Position and complications of pedicle screw insertion with or without image-navigation techniques in the thoracolumbar spine: a meta-analysis of comparative studies

Image quality and radiation dose in spinal surgery: a comparison of three imaging systems in phantom

Purpose

Using optimal settings for x-ray scans is crucial for obtaining three-dimensional images of high quality while keeping the patient dose low. Our work compares dose and image quality (IQ) of three intraoperative imaging systems [O-arm cone-beam computed tomography (CBCT), ClarifEye C-arm CBCT, and Airo computed tomography] used for spinal surgery.

Approach

Patients of 70, 90, and 110 kg were simulated with an anthropomorphic phantom by adding tissue-equivalent material. Titanium inserts were placed in the phantom spine for reproducing metal artifacts in the images. Organ dose was measured with thermo-luminescent dosimeters for effective dose (E ) calculation. Subjective IQ was assessed by ranking the images acquired with the manufacturer-defined imaging protocols. Objective IQ was assessed with a customized Catphan phantom.

Results

The ClarifEye protocols resulted in the lowest E ranging from 1.4 to 5.1 mSv according to phantom size and protocol. The highest E was measured for the high-definition protocol of O-arm (E 2.2 to 9 mSv) providing the best subjective IQ for imaging of the spine without titanium inserts. For the images with metal, the best IQ was obtained with ClarifEye. Airo (E 5.5 to 8.4 mSv) was ranked with the lowest IQ for images without metal while the rank improved for images with metal. Airo images had better uniformity, noise, and contrast sensitivity compared with CBCTs but worse high-contrast resolution. The values of these parameters were comparable between the CBCT systems.

Conclusions

Both CBCT systems provided better IQ compared with Airo for navigation of lumbar spinal surgery for the original phantom. Metal artifacts particularly affect O-arm images decreasing the subjective IQ. The high spatial resolution of CBCT systems resulted in a relevant parameter for the visibility of anatomical features important for spine navigation. Low dose protocols were enough to obtain a clinically acceptable contrast-to-noise ratio in the bones.

3D Visualisation of the Spine

The 3D visualisation of the spine is thought of from multiple viewpoints. Firstly, radiological imaging is considered, with plain radiography, CT and MRI imaging discussed in detail with relevant applications to spinal surgery.3D printing can be used in spinal surgery with multiple applications including education, pre-operative planning for complex cases and making patient-specific guides and implants. The rapidly growing field of intraoperative navigation and robotics have been discussed, in addition to their benefits and limitations within spinal surgery, as well as some technical tips.An understanding of relevant anatomy and biomechanics is necessary for any surgeon, and so this chapter describes the key concepts to be familiar with, particularly the spinal motion segment and the different methods for classifying spinal injuries and how that relates to stability. The concepts discussed have been brought together by applying this knowledge to some interesting clinical cases. They highlight the importance of 3D visualisation of the spine, which must be considered throughout the decision-making process when managing patients. Spinal surgeons use multiple imaging modalities, knowledge of anatomy and biomechanics, as well as considering the need for navigation in more complex cases, all on a daily basis. With the advancement of technology available for 3D visualisation of the spine, we will be able to improve patient outcomes even further in the future.

Statistical shape modelling of the thoracic spine for the development of pedicle screw insertion guides

Spinal fixation and fusion are surgical procedures undertaken to restore stability in the spine and restrict painful or degenerative motion. Malpositioning of pedicle screws during these procedures can result in major neurological and vascular damage. Patient-specific surgical guides offer clear benefits, reducing malposition rates by up to 25%. However, they suffer from long lead times and the manufacturing process is dependent on third-party specialists. The development of a standard set of surgical guides may eliminate the issues with the manufacturing process. To evaluate the feasibility of this option, a statistical shape model (SSM) was created and used to analyse the morphological variations of the T4-T6 vertebrae in a population of 90 specimens from the Visible Korean Human dataset (50 females and 40 males). The first three principal components, representing 39.7% of the variance within the population, were analysed. The model showed high variability in the transverse process (~ 4 mm) and spinous process (~ 4 mm) and relatively low variation (< 1 mm) in the vertebral lamina. For a Korean population, a standardised set of surgical guides would likely need to align with the lamina where the variance in the population is lower. It is recommended that this standard set of surgical guides should accommodate pedicle screw diameters of 3.5-6 mm and transverse pedicle screw angles of 3.5°-12.4°.

