Correlation between the ease of cage plates implantation and endplate Hounsfield unit value during ACDF: a retrospective study

Abstract

Objective

To investigate the correlation between the implantation status of the ROI-C cervical cage plates and the Hounsfield unit(HU) value of the target vertebral endplate during anterior cervical decompression and fusion (ACDF)surgery.

Methods

Review of patient data undergoing ACDF from January 2018 to December 2021. Data on gender, age, body mass index, history of hypertension, diabetes, hyperlipidemia, smoking, alcohol consumption, cervical cage plates status, and HU values of the cervical vertebral endplate. Logistic regression analysis was used to evaluate the relationship between the HU values and the plates status.

Results

A total of 17 cases (12.1%) had misplaced implants during surgery. There were statistical differences in gender, long-term smoking history, drinking history, and cervical vertebral endplate HU values between the abnormal implantation group and the normal implantation group (P < 0.05). The cervical vertebral endplate HU values in the abnormal implantation group were significantly higher than those in the normal implantation group (729.3 ± 36.2 HU vs. 484.4 ± 59.2 HU, P < 0.001). In the logistic regression analysis, cervical endplate HU value (OR 1.081; 95% CI 1.016–1.375) was an independent factor influencing improper plate implantation. The area under the ROC curve (AUC) for the cervical endplate HU value in predicting implantation difficulty was 0.836 (P < 0.05), with an optimal threshold of 724 HU (sensitivity 83.2%; specificity 90.4%).

Conclusions

The cervical vertebral segment endplate HU value can independently predict whether the implantation of the plates is misplaced during ACDF surgery.

Introduction

Anterior cervical decompression and fusion (ACDF) surgery is a commonly employed procedure for treating degenerative cervical conditions, owing to its advantages such as minimal trauma, thorough decompression, effective restoration of intervertebral height, and maintenance of physiological lordosis [1, 2]. Following the initial proposal of ACDF by Smith and Robinson in 1958 [3], autologous iliac bone was first utilized for interbody fusion. However, due to drawbacks such as prolonged external fixation and a high incidence of pseudoarthrosis, a fusion technique involving a steel plate combined with an intervertebral fusion device emerged. This fusion method has been shown to accelerate degeneration in adjacent cervical segments. In comparison to the traditional anterior approach with a steel plate combined with a Cage, the zero-profile interbody fusion and fixation system exhibit comparable fusion rates, lower profile, and a lesser impact on adjacent segment degeneration [4, 5]. Its clinical application has gradually increased in recent years.

Currently, anchored cervical fusion cage (AC), utilized in clinical practice, primarily consist of screw fixation and plate fixation types. The screw fixation category of AC poses risks of screw loosening and breakage postoperatively, with limitations on bone graft volume. The plate fixation type of AC aligns more with the morphological characteristics of the cervical intervertebral space, allowing for effective immediate stability and lower rates of fusion device subsidence. ROI-C is a type of cervical interbody fusion cage, consisting of a PEEK material cage and two endplates, and it is widely used in clinical applications. In some ACDF procedures, patients with excessively strong cervical endplate may experience difficulties in proper plates insertion, leading to increased intraoperative and postoperative complications that can impact surgical outcomes. A thorough preoperative assessment of the patient’s cervical endplate strength holds significance in guiding the implantation of ROI-C plates during ACDF procedures.

Dual Energy X-ray Absorptiometry (DXA) is currently the gold standard for measuring bone density. However, conventional DXA scans are primarily used for lumbar spine measurements, only reflecting the overall bone density status of the vertebral body and cannot accurately depict the bone quality of the cervical spine. Computed tomography (CT) images divide the human body into numerous volume units, and the material within each unit’s attenuation coefficient to X-rays represents the material density of that unit, known as the CT value, measured in HU [6].The HU value method can be employed for zone-specific measurements of the cervical spine, and the magnitude of HU value can, to a certain extent, reflect the strength or weakness of local bone density in the cervical spine [7].

Therefore, this study retrospectively reviewed cases from 2018 to 2021 where difficulty was encountered in inserting wedges during ACDF procedures. The HU values of the upper and lower vertebral endplate in the surgical segments were measured. Preliminary screening was performed to identify the critical range of HU value for endplate where plates insertion might be challenging. The study aimed to explore solutions for overcoming difficulties in plate implantation during surgery and how to reduce the occurrence of complications, providing clinical practitioners with valuable insights.

