Comparison of image registration performed with MV cone beam CT and CT on rails and Syngo™ Adaptive Targeting software

BackgroundMinimization of geometric errors in treatment delivery is essential in modern conformal and intensity-modulated techniques.AimIn this paper two Siemens systems, MVision megavoltage cone beam CT, and CTVision (CT on rails), are compared.Material and MethodsThe reproducibility and uncertainty of the image registration procedure performed with Adaptive Targeting (AT) software were evaluated. Both systems were evaluated by means of simulating the clinical situation with an anthropomorphic phantom in three anatomical sites: head & neck, thorax and pelvis.ResultsThe results for two methods of image registration, manual and automatic, were evaluated separately. The manual procedure was used by two users, more and less experienced.ConclusionsThe MVision system and CTVision and the Therapist Adaptive software ensure image registration with the uncertainty of about 2.0 mm (2 standard deviations). In the case of the automatic registration method better reproducibility of image registration was obtained for MVision. For CTVision the necessity of manual identification of the machine isocentre made the registration less reproducible. In the case of MVision, the automatic method was more reproducible than the manual one (smaller dispersion of results). In the case of CTVision, similar results were obtained for both registration methods. In the case of manual registration slightly better reproducibility for CT data acquired at 2 mm slice thickness and 2 mm slice separation than for data acquired at 5 mm slice thickness and 5 mm slice separation were obtained. Similar results of manual registration performed by more and less experienced users were obtained.     

Elimination of Ligation Dependent Artifacts in T4 RNA Ligase to Achieve High Efficiency and Low Bias MicroRNA Capture

Adapter ligation is a critical first step in many microRNA analysis methods including microarray, qPCR, and sequencing. Previous studies have shown that ligation bias can have dramatic effects on both the fidelity of expression profiles and reproducibility across samples. We have developed a method for high efficiency and low bias microRNA capture by 3′ adapter ligation using T4 RNA ligase that does not require pooled adapters. Using a panel of 20 microRNA, we investigated the effects of ligase type, PEG concentration, ligase amount, adapter concentration, incubation time, incubation temperature, and adapter design on capture efficiency and bias. Of these factors, high PEG% was found to be critical in suppressing ligation bias. We obtained high average capture efficiency and low CV across the 20 microRNA panel, both in idealized buffer conditions (86%±10%) and total RNA spiking conditions (64%±17%). We demonstrate that this method is reliable across microRNA species that previous studies have had difficulty capturing and that our adapter design performs significantly better than the common adapter designs. Further, we demonstrate that the optimization methodology must be specifically designed for minimizing bias in order to obtain the ideal reaction parameters.     

New diagnostic and therapeutic tools in stereotaxy

A definitive pathoanatomic diagnosis was achieved in 14 biopsies of deep cerebral tumors in which the Laitinen CT adapter was utilized. In 5 patients, a third-ventricular colloid cyst was aspirated or resected by stereotactic endoscopy, with excellent results after a mean follow-up time of 2.5 years. Several instruments, including a diagnostic ultrasound probe, an ultrasonic aspirator, a combination laser and an endoscope can be used stereotactically when mounted on a special instrument carrier. Integration of the Laitinen stereotactic device and the CT adapter was developed to allow noninvasive stereotactic radiotherapy in a conventional fractionation schedule by a standard linear accelerator. Technical experiences using this radiosurgical system in over 30 sessions for treating inoperable cerebral arteriovenous malformations are promising, but the follow-up time is too short for evaluating the clinical effect.     

Low-dose CT imaging of radio-opaque markers for assessing human rotator cuff repair: accuracy, repeatability and the effect of arm position