Image Guidance in Spinal Surgery: A Critical Appraisal and Future Directions

BACKGROUND

Image-guided spinal surgery (IGSS) underwent rapid development over the past decades. The goal of IGSS is to increase patient safety and improve workflow. We present an overview of the history of IGSS, illustrate its current state, and highlight future developments. Currently, IGSS requires an image set, a tracking system, and a calibration method.

IMAGING

Two-dimensional images have many disadvantages as a source for navigation. Currently, the most common navigation technique is three-dimensional (3D) navigation based on cross-sectional imaging techniques such as cone-beam computed tomography (CT) or fan-beam CT.

TRACKING

Electromagnetic tracking uses an electromagnetic field to localize instruments. Optical tracking using infrared cameras has currently become one of the most common tracking methods in IGSS.

CALIBRATION

The three most common techniques currently used are the point-matching registration technique, the surface-matching registration technique, and the automated registration technique.

FUTURE

Augmented reality (AR) describes a computer-generated image that can be superimposed onto the real-world environment. Marking pathologies and anatomical landmarks are a few examples of many possible future applications. Additionally, AR offers a wide range of possibilities in surgical training. The latest development in IGSS is robotic-assisted surgery (RAS). The presently available data on RAS are very encouraging, but further improvements of these procedures is expected.

CONCLUSION

IGSS significantly evolved since its inception and is becoming a routinely used technology. In the future, IGSS will combine the advantages of "active/freehand 3D navigation" with AR and RAS and will one day find its way into all aspects of spinal surgery, not only in instrumented procedures.

Advances in tissue state recognition in spinal surgery: a review

Spinal disease is an important cause of cervical discomfort, low back pain, radiating pain in the limbs, and neurogenic intermittent claudication, and its incidence is increasing annually. From the etiological viewpoint, these symptoms are directly caused by the compression of the spinal cord, nerve roots, and blood vessels and are most effectively treated with surgery. Spinal surgeries are primarily performed using two different techniques: spinal canal decompression and internal fixation. In the past, tactile sensation was the primary method used by surgeons to understand the state of the tissue within the operating area. However, this method has several disadvantages because of its subjectivity. Therefore, it has become the focus of spinal surgery research so as to strengthen the objectivity of tissue state recognition, improve the accuracy of safe area location, and avoid surgical injury to tissues. Aside from traditional imaging methods, surgical sensing techniques based on force, bioelectrical impedance, and other methods have been gradually developed and tested in the clinical setting. This article reviews the progress of different tissue state recognition methods in spinal surgery and summarizes their advantages and disadvantages.

Radiation Exposure in Posterior Lumbar Fusion: A Comparison of CT Image-Guided Navigation, Robotic Assistance, and Intraoperative Fluoroscopy

STUDY DESIGN

Retrospective clinical review.

OBJECTIVE

To assess the use of intraoperative computed tomography (CT) image-guided navigation (IGN) and robotic assistance in posterior lumbar surgery and their relationship with patient radiation exposure and perioperative outcomes.

METHODS

Patients ≥18 years old undergoing 1- to 2-level transforaminal lateral interbody fusion in 12-month period were included. Chart review was performed for pre- and intraoperative data on radiation dose and perioperative outcomes. All radiation doses are quantified in milliGrays (mGy). Univariate analysis and multivariate logistic regression analysis were utilized for categorical variables. One-way analysis of variance with post hoc Tukey test was used for continuous variables.

RESULTS

A total of 165 patients were assessed: 12 IGN, 62 robotic, 56 open, 35 fluoroscopically guided minimally invasive surgery (MIS). There was a lower proportion of women in open and MIS groups (P = .010). There were more younger patients in the MIS group (P < .001). MIS group had the lowest mean posterior levels fused (P = .015). Total-procedure radiation, total-procedure radiation/level fused, and intraoperative radiation was the lowest in the open group and highest in the MIS group compared with IGN and robotic groups (all P < .001). Higher proportion of robotic and lower proportion of MIS patients had preoperative CT (P < .001). Estimated blood loss (P = .002) and hospital length of stay (P = .039) were lowest in the MIS group. Highest operative time was observed for IGN patients (P < .001). No differences were observed in body mass index, Charlson Comorbidity Index, and postoperative complications (P = .313, .051, and .644, respectively).

