Constrained tibial vibration in mice: a method for studying the effects of vibrational loading of bone

Vibrational loading can stimulate the formation of new trabecular bone or maintain bone mass. Studies investigating vibrational loading have often used whole-body vibration (WBV) as their loading method. However, WBV has limitations in small animal studies because transmissibility of vibration is dependent on posture. In this study, we propose constrained tibial vibration (CTV) as an experimental method for vibrational loading of mice under controlled conditions. In CTV, the lower leg of an anesthetized mouse is subjected to vertical vibrational loading while supporting a mass. The setup approximates a one degree-of-freedom vibrational system. Accelerometers were used to measure transmissibility of vibration through the lower leg in CTV at frequencies from 20 Hz to 150 Hz. First, the frequency response of transmissibility was quantified in vivo, and dissections were performed to remove one component of the mouse leg (the knee joint, foot, or soft tissue) to investigate the contribution of each component to the frequency response of the intact leg. Next, a finite element (FE) model of a mouse tibia-fibula was used to estimate the deformation of the bone during CTV. Finally, strain gages were used to determine the dependence of bone strain on loading frequency. The in vivo mouse leg in the CTV system had a resonant frequency of 60 Hz for +/-0.5 G vibration (1.0 G peak to peak). Removing the foot caused the natural frequency of the system to shift from 60 Hz to 70 Hz, removing the soft tissue caused no change in natural frequency, and removing the knee changed the natural frequency from 60 Hz to 90 Hz. By using the FE model, maximum tensile and compressive strains during CTV were estimated to be on the cranial-medial and caudolateral surfaces of the tibia, respectively, and the peak transmissibility and peak cortical strain occurred at the same frequency. Strain gage data confirmed the relationship between peak transmissibility and peak bone strain indicated by the FE model, and showed that the maximum cyclic tibial strain during CTV of the intact leg was 330+/-82microepsilon and occurred at 60-70 Hz. This study presents a comprehensive mechanical analysis of CTV, a loading method for studying vibrational loading under controlled conditions. This model will be used in future in vivo studies and will potentially become an important tool for understanding the response of bone to vibrational loading.     

Identification of in-vivo vibration modes of human tibiae by modal analysis

When attempting to evaluate the mechanical properties of human bones in vivo by mechanical vibration analysis, some essential requirements must be met. A quantitative relation between measured vibration parameters (e.g., natural frequency) and mechanical bone properties must be available, in-vivo vibration modes should correctly be identified and the associated natural frequencies reproducibly and accurately measured, the influence of joints and soft tissues must be known. These problems were addressed by modal analysis (i.e., experimental determination of natural frequencies, mode shapes and damping ratios) of human tibiae in the following situations: 1) dry excised tibiae, 2) fresh excised tibiae, 3) in-vivo tibiae, 4) tibiae in an amputated leg, in different steps of dissection. In the in-vivo measuring conditions used by the authors, the tibia vibration is practically free-free. Two single bending modes (at +/- 270 Hz and +/- 340 Hz, respectively), each of them corresponding with one principal direction for bending, were identified. The difference between the natural frequencies observed in vivo and those of fresh excised tibiae is almost completely caused by the effect of muscles (added mass and damping), whereas joints and skin play only a minor role. Frequency differences between fresh and dry excised tibiae are largely accounted for by the absence of bone marrow in the latter.     

Adaptive changes in micromechanical environments of cancellous and cortical bone in response to in vivo loading and disuse

The skeleton accommodates changes in mechanical environments by increasing bone mass under increased loads and decreasing bone mass under disuse. However, little is known about the adaptive changes in micromechanical behavior of cancellous and cortical tissues resulting from loading or disuse. To address this issue, in vivo tibial loading and hindlimb unloading experiments were conducted on 16-week-old female C57BL/6J mice. Changes in bone mass and tissue-level strains in the metaphyseal cancellous and midshaft cortical bone of the tibiae, resulting from loading or unloading, were determined using microCT and finite element (FE) analysis, respectively. We found that loading- and unloading-induced changes in bone mass were more pronounced in the cancellous than cortical bone. Simulated FE-loading showed that a greater proportion of elements experienced relatively lower longitudinal strains following load-induced bone adaptation, while the opposite was true in the disuse model. While the magnitudes of maximum or minimum principal strains in the metaphyseal cancellous and midshaft cortical bone were not affected by loading, strains oriented with the long axis were reduced in the load-adapted tibia suggesting that loading-induced micromechanical benefits were aligned primarily in the loading direction. Regression analyses demonstrated that bone mass was a good predictor of bone tissue strains for the cortical bone but not for the cancellous bone, which has complex microarchitecture and spatially-variant strain environments. In summary, loading-induced micromechanical benefits for cancellous and cortical tissues are received primarily in the direction of force application and cancellous bone mass may not be related to the micromechanics of cancellous bone.     

