Load-Sharing and Kinematics of the Human Cervical Spine Under Multi-Axial Transverse Shear Loading: Combined Experimental and Computational Investigation.

The cervical spine experiences shear forces during everyday activities and injurious events yet there is a paucity of biomechanical data characterizing the cervical spine under shear loading. This study aimed to (1) characterize load transmission paths and kinematics of the subaxial cervical spine under shear loading, and (2) assess a contemporary finite element cervical spine model using this data. Subaxial functional spinal units (FSUs) were subjected to anterior, posterior, and lateral shear forces (200 N) applied with and without superimposed axial compression preload (200 N) while monitoring spine kinematics. Load transmission paths were identified using strain gauges on the anterior vertebral body and lateral masses and a disc pressure sensor. Experimental conditions were simulated with cervical spine finite element model FSUs (GHBMC M50 version 5.0). The mean kinematics, vertebral strains, and disc pressures were compared to experimental results. The shear force-displacement response typically demonstrated a toe region followed by a linear response, with higher stiffness in anterior shear relative to lateral and posterior shear. Compressive axial preload decreased posterior and lateral shear stiffness and increased initial anterior shear stiffness. Load transmission patterns and kinematics suggest the facet joints play a key role in limiting anterior shear while the disc governs motion in posterior shear. The main cervical spine shear responses and trends are faithfully predicted by the GHBMC cervical spine model. These basic cervical spine biomechanics and the computational model can provide insight into mechanisms for facet dislocation in high severity impacts, and tissue distraction in low severity impacts.

[12 years of Computer-Aided Surgery around the Head : Developments in surgical planning and simulation from a Bern perspective]. / 12 Jahre Computer-Aided Surgery around the Head : Entwicklungen in der chirurgischen Planung und Simulation aus Berner Perspektive.

Over the past years, the multidisciplinary character of the international Computer-Aided Surgery around the Head (CAS-H) symposium has advanced many medical technologies, which were often adopted by industry. In Bern, the synergetic effects of the CAS-H symposium have enabled many experiences and developments in the area of computer-aided surgery. Planning and simulation methods in the areas of craniomaxillofacial surgery and otorhinolaryngology were developed and tested in clinical settings. In the future, further CAS-H symposia should follow, in order to promote the possibilities and applications of computer-assisted surgery around the head.

[Navigation and robotics of the lateral skull base]. / Navigation und Robotik an der Otobasis.

Computer-aided microscopic surgery of the lateral skull base is a rare intervention in daily practice. It is often a delicate and difficult minimally invasive intervention, since orientation between the petrous bone and the petrous bone apex is often challenging. In the case of aural atresia or tumors the normal anatomical landmarks are often absent, making orientation more difficult. Navigation support, together with imaging techniques such as CT, MR and angiography, enable the surgeon in such cases to perform the operation more accurately and, in some cases, also in a shorter time. However, there are no internationally standardised indications for navigated surgery on the lateral skull base. Miniaturised robotic systems are still in the initial validation phase.

[Computer-aided surgery of the paranasal sinuses and the anterior skull base]. / Computerassistierte Chirurgie der Nasennebenhöhlen und der vorderen Schädelbasis.

Endoscopic or microscopic surgery for chronic rhinosinusitis with or without nasal polyps is a routine intervention in daily practice. It is often a delicate and difficult minimally invasive intervention in a narrow space, with a tunnel view of 4 mm in the case of endoscopy and frequent bleeding in chronically inflamed tissue. Therefore, orientation in such a "labyrinth" is often difficult. In the case of polyp recurrence or tumors, the normal anatomical landmarks are often missing, which renders orientation even more difficult. In such cases, computer-aided navigation together with images such as those from computed tomography or magnetic resonance imaging can support the surgeon to make the operation more accurate and, in some cases, faster. Computer-aided surgery also has great potential for education.

Accuracy considerations in navigated cup placement for total hip arthroplasty.