CONCLUSION

IGN and robotic assistance in posterior lumbar fusion were associated with higher intraoperative and total-procedure radiation exposure than open cases without IGN/robotics, but significantly less than MIS without IGN/robotics, without differences in perioperative outcomes. Fluoro-MIS procedures reported highest radiation exposure to patient, and of equal concern is that the proportion of total radiation dose also applied to the surgeon and operating room staff in fluoro-MIS group is higher than in IGN/robotics and open groups.

Prospective Evaluation of the Time Required for Insertion of 380 Lumbar and Sacral Pedicle Screws Using Navigation with an Intraoperative 3-Dimensional Imaging System

Background

The aim of this study was to evaluate the time required for various parts of the procedure to insert lumbar and sacral pedicle screws using navigation with an intraoperative, 3-dimensional imaging system. Comparison of these timings was carried out for different surgical indications.

Methods

This was a single-surgeon prospective cohort study of 69 consecutive patients (between August 2013 and June 2018) who underwent insertion of 380 pedicle screws into the lumbar and sacral vertebrae. Surgical indications, average time required for surgical exposure and attachment of the reference frame, average time required until completion of the first pedicle screw insertion, and average time required for insertion of a single pedicle screw were evaluated.

Results

The average time required from skin incision to reference frame attachment was 28.3 ± 20.4 (mean ± SD) minutes, and the average time required from reference frame attachment to completion of first pedicle screw insertion was 22.3 ± 9.6 minutes. The average time required for insertion of a single pedicle screw was 7.8 ± 2.7 minutes. When surgical indications were compared, the average time required for insertion of a single pedicle screw was 7.7 ± 2.6 minutes in surgery for spondylosis-related stenosis, 8.1 ± 2.8 minutes for degenerative scoliosis, and 8.2 ± 3.6 minutes for metastatic tumor (P = .89). There were no significant changes in these timings over consecutive 6-month periods.

Conclusions

There is no significant learning curve and no significant difference in navigation setup and pedicle screw insertion timings with intraoperative 3-dimensional navigation systems for surgeries of different pathologies and levels of surgery.

Level of Evidence

2.

Technical Note: Pedicle Cement Augmentation with Proximal Screw Toggle and Loosening

Background

Cement augmentation is a technique used to increase the stability and purchase of pedicle screws in poor quality bone. Various methods can be applied for cement delivery, such as cement injection before screw placement and the use of fenestrated screws. However, potential problems can arise with the use of cement augmentation.

Case Presentation

A 66‐year‐old man with a lower trunk deformity, severe kyphosis, and sagittal imbalance following fusion (L_2‐5), with minimal comorbidities, was referred to our unit 9 months after surgery. Pain and progressive kyphosis were investigated clinically and radiographically with computed tomography (CT) scans to assess the status of the hardware and fusion. CT imaging revealed that cement was present only at the distal tip of the fenestrated screws at the L4 vertebral level. A non‐union was present along with loosening and a halo around the body of the pedicle screws, and there was evidence of pullout of inferior screws.

Conclusion

Single‐level cement augmentation of pedicle screw in a posterior construct and distal tip cement augmentation of the screw results in a fixed pivot point. Micromotion in cranio‐caudal loading during flexion and extension may result in screw toggling with the single‐level cement‐augmented tip as a fulcrum. This may cause screw loosening, which can lead to pullout and loss of construct stability. The halo around the screw suggests bone loss and/or a fibrous tissue interface, which further complicates revision surgery. Stress shielding and polymethylmethacrylate cement present additional difficulties.

The findings of this technical note question the risks and benefits of cement‐augmented fenestrated pedicle screw fixation for spinal fusion. Although incidences of such cases are uncommon, surgeons should perform this technique with caution. Accurate restoration of lumbar lordosis during index procedures is important to minimize the risk of construct failure.

