The authors state that they have no conflicts of interest.
Mediolateral three-point bending of the rat midfemur was developed to enable the assessment of the mechanical competence of the elliptic bone cross-section in terms of its widest diameter, the apparent primary direction of bone adaptation to loading.
Introduction: Today, the most commonly used method to characterize the biomechanical properties of appendicular long bones is the three-point bending testing of the midfemur in the anteroposterior (AP) direction. However, as the diameter of the elliptic cross-section of femoral diaphysis is widest in the orthogonal mediolateral (ML) direction, the femoral diaphysis should also show the highest resistance to bending along this direction. The objective of this study was thus to introduce and validate a mechanical testing protocol for femoral midshaft along the ML direction.
Materials and Methods: To determine the repeatability of the novel testing protocol, 38 pairs of rat femora underwent a comprehensive structural analysis by pQCT followed by ML three-point bending. For comparison of the repeatability, corresponding tests were performed on the femoral neck. To validate the novel testing direction, the left hindlimb of 24 rats was neurectomized for 6 months, whereas the right limb served as an intact control. After excision, one half of these pairs of femora were randomly subjected to three-point bending test in the conventional AP direction and the remaining in the orthogonal ML direction.
Results: The precision (CVrms) of breaking load, stiffness, and energy absorption of the femoral midshaft in the ML direction was 3.8%, 6.6%, and 14.5%, respectively. The corresponding values for femoral neck compression test were 7.6%, 17.9%, and 18.7%, respectively. The loading-induced effect on the femoral midshaft (difference between the neurectomized [nonloaded] and contralateral intact [loaded] femur) was +2.2%, +1.9%, and +2.1% in the AP direction and −18.9%, −17.6%, and −20.3% in the ML direction (p < 0.01 for all comparisons), respectively.
Conclusions: Our results show that testing of rat femoral midshaft in the ML direction is a precise and biologically valid method to determine the structural strength of this widely used skeletal site in experimental bone research.
Through recent technological advances, the research methodology available for the evaluation and characterization of the skeleton has greatly improved. Rather than being able to only extract simple quantities of bones—such as mineral mass or density or outer dimensions—today we can even perform genome-wide scans in attempts to identify the genetic origin of bone fragility. However, this apparent development might have come with a cost, because there is evidence for a somewhat alarming methodological trend in skeletal research. Despite the fact that bones have primarily evolved to allow efficient locomotion of the body,(1–3) and accordingly, the bone structure and consequent structural rigidity and strength depicts the ultimate phenotype of the skeleton,(4,5) it seems that structural strength testing is currently considered primitive among skeletal researchers.(4)
According to our survey of the methodology used in recent bone research,(4) the most commonly used method for the characterization of long bone biomechanical properties of the appendicular skeleton is the three-point bending testing of the femoral midshaft. The arguments favoring the use of this test include the suitable size of the bone, good accessibility during dissection, well-documented and validated testing protocol, and extensive existing literature for comparative purposes. For obvious anatomical and practical reasons, the femur is usually placed onto the testing apparatus on its flat posterior surface and tested in the anteroposterior (AP) direction. However, in line with the established functional bone adaptation to loading, first described as the Wolff's law,(6) bones—as locomotive organs—adapt their structural rigidity and strength to incident loading through changes in the structural particulars (mineral mass, geometry, architecture, material properties). Along this principle (later simplified by D'arcy Thompson as “form follows function”(7)), one can assume that the mediolateral direction (ML), given the widest diameter of the elliptic cross-section at the rat midfemur, represents the apparent primary direction of skeletal adaptation to locomotive loading.(8) If true, the common AP testing direction of the rat femora can be argued not contextually optimal, but the testing should rather be carried out in the ML direction (Fig. 1); otherwise, there remains a risk that some essential information regarding the effects of any intervention, particularly that of altered mechanical loading, on the femur structure and mechanical competence might be missed.