Computer assisted orthopaedic surgery (CAOS) technology has recently been introduced to overcome problems resulting from acetabular component malpositioning in total hip arthroplasty. Available navigation modules can conceptually be categorized as computer tomography (CT) based, fluoroscopy based, or image-free. The current study presents a comprehensive accuracy analysis on the computer assisted placement accuracy of acetabular cups. It combines analyses using mathematical approaches, in vitro testing environments, and an in vivo clinical trial. A hybrid navigation approach combining image-free with fluoroscopic technology was chosen as the best compromise to CT-based systems. It introduces pointer-based digitization for easily assessable points and bi-planar fluoroscopy for deep-seated landmarks. From the in vitro data maximum deviations were found to be 3.6 degrees for inclination and 3.8 degrees for anteversion relative to a pre-defined test position. The maximum difference between intraoperatively calculated cup inclination and anteversion with the postoperatively measured position was 4 degrees and 5 degrees, respectively. These data coincide with worst cases scenario predictions applying a statistical simulation model. The proper use of navigation technology can reduce variability of cup placement well within the surgical safe zone. Surgeons have to concentrate on a variety of error sources during the procedure, which may explain the reported strong learning curves for CAOS technologies.

A CT-free, intra-operative planning and navigation system for minimally invasive anterior spinal surgery - an accuracy study.

OBJECTIVE: A comprehensive study was performed to evaluate the accuracy of a newly developed CT-free, intra-operative planning and navigation system for anterior spine surgery. MATERIALS AND METHODS: Instruments and an image intensifier were tracked using the SurgiGATE navigation system. A laboratory study was performed on 27 plastic vertebrae. Fiducial markers were implanted in the vertebrae for accuracy evaluation purposes, and a dynamic reference base was placed on the vertebrae to establish a patient coordinate system (P-COS). Two fluoroscopic images were used for intra-operative planning. The graft bed plan was recorded in P-COS, followed by surgical formation of the graft bed, which was visualized. To evaluate the accuracy, the vertebrae were scanned with CT, and the markers were used to calculate an accurate paired-point registered transformation between the CT coordinate system and P-COS. RESULTS: Using the new SPO module, accurate planning and navigation of a resection of the vertebral body is possible using two fluoroscopic images. The overall mean error between the planned resection volume and the actual resection was 0.98 mm. In addition, the module can serve as an educational tool for training spine surgeons. CONCLUSIONS: The new fluoroscopy-based system can be used safely for accurate performance of anterior resection during spondylodesis. New methods for safe and accurate registration during anterior spine surgery need to be developed.

Computer-assisted, fluoroscopy-based ventral spondylodesis of thoracolumbar fractures.

OBJECTIVE: To design and evaluate a novel computer-assisted, fluoroscopy-based planning and navigation system for minimally invasive ventral spondylodesis of thoracolumbar fractures. MATERIALS AND METHODS: Instruments and an image intensifier are tracked with the SurgiGATE navigation system (Praxim-Medivision). Two fluoroscopic images, one acquired from anterior-posterior (AP) direction and the other from lateral-medial (LM) direction, are used for the complete procedure of planning and navigation. Both of them are calibrated with a custom-made software to recover their projection geometry and to co-register them to a common patient reference coordinate system, which is established by attaching an opto-electronically trackable dynamic reference base (DRB) on the operated vertebra. A bi-planar landmark reconstruction method is used to acquire deep-seated anatomical landmarks such that an intraoperative planning of graft bed can be interactively done. Finally, surgical actions such as the placement of the stabilization devices and the formation of the graft bed using a custom-made chisel are visualized to the surgeon by superimposing virtual instrument representations onto the acquired images. The distance between the instrument tip and each wall of the planned graft bed are calculated on the fly and presented to the surgeon so that the surgeon could formalize the graft bed exactly according to his/her plan. RESULTS: Laboratory studies on phantom and on 27 plastic vertebras demonstrate the high precision of the proposed navigation system. Compared with CT-based measurement, a mean error of 1.0 mm with a standard deviation of 0.1 mm was found. CONCLUSIONS: The proposed computer assisted, fluoroscopy-based planning and navigation system promises to increase the accuracy and reliability of minimally invasive ventral spondylodesis of thoracolumbar fractures.

New orthopaedic implant management tool for computer-assisted planning, navigation, and simulation: from implant CAD files to a standardized XML-based implant database.

