Frequency dependence of apparent ultrasonic backscatter from human cancellous bone

This study examines the frequency dependence of apparent ultrasonic backscatter from human cancellous bone as quantified by the apparent backscatter transfer function (ABTF). The term 'apparent' means that the backscatter signals are not compensated for the frequency-dependent effects of diffraction and attenuation. Backscatter measurements were performed in vitro on 22 specimens of bone using five transducers ranging in centre frequency from 1 to 10 MHz. The ABTF was measured at multiple sites and spatially averaged. The resulting spatially averaged ABTF (in dB) generally was a monotonically decreasing, quasi-linear function of frequency over the analysis bandwidth of the study (0.6-9.1 MHz). The apparent backscattered power tended to decrease with specimen density and become more strongly frequency dependent. Three parameters were determined from the spatially averaged ABTF. Apparent integrated backscatter (AIB) was determined by frequency averaging the spatially averaged ABTF. The frequency slope of apparent backscatter (FSAB) and the zero frequency intercept of apparent backscatter (FIAB) were determined from the slope and intercept of the spatially averaged ABTF, respectively. AIB and FSAB demonstrated moderate to good linear correlations with specimen density (|r| = 0.570-0.933). Correlations with density were weaker for the intercept-based parameter FIAB (|r| = 0.299-0.676).     

Effect of marrow on the high frequency ultrasonic properties of cancellous bone

A number of investigators have performed in vitro measurements of cancellous bone to determine how various ultrasonic parameters depend on bone density and trabecular orientation. To facilitate handling and storage of bone specimens, the marrow is often removed prior to ultrasonic measurements. However, the assumption that marrow does not affect ultrasonic measurements at high frequencies (>1 MHz) has not been tested. The goal of this study is to determine the effect of marrow on the ultrasonic properties of bovine cancellous bone at frequencies greater than 1 MHz. Twelve specimens of cancellous bone were obtained from the proximal end of four bovine tibia. Ultrasonic measurements consisting of normalized broadband ultrasonic attenuation (nBUA), speed of sound (SOS) and apparent integrated backscatter (AIB) were measured in each specimen using 2.25 MHz (centre frequency) broadband ultrasonic pulses. These measurements were performed before and after marrow removal either along the superoinferior (SI) or mediolateral (ML) direction. SOS and nBUA showed no significant difference (p > 0.05) for either direction of propagation after marrow removal. AIB showed no significant difference in the SI direction. For the ML direction, a small but statistically significant difference (p = 0.044) was observed after marrow removal.     

Ultrasound method applied to characterize healthy femoral diaphysis of Wistar rats in vivo

A simple experimental protocol applying a quantitative ultrasound (QUS) pulse-echo technique was used to measure the acoustic parameters of healthy femoral diaphyses of Wistar rats in vivo. Five quantitative parameters [apparent integrated backscatter (AIB), frequency slope of apparent backscatter (FSAB), time slope of apparent backscatter (TSAB), integrated reflection coefficient (IRC), and frequency slope of integrated reflection (FSIR)] were calculated using the echoes from cortical and trabecular bone in the femurs of 14 Wistar rats. Signal acquisition was performed three times in each rat, with the ultrasound signal acquired along the femur''s central region from three positions 1 mm apart from each other. The parameters estimated for the three positions were averaged to represent the femur diaphysis. The results showed that AIB, FSAB, TSAB, and IRC values were statistically similar, but the FSIR values from Experiments 1 and 3 were different. Furthermore, Pearson''s correlation coefficient showed, in general, strong correlations among the parameters. The proposed protocol and calculated parameters demonstrated the potential to characterize the femur diaphysis of rats in vivo. The results are relevant because rats have a bone structure very similar to humans, and thus are an important step toward preclinical trials and subsequent application of QUS in humans.     

