Journal of Biomechanics 47 (2014) 3580–3583
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Journal of Biomechanics journal homepage: www.elsevier.com/locate/jbiomech www.JBiomech.com
Short communication
Accuracy and reproducibility of bending stiffness measurements by mechanical response tissue analysis in artificial human ulnas Patricia A. Arnold, Emily R. Ellerbrock, Lyn Bowman, Anne B. Loucks n Department of Biological Sciences, Ohio University, Athens, OH 45701, USA
art ic l e i nf o
a b s t r a c t
Article history: Accepted 3 September 2014
Osteoporosis is characterized by reduced bone strength, but no FDA-approved medical device measures bone strength. Bone strength is strongly associated with bone stiffness, but no FDA-approved medical device measures bone stiffness either. Mechanical Response Tissue Analysis (MRTA) is a non-significant risk, non-invasive, radiation-free, vibration analysis technique for making immediate, direct functional measurements of the bending stiffness of long bones in humans in vivo. MRTA has been used for research purposes for more than 20 years, but little has been published about its accuracy. To begin to investigate its accuracy, we compared MRTA measurements of bending stiffness in 39 artificial human ulna bones to measurements made by Quasistatic Mechanical Testing (QMT). In the process, we also quantified the reproducibility (i.e., precision and repeatability) of both methods. MRTA precision (1.071.0%) and repeatability (3.1 73.1%) were not as high as those of QMT (0.27 0.2% and 1.3þ1.7%, respectively; both po 10 4). The relationship between MRTA and QMT measurements of ulna bending stiffness was indistinguishable from the identity line (p¼0.44) and paired measurements by the two methods agreed within a 95% confidence interval of 7 5%. If such accuracy can be achieved on real human ulnas in situ, and if the ulna is representative of the appendicular skeleton, MRTA may prove clinically useful. & 2014 Elsevier Ltd. All rights reserved.
Keywords: Mechanical response tissue analysis Quasistatic mechanical testing Bending stiffness Composite ulna
1. Introduction Osteoporosis is a skeletal disorder characterized by reduced bone strength and increased risk of fracture (National Institutes of Health, 2001), but no FDA-approved device measures bone strength. Consequently, osteoporosis is diagnosed by measuring bone mineral density (BMD) (Schousboe et al., 2013), even though BMD does not predict fractures well: among 200,000 postmenopausal women, 96% of those diagnosed with osteoporosis did not fracture, while 81% of fractures occurred in women who did not have osteoporosis (Siris et al., 2001). Bone strength is strongly associated (r40.95) with bone stiffness (Borders et al., 1977; Fyhrie and Vashishth, 2000; Jurist and Foltz, 1977; Roberts et al., 1996), but no FDA-approved device measures bone stiffness either. The reference method for measuring bone stiffness and strength, Quasistatic Mechanical Testing (QMT), can only be employed in vitro. Mechanical Response Tissue Analysis (MRTA) is a non-significant risk, noninvasive, radiation-free, vibration analysis technique for making direct functional measurements of the bending stiffness of long bones in humans in vivo (Steele et al., 1988). Because bending tests are especially sensitive to mid-span mechanical properties, MRTA
n
Corresponding author. Tel.: þ 1 740 593 2286; fax: þ 1 740 593 0300. E-mail address: [email protected] (A.B. Loucks).
http://dx.doi.org/10.1016/j.jbiomech.2014.09.005 0021-9290/& 2014 Elsevier Ltd. All rights reserved.
may be useful for measuring the bending stiffness of cortical bone. About 80% of fractures after age 60 occur at cortical bone sites (Kanis et al., 2001). MRTA has been used for research (Miller et al., 2013), but little has been published about its accuracy. To begin investigating this, we compared MRTA and QMT measurements of the bending stiffness of artificial human ulna bones. The ulna is convenient for MRTA testing in vivo, due to its superficiality and near-ideal biomechanics in bending. We began with artificial bones because they have dimensions and mechanical properties similar to real bones (Dunlap et al., 2008; Gardner et al., 2010; Heiner, 2008), and because they require no special handling, storage or disposal. 2. Methods 2.1. Specimens Custom Sawboness 4th generation composite human ulna bones (N¼ 39, Model #3426, Pacific Research Laboratories, Inc., Vashon, WA) were purchased. These artificial ulnas are comprised of a polyurethane foam core emulating cancellous bone covered by a glass-filled epoxy shell emulating cortical bone. Ulna geometry was standardized within manufacturing tolerances, while the percentage of glass fill in the epoxy was varied to achieve a range of bending stiffness across which to compare MRTA and QMT measurements. Four ulnas were manufactured at each of 9 levels of excess glass fill ( 10%, 7.5%, 5%, 2.5%, 0%, þ 2.5%, þ 5%, þ7.5%, and þ10%), where 0% is the standard proprietary percentage. Two proof-of-concept ulnas with þ 6% excess glass fill
P.A. Arnold et al. / Journal of Biomechanics 47 (2014) 3580–3583 and an anomalous ulna with 0% excess glass fill were also tested and included in the data analysis. Ulnas were received in four batches. 2.2. Data collection For both methods, ulnas were supported and loaded in 3-point bending in a manner similar to that used in MRTA tests of human subjects in vivo. As illustrated in the Supplementary material, ulnas were oriented horizontally, posterior surface up, with the load applied downward at the midpoint of the span between supports. Proximally, the trochlear notch of the ulna was supported by the articulating trochlea at the distal end of a 4th generation composite Sawboness humerus (Model #3404, Pacific Research Laboratories) that was held upright in a bone clamp (Model #1605, Pacific Research Laboratories). Distally, the anterior surface of the distal radioulnar joint was supported by the top of a vertical 50 mm 75 mm 300 mm steel block. To prevent confounding by variations in axial rotation of the ulna, axial rotation was standardized before each test by aligning a mark on the tubercle of the coronoid process on the medial side of the proximal end of each ulna with a mark on the medial side of the trochlea at the distal end of the humerus. 