Computer-Assisted Orthopaedic Surgery (CAOS) has made much progress over the last 10 years. Navigation systems have been recognized as important tools that help surgeons, and various such systems have been developed. A disadvantage of these systems is that they use non-standard formalisms and techniques. As a result, there are no standard concepts for implant and tool management or data formats to store information for use in 3D planning and navigation. We addressed these limitations and developed a practical and generic solution that offers benefits for surgeons, implant manufacturers, and CAS application developers. We developed a virtual implant database containing geometrical as well as calibration information for orthopedic implants and instruments, with a focus on trauma. This database has been successfully tested for various applications in the client/server mode. The implant information is not static, however, because manufacturers periodically revise their implants, resulting in the deletion of some implants and the introduction of new ones. Tracking these continuous changes and keeping CAS systems up to date is a tedious task if done manually. This leads to additional costs for system development, and some errors are inevitably generated due to the huge amount of information that has to be processed. To ease management with respect to implant life cycle, we developed a tool to assist end-users (surgeons, hospitals, CAS system providers, and implant manufacturers) in managing their implants. Our system can be used for pre-operative planning and intra-operative navigation, and also for any surgical simulation involving orthopedic implants. Currently, this tool allows addition of new implants, modification of existing ones, deletion of obsolete implants, export of a given implant, and also creation of backups. Our implant management system has been successfully tested in the laboratory with very promising results. It makes it possible to fill the current gap that exists between the CAS system and implant manufacturers, hospitals, and surgeons.

A comparative biomechanical investigation of anterior lumbar interbody cages: central and bilateral approaches.

BACKGROUND: Some biomechanical studies have been performed to evaluate the stabilization provided by interbody cages, but there are virtually no comparative data for the different designs. Furthermore, most investigators have used animal models, which may have led to different results due to morphological variation in the end plates and articular facets. The objectives of the current study were to evaluate whether two different anterior cage designs (BAK and SynCage) performed differently with respect to immediate stabilization of the spine, whether the cages stabilized the spine significantly compared with its intact condition, and whether the addition of supplementary translaminar screw fixation further stabilized the spine. Stabilization was defined as a reduction in motion after insertion of an implant. METHODS: Twelve lumbar functional spinal units from human cadavera were tested under pure moments of flexion, extension, bilateral axial rotation, and bilateral lateral bending to a maximum of ten newton-meters. The relative intervertebral motions were measured, with use of an optoelectronic camera system, under three test conditions: with the spine intact, after insertion of anterior interbody cages, and after insertion of anterior interbody cages supplemented with translaminar screw fixation. Six specimens were tested for each type of cage: a bilateral, porous, threaded cylinder (BAK) and a central, porous, contoured implant with end-plate fit (SynCage). RESULTS: The cages performed in a similar manner in all directions of loading, with no significant differences between the two designs. The cages significantly stabilized the spine compared with its intact condition in flexion, axial rotation, and lateral bending (the median value for motion was 40, 48, and 29 percent of the value for the intact condition, respectively; p = 0.002 for all three directions). Compared with the cages alone, translaminar screw fixation provided no additional stabilizing effect in these directions but it significantly increased the stability of the spine in extension (the median value for motion was 34 percent of the value with the cages alone; p = 0.013). CONCLUSIONS: There were no differences in the stabilization provided by the two different cage designs. Use of the cages alone stabilized the spine in all directions except extension, and use of supplementary translaminar screw fixation provided additional stabilization only in extension. CLINICAL RELEVANCE: This study demonstrated that interbody cages do not stabilize the lumbar spine in extension, and this observation was not altered by the use of substantially different designs. If the lack of stabilization in extension is a clinical problem, possible solutions include the avoidance of extension postoperatively or the use of supplementary fixation.

A minimally disruptive technique for measuring intervertebral disc pressure in vitro: application to the cervical spine.

A novel technique to measure in vitro disc pressures in human cervical spine specimens was developed. A miniature pressure transducer was used and an insertion technique was designed to minimise artefacts due to insertion. The technique was used to measure the intradiscal pressure in cervical spines loaded in pure axial compression. The resulting pressure varied linearly with the applied compressive force with coefficients of determination (r(2)) greater than 0.99 for each of the four specimens. Peak pressures between 2.4 and 3.5MPa were recorded under 800N of compression.

In vitro axial preload application during spine flexibility testing: towards reduced apparatus-related artefacts.

