiol. 40 (3) (2017) 331–342.