A new method for the accurate measurement of higher-order frequency response functions of nonlinear structural systems

Higher-order frequency response functions (FRFs) are important to the analysis and identification of structural nonlinearities. Though much research effort has been devoted recently to their potential applications, practical issues concerning the difficulty and accuracy of higher-order FRF measurement have not been rigorously assessed to date. This paper presents a new method for the accurate measurement of higher-order FRFs. The method is developed based on sinusoidal input, which is ideal for exciting a nonlinear structure into desired regimes with flexible control, and the correlation technique, which is a novel signal processing method capable of extracting accurate frequency components present in general nonlinear responses. The correlation technique adopted is a major improvement over Fourier transform based existing methods since it eliminates leakage and aliasing errors altogether and proves to be extremely robust in the presence of measurement noise. Extensive numerical case studies have been carried out to critically assess the capability and accuracy of the proposed method and the results achieved are indeed very promising. Interesting nonlinear behavior such as frequency shift and jump have been observed in first-, second- and third-order FRFs, as well as solitary islands which have been identified over which higher-order FRFs virtually do not change as input force amplitude varies. Higher-order FRFs over such solitary islands are essentially their theoretical counterparts of Volterra transfer functions which can be measured with very low input force and can be profitably employed for the identification of physical parameters of structural nonlinearities. Subsequently, a nonlinear parameter identification method has also been developed using measured higher-order FRFs and results are presented and discussed.

Molecular cloning of a new wheat calreticulin gene TaCRT1 and expression analysis in plant defense responses and abiotic stress resistance

Calreticulin proteins play essential roles in regulating various metabolic processes and in molecular signal transduction in animals and plants. Using homologous PCR, we screened a cDNA library of the wheat resistance gene Yr5 from a near-isogenic line in the susceptible common wheat variety Taichung 29, which was inoculated with an incompatible race CYR32 of Puccinia striiformis. We isolated a novel full-length cDNA encoding calreticulin protein, which we named TaCRT1. Sequence analyses indicated that TaCRT1 contains an open reading frame of 1287 bp in length; it was deduced to encode 428 amino acids. Clustering analysis showed that TaCRT1 belongs to group III of the calreticulin protein family. Semi-quantitative RT-PCR was used to analyze expression profiles of the isolated gene under biotic and abiotic stresses. Expression of TaCRT1 was suppressed by exogenous application of phytohormones, such as abscisic acid and methyl jasmonate, and by dehydration; but it was induced by CYR32 infection and cold treatment. Based on the expression patterns, we propose that TaCRT1 participates in regulatory processes involved in defense responses and stress resistance in wheat.

A new REBO potential based atomistic structural model for graphene sheets

A new atomistic structural model is developed here for graphene sheets based on the stiffnesses from the REBO potential. Using this model, the flexural vibration natural frequencies and buckling loads of rectangular single-layer graphene sheets of different sizes, chiralities and boundary conditions are calculated. The newly developed atomistic structural model is verified by comparing the calculated fundamental natural frequencies for small-sized graphene sheets with those obtained from ab initio density functional theory (DFT) frequency analysis. The vibration and buckling analysis results are also compared with those of an earlier atomistic structural model based on the AMBER potential as well as the equivalent continuum model for graphene sheets. Through this study, it is observed that graphene sheets display very slight anisotropic characteristics in flexural vibration and buckling. Also, it is shown that the atomistic structural model cannot be replaced by a classical equivalent continuum model such as a plate model. Most significantly, we verify that the new atomistic structural model based on the REBO potential predicts more accurate natural frequencies and buckling loads for graphene sheets, which are considerably lower than those predicted by the earlier atomistic structural model based on the AMBER potential.

Characteristics of sagittal vertebral alignment in flexion determined by dynamic radiographs of the cervical spine

STUDY DESIGN

This study was conducted to depict the change patterns of intervertebral motion of the cervical spine during flexion, upright, and extension positions using dynamic radiographs. Special interest was focused on the flexion position.

OBJECTIVES

To find reliable criteria for judging the normal intervertebral flexibility based on a survey of the normal population.

METHODS

The lateral dynamic radiographs of 75 normal subjects were analyzed by digitization and computer calculation. The characteristics of intervertebral positions were investigated using flexion radiographs.

