Tony S. Keller

Predicting the compressive mechanical behavior of bone.

The principal objectives of this study were to determine the mathematical dependency of the compressive mechanical properties of human bone on several commonly used measures of bone composition, and to assess variations in this dependency based upon the composition range spanned by the data. Destructive mechanical tests were conducted along the superior-inferior axis of 496 cubic specimens of human trabecular and cortical bone from five male donors (ages 46-84 yr), including specimens from lumbar vertebrae and femoral metaphyses and diaphyses. There was over a 3000-fold variation in strength (S, ultimate stress) and over a 20,000-fold variation in stiffness (E, elastic modulus) over the range of apparent dry density (rho a = 0.05-1.89 g cm-3), apparent ash density (rho alpha = 0.03-1.22 g cm-3) and mineral content (alpha = 17.4-66.2%) examined. Both linear and power models produced very high correlations (R2 > 0.81) between mechanical properties and bone composition, but the linear models resulted in a much greater percent deviation (PD) of the predicted dependent variable with respect to the measured value, in comparison to power models. The best correlations were obtained using rho alpha as the only independent variable: S (MPa) = 117 rho alpha 1.93 +/- 0.04 (R2 = 0.969, PD = 29.9, E (GPa) = 10.5 rho alpha 2.57 +/-0.04 (R2 = 0.965, PD = 46.7). Power models of bone stiffness and strength, incorporating only low density data (rho alpha < 0.2 g cm-3, rho a < 0.3), were characterized by approximately squared exponents and these models underestimated the stiffness (five-fold) and overestimated the strength (two-fold) for higher density data, which were characterized by exponents greater than two. Using a subset of the data based upon an apparent dry density range of 0.22 < rho a < 1.89 g cm-3, it was possible to obtain a mathematical relationship in which bone stiffness and strength were precisely proportional to the cube and square, respectively, of the apparent dry density. These results indicate that the mathematical dependency of bone compressive mechanical properties on composition is closely dependent upon the density and mineral content range examined and, in terms of a single compositional measure, is best predicted by apparent ash density expressed as a power function.

Relationship between vertical ground reaction force and speed during walking, slow jogging, and running.

OBJECTIVE: To obtain descriptive information between vertical ground reaction force (GRF)-time histories and gait speed, running style, and gender. DESIGN: GRF-time history measurements were obtained from male and female subjects during walking, slow jogging, jogging and running on an indoor platform. BACKGROUND: Previous studies have established GRF descriptor variables for male subjects running at speeds from 3 to 6 m s(-1), but very little descriptive data exists for slower or faster running, nor have previous studies reported GRF descriptors separately for female subjects. METHODS: GRF-time histories were recorded for 13 male and 10 female recreational athletes during walking and slow jogging at speeds between 1.5 and 3.0 m s(-1), and running at speeds between 3.5 and 6.0 m s(-1). Vertical GRF-time data for trials with speeds within 0.2 m s(-1) of the prescribed speed were analysed to determine thrust maximum GRF (F(z)) and loading rate (G(z)). RESULTS: In both male and female subjects, F(z) increased linearly during walking and running from 1.2 BW to approximately 2.5 BW at 6.0 m s(-1), remaining constant during forward lean sprinting at higher speeds. F(z) was linearly correlated to G(z), the latter ranging from 8 to 30 BW s(-1) over this speed range. Slow jogging was associated with a > 50% higher F(z) and G(z) in comparison to walking or fast running. CONCLUSIONS: Similar GRF descriptor data and velocity relationships were obtained for male and female subjects. Impact forces were greatest when the subjects adopted a higher, less fixed centre of gravity during slow jogging. RELEVANCE: These results suggest that vertical GRF norms can be established for male and female subjects alike, and that slow or fast running with a lower, fixed centre of gravity decreases impact forces.