Patients and methods

Patients cohort

This study retrospectively reviewed patient data from January 2018 to December 2021, who underwent ACDF for cervical degenerative diseases at Dongzhimen Hospital.

Inclusion criteria: (1) Diagnosed with radicular or myelopathic cervical spondylosis based on symptoms, physical signs, and imaging findings; (2) Ineffectiveness of regular conservative treatment for three months with a worsening trend; (3) Underwent ACDF surgery using a dual-wedge self-locking fusion system; (4) Preoperative cervical CT examination performed at our hospital within three months.

Exclusion criteria: (1) Congenital cervical deformity, cervical fracture, or dislocation; (2) Developmental cervical spinal canal stenosis; (3) Ossification of the posterior longitudinal ligament and/or calcification of the yellow ligament; (4) Concurrent cervical tumors or infections; (5) History of previous cervical spine surgery; (6) Severe history of mental illness.

A total of 153 patients were initially reviewed, and based on the inclusion and exclusion criteria, a final cohort of 141 patients was included, comprising 72 males and 69 females, with an average age of 60.5 ± 7.0 years (ranging from 47 to 79 years). There were 21 cases with single-level involvement, 64 cases with two-level involvement, and 56 cases with three-level involvement. According to the plate implantation status, patients were categorized into the Normal Implantation Group (124 cases with proper wedge placement) and the Abnormal Implantation Group (17 cases with misplaced wedges). The follow-up period was 31.5 ± 7.2 months, ranging from 24 to 47 months.

Surgical method

All surgeries were performed by the corresponding author. Preoperatively, patients underwent tracheal displacement training for 2 to 3 days. The patient is positioned supine with the neck moderately extended. A transverse incision, approximately 4 to 6 cm in length, is made on the right side of the anterior neck. Successively, the skin, subcutaneous tissue, and the sternocleidomastoid muscle are incised. The corresponding intervertebral disc is exposed through the interval between the carotid sheath and the visceral sheath. The diseased intervertebral disc and posterior longitudinal ligament are removed, thoroughly clearing ruptured nucleus pulposus tissue. Adequate scraping is performed on the hypertrophic posterior edge of the vertebral body and the articular process, and a 2 mm-diameter laminar bone rongeur is used to open the neural foramen, achieving complete decompression of the nerve root. The upper and lower endplates are addressed, the neck is placed in the functional position, and a corresponding trial mold is used to assess the appropriate height, matching the normal intervertebral disc height and ensuring relative stability. Subsequently, the respective model of the ROI-C cervical cage is inserted, and homologous allograft bone is placed within the fusion device. After satisfactory fluoroscopic positioning, the dual plates are inserted into the vertebral body for anchorage and tightening. Confirmation of satisfactory plate implantation (if difficult or improper, record promptly postoperatively), wound irrigation, placement of rubber drains, and layered closure follow.

Clinical data and imaging measurements

Individual data include age, gender, body mass index (BMI, kg/m2), history of hypertension, diabetes, hyperlipidemia, and smoking and drinking habits. Surgical data include the fused segments of the operation.

All patients underwent cervical three-dimensional reconstruction CT within the three months preceding the surgery, using a Siemens dual-source CT machine (scanning tube voltage set at 120 kV). Two experienced spine surgeons independently utilized the Picture Archiving and Communication Systems (PACS) for image measurement, and the average value were recorded. CT measurement parameters: in the sagittal and coronal planes of the CT scans, three planes perpendicular to the horizontal plane were selected. Care was taken to avoid cancellous bone areas, and in the cross-sectional view, a region of interest (ROI) encompassing the cervical vertebral endplates, as large as possible, was drawn. The average HU value within the ROI was recorded (Fig. 1). Endplate HU value were obtained by averaging the HU value from six planes. Using this method, HU value of the upper and lower endplates within the surgical cervical intervertebral space were measured for each patient. For the Abnormal Implantation Group, the HU value represented the mean HU value of the endplates in the surgical segments where the wedges were improperly implanted. For the Normal Implantation Group, the HU value represented the mean HU value of all endplates in the surgical segments. One month later, 30 randomly selected patients underwent a second round of HU value measurements by the same two assessors.