Ultrasonic characterization of cancellous bone using apparent integrated backscatter

Apparent integrated backscatter (AIB) is a measure of the frequency-averaged (integrated) backscattered power contained in some portion of a backscattered ultrasonic signal. AIB has been used extensively to study soft tissues, but its usefulness as a tissue characterization technique for cancellous bone has not been demonstrated. To address this, we performed measurements on 17 specimens of cancellous bone over two different frequency ranges using a 1 MHz and 5 MHz broadband ultrasonic transducer. Specimens were obtained from bovine tibiae and prepared in the shape of cubes (15 mm side length) with faces oriented along transverse (anterior, posterior, medial and lateral) and longitudinal (superior and inferior) principal anatomic directions. A mechanical scanning system was used to acquire multiple backscatter signals from each direction for each cube. AIB demonstrated highly significant linear correlations with bone mineral density (BMD) for both the transverse (R2 = 0.817) and longitudinal (R2 = 0.488) directions using the 5 MHz transducer. In contrast, the correlations with density were much weaker for the 1 MHz transducer (R2 = 0.007 transverse, R2 = 0.228 longitudinal). In all cases where a significant correlation was observed, AIB was found to decrease with increasing BMD.     

Spatial variation of acoustic properties is related with mechanical properties of trabecular bone

In clinical applications, ultrasound parameters are measured as an average value over a region of interest (ROI) or as a value at a single measurement point. Due to natural adaptation to loading conditions, trabecular bone is structurally, compositionally and mechanically heterogeneous and anisotropic. Thus, spatial variation of ultrasound parameters within ROI may contain valuable information on the mechanical integrity of trabecular bone. However, this issue has not been thoroughly investigated. In the present study, we aimed at investigating the significance of the spatial variation of ultrasound parameters for the prediction of mechanical properties of human trabecular bone. For this aim, parametric maps of apparent integrated backscattering (AIB), integrated reflection coefficient (IRC), speed of sound (SOS), average attenuation (AA) and normalized broadband ultrasound attenuation (nBUA) were calculated for femoral and tibial bone cylinders (n = 19-20). Further, the effect of time window length on the AIB, variation of AIB within ROI and association between AIB and bone mechanical properties were characterized. Based on linear correlation analysis, spatial variation of AIB, assessed as standard deviation of measurements within ROI, was a strong predictor of bone ultimate strength (r = -0.82, n = 19, p < 0.01). Further, the time window length affected absolute values of AIB and strength of correlation between AIB and bone ultimate strength. Interestingly, linear combination of mean IRC and spatial variation of AIB within ROI was the strongest predictor of bone ultimate strength (r = 0.92, n = 19, p < 0.01). In conclusion, our findings suggest that the measurement of two-dimensional parametric maps of ultrasound parameters could yield information on bone status not extractable from single point measurements. This highlights the potential of parametric imaging in osteoporosis diagnostics.     

Effects of glucocorticoid on BMD, micro-architecture and biomechanics of cancellous and cortical bone mass in OVX rabbits

The incidence of osteoporosis continues to increase with progressively aging populations. The purpose of this study was to detect the effects of glucocorticoid (GC) treatment on bone mineral density (BMD), biomechanical strength and micro-architecture in cancellous and cortical bone in ovariectomized (OVX) rabbits. Twenty adult female New Zealand white rabbits were randomly divided into three groups. The OVX-GC group (n=8) received a bilateral ovariectomy first and then daily GC treatment (methylprednisolone sodium succinate, 1mg/kg/day) for 4 weeks beginning 2 weeks after ovariectomy treatment. The OVX group (n=4) received a bilateral ovariectomy without GC treatment. The sham group (n=8) only received the sham operation. BMD was determined prior to and 6 weeks after the operation in the spine. Six weeks after the operation, the animals were sacrificed, and cancellous bone specimens were harvested from the femoral condyle and lumbar vertebrae. Cortical bone specimens were obtained from the femoral midshaft. The femoral specimens were scanned for apparent BMD. All specimens were tested mechanically and analyzed by microcompute tomography (micro-CT). In cancellous bone, GC treatment resulted in significant decreases in BMD, bone biomechanical strength and micro-architecture parameters in lumbar vertebrae. Similar trends in BMD and micro-architectural changes were also observed in the femoral condyle in the OVX-GC group compared with the sham group. However, there was no significant decline in any parameter in either lumbar vertebrae or femoral condyle in the OVX group. Similarly, no significant difference was found in any parameter in cortical bone among the three groups. Thus, the 4-week GC treatment in OVX rabbits could result in a significant bone loss in cancellous bone but not in cortical bone. This model is comparable to the osteoporosis-related changes in humans. OVX alone was not sufficient to induce osteoporosis.     