The influence of bone volume fraction and ash fraction on bone strength and modulus

Although bone strength and modulus are known to be influenced by both volume fraction and mineral content (ash fraction), the relative influence of these two parameters remains unknown. Single-parameter power law functions are used widely to relate bone volume or ash fraction to bone strength and elastic modulus. In this study we evaluate the potential for predicting bone mechanical properties with two-parameter power law functions of bone volume fraction (BV/TV) and ash fraction (alpha) of the form y = a(BV/TV)(b) alpha(c) (where y is either ultimate strength or elastic modulus). We derived an expression for bone volume fraction as a function of apparent density and ash fraction to perform a new analysis of data presented by Keller in 1994. Exponents b and c for the prediction of bone strength were found to be 1.92 +/- 0.02 and 2.79 +/- 0.09 (mean +/- SE), respectively, with r(2) = 0.97. The value of b was found to be consistent with that found previously, whereas the value of c was lower than values previously reported. For the prediction of elastic modulus we found b and c to be 2.58 +/- 0.02 and 2.74 +/- 0.13, respectively, with r(2) = 0.97. The exponent related to ash fraction was typically larger than that associated with bone volume fraction, suggesting that a change in mineral content will, in general, generate a larger change in bone strength and stiffness than a similar change in bone volume fraction. These findings are important for interpreting the results of antiresorptive drug treatments that can cause changes in both ash and bone volume fraction.

Regional variations in the compressive properties of lumbar vertebral trabeculae. Effects of disc degeneration

The compressive mechanical properties of human lumbar vertebral trabeculae were examined on the basis of anatomic origin, bone density, and intervertebral disc properties. Trabecular bone compressive strength and stiffness increased with increasing bone density, the latter proportional to strength and stiffness to the one-half power. Regional variations within each segment were found, the most prevalent differences occurring in regions of bone overlying the disc nucleus in comparison with bone overlying the disc anulus. For normal discs, the ratio of strength of bone overlying the disc nucleus to bone overlying the disc anulus was 1.25, decreasing to 1.0 for moderately degenerated discs. These results suggest that an interdependency of trabecular bone properties and intervertebral disc properties may exist.

Prediction of osteoporotic spinal deformity

Study Design. A biomechanical model was developed from full-spine lateral radiographs to predict osteoporotic spinal deformity in elderly subjects. Objective. To investigate the biomechanics of age-related spinal deformity and concomitant height loss associated with vertebral osteoporosis. Summary of Background Data. Vertebral bone loss and disc degeneration associated with aging causes bone and disc structures to weaken and deform as a result of gravity and postural stresses. Methods. An anatomically accurate sagittal-plane, upright-posture biomechanical model of the anterior spinal column (C2–S1) was created by digitizing lateral full-spine radiographs of 20 human subjects with a mean height of 176.8 cm and a mean body weight of 76.6 kg. Body weight loads were applied to the model, after which intervertebral disc and vertebral body forces and deformation were computed and the new spine geometry was calculated. The strength and stiffness of the vertebral bodies were reduced according to an osteopenic aging model and modulus reduction algorithm, respectively. Results. The most osteopenic model (L3 Fult = 750 N) produced gross deformities of the spine, including anterior wedge-like fracture deformities at T7 and T8. In this model, increases in thoracic kyphosis and decreases in vertebral body height resulted in a 25.2% decrease in spinal height (C2-S1), an 8.6% decrease in total body height, and a 15.1-cm anterior translation of the C2 spine segment centroid. The resulting deformity qualitatively resembled deformities observed in elderly individuals with osteoporotic compression fractures. Conclusions. These predictions suggest that postural forces are responsible for initiation of osteoporotic spinal deformity in elderly subjects. Vertebral deformities are exacerbated by anterior translation of the upper spinal column, which increases compressive loads in the thoracolumbar region of the spine.

1990 Volvo Award in experimental studies. The dependence of intervertebral disc mechanical properties on physiologic conditions.

In vivo creep-recovery and disc pressure measurements were performed on the lumbar spine of immature and mature swine. The creep-recovery measurements were performed using a custom materials testing apparatus designed to apply static or dynamic loads to the spine of anesthetized animals. A series of three separate experiments were performed to assess the effects of: (I) animal death, (II) graded injury to the disc anulus, and (III) respiratory mechanics on the biomechanical response of the porcine L1–L3 vertebral unit (VU). In Experiments I and II, creep rate, modulus, and viscosity parameters were computed using a three-parameter solid rheological analysis of the displacement-time response recorded during the application of a 300-N load. In Experiment III, the effects of respiratory volume and frequency changes on disc pressure were assessed in the unloaded, statically loaded, and immobilized porcine VU. Our results indicated that the adult VU tended to be stiffer, deform or creep more slowly, and had a significantly higher viscosity than the VU of immature pigs. The results of Experiment I demonstrated that the biomechanical response for the VU was significantly altered by the death of the animal; the VU of the living animal (adolescent or mature) was more compliant and deformed at a faster rate than the VU of the same animal after death. Disc injury produced changes in stiffness, viscosity, and creep rate analogous to that of aging, and on the basis of the graded injuries created in this study, it appears that a small defect in the annulus is just as deleterious as removing a large section of anular material. The results of Experiment III indicated that respiration plays an important role in the normal, in vivo mechanical and nutritional behavior of the porcine VU. Altogether, these results demonstrate that, in the absence of normal physiologic conditions, one may not be able to reliably predict the mechanical response of the lumbar spine, and suggest that standards for the testing, handling, and storage of biologic tissue should be established.