Fig. 1

Measurement of the Hounsfield Units (HU) value of the target cervical vertebral endplate in the Picture Archiving and Communication System (PACS). In the CT coronal section (a) and sagittal section (b), three image planes perpendicular to the horizontal plane, namely a1, a2, a3 and b1, b2, b3, were selected. The average HU value within the region of interest (ROI) were obtained

Another senior spine surgeon, based on cervical X-ray images, assessed the situation of the self-locking fusion device plate s. The evaluation included determining whether they were improperly implanted, encompassing cases of non-implantation and displacement. Difficulty in Implanting the Cage Plate: The surgeon experiences significant resistance when striking the cage plate with regular force, making it difficult to implant smoothly. Increasing the striking force by one to several times allows the cage plate to slowly enter the upper and lower endplates, but it cannot be fully inserted.

Statistical methods

The data were analyzed using SPSS 22.0 software. Continuous variables (age, BMI, endplate HU value) were expressed as mean ± standard deviation (x̄±s), and categorical variables (gender, history of hypertension, diabetes, hyperlipidemia, long-term smoking、drinking history (≥ 10 years), and whether the plates were improperly implanted) were presented as counts. Intra-class correlation coefficients (ICCs) were used to assess intra- and inter-rater reliability for HU value measurements. An ICC of 1 indicates complete reliability; ICC values between 0.8 and 0.99 suggest very reliable measurements; ICC values between 0.6 and 0.79 suggest moderately reliable measurements; ICC values between 0.4 and 0.59 suggest fair reliability; ICC values below 0.40 suggest poor reliability. An inter-rater ICC greater than 0.80 was considered reliable. For continuous variables (age, BMI, endplate HU values), normality and homogeneity of variance were assessed. If these assumptions were met, independent sample t-tests were used for between-group comparisons; otherwise, the Mann⁃Whitney U test was used. Categorical variables were presented as frequencies, and between-group comparisons were performed using the χ2 test. Logistic regression analysis was conducted to assess the relationship between endplate HU values, age, gender, BMI, history of hypertension, diabetes, hyperlipidemia, smoking, drinking, and improperly implanted plates. Receiver Operating Characteristic(ROC) curves were employed to evaluate the predictive value of HU values for improperly implanted plates, with a cut-off value determined based on the maximum Youden Index. The significance level (α) was set at 0.05 for all tests.

Results

Consistency analysis of HU value measurements

Consistency analysis was conducted for both intra-rater (repeated measurements by the same assessor) and inter-rater (measurements by two different assessors) HU value measurements. The results indicated that the intra-rater and inter-rater ICC values were both greater than 0.80, suggesting a high level of reliability and consistency. Refer to Table 1 for specific details.

Table 1 Intra-rater and inter-rater reliability of HU value measurements

Analysis of risk factors for abnormal implantation of plates

The HU value of the endplates in the surgical segments for patients in the abnormal implantation group was significantly higher at 729.3 ± 36.2 HU compared to the normal implantation group, where the HU value was 484.4 ± 59.2 HU (P<0.001). The proportion of male patients in the abnormal implantation group was higher at 76.5% compared to 47.6% in the normal group (P<0.05). The abnormal implantation group had a higher proportion of patients with a history of long-term smoking at 82.4% compared to 35.5% in the normal group (P<0.001). Similarly, the proportion of patients with a history of long-term drinking was higher in the abnormal implantation group at 82.4% compared to 19.4% in the normal group (P<0.001). There were no statistically significant differences in age, BMI, hypertension, diabetes, and hyperlipidemia history between the abnormal implantation group and the normal implantation group (P>0.05). Refer to Table 2 for specific details.

Table 2 Comparison of normal and abnormal implantation groups

Predictive value of endplate HU value for difficult implantation of plate

According to the variables in Table 2 with P < 0.05, they were considered potential risk factors affecting the difficulty of cage plate implantation and included in the multivariate logistic regression analysis (Table 3). The results showed that a history of long-term smoking (OR 8.485; 95% [2.312–31.136]), a history of long-term drinking (OR 19.444; 95% [5.173–73.091]), and the endplate CT value at the surgical segment (OR 1.081; 95% [1.016–1.375]) are independent risk factors for the difficulty of cage plate implantation; age, gender and BMI were not a predictive factor for implantation difficulty.