Effects of end boundary conditions and specimen geometry on the viscoelastic properties of cancellous bone measured by dynamic mechanical analysis

The viscoelastic properties of cancellous bone can be measured nondestructively in compression testing using a dynamic mechanical analyzer. In this study, we examined the effects of end boundary conditions and specimen geometry on the viscoelastic properties of cancellous bone measured by dynamic mechanical analysis. During dynamic compression testing, the cancellous bone specimens may be mechanically fixed (e.g., glued) to the loading platens or they may be free to expand across the platen surface. When specimens of cancellous bone were tested between platens with gluing, the dependence of loss tangent on frequency was not consistent with previously observed strain-rate-dependent mechanical behavior of cancellous bone. When long specimens of cancellous bone (length = 10 mm, diameter = 8 mm) were tested without gluing, the relationship between loss tangent and frequency depended on the level of load applied. For short specimens (length = 5 mm, diameter = 8 mm) tested without gluing, however, the frequency dependence of loss tangent agreed with existing data reported for the strain-rate-dependent behavior of cancellous bone and also with the frequency dependence of cortical bone viscoelasticity. Therefore, we recommend that short cancellous bone cylinders with a length of 5 mm and a diameter of 8 mm should be used without gluing in the dynamic mechanical analysis of cancellous bone. This is consistent with the American Society for Testing and Materials testing recommendations for plastics, but different from current practice for unimodal mechanical testing of cancellous bone.     

Single-trabecula building block for large-scale finite element models of cancellous bone

Recent development of high-resolution imaging of cancellous bone allows finite element (FE) analysis of bone tissue stresses and strains in individual trabeculae. However, specimen-specific stress/strain analyses can include effects of anatomical variations and local damage that can bias the interpretation of the results from individual specimens with respect to large populations. This study developed a standard (generic) ‘building-block’ of a trabecula for large-scale FE models. Being parametric and based on statistics of dimensions of ovine trabeculae, this building block can be scaled for trabecular thickness and length and be used in commercial or custom-made FE codes to construct generic, large-scale FE models of bone, using less computer power than that currently required to reproduce the accurate micro-architecture of trabecular bone. Orthogonal lattices constructed with this building block, after it was scaled to trabeculae of the human proximal femur, provided apparent elastic moduli of ∼ 150 MPa, in good agreement with experimental data for the stiffness of cancellous bone from this site. Likewise, lattices with thinner, osteoporotic-like trabeculae could predict a reduction of ∼30% in the apparent elastic modulus, as reported in experimental studies of osteoporotic femora. Based on these comparisons, it is concluded that the single-trabecula element developed in the present study is well-suited for representing cancellous bone in large-scale generic FE simulations.     

基于超声背散射信号分析松质骨中的声阻抗

采用背散射法,研究用声阻抗评价松质骨状况.对松质骨中的超声散射特性进行了分析和讨论,并将分析结果和Faran理论模型进行比较分析;最后对理论和实验所得的牛胫骨、人离体跟骨和人在体跟骨松质骨中的声阻抗分布进行了分析讨论.结果表明松质骨中的声阻抗随入射频率的增加而非线性的增加,理论和实验结果是一致的.当患有骨质疏松时,松质骨密度将减小,因此,与健康松质骨中的声阻抗相比,患骨质疏松松质骨中的声阻抗较小.     

脱钙过程中松质骨骨量、微结构和声学参数的相关性研究

目的 研究脱钙过程中松质骨的超声声学参数、骨量和骨微结构的变化,以及骨量、骨微结构和声学参数的相关性。方法 15块长方体松质骨样本经脱脂后进行分阶段脱钙,对脱钙前样本和经每一阶段脱钙的样本进行Micro CT扫描和超声测量,计算得到脱钙过程中骨量与骨微结构参数和超声声学参数,对超声声学参数与骨量和骨微结构参数进行相关性分析。结果 随着松质骨样本钙的流失,骨密度、骨表面密度和骨小梁体积比不断降低,骨小梁形态参数（结构模型因子和骨小梁面积比）上升,骨小梁的厚度和数目下降,骨小梁间隙增大,各向异性程度上升;声传导速度先升后降,宽带超声衰减呈现轻微的下降趋势;松质骨的声学参数与骨密度和骨微结构都有较强的相关性。结论 超声声学参数不但与骨密度,而且和骨微结构相关,定量超声技术有望为基于超声的骨质疏松早期诊断技术的发展提供参考。     