Mechanical boundary conditions of fracture healing: borderline indications in the treatment of unreamed tibial nailing

Unreamed nailing favors biology at the expense of the achievable mechanical stability. It is therefore of interest to define the limits of the clinical indications for this method. The extended usage of unreamed tibial nailing resulted in reports of an increased rate of complications, especially for the distal portion of the tibia. The goals of this work were to gain a thorough understanding of the load-sharing mechanism between unreamed nail and bone in a fractured tibia, to identify the mechanical reasons for the unfavorable clinical results, and to identify borderline indications due to biomechanical factors. In a three-dimensional finite element model of a human tibia, horizontal defects were stabilized by means of unreamed nailing for five different fracture locations, including proximal and distal borderline indications for this treatment method. The loading of the bone, the loading of the implant and the inter-fragmentary strains were computed. The findings of this study show that with all muscle and joint contact forces included, nailing leads to considerable unloading of the interlocked bone segments. Unreamed nailing of the distal defect results in an extremely low axial and high shear strain between the fragments. The results suggest that mechanical conditions are advantageous to unreamed nailing of proximal and mid-diaphyseal defects. Apart from biological reasons, clinical problems reported for distal fractures may be due to the less favorable mechanical conditions in unreamed nailing. From a biomechanical perspective, the treatment of distal tibial shaft fractures by means of unreamed nailing without additional fragment contact or without stabilizing the fibula should be carefully reconsidered.     

A new mechanical stimulator for cultured bone cells using piezoelectric actuator

In this study, a new mechanical stimulator using the piezoelectric actuator was developed to give cultured bone cells mechanical strains with more physiologic magnitude, frequency components, and waveform. This stimulator provides bone cells in a three-dimensional collagen gel block culture mechanical strains with magnitude of 200-40,000 microstrain and frequency of DC-100 Hz, which sufficiently covers physiological strains on bone. Furthermore, the stimulator can generate not only common strain waveforms like sine and rectangular waves, but also arbitrary strain waveforms synthesized on a personal computer. In particular, the controllability of strain frequency and waveform is an advance over that of previous stimulators. Thus, this device can facilitate new findings regarding bone cell responses to mechanical stimuli.     

Rest-inserted loading rapidly amplifies the response of bone to small increases in strain and load cycles.

We hypothesized that a 10-s rest interval (at zero load) inserted between each load cycle would increase the osteogenic effects of mechanical loading near previously identified thresholds for strain magnitude and cycle numbers. We tested our hypothesis by subjecting the right tibiae of female C57BL/6J mice (16 wk, n = 70) to exogenous mechanical loading within a peri-threshold physiological range of strain magnitudes and load cycle numbers using a noninvasive murine tibia loading device. Bone responses to mechanical loading were determined via dynamic histomorphometry. More specifically, we contrasted bone formation induced by cyclic vs. rest-inserted loading (10-s rest at zero load inserted between each load cycle) by first varying peak strains (1,000, 1,250, or 1,600 micro epsilon) at fixed cycle numbers (50 cycles/day, 3 days/wk for 3 wk) and then varying cycle numbers (10, 50, or 250 cycles/day) at a fixed strain magnitude (1,250 micro epsilon). Within the range of strain magnitudes tested, the slope of periosteal bone formation rate (p.BFR/BS) with increasing strain magnitudes was significantly increased by rest-inserted compared with cyclical loading. Within the range of load cycles tested, the slope of p.BFR/BS with increasing load cycles of rest-inserted loading was also significantly increased by rest-inserted compared with cyclical loading. In sum, the data of this study indicate that inserting a 10-s rest interval between each load cycle amplifies bone's response to mechanical loading, even within a peri-threshold range of strain magnitudes and cycle numbers.     