Presently, there is little consensus about how, or even if, axial preload should be incorporated in spine flexibility tests in order to simulate the compressive loads naturally present in vivo. Some preload application methods are suspected of producing unwanted "artefact" forces as the specimen rotates and, in doing so, influencing the resulting kinematics. The objective of this study was to quantitatively compare four distinct types of preload which have roots in contemporary experimental practice. The specific quantities compared were the reaction moments and forces resulting at the intervertebral disc and specimen kinematics. The preload types incorporated increasing amounts of caudal constraint on the preload application vector ranging from an unconstrained dead-load arrangement to an apparatus that allowed the vector to follow rotations of the specimen. Six human cadaveric spine segments were tested (1-L1/L2, 3-L2/L3, 1-L3/L4 and 1-L4/L5). Pure moments were applied to the specimens with each of the four different types of compressive preload. Kinematic response was measured using an opto-electronic motion analysis system. A six-axis load cell was used to measure reaction forces and moments. Artefact reaction moments and shear forces were significantly affected by preload application method and magnitude. Unconstrained preload methods produced high artefact moments and low artefact shear forces while more constrained methods did the opposite. A mechanical trade-off is suggested by our results, whereby unwanted moment can only be prevented at the cost of shear force production. When comparing spine flexibility studies, caution should be exercised to ensure preload was applied in a similar manner for all studies. Unwanted moments or forces induced as a result of preload application method may render the comparison of two seemingly similar studies inappropriate.

Biomechanical properties of sterilized human auditory ossicles.

Bone allograft material is treated with sterilization methods to prevent the transmission of diseases from the donor to the recipient. The effect of some of these treatments on the integrity of the bone is unknown. This study was performed to evaluate the effect of several sterilization methods on the mechanical behaviour of human middle ear bones. Due to the size and composition of the bones (approximately 1.5 mm diameter by 4 mm long), mechanical testing options were limited to the traditional platens compression test. Experiments were first performed with synthetic bone to evaluate the precision of this test applied to small specimens. Following this, fresh frozen human ossicles were thawed and sterilized with (i) 1 N NaOH (n = 12); (ii) 0.9% LpH, a phenolic solution (n = 12); or (iii) steam at 134 degrees C (n = 18). A group of 26 control specimens did not receive any sterilization treatment. Material and structural properties were determined from axial compression testing. Results from the synthetic bone showed that the test was reproducible, with standard deviations less than 20% of the means. Significant differences occurred in stiffness and ultimate force values between NaOH-treated and autoclaved bones when compared to normals (p<0.05), but not for LpH-treated bones. LpH is not approved for medical use, so NaOH is the most appropriate of the treatments studied for the sterilization of ossicle allografts.

Animation of in vitro biomechanical tests.

Interdisciplinary communication of three-dimensional kinematic data arising from in vitro biomechanical tests is challenging. Complex kinematic representations such as the helical axes of motion (HAM) add to the challenge. The difficulty increases further when other quantities (i.e. load or tissue strain data) are combined with the kinematic data. The objectives of this study were to develop a method to graphically replay and animate in vitro biomechanical tests including HAM data. This will allow intuitive interpretation of kinematic and other data independent of the viewer's area of expertise. The value of this method was verified with a biomechanical test investigating load-sharing of the cervical spine. Three 3.0 mm aluminium spheres were glued to each of the two vertebrae from a C2-3 segment of a human cervical spine. Before the biomechanical tests, CT scans were made of the specimen (slice thickness=1.0 mm and slice spacing=1.5 mm). The specimens were subjected to right axial torsion moments (2.0 Nm). Strain rosettes mounted to the anterior surface of the C3 vertebral body and bilaterally beneath the facet joints on C3 were used to estimate the force flow through the specimen. The locations of the aluminium spheres were digitised using a space pointer and the motion analysis system. Kinematics were measured using an optoelectronic motion analysis system. HAMs were calculated to describe the specimen kinematics. The digitised aluminium sphere locations were used to match the CT and biomechanical test data (RMS errors between the CT and experimental points were less than 1.0 mm). The biomechanical tests were "replayed" by animating reconstructed CT models in accordance with the recorded experimental kinematics, using custom software. The animated test replays allowed intuitive analysis of the kinematic data in relation to the strain data. This technique improves the ability of experts from disparate backgrounds to interpret and discuss this type of biomechanical data.

Design and evaluation of a cryogenic soft tissue fixation device -- load tolerances and thermal aspects.

