Characterizing bone strain distributions in vivo using three triple rosette strain gages.

Three triple-element rosette strain gages were attached to the equine third metacarpal midshaft to record site-specific strains engendered by locomotion. The distribution of strains acting upon the midshaft cross section were characterized using a combined beam theory and finite element model analysis that did not presume the manner by which the bone was inertially loaded. A medium-speed trot (3.6 ms-1) was chosen as a representative speed and gait, with normal and shear strains, and strain energy density (SED) distributions determined throughout the stance and subsequent swing phase. Importantly, the sites of maximum compression (-2400 mu epsilon), tension (810 mu epsilon), shear (1500 mu epsilon), and SED (54 kPa) were not located at any of the gage attachment sites, emphasizing that a minimum of three rosette gages are necessary to resolve the peaks and locations of functionally induced normal and shear strains. Considering the nonuniform strain distributions across the cortex, we conclude that the third metacarpal is subject to a complex loading milieu comprised of bending, axial compression, end shear, and torsion. As this complex manner of loading was consistent through the entire stance phase, it would appear that, at least during the trot, specific sites within the same cross section are subject to vastly different magnitudes of strain stimulus.     

A feasibility study for the use of a silastic gage as an in vivo muscle force transducer

This study investigates the feasibility of utilizing silastic gages for in vivo dynamic muscle force measurement. The gastrocnemius muscle of a fifty-one pound black short hair dog was selected for the test. The study shows that such measurements can be reliably performed in vivo for short durations without interfering with the natural movement of the animal. The durability of the gage appears to be primarily limited by the biological rejection process at the gage site.     

Dynamic performance characteristics of the liquid metal strain gage

Performance characteristics of the liquid metal strain gage (LMSG) were evaluated by both static and dynamic bench testing. Statically, the devices were found to have outputs closely proportional to engineering strains, up to strain levels of 40%. While individual gage factors varied appreciably (up to 50%), each of the gages studied showed excellent reproducibility of behavior. Dynamically, the response to sinusoidal strain inputs was frequency-independent up to 50 Hz, and there was no detectable phase shift. Similarly, the LMSG response to constant-speed displacement inputs was velocity-independent over the range of nominal strain rates from 20 s-1 to 0.02 s-1. The devices proved capable of maintaining stable outputs when held stretched to fixed lengths, even if such tests were performed immediately following stepwise displacement inputs. Thermal artifacts were found to be modest (0.185% apparent strain per degree C), and there was no appreciable sensitivity to non-axial strains. When mounted on an in vitro ligament preparation, the LMSG measured apparent ligament strain similar to that detected by a video dimension analyzer. A protocol by which an implanted LMSG could be used to infer in vivo muscle forces was demonstrated, based on recordings of tendo-Achilles strains developed by a rabbit during slow hopping.     

The effects of grip proximity on perceived local in vitro tendon strain

In vitro tensile loadings were performed on a series of sequentially-shortened canine tendon specimens which had been instrumented with mercury strain gages. The purpose of the experiments was to determine the tendon length necessary to ensure that the perceived local strain was effectively independent of the gripping configuration. The results showed that the mercury strain gage outputs exhibited statistically significant departures from initial (long tendon) values only when the tendons were shortened to lengths of less than about eight diameter multiples.     

Uniform stress state in bone structure with residual stress.

Residual stress and strain in living tissues have been investigated from the viewpoint of mechanical optimality maintained by adaptive remodeling. In this study, the residual stresses in the cortical-cancellous bone complex of bovine coccygeal vertebrae were examined. Biaxial strain gages were bonded onto the cortical surface, so that the gage axes were aligned in the cephalocaudal and circumferential directions. Strains induced by removal of the end-plate and the cancellous bone were recorded sequentially. The results revealed the existence of compressive residual stress in the cortical bone and tensile residual stress in the cancellous bone in both the cephalocaudal and the circumferential direction. The observed strains were examined on the basis of the uniform stress hypothesis using a three-bar model for the cephalocaudal direction and a three-layered cylinder model for the circumferential direction. In this model study, the magnitude of effective stresses, which is defined as the macroscopic stress divided by the area fraction of bone material, was found not to differ significantly between cephalocaudal and circumferential directions, although they were evaluated using independent models. These results demonstrate that the uniform stress state of the cortical-cancellous bone structure is consistent with results obtained in the cutting experiment when the existence of residual stress is taken into account.     