The effects of misalignment during in vivo loading of bone: Techniques to detect the proximity of objects in three-dimensional models

Theories of mechanical adaptation of bone suggest that mechanical loading causes bone formation at discrete locations within bone microstructure experiencing the greatest mechanical stress/strain. Experimental testing of such theories requires in vivo loading experiments and high-resolution finite element models to determine the distribution of mechanical stresses. Finite element models of in vivo loading experiments typically assume idealized boundary conditions with applied load perfectly oriented on the bone, however small misalignments in load orientation during an in vivo experiment are unavoidable, and potentially confound the ability of finite element models to predict locations of bone formation at the scale of micrometers. Here we demonstrate two different three-dimensional spatial correlation methods to determine the effects of misalignment in load orientation on the locations of high mechanical stress/strain in the rodent tail loading model. We find that, in cancellous bone, the locations of tissue with high stress are maintained under reasonable misalignments in load orientation (p<0.01). In cortical bone, however, angular misalignments in the dorsal direction can alter the locations of high mechanical stress, but the locations of tissue with high stress are maintained under other misalignments (p<0.01). We conclude that, when using finite element models of the rodent tail loading model, small misalignments in loading orientation do not affect the predicted locations of high mechanical stress within cancellous bone.     

Experimentally tested computer modeling of stress fractures in rats

The objective of this study was to develop a finite-element (FE) modeling methodology for studying the etiology of a stress fracture (SF). Several variants of three-dimensional FE models of a rat hindlimb, which differed in length or stiffness of tissues, enabling the analyses of mechanical strains and stress in the tibia, were created. We compared the occurrence of SFs in an animal model to validate locations of peak strains/stresses in the FE models. Four Sprague-Dawley male rats, age ~7 wk, were subjected to mechanical cyclic loads of 1.2 Hz and ~6 N, which were delivered to their hindlimb for 30 min, 3 times/wk, up to 12 wk, by using a specially designed apparatus. The results showed that 1) FE modeling predicted the maximal strains/stresses (~220,0 με and ~29 MPa, respectively) between the mid- and proximal thirds of the tibia; 2) in a longer shin, greater and more inhomogeneous tensile strains/stresses were evident, at the same location; 3) anatomical variants in shin length influenced the strain/stress distributions to a greater extent with respect to changes in mechanical properties of tissues; and 4) bone stiffness was more dominant than muscle stiffness in affecting the strain/stress distributions. In the animal study, 35,000 loading cycles were associated with the formation of a SF. The location of the identified SF in the rat limb verified the FE model. We find the suggested model a valuable tool in studying various aspects of SFs.     

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.     

Assessment of tibial stiffness by vibration testing in situ--III. Sensitivity of different modes and interpretation of vibration measurements

Post mortem vibration measurements on one human tibia during gradual transection reveal the vibration modes and frequencies of a tibia during a simulated healing. The modes are identified in a tibia in an above knee amputation specimen with the leg in two positions: hanging down with the knee flexed (90 degrees) and supported in a special designed bone clamping splint (knee flexed 45 degrees). The vibration measurements are analysed using Modal Analysis and are translated to mechanical stiffness by mathematical modelling. The single bending 'free-free' mode turned out to be more sensitive to weakening of one cross-section than the 'rigid body' and single bending 'hinged-spring' modes. The error on the assessed value of the stiffness is a multiple of the error on the measured frequencies. This multiplication factor decreases for more sensitive modes. In this experiment, the results are accurate enough to reflect the asymmetric weakening imposed upon the tibia. Attempts are made towards automatization of the measurement and analysis in order to get a system for clinical use. The actual system is still too cumbersome and time consuming for standard clinical use.     

Relationship between the shape and density distribution of the femur and its natural frequencies of vibration

It has been recently suggested that mechanical loads applied at frequencies close to the natural frequencies of bone could enhance bone apposition due to the resonance phenomenon. Other applications of bone modal analysis are also suggested. For the above-mentioned applications, it is important to understand how patient-specific bone shape and density distribution influence the natural frequencies of bones. We used finite element models to study the effects of bone shape and density distribution on the natural frequencies of the femur in free boundary conditions. A statistical shape and appearance model that describes shape and density distribution independently was created, based on a training set of 27 femora. The natural frequencies were then calculated for different shape modes varied around the mean shape while keeping the mean density distribution, for different appearance modes around the mean density distribution while keeping the mean bone shape, and for the 27 training femora. Single shape or appearance modes could cause up to 15% variations in the natural frequencies with certain modes having the greatest impact. For the actual femora, shape and density distribution changed the natural frequencies by up to 38%. First appearance mode that describes the general cortical bone thickness and trabecular bone density had one of the strongest impacts. The first appearance mode could therefore provide a sensitive measure of general bone health and disease progression. Since shape and density could cause large variations in the calculated natural frequencies, patient-specific FE models are needed for accurate estimation of bone natural frequencies.     

