Medical Engineering and Physics 37 (2015) 460–468

Contents lists available at ScienceDirect

Medical Engineering and Physics journal homepage: www.elsevier.com/locate/medengphy

Mechanical characterization of bone anchors used with a bone-attached, parallel robot for skull surgery Jan-Philipp Kobler a,∗, Lenka Prielozny b , G. Jakob Lexow b , Thomas S. Rau b , Omid Majdani b , Tobias Ortmaier a a b

Institute of Mechatronic Systems, Leibniz Universität Hannover, 30167 Hanover, Germany Hannover Medical School, 30625 Hanover, Germany

a r t i c l e

i n f o

Article history: Received 1 September 2014 Revised 11 December 2014 Accepted 26 February 2015

Keywords: Surgical robotics Bone anchor Biomechanics Mechanical characterization

a b s t r a c t Bone-attached robots and microstereotactic frames, intended for deep brain stimulation and minimally invasive cochlear implantation, typically attach to a patient’s skull via bone anchors. A rigid and reliable link between such devices and the skull is mandatory in order to fulfill the high accuracy demands of minimally invasive procedures while maintaining patient safety. In this paper, a method is presented to experimentally characterize the mechanical properties of the anchor–bone linkage. A custom-built universal testing machine is used to measure the pullout strength as well as the spring constants of bone anchors seated in four different bone substitutes as well as in human cranial bone. Furthermore, the angles at which forces act on the bone anchors are varied to simulate realistic conditions. Based on the experimental results, a substitute material that has mechanical properties similar to those of cranial bone is identified. The results further reveal that the pullout strength of the investigated anchor design is sufficient with respect to the proposed application. However, both the measured load capacity as well as the spring constants vary depending on the load angles. Based on these findings, an alternative bone anchor design is presented and experimentally validated. Furthermore, the results serve as a basis for stiffness simulation and optimization of bone-attached microstereotactic frames. © 2015 IPEM. Published by Elsevier Ltd. All rights reserved.

1. Introduction Precision skull surgery requires specialized instrumentation to satisfy demanding requirements in minimally invasive cochlear implantation, deep brain stimulation electrode placement and related applications. Surgical robotics for use in these fields must provide the surgeon with an instrument guidance of submillimetric accuracy [1]. Recently, promising results have been achieved with microstereotactic frames and miniaturized robots that attach directly to the skull of the patient. R by An example of a commercialized system is the SpineAssist Mazor Surgical Technologies Inc. (Caesarea, Israel and Norcross, GA, USA), which is rigidly mounted onto the patient using a fixation frame. The hexapod-based guidance assistant (formerly known as MARS) has been developed for spine surgery [2,3] but could potentially be used for incisions at the skull as well [4]. The StarFixTM (FHC, Inc., Bowdoin, ME) [5–7] is a passive, customized microstereostatic frame, made via

∗

Corresponding author. Tel.: +49 51176217840. E-mail addresses: [email protected] (J.-P. Kobler), [email protected] (G. Jakob Lexow). http://dx.doi.org/10.1016/j.medengphy.2015.02.012 1350-4533/© 2015 IPEM. Published by Elsevier Ltd. All rights reserved.

rapid prototyping based on a predefined drill guidance model. It is mounted on preoperatively implanted anchors, whose locations are derived by obtaining a CT scan and subsequent automatic segmentation during intervention planning. Moreover, Labadie et al. proposed a bone-attached, customized, microstereotactic frame serving as a drill guide [8–10] which is milled intraoperatively using a CNC machine. Recently, Kratchman et al. developed an automated parallel robot for minimally invasive cochlear implantation and deep brain stimulation, which is mounted on a rigid pre-positioning frame attached to the skull of the patient [11]. Furthermore, a microstereotactic frame that is adjusted by a robot, immobilized, and then used as a tool guide in deep brain stimulation was presented previously by Kratchman and Fitzpatrick [12]. In order to provide enhanced flexibility during the surgical procedure, the authors propose a passive parallel robot (Stewart-Gough platform) which can be directly attached to bone anchors, eliminating the need for a rigid fixation frame. An illustration of the proposed mechanism is given in Fig. 1. The main idea is to use the spherical heads of the bone anchors both as fiducials during task planning and as base joints of the robot. Manually adjustable struts connect the platform, i.e., the linear drill guide, to the base points and serve as prismatic joints to align the surgical tool with a predefined trajectory.

J.-P. Kobler et al. / Medical Engineering and Physics 37 (2015) 460–468

461

Fig. 1. Concept of a passive parallel robot which serves as a drill guide in minimally invasive cochlear implantation. The mechanism attaches to bone anchors with spherical heads implanted in a patient’s skull.