RESULTS

From extension to flexion, the angles of intervertebral angular displacement changed from lordosis with different degrees to nearly 0 degrees, which means the adjacent endplates are almost parallel, except at C1-C2; the intervertebral translation changes from slightly retrolisthetic to zero displacement. Using C2-C3 as a baseline to calculate the intervertebral differences of angular displacement and translation in flexion radiographs, nearly all the intervertebral differences of angular displacement were less than 7 degrees, and those of translation were less than 0.06 mm.

CONCLUSIONS

Qualitative changes from extension to flexion and quantitative values of intervertebral differences in flexion radiographs help define the normal flexibility of the cervical spine more accurately.

In vitro and in vivo mechanical evaluations of plasma-sprayed hydroxyapatite coatings on titanium implants: the effect of coating characteristics

This study was undertaken to evaluate the effect of coating characteristics on the mechanical strengths of the plasma-sprayed HA-coated Ti-6Al-4V implant system both in vitro and in vivo. Two types of HA coatings (HACs) with quite different microstructures, concentrations of impurity-phases, and indices-of-crystallinity were used. In vitro testings were done by measuring the bonding-strength at the Ti-6Al-4V-HAC interface, with HACs that had and had not been immersed in a pH-buffered, serum-added simulated body fluid (SBF). The shear-strength at the HAC-bone interface was investigated in a canine transcortical femoral model after 12 and 24 weeks of implantation. The results showed a bonding degradation of approximately 32% or higher of the original strength after 4 weeks of immersion in SBF, and this predominantly depended on the constructed microstructure of the HACs. After the push-out measurements, it was demonstrated that the HACs with higher bonding-strength in vitro would correspondingly result in significantly higher shear-strength at each implant period in vivo. Nevertheless, there were no substantial histological variations between the two types of HACs evaluated. The most important point elucidated in this study was that, among coating characteristics, the microstructure was the key factor in influencing the mechanical stability of the HACs both in vitro and in vivo. As a consequence, a denser HAC was needed to ensure mechanical stability at both interfaces.

Significant roentgenographic parameters for evaluating the flexibility of acute thoracolumbar burst fractures. An in vitro study

Plain lateral radiographs in a neutral position were studied in ten acute thoracolumbar burst fractures produced by high speed impact on three vertebrae human cadaveric spine segments. Six linear geometric parameters were measured on each film. The ratio of each value in the neutral injured to the intact condition was correlated linearly with the motion parameters obtained from post-traumatic three-dimensional flexibility data (neutral zone NZ; range of motion ROM). Anterior unit height (vertebra+adjacent discs) had the highest correlation with the neutral zone and flexibility in all directions, especially flexion-extension (NZ, R2 = 0.93; flexion ROM, R2 = 0.86; extension ROM, R2 = 0.79) lateral bending (NZ, R2 = 0.83; ROM, R2 = 0.90) and right axial rotation (NZ, R2 = 0.53; ROM, R2 = 0.86). The deformation ratio (average height to depth) correlated most with the neutral zone in left axial rotation (R2 = 0.91) and right lateral bending (R2 = 0.92). Due to the high correlations obtained, these parameters should be evaluated in clinical situations to assess their effectiveness in predicting the instability of burst fractures. Ultimately, prospective clinical studies are required to verify their clinical utility.

Two-stage cementless revision THR after infection. 5 recurrences in 40 cases followed 2.5-7 years

We revised 40 infected hip prostheses in 40 patients as a two-stage procedure, including intravenous and oral antibiotics, gentamicin beads, and delayed cementless implantation of porous-coated THR. The duration of antibiotic treatment was 8 weeks. The interval from resection to reimplantation was, on average, 48 (8-108) weeks. 39 patients were followed, on average, 4 (2.5-7) years. 5 patients had a recurrent infection. In patients who did not have a recurrent infection, the Harris hip score exceeded 80 in 32 patients. Radiographically, femoral component migration of 2-6 mm was noted in 3 cases. The recurrent infection rate, and the functional and radiographic results are comparable with those obtained using a two-stage procedure with antibiotic cement.

Cementless reimplantation of hydroxyapatite-coated total hips after periprosthetic infections

From February 1991 to July 1993, 26 hydroxyapatite (HA) coated total hips were implanted in 26 patients with infected hip prostheses. Seven were done as one-stage exchange arthroplasties and the other 19 were delayed reimplantations. Successful reimplantation was defined as a functioning hip without recurrence of infection at least 2 years after reimplantation. During a follow-up period of 25 to 54 months, 24 of the reimplantations were successful. Our success rate using the HA-coated prosthesis is similar to previous reports that used antibiotic impregnated bone cement. The HA method avoids the complications encountered with bone cement.