Site specific bone adaptation response to mechanical loading

Over 25 million Americans suffer from osteoporosis. Bone size and strength depends both upon the level of adaptation due to physical activity (applied load), and genetics. We hypothesized that bone adaptation to loads differs among mice breeds and bone sites. Forty-five adult female mice from three inbred strains (C57BL/6 [B6], C3H/HeJ [C3], and DBA/2J [D2]) were loaded at the right tibia and ulna in vivo with non-invasive loading devices. Each loading session consisted of 99 cycles at a force range that induced approximately 2000 microstrain (microepsilon) at the mid-shaft of the tibia (2.5 to 3.5 N force) and ulna (1.5 to 2 N force). The right and left ulnae and tibiae were collected and processed using protocols for histological undecalcified cortical bone slides. Standard histomorphometry techniques were used to quantify new bone formation. The histomorphometric variables include percentage mineralizing surface (%MS), mineral apposition rate (MAR), and bone formation rate (BFR). Net loading response [right-left limb] was compared between different breeds at tibial and ulnar sites using two-way ANOVA with repeated measures (p<0.05). Significant site differences in bone adaptation response were present within each breed (p<0.005). In all the three breeds, the tibiae showed greater percentage MS, MAR and BFR than the ulna at similar in vivo load or mechanical stimulus (strain). These data suggest that the bone formation due to loading is greater in the tibiae than the ulnae. Although, no significant breed-related differences were found in response to loading, the data show greater trends in tibial bone response in B6 mice as compared to D2 and C3 mice. Our data indicate that there are site-specific skeletal differences in bone adaptation response to similar mechanical stimulus.     

Measurement of microstructural strain in cortical bone

It is well known that mechanical factors affect bone remodeling such that increased mechanical demand results in net bone formation, whereas decreased demand results in net bone resorption. Current theories suggest that bone modeling and remodeling is controlled at the cellular level through signals mediated by osteocytes. The objective of this study was to investigate how macroscopically applied bone strains similar in magnitude to those that occur in vivo are manifest at the microscopic level in the bone matrix. Using a digital image correlation strain measurement technique, experimentally determined bone matrix strains around osteocyte lacuna resulting from macroscopic strains of approximately 2,000 microstrain (0.2%) reach levels of over 30,000 microstrain (3%) over fifteen times greater than the applied macroscopic strain. Strain patterns were highly heterogeneous and in some locations similar to observed microdamage around osteocyte lacuna indicating the resulting strains may represent the precursors to microdamage. This information may lead to a better understanding of how bone cells are affected by whole bone functional loading.     

Cyclic mechanical compression increases mineralization of cell-seeded polymer scaffolds in vivo

Despite considerable documentation of the ability of normal bone to adapt to its mechanical environment, very little is known about the response of bone grafts or their substitutes to mechanical loading even though many bone defects are located in load-bearing sites. The goal of this research was to quantify the effects of controlled in vivo mechanical stimulation on the mineralization of a tissue-engineered bone replacement and identify the tissue level stresses and strains associated with the applied loading. A novel subcutaneous implant system was designed capable of intermittent cyclic compression of tissue-engineered constructs in vivo. Mesenchymal stem cell-seeded polymeric scaffolds with 8 weeks of in vitro preculture were placed within the loading system and implanted subcutaneously in male Fisher rats. Constructs were subjected to 2 weeks of loading (3 treatments per week for 30 min each, 13.3 N at 1 Hz) and harvested after 6 weeks of in vivo growth for histological examination and quantification of mineral content. Mineralization significantly increased by approximately threefold in the loaded constructs. The finite element method was used to predict tissue level stresses and strains within the construct resulting from the applied in vivo load. The largest principal strains in the polymer were distributed about a modal value of -0.24% with strains in the interstitial space being about five times greater. Von Mises stresses in the polymer were distributed about a modal value of 1.6 MPa, while stresses in the interstitial tissue were about three orders of magnitude smaller. This research demonstrates the ability of controlled in vivo mechanical stimulation to enhance mineralized matrix production on a polymeric scaffold seeded with osteogenic cells and suggests that interactions with the local mechanical environment should be considered in the design of constructs for functional bone repair.     