Electromyographic reflex responses to mechanical force, manually assisted spinal manipulative therapy.

Study Design. Surface electromyographic reflex responses associated with mechanical force, manually assisted (MFMA) spinal manipulative therapy were analyzed in this prospective clinical investigation of 20 consecutive patients with low back pain. Objectives. To characterize and determine the magnitude of electromyographic reflex responses in human paraspinal muscles during high loading rate mechanical force, manually assisted spinal manipulative therapy of the thoracolumbar spine and sacroiliac joints. Summary of Background Data. Spinal manipulative therapy has been investigated for its effectiveness in the treatment of patients with low back pain, but its physiologic mechanisms are not well understood. Noteworthy is the fact that spinal manipulative therapy has been demonstrated to produce consistent reflex responses in the back musculature; however, no study has examined the extent of reflex responses in patients with low back pain. Methods. Twenty patients (10 male and 10 female, mean age 43.0 years) underwent standard physical examination on presentation to an outpatient chiropractic clinic. After repeated isometric trunk extension strength tests, short duration ( 2.5 p-p baseline sEMG output (>3.5% relative mean sEMG output). SEMG threshold was further assessed for correlation of patient self-reported pain and disability. Results. Consistent, but relatively localized, reflex responses occurred in response to the localized, brief duration MFMA thrusts delivered to the thoracolumbar spine and SI joints. The time to peak tension (sEMG magnitude) ranged from 50 to 200 msec, and the reflex response times ranged from 2 to 4 msec, the latter consistent with intraspinal conduction times. Overall, the 20 treatments produced systematic and significantly different L5 and L3 sEMG responses, particularly for thrusts delivered to the lumbosacral spine. Thrusts applied over the transverse processes produced more positive sEMG responses (25.4%) in comparison with thrusts applied over the spinous processes (20.6%). Left side thrusts and right side thrusts over the transverse processes elicited positive contralateral L5 and L3 sEMG responses. When the data were examined across both treatment level and electrode site (L5 or L3, L or R), 95% of patients showed positive sEMG response to MFMA thrusts. Patients with frequent to constant low back pain symptoms tended to have a more marked sEMG response in comparison with patients with occasional to intermittent low back pain. Conclusions. This is the first study demonstrating neuromuscular reflex responses associated with MFMA spinal manipulative therapy in patients with low back pain. Noteworthy was the finding that such mechanical stimulation of both the paraspinal musculature (transverse processes) and spinous processes produced consistent, generally localized sEMG responses. Identification of neuromuscular characteristics, together with a comprehensive assessment of patient clinical status, may provide for clarification of the significance of spinal manipulative therapy in eliciting putative conservative therapeutic benefits in patients with pain of musculoskeletal origin.

The effects of simulated weightlessness on bone biomechanical and biochemical properties in the maturing rat

Histomorphometric and biomechanical changes in bone resulting from hypogravity (simulated weightlessness) were examined in this study. Using a head-down hindlimb suspension model, three groups of six male rats underwent simulated weightlessness for periods of one, two and three weeks while a fourth recovery group was suspended for two weeks followed by two weeks of normal activity. Biomechanical data were collected during static and dynamic bending and torsion tests on intact femora. Histomorphometric values were determined from midshaft bone cross sections and material properties were obtained using ash and calcium assays. The experimental groups exhibited significantly lower geometric and material properties than the controls, resulting in structural hypotrophy; geometric and material changes contributed equally to the structural changes. Recovery following a return to normal activity was indicated, although full recovery may take longer than the weightlessness period. In the rat, altered maturation and reduced bone strength were the sequelae of weightlessness.