Due to the direct attachment, neither intraoperative navigation nor explicit point-based registration between patient and device is required. The accuracy of the mechanism is further increased by implementing reconfigurability and by exploiting redundant degrees of freedom of the mechanism during incision planning: considering a drilling task, two redundant degrees of freedom, i.e., platform height and rotation around the drill axis, can be exploited in order to optimize certain performance criteria of the manipulator with respect to stiffness and singularity avoidance. A detailed description of the device and the surgical workflow has been presented elsewhere [13]. All the above mentioned concepts require a rigid and reliable link between the skull and the drill guide to ensure patient safety and maximum accuracy. Especially firm placement of the bone anchors is essential since any movement must be avoided. Thus, their mechanical load capacity as well as their resilience play a crucial role considering the design of future prototypes. Furthermore, during the surgical procedure, forces and torques act on such devices, resulting from both manual operation and the bone drilling process. Such loads are transmitted through the rigid mechanisms and result in tensile or compressive forces applied to the bone anchors [13]. In previous work, the authors have presented a method to optimize the design of the parallel robot for kinematic accuracy [14]. Furthermore, a study focused on loads, occurring during guided drilling, revealed that the maximum interaction force applied by the surgeon, oriented perpendicular to the drilling axis, is approximately 12 N [15]. If this force is applied 5 cm above the platform, a simulation according to the method presented elsewhere by Kobler et al. [13] yields that the resulting forces acting upon the bone anchors can be up to 50 N. Deflections of the bone anchors under load, in turn, lead to deviations of the drill from its desired trajectory. With respect to patient safety, such deviations must be minimized. In the worst case, the screw connection can fail due to overload. Possible failure modes of the self-tapping fasteners are either associated with the screws (bolt breaking, thread stripping) or the material into which they are inserted (thread stripping) [16]. In this context, several researchers have reported on the mechanical characterization of bone screws for dental implantation [17,18]. Furthermore, the load capacity of monocortical screws in osteoporotic bone [19] and the pullout strength of suture anchors [20] have been studied. However, both the screw design as well as the bone samples used in these studies differ significantly when compared to the application considered here. Hence, the mechanical properties of the anchor–bone linkage need to be determined under conditions that match the intended use with a bone-attached robot. Therefore, in this contribution we present the results of comprehensive studies that have been conducted in order to experimentally assess the pullout strength of bone anchors as well

Fig. 2. Technical drawing (top) and photograph (bottom) of the bone anchor used in this study. All dimensions given in mm.

as their spring constants when seated in bone. The remainder of the paper is organized as follows. In Section 2 the specifications of the considered bone anchor are given. Furthermore, the experimental setup is presented as well as the proposed test procedure. The resulting pullout strength and spring constants of the anchor-bone linkage are listed in Section 3. Section 4 discusses the results in the scope of the intended application and gives an outlook on future work. 2. Materials and methods 2.1. Specifications of the investigated bone anchors The dimensions of the bone anchors being investigated in this paper are given in Fig. 2. Given the assumption that a deeper insertion leads to stronger fastening, the screw thread is designed to be as long as reasonably possible limited only by the thickness of the bone. Measurements of the skull thickness in clinical CT data using a custom-made software [21] showed sufficient positions for bone anchors assuming a maximum insertion depth of up to 5 mm, thus defining the dimensions of the initial design. The bone screw is equipped with a cylindrical, self-cutting HA 2 thread manufactured according to ISO 5835. In order to facilitate handling, the middle part of the anchor has a hexagonal shape adapted to an off-the-shelf hexagon wrench key. The spherical head, which serves as the base joint of the proposed parallel robot, is screwed onto the M 1.6 thread bar once the bone anchor is seated in bone. The bone anchors are machine-made from TiAl6V4 titanium alloy (titanium grade 5), which has a tensile strength of 850–1120 N mm−2 , a fatigue strength of 440–690 N mm−2 and a breaking elongation of 10–15%. The strength of this material is superior to surgical steel (e.g. X2CrNiMo1812) while being both biocompatible and resistant to corrosion. Furthermore, it is well known that the number of artifacts in computed tomography (CT) images is generally lower compared to anchors made from stainless steel [22]. 2.2. Measurement of pullout strength and spring constants Considering the proposed concept of a bone attached parallel robot, forces and torques occurring at its end effector are transmitted through the rigid mechanism, resulting in tensile and compressive forces being applied to the bone anchors. Such forces and torques mainly result from the surgeon interacting with the instrument guidance during surgery, and from the drilling process itself. Unfortunately, any motions of the bone anchors lead to spatial deviations

462

J.-P. Kobler et al. / Medical Engineering and Physics 37 (2015) 460–468

load case I f

load case II

load case III

f 45◦

90◦ f

Fig. 3. Load cases considered to experimentally assess the mechanical strength of implanted bone anchors. Each load case is characterized by the angle at which the tensile force f is applied.

from the desired end effector pose (position and orientation). This results in deviations of the drill from its desired trajectory. Hence, in case the bone anchors deflect significantly under load, safe operation of the device is no longer guaranteed. Moreover, the bone anchors must not fail when typical tensile forces are applied. Therefore, the pullout strength of the anchors, i.e., the force required to pull the anchor from the bone, is experimentally assessed in this paper. Furthermore, the deflection of the anchors under load, referred to as their spring constant, is determined. With respect to clinical application, the locations of the mechanism’s base joints vary strongly depending on patient anatomy. Hence, the angles at which the forces act on the bone anchors change in consequence of different configurations of the parallel mechanism, which is desired since the head of the anchor serves as a spherical joint. In order to account for such variations in the experiments, the direction of the applied force is varied according to the schematic given in Fig. 3, resulting in three different load cases. 2.2.1. Experimental setup The experimental setup comprises a custom built, manually operated universal testing machine (see also Fig. 4). Bone samples with implanted anchors are attached to a holder which is mounted at the base of the machine via a rotational joint. Hence, the direction of the force applied to the bone anchor can be adjusted by manipulating the rotational joint. The spherical head of the bone anchor under test is connected to the moving part of the machine using an adapter which provides a spherical cavity. In order to acquire the force ap-