Table 3 Binary logistic regression analysis of risk factors for difficult plates implantation

The ROC curve was used to analyze the predictive value of cervical endplate CT values for the difficulty of implanting interbody fusion cage plates. The area under the curve (AUC) for predicting implantation difficulty based on preoperative vertebral endplate HU value was 0.836 (95% CI: 0.788, 0.915), indicating a good predictive effect (AUC > 0.8). The critical CT value for predicting implantation difficulty, corresponding to the maximum Youden index, was 724 HU, with a sensitivity of 0.832 and a specificity of 0.904 (Fig. 2). In the normal group, a total of 5 patients had cervical endplate CT values exceeding 724 HU (4.03%), while in the abnormal group, a total of 14 patients had cervical endplate CT values exceeding 724 HU (82.35%).

Fig. 2

Receiver Operating Characteristic (ROC) curve for cervical vertebral endplate HU value and malpositioned grafts, with a critical Hounsfield Units (HU) threshold of 724 HU

Typical case

Patient Li, male, 64 years old, with a 30-year history of smoking (10 cigarettes per day) and a 30-year history of alcohol consumption (approximately 50 g per day). Admitted to the hospital due to a 3-year history of “unsteady walking” and diagnosed with myelopathic cervical spondylosis. Underwent anterior cervical decompression, removal of the herniated nucleus pulposus, and interbody fusion with a bone graft and implantation of a fusion device. During the surgery, the upper plate in the C3-4 segment could not be inserted, and the upper plate in the C5-6 segment was not properly placed. The HU values measured for the patient’s C3 lower endplate, C4 upper endplate, C4 lower endplate, C5 upper endplate, C5 lower endplate, and C6 upper endplate were 789, 860, 833, 760, 802, and 700 HU, respectively. At 1 week postoperatively, the patient’s unsteady walking improved compared to preoperatively. At the last follow-up (33 months postoperatively), the patient exhibited a normal gait, and the sensation of stepping on cotton was essentially eliminated. Radiological data before and after surgery are shown in Fig. 3.

Fig. 3

Patient Li, preoperative cervical spine X-rays showing multiple degenerations and extensive hyperplasia (a, b); cervical spine CT and MRI (c, d, e, f) revealing disc protrusions at C3-4, C4-5, C5-6 with partial calcification, and evident spinal cord compression. Postoperative cervical spine X-rays (g, h) indicating the lower graft in position at the C3-4 level, while the upper graft at C5-6 is incompletely inserted. Follow-up X-rays (i, j) at the last visit demonstrate bony fusion of the anterior and posterior edges of the vertebral bodies at C3-4 and C4-5 segments, and the upper graft at C5-6 forming a bony enclosure at the anterior end, showing no further displacement compared to the postoperative images

Discussion

The ACDF procedure was initially proposed by Cloward [8] and Robinson, Smith [3] in the 1950s. After half a century of development, the fusion technique combining an anterior plate and cage has gradually become the preferred approach for ACDF. This method significantly restores intervertebral height, maintains segmental lordosis, and achieves a higher rate of bone fusion, making it one of the routine surgical methods for treating degenerative cervical diseases [9]. Due to complications such as postoperative swallowing difficulties, screw loosening or breakage, and adjacent segment degeneration after ACDF, the zero-profile cage was designed and gradually introduced into clinical practice [10, 11].

The zero-profile cage, while maintaining the advantages of traditional anterior plate combined with cage, incurs smaller surgical trauma, causing less damage to the cervical spine and anterior structures. It better preserves the biomechanical stability of the cervical spine, effectively reducing postoperative complications such as swallowing difficulties and adjacent segment degeneration. As a result, it has gradually gained favor among spine surgeons [12, 13]. The ROI-C interbody fusion device is a double-plate self-locking cervical fusion device. The pre-bent bridge-shaped plates are equipped with “barb” mechanisms on both sides, which lock into the endplate upon proper implantation to provide immediate stability and prevent the fusion device from shifting. It is widely used in clinical practice [14].