Accordingly, the objectives of this study were (1) to develop a method for testing the biomechanical properties of rat femoral midshaft in the ML direction; (2) to determine the precision of the new testing method and to compare it to the precision of the mechanical testing of the femoral neck, the other commonly used biomechanical testing method for rat bones; and (3) to assess the biological validity of this approach by comparing the adaptive responses of the midfemur to altered loading in orthogonal AP and ML directions.
MATERIALS AND METHODS
Twenty male and 18 female rats of the Sprague-Dawley strain were used to provide a sample with sufficient biological variation for the repeatability study of the new method. The age of the rats ranged from 97 to 296 days and the body weight ranged from 240 to 580 g. The animals were housed in cages (16 × 27 × 42 cm), two animals per cage, at 20°C with a light cycle of 12 h. They were allowed to move freely and fed standard laboratory chow and water. The rats were killed, both femora were carefully excised at the hip and knee joints, and all surrounding skin, muscle, and other soft tissues were removed. The femora were wrapped in a saline-soaked gauze bandage to prevent dehydration and stored at −20°C in small, sealed freezer bags. This procedure has been shown not to affect the mechanical properties of bone.(9,10)
For the biological validation of the new testing protocol, we hypothesized that the ML direction, as showing the widest diameter of the elliptic cross-section of femoral diaphysis, represents the primary loading direction, and thus the effects of loading should be distinct in this direction rather than in the orthogonal AP direction. Accordingly, an additional 24 female rats were subjected to unilateral sciatic neurectomy at the age of 3 weeks as described previously.(11) In brief, under general anesthesia, the left sciatic nerve of each rat was exposed through a dorsolateral incision made on the hip and a 1.0-cm section of the nerve was excised. The right limb was left intact to serve as a normally loaded control. The animals were housed in cages (16 × 27 × 42 cm), two animals per cage, at 20°C with a light cycle of 12 h for 27 weeks. They were allowed to move freely and fed standard laboratory chow and water. The research protocol was reviewed and approved by the Ethics Committee for Animal Experiments of the University of Tampere. After the 27-week intervention, the rats were killed, and both femora were collected as described above. To show the effects of loading along the ML and AP axis, 12 randomly selected pairs of femora were subjected to three-point bending in the ML direction and the remaining 12 pairs in the conventional AP direction.
At the day of testing, the femora were slowly thawed to room temperature and kept wrapped in the saline-soaked gauzes except during measurements. Each bone and its contralateral pair underwent the analysis on the same day and the test order of bones was random. All bones were analyzed by the same operator.
The cross-sections of the femoral midshaft and neck were scanned with pQCT (Stratec XCT Research M, software version 5.40B; Stratec Medizintechnik, Pforzheim, Germany). For the analysis of the midshaft, the bones were inserted into a specially constructed plastic tube with the shaft in axial direction, and one cross-sectional slice from each bone was scanned at 50% of the length of the femur.(12) The voxel size was 0.070 × 0.070 × 0.5 mm3, and the scan speed was 3.0 mm/s. Total cross-sectional area (tCSA), cortical cross-sectional area (cCSA), cortical BMD (cBMD), and cross-sectional moment of inertia (CSMI) in the ML and AP directions were recorded as given by the pQCT software.
For the pQCT assessment of the femoral neck, the bones were inserted with the femoral neck in an axial direction into a specially constructed plastic tube.(13) The scan line was adjusted to the midneck using the scout view option of the pQCT software. The voxel size and scan speed were same as described above. Total cross-sectional area (tCSA), total BMC (tBMC), total BMD (tBMD), and cross-sectional moment of inertia (CSMI) in the superoinferior (SI) and AP directions were recorded.