(a)

plied to the bone anchor under test, a force-torque sensor (FT Mini40, ATI Industrial Automation, Inc.) is used. Here, only the measuring direction corresponding to the movement of the bone anchor adapter is of relevance. In this direction, the sensor has a calibrated measurement range of ±500 N. Additionally, an inductive position encoder (WA20, Hottinger Baldwin Messtechnik, Darmstadt, Germany) is used to measure the displacement of the bone anchors during the pullout experiments. 2.2.2. Materials The mechanical properties of the human bone vary not only between different bones but also between different regions of the skull. The proposed fixation of the head-mounted robot requires bone anchors in the parietal and temporal bone, whose characteristics in adults have been reported in the following publications. The results are summed up in Table 1. If possible only data from relevant regions of the skull have been included. McElhaney et al. [23] measured stress and strain on human bone samples from 17 embalmed calvaria. Small specimens cut from the samples were tested under quasistatic load. The results were compared to fresh samples from 40 donors showing no significant difference between fresh and embalmed bone. Wood [24] used fresh specimens of compact bone from the temporal, parietal and frontal skull of 30 donors. Focusing on the dynamic response he tested the samples under load frequencies between 0.005 Hz and 150 Hz. Higher frequencies led to a higher modulus of elasticity. Peterson and Dechow [25,26] investigated the anisotropy of elastic properties of the cortical layer of the skull. Therefore, they calculated the elastic and shear moduli from the velocity of ultrasound propagation in different directions. The samples were taken from different regions of the skull. In the first study 5 of the 10 skulls were rehydrated from dry specimens. The others including the 15 skulls used in the second study were fresh. Delille et al. [27] examined samples from 20 fresh skulls in a three-point bending test at a load speed of 10 mm min−1 . Again the samples were taken from different regions of the head. Motherway et al. [28] also performed a three-point bending test, but at much higher speeds ranging from 0.5 m s−1 to 2.5 m s−1 . In general, the elastic modulus increased with load speed. The samples originated from fresh parietal and frontal skull bone of 8 donors. In this study, so called laminated test blocks, provided by Sawbones Europe (Malmö, Sweden), are chosen as cortical bone substitutes. In order to match the characteristics of the human cranium, these blocks are made from solid rigid polyurethane foam, which is laminated with short-fiber-filled epoxy sheets having a thickness of

(b)

(c)

Fig. 4. Experimental setup used to conduct the pullout experiments (a), close-up of spherical bone anchor head within the custom made adapter (b), bone anchor under test according to load case II (c).

J.-P. Kobler et al. / Medical Engineering and Physics 37 (2015) 460–468

463

Table 1 Average mechanical properties of cranial bone as reported in literature. Year

Cortical layer E

1970 [23] 1971 [24] 2002 [25] 2003 [26] 2003 [26] 2007 [27] 2007 [27] 2009 [28]

12.3a 10.3–22.1b 13.0–21.0c 13.1–20.3c 13.4–23.4c

Diploe G

ρ

E

G

Complete bone

ρ

1.4 4.4–6.8c 4.6–6.8c 4.7–7.1c

E

G

Region

ρ

5.4

1.41

5.0 11.3 5.7–18.1b

1.71 1.71

1.87 1.81 1.87

– – Parietal Parietal Temporal Parietal Temporal Parietal

Density ρ given in g cm−3 , tension and shear moduli E, G given in GPa. a Multiplied by 10 to correct an assumed typing error according to context and figures. b Depends on testing speed. c Depends on loading direction. Table 2 Mechanical properties of synthetic bone substitutes. Material

SFFEa

SRPUb 20

SRPUb 50

Density Tensile modulus longit. Tensile modulus transv. Tensile modulus Shear modulus Compressive modulus

1.64 16.0 10.0 − − 16.7

0.32 − − 0.248 0.049 0.21

0.80 − − 1.469 0.178 1.148

Density given in g cm−3 , moduli given in GPa. a Short-fiber-filled epoxy. b Solid rigid polyurethane. Table 3 Abbreviations used to distinguish the bone substitutes. Abbrev.

Laminate (cortical layer)

Test block (diploe)

(a) (b) (c) (d)

– – Solid rigid polyurethane 50 Short-fiber-filled epoxy

Solid rigid polyurethane 20 Solid rigid polyurethane 50 Solid rigid polyurethane 20 Solid rigid polyurethane 20

3 mm. Referring to Table 1, epoxy sheets are assumed to resemble the cortical layer while the polyurethane foam is considered similar to diploe. The mechanical properties of the chosen materials are given in Table 2. The synthetic bone substitutes allow for a large number of experiments under defined and reproducible conditions, i.e., material properties in this particular case. However, due to the fact that such substitutes are not well established in the literature, further pullout experiments are performed using human cadaver cranial bone to verify the suitability of the test blocks. Since the values given in Table 1 indicate significant variations regarding the mechanical properties of the human cranium, additionally, test blocks solely consisting of solid rigid polyurethane foam are included in the study to increase the number of cranial bone substitute candidates. In total, two laminated and two pure test materials are used and then compared to the human samples. For improved readability, the abbreviations given in Table 3 are introduced in order to distinguish between the four material compounds. Prior to the pullout tests, all specimens are cut to blocks having an approximate size of 15 mm × 40 mm × 15 mm. The human samples are taken from regions which are considered suitable due to sufficient skull thickness. Further details regarding those regions can be found in [14]. The skull specimens were stored frozen and thawed before the experiments. Freezing is reported as having minimal effect on the mechanical properties of bone [29]. 2.2.3. Measurement protocol A pilot hole having a diameter of 1.5 mm was drilled into the bone specimen prior to each experiment due to the fact that the bone screw is self-cutting but not self-drilling. This value was chosen based on