Apparent viscoelastic anisotropy as measured from nondestructive oscillatory tests can reflect the presence of a flaw in cortical bone

There is evidence that damage, viscoelastic stiffness properties, and postyield mechanical properties are related in bone tissue. Our objective was to test whether presence of a flaw would have an influence on the apparent viscoelastic properties of bone. Examining the effect of flaw orientation on apparent viscoelastic properties and utilization of dynamic mechanical analysis (DMA) as a nondestructive means for detection of damage were our secondary objectives. Cortical bone beams (2 x 2 x 19 mm) machined from the cranial cortex of the radii of six Warhill sheep were used. The specimens were placed in a DMA machine and baseline measurements of storage modulus (E1) and loss factor (tan delta), once for loads in the craniocaudal and once in the mediolateral directions, were performed using a three-point bending configuration for a frequency range of 1-10 Hz. Craniocaudal/mediolateral measurement ratio was calculated as a measure of anisotropy for tan delta and E1. After cutting a thin through-thickness macroscopic notch on the caudal surface at the center of each beam, oscillatory tests were repeated. Two-way repeated measures analysis of variance followed by Tukey's test was used with group (craniocaudal, mediolateral, notched craniocaudal, and notched mediolateral measurements) and frequency as factors. Regression analysis and analysis of covariance were used for examining the relationship between viscoelastic parameters and frequency. Tan delta and E1 were not different between craniocaudal and mediolateral measurements before the flaw was introduced (p > 0.8 and p = 1, respectively). In the presence of the flaw, tan delta was significantly increased (p < 0.003) whereas E1 was significantly reduced (p < 0.001) for craniocaudal measurements. Tan delta and E1 were nearly isotropic in the tested directions before the introduction of a flaw into the bone tissue. Introduction of a flaw resulted in increased tan delta and E1 anisotropy. Presence of a notch resulted in a significant increase in tan delta anisotropy with increasing frequency. In conclusion, we have demonstrated that cortical bone tissue exhibits a different apparent viscoelastic behavior in the presence of a flaw and depending on the flaw's orientation. Our finding that the presence of a notch and its orientation can be detected by nondestructive DMA suggests that in vivo techniques may be developed for detection of cortical bone damage.     

Ultrasonic characterization of human trabecular bone microstructure

New quantitative ultrasound (QUS) techniques involving ultrasound backscattering have been introduced for the assessment of bone quality. QUS parameters are affected by the transducer characteristics, e.g. frequency range, wave and pulse length. Although frequency-dependent backscattering has been studied extensively, understanding of the ultrasound scattering phenomenon in trabecular bone is still limited. In the present study, the relationships between QUS parameters and the microstructure of human trabecular bone were investigated experimentally and by using numerical simulations. Speed of sound (SOS), normalized broadband ultrasound attenuation (nBUA), average attenuation, integrated reflection coefficient (IRC) and broadband ultrasound backscatter (BUB) were measured for 26 human trabecular bone cylinders. Subsequently, a high-resolution microCT system was used to determine the microstructural parameters. Moreover, based on the sample-specific microCT data, a numerical model for ultrasound propagation was developed for the simulation of experimental measurements. Experimentally, significant relationships between the QUS parameters and microstructural parameters were demonstrated. The relationships were dependent on the frequency, and the strongest association (r = 0.88) between SOS and structural parameters was observed at a centre frequency of 5 MHz. nBUA, average attenuation, IRC and BUB showed somewhat lower linear correlations with the structural properties at a centre frequency of 5 MHz, as compared to those determined at lower frequencies. Multiple regression analyses revealed that the variation of acoustic parameters could best be explained by parameters reflecting the amount of mineralized tissue. A principal component analysis demonstrated that the strongest determinants of BUB and IRC were related to the trabecular structure. However, other structural characteristics contributed significantly to the prediction of the acoustic parameters as well. The two-dimensional numerical model introduced in the present study demonstrated good agreement with the experimental measurements. However, further studies with the simulation model are warranted to systematically investigate the relation between the structural parameters and ultrasound scattering.     