Previous studies have used radiostereometric analysis (RSA) to assess the integrity and mechanical properties of repaired tendons and ligament grafts. A conceptually similar approach is to use CT imaging to measure the 3D position and distance between implanted markers. The purpose of this study was to quantify the accuracy and repeatability of measuring the position and distance between metallic markers placed in the rotator cuff using low-dose CT imaging. We also investigated the effect of repeated or variable positions of the arm on position and distance measures. Six human patients had undergone rotator cuff repair and placement of tantalum beads in the rotator cuff at least one year prior to participating in this study. On a single day each patient underwent nine low-dose CT scans in seven unique arm positions. CT scans were analyzed to assess bias, precision and RMS error of the measurement technique. The effect of repeated or variable positions of the arm on the 3D position of the beads and the distance between these beads and suture anchors in the humeral head were also assessed. Results showed the CT imaging method is accurate and repeatable to within 0.7 mm. Further, measures of bead position and anchor-to-bead distance are influenced by arm position and location of the bead within the rotator cuff. Beads located in the posterior rotator cuff moved medially as much as 20 mm in abduction or external rotation. When clinically relevant CT arm positions such as the hand on umbilicus or at side were repeated, bead position varied less than 4 mm in any anatomic direction and anchor-to-bead distance varied +2.8 to -1.6 mm (RMS 1.3 mm). We conclude that a range of ± 3 mm is a conservative estimate of the uncertainty in anchor-to-bead distance for patients repeatedly scanned in clinically-relevant arm positions.     

Performance of upflow anaerobic sludge blanket (UASB) reactor treating wastewaters containing carbon tetrachloride

The anaerobic biodegradation of carbon tetrachloride (CT) was investigated during the granulation process by reducing the hydraulic retention time, increasing the chemical oxygen demand (COD) and CT loadings in a 2l laboratory-scale upflow anaerobic sludge blanket (UASB) reactor. Anaerobic unacclimated sludge and glucose were used as seed and primary substrate, respectively. Granules were developed 4 weeks after start-up, which grew at an accelerated rate for 8 months, and then became fully grown. The effect of operational parameters such as influent CT concentrations, COD, CT loading, food to biomass ratio and specific methanogenic activity (SMA) were also considered during granulation. The granular sludge cultivated had a maximum diameter of 2.1 mm and SMA of 1.6 g COD/g total suspended solid (TSS) day. COD and CT removal efficiencies of 92 and 88% were achieved when the reactor was firstly operating at CT and COD loading rates of 17.5 mg/l day and 12.5 g/l day, respectively. This corresponds to hydraulic retention time of 0.28 day and food to biomass ratio of 0.5 g COD/g TSS day. Kinetic coefficients of maximum specific substrate utilization rate, half velocity coefficient, growth yield coefficient and decay coefficient were determined to be 2.4 × 10^–3 mg CT/TSS day^–1, 1.37 mg CT/l, 0.69 mg TSS/mg CT and 0.046 day^–1, respectively for CT biotransformation during granulation.     

Availability of applying diaphragm matching with the breath-holding technique in stereotactic body radiation therapy for liver tumors

PurposeImage-guided radiotherapy (IGRT) based on bone matching can produce large target-positioning errors because of expiration breath-hold reproducibility during stereotactic body radiation therapy (SBRT) for liver tumors. Therefore, the feasibility of diaphragm-based 3D image matching between planning computed tomography (CT) and pretreatment cone-beam CT was investigated.MethodsIn 59 liver SBRT cases, Lipiodol uptake after transarterial chemoembolization was defined as a tumor marker. Further, the relative isocenter coordinate that was obtained by Lipiodol matching was defined as the reference coordinate. The distance between the relative isocenter coordinate and reference coordinate, which was obtained from diaphragm matching and bone matching techniques, was defined as the target positioning error. Furthermore, the target positioning error between liver matching and Lipiodol matching was evaluated.ResultsThe positioning errors in all directions by the diaphragm matching were significantly smaller than those obtained by using by the bone matching technique (p < 0.05). Further, the positioning errors in the A-P and C-C directions that were obtained by using liver matching were significantly smaller than those obtained by using bone matching (p < 0.05). The estimated PTV margins calculated by the formula proposed by van Herk for diaphragm matching, liver matching, and bone matching were 5.0 mm, 5.0 mm, and 11.6 mm in the C-C direction; 3.6 mm, 2.4 mm, and 6.9 mm in the A-P direction; and 2.6 mm, 4.1 mm, and 4.6 mm in the L-R direction, respectively.ConclusionsDiaphragm matching-based IGRT may be an alternative image matching technique for determining liver tumor positions in patients.     