Vibrational characteristics of bone fracture and fracture repair: application to excised rat femur

BACKGROUND: The vibrational characteristics of any object are directly dependent on the physical properties of that object. Therefore, changing the physical properties of an object will cause the object to adopt changed natural frequencies. A fracture in a bone results in the loss of mechanical stability of the bone. This change in mechanical properties of a bone should result in a change of the resonant frequencies of that bone. A vibrational method for bone evaluation has been introduced. METHOD OF APPROACH: This method uses the radiation force of focused amplitude-modulated ultrasound to exert a vibrating force directly, and remotely, on a bone. The vibration frequency is varied in the range of interest to induce resonances in the bone. The resulting bone motion is recorded and the resonance frequencies are determined. Experiments are conducted on excised rat femurs and resonance frequencies of intact, fractured, and bonded (simulating healed) bones are measured. RESULTS: The experiments demonstrate that changes in the resonance frequency are indicative of bone fracture and healing, i.e., the fractured bone exhibits a lower resonance frequency than the intact bone, and the resonance frequency of the bonded bone approaches that of the intact bone. CONCLUSION: It is concluded that the proposed radiation force method may be used as a remote and noninvasive tool for monitoring bone fracture and healing process, and the use of focused ultrasound enables one to selectively evaluate individual bones.     

Increased Expression of Matrix Extracellular Phosphoglycoprotein (MEPE) in Cortical Bone of the Rat Tibia after Mechanical Loading: Identification by Oligonucleotide Microarray

Skeletal integrity in humans and animals is maintained by daily mechanical loading. It has been widely accepted that osteocytes function as mechanosensors. Many biochemical signaling molecules are involved in the response of osteocytes to mechanical stimulation. The aim of this study was to identify genes involved in the translation of mechanical stimuli into bone formation. The four-point bending model was used to induce a single period of mechanical loading on the right tibia, while the contra lateral left tibia served as control. Six hours after loading, the effects of mechanical loading on gene-expression were determined with microarray analysis. Protein expression of differentially regulated genes was evaluated with immunohistochemistry. Nine genes were found to exhibit a significant differential gene expression in LOAD compared to control. MEPE, Garnl1, V2R2B, and QFG-TN1 olfactory receptor were up-regulated, and creatine kinase (muscle form), fibrinogen-B beta-polypeptide, monoamine oxidase A, troponin-C and kinesin light chain-C were down-regulated. Validation with real-time RT-PCR analysis confirmed the up-regulation of MEPE and the down-regulation of creatine kinase (muscle form) and troponin-C in the loaded tibia. Immunohistochemistry showed that the increase of MEPE protein expression was already detectable six hours after mechanical loading. In conclusion, these genes probably play a role during translation of mechanical stimuli six hours after mechanical loading. The modulation of MEPE expression may indicate a connection between bone mineralization and bone formation after mechanical stimulation.     

An MRI-based method to align the compressive loading axis for human cadaveric knees

There is a need to align the mechanical axis of the tibia with the axis of loading for studies involving tibiofemoral compression to interpret results and to ensure repeatability of loading within and among specimens. Therefore, the objectives of this study were (1) to develop a magnetic resonance imaging (MRI)-based alignment method for use with apparatuses applying tibiofemoral joint compression, (2) to demonstrate the usefulness of the method by aligning cadaveric knees in an apparatus that could apply tibiofemoral joint compression, and (3) to quantify the error associated with the alignment method. A four degree-of-freedom adjustable device was constructed to allow determination and alignment of the mechanical axis of the tibia of cadaveric knee joints with the axis of loading of an apparatus applying tibiofemoral joint compression. MRI was used to determine the locations of bony landmarks in three dimensions defining the mechanical axis of the tibia relative to an initial orientation of the four degree-of-freedom device. Adjustment values of the device were then computed and applied to the device to align the mechanical axis of the tibia with the axis of a compressive loading apparatus. To demonstrate the usefulness of the method, four cadaveric knees were aligned in the compressive loading apparatus. The vectors describing the mechanical axis of the tibia and the loading axis of the apparatus before and after adjustment of the four degree-of-freedom device were computed for each cadaveric knee. After adjustment of the four degree-of-freedom device, the mechanical axis of the tibia was collinear with the loading axis of the apparatus for each cadaveric knee. The errors in the adjustment values introduced by inaccuracies in the MR images were quantified using the Monte Carlo technique. The precisions in the translational and rotational adjustments were 1.20 mm and 0.90 deg respectively. The MR-based alignment method will allow consistent interpretation of results obtained during tibiofemoral compressive studies conducted using the apparatus described in this paper by providing a well-defined loading axis. The alignment method can also be adapted for use with other apparatuses applying tibiofemoral compression.     