便携式超声背向散射骨密度仪设计

目的设计基于背向散射信号来评判骨密度情况的便携式超声骨密度仪,为实现超声骨密度仪的低成本和便携性提供一种解决方案。方法使用现场可编程门阵列(field programmable gate array,FPGA)作为主控以控制整个系统正常工作,配合信号调理、高速模数转换器(analog-to-digital converter,ADC)和USB传输电路,来实现高压脉冲控制模块、增益控制模块、信号采集、数据传输。最后对系统噪声和采集到的背向散射信号进行测试,并用松质骨样本进行骨密度测量的测试。结果系统整体尺寸为15 cm×10 cm×3 cm,数据传输速率可达60 MB/s,噪声水平低。结论设计了一种USB接口的便携式背向散射超声骨密度仪,在USB接口供电时,可以有效地获取背向散射信号。     

The use of tonebursts as an alternative to broadband signals in the measurement of speed of sound in human cancellous bone

Speed of sound (SOS) measurements, typically made using 1 MHz broadband pulses, are increasingly used in the clinical diagnosis of bone disorders. Previous in vitro studies indicate that broadband ultrasound pulses are susceptible to distortion in cancellous bone, leading to imprecise arrival time and SOS measurements. We investigated the effect of bandwidth and frequency on SOS by comparing measurements made using 1 MHz broadband with 1 MHz and 300 kHz narrowband toneburst signals in 15 human proximal femur cancellous bone specimens. There was no significant difference in the value of SOS measured from the leading edge of 1 MHz broadband, 1 MHz toneburst and 300 kHz toneburst signals. Values of SOS in later regions of 1 MHz and 300 kHz tonebursts fell significantly (p < 0.001) when compared to earlier regions. This decrease in SOS levelled off by the third complete cycle of 300 kHz toneburst signals, reaching a plateau value of 1961 +/- 239 m s-1. No plateau SOS value was obtained in 1 MHz tonebursts. The reproducibility of SOS, as measured by the coefficient of variation, was higher for later regions of 300 kHz tonebursts than for the leading edge of 300 kHz toneburst and 1 MHz broadband signals (p < 0.005). The correlation between ultrasound measured modulus and compressive Young's modulus improved when 300 kHz tonebursts (r2 = 0.83) rather than 1 MHz broadband (r2 = 0.77) signals were used to calculate SOS. The improved SOS reproducibility of later regions 300 kHz tonebursts suggest that it may be beneficial to use such signals rather than 1 MHz broadband pulses in SOS measurement. Since no reliable SOS measurements could be obtained from any region of 1 MHz tonebursts, the use of high frequency toneburst signals in cancellous bone has little value.     

Ultrasonic characterisation in determining elastic modulus of trabecular bone material

The pulse transmission ultrasonic technique is used to characterise the actual pathway and the wavelength dependence in relation to the bone specimen and microstructural dimensions. The average velocity through individual trabecular bone is 2901 m s⁻¹ (SD 161), and the mean velocity through cylindrical cancellous bone specimens is 2717 m s⁻¹ (SD 171). Thus, the velocity through the cylindrical cancellous bone specimens is underestimated by as much as 6.4% of that through individual trabeculae. There is statistically significant difference in the ultrasonic velocity between individual trabeculae and cylindrical cancellous bone specimens (p=0.0012).     

On the Failure Initiation in the Proximal Human Femur Under Simulated Sideways Fall

The limitations of areal bone mineral density measurements for identifying at-risk individuals have led to the development of alternative screening methods for hip fracture risk including the use of geometrical measurements from the proximal femur and subject specific finite element analysis (FEA) for predicting femoral strength, based on quantitative CT data (qCT). However, these methods need more development to gain widespread clinical applications. This study had three aims: To investigate whether proximal femur geometrical parameters correlate with obtained femur peak force during the impact testing; to examine whether or not failure of the proximal femur initiates in the cancellous (trabecular) bone; and finally, to examine whether or not surface fracture initiates in the places where holes perforate the cortex of the proximal femur. We found that cortical thickness around the trochanteric-fossa is significantly correlated to the peak force obtained from simulated sideways falling (R ² = 0.69) more so than femoral neck cortical thickness (R ² = 0.15). Dynamic macro level FE simulations predicted that fracture generally initiates in the cancellous bone compartments. Moreover, our micro level FEA results indicated that surface holes may be involved in primary failure events.     