In vivo strain gage implantation in rats

A technique for the fabrication of encapsulated micro-miniature rosette strain gages for in vivo implantation is described. The gage units have an overall area of ten square millimeters (2.5 mm × 4.0 mm), and hence can be installed in very small experimental animals, particularly rodents. Using a rat model, strain data for up to 12 days have been obtained and in vitro studies have validified the in vivo strain recordings.     

An experimental method for measuring force on the spinal facet joint: description and application of the method.

A technique is described for measuring load magnitude and resultant load contact location in the facet joint in response to applied loads and moments, and the technique applied to the canine lumbar spine motion segment. Due to the cantilever beam geometry of the cranial articular process, facet joint loads result in surface strains on the lateral aspect of the cranial articular process. Strains were quantified by four strain gages cemented to the bony surface of the process. Strain measured at any one gage depended on the loading site on the articular surface of the caudal facet and on the magnitude of the facet load. Determination of facet loads during in vitro motion segment testing required calibration of the strains to known loads of various magnitudes applied to multiple sites on the caudal facet. The technique is described in detail, including placement of the strain gages. There is good repeatability of strains to applied facet loads and the strains appear independent of load distribution area. Error in the technique depends on the location of the applied facet loads, but is only significant in nonphysiologic locations. The technique was validated by two independent methods in axial torsion. Application of the technique to five in vitro canine L2-3 motion segments testing resulted in facet loads (in newtons, N) of 74+ / -23 N (mean + / -STD) in 2 newton-meter, Nm, extension, to unloaded in flexion. Lateral bending resulted in loads in the right facet of 40+ / -32 N for 1 Nm right lateral bending and 54+ / -29 N for 1 Nm left lateral bending. 4 Nm Torsion with and without 100 N axial compression resulted in facet loads of 92+ / -27 N and 69+ / -19 N, respectively. The technique is applicable to dynamic and in vivo studies.     

A new bi-axial cantilever beam design for biomechanics force measurements

The demand for measuring forces exerted by animals during locomotion has increased dramatically as biomechanists strive to understand and implement biomechanical control strategies. In particular, multi-axial force transducers are often required to capture animal limb coordination patterns. Most existing force transducers employ strain gages arranged in a Wheatstone bridge on a cantilever beam. Bi-axial measurements require duplicating this arrangement in the transverse direction. In this paper, we reveal a method to embed a Wheatstone bridge inside another to allow bi-axial measurements without additional strain gages or additional second beams. This hybrid configuration resolves two force components from a single bridge circuit and simplifies fabrication for the simultaneous assessment of normal and transverse loads. This design can be implemented with two-dimensional fabrication techniques and can even be used to modify a common full bridge cantilever force transducer. As a demonstration of the new design, we built a simple beam which achieved bi-axial sensing capability that outperformed a conventional half-bridge-per-axis bi-axial strain gage design. We have used this design to measure the ground reaction forces of a crawling caterpillar and a caterpillar-mimicking soft robot. The simplicity and increased sensitivity of this method could facilitate bi-axial force measurements for experimental biologists.     

