Glen L. Niebur

Comparison of the elastic and yield properties of human femoral trabecular and cortical bone tissue.

The ability to determine trabecular bone tissue elastic and failure properties has biological and clinical importance. To date, trabecular tissue yield strains remain unknown due to experimental difficulties, and elastic moduli studies have reported controversial results. We hypothesized that the elastic and tensile and compressive yield properties of trabecular tissue are similar to those of cortical tissue. Effective tissue modulus and yield strains were calibrated for cadaveric human femoral neck specimens taken from 11 donors, using a combination of apparent-level mechanical testing and specimen-specific, high-resolution, nonlinear finite element modeling. The trabecular tissue properties were then compared to measured elastic modulus and tensile yield strain of human femoral diaphyseal cortical bone specimens obtained from a similar cohort of 34 donors. Cortical tissue properties were obtained by statistically eliminating the effects of vascular porosity. Results indicated that mean elastic modulus was 10% lower (p<0.05) for the trabecular tissue (18.0+/-2.8 GPa) than for the cortical tissue (19.9+/-1.8 GPa), and the 0.2% offset tensile yield strain was 15% lower for the trabecular tissue (0.62+/-0.04% vs. 0.73+/-0.05%, p<0.001). The tensile-compressive yield strength asymmetry for the trabecular tissue, 0.62 on average, was similar to values reported in the literature for cortical bone. We conclude that while the elastic modulus and yield strains for trabecular tissue are just slightly lower than those of cortical tissue, because of the cumulative effect of these differences, tissue strength is about 25% greater for cortical bone.

High-resolution finite element models with tissue strength asymmetry accurately predict failure of trabecular bone

The ability to predict trabecular failure using microstructure-based computational models would greatly facilitate study of trabecular structure-function relations, multiaxial strength, and tissue remodeling. We hypothesized that high-resolution finite element models of trabecular bone that include cortical-like strength asymmetry at the tissue level, could predict apparent level failure of trabecular bone for multiple loading modes. A bilinear constitutive model with asymmetric tissue yield strains in tension and compression was applied to simulate failure in high-resolution finite element models of seven bovine tibial specimens. Tissue modulus was reduced by 95% when tissue principal strains exceeded the tissue yield strains. Linear models were first calibrated for effective tissue modulus against specimen-specific experimental measures of apparent modulus, producing effective tissue moduli of (mean+/-S.D.) 18.7+/-3.4GPa. Next, a parameter study was performed on a single specimen to estimate the tissue level tensile and compressive yield strains. These values, 0.60% strain in tension and 1.01% strain in compression, were then used in non-linear analyses of all seven specimens to predict failure for apparent tensile, compressive, and shear loading. When compared to apparent yield properties previously measured for the same type of bone, the model predictions of both the stresses and strains at failure were not statistically different for any loading case (p>0.15). Use of symmetric tissue strengths could not match the experimental data. These findings establish that, once effective tissue modulus is calibrated and uniform but asymmetric tissue failure strains are used, the resulting models can capture the apparent strength behavior to an outstanding level of accuracy. As such, these computational models have reached a level of fidelity that qualifies them as surrogates for destructive mechanical testing of real specimens.

Convergence behavior of high-resolution finite element models of trabecular bone.

The convergence behavior of finite element models depends on the size of elements used, the element polynomial order, and on the complexity of the applied loads. For high-resolution models of trabecular bone, changes in architecture and density may also be important. The goal of this study was to investigate the influence of these factors on the convergence behavior of high-resolution models of trabecular bone. Two human vertebral and two bovine tibial trabecular bone specimens were modeled at four resolutions ranging from 20 to 80 microns and subjected to both compressive and shear loading. Results indicated that convergence behavior depended on both loading mode (axial versus shear) and volume fraction of the specimen. Compared to the 20 microns resolution, the differences in apparent Youngs modulus at 40 microns resolution were less than 5 percent for all specimens, and for apparent shear modulus were less than 7 percent. By contrast, differences at 80 microns resolution in apparent modulus were up to 41 percent, depending on the specimen tested and loading mode. Overall, differences in apparent properties were always less than 10 percent when the ratio of mean trabecular thickness to element size was greater than four. Use of higher order elements did not improve the results. Tissue level parameters such as maximum principal strain did not converge. Tissue level strains converged when considered relative to a threshold value, but only if the strains were evaluated at Gauss points rather than element centroids. These findings indicate that good convergence can be obtained with this modeling technique, although element size should be chosen based on factors such as loading mode, mean trabecular thickness, and the particular output parameter of interest.