Repositioning accuracy of a novel thermoplastic mask for head and neck cancer radiotherapy

PurposeThe aim of this study was to assess the reproducibility of patient shoulder position immobilized with a novel and innovative prototype mask (E-Frame, Engineering System).MethodsThe E-frame mask fixes both shoulders and bisaxillary regions compared with that of a commercial mask (Type-S, CIVCO). Thirteen and twelve patients were immobilized with the Type-S and E-Frame mask systems, respectively. For each treatment fraction, cone-beam CT (CBCT) images of the patient were acquired and retrospectively analyzed. The CBCT images were registered to the planning CT based on the cervical spine, and then the displacements of the acromial extremity of the clavicle were measured.ResultsThe systematic and random errors between the two mask systems were evaluated. The differences of the systematic errors between the two mask systems were not statistically significant. The mean random errors in the three directions (AP, SI and LR) were 2.7 mm, 3.1 mm and 1.5 mm, respectively for the Type-S mask, and 2.8 mm 2.5 mm and 1.4 mm, respectively for the E-Frame mask. The random error of the E-Frame masks in the SI direction was significantly smaller than that of the Type-S. The number of cases showing displacements exceeding 10 mm in the SI direction for at least one fraction was eight (61% of 13 cases) and three (25% of 12 cases) for Type-S and E-Frame masks, respectively.ConclusionsThe E-Frame masks reduced the random displacements of patient’s shoulders in the SI direction, effectively preventing large shoulder shifts that occurred frequently with Type-S masks.     

Detection of bone erosions in rheumatoid arthritis wrist joints with magnetic resonance imaging, computed tomography and radiography

Background

The objectives of the present study were, with multidetector computed tomography (CT) as the reference method, to determine the performance of magnetic resonance imaging (MRI) and radiography for the detection of bone erosions in rheumatoid arthritis wrist bones, and to test whether measuring volumes of erosions on CT and MRI is reproducible and correlated to semiquantitative assessments (scores) of erosions on CT, MRI and radiography.

Methods

Seventeen patients with rheumatoid arthritis and four healthy control individuals underwent CT, MRI and radiography of one wrist, performed on the same day. CT was performed on a Philips Mx8000IDT unit (voxel size 0.4 mm × 0.4 mm × 1 mm) and MRI was performed on a Philips Panorama 0.6T unit (voxel size 0.4 mm × 0.4 mm × 0.4 mm). Images were evaluated separately for erosions in all wrist bones and were scored according to the principles of the Outcome Measures in Rheumatology Rheumatoid Arthritis MRI Scoring System (CT and MRI) and the Sharp/van der Heijde (radiographs) scoring methods. Measurements of erosion volumes of all erosions were performed twice with a 1-week interval.

Results

With CT as the reference method, the overall sensitivity, specificity and accuracy (concordance) of MRI for detecting erosions were 61%, 93% and 77%, respectively, while the respective values were 24%, 99% and 63% for radiography. The intramodality agreements when measuring erosion volumes were high for both CT and MRI (Spearman correlation coefficients 0.92 and 0.90 (both P < 0.01), respectively). Correlations between volumes and scores of individual erosions were 0.96 for CT and 0.99 for MRI, while they were 0.83 (CT) and 0.80 (MRI) for persons' total erosion volume and total score (all P < 0.01).

Conclusion

With CT as the reference method, MRI showed moderate sensitivity and good specificity and accuracy for detection of erosions in rheumatoid arthritis and healthy wrist bones, while radiography showed very low sensitivity. The tested volumetric method was highly reproducible and correlated to scores of erosions.     

Fast 3D reconstruction of the lower limb using a parametric model and statistical inferences and clinical measurements calculation from biplanar X-rays

In clinical routine, lower limb analysis relies on conventional X-ray (2D view) or computerised tomography (CT) Scan (lying position). However, these methods do not allow 3D analysis in standing position. The aim of this study is to propose a fast and accurate 3D-reconstruction-method based on parametric models and statistical inferences from biplanar X-rays with clinical measurements' (CM) assessment in standing position for a clinical routine use. For the reproducibility study, the 95% CI was under 2.7° for all lower limbs' angular measurements except for tibial torsion, femoral torsion and tibiofemoral rotation (?相似文献   

3D reconstruction of the ribs from lateral and frontal X-rays in comparison to 3D CT-scan reconstruction