Quantification of a rat tail vertebra model for trabecular bone adaptation studies

A feedback controlled loading apparatus for the rat tail vertebra was developed to deliver precise mechanical loads to the eighth caudal vertebra (C8) via pins inserted into adjacent vertebrae. Cortical bone strains were recorded using strain gages while subjecting the C8 in four cadaveric rats to mechanical loads ranging from 25 to 100 N at 1 Hz with a sinusoidal waveform. Finite element (FE) models, based on micro computed tomography, were constructed for all four C8 for calculations of cortical and trabecular bone tissue strains. The cortical bone strains predicted by FE models agreed with strain gage measurements, thus validating the FE models. The average measured cortical bone strain during 25-100 N loading was between 298 +/- 105 and 1210 +/- 297 microstrain (muepsilon). The models predicted average trabecular bone tissue strains ranging between 135 +/- 35 and 538 +/- 138 mu epsilon in the proximal region, 77 +/- 23-307 +/- 91 muepsilon in the central region, and 155 +/- 36-621 +/- 143 muepsilon in the distal region for 25-100 N loading range. Although these average strains were compressive, it is also interesting that the trabecular bone tissue strain can range from compressive to tensile strains (-1994 to 380 mu epsilon for a 100 N load). With this novel approach that combines an animal model with computational techniques, it could be possible to establish a quantitative relationship between the microscopic stress/strain environment in trabecular bone tissue, and the biosynthetic response and gene expression of bone cells, thereby study bone adaptation.     

Validity of photoelastic strain measurement on cadaveric proximal femora

Rosette strain gages indicate shear and principal strains at specific points, whereas photoelastic coatings provide shear strain information over a broad area. Information regarding bone loading and load transfer from a prosthetic implant to adjacent bone can be obtained using either strain-measuring technique on loaded femora. This study compared proximal femoral strains derived from photoelastic coatings to those obtained from rosette strain gages applied directly to the bone in order to determine the relationships between photoelastic shear strains and rosette shear and principal strains. Photoelastic shear strains underestimated rosette shear strains and exceeded the larger of the rosette principal strains. Principal strains derived from photoelastic coatings augmented with strain separator gages underestimated their rosette counterparts in most instances. Correlation was strong and nearly linear for all measures, indicating that photoelastic coatings can accurately express proportional strain changes despite imperfect agreement in absolute strain magnitudes. The best agreement between absolute strain magnitudes occurred in the proximal medial, or calcar, region. Understanding the relationships between the various measures obtained using the two strain measurement methods will allow more accurate estimates of actual strains to be made from photoelastic coatings.     

In vivo bone strain in the mandible of Galago crassicaudatus.

Single element foil strain gages were bonded to mandibular cortical bone in eight specimens of Galago crassicaudatus. The gage was bonded below the Pm4 or M2 adjacent to the lower border of the mandible. The bonded strain gage was connected to form one arm of a Wheatstone bridge. Following recovery from the general anesthetic, the restrained Galago bit either a piece of wood, a food object, or a bite force transducer. During these biting episodes, mandibular bone strain deformed the strain gage and the resulting change in electrical resistance of the gage caused voltage changes across the Wheatstone bridge. These changes, directly proportional to the amount of bone strain along the gage site, were recovered by a strip chart recorder. Bone strain was measured on both the working and balancing sides of the jaws. Maximum values of bone strain and bite force were 435 microstrain (compression) and 8.2 kilograms respectively. During bending of the mandible, the correlation between bone strain (tension or compression) and bite force ranged from -0.893 (tension) to 0.997 (compression). The experiments reported here demonstrate that only a small percentage of the Galago bite force is due to balancing side muscle force during isometric unilateral molar biting. In addition, these experiments demonstrate that the Galago mandible is bent in a predictable manner during biting. The amount of apparent mandibular bone strain is dependent on (1) the magnitude of the bite force and (2) the position of the bite point.     

Fabrication and Implantation of Miniature Dual-element Strain Gages for Measuring In Vivo Gastrointestinal Contractions in Rodents.