Roles of deltoid and rotator cuff muscles in shoulder elevation

OBJECTIVE: The objective of this study was to measure abduction moment arms of the supraspinatus, subscapularis, infraspinatus, and deltoid (anterior, middle, and posterior portions) muscles during humeral elevation in the scapular plane (abduction). DESIGN: Moment arms were measured by conducting an in vitro experiment. BACKGROUND: The moment arm of a muscle represents its mechanical advantage, which is an important determinant of muscle function. METHODS: Measurements were made on 10 fresh frozen cadaveric specimens. Tendon excursions were measured as the humerus was elevated in the plane of the scapula. The principle of virtual work was used to estimate the muscle moment arm of each muscle by computing the slope of the tendon excursion versus joint angle relationship. RESULTS: Moment arms were affected by joint angle in a non-linear fashion. The anterior deltoid, middle deltoid, subscapularis, and infraspinatus muscles had abduction moment arms throughout most of the range of motion studied. The posterior deltoid had an adduction moment arm. Internal and external humeral rotation affected the elevation moment arms of all six muscles. CONCLUSIONS: Abduction moment arm magnitudes of the muscles studies vary throughout the arc of elevation. This study was limited by considering broad muscles to have a single line of action. RELEVANCE: The positive elevation moment arms of the infraspinatus and subscapularis muscles indicate that they can elevate the arm in addition to acting as stabilizers. Thus this study suggests a biomechanical explanation for the clinical success of conservative treatment for rotator cuff tears.

The relevance of the moment arm of shoulder muscles with respect to axial rotation of the glenohumeral joint in four positions

OBJECTIVE This study was undertaken to determine the efficiency of the shoulder girdle muscles during axial humeral rotation based on measurements of the moment arms. DESIGN The instantaneous muscle moment arms of 10 shoulder muscles, including the three portions of the deltoid, the rotator cuff muscles, teres major, and the thoracohumeral muscle group, were measured during four specified glenohumeral rotations. BACKGROUND Axial humeral rotation is a commonly performed movement during activities of daily living and is a targeted motion of shoulder rehabilitation, particularly in those protocols emphasizing rotator cuff strengthening. An understanding of the function of the movers and stabilizers of the shoulder requires such basic information of muscle moment arms. METHODS The instantaneous moment arm values of the muscles were derived from the slope of the plot of tendon excursion versus glenohumeral joint rotation angle. Motion studied included axial rotation with the humerus elevated 90 degrees in the coronal, scapular, and sagittal planes, as well as in the neutral position with the arm at the side. RESULTS Based on the findings, with the humerus in both neutral and elevated positions, the infraspinatus is potentially the most powerful external rotator, followed by teres minor and posterior deltoid. Subscapularis and possibly pectoralis major are the most effective internal rotators in this position. CONCLUSIONS The moment arm in providing axial humeral rotation of 10 shoulder muscles in four planes were obtained. In general, the teres minor and infraspinatus had the largest moment arms in external rotation, and the subscapularis had the largest moment arm in internal rotation. The muscle function for axial humeral rotation was found to be modified by the plane of arm elevation. RELEVANCE The data could be used for developing exercise programs in physical therapy.

Biomechanical effects of intraspecimen variations in tissue modulus for trabecular bone

Although recent nanoindentation studies have revealed the existence of substantial variations in tissue modulus within single specimens of trabecular bone, little is known regarding the biomechanical effects of such intraspecimen variations. In this study, high-resolution finite element modeling was used to investigate these effects. With limited literature information on the spatial distribution of intraspecimen variations in tissue modulus, two plausible spatial distributions were evaluated. In addition, three specimens (human femoral neck, human vertebral body, and bovine proximal tibia) were studied to assess the role of trabecular architecture. Results indicated that for all specimen/distribution combinations, the apparent modulus of the whole specimen decreased nonlinearly with increasing coefficient of variation (COV) of tissue modulus within the specimen. Apparent modulus decreased by <4% when tissue modulus COV was increased from 0% to 20% but decreased by 7-24%, depending on the assumed spatial distribution, for an increase in tissue modulus COV from 20% to 50%. For compressive loading to the elastic limit, increasing tissue modulus COV from 20% to 50% caused up to a 28-fold increase in the amount of failed tissue, depending on assumed spatial distribution and trabecular architecture. We conclude that intraspecimen variations in tissue modulus, if large, may have appreciable effects on trabecular apparent modulus and tissue-level failure. Since the observed effects depended on the assumed spatial distribution of the tissue modulus variations, a description of such distributions, particularly as a function of age, disease, and drug treatment, may provide new insight into trabecular bone structure-function relationships.