In vitro bone growth responds to local mechanical strain in three-dimensional polymer scaffolds

Mechanical stimulation plays a key role in healing and remodelling of bone tissue in vivo, and is used in bone tissue regeneration strategies in vitro. Although macroscopic compression of three-dimensional (3-D) seeded constructs can increase bone formation, it is not yet reported how this response is related to differences in local mechanical strains inside the scaffolds. In this study, we experimentally test the hypothesis that differences in local average of heterogeneous strains in a polymer scaffold will correlate with induced differences in the local biological response.Twenty-four poly(l-lactic acid) porous scaffolds seeded with rat bone cells were cultured first for 2 and 3 weeks under static conditions, respectively. Then for 1 week, half of the scaffolds were cyclically compressed (1.5%, 1 Hz), 1 h daily, with continuous perfusion (0.1 ml/min). The remaining half was kept under static conditions. The pore-surface strains in the scaffolds at the start of culture were calculated with micro-finite element modelling based on micro-Computed Tomography (μCT) images. The locations of mineralized nodules were determined from μCT images and coupled to the calculated strains.Detectable mineralized nodules (>10³ μm³) were only present in the loaded samples. Averages of absolute principal strains at the start of culture were significantly higher at nodule sites than at sites without a nodule.The results support the hypothesis that regenerating bone tissue in a 3-D porous scaffold responds to local mechanical strain. The methodology presented in this study can contribute design optimisation of tissue regeneration strategies relying on mechanical stimulation.     

Acoustic-induced motion of the bushcricket (Mecopoda elongata, Tettigoniidae) tympanum

Bushcrickets have a tonotopically organised hearing organ, the so-called crista acustica, in the tibia of the forelegs. This organ responds to a frequency range of about 5–80 kHz and lies behind the anterior tympanum on top of a trachea branch. We analyzed the sound-induced vibration pattern of the anterior tympanum, using a Laser-Doppler-Vibrometer Scanning microscope system, in order to identify frequency-dependent amplitude and phase of displacement. The vibration pattern evoked by a frequency sweep (4–79 kHz) showed an amplitude maximum which would correspond to the resonance frequency of an open tube system. At higher frequencies of about 30 kHz a difference in the amplitude and phase response between the distal and the proximal part of the tympanum was detected. The inner plate of the tympanum starts to wobble at this frequency. This higher mode in the motion pattern is not explained by purely acoustic characteristics of the tracheal space below the tympanum but may depend on the mechanical impedance of the tympanum plate. In accordance with a previous hypothesis, the tympanum moves over the whole tested frequency range in the dorso-ventral direction like a hinged flap with the largest displacement in its ventral part and no higher modes of vibration.     

The compressive mechanical properties of diabetic and non-diabetic plantar soft tissue

Diabetic subjects are at an increased risk of developing plantar ulcers. Knowledge of the physiologic compressive properties of the plantar soft tissue is critical to understanding the possible mechanisms of ulcer formation and improving treatment options. The purpose of this study was to determine the compressive mechanical properties of the plantar soft tissue in both diabetic and non-diabetic specimens from six relevant locations beneath the foot, namely the hallux (big toe), first, third, and fifth metatarsal heads, lateral midfoot, and calcaneus (heel). Cylindrical specimens (1.905 cm diameter) from these locations were excised and separated from the skin and bone from 4 diabetic and 4 non-diabetic age-matched, elderly, fresh-frozen cadaveric feet. Specimens were then subjected to biomechanically realistic strains of ～50% in compression using triangle wave tests conducted at five frequencies ranging from 1 to 10 Hz to determine tissue modulus, energy loss, and strain rate dependence. Diabetic vs. non-diabetic results across all specimens, locations, and testing frequencies demonstrated altered mechanical properties with significantly increased modulus (1146.7 vs. 593.0 kPa) but no change in energy loss (68.5 vs. 67.9%). All tissue demonstrated strain rate dependence and tissue beneath the calcaneus was found to have decreased modulus and energy loss compared to other areas. The results of this study could be used to generate material properties for all areas of the plantar soft tissue in diabetic or non-diabetic feet, with implications for foot computational modeling efforts and potentially for pressure alleviating footwear that could reduce plantar ulcer incidence.