When implanting the ROI-C plates, the front end may penetrate the cervical vertebral endplate and enter the vertebral body, and the notched structure gets embedded into the endplate, securing the implant in place, as illustrated in Fig. 4. The front end of the implant has a non-sharp structure with a certain thickness, requiring a certain degree of force to be hammered in smoothly. In some elderly patients with hardened endplates, implantation of the plates can be challenging, and it may be difficult to control the hammering force, potentially increasing surgical complications. If the cervical vertebral endplate is too hard, and the standard hammering force cannot penetrate the implant, the surgeon may increase the hammering force, leading to potential implant fractures or spinal cord concussion. Additionally, if the patient’s anesthesia depth is shallow during the hammering process, excessive force can cause involuntary movements, resulting in spinal cord damage due to excessive vibrations within the vertebral canal. A hardened endplate corresponds to an increased duration of implantation, and prolonged traction on the adjacent soft tissues may lead to difficulties in swallowing, recurrent laryngeal nerve paralysis, and other complications after surgery. To prevent these issues, surgeons may reduce the hammering force. However, this often leads to inadequate implantation in patients with excessively strong cervical vertebral endplates, causing implant retreat or extrusion after surgery, compromising the stability of the interbody fusion device, and ultimately resulting in fusion failure. In this study, 1 patient in the abnormal implantation group experienced spinal cord shock during surgery, which improved with symptomatic treatment postoperatively; 2 patients developed swallowing difficulties after surgery, which also improved with treatment; and 5 patients had gradual anterior migration of the fusion device during follow-up, with 1 patient reporting a foreign body sensation in the throat, which improved with symptomatic treatment. In the normal implantation group, 5 patients experienced postoperative swallowing difficulties, all of which improved with symptomatic treatment; 3 patients had anterior migration of the fusion device but reported no discomfort.

Fig. 4

Schematic representation of the ROI-C self-stabilizing fusion device, featuring a blunt structure at the graft’s leading edge. Bilateral “barb”-like self-locking mechanisms prevent displacement of the implanted fusion device. Note: Image sourced from the LDR Medical official website: https://www.medicalexpo.com/prod/ldr-medical/product-81488-518592.html

The HU value measurement method is simple, yields accurate results, and reflects tissue density in the measured area with good practicality for assessing bone quality, attracting widespread attention domestically and internationally [15]. The conventional method for measuring HU values of cervical vertebral bodies involves drawing as large a ROI as possible within the trabecular bone of the vertebral body on the transverse section, and then obtaining the average HU value. The vertebral endplate is divided into bony endplate and cartilaginous endplate. The bony endplate is formed by gradual ossification of the cartilage plate in the growth and development process, presenting a mildly concave shape. The cartilaginous endplate covers the central portion of the vertebral endplate with a thin layer of transparent cartilage. The cervical vertebral endplate has a mildly concave shape, making it challenging to use the conventional method to measure HU values. To obtain the true HU values of the cervical vertebral endplate as accurately as possible, this study selected three planes perpendicular to the upper and lower endplates of the cervical vertebrae in both sagittal and coronal views. Care was taken to avoid the trabecular bone region of the vertebral body, and a large square ROI was drawn in the cross-section to read the average HU value within the ROI.

This study retrospectively examined the HU value of cervical vertebral endplates and the status of cage implantation in patients undergoing ACDF surgery. The aim was to determine the critical range of cervical vertebral endplate HU value associated with difficulties in the ROI-C plates. Based on this HU value range, the study aimed to predict the intraoperative plates implantation status in patients undergoing ACDF. The results indicated that patients in the difficult plates implantation group had significantly higher HU values in the cervical vertebral endplates of the operated segments compared to the normal implantation group (P<0.001). It is noteworthy that, in the difficult plates implantation group, there was a higher proportion of patients with a history of long-term smoking and drinking, and a higher proportion of male patients compared to female patients in contrast to the normal plates implantation group.

Current research indicates that smoking and alcohol consumption are risk factors for osteoporosis [16]. Prolonged smoking or drinking can lead to sparse trabeculae and decreased bone density in the vertebral bodies. Nicotine, the most abundant substance in tobacco, can alter the permeability of blood vessel walls, impeding the exchange of substances between blood and tissues [17]. This results in inefficient absorption and utilization of proteins and calcium by blood vessels. Other compounds in tobacco can alter blood acidity, promoting bone dissolution. Alcohol can inhibit the growth of mesenchymal stem cells in bone marrow and their transformation into osteoblasts, affecting the activity of bone cells [18]. The degenerative mechanism of cartilaginous endplates primarily involves degeneration and calcification, leading to increased hardness and higher bone density of the cartilaginous endplates [19, 20]. The bone density of the endplates may not necessarily change consistently with the bone density of the vertebral bodies [21]. While vertebral body bone density decreases, the bone density beneath the endplates may show no significant change or an increase.