2.2.1. QMT data collection QMT data were collected with a 10 kN load frame (QTest-Elite, MTS Systems Corporation, Eden Prairie, MN) using a 25 N load cell (Model 4501017B, MTS Systems Corporation) to measure applied force. To prevent viscous and inertial effects from confounding elastic force measurements, data (Fig. 1, Top) were collected at a crosshead speed of 0.1608 mm/min (i.e., 1 step of the stepper motor driving the crosshead per data point at 10 Hz) for a strain rate o 0.0001/s. Loading cycles of 0–20 N were repeated until the coefficient of variation (CV ¼ standard deviation/mean) of bending stiffness (KB) in the last five cycles was o 1.0%. This CV was recorded as the index of QMT measurement precision. Ulnas were then dismounted. The mean of three such measurements was taken as the QMT measurement of KB, and the CV of these measurements was recorded as the index of QMT measurement repeatability. 2.2.2. MRTA data collection MRTA data were collected with a custom MRTA system comprised of an impedance head for measuring force and acceleration (Model 288D01, PCB Piezotronics, Inc., Depew, NY), an electromechanical shaker with integrated power amplifier (Model K2007E01, The Modal Shop, Inc., Cincinnati, OH), a dynamic signal analyzer (Photonþ, Brüel & Kjær North America, Inc., Norcross, GA), and a laptop computer with signal processing and waveform source software (RT Pro, Brüel & Kjær North America, Inc.). Rubber tourniquets (x-tourn™ Cat 18679, Avcor Health Care Products, Ft Worth, TX) were used to prevent the coupling of extraneous vibrations of the mechanical structure into the ulna, and to emulate skin between the ulna and the force probe. The applied load was comprised of a 1 N oscillating component randomly spanning a range of frequencies from 40 to 1200 Hz superimposed upon a
3581
manually adjusted static component of 10–20 N. While observing the imaginary part of the accelerance (i.e., acceleration/force) frequency response function (FRF) (Fig. 1, Bottom), the static component was adjusted to increase the stiffness of the skin and thereby to raise and separate a higher frequency resonance determined primarily by the mechanical properties of the skin from the lower frequency resonance determined primarily by the mechanical properties of the ulna. Frequency response functions were recorded three times at 1 Hz intervals and the CV of the resulting KB measurements was recorded as the index of MRTA measurement precision. Ulnas were then dismounted. The mean of three such measurements was taken as the MRTA measurement of KB, and the CV of these measurements was recorded as the index of MRTA measurement repeatability. 2.3. Data analysis Because the slenderness ratio of the artificial ulna exceeded 20, shear forces were ignored and the ulna was modeled as a simply supported beam in bending with stiffness KB. Then, even though the ulnas were the same length, ulna flexural rigidity (EI) was calculated from Euler beam theory for later comparison to real human ulnas of various lengths: EI ¼ K B L3 =48
ð1Þ
where L ¼0.245 m was the span across which the ulna was supported. 2.3.1. QMT data analysis In QMT bending tests, we derived KB from the steepest slope of the force/ displacement curve over half the 20 N range of applied force, in practice, always the upper half. Within the elastic range of the ulna, this measured stiffness KM reflects the series combination of KB and the stiffness of the test frame (KF ¼ 83.44 N/mm in our case), which was dominated by the most compliant part, i.e., the load cell (Fig. 2, Left) K M ¼ K B K F = ðK B þ K F Þ
ð2Þ
Rearrangement of Eq. (2) yielded KB as K B ¼ K M K F =ðK F –K M Þ
ð3Þ
2.3.2. MRTA data analysis Like previous MRTA practitioners (Steele et al., 1988), we modeled the dynamic behavior of the ulna and overlying skin as a 7-parameter mechanical system (Fig. 2, Right), including the mass, stiffness and damping of the skin (MS, KS, BS) and of the bone (MB, KB, BB) together with an allowance for damping by surrounding soft tissue (Bp). The procedure by which optimum FRF data were selected for model fitting is described in the Supplementary material. Unlike previous practitioners, we fitted the complex, continuous-time transfer functions of both the stiffness and compliance of the skin-bone system to the corresponding FRFs derived from the accelerance FRF of each ulna. Invariably, the coefficient of determination (R2) for fits to stiffness exceeded those for fits to compliance, the lowest of which was 0.977. Then we calculated EI from the average of the two estimates of KB in the two fits. 2.4. Statistical analysis The precision and repeatability of MRTA and QMT measurements were compared by paired Student's t-tests. The association of paired MRTA and QMT measurements was determined by regression analysis. Bland–Altman analysis (Bland and Altman, 1986) was used to quantify the bias and limits of agreement between them.
Fig. 1. Raw force vs displacement data collected by QMT (Top) and raw complex accelerance frequency response function data collected by MRTA (Bottom).
Fig. 2. Mechanical models assumed in the analysis of data from the 3-point bending tests by QMT (Left) and MRTA (Right). F¼ applied force. KF ¼ stiffness of QMT test frame. MS, MB ¼ mass of skin, bone. KS, KB ¼stiffness of skin, bone. DS, DB, DP ¼damping of skin, bone, peripheral tissue.
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P.A. Arnold et al. / Journal of Biomechanics 47 (2014) 3580–3583
3. Results 3.1. Specimen variation Details of variations in artificial ulna mass (48–61 g) and EI (10– 26 Nm2) between and within levels of glass fill in the epoxy emulating cortical bone are reported in the Supplementary material. 3.2. Reproducