Cross-sectional geometry of the human femur in the mid-third region

Influence of interstitial fluid pressure, porosity, loading magnitude, and anisotropy in cortical bone adaptation

Adaptive elasticity in cortical bone has traditionally been modeled using Strain Energy Density (SED). Recent studies have highlighted the importance of interstitial fluid in bone adaptation, yet no research has quantified the role of interstitial fluid pressure and its effects, specifically incorporating both SED and interstitial fluid pressure in the adaptation process. This study introduces a novel formulation combining theory of porous media and theory of adaptive elasticity that considers both SED and interstitial fluid's pressure in cortical bone adaptation. The formulation is solved using ANSYS Fluent and a MATLAB script, and sensitivity analyses were conducted, analyzing various porosities, loading magnitudes, anisotropic properties of cortical bone, and involvement coefficients of interstitial fluid's pressure. This study reveals that bones with different vascular porosities (PV) tend to achieve similar density distributions under uniform loading over time. This highlights the significant role of interstitial fluid pressure in accelerating the convergence to optimal bone properties, especially in specimens with larger PV porosities. The findings emphasize the importance of fluid pressure in bone remodeling, aligning with previous studies. Furthermore, this study demonstrates that considering transversely isotropic material properties can significantly alter the remodeling configuration compared to isotropic material properties. This highlights the importance of accurately representing the anisotropic nature of cortical bone in models to better predict its adaptive responses. However, aspects such as fluid density variations and bone geometry changes remain unexplored, suggesting directions for future research. Overall, this research enhances the understanding of cortical bone adaptation and its mechanical interactions.

Pelvic Construct Prediction of Trabecular and Cortical Bone Structural Architecture

The pelvic construct is an important part of the body as it facilitates the transfer of upper body weight to the lower limbs and protects a number of organs and vessels in the lower abdomen. In addition, the importance of the pelvis is highlighted by the high mortality rates associated with pelvic trauma. This study presents a mesoscale structural model of the pelvic construct and the joints and ligaments associated with it. Shell elements were used to model cortical bone, while truss elements were used to model trabecular bone and the ligaments and joints. The finite element (FE) model was subjected to an iterative optimization process based on a strain-driven bone adaptation algorithm. The bone model was adapted to a number of common daily living activities (walking, stair ascent, stair descent, sit-to-stand, and stand-to-sit) by applying onto it joint and muscle loads derived using a musculoskeletal modeling framework. The cortical thickness distribution and the trabecular architecture of the adapted model were compared qualitatively with computed tomography (CT) scans and models developed in previous studies, showing good agreement. The sensitivity of the model to changes in material properties of the ligaments and joint cartilage and changes in parameters related to the adaptation algorithm was assessed. Changes to the target strain had the largest effect on predicted total bone volumes. The model showed low sensitivity to changes in all other parameters. The minimum and maximum principal strains predicted by the structural model compared to a continuum CT-derived model in response to a common test loading scenario showed good agreement with correlation coefficients of 0.813 and 0.809, respectively. The developed structural model enables a number of applications such as fracture modeling, design, and additive manufacturing of frangible surrogates.

Pre-planning of intramedullary nailing procedures: A methodology for predicting the position of the distal hole

Inserting the distal locking screws is a challenging step of the intramedullary nailing procedures due to the nail deformation that makes the proximally mounted targeting systems ineffective. A pre-planning methodology is proposed, based on an analytical model of the nail-bone construct, to predict the nail deformation during surgery using orthogonal preoperative radiographs. Each of the femoral shaft and the nail was modeled as a curved tubular Euler-Bernoulli beam. The unknown positions and forces of the nail-bone interaction were found using a systematic trial and error approach, which minimized the total strain energy of the system while satisfying the force and geometrical constraints. The predictions of the model for the nail deformation were compared with the experimental results of five cadaver specimens in 15 test conditions. Relatively large displacements (up to 13 mm) were found for the distal hole in sagittal plane only. The model predictions were in close agreement with the experimental results, with a root mean square error of 1.2 mm. It was concluded that the proposed pre-planning methodology is promising for practical clinical use in intramedullary nailing operations, in order to provide the compensatory information that is required for tuning of proximally mounted targeting systems.

Morphological Measurement of Supracondylar Femur Based on Digital Technology in Chinese Han Population

OBJECTIVE

Relatively few studies have reported on the morphology of the supracondylar femur, which is a fundamental factor affecting prosthetic reconstruction. The objectives of the present study were to measure the morphological parameters of the supracondylar femur, to classify the supracondylar femur, and to provide theoretical guidance for the development of distal femoral prostheses.

METHODS

The study consisted of 82 patients of Han Chinese nationality in North China. There were 57 men and 25 women included in the study, with an average age of 50.9 years (range, 18-87 years). Effective CT data should include a range of more than 10 cm for the distal femur. CT data for the right distal supracondylar femurs was obtained from DICOM files. Results for the cancellous bone and marrow cavity were retained, and information for the cortical bone was erased to obtain information of the lumen. Measurements of the intracortical cavity have not been reported previously. Lumen models were reconstructed with Mimics 17.0 software. The surfaces of the lumen models were smoothed with Geomagic studio 12.0 software. Using the Solidworks 2014 software, we established a 3-D coordinate system, where variables of the lumen were examined. Correlations between the various measurements were calculated.

RESULTS

The supracondylar region of the femur was divided into five levels, and the length, breadth, height, and angle values were measured at each level. There were strong correlations between the length indexes (transverse diameter [EF], medial anteroposterior diameter [AC], middle anteroposterior diameter [GH], and lateral anteroposterior diameter [BD]) and the volume index (V). There were also strong correlations among the length indicators (EF, AC, GH, and BD) in each layer. Angle γ was correlated with the lateral anteroposterior diameter (BD) at L2-L6 layers (r = -0.383, -0.385, -0.296, -0.258, -0.24; all P < 0.05) and with the height index (h) at L4-L6 layers (r = -0.244, -0.385, -0.506; all P < 0.05). The most representative parameters were the medial anteroposterior diameter (AC2 R2 = 0.865; AC6 R2 = 0.932), the coronal width ratio, and the sagittal width ratio with volume. The analysis found that the lumen shape of flower-top hat accounted for 81% at most.

CONCLUSIONS

The supracondylar femur has an asymmetrical structural area. The coronal plane is dominated by a flowerpot-like morphology, and the sagittal plane is narrowest in the lateral 1/3 and resembles a top-hat-like morphology. Our results provide theoretical guidance for developing distal femoral prostheses and for their clinical application.

MUSCLE FORCE MAGNITUDES IN THE HUMAN LEG FOR ISOMETRIC EXERCISES WITH VARIOUS RESULTANT FORCE DIRECTIONS AND JOINT ANGLES

Using a gradient-based numerical optimization routine, the force magnitudes required of 10 major sagittal plane leg muscles to create a constant magnitude isometric resultant force against a fixed surface at the toe directed anteriorly, posteriorly, superiorly, and inferiorly were quantitatively predicted for three sets of joint angles: a straight leg configuration, with the knee flexed, and with both the hip and knee flexed. Comparisons over the conditions studied for each individual system muscle found that the maximum variation occurred in knee and hip extensor forces (up to two orders of magnitude). Comparisons within the set of active muscles for each studied condition identified dominant muscles and muscle functions. All anteriorly-directed and posteriorly-directed resultants required a small number of muscles with common functions (mainly knee or hip extensors) and large force magnitudes (O(1000[Formula: see text]N)). In contrast, a large number of muscles, with wide-ranging synergistic and antagonistic functions, acting across multiple joints with relatively small magnitudes (O(100[Formula: see text]N)) were needed to create the superiorly-directed resultant with flexed hip and knee. With good correlation to experimentally measured trends in the interrelationships between leg joint angles and isometric forces, the systematic muscle force prediction and analysis presented in this work can be used to guide the design of targeted muscle strengthening exercises and study of muscle-specific injury.

Full circle: 3D femoral mapping demonstrates age-related changes that influence femoral implant positioning

The geometry of the femur is important in the final position of an intramedullary implant; we hypothesised that the femoral geometry changes with age and this may predispose the elderly to anterior mal-positioning of these implants. We used CT DICOM data of 919 intact left femora and specialist software that allowed us to defined landmarks for measurement reference - such as the linea aspera - on a template bone that could be mapped automatically to the entire database. We found that older (>80 years) cortical bone is up to 1.5 mm thinner anteriorly and 2 mm thinner posteriorly than younger (<40 years) bone but the rate of change of posterior to anterior cortex thickness is greater in the older bone. We also found the isthmus in the elderly to be more distal and less substantial than in the younger bone. This study has demonstrated femoral geometry changes with age that may explain our perception that the elderly are at increased risk for anterior mal-positioning of intramedullary implants.

Three-Dimensional Analysis of the Curvature of the Femoral Canal in 426 Chinese Femurs

PURPOSE

The human femur has long been considered to have an anatomical anterior curvature in the sagittal plane. We established a new method to evaluate the femoral curvature in three-dimensional (3D) space and reveal its influencing factors in Chinese population.