Immediately after the pQCT measurements, the midshafts of the femora (the femora of the nonoperated rats and 12 pairs of femora of the neurectomized rats) were subjected to ML three-point bending using a Lloyd material testing machine (LR5K; J. J. Lloyd Instruments, Southampton, UK). The femora were placed on their lateral surface on the lower supports (stainless steel plates with rounded edges of 4.0 mm diameter) of the bending apparatus. For each bone, these supports were placed individually so the one was under the trochanter major and the other under the distal femur (Fig. 2A). To prevent the otherwise unavoidable twisting of the bone to the AP position during loading, the intercondylar fossa of each femur was gently pressed between the blades of blunt pliers tightly attached to the bending apparatus (Fig. 2A). Before the actual testing, a small stabilizing preload (10N) was applied on the medial surface of the femur at a rate of 0.1 mm/s using a steel cross-bar fixture (a plate with rounded edges of 10 mm diameter), the plate being oriented perpendicularly to the long axis of the bone and at the midpoint between the lower supports. The bending load was applied at a rate of 1.0 mm/s until failure of the specimen. The breaking load, stiffness, and energy absorption of the femoral midshaft were determined from the load-deformation curve (Fig. 3).
After the ML three-point bending of the femoral shaft, the femoral neck compression test was carried out according to the protocol described in detail previously.(14,15) Briefly, the proximal half of each femur was mounted in a specially constructed fixation device.(16) The specimen was placed under the material testing machine, and a vertical load was applied to the top of the femoral head using a brass cross-bar until failure of the femoral neck. The preloading and actual loading were carried out as described above. The breaking load, stiffness, and energy absorption of the femoral neck were determined from the load-deformation curve (Fig. 3).
The other 12 pairs of femora of the neurectomized rats were tested in the AP direction according to the protocol described in detail previously.(14) Briefly, for the three-point bending, the femora were placed on their posterior surface on the lower supports of the bending apparatus. For each bone, these supports were placed individually (first just distal to the trochanter minor and the other just proximal to the condyles of the femur). After the adjustment of the supports, a bending load using brass cross-bar was applied to the femoral midshaft perpendicularly to the long axis of the bone until the failure of the specimen. The preloading, actual loading, and analysis of the load-deformation curve were carried out as described above.
The repeatability of the biomechanical testing of the rat femora was determined by comparing the data from the right and left femora of the nonoperated rats. This approach makes an inherent assumption that the right-to-left biomechanical properties and geometry of femora are equal, which may not always be entirely accurate.(17,18) However, it can be anticipated that, under normal circumstances, there is no systematic difference between the structural and mechanical characteristics of the right and left femora, and the present approach is well grounded. To verify this, for all pQCT and mechanical testing variables, the 95% limits of agreement (i.e., average right-to-left difference ± twice the SD of these side-to-side differences [SDmeas]) were determined according to Bland and Altman.(19) If the zero difference resides clearly within the 95% limits of agreement, it is very unlikely that there would be any true side-to-side difference between the femora. In addition to the above described absolute measure of repeatability, two proportionate measures of precision, the average root mean square CV (CVrms)(20) and the reliability coefficient (R = 100[1 − SDmeas2/SDtotal2] in percentage), were determined. The advantage of the reliability coefficient over the commonly used CVrms is that the R value takes the total observed variance into account and it can be interpreted as an error-free proportion of the intersubject variability (i.e., biological variance [SDbiol]) observed in a given population.
The effect of the direction of biomechanical testing was analyzed using two-way factorial ANOVA with testing direction (AP versus ML) and unilateral neurectomy (loaded versus nonloaded) as the fixed factors.
In the ML three-point bending, one bone rotated to the AP position before the actual failure and was, therefore, excluded from the analysis. Accordingly, 37 of 38 pairs of femora (97%) underwent a successful testing and were available for data analysis. The failure mechanism of the bones was very consistent, the failure taking place exactly at the midshaft with the fracture line being perpendicular to the long axis of the bone. For comparison, the femoral neck compression testing was successful in 34 of 38 pairs (89%).