the results of a preceding study, in which pilot hole diameters were assessed in steps of 0.1 mm. Regardless of the considered material, it was revealed that a diameter of 1.5 mm resembles the best compromise between the torque required for insertion and the quality of the thread created in the bone substitute. After pilot hole drilling, the bone anchor was inserted perpendicularly and flush to the surface of the sample, and the spherical head was attached. Finally, the anchor was pulled from the bone using the universal testing machine described in Section 2.2.1. During the pullout testing, the displacement of the anchor as well as the forces and torques applied were recorded at a sampling rate of 1 kHz. In total, 120 pullout experiments were performed in synthetic bone (n = 10 per material and load case). Additionally, 30 tests were carried out using cadaveric bone. Since one aim was to identify an appropriate bone substitute, 20 trials were performed according to load case I in order to obtain a meaningful data basis. At a later stage, 5 trials were done according to load cases II and III, respectively. 3. Results The pull out testing was successfully performed in 147 experiments according to the protocol described above. In two cases (load case I, material (d), and load case II, material (d)), the displacement sensor failed. Subsequently, the relevant trials are excluded from the evaluations. One experiment using a human cranial bone sample was stopped prior to pulling the anchor from the specimen because the measured force (577.3 N) exceeded the calibrated measurement range of the sensor. 3.1. Evaluation procedure To illustrate the subsequent evaluation procedure, Fig. 5 gives the force data recorded during one representative trial (human cranial bone specimen, load case I), plotted over the measured anchor displacement. The blue cross indicates the force required to pull the anchor from the bone, corresponding to the pullout strength. In order to determine the spring constant, a subset of the recorded data where the applied force ranges from 5 N to 60 N is considered. This range is believed to be most relevant with respect to the intended application of the anchors. Linear regression is applied to all data points within the aforementioned bounds. Hence, the spring constant c corresponds to the slope of the fitted line segment:

c=

f . d

In order to obtain a compact representation of the data contained in the recorded force-deformation curves, in the following, the values of pullout strength as well as the spring constants are displayed using box plots [30]. This representation is chosen since it does not require any assumptions regarding the underlying statistical distributions

464

J.-P. Kobler et al. / Medical Engineering and Physics 37 (2015) 460–468

Fig. 5. Sample data obtained during one representative pullout trial (load case I) using a human cranial bone specimen. The force acting on the anchor is plotted over the resulting displacement (gray curve). A blue cross depicts the maximum applicable force, which causes the anchor to break free from the bone sample. Linear regression is applied to all data points within the range indicated by the red crosses. The slope of the fitted line (dashed red) is considered the spring constant of the anchor–bone linkage. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)

600 material (a) material (b) material (c) material (d) cranial bone

500

force [N]

400

300

200

Considering load case I, median values of 65.2 N and 353.8 N are determined for the solid rigid polyurethane foam materials (a) and (b), respectively. The median pullout strength using the laminated material (c) is found to be 246.9 N, while it is 423.6 N when the anchors are seated in material (d). It is generally observed that the variations in the maximum load capacity, i.e., the deviations from the median, increase with the applied force. The most notable variations are observed when samples of human cranial bone are used. Within the performed experiments, the measured pullout strength ranges from 134.1 N to 577.3 N, the median being 392.9 N. When a force acts on the bone anchors according to load case II, the pullout strength decreases depending on the material properties of the specimens. The relative change from load case I is comparable throughout the set of materials. As a result, the absolute values measured using materials (b), (c), and (d) are more similar, ranging from 210 N to 320 N. Accordingly, the deviations from the determined median values are reduced. The results of the experiments done on cranial bone closely match those obtained using material (d). Even lower pullout strength is observed in the experiments performed according to load case III. The decrease in the measured forces with respect to load cases I and II is evident when the non laminated polyurethane blocks (materials (a) and (b)) are used. Considering the materials (c) and (d), increasing variations are observed, which are distinct in comparison with load cases I and II. Particularly the behavior of the anchors seated in material (d) is remarkable. In 5 out of 10 trials, the pullout strength exceeds the median value observed under load case II. This phenomenon is even more apparent when cranial bone is used as test material. In this case, the median exceeds the corresponding value determined for load case II by 25 N. However, regardless of the considered load case, the pullout strength values obtained using material (d) match those of the cranial bone samples best.