Mechanical studies of soft connective tissues often encounter methodological difficulties, particularly in the secure fixation of the tissues. A simple, inexpensive technique which allowed stable cryofixation of soft tissues in uniaxial loading machines was developed. The cryogenic fixation device was evaluated in terms of its fixation strength and the temperature gradients within the tested tissues. Human patellar ligaments and quadriceps tendons were tested successfully to an average failure load of 2219N (S.D. 448N) with mid-substance failures occurring in 90% of the specimens. The temperature gradients within porcine flexor and extensor tendons were determined and found to exhibit a typical diffusion profile. The fixation quality was dependent upon the initial block temperature and the desired testing time. In summary, the cryofixation device presented here is an effective tool for soft tissue fixation but the effect of this type of fixation on internal tissue temperatures and possible testing times must be acknowledged.

Frameless optical computer-aided tracking of a microscope for otorhinology and skull base surgery.

OBJECTIVES: To integrate a digitally controlled operating microscope without a laser autofocus system into a frameless optical computer-aided surgery system and to test the accuracy and usability of this system in otorhinological surgery. DESIGN: Experimental study and case series. SETTING: Department of Oto-Rhino-Laryngology, Head and Neck Surgery, Inselspital, and the Maurice E. Müller Institute for Biomechanics, University of Bern, Bern, Switzerland. PATIENTS: Eight computer-aided microscopic surgical procedures were performed between January and October 2000 on patients with various diseases of the anterior and lateral skull base. RESULTS: The practical accuracy of the navigated microscope on the lateral side of a cadaver skull was 2.27 +/- 0.25 mm and on the anterior side of the same skull was 2.07 +/- 0.35 mm. In all 8 cases of computer-aided microscopic surgery, no complications occurred. Clinical inaccuracy was 2 to 3 mm. CONCLUSION: Integration of a low-cost, non-laser autofocus microscope into our computer-aided surgery system was successfully performed and offers surgeons the ability to combine the precise optics of the operating microscope with the localization power of a computer-aided system.

A biomechanical comparison of cervical laminaplasty and cervical laminectomy with progressive facetectomy.

The effects of multilevel cervical laminaplasty and laminectomy with increasing amounts of facetectomy on stability of the cervical spine were tested with physiologic loading in nine cadaveric specimens. Cervical spines, levels C2-C7, were tested with physiologic loading in a constraint-free test system, the motion of each body being tracked in a three-dimensional coordinate system. Cervical laminectomy with 25% or more facetectomy resulted in a highly significant increase in cervical motion compared to the intact specimens for the dominant motions of flexion/extension (P < 0.003), axial torsion (P < 0.001), and lateral bending (P < 0.001). Cervical laminaplasty was not significantly different from the intact control, except for a marginal increase in axial torsion. Coupled motion did not change with laminaplasty or laminectomy with progressive facetectomy. As little as 25% facetectomy adversely affects stability after multilevel cervical laminectomy. Cervical laminaplasty avoids this problem, while still affording multilevel decompression. Therefore in patients undergoing cervical laminectomy accompanied by more than 25% bilateral facetectomy, concurrent arthrodesis should be performed.

Constrained testing conditions affect the axial rotation response of lumbar functional spinal units.

STUDY DESIGN: Human cadaveric spine specimens were tested in axial rotation using constrained and unconstrained methods. OBJECTIVES: To determine the degree to which constrained methods affect the response of the functional spinal unit in axial rotation at lumbar and lumbosacral levels. SUMMARY OF BACKGROUND DATA: A substantial controversy exists in the literature regarding the appropriateness of different testing methods. No study has been found in which the effect of constraint on axial rotation behavior was objectively examined. METHODS: Ten human cadaveric spine specimens (five L3-L4, five L5-S1) were tested in axial rotation, using both constrained and unconstrained methods. In the unconstrained test, pure moments were applied to the upper vertebra, and its complete three-dimensional motion was measured using an optoelectronic camera system. In the constrained test, the specimens were loaded in a fixed-axis servohydraulic test machine individually around five rotational axis positions within the vertebral body, and the rotational motion was measured. RESULTS: The rotational angles in the constrained tests were not different among the five rotational axis positions. However, the maximum rotation from the five axis positions was approximately 40% greater than the minimum rotation, a significant difference. The axial rotational motion of the unconstrained tests was always less than the maximum rotation measured in the constrained test. However, the total rotational angle using the helical axis of motion was not significantly different from the constrained angles. CONCLUSIONS: The large differences between maximum and minimum rotation angles demonstrate that the behavior of the functional spinal unit in axial rotation is sensitive to the axis's position but the location of the axis is not repeatable. This supports the use of unconstrained methods in spinal testing.