Gastrointestinal dysfunction remains a major cause of morbidity and mortality. Indeed, gastrointestinal (GI) motility in health and disease remains an area of productive research with over 1,400 published animal studies in just the last 5 years. Numerous techniques have been developed for quantifying smooth muscle activity of the stomach, small intestine, and colon. In vitro and ex vivo techniques offer powerful tools for mechanistic studies of GI function, but outside the context of the integrated systems inherent to an intact organism. Typically, measuring in vivo smooth muscle contractions of the stomach has involved an anesthetized preparation coupled with the introduction of a surgically placed pressure sensor, a static pressure load such as a mildly inflated balloon or by distending the stomach with fluid under barostatically-controlled feedback. Yet many of these approaches present unique disadvantages regarding both the interpretation of results as well as applicability for in vivo use in conscious experimental animal models. The use of dual element strain gages that have been affixed to the serosal surface of the GI tract has offered numerous experimental advantages, which may continue to outweigh the disadvantages. Since these gages are not commercially available, this video presentation provides a detailed, step-by-step guide to the fabrication of the current design of these gages. The strain gage described in this protocol is a design for recording gastric motility in rats. This design has been modified for recording smooth muscle activity along the entire GI tract and requires only subtle variation in the overall fabrication. Representative data from the entire GI tract are included as well as discussion of analysis methods, data interpretation and presentation.     

Long bone torsion: II. A combined experimental and computational method for determining an effective shear modulus

A technique is established which allows an effective torsional shear modulus to be determined for long bones, while remaining nondestructive to whole bone specimens. Strain gages are bonded to the diaphysis of the bone. Strains are then recorded under pure torsional loads. Theoretical stress predictions are combined with experimental strain recordings to arrive at a modulus value. Shear modulus calculations for four canine radii are reported using theoretical stress predictions from circular, elliptical and finite element models of the transverse bone geometry. The effective shear modulus, obtained from an average of the shear moduli determined at strain gage locations, serves to average the heterogeneous shear modulus distribution over the cross section. The shear modulus obtained is that associated with the "circumferential" direction in transverse planes.     

Elastic properties and masticatory bone stress in the macaque mandible

One important limitation of mechanical analyses with strain gages is the difficulty in directly estimating patterns of stress or loading in skeletal elements from strain measurements. Because of the inherent anisotropy in cortical bone, orientation of principal strains and stresses do not necessarily coincide, and it has been demonstrated theoretically that such differences may be as great as 45 degrees (Cowin and Hart, 1990). Likewise, relative proportions of stress and strain magnitudes may differ. This investigation measured the elastic properties of a region of cortical bone on both the buccal and lingual surfaces of the lower border of the macaque mandible. The elastic property data was then combined with macaque mandibular strain data from published and a new in vivo strain gage experiment to determine directions and magnitudes of maximum and minimum principal stresses. The goal was to compare the stresses and strains and assess the differences in orientation and relative magnitude between them. The main question was whether these differences might lead to different interpretations of mandibular function. Elastic and shear moduli, and Poisson's ratios were measured using an ultrasonic technique from buccal and lingual cortical surfaces in 12 macaque mandibles. Mandibular strain gage data were taken from a published set of experiments (Hylander, 1979), and from a new experiment in which rosette strain gauges were fixed to the buccal and lingual cortices of the mandibular corpus of an adult female Macaca fascicularis, after which bone strain was recorded during mastication. Averaged elastic properties were combined with strain data to calculate an estimate of stresses in the mandibular corpus. The elastic properties were similar to those of the human mandibular cortex. Near its lower border, the macaque mandible was most stiff in a longitudinal direction, less stiff in an inferosuperior direction, and least stiff in a direction normal to the bone's surface. The lingual aspect of the mandible was slightly stiffer than the buccal aspect. Magnitudes of stresses calculated from average strains ranged from a compressive stress of -16.00 GPa to a tensile stress of 8.84 GPa. The orientation of the principal stresses depended on whether the strain gage site was on the working or balancing side. On the balancing side of the mandibles, maximum principal stresses were oriented nearly perpendicular to the lower border of the mandible. On the working side of the mandibles, the orientation of the maximum principal stresses was more variable than on the balancing side, indicating a larger range of possible mechanisms of loading. Near the lower border of the mandible, differences between the orientation of stresses and strains were 12 degrees or less. Compared to ratios between maximum and minimum strains, ratios between maximum and minimum stresses were more divergent from a ratio of 1.0. Results did not provide any major reinterpretations of mandibular function in macaques, but rather confirmed and extended existing work. The differences between stresses and strains on the balancing side of the mandible generally supported the view that during the power stroke the mandible was bent and slightly twisted both during mastication and transducer biting. The calculated stresses served to de-emphasize the relative importance of torsion. On the working side, the greater range of variability in the stress analysis compared to the strain analysis suggested that a more detailed examination of loadings and stress patterns in each individual experiment would be useful to interpret the results. Torsion was evident on the working side; but in a number of experiments, further information was needed to interpret other superimposed regional loading patterns, which may have included parasagittal bending and reverse parasagittal bending.     