3.3. Spring constants of implanted bone anchors

100

0 I

II

III

load case [-] Fig. 6. Experimentally determined pullout strength of bone anchors for different test materials and different load cases. The bottom and top of the box correspond to the first and third quartiles, respectively. The ends of the whiskers denote either the lowest datum still within 1.5 times the interquartile range of the 25th percentile, or the highest datum still within 1.5 times the interquartile range of the 75th percentile. Any value not included between the whiskers is considered an outlier, represented by a small circle.

of the measured values. The bottom and top of the box correspond to the first and third quartiles, respectively, while the band inside the box gives the median. Furthermore, the ends of the whiskers denote either the lowest datum still within 1.5 times the interquartile range of the lower quartile, or the highest datum still within 1.5 times the interquartile range of the upper quartile. Any value not included between the whiskers is considered an outlier, represented by a small circle. 3.2. Pullout strength of implanted bone anchors The forces required to pull the anchors from the test materials are given in Fig. 6 for load cases I to III. The box plot gives the maximum values measured in each experiment before the anchor broke free of the bone sample. Hence, the maximum force occurs at the time the anchor starts to break free from the specimen.

The spring constants determined via the evaluation procedure described in Section 3.1 are given in Fig. 7. It is generally observed that, compared to the pullout strength, the spring constants are far more sensitive to changes in sample material and loading direction. Regarding load case I, median values of 125.4 N mm−1 , 355.4 N mm−1 , and 353.2 N mm−1 are determined for materials (a), (b), and (c), respectively. The experiments performed using material (d), which has a top layer of short-fiber-filled epoxy, yield considerably higher spring constants, the median being 921.4 N mm−1 . Similar to the pullout strength, the most notable variations in the spring constants result when human cranial bone specimens are employed. The observed values, except for two outliers, range from 486.7 N mm−1 to 1247 N mm−1 , while the median is 760.1 N mm−1 . The spring constants determined when testing according to load case II are considerably reduced compared to load case I. Considering materials (a), (b), and (c) the observed values do not exceed 50 N mm−1 . Again, anchors being seated in material (d) exhibit less displacement under load, resulting in spring constants ranging from 105.1 N mm−1 to 167.3 N mm−1 . Similar values ranging from 110.5 N mm−1 to 174.6 N mm−1 are observed when cranial bone samples are used. The spring constants obtained from the experiments according to load case III exhibit significant deviations from the previously observed results and phenomena. On the one hand, spring constants decrease with respect to load case II when the non laminated materials (a) and (b) are used. On the other hand, when testing the two-compound materials (c) and (d) as well as cranial bone, the measured values exhibit peaks, exceeding the results from load cases I and II. Hence, there is again good agreement between material (d) and cranial bone under load cases I and II, respectively, but

J.-P. Kobler et al. / Medical Engineering and Physics 37 (2015) 460–468

(a)

(b)

(c)

465

(d)

Fig. 7. Experimentally determined spring constants of bone anchors for different test materials and different load cases (a), close-up of load case II (b), close-up of bone substitutes (a) and (b) under load case III (c) and close-up of human cranial bone under load case III (d).

With load case I, the laminated test materials (c) and (d) as well as the human cranial bone samples fail in direct proximity to the bone cutting thread (thread stripping), i.e., at locations where the maximum stress due to the applied load occurs. Considering the homogenous materials (a) and (b), larger parts containing the bone anchor thread break from the test blocks, as depicted in Fig. 8. When the load is applied according to case II, the thread which is cut into the bone sample fails regardless of the used material. This is due to the fact that stress resulting from the force load is no longer uniformly distributed over the thread flanks, which causes the thread to fail where the stress is at a local maximum. Even though forces up to 300 N are applied, after the experiments, the bone anchors are neither visually damaged nor bent. The same accounts for the experiments performed according to load case III using materials (a), (b), and (c). However, load case III pullout tests on anchors seated in samples of material (d) as well as cranial bone result in failures of the anchors as depicted in Fig. 8. In these cases, the bone cutting threads remain seated within the specimens, while the anchor breaks either at the undercut below or above the hexagonal. This reveals that the measured displacements are mainly due to bending of the titanium screw, which subsequently explains the considerably increased spring constants. Again, similar failure modes are observed with cranial bone and the substitute material (d). 3.5. Further studies According to the obtained results, substitute material (d) is considered a suitable alternative to human cranial bone regarding the mechanical characterization of bone anchors. Both the pullout strength as well as the spring constants match the results obtained using human cranial bone specimens most closely. Based on these findings, in the following, the results of two further studies are presented. Fig. 8. Failure modes of bone anchors under load. Failure in direct proximity to the bone cutting thread (top), breaking of large parts containing the bone cutting thread (center), and bone anchor failure (bottom).

considerably lower spring constants result for the bone when testing at load case III. 3.4. Failure modes of bone anchors under load When pulling the anchors from the bone samples, it is generally observed that the test materials fail rather than the bone anchors.

3.5.1. Spring characteristic of the anchor–bone linkage In order to determine a more complete spring characteristic of bone anchors seated in test blocks made from material (d), additional pullout test are carried out, characterized by the fact that the angle of the applied tensile force is varied in steps of 10◦ , ranging from 10◦ to 80◦ . Two trials are performed per load direction, and the calculated spring constants are averaged. The resulting spring characteristic, combined with the previously obtained values, is given in Fig. 9. It is revealed that, starting from load case I, the spring constants decrease until the load angle reaches 60◦ . When the load angle

466

J.-P. Kobler et al. / Medical Engineering and Physics 37 (2015) 460–468

Fig. 9. Spring characteristic of the anchor–bone linkage for different load angles using material (d) and cranial bone.

Fig. 10. Initial (top) and alternative (bottom) bone anchor design.

is further increased, the spring constants increase accordingly, which is due to the mode of failure described in the previous section.