Atlantoaxial rotatory instability secondary to odontoid hypoplasia as a cause of acute torticollis in children: report of one case

One patient with the chief complaint of acute torticollis was diagnosed as atlantoaxial rotatory instability secondary to hypoplasia of odontoid process. The diagnosis was confirmed by cervical radiography and computerized tomography. The attack of wryneck was first misdiagnosed as cervical muscle strain. Detailed physical examination revealed the tenderness to be located not at the sternocleidomastoid muscle. The fixed and painful rotatory deformity strongly indicated a cervical spinal lesion. Plain radiographic tests of the cervical spine revealed atlantoaxial rotational subluxation. Hypoplasia of the odontoid process, rarely reported as associated with this problem, was noted. Computerized tomographic tests further delineated the pathological alterations. Treatment with gentle reduction and traction for three days, and maintenance with neck collar for the three subsequent weeks, achieved a successful solution. No recurrence was noted after a two-year observation period.

Fat in the prediction of bone strength of porcine lumbar vertebrate by quantitative computed tomography

The influence of fat content on quantitative computed tomography (QCT) values was studied using porcine lumbar vertebrae as a model. A total of 72 cancellous bone columns, prepared from 18 vertebrae, underwent QCT examination before and after defatting. Mechanical testing and ashing were performed to obtain the ultimate strength and bone mineral content. The ultimate strength was calculated as a power function of apparent density using linear regression on a log-log plot and the power coefficient was 1.88. QCT values were positively correlated with bone density. QCT values of defatted specimens correlated much better with ultimate strength than those of fresh specimens. The average fat content was 27.2%. The QCT values decreased linearly with increasing fat content with a slope of 7.9 mg/cm3/% fat and a correlation coefficient of 0.65. The results provided basic data for the calibration of the machine and the principles for the interpretation of QCT values excluding the fat influence.

Dynamic canal encroachment during thoracolumbar burst fractures

In the burst fractures seen clinically, often poor correlation exists between the neurological deficit and the canal encroachment measured on post-trauma radiographic images. The purpose of the present study was to determine whether the dynamic canal encroachment during the trauma is greater than the static canal encroachment posttrauma. We successfully produced burst fractures in nine of 15 fresh human cadaveric thoracolumbar spine specimens (T11-L1). The specimens were incrementally impacted in a high-speed trauma apparatus until fracture occurred. During the trauma, dynamic canal encroachments were measured using three specially designed transducers placed in the canal at the levels of the superior end-plates of the T12 and L1 and the T12/L1 disk. After the trauma, residual static spinal canal encroachments were measured from the radiographs of the specimens that were prepared with 1.6-mm diameter steel balls lining the canal in the midsagittal plane. We found that the average canal diameter was 16.6 +/- 1.3 mm and the static canal encroachment was 18.0% of the canal diameter. The corresponding dynamic canal encroachment was 33.3%. Thus, the dynamic canal encroachment was 85% more than the static measurement. The clinical significance of this study lies in providing awareness to the clinician that the dynamic canal encroachment is significantly greater than the static canal encroachment seen on posttrauma radiographs or computed tomography scans. The finding may also explain the clinical observation of poor correlation between the canal encroachment measured radiographically and the neurological deficit.

Flexion-extension rhythm in the lumbosacral spine

STUDY DESIGN AND OBJECTIVES

This study was conducted to depict the qualitative and quantitative changes of intervertebral rotation and translation from L1-L2 to L5-S1 during flexion, standing, and extension using dynamic lumbosacral radiographs.

METHODS

A radiopaque ruler was placed on the back of each subject for the normalization of translational value. Eighty-nine volunteers were examined.

RESULTS

From extension to flexion, all of the intervertebral rotations approached 0 degree from the lordotic position; the translations changed from slightly retro-listhetic to zero displacement. Using L3-L4 as a baseline for calculating the intervertebral differences in flexion, all of the rotational differences were less than 1.5 degrees, except at L5-S1, which remained 5 degrees. The mean translational difference was less than 0.6 mm, except at L5-S1, where it remained 1.5 mm.

CONCLUSIONS

The amount of total flexibility was level-dependent and its frequency distribution is important. Qualitative rhythmic changes from extension to flexion and quantitative values of intervertebral difference in flexion help define the normal flexibility more accurately.