Subject-specific three-dimensional (3D) reconstructions of the ribs can be obtained from biplanar X-rays. The goal of this study was to evaluate the accuracy and the inter-observer reproducibility of this technique in comparison to CT-scan reconstructions. CT scans and biplanar X-rays were obtained from 50 ribs (from three cadaveric rib cages). Three experienced experimenters reconstructed each rib from biplanar X-rays. Morphometric parameters were then computed from the rib midlines. Differences were computed between parameters obtained from the 3D reconstructions based on biplanar X-rays and from CT scans. The accuracy was computed as the mean of this difference for the 50 ribs from all three experimenters. The inter-observer variability was assessed using the coefficient of variation (CV) between the three observers. The CT-scan reconstructions were considered to be the gold standard in spite of their limitations for rib reconstructions. According to the different linear parameters, the accuracy of the reconstructions was found to be between -6mm (-2%) and 3mm, (4%). The accuracy of the current method was close to that of CT-scan reconstructions. The inter-observer variability was between 3% and 6%. Frontal and lateral X-rays are commonly obtained clinically, so 3D reconstructions can be used without increased radiation exposure to the patient.     

Investigation of 3D glenohumeral displacements from 3D reconstruction using biplane X-ray images: Accuracy and reproducibility of the technique and preliminary analysis in rotator cuff tear patients

Rotator cuff (RC) tears may be associated with increased glenohumeral instability; however, this instability is difficult to quantify using currently available diagnostic tools. Recently, the three-dimensional (3D) reconstruction and registration method of the scapula and humeral head, based on sequences of low-dose biplane X-ray images, has been proposed for glenohumeral displacement assessment. This research aimed to evaluate the accuracy and reproducibility of this technique and to investigate its potential with a preliminary application comparing RC tear patients and asymptomatic volunteers. Accuracy was assessed using CT scan model registration on biplane X-ray images for five cadaveric shoulder specimens and showed differences ranging from 0.6 to 1.4 mm depending on the direction of interest. Intra- and interobserver reproducibility was assessed through two operators who repeated the reconstruction of five subjects three times, allowing defining 95% confidence interval ranging from ±1.8 to ±3.6 mm. Intraclass correlation coefficient varied between 0.84 and 0.98. Comparison between RC tear patients and asymptomatic volunteers showed differences of glenohumeral displacements, especially in the superoinferior direction when shoulder was abducted at 20° and 45°. This study thus assessed the accuracy of the low-dose 3D biplane X-ray reconstruction technique for glenohumeral displacement assessment and showed potential in biomechanical and clinical research.     

Male-male mountings in polyandrous bearded vultures Gypaetus barbatus: an unusual behaviour in raptors

Male-male mountings appear to be very common in polyandrous bearded vulture Gypaetus barbatus trios. We observed sexual activity in two trios that occupied the same territory in different years. We recorded a total of 167 copulation attempts. The percentage of male-male mountings recorded was 26.1 and 11.4%, in the period of 1991–1992 and 2000–2001, respectively, with respect to total, homo- and heterosexual matings. We conclude that homosexual interactions do not appear to be directly associated with intrasexual competition (i.e. hierarchical dominance, sperm competition). Rather, our results are more consistent with the idea that this behaviour can regulate the aggression of the males in these groups.     

"Direct DICOM Slice Landmarking” A Novel Research Technique to Quantify Skeletal Changes in Orthognathic Surgery

The limitations of the current methods of quantifying the surgical movements of facial bones inspired this study. The aim of this study was the assessment of the accuracy and reproducibility of directly landmarking of 3D DICOM images (Digital Imaging and Communications in Medicine) to quantify the changes in the jaw bones following surgery. The study was carried out on plastic skull to simulate the surgical movements of the jaw bones. Cone beam CT scans were taken at 3mm, 6mm, and 9mm maxillary advancement; together with a 2mm, 4mm, 6mm and 8mm “down graft” which in total generated 12 different positions of the maxilla for the analysis. The movements of the maxilla were calculated using two methods, the standard approach where distances between surface landmarks on the jaw bones were measured and the novel approach where measurements were taken directly from the internal structures of the corresponding 3D DICOME slices. A one sample t-test showed that there was no statistically significant difference between the two methods of measurements for the y and z directions, however, the x direction showed a significant difference. The mean difference between the two absolute measurements were 0.34±0.20mm, 0.22±0.16mm, 0.18±0.13mm in the y, z and x directions respectively. In conclusion, the direct landmarking of 3D DICOM image slices is a reliable, reproducible and informative method for assessment of the 3D skeletal changes. The method has a clear clinical application which includes the analysis of the jaw movements “orthognathic surgery” for the correction of facial deformities.     