Chondrocytes in cartilage endplates usually remain in a quiescent state and proliferate only when activated [22]. Therefore, the survival and death of chondrocytes are crucial for the preservation of articular cartilage. Studies have shown that cigarette smoke extract can inhibit the vitality, proliferation, and matrix formation of chondrocytes. When the concentration of cigarette smoke extract reaches 10%, it generates a large number of free radicals and induces cell death [23].

Previous studies have also shown that patients who smoke or consume alcohol have a higher incidence of complications after spinal surgery. Khurana et al. summarized literature and found that smokers are more prone to atherosclerosis, with a higher risk of thrombosis formation [24]. Consequently, the blood supply to the spinal tissues in the surgical area is obstructed, leading to local hypoxia, inflammation, protein hydrolysis, and cell loss. Ultimately, these processes contribute to the damage of intervertebral discs, cartilage, synovium, and other structures.Preoperative alcohol consumption can affect patients’ blood pressure and electrolyte balance, and long-term alcohol consumption can impact the recovery of symptoms after lumbar spine surgery [25, 26]. For patients with a history of long-term smoking or drinking, it is necessary to assess the vertebral endplate bone density before surgery to formulate alternative plans for the potential difficulty of plates implantation during the procedure. In addition, the proportion of smoking and alcohol consumption is significantly higher among male patients in China compared to females. This may be one of the reasons why the proportion of males with difficulties in interbody fusion device implantation is higher than that of females in this study.

To maximize the avoidance of difficulties in implanting ROI-C cage plates due to excessive vertebral endplate bone density and the corresponding occurrence of complications, our team has the following clinical experiences:

• (1) Before performing ACDF with the use of ROI-C cage, it is advisable to measure the HU value of the target cervical vertebra vertebral endplate. If the HU value exceeds 700 HU, there may be significant resistance during plates implantation. To prevent the occurrence of implantation failure, it is recommended to finely polish the vertebral endplate in the implantation area in advance. The vertebral endplate beneath the cervical spine exhibits an irregular arc shape with relatively high bone density, especially in the posterior and lateral aspects. To maximize conformity with the implant, it is essential to polish a portion of the endplate, increasing the contact area with the implant and reducing the probability of cage subsidence [27,28,29]. However, it should be noted that endplate polishing may decrease the strength of the endplate to a certain extent, increasing the risk of implant subsidence. The optimal degree of endplate polishing remains a matter lacking a unified standard internationally. Our team’s experience is to moderately polish the bony endplate while completely removing the cartilaginous endplate.

• (2) If the HU value of the target cervical vertebra endplate exceeds 700 HU, thorough communication with the anesthetist is crucial before implanting the plates. Ensuring adequate depth of anesthesia is essential to avoid inadvertent patient movement during the plates implantation process.

• (3) For patients with high HU values of cervical vertebra endplates and a history of long-term smoking and/or alcohol consumption, preoperative tracheal displacement training is recommended to prevent complications such as difficulty swallowing, which may arise due to prolonged traction on the surrounding tissues during the extended cage implantation. Postoperatively, smoking cessation, alcohol restriction, and regular treatment for osteoporosis are advised.

• (4) If the HU value of the cervical vertebra endplate is excessively high, surpassing 800 HU, but the CT value of the cervical vertebra body is relatively normal, consideration may be given to choosing the screw-fixation type Zero-P zero-profile interbody cage. Preoperative preparation of the screw path with a tap is recommended before screw implantation.

Limitation

This study has some limitations. All cases were from a single center, and the sample size was relatively small, which may have led to a lack of statistical significance for some risk factors affecting bone quality reported in previous studies. Additionally, as a retrospective study, not all patients underwent cervical CT scans at our hospital before surgery, which may have caused selection bias. Larger sample sizes and prospective randomized controlled trials are needed in the future to confirm the current findings.

Conclusion

The HU value of the cervical vertebra endplate has potential predictive value for the implantation situation of the ROI-C cage plates. For patients with CT values exceeding the critical threshold, it is advisable to inform them of the potential difficulty in plates implantation preoperatively.