Clinical and psychofunctional measures of conservative decompression surgery for lumbar spinal stenosis: a prospective cohort study

Abstract. Less invasive decompressive surgery has emerged as a logical surgical treatment alternative to wide decompression of spinal stenosis. The clinical outcomes of such conservative surgical treatment, however, are not well known. The aim of the study was to evaluate short-term psychometric and functional outcomes after conservative decompressive surgery for lumbar canal stenosis. Forty patients had a lumbar laminectomy procedure, which preserved the integrity of the neural arches, facet joints and most muscle attachments. Pre-operative clinical evaluation of the patients included: Waddells non-organic signs (NOS) performed by an independent surgeon observer; three self-report questionnaires – the Waddell Disability Index (WDI), the Oswestry Low Back Pain Disability Questionnaire (ODI), and the Low Back Outcome Score (LBOS); and a general questionnaire that included a visual analog pain intensity scale (VAS). Post-operative clinical evaluations and questionnaires were obtained in 36 subjects (mean age 59.8 years) after a 1.7-year follow-up (range 1–2.6 years). Pre-operative versus post-operative statistical comparisons of the data were performed using adjusted error rates within families of predictors. Successful surgical outcome was defined as an improvement in at least three of the following four criteria: self-reported pain on a VAS, self-reported functional status measured by LBOS, reduction of pain during walking and reduction of leg pain. At follow-up, there was a statistically significant improvement in VAS pain intensity, ODI, WDI, and LBOS. Patients classified as having mixed stenosis had a higher incidence of continuous pain symptoms in comparison with acquired stenosis, but there was no differential improvement with treatment depending upon stenosis classification and/or number of operative levels. Overall, 58% (21/36) of patients met the successful surgical outcome criteria, including 14 subjects who met all four success criteria. Based upon a stringent definition of successful surgical outcome, the results of a conservative laminectomy were as good as those of more aggressive decompressive procedures presented in the literature. Our findings indicate that, even in a highly organic disorder such as spinal stenosis, illness behavior plays an important role in predicting surgical outcome.

Vertebroplasty and kyphoplasty affect vertebral motion segment stiffness and stress distributions: a microstructural finite-element study.

Study Design. The mechanical behavior of a thoracic motion segment following cement augmentation was studied using the finite-element method. Objective. To examine effects of cement augmentation on motion segment stiffness and load transfer. Summary of Background Data. Vertebroplasty and kyphoplasty procedures are meant to stiffen and strengthen the vertebral body, but the optimal cement volume and placement to achieve these goals without altering load transfer to adjacent segments are unknown. Methods. A microstructural finite-element model of a vertebral motion segment was constructed from micro-CT images. Microdamage within the vertebral body trabecular structure was modeled using an elasto-plastic modulus reduction scheme. Three motion segment damage models were created: I = 18% apparent modulus reduction (least damage), II = 45%, and III = 85% (most damage); and several one- and two-segment polymethylmethacrylate cement repair strategies (partial fill kyphoplasty, replacement of bone and marrow; and both partial fill and complete fill vertebroplasty, replacement of marrow only) were studied. Average disc and bone stresses and motion segment apparent compressive stiffness were compared with baseline (undamaged and untreated) simulation results. Results. In terms of maximizing stiffness and minimizing stress alterations in the adjacent vertebral body and increasing motion segment apparent stiffness, we found that, other than complete fill, the most effective single-segment cement repair strategy was vertebroplasty on the periphery of the superior segment overlying the disc anulus (<0.1% overall vertebral body bone stress alteration and 83% stiffness increase, respectively, damage Model III). Two-segment vertebroplasty (all repair models) restored motion segment stiffness to baseline levels in all damage models, while single-segment vertebroplasty (all repair models) restored stiffness to baseline levels only in damage Model I. Single- and two-segment kyphoplasty was effective in restoring stiffness to baseline levels for Model I only. Compared with the baseline model, cement augmentation decreased average treated segment bone stresses (up to 66%, complete fill vertebroplasty elasto-plastic modulus reduction Model III), increased average intervertebral disc nucleus stresses (up to 59%, kyphoplasty elasto-plastic modulus reduction Model III), and increased average adjacent segment, endplate region stresses (up to 2.8%, kyphoplasty elasto-plastic modulus reduction Model II). Adjacent (untreated) segment peak bone stresses were increased (up to 45%, kyphoplasty, Model III) in endplate regions underlying the intervertebral disc nucleus. Conclusions. The damage-repair simulations indicated that cement augmentation improves motion segment stiffness but substantially alters bone stress distributions in treated and adjacent segments.