Robotic-assisted navigated minimally invasive pedicle screw placement in the first 100 cases at a single institution

Proper pedicle screw placement is an integral part of spine fusion requiring expertly trained spine surgeons. Advances in medical imaging guidance have improved accuracy. There is high interest in the emerging field of robot-assisted spine surgery; however, safety and accuracy studies are needed. This study describes the pedicle screw placement of the first 100 cases in which navigated robotic assistance was used in a private practice clinical setting. A single-surgeon, single-site retrospective Institutional Review Board-exempt review of the first 100 navigated robot-assisted spine surgery cases was performed. An orthopaedic surgeon evaluated screw placement using plain film radiographs. In addition, pedicle screw malposition, reposition, and return to operating room (OR) rates were collected. Results demonstrated a high level (99%) of successful surgeon assessed pedicle screw placement in minimally invasive navigated robot-assisted spine surgery, with no malpositions requiring return to the OR.

Radiation dose and image quality comparison during spine surgery with two different, intraoperative 3D imaging navigation systems

Careful protocol selection is required during intraoperative three-dimensional (3D) imaging for spine surgery to manage patient radiation dose and achieve clinical image quality. Radiation dose and image quality of a Medtronic O-arm commonly used during spine surgery, and a Philips hybrid operating room equipped with XperCT C-arm 3D cone-beam CT (hCBCT) are compared. The mobile O-arm (mCBCT) offers three different radiation dose settings (low, standard, and high), for four different patient sizes (small, medium, large, and extra large). The patient's radiation dose rate is constant during the entire 3D scan. In contrast, C-CBCT spine imaging uses three different field of views (27, 37, and 48 cm) using automatic exposure control (AEC) that modulates the patient's radiation dose rate during the 3D scan based on changing patient thickness. hCBCT uses additional x-ray beam filtration. Small, medium, and large trunk phantoms designed to mimic spine and soft tissue were imaged to assess radiation dose and image quality of the two systems. The estimated measured "patient" dose for the small, medium, and large phantoms imaged by the mCBCT considering all the dose settings ranged from 9.4-27.6 mGy, 8.9-33.3 mGy, and 13.8-40.6 mGy, respectively. The "patient" dose values for the same phantoms imaged with hCBCT were 2.8-4.6 mGy, 5.7-10.0 mGy, and 11.0-15.2 mGy. The CNR for the small, medium, and large phantoms was 2.9 to 3.7, 2.0 to 3.0, and 2.5 to 2.6 times higher with the hCBCT system, respectively. Hounsfield unit accuracy, noise, and uniformity of hCBCT exceeded the performance of the mCBCT; spatial resolution was comparable. Added x-ray beam filtration and AEC capability achieved clinical image quality for intraoperative spine surgery at reduced radiation dose to the patient in comparison to a reference O-arm system without these capabilities.

Percutaneous fixation of thoracolumbar vertebral fractures

Surgical treatment of patients with thoracolumbar vertebral fracture without neurological deficit is still controversial.

Management of vertebral fracture with percutaneous fixation was first reported in 2004.

Advantages of percutaneous fixation are: less tissue dissection; decreased post-operative pain; decreased bleeding and operative time (depending on the steep learning curve); better screw positioning with fluoroscopy compared with an open freehand technique; and a decreased infection rate.

The limitations of percutaneous fixation of vertebral fractures include increased radiation exposure to the patient and the surgeon, together with the steep learning curve for this technique.

Adding a screw at the level of the fractured vertebra has the advantages of incorporating fewer motion segments with less operative time and bleeding. This also increases the axial, sagittal and torsional stiffness of the construct.

Percutaneous fixation alone without grafting is sufficient for treating type A and B1 (AO classification) thoracolumbar fractures with satisfactory results concerning kyphosis reduction when compared with open instrumentation and fusion and with open fixation.

Type C and B2 fractures (ligamentous injuries) should undergo fusion since the ligamentous healing is mechanically weak, increasing the risk of instability.

This review offers a detailed description of percutaneous screw insertion and discusses the advantages and disadvantages.

Cite this article: EFORT Open Rev 2018;3:604-613. DOI: 10.1302/2058-5241.3.170026.

Learning curve analysis of 3D-fluoroscopy image-guided pedicle screw insertions in lumbar single-level fusion procedures

INTRODUCTION

The implementation of 3D-navigation in the operating theater is reported to be complex, time consuming, and radiation intense. This prospective single-center cohort study was performed to objectify these assumptions by determining navigation-related learning curves in lumbar single-level posterior fusion procedures using 3D-fluoroscopy for real-time image-guided pedicle screw (PS) insertions.