Judged from the 95% limits of agreement data, there was no indication for a systematic side-to-side difference between right and left femur (Table 1). CVrms in the biomechanical measurements ranged from 3.8% (breaking load of the ML three-point bending) to 18.7% (energy absorption of the femoral neck compression; Table 1). When the intersubject variation was taken into account, the poorer repeatability of the femoral neck compression became even more pronounced (e.g., R values of 86% and 47% in the measurement of breaking load in the three-point bending and neck compression tests, respectively). Accordingly, the ML three-point bending of the femoral shaft was more repeatable of these two biomechanical testing protocols. Regarding the precision of different biomechanical variables, the determination of stiffness and energy absorption showed clearly poorer repeatability than the breaking load, particularly in the femoral neck compression test (Table 1), for which the individual determinations of stiffness and energy absorption appeared to be of no informative value (R < 0).
Table Table 1.. Descriptive Data and Precision of the Tomographic and Biomechanical Measurements of the Nonoperated Rat Femora
Regarding the biological validation of the new procedure, the loading-induced increase in bone CSMI and structural strength was solely seen in the ML plane (p < 0.01 for the interaction in all parameters; Tables 2 and 3), whereas there was no difference between the neurectomized and contralateral intact femur in the AP direction. This distinction provides quite a persuasive proof of the appropriateness of the novel testing direction.
Table Table 2.. Descriptive Data of the Neurectomy Study
Table Table 3.. Effect of Neurectomy on the Mechanical Competence and Geometrical Indices of Femoral Midshafts Tested in Mediolateral (ML) and Anteroposterior (AP) Directions
According to the primary locomotive function of the skeleton, mechanical competence of the bones represents the ultimate measure of bone phenotype.(4) The structural rigidity of the skeleton is principally maintained by a mechanosensory feedback system that senses the loading-induced deformations within the bones and copes with the locomotive challenges through modifications in bone size and shape (i.e., through geometric, structural, and architectural adaptation).(21) New bone is laid on regions that are subject to loading that exceeds clearly the customary loading range, whereas bone is removed from regions that experience reduced loading well below the customary loading range.(6) Considering the elliptic cross-sections of most long bone diaphyses, it was hypothesized that the widest diameter of the midshaft (and accordingly, the direction of most resistance to bending loading) represents the apparent primary adaptive direction to locomotive loading. In this paper, this hypothesis was corroborated by first introducing a repeatable protocol for testing the rat femoral midshaft in the ML direction and validating this approach by showing that the adaptive changes (increases in the CSMI and structural strength) in the femoral midshaft caused by altered loading environment were observed almost exclusively in the ML than in the AP direction (Tables 2 and 3).
We, among others, have previously assessed the mechanical competence of rat femoral midshaft using the conventional three-point bending in the AP direction.(14,15,22) Although biomechanical testing of bones, similarly to any other in vitro measurement, obviously represents an oversimplification of the complexity of the actual in vivo situation, the intention is to test the skeletal structure of interest as closely as possible in terms of predominant loading environment. Considering that our necrectomy-induced changes in the AP bending were quite similar to those reported previously caused by absence of loading(22–29) (the three-point bending testing of the femoral midshaft was carried out in AP direction in all of these studies), whereas the corresponding effects of neurectomy were predominant in the ML direction (Table 3), it is possible that the effects of mechanical loading and unloading on bones have been somewhat underestimated in the existing literature. Thus, the results of our present unilateral neurectomy experiment quite convincingly show that the ML three-point bending of the rat femoral diaphysis is biologically reasonable and valid approach and should thus be preferred over the conventional AP bending, at least when assessing loading-induced changes or when loading is somehow present in the intervention. In this context, it is acknowledged that the present conclusions may not be applicable for treatments involving systemic effects, such as pharmacological or nutritional treatments. Also, even within the realm of mechanical loading studies, there is no absolute guarantee that all cases will display similar, direction-specific results as observed in this study.