A preliminary biomechanical assessment of a polymer composite hip implant using an infrared thermography technique validated by strain gage measurements

With the resurgence of composite materials in orthopaedic applications, a rigorous assessment of stress is needed to predict any failure of bone-implant systems. For current biomechanics research, strain gage measurements are employed to experimentally validate finite element models, which then characterize stress in the bone and implant. Our preliminary study experimentally validates a relatively new nondestructive testing technique for orthopaedic implants. Lock-in infrared (IR) thermography validated with strain gage measurements was used to investigate the stress and strain patterns in a novel composite hip implant made of carbon fiber reinforced polyamide 12 (CF/PA12). The hip implant was instrumented with strain gages and mechanically tested using average axial cyclic forces of 840 N, 1500 N, and 2100 N with the implant at an adduction angle of 15 deg to simulate the single-legged stance phase of walking gait. Three-dimensional surface stress maps were also obtained using an IR thermography camera. Results showed almost perfect agreement of IR thermography versus strain gage data with a Pearson correlation of R(2) = 0.96 and a slope = 1.01 for the line of best fit. IR thermography detected hip implant peak stresses on the inferior-medial side just distal to the neck region of 31.14 MPa (at 840 N), 72.16 MPa (at 1500 N), and 119.86 MPa (at 2100 N). There was strong correlation between IR thermography-measured stresses and force application level at key locations on the implant along the medial (R(2) = 0.99) and lateral (R(2) = 0.83 to 0.99) surface, as well as at the peak stress point (R(2) = 0.81 to 0.97). This is the first study to experimentally validate and demonstrate the use of lock-in IR thermography to obtain three-dimensional stress fields of an orthopaedic device manufactured from a composite material.     

Design and construction of a transducer for bite force registration

This study describes the development of a system for quantification of human biting forces by (1) determining the mechanical properties of an epoxy resin reinforced with carbon fiber, (2) establishing the transducer's optimal dimensions to accommodate teeth of various widths while minimizing transducer thickness, and (3) determining the optimal location of strain gages using a series of mechanical resistance and finite element (FE) analyses. The optimal strain gage location was defined as the position that produced the least difference in strain pattern when the load was applied by teeth with two different surface areas. The result is a 7.3-mm-thick transducer with a maximum load capacity beyond any expected maximum bite force (1500 N). This system includes a graphic interface that easily allows acquisition and registration of bite force by any health-sciences or engineering professional.     