METHODS

3D models of 426 femurs and the medullary canal were constructed using Mimics software. We standardized the positions of all femurs using 3ds Max software. After measuring the anatomical parameters, including the radius of femoral curvature (RFC) and banking angle, of the femurs using the established femur-specific coordinate system, we analyzed and determined the relationships between the anatomical parameters of the femur and the general characteristics of the population.

RESULTS

Pearson's correlation analyses showed that there were positive correlations between the RFC and height (r = 0.339, p < 0.001) and the femoral length and RFC (r = 0.369, p < 0.001) and a negative correlation between the femoral length and banking angle (r = -0.223, p < 0.001). Stepwise linear regression analyses showed that the most relevant factors for the RFC and banking angle were the femoral length and gender, respectively.

CONCLUSIONS

This study concluded that the banking angle of the femur was significantly larger in female than in male.

Development and implementation of a coupled computational muscle force optimization bone shape adaptation modeling method

Improved methods to analyze and compare the muscle-based influences that drive bone strength adaptation can aid in the understanding of the wide array of experimental observations about the effectiveness of various mechanical countermeasures to losses in bone strength that result from age, disuse, and reduced gravity environments. The coupling of gradient-based and gradientless numerical optimization routines with finite element methods in this work results in a modeling technique that determines the individual magnitudes of the muscle forces acting in a multisegment musculoskeletal system and predicts the improvement in the stress state uniformity and, therefore, strength, of a targeted bone through simulated local cortical material accretion and resorption. With a performance-based stopping criteria, no experimentally based or system-based parameters, and designed to include the direct and indirect effects of muscles attached to the targeted bone as well as to its neighbors, shape and strength alterations resulting from a wide range of boundary conditions can be consistently quantified. As demonstrated in a representative parametric study, the developed technique effectively provides a clearer foundation for the study of the relationships between muscle forces and the induced changes in bone strength. Its use can lead to the better control of such adaptive phenomena.

Three-dimensional computed tomography-based modeling of sagittal cadaveric femoral bowing and implications for intramedullary nailing

OBJECTIVES

To establish the nature and extent of femur sagittal bowing by determining outer and inner anterior cortex geometries and sizes using analytical 3-dimensional computed tomography modeling and relate the resultant femoral curvature with the curvatures of available intramedullary nails.

METHODS

Computed tomography scans were rendered in 3D using modeling software to reconstruct 2 geometries: (1) outer cortex and (2) medullary canal. Femoral bow in the sagittal plane and the anterior cortical thickness were measured. Three curvature points were selected on both the geometries. Exterior anterior cortex radius of curvature (AROC) and medullary canal radius of curvature (MROC) were compared within and between each femur pair.

RESULTS

Three groups of femurs exhibiting significantly different geometry patterns emerged: (1) AROC significantly greater than MROC, (2) AROC equivalent to MROC, and (3) AROC significantly smaller than MROC. Anterior cortical thickness ranged from 2.2 to 7.0 mm was significantly different for males versus females, and it varied inversely with age.

CONCLUSIONS

The study confirms that the radius of curvature of most intramedullary nails exceeds the sagittal radius of curvature of most adult femurs (both AROC and MROC). An intramedullary nail selected based on the anterior curvature would impinge on the anterior cortices at the proximal and distal anterior aspects of the femur in specimens with AROC > MROC. Conversely, in specimens with AROC < MROC, an intramedullary nail selected based on the anterior curvature would impinge on the proximal and distal posterior cortices. That cortical thickness varied significantly in accordance with gender and age is also relevant to surgical planning. MROC, in addition to the AROC alone, should be one of several design parameters used to match specific intramedullary nail design to an individual patient.

Effect of amputation level on the stress transferred to the femur by an artificial limb directly attached to the bone

Attachment of an artificial limb directly to the skeleton has a number of potential benefits and the technique has been implemented for several amputation sites. In this paper the transfer of stress from an external, transfemoral prosthesis to the femur during normal walking activity is investigated. The stress distribution in the femur and at the implant-bone interface is calculated using finite element analysis for the 3D geometry and inhomogeneous, anisotropic material properties obtained from a CT scan of a healthy femur. Attachment of the prosthetic leg at three different levels of amputation is considered. Stress concentrations are found at the distal end of the bone and adjacent to the implant tip and stress shielding is observed adjacent to the implant. It is found that the stress distribution in the femur distal to the epiphysis, where the femur geometry is close to cylindrical, can be predicted from a cylindrical finite element model, using the correct choice of bone diameter as measured from a radiograph. Proximal to the lesser trochanter the stress decreases as the femur geometry diverges significantly from a cylinder. The stress concentration at the distal, resected end of the bone is removed when a collared implant is employed. These findings form the basis for appropriate settings of an external fail-safe device to protect the bone from excessive stress in the event of an undue load.