(a)

3.5.2. Alternative bone anchor design With respect to the proposed application as base joints of a boneattached robot, results reveal that the pullout strength, i.e., the load capacity of the anchor–bone linkage, is considerably higher than required according to the simulation data given in the introduction. This fact opens the opportunity to modify the design of the bone cutting screw to increase patient safety and to improve the intraoperative handling. The following changes are made to the initial design shown in Fig. 2: due to the unexpectedly high pullout strength, the length of the bone cutting thread is reduced in order to minimize the risk of violating the dura when placing the anchor. Furthermore, the alternative bone screw has a tapered shape in order to reduce the pilot hole diameter. In this context, a cutting edge is added to facilitate the removal of bone when screwing the anchor in. Fig. 10 shows the initial and alternative bone anchors. In order to validate the load capacity of the modified screw design, five pullout tests per load case were performed according to the previously described protocol using substitute material (d). Due to the tapered thread of the modified screw design, the diameter of the pilot hole was reduced to 1.3 mm. The pullout strength values as well as the spring constants of both the initial and the optimized bone anchor are given in Fig. 11. The results reveal that the pullout strength of the alternative anchor is on a similar order of magnitude compared to the initial design, even though the length of the screw has been reduced. Furthermore, the deviations from the median value are reduced. This phenomenon is attributed to the tapered thread, which improves the guidance of the screw within the pilot hole. As a result, the fixation of the alternative anchor is more reproducible compared to the initial design. Similar results are obtained considering the spring constants when testing according to load cases I and II, respectively. At load case III the spring constant is lower compared to the initial design. Considering the failure mode and the influence of the screw deformation this is the expected consequence of the thinner struts in the modified design. The increased spring constant with respect to load case II and the failure mode are consistent with previously obtained results. 4. Discussion The presented studies have been conducted in order to experimentally assess the pullout strength and the spring constants of anchors, which are used with a bone-attached robot for skull surgery. Four bone substitutes have been compared in order to evaluate the effect of material properties on the mechanical characteristics of the

(b)

(c)

(d)

Fig. 11. Experimentally determined pullout strength (a) and spring constants of initial and alternative bone anchor design under different load cases: close-up of load case I (b), close-up of load case II (c) and close-up of load case III (d).

J.-P. Kobler et al. / Medical Engineering and Physics 37 (2015) 460–468

anchor–bone linkage. Results reveal that the load capacities vary strongly depending on the used material. The pullout strength as well as the spring constants increase with the density (and corresponding properties given in Table 2) of the test blocks. Considering the spring constants, as already mentioned in Section 3.4, it is the laminate rather than the test block that has the most significant influence on the results. When comparing the results obtained using human cranial bone specimens, it is revealed that they are most similar to those of substitute material (d). Considering load case I, the pullout strength median values differ by approximately 30 N. When evaluating the spring constant, the deviation between the median values amounts to 161 N mm−1 . Under load case II, the results are even more similar, while the most distinct mismatch is observed when evaluating the spring constant during testing according to load case III. On the one hand, this difference is likely due to the fact that the flatness of the synthetic material allows the shoulder of the anchor to be completely flush with the surface of the bone substitute, whereas it is unrealistic to expect this condition in human cranial bone. On the other hand, the mismatch could be caused by the condition of the bone samples. Being cut from fresh skull specimen they were moist, thinner than the substitute blocks and irregularly shaped. This might have caused insufficient fixation or deformation of the sample under load leading to lower measured spring constants. Even though the different characteristics must not be neglected, with respect to the proposed application, we consider material (d) an appropriate substitute for human cadaver cranial bone based on the experimental results. According to data given in Tables 1 and 2, this was to be expected, and the results show that the other materials considered in this study are not suitable for such experiments. Apart from the composition of the test materials, several other parameters, which have not been investigated in this study, influence the mechanical characteristics of the anchor–bone linkage. Among them are properties of the bone-cutting thread, such as its pitch and the number of screw threads. Furthermore, it was found that the diameter of the pilot hole has a significant influence on the quality of the thread which is cut into the specimen. In this context, it is important to note that the determined spring constants depend on the initial screw height above the bone surface, which is assumed to be constant and defined by the dimensions of the bone anchor. Finally, variations are induced due to the manual insertion and tightening of the screw. Hence, using a mechanical device to provide assured seating of bone screws, as proposed by Mitchell and Balachandran [31,32], is expected to reduce the variations in mechanical properties of the anchor–bone linkage. Within this study, only tensile forces have been studied while generally both tensile and compressive forces act on the anchors. Considering the bone substitutes, their mechanical properties (Table 2) suggest similar or greater load capacities when compressive forces are applied. Referring to the spring constants of cranial bone samples under compressive load, experimental results are given in [33]. Based on the presented findings, the values can be assumed to be approximately twice as large compared to spring constants under tensile loads, which is beneficial since the linkage is more rigid. Considering further developments in the field of bone-attached robots, the experimentally determined spring constants represent a valuable contribution. Given a specific force and corresponding load angle, the spring characteristic (Fig. 9) can be used to estimate the resulting displacement of the bone anchor head, i.e., the base joint of the mechanism. Then, using the solution of the direct kinematics, an approximation of the position error at the tip of the drilling tool can be obtained [13]. The spring characteristic reveals that, according to the results obtained using material (d), the largest deflection of an anchor can be expected for load angles ranging from 30◦ to 60◦ . However, the available data for cranial bone suggests that it is unrealistic to expect the stiffness of the anchor–bone linkage to increase once the