Moments and forces during pedicle screw insertion. In vitro and in vivo measurements.

STUDY DESIGN: Moments and forces during pedicle screw insertion were measured in vivo and in vitro and were correlated to several parameters of the screw-bone interface. OBJECTIVES: To compare the in vitro and in vivo screw insertion loads and to relate these measurements to bone mineral density, pedicle size, and other screw parameters (material, diameter). SUMMARY OF BACKGROUND DATA: The in vitro screw insertion torque has been correlated to the screw pullout forces and the number of cycles to ultimate interface failure. However, there are no comparable in vivo data. METHODS: One hundred three pedicle screws were included in the study, 43 in vivo and 60 in vitro. Duel-energy x-ray absorptiometry boen mineral density data were available for 20 in vivo and 32 in vitro specimens. A custom-made sterilizable six-axis load cell was integrated into a torque wrench, enabling the recording of the applied moments and forces during screw insertion. Statistical analysis was performed to detect differences and correlations. RESULTS: The mean in vivo insertion torque (1.29 Nm) was significantly greater than the in vitro value (0.67 Nm). The linear correlation between insertion torque and bone mineral density was significant for the in vitro data but not for the in vivo data. No correlation was observed between insertion torque and pedicle diameter. Two patterns of torque were observed during the insertion process. CONCLUSIONS: There is a significant difference between the insertion loads measured in vivo and those measured in vitro. Additional research is needed to verify whether this method provides an indication of screw fixation quality.

The effect of nucleotomy on lumbar spine mechanics in compression and shear loading.

STUDY DESIGN: An in vitro biomechanical investigation on human cadaveric specimens was conducted before and after nucleotomy. Endplate and vertebral body deformation patterns were measured under compression and shear loading, in addition to kinematics and disc pressure. OBJECTIVE: The working hypotheses of this study were that in compression, nucleotomy results in an altered deformation pattern of the endplate and that in shear, nucleotomy does not result in an altered endplate deformation pattern or disc pressure. SUMMARY OF BACKGROUND DATA: The pressure distributions within the intervertebral disc have been studied in compression loading but not in shear loading. Severe degeneration and surgical nucleotomy result in small nuclear pressure and altered loading distribution in compression. The effect of these changes on the vertebral endplate and the response under shear loads are not well understood. METHODS: Five L3-L4 and two L4-L5 functional spinal units were tested under compression and shear loading, intact and after nucleotomy. Vertebral body deformations, intradiscal pressure, and intervertebral kinematics were measured. A series of compression-type (maximum 1000 N) and shear-type (maximum 500 N) loads were applied. RESULTS: With nucleotomy, the disc pressure and the endplate strains decreased under compression, but the vertebral rim strains did not change. In shear, the vertebral rim and endplate strains did not change with nucleotomy. Disc pressure was lower in shear than in compression. CONCLUSION: Nucleotomy resulted in decreased disc pressure, decreased endplate deformation, and modified loading patterns onto the inferior vertebra in compression loading. However, nucleotomy did not appreciably affect the behavior of the disc in shear loading.

Experimental study of atlas injuries. I. Biomechanical analysis of their mechanisms and fracture patterns.

Understanding injury mechanisms is important for the prevention, diagnosis, and treatment of spinal injuries. Using 10 fresh cadaveric human spine specimens of occiput to C3, clinically similar injuries of the atlas (C1) were produced with high-speed (4.4 m/sec) axial compression. The traumatic event was biomechanically monitored. The resulting injuries were studied with radiography, computed tomography, and a multidirectional instability test. The average compressive failure force was 3,050 N for specimens impacted in neutral posture (n = 437) and 2,100 N for those in extended posture (n = 282). Corresponding values for the impulse were 34.9 Nsec (n = 8.3) and 17.6 Nsec (n = 1.8). Average instability for both groups, as measured by the neutral zone and range of motion, increased by 90% and 44%, respectively, in flexion-extension and 20% in lateral bending, but not in axial rotation. These findings confirm the clinical observations.