A model-based approach to measure the minimum joint space width of total knee replacements in standard radiographs

Excessive wear in total knee arthroplasty is detected by measuring the minimum joint space width (mJSW) in anterioposterior radiographs. The accuracy of conventional measurement methods is limited and can be improved using model-based techniques. In this study, the model-based wear measurement (MBWM) is introduced. Its accuracy and reproducibility are assessed and compared to the conventional measurement. Forty anterioposterior radiographs were obtained of a knee prosthesis using a phantom setup. Both measurement methods were applied and the accuracy and precision were compared. The reproducibility was calculated with inter- and intra-observer experiments. Three observers measured the mJSW in 30 clinical radiographs with both the conventional measurement and the MBWM and repeated this after 6 weeks. The experiments were conducted with a NexGen mobile bearing and fixed bearing prostheses. In the phantom experiment, the accuracy (mean of the absolute error) was significantly higher (t-test, p<0.01) for the MBWM as for the conventional measurement (0.15 mm versus 0.43 mm, 0.14 mm versus 0.35 mm for the mobile and fixed bearing, respectively). The standard deviation of the measurements is the smallest for the MBWM measurement for both prosthesis types (0.16 mm versus 0.47 mm, Levene's test, p<0.01). In the reproducibility experiment, both the intra- and inter-observer agreements were higher for the MBWM than for the conventional method. The results show that the MBWM is superior to the conventional measurement in both accuracy and reproducibility. Although the use of a phantom experiment poses some limitations in conveying the findings to clinical practice, this improved mJSW measurement can lead to better wear detection for surgery decisions and research purposes.     

Iterative reconstruction methods in X-ray CT

Iterative reconstruction (IR) methods have recently re-emerged in transmission x-ray computed tomography (CT). They were successfully used in the early years of CT, but given up when the amount of measured data increased because of the higher computational demands of IR compared to analytical methods. The availability of large computational capacities in normal workstations and the ongoing efforts towards lower doses in CT have changed the situation; IR has become a hot topic for all major vendors of clinical CT systems in the past 5 years.This review strives to provide information on IR methods and aims at interested physicists and physicians already active in the field of CT. We give an overview on the terminology used and an introduction to the most important algorithmic concepts including references for further reading. As a practical example, details on a model-based iterative reconstruction algorithm implemented on a modern graphics adapter (GPU) are presented, followed by application examples for several dedicated CT scanners in order to demonstrate the performance and potential of iterative reconstruction methods. Finally, some general thoughts regarding the advantages and disadvantages of IR methods as well as open points for research in this field are discussed.     

Mounting frequency and number of cloacal contacts increase with age in common terns Sterna hirundo

We investigated courtship feeding and copulatory behaviour of common terns Sterna hirundo in relation to age. We found a significant positive correlation between the number of courtship feedings delivered to females and the number of mountings. Moreover, both courtship feeding and mounting rates were positively correlated with female and male age. Also, the number of cloacal contacts per mounting increased significantly with male or female age, which may indicate an increase in copulatory ability with age. The number of mountings for older birds was up to three times that for younger birds. Presuming that transfer of sperm is proportional to the number of cloacal contacts, older birds may have transferred up to six times more sperm than younger birds during the pre-laying and laying period. These results may account for the preference of young females for older mates as well as for older extra-pair mates.     

Fast 3D reconstruction of the lower limb using a parametric model and statistical inferences and clinical measurements calculation from biplanar X-rays

In clinical routine, lower limb analysis relies on conventional X-ray (2D view) or computerised tomography (CT) Scan (lying position). However, these methods do not allow 3D analysis in standing position. The aim of this study is to propose a fast and accurate 3D-reconstruction-method based on parametric models and statistical inferences from biplanar X-rays with clinical measurements' (CM) assessment in standing position for a clinical routine use. For the reproducibility study, the 95% CI was under 2.7° for all lower limbs' angular measurements except for tibial torsion, femoral torsion and tibiofemoral rotation ( < 5°). The 95% CI were under 2.5 mm for lower limbs' lengths and 1.5 to 3° for the pelvis' CM. Comparisons between X-rays and CT-scan based 3D shapes in vitro showed mean differences of 1.0 mm (95% CI = 2.4 mm). Comparisons of 2D lower limbs' and 3D pelvis' CM between standing ‘Shifted-Feet’ and ‘Non-Shifted-Feet’ position showed means differences of 0.0 to 1.4°. Significant differences were found only for pelvic obliquity and rotation. The reconstruction time was about 5 min.     