467

Fig. 12. Comparison of two platform concepts. Based on the experimental results, a small platform diameter (left) yields critical load angles, under which the spring constant of the anchor–bone linkage is low. Increasing the platform diameter (right) has a beneficial effect on the load angles, i.e., the compliance of the mechanism’s base joints.

load angles exceed 60◦ . Due to this fact, we conclude that load angles greater than 30◦ should be avoided to ensure minimum compliance of the bone-attached robot. On the one hand, this can be achieved by optimizing the mechanism’s redundant degrees of freedom, which in turn influence the angles at which the struts connect to the anchors. On the other hand, the design of the platform can be modified in order to avoid critical load angles. A schematic representation of different platform diameters is given in Fig. 12. It is revealed that a larger platform diameter typically results in decreased load angles, improving the overall stiffness of the parallel robot. 5. Conclusion The bone anchors investigated in the presented study have proven to be suitable as rigid base joints of a passive parallel kinematic robot due to sufficient pullout resistance. However, both the load capacities as well as the spring constants of the anchor–bone linkage vary according to the angle at which a load is applied. When comparing synthetic biomechanical test materials, mechanical similarities between one particular test block composition (referred to as material (d)) and human cadaver cranial bone were observed. Based on the findings, a modified bone anchor design has been derived, which improves the intraoperative handling and reduces the invasiveness when placing the anchors. Using the proposed experimental setup, the mechanical properties of the alternative design have been found to match those of an initial bone anchor specification. The experimentally determined spring characteristics are valuable considering the further development and optimization of the bone-attached robot. They provide the basis for future approaches to stiffness optimization of such mechanisms. Conflict of interest None declared. Acknowledgment This work was funded by the German Research Foundation (DFG). The project numbers are OR 196/10-1 and MA 4038/6-1. References [1] Schipper J, Aschendorff A, Arapakis I, Klenzner T, Teszler CB, Ridder GJ, et al. Navigation as a quality management tool in cochlear implant surgery. J Laryngol Otol 2004;118:764–70. doi: 10.1258/0022215042450643. [2] Wolf A, Shoham M, Michael S, Moshe R. Feasibility study of a mini, boneattached, robotic system for spinal operations: analysis and experiments. Spine 2004;29(2):220–8. [3] Pechlivanis I, Kiriyanthan G, Engelhardt M, ScholzM, Lücke S, Harders A, et al. Percutaneous placement of pedicle screws in the lumbar spine using a bone mounted miniature robotic system: first experiences and accuracy of screw placement. Spine 2009;34(4):392–8. doi: 10.1097/BRS.0b013e318191ed32.

468

J.-P. Kobler et al. / Medical Engineering and Physics 37 (2015) 460–468

[4] Shamir R, Freiman M, Joskowicz L, Shoham M, Zehavi E, Shoshan Y. Robotassisted image-guided targeting for minimally invasive neurosurgery: planning, registration, and in-vitro experiment. Med Image Comput Comput Assist Interv 2005;8(2):131–8. doi: 10.1007/11566489_17. [5] Warren FM, Balachandran R, Fitzpatrick JM, Labadie RF. Percutaneous cochlear access using bone-mounted, customized drill guides: demonstration of concept in vitro. Otol Neurotol 2007;28(3):325–9. doi: 10.1097/01.mao.0000253287.86737.2e. [6] Balachandran R, Fitzpatrick JM, Labadie RF. Accuracy of image-guided surgical systems at the lateral skull base as clinically assessed using bone-anchored hearing aid posts as surgical targets. Otol Neurotol 2008;29(8):1050–5. doi: 10.1097/MAO.0b013e3181859a08. [7] Labadie RF, Noble JH, Dawant BM, Balachandran R, Majdani O, Fitzpatrick JM. Clinical validation of percutaneous cochlear implant surgery: initial report. Laryngoscope 2008;118(6):1031–9. doi: 10.1097/MLG.0b013e31816b309e. [8] Balachandran R, Mitchell JE, Blachon G, Noble JH, Dawant BM, Fitzpatrick JM, et al. Percutaneous cochlear implant drilling via customized frames: an in vitro study. Otol Head Neck Surg 2010;142(3):421–6. doi: 10.1016/j.otohns.2009.11.029. [9] Labadie RF, Balachandran R, Mitchell J, Noble JH, Majdani O, Haynes D, et al. Clinical validation study of percutaneous cochlear access using patient-customized microstereotactic frames. Otol Neurotol 2010;31(1):94. doi: 10.1097/MAO.0b013e3181c2f81a. [10] McRackan T, Balachandran R, Blachon G, Mitchell J, Noble JH, Wright C, et al. Validation of minimally invasive, image-guided cochlear implantation using advanced bionics, cochlear, and medel electrodes in a cadaver model. Int J Comput Assist Radiol Surg 2013;8(6):989–95. doi: 10.1007/s11548-013-0842-6. [11] Kratchman LB, Blachon GS, Withrow TJ, Balachandran R, Labadie RF, Webster RJ. Design of a bone-attached parallel robot for percutaneous cochlear implantation. IEEE Trans Biomed Eng 2011;58(10):2904–10. doi: 10.1109/TBME.2011.2162512. [12] Kratchman LB, Fitzpatrick JM. Robotically-adjustable microstereotactic frames for image-guided neurosurgery. In: Proc. SPIE; vol. 8671. 2013. p. 86711U. doi: 10.1117/12.2008172. [13] Kobler JP, Kotlarski J, Öltjen J, Baron S, Ortmaier T. Design and analysis of a headmounted parallel kinematic device for skull surgery. Int J Comput Assist Radiol Surg 2012;7(1):137–49. doi: 10.1007/s11548-011-0619-8. [14] Kobler JP, Kotlarski J, Lexow GJ, Majdani O, Ortmaier T. Design optimization of a bone-attached, redundant and reconfigurable parallel kinematic device for skull surgery. In: Proc. of the IEEE ICRA. 2014. p. 2364–71. doi: 10.1109/ICRA.2014.6907187. [15] Kobler JP, Wall S, Lexow GJ, Lang CP, Majdani O, Kahrs LA, et al. An experimental evaluation of loads occurring during guided drilling for cochlear implantation. Int J Comput Assist Radiol Surg 2015 (published online). doi: 10.1007/s11548-0151153-x. [16] Bickford JH. An introduction to the design and behavior of bolted joints. 3 ed. CRC Press; 1995. [17] You ZH, Bell WH, Schneiderman ED, Ashman RB. Biomechanical properties of small bone screws. J Oral Maxillofac Surg 1994;52(12):1293–302. doi: 10.1016/0278-2391(94)90052-3.