The cortical step sign as a tool for assessing and correcting rotational deformity in femoral shaft fractures

OBJECTIVES

Rotational malalignment during femoral nailing is common. The difference in cortical width of the proximal and distal fracture fragments, the cortical step sign, is a commonly used yet poorly studied method of evaluating rotational alignment. This study aims to critically analyze the cortical step sign in cadaveric specimens using radiographic and direct measurements.

METHODS

One-centimeter segments from 20 cadaveric femora were harvested from the proximal, middle, and distal diaphyses. The medial and lateral cortical widths were measured in neutral and at 10 degrees , 20 degrees , and 30 degrees of internal rotation and external rotation directly from the gross specimens and indirectly using radiographs and cross-sectional imaging.

RESULTS

Anatomic, radiographic, and cross-sectional imaging measurements all demonstrated that cortical width changes with femoral rotation. Rotation (both internal rotation and external rotation) of the proximal and middle segments led to a decrease in medial cortical width and lateral cortical width in 70% to 100% of samples (up to 2.2 mm, or 20% of cortical width) indicating that the cortices are thickest directly medially and laterally in neutral rotation. In the distal femur, however, internal rotation and external rotation led to an increase in medial cortical width and lateral cortical width in 80% to 95% of cases (up to 1.75 mm), except in the case of the medial cortical width in internal rotation, which decreased in 80% of the specimens (up to 1.3 mm).

CONCLUSIONS

The cortical step sign, or incongruity of cortical widths on either side of a femur fracture, is indicative of rotational malreduction. Whether such malreduction is the result of internal rotation or external rotation, however, cannot be easily determined from this radiographic sign.

Vibration exercise for treatment of osteoporosis: a theoretical model

Orthopaedic rehabilitation of osteoporosis by muscle vibration exercise is investigated theoretically using Wolff's theory of strain-induced bone 'remodelling'. The remodelling equation for finite amplitude vibration to be transmitted to the bone via muscle corresponds to a slowly time-varying non-linear dynamic system. This slowly time-varying system is governed by a Riccatti equation with rapidly varying coefficients that oscillate with the frequency of the applied vibration. An averaging technique is used to determine the effective force transmitted to the bone. This force is expressed in terms of the stiffness and damping parameters of the connected muscle. The analytical result predicts that, in order to obtain bone reinforcement, the frequency and amplitude of vibration should not exceed specified levels. Furthermore, low-frequency vibration does not stimulate the bone sufficiently to cause significant remodelling. The theoretical model herein confirms the clinical recommendations regarding vibration exercise and its effects on rehabilitation. In a numerical example, the model predicts that a femur with reduced bone mass as a result of bed rest will be healed completely by vibration consisting of an acceleration of 2g applied at a frequency of 30 Hz over a period of 250 days.

Penetration of the distal femoral anterior cortex during intramedullary nailing for subtrochanteric fractures: a report of three cases

Three cases of anterior distal femoral cortex penetration during intramedullary nailing for subtrochanteric fractures are documented. Case 1 involved a Zimmer (Warsaw, IN) M/DN antegrade femoral nail, case 2 a Howmedica (Allendale, NJ) long-stem Gamma nail, and case 3 a Synthes (Paoli, PA) titanium femoral nail with spiral blade locking. The anterior Zimmer nail penetration resulted in a displaced supracondylar fracture, which subsequently required revision. The Gamma nail as well as the Synthes nail were left impaled through the distal femoral cortex, and the subtrochanteric fractures went on to union. The anteroposterior radius of curvature for the Zimmer, the long Gamma, and the Synthes nail are 257 cm, 300 cm, and 150 cm, respectively. It has been estimated that the radius of curvature of the femoral diaphyseal canal is 114 to 120 cm. It appears that the difference in femoral anteroposterior bow between the bone and the implant is a contributing factor to distal femoral anterior cortex penetration in intramedullary nailing of subtrochanteric fractures.