Axes of motion of thoracolumbar burst fractures

The neurological injury associated with thoracolumbar burst fractures may be due to the acute trauma event or due to chronic instability. For functional diagnosis and appropriate treatment, knowledge of the altered motion patterns of burst fractures may be helpful. Thirteen human cadaveric spine specimens were impacted at high speed in axial compression, resulting in 10 clinically relevant burst fractures. The specimens were subjected to a three-dimensional flexibility test (flexion, extension, bilateral lateral bending, and bilateral axial torque) before and after trauma. The vertebral motion across the burst fracture was described in terms of the helical axis of motion (HAM), a set of parameters that concisely and completely describes the three-dimensional motion. The vertebral rotations about the HAM increased significantly with burst fracture in all loading directions: flexion 8.1-17.7 degrees, extension 7.2-12.5 degrees, lateral bending 8.5-20.6 degrees (to one side), and axial torque 3.6-12.6 degrees (to one side). The HAM shifted significantly in a posterior direction with burst fracture in flexion (11-mm shift), extension (15-mm shift), and axial torque (11-mm shift). No other significant shifts in the HAM position were observed. The translation along the HAM and the orientation of the HAM did not change significantly with injury in any of the loading directions. The results provide clinically relevant information regarding the optimal treatment of thoracolumbar burst fractures. Specifically, fixation methods for burst fractures must be particularly stiff in lateral bending and axial rotation, the directions of greatest instability.

Thoracolumbar burst fracture. A biomechanical investigation of its multidirectional flexibility

Assessment of clinical instability of thoracolumbar burst fractures remains controversial and subjective. The purpose of the study was to obtain objective measures of acute instability of these fractures. Thirteen fresh cadaveric human spine specimens (T11-L1) were subjected to high-speed axial trauma, resulting in burst fractures in 10 specimens. Multidirectional flexibilities were measured when the specimen was intact and after the trauma. The average ranges of motion of the burst fractures, measured as percentages of the corresponding intact values at 7.5 Newton-meters, were 202%, 403%, 266%, and 462% for flexion/extension, axial rotation, lateral bending, and tension/compression, respectively. For the neutral zone motion parameter, the motions of the burst fracture were even greater: 670%, 1650%, 779%, and 650%, respectively. All of the increases were significant (P < 0.05). The clinical significance of the study lies in its finding of high multidirectional acute instability of the thoracolumbar burst fracture, especially in axial rotation.

Functional radiographs of acute thoracolumbar burst fractures. A biomechanical study

The geometric changes of acute thoracolumbar burst fractures under extension and traction loadings were analyzed using functional radiographs. The injuries were produced in an in vitro high-speed impact model. The changes in nine geometric parameters (three angular and six linear) were analyzed from neutral posture to extension and traction positions. In the extended position, all parameters, except the posterior vertebral height and vertebral diameter, were significantly different from the neutral posture values. Also in extension, the posterior vertebral height, vertebral diameter, and posterior unit height were significantly different from their intact values. In the traction position, all nine geometric parameters changed significantly from the neutral posture, whereas only the vertebral diameter remained significantly different from its intact value. These findings demonstrated the treatment advantages of applying traction force to acute burst fractures in contrast to extension moments. Further, changes in the angular parameters due to motion from neutral to extension posture demonstrated that the acute flexibility of the three-vertebrae segment was contributed almost equally by the upper disc (35%), lower disc (27%), and fractured vertebra (38%).

Gas-containing "ganglion" cyst of lumbar posterior longitudinal ligament at L3. Case report

A case of "ganglion" cyst was found to originate from the L3 lumbar posterior longitudinal ligament at the pedicular level. The patient had moderate lumbar degenerative scoliosis. The cyst had no connection with the intervertebral disc, dural sac, facet joint or nerve root. Instead of mucous or myxoid material, it contained gas. Pathology showed a thick collagenous fibrous wall with no particular linings. No synovial component could be found by immunohistochemical stains. Pathologic findings including hemosiderin deposition, chronic inflammatory cell infiltration, and calcified spots supported a chronic process of cystic degeneration of the ligament.