Experimental investigation of the scaphoid strain during wrist motion

The scaphoid is the most frequently fractured of the carpal bones [Taleisnik, J., The Wrist, Churchill Livingstone, New York (1985)]. This project was undertaken to qualitatively evaluate the strain in the scaphoid during wrist motion using a newly developed strain gage method. Strain gage resettes were mounted within the scaphoid and the range of motion of the hand was monitored using a custom designed electrogoniometer and data acquisition system. Ten specimens were utilized for this study. Results indicated that supination/pronation (S/P) of the forearm did not affect the strain in the scaphoid. A map of the strain in the waist of the scaphoid, as a function of flexion/extension (F/E) and radial/ulnar deviation (R/U), was generated. The contour plot of scaphoid strain vs range of motion (ROM) shows a valley where strains are low. Minimum scaphoid strain was found near neutral F/E and 15° of ulnar deviation.     

A Wzz (Cld) protein determines the chain length of K lipopolysaccharide in Escherichia coli O8 and O9 strains.

The modal distribution of O-antigen chain length is determined by the Wzz (Cld/Rol) protein in those cases in which it has been studied. The system of O-antigen synthesis in Escherichia coli serotypes O8 and O9 is different from that reported for most other bacteria, and chain length distribution is thought not to be determined by a Wzz protein. We report the existence in E. coli O8 and O9 strains of wzz genes which are very similar to and have sequences within the range of variation of those which determine the chain length of typical O antigens. We also find that wzz genes previously identified by their effect on O-antigen chain length, when cloned and transferred to O8 and O9 strains, affect the chain length of a capsule-related form of LPS, K(LPS). We conclude that in at least some O8 and O9 strains there is a wzz gene which controls the chain length of K(LPS) but has no effect on the O8 or O9 antigen.     

Flexible multibody simulation approach in the analysis of tibial strain during walking

Strains within the bone tissue play a major role in bone (re)modeling. These small strains can be assessed using experimental strain gage measurements, which are challenging and invasive. Further, the strain measurements are, in practise, limited to certain regions of superficial bones only, such as the anterior surface of the tibia. In this study, tibial strains occurring during walking were estimated using a numerical approach based on flexible multibody dynamics. In the introduced approach, a lower body musculoskeletal model was developed by employing motion capture data obtained from walking at a constant velocity. The motion capture data were used in inverse dynamics simulation to teach the muscles in the model to replicate the motion in forward dynamics simulation. The maximum and minimum tibial principal strains predicted by the model were 490 and -588 microstrain, respectively, which are in line with literature values from in vivo measurements. In conclusion, the non-invasive flexible multibody simulation approach may be used as a surrogate for experimental bone strain measurements and thus be of use in detailed strain estimations of bones in different applications.     

Experimental and finite element analysis of the rat ulnar loading model-correlations between strain and bone formation following fatigue loading

The rat forelimb compression model has been used widely to study bone response to mechanical loading. We used strain gages to assess load sharing between the ulna and radius in the forelimb of adult Fisher rats. We used histology and peripheral quantitative computed tomography (pQCT) to quantify ulnar bone formation 12 days after in vivo fatigue loading. Lastly, we developed a finite element model of the ulna to predict the pattern of surface strains during compression. Our findings indicate that at the mid-shaft the ulna carries 65% of the applied compressive force on the forelimb. We observed large variations in fatigue-induced bone formation over the circumference and length of the ulna. Bone formation was greatest 1-2 mm distal to the mid-shaft. At the mid-shaft, we observed woven bone formation that was greatest medially. Finite element analysis indicated a strain pattern consistent with a compression-bending loading mode, with the greatest strains occurring in compression on the medial surface and lesser tensile strains occurring laterally. A peak strain of -5190 microepsilon (for 13.3N forelimb compression) occurred 1-2 mm distal to the mid-shaft. The pattern of bone formation in the longitudinal direction was highly correlated to the predicted peak compressive axial strains at seven cross-sections (r2 = 0.89, p = 0.014). The in-plane pattern of bone formation was poorly correlated to the predicted magnitude of axial strain at 51 periosteal locations (r2 = 0.21, p < 0.001), because the least bone formation was observed where tensile strains were highest. These findings indicate that the magnitude of bone formation after fatigue loading is greatest in regions of high compressive strain.