Reproducibility of surface EMG variables in isometric sub-maximal contractions of jaw elevator muscles.

The aims of this study were: (1) to develop and assess reproducibility of a new method for measuring masticatory force in the intercuspal position; (2) to test the reproducibility of surface EMG signal amplitude and spectral variables in constant force contractions of jaw elevator muscles and its dependency on inter-electrode distance. The study was performed on the masseter and temporalis anterior muscles of both sides of nine healthy volunteers. An intraoral compressive-force sensor was used to measure maximal voluntary contraction forces in the intercuspal position and to provide a visual feedback on sub-maximal forces to the subject. Three experimental sessions were performed in three days. In each session, three isometric contractions at 80% of the maximal force were sustained by the subjects for 30s. The intra-class correlation coefficient (ICC) of the maximal force measure was 71.9%. ICC of average rectified value and mean power spectral frequency of the EMG signal increased with inter-electrode distance, with values larger than 70% with 30 mm inter-electrode distance. It was concluded that surface EMG variables measured in isometric contractions of the jaw elevator muscles with the proposed force recording system show good reproducibility for clinical applications when a 30 mm inter-electrode distance is considered.     

An adapter for defined sample volumes makes it possible to count absolute particle numbers in flow cytometry.

A device is described which makes it possible to count absolute particle (cell) numbers per volume by flow cytometry. It can easily by adapted to several types of flow cytometers, especially to the Coulter EPICS V and EPICS 750 series. A volume adapter has been installed in place of the normal sample handling system without any further modifications of the instrument or the data acquisition program. The adapter consists of a special pipette with two opto-electronic detectors for the beginning and end of the measuring period. These switch on/off a shutter for the illuminating laser beam so that acquisition of the data is controlled indirectly. Sample volumes of 50 microliters were measured at flow rates up to 10(3) particles/s. Calibration beads as well as blood cells were enumerated according to FALS (forward angle light scatter), to SSC (90 degrees light scatter), and to fluorescence parameters. The results were compared to the evaluation made on a Coulter counter or in a Neubauer chamber of a light microscope. Using a concentration of 1 x 10(5)-5 x 10(5) particles/ml, the absolute numbers of particles were determined with a high reproducibility and an estimated error rate of 2-5%.     

Imaging of interstitial cryotherapy--an in vitro comparison of ultrasound, computed tomography, and magnetic resonance imaging.

RATIONALE AND OBJECTIVES: To evaluate the imaging capabilities of ultrasound (US), computed tomography (CT), and magnetic resonance imaging (MRI) in monitoring interstitial cryotherapy and to compare them with visual control. METHODS: An experimental MR-compatible, vacuum-insulated and liquid nitrogen-cooled cryoprobe was inserted under in vitro conditions into a porcine liver, which was kept at a temperature of 37 +/- 1 degrees C, in a water bath with continuous stirring. The freezing procedure was controlled macroscopically, by US (Toshiba Sonolayer, 7.5-MHz linear array transducer), by CT (Siemens Somatom Plus, slice thickness 2-8 mm, 165-210 mA at 120 kV), and by MRI (Philips Gyroscan ACS-NT, FFE TR/TE/FA = 15/5.4/25 degrees, T1-SE 550/20, T2-TSE 1800/100) after the iceball reached its maximum size. RESULTS: The maximum iceball diameter around the probe tip was 12.0 mm by visual control, 12.4 mm by US, 12.7 mm by CT, and within 12.8 mm by spin echo sequences and 11 mm by gradient echo sequence. Due to the nearly signal-free appearance of the frozen tissue on MR images, the ice/tissue contrast on T1-weighted and gradient echo images was superior to T2-weighted images and CT images. Sonographically, the ice formation appeared as a hyperechoic sickle with nearly complete acoustic shadowing. CONCLUSION: Due to the better ice/tissue contrast, T1-weighted or gradient echo MR images were superior to CT and US in monitoring interstitial cryotherapy. Gradient echo sequences generally underestimated the ice diameter by 15%.