Electric and dielectric properties of wet human cancellous bone as a function of frequency

In this study the electrical and dielectric properties of wet human cancellous bone from distal tibiae were examined as a function of frequency and direction. The resistance and capacitance of the cancellous bone specimens were measured at near 100% relative humidity. The measurements were made in all three orthogonal directions at discrete frequencies ranging from 120 Hz to 10 MHz using an LCR meter. At a frequency of 100 kHz, the mean resistivity and specific capacitance for the thirty cancellous bone specimens were 500 ohm-cm and 8.64 pF/cm in the longitudinal direction, 613 ohm-cm and 15.25 pF/cm in the anterior-posterior direction, and 609 ohm-cm and 14.64 pF/cm in the lateral-medial direction. All electrical and dielectric properties except the resistivity and the impedance were highly frequency dependent for the frequency range tested. All electrical and dielectric properties were transversely isotropic as the values for the longitudinal direction were different from values obtained for the two transverse directions and properties in the two transverse directions were approximately similar. Presented in part at the Fifth Southern Biomedical Engineering Conference held in Shreveport, Louisiana, October 20 and 21, 1988, and at the 13th Annual Meeting of the Society for Biomaterials held in New York, June 3–7, 1987. This work was supported by a grant No. ECS-8312680 from the National Science Foundation.     

Assessment of cancellous bone mechanical properties from micro-FE models based on micro-CT, pQCT and MR images.

Recently, new micro-finite element (micro-FE) techniques have been introduced to calculate cancellous bone mechanical properties directly from high-resolution images of its internal architecture. Also recently, new peripheral quantitative computed tomography (pQCT) and magnetic resonance (MR) imaging techniques have been developed that can create images of whole bones in vivo with enough detail to visualize the internal cancellous bone architecture. In this study we aim to investigate if the calculation of cancellous bone mechanical properties from micro-FE models based on such new pQCT and MR images is feasible. Three bone specimens were imaged with the pQCT scanning system and the MR-imaging system. The specimens were scanned a second time using a micro-CT scanner with a much higher resolution. Digitized reconstructions were made based on each set of images and converted to micro-FE models from which the bone elastic properties were calculated. It was found that the results of both the pQCT and the MR-based FE-models compared well to those of the more accurate micro-CT based models in a qualitative sense, but correction factors will be needed to get accurate values.     

The interaction of ultrasound with cancellous bone.

The Biot theory is used in an attempt to explain the frequency dependence of ultrasonic attenuation, f(alpha), in cancellous bone. Measurements of f(alpha) in samples of cancellous bone are compared with values calculated using parameters established from bone samples by statistical histomorphometry. Ultrasonic attenuation in cancellous bone correlates with trabecular bone volume but the Biot theory, although producing qualitative agreement produces quantitative results which are significantly deviant using parameters presently available. At the present time, too many of the Biot parameters are insufficiently defined for cancellous bone, to allow a complete test of the model.     

Influence of preparation techniques to the strength of the bone–cement interface behind the flange in total knee arthroplasty

IntroductionRecent clinical studies show an increased risk of femoral loosening in high-flexion TKA. Loosening seems to occur behind the anterior flange, which is covering both cancellous bone and cortical bone. It is important to optimize the interface strength between cement and both bone types to increase femoral component fixation. This study was performed to determine the cement–cortical bone interface strength for different preparation techniques.Material and methodsA pure tensile and shear force was applied to interface specimens. The cortical surface area was prepared in three different ways: (1) Unprepared cortical bone with periosteum; (2) Periosteum removed and cortical bone roughened with a rasp; (3) Periosteum removed and three Ø3.2 mm holes drilled through the cortex. A reference group was added with a cancellous bone surface.ResultsThe interface tensile strength of Group 1 was 0.06 MPa and the shear strength was 0.05 MPa. For Group 2, respectively 0.22 MPa and 1.12 MPa. For Group 3, respectively 1.15 MPa and 1.77 MPa. For cancellous bone a tensile strength of 1.79 MPa and a shear strength of 3.85 MPa were measured.ConclusionThe strength of the cement–cancellous bone interface is superior to the cement–cortical bone interface. The preferred preparation technique of the cortical bone is to remove all the periosteum and drill holes through the cortex within the footprint of the anterior flange, to prevent cortical weakening.Clinical relevanceUltimately, the proposed preparation technique will lead to longer implant survival, particularly for prostheses which are used in the high-flexion range.