Mechanical advantage of the thumb muscles

The purpose of this study was to measure the moment arms of four extrinsic muscles (flexor pollicis longus, extensor pollicis longus, extensor pollicis brevis, and abductor pollicis longus) and four intrinsic muscles (flexor pollicis brevis, abductor pollicis brevis, adductor pollicis, and opponents pollicis) of the thumb at the interphalangeal, the metacarpophalangeal, and the carpometacarpal joints in the same cadaver specimens and to examine the specific role of each muscle. Measurements were made on seven fresh frozen cadaver hands. The moment arms were measured during flexion/extension of the interphalangeal joint, flexion/extension and adduction/abduction of the metacarpophalangeal joint, and flexion/extension and adduction/abduction of the carpometacarpal joint. Moment arms were computed using the slope of the tendon excursion joint angle relationship. The specific function of each muscle was determined by multiplying the measured moment arms by the maximum force that each muscle can generate. It was found that the flexor pollicis longus was a pure flexor while flexor pollicis brevis was an adductor as well as a flexor, the extensor pollicis longus was an extensor and an adductor, extensor pollicis brevis was an extensor and a mild abductor, the abductor pollicis longus was an extensor as well as an abductor, the abductor pollicis brevis was mainly an abductor, the adductor pollicis was a major flexor as well as an adductor, and the opponents pollicis was a flexor and an abductor.

Motion and laxity of the capitellocondylar total elbow prosthesis

The motion and laxity of the capitellocondylar unconstrained total elbow prosthesis were assessed, with use of an electromagnetic tracking device and stimulated muscle-loading, after implantation in seventeen cadaveric elbows. The axis of motion of the elbows with the capitellocondylar implants averaged 2.1 +/- 2.3 degrees more varus angulation than that of the intact elbows. This difference may be attributed to the design of the implant, as the 5-degree-valgus humeral component used in this study has a smaller valgus inclination than the articular surface of the distal aspect of the humerus. Although the maximum valgus-varus laxity of the capitellocondylar elbow prostheses was, on the average, 4.3 +/- 2.4 degrees greater than normal (with simulated muscle-loading), the data must be interpreted in light of the fact that this in vitro study did not allow for soft-tissue healing. The prosthetic components tracked well, and there were no dislocations or malarticulations provided that appropriate soft-tissue tensioning and positioning of the components had been achieved at the time of implantation. Sectioning of either the medial or the lateral collateral ligament resulted in gross instability of the joint after capitellocondylar arthroplasty. The ulnar attachment of the medial collateral ligament was found to be vulnerable to injury during the positioning of the ulnar component of this implant.

Hydroxyapatite reinforced collagen scaffolds with improved architecture and mechanical properties.

Hydroxyapatite (HA) reinforced collagen scaffolds have shown promise for synthetic bone graft substitutes and tissue engineering scaffolds. Freeze-dried HA-collagen scaffolds are readily fabricated and have exhibited osteogenicity in vivo, but are limited by an inherent scaffold architecture that results in a relatively small pore size and weak mechanical properties. In order to overcome these limitations, HA-collagen scaffolds were prepared by compression molding HA reinforcements and paraffin microspheres within a suspension of concentrated collagen fibrils (∼ 180 mg/mL), cross-linking the collagen matrix, and leaching the paraffin porogen. HA-collagen scaffolds exhibited an architecture with high porosity (85-90%), interconnected pores ∼ 300-400 μm in size, and struts ∼ 3-100 μm in thickness containing 0-80 vol% HA whisker or powder reinforcements. HA reinforcement enabled a compressive modulus of up to ∼ 1 MPa, which was an order of magnitude greater than unreinforced collagen scaffolds. The compressive modulus was also at least one order of magnitude greater than comparable freeze-dried HA-collagen scaffolds and two orders of magnitude greater than absorbable collagen sponges used clinically. Moreover, scaffolds reinforced with up to 60 vol% HA exhibited fully recoverable elastic deformation upon loading to 50% compressive strain for at least 100,000 cycles. Thus, the scaffold mechanical properties were well-suited for surgical handling, fixation, and bearing osteogenic loads during bone regeneration. The scaffold architecture, permeability, and composition were shown to be conducive to the infiltration and differentiation of adipose-derive stromal cells in vitro. Acellular scaffolds were demonstrated to induce angiogenesis and osteogenesis after subcutaneous ectopic implantation by recruiting endogenous cell populations, suggesting that the scaffolds were osteoinductive.

Topology Optimization Using a Hybrid Cellular Automaton Method With Local Control Rules

The hybrid cellular automaton (HCA) algorithm is a methodology developed to simulate the process of structural adaptation in bones. This methodology incorporates a distributed control loop within a structure in which ideally localized sensor cells activate local processes of the formation and resorption of material. With a proper control strategy, this process drives the overall structure to an optimal configuration. The controllers developed in this investigation include two-position, proportional, integral and derivative strategies. The HCA algorithm combines elements of the cellular automaton (CA) paradigm with finite element analysis (FEA). This methodology has proved to be computationally efficient to solve topology optimization problems. The resulting optimal structures are free of numerical instabilities such as the checkerboarding effect. This investigation presents the main features of the HCA algorithm and the influence of different parameters applied during the iterative optimization process. DOI: 10.1115/1.2336251