Lumbosacral kinematics in the sagittal plane: a radiographic study in vivo

Lateral functional radiographs of flexion and extension using Putto's method were examined in 89 normal subjects. A specially-designed radiopaque ruler was placed on each film for calibration. A computer-assisted method was used for digitization and analysis. There were weak negative correlations between age and range of motion, especially at the L4-L5 level (r = 0.437). No significant correlation was noted between age and translation. For flexion-extension rotation, although large variations may limit its usefulness in judging instability in some clinical settings, the data still provide a good diagnostic basis. For translation changes, 2 mm is regarded as acceptable in most cases at levels from L1 to L5, but not at the level of L5-S1 where the average translation change was only 0.4 mm. The differences in the absolute translation value among different positions were not statistically significant (p = 0.064).

Three-dimensional mechanical properties of the thoracolumbar junction

The thoracolumbar junction region is a frequent site of spinal trauma. Accurate knowledge of the normal mechanical behavior of the intervertebral joints in this region is of importance to the clinician in treating the spinal injuries. The present study documented the complete three-dimensional motions of levels T11-T12 and T12-L1 in the thoracolumbar region. Pure moments of flexion/extension, bilateral axial torque, and bilateral lateral bending were applied to 11 three-vertebrae human cadaveric specimens (T11-L1) to a maximum of 7.5 Nm. Intervertebral motions were calculated using stereophotogrammetry and presented in the form of load-displacement curves, each containing three rotations and three translations at one intervertebral level. Average +/- SD flexion, extension, axial rotation, and lateral bending ranges of motion to one side were 2.7 +/- 1.3 degrees, 2.4 +/- 1.3 degrees, 1.8 +/- 0.7 degrees, and 3.5 +/- 1.1 degrees, respectively, at level T11-T12. The same ranges of motion at T12-L1 were 2.9 +/- 1.4 degrees, 3.9 +/- 1.4 degrees, 1.2 +/- 0.7 degrees, and 3.7 +/- 1.1 degrees, respectively. The extension and axial rotation ranges of motion at level T11-T12 were found to be significantly different than the same motions at T12-L1. The different geometry in the facet joints explains these observed differences in the mechanical behavior of T11-T12 and T12-L1.

Lumbar lordosis: normal adults

Lumbar curvatures in 149 normal adults from the general population were studied. There were 76 men and 73 women with an average age of 50 years. The mean values of lumbar lordotic angle (LLA), lumbosacral angle (LSA) and sacral inclination angle (SIA) were 33.2 +/- 12.1 degrees, 11.4 +/- 4.7 degrees and 26.4 +/- 10 degrees, respectively. A high correlation was noted between LLA and SIA (r = 0.883, p = 0.0001). LLA is an ideal parameter for the evaluation of lumbar lordosis. The normal value of LLA can be defined as 20-45 degrees with a range of 1 SD. No significant differences were noted in these three angles between males and females in any age group (LLA, p = 0.647; LSA, p = 0.80; SLA, p = 0.189). Also, X-ray findings indicated there were no significant differences between these three angles in spondylotic spines and those spines with a normal appearance from X-ray finding. The average LLA increased with age. Significant lumbar lordotic angle differences were noted between those patients less than 35 years of age and those greater than 60 years, as well as in the 35-60 age group and the greater than 60 age group (p = 0.0056).

[Quantification of acetabular coverage in normal adult]

Quantification of acetabular coverage is important and can be expressed by superimposition of cartilage tracings on the maximum cross-sectional area of the femoral head. A practical Autolisp program on PC AutoCAD has been developed by us to quantify the acetabular coverage through numerical expression of the images of computed tomography. Thirty adults (60 hips) with normal center-edge angle and acetabular index in plain X ray were randomly selected for serial drops. These slices were prepared with a fixed coordination and in continuous sections of 5 mm in thickness. The contours of the cartilage of each section were digitized into a PC computer and processed by AutoCAD programs to quantify and characterize the acetabular coverage of normal and dysplastic adult hips. We found that a total coverage ratio of greater than 80%, an anterior coverage ratio of greater than 75% and a posterior coverage ratio of greater than 80% can be categorized in a normal group. Polar edge distance is a good indicator for the evaluation of preoperative and postoperative coverage conditions. For standardization and evaluation of acetabular coverage, the most suitable parameters are the total coverage ratio, anterior coverage ratio, posterior coverage ratio and polar edge distance. However, medial coverage and lateral coverage ratios are indispensable in cases of dysplastic hip because variations between them are so great that acetabuloplasty may be impossible. This program can also be used to classify precisely the type of dysplastic hip.