Investigating the form-function interface in African apes: Relationships between principal moments of area and positional behaviors in femoral and humeral diaphyses

Investigations of cross-sectional geometry in nonhuman primate limb bones typically attribute shape ratios to qualitative behavioral characterizations, e.g., leaper, slow climber, brachiator, or terrestrial vs. arboreal quadruped. Quantitative positional behavioral data, however, have yet to be used in a rigorous evaluation of such shape-behavior connections. African apes represent an ideal population for such an investigation because their relatedness minimizes phylogenetic inertia, they exhibit diverse behavioral repertoires, and their locomotor behaviors are known from multiple studies. Cross-sectional data from femoral and humeral diaphyses were collected for 222 wild-shot specimens, encompassing Pan paniscus and all commonly recognized African ape subspecies. Digital representations of diaphyseal cross sections were acquired via computed tomography at three locations per diaphysis. Locomotor behaviors were pooled broadly into arboreal and terrestrial categories, then partitioned into quadrupedal walking, quadrumanous climbing, scrambling, and suspensory categories. Sex-specific taxonomic differences in ratios of principal moments of area (PMA) were statistically significant more often in the femoral diaphysis than the humeral diaphysis. While it appears difficult to relate a measure of shape (e.g., PMA ratio) to individual locomotor modes, general locomotor differences (e.g., percentage arboreal vs. terrestrial locomotion) are discerned more easily. As percentage of arboreal locomotion for a group increases, average cross sections appear more circular. Associations between PMA ratio and specific locomotor behaviors are less straightforward. Individual behaviors that integrate eccentric limb positions (e.g., arboreal scrambling) may not engender more circular cross sections than behaviors that incorporate repetitive sagittal movements (e.g., quadrupedal walking) in a straightforward manner.

Acoustical characterization of bone using a cylindrical model and time of flight method: edge reconstruction and ultrasound velocity determination in cortical bone and in medullar marrow

Our objective is to evaluate the external and internal dimensions of bone diaphysis and the speed of sound in cortical bone and in medullar marrow. The diaphysis is modelled by a cylindrical hollow tube. The theory of rays is used and an approximation allows us to break free from the data gained by ultrasonic field amplitude. Then, acoustical and dimensional parameters are only related to the time of flight of reflected and transmitted acoustic echoes in the tube. From the arrival time of particular echoes, the inverse problem resolution then allows us to experimentally determine the sought parameters. This method is validated in vitro on a bovine femur and gives satisfactory results.

Modelling femoral curvature in the sagittal plane: a cadaveric study

This study examined the possibility of representing the mid third of the human femur with two straight sections. This portion of the femur visually has a distinct curvature, which can potentially present problems when considering implant stem designs to be introduced in this region. Sixteen femora were sectioned at 10 mm intervals along the femoral shaft in the mid third region (35-65 per cent of femoral length). Photographic records were obtained of each section against a consistent axis system to which all coordinates were referenced. The position of the centre of the medullary canal cross-sectional area along the femur, in relation to fixed orthogonal planes, has been analysed; the outer anterior cortex was also modelled. The results showed that the medullary centre of area plots and the anterior cortex coordinates are suitably modelled as two straight lines. For each bone it was possible to define the intersection point between the two straight sections (point of angulation), and the subtended angle between these sections (angle of incidence). The average point of angulation for the medullary plots occurred at 57 per cent along the femur, while the mean angle of incidence was 6.5 degrees. The anterior surface had an average point of angulation at 58 per cent along the femur with the mean angle of incidence being 22.2 degrees. The centre-line of the medulla was also found to be almost parallel to the outer anterior surface for sections distal to the point of angulation. It is proposed therefore, that this difference in angulation is the result of medullary expansion/cortical thinning towards the proximal extremity of the femur, causing the straight-line model of the medulla to angulate less than the outer anterior cortex.

HIDE: a new hybrid environment for the design of custom-made hip prosthesis

This technical note describes a new software environment (HIPCOM design environment, HIDE) for the design of custom-made total hip replacements. These devices are frequently designed using general-purpose mechanical computer-aided design (CAD) programs using a set of bone contours extracted from the computer tomography (CT) images as anatomical reference. On the contrary, the HIDE system was developed to let the operator directly design the stem shape onto the CT images in a single-step operation. The operator can directly import CT data in DICOM format or use special functions to reconvert to a digital stack, the CT images printed on a radiological film. Once the stack of CT images is loaded, the operator can design the implant shape by imposing control sections directly on the CT images. The interpolation of these control sections produces the basic 3D shape of the custom-made stem. The shape is then exported to the CAD-computer-aided manufacturing (CAM) program to refine the design and to generate the part program to manufacture the implant with a CNC tooling machine. Using HIDE, the duration of design steps it affected was reduced by more than 50% with respect to the standard method in use at the manufacturer site. HIDE also improved the accuracy and the repeatability of the whole procedure. The learning curve became flat after only ten cases. These good results were achieved because of the integration of the vectorial description of the prosthetic component with the raster description of the CT data that allowed the designer to use all details available in the CT images.