MATERIALS AND METHODS

From August 2011 through July 2016, a total of 320 navigated PSs were inserted during 80 lumbar single-level posterior fusion procedures by a single surgeon without any prior experience in image-guided surgery. PS misplacements, navigation-related pre- and intraoperative time demand, and procedural 3D-radiation dose (dose-length-product, DLP) were prospectively recorded and congregated in 16 subgroups of five consecutive procedures to evaluate improving PS insertion accuracy, decreasing navigation-related time demand, and reduction of 3D-radiation dose.

RESULTS

After PS insertion and intraoperative O-arm control scanning, 11 PS modifications were performed sporadically without showing "learning curve dependencies" (PS insertion accuracies in subgroups 96.6 ± 6.3%). Average navigation-related pre-surgical time from patient positioning on the operating table to skin incision decreased from 61 ± 6 min (subgroup 1) to 28 ± 2 min (subgroup 16, p < 0.00001). Average 3D-radiation dose per surgery declined from 919 ± 225 mGycm (subgroup 1) to 66 ± 4 mGycm (subgroup 16, p < 0.0001).

CONCLUSIONS

In newly inaugurated O-arm based image-guidance, lumbar PS insertions can be performed at constantly high accuracy, even without prior experience in navigated techniques. Navigation-related time demand decreases considerably due to accelerating workflow preceding skin incision. Procedural 3D-radiation dose is reducible to a fraction (13.2%) of a lumbar diagnostic non-contrast-enhanced computed tomography scan's radiation dose.

Accuracy of minimally invasive percutaneous thoracolumbar pedicle screws using 2D fluoroscopy: a retrospective review through 3D CT analysis

BACKGROUND

In the literature, there is a large variation in the reported misplacement rates of pedicle screws. The use of minimally invasive surgical techniques is increasing and as such there has only been a small amount of data to look at the misplacement rate of percutaneously inserted thoracic and lumbar pedicle screws.

METHODS

A retrospective analysis of post-operative computed tomography (CT) scans were performed on 108 patients who underwent minimally invasive percutaneously inserted thoracic and lumbar pedicle screws by a single surgeon. Analysis of the screw trajectory using strict guidelines was performed using multiplanar reconstruction CT scan data to determine the accuracy of the pedicle screws.

RESULTS

A total of 614 screws were inserted in vertebral levels T2 to S1. Twenty-five (4.07%) screws were considered misplaced having breached the pedicular cortex. Thoracic pedicle screws had a statistically higher misplacement rate than lumbar pedicle screws (14.67% vs. 2.60% respectively, P<0.001). A single screw required replacement (0.16%) and there were no permanent neurological deficits. The misplacement rates were lower than those reported for open screw placement and equivalent to 3D CT navigated misplacement rates.

CONCLUSIONS

Percutaneously inserted pedicle screws using 2D fluoroscopy offers a safe and accurate option for spinal stabilisation with an extremely low misplacement rate and morbidity. Overall, the low misplacement rates were equivalent and in most cases lower compared to open and computer assisted navigation techniques. However, we would recommend that given a misplacement rate of 14.67% for thoracic pedicle screws that computer assisted navigation may be able to offer further improvements in accuracy.

Reliability of the Planned Pedicle Screw Trajectory versus the Actual Pedicle Screw Trajectory using Intra-operative 3D CT and Image Guidance

BACKGROUND

Technological advances, including navigation, have been made to improve safety and accuracy of pedicle screw fixation. We evaluated the accuracy of the virtual screw placement (Stealth projection) compared to actual screw placement (intra-operative O-Arm) and examined for differences based on the distance from the reference frame.

METHODS

A retrospective evaluation of prospectively collected data was conducted from January 2013 to September 2013. We evaluated thoracic and lumbosacral pedicle screws placed using intraoperative O-arm and Stealth navigation by obtaining virtual screw projections and intraoperative O-arm images after screw placement. The screw trajectory angle to the midsagittal line and superior endplate was compared in the axial and sagittal views, respectively. Percent error and paired t-test statistics were then performed.

RESULTS

Thirty-one patients with 240 pedicle screws were analyzed. The mean angular difference between the virtual and actual image in all screws was 2.17° ± 2.20° on axial images and 2.16° ± 2.24° on sagittal images. There was excellent agreement between actual and virtual pedicle screw trajectories in the axial and sagittal plane with ICC = 0.99 (95%CI: 0.992-0.995) (p<0.001) and ICC= 0.81 (95%CI: 0.759-0.855) (p<0.001) respectively. When comparing thoracic and lumbar screws, there was a significant difference in the sagittal angulation between the two distributions. No statistical differences were found distance from the reference frame.