[18] Carano A, Lonardo P, Velo S, Incorvati C. Mechanical properties of three different commercially available miniscrews for skeletal anchorage. Prog Orthod 2005;6(1):82–97. [19] Seebeck J, Lill C, Morlock MM, Schneider E. Implantatverankerung in osteoporotischem Knochen mittels monokortikaler Schrauben (implant fixation in osteoporotic bone using monocortical screws). Trauma Berufskrankheit 1999;1(4):411–14. doi: 10.1007/s100390050073. [20] Poukalova M, Yakacki CM, Guldberg RE, Lin A, Saing M, Gillogly SD, et al. Pullout strength of suture anchors: effect of mechanical properties of trabecular bone. J Biomech 2010;43(6):1138–45. doi: 10.1016/j.jbiomech.2009.12.007. [21] Lexow GJ, Rau TS, Eckardt F, Kobler JP, Ortmaier T, Lenarz T, et al. Automatisierte Bestimmung der Schädelknochendicke in CT- und DVT-Bilddaten. 11 Jahrestagung der Deutschen Gesellschaft für Computer- und Roboterassistierte Chirurgie eV (CURAC), Düsseldorf 2012. [22] Fiala TGS, Novelline RA, Yaremchuk MJ. Comparison of CT imaging artifacts from craniomaxillofacial internal fixation devices. Plast Reconstr Surg 1993;92(7):1227–32. [23] McElhaney JH, Fogle JL, Melvin JW, Haynes RR, Roberts VL, Alem NM. Mechanical properties of cranial bone. J Biomech 1970;3(5):495–511. doi: 10.1016/00219290(70)90059-X. [24] Wood JL. Dynamic response of human cranial bone. J Biomech 1971;4(1):1–12. [25] Peterson J, Dechow PC. Material properties of the inner and outer cortical tables of the human parietal bone. Anat Rec 2002;268(1):7–15. doi: 10.1002/ar.10131. [26] Peterson J, Dechow PC. Material properties of the human cranial vault and zygoma. Anat Rec A Discov Mol Cell Evol Biol 2003;274(1):785–97. doi: 10.1002/ar.a.10096. [27] Delille R, Lesueur D, Potier P, Drazetic P, Markiewicz E. Experimental study of the bone behaviour of the human skull bone for the development of a physical head model. Int J Crashworthiness 2007;12(2):101–8. doi: 10.1080/13588260701433081. [28] Motherway JA, Verschueren P, der Perre GV, Sloten JV, Gilchrist MD. The mechanical properties of cranial bone: the effect of loading rate and cranial sampling position. J Biomech 2009;42(13):2129–35. doi: 10.1016/j.jbiomech.2009.05.030. [29] Zioupos P, Smith CW, An YH. Factors affecting mechanical properties of bone. In: Mechanical testing of bone and the bone-implant interface. CRC Press; 2000. [30] McGill R, Tukey JW, Larsen WA. Variations of box plots. Am Stat 1978;32(1): 12–16. [31] Mitchell J, Labadie RF, Fitzpatrick JM. Design of a novel device to provide assured seating of bone implanted fiducial markers. J Med Devices 2010;4(2):025002. doi: 10.1115/1.4001585. [32] Balachandran R, Fritz MA, Dietrich MS, Danilchenko A, Mitchell JE, Oldfield VL, et al. Clinical testing of an alternate method of inserting bone-implanted fiducial markers. Int J Comput Assist Radiol Surg 2014; 9(5):913–20. doi: 10.1007/s11548014-0980-5. [33] Kebernik M. Charakterisierung der mechanischen Eigenschaften der SchraubenKnochen-Verbindung im kortikalen Knochen. Ph.D. thesis. Medizinische Fakultät der Universität Ulm; 2005.