In addition to the mere loading direction, the execution of biomechanical testing (and any scientific experiment, for that matter) necessitates the recognition of some basic methodological issues. The fundamental principles regarding the practical execution of biomechanical testing have been extensively reviewed by Turner and Burr.(30) In addition, the repeatability of the any used measurement is crucial, as according to basic principles of statistics, a poor repeatability entails excess variability in the data and thus directly pertains to the validity of the data obtained. Therefore, the second goal of this study was to compare the repeatability of the novel testing protocol to that of the femoral neck compression test, another commonly used test in experimental osteoporosis research. The CVrms values we obtained for the mechanical testing in the ML direction and the femoral neck compression are fully comparable to those reported previously for the AP bending of the femoral midshaft (3.3–5.8%(14,31)), the bending of the tibial midshaft (5.1%(32)), the femoral neck compression test (8.2–14.7%(14,32)), and the femoral neck in fall-simulation (10.1%(33)).
The concept of repeatability or precision and the approach of providing a single value to characterize method variance (e.g., CV) is not as straightforward as one would assume. Even if the CVrms of a method would be seemingly good (e.g., 1%), the measurement can be considered to have poor repeatability if the biological variance in the given variable is very small—say only a couple percent. However, a measurement with the same CV value has an excellent precision if the intersubject variance is 10% or more. This is why it is impossible to give even a trend-setting single precision value for a “good result,” and accordingly, we provided another index of repeatability, the R value (Table 1). The advantage of the R value over conventional CV is that it also takes the biological variance into account and can thus be interpreted as an error-free proportion of the intersubject variability observed in a given population. An R value of 90% (e.g., the precision error of the method is 3% and the total variance in the measured variable is ∼10%) may be considered good in biological sciences. However, considering the complex nature of biomechanics, one could argue that an R value of 75% (i.e., the variance caused by method is 50% of the total variance in the given variable) is acceptable. If the variance caused by measurement equals the total variance, the R value becomes zero (R = 0). If the R value is close to 0% or lower, obviously a single measurement has little informative value, if any, in the biological sense, but it is reminded that with larger sample sizes, systematic differences or treatment effects may be exposed even with a method with negligible R value.
There are some issues and concerns pertinent to the new ML testing method per se that require further consideration. First, as researchers are continually creating new knockout or transgenic mouse models to explore the genetic basis of various skeletal traits,(34) the applicability of the present method to mouse bones is naturally of considerable interest. Although our data do not provide a direct answer, we do not see any practical reason as to why ML testing of the femora could not also be applied to the clearly smaller bones of mice, particularly as the three-point bending of the mouse femoral midshaft in the orthogonal (AP) direction is shown to be feasible with acceptable precision (CVrms 10.1% for breaking load).(33) Second, regarding the practical execution of the ML three-point bending of the femoral midshaft, one may wonder whether the bony ridge inferolateral to the trochanter major (“linea aspera” or the gluteal insertion site of the femur; Fig. 2A) could affect the mechanical behavior of the femoral midshaft in the ML direction. However, considering that the results of the ML testing are in perfect agreement with the pQCT data (CSMI values) obtained from the midshaft, it is likely that no such confounding effects exist to considerable extent (Table 3). Third, further regarding the execution of the ML testing one can argue that the gripping of the distal end of the femur by the pliers to prevent the undesired twisting of the bone during testing could alter the loading environment, resulting thus in the loss of the “physiologic loading” of the femur. It is possible that fixing the femur from one end is not optimal and this procedure might change the loading environment to some extent, but on the other hand, it should be noted that without gripping, the inevitable twisting of the bones would severely compromise the consistency of data. It should also be recalled that the natural loading on the femur is primarily axial rather than a load subjected perpendicularly on its medial surface. Accordingly, the novel method introduced in this study only more appropriately takes the natural loading direction into account, but certainly does not provide a perfect equivalent to in vivo loading situation.
In conclusion, we have introduced and validated a new testing method for assessing the structural rigidity of the rat femur in the ML direction, the apparent principal adaptive direction to locomotive loading. Our results not only show that the method is biologically valid and sufficiently precise but also that, in the structural testing of rat bones, the determination of bone breaking load displays clearly superior repeatability to that of bone stiffness and energy absorption.
This study was supported by grants from the Competitive research funding of the Pirkanmaa Hospital District, the Research Council for Physical Education and Sports, Ministry of Education, and the AO Research Fund, Switzerland.