CONCLUSION

The virtual projection view is clinically accurate compared to the actual placement on intra-operative CT in both the axial and sagittal views. There is slight imprecision (~2°) in the axial and sagittal planes and a minor difference in the sagittal thoracic and lumbar angulation, although these did not affect clinical outcomes. In general, we find that pedicle screw placement using intraoperative cone beam CT and navigation to be accurate and reliable, and as such have made it a routine part of our spine practice. This study was approved by the University of Minnesota IRB (#1303E30544).

A New Electromagnetic Navigation System for Pedicle Screws Placement: A Human Cadaver Study at the Lumbar Spine

Introduction

Technical developments for improving the safety and accuracy of pedicle screw placement play an increasingly important role in spine surgery. In addition to the standard techniques of free-hand placement and fluoroscopic navigation, the rate of complications is reduced by 3D fluoroscopy, cone-beam CT, intraoperative CT/MRI, and various other navigation techniques. Another important aspect that should be emphasized is the reduction of intraoperative radiation exposure for personnel and patient.

The aim of this study was to investigate the accuracy of a new navigation system for the spine based on an electromagnetic field.

Material and Method

Twenty pedicle screws were placed in the lumbar spine of human cadavers using EMF navigation. Navigation was based on data from a preoperative thin-slice CT scan. The cadavers were positioned on a special field generator and the system was matched using a patient tracker on the spinous process. Navigation was conducted using especially developed instruments that can be tracked in the electromagnetic field. Another thin-slice CT scan was made postoperatively to assess the result. The evaluation included the position of the screws in the direction of trajectory and any injury to the surrounding cortical bone. The results were classified in 5 groups: grade 1: ideal screw position in the center of the pedicle with no cortical bone injury; grade 2: acceptable screw position, cortical bone injury with cortical penetration ≤ 2 mm; grade 3: cortical bone injury with cortical penetration 2,1-4 mm, grad 4: cortical bone injury with cortical penetration 4,1-6 mm, grade 5: cortical bone injury with cortical penetration >6 mm.

Results

The initial evaluation of the system showed good accuracy for the lumbar spine (65% grade 1, 20% grade 2, 15% grade 3, 0% grade 4, 0% grade 5). A comparison of the initial results with other navigation techniques in literature (CT navigation, 2D fluoroscopic navigation) shows that the accuracy of this system is comparable.

Conclusion

EMF navigation offers a high accuracy in Pedicle screw placement with additional advantages compared to other techniques. The short set-up time and easy handling of EMF navigation should be emphasized. Additional advantages are the absence of intraoperative radiation exposure for the operator and surgical team in the current set-up and the operator’s free mobility without interfering with navigation. Further studies with navigation at higher levels of the spine, larger numbers of cases and studies with control group are planned.

Navigation of pedicle screws in the thoracic spine with a new electromagnetic navigation system: a human cadaver study

INTRODUCTION

Posterior stabilization of the spine is a standard procedure in spinal surgery. In addition to the standard techniques, several new techniques have been developed. The objective of this cadaveric study was to examine the accuracy of a new electromagnetic navigation system for instrumentation of pedicle screws in the spine.

MATERIAL AND METHOD

Forty-eight pedicle screws were inserted in the thoracic spine of human cadavers using EMF navigation and instruments developed especially for electromagnetic navigation. The screw position was assessed postoperatively by a CT scan.

RESULTS

The screws were classified into 3 groups: grade 1 = ideal position; grade 2 = cortical penetration <2 mm; grade 3 = cortical penetration ≥2 mm. The initial evaluation of the system showed satisfied positioning for the thoracic spine; 37 of 48 screws (77.1%, 95% confidence interval [62.7%, 88%]) were classified as group 1 or 2.

DISCUSSION

The screw placement was satisfactory. The initial results show that there is room for improvement with some changes needed. The ease of use and short setup times should be pointed out. Instrumentation is achieved without restricting the operator's mobility during navigation.

CONCLUSION

The results indicate a good placement technique for pedicle screws. Big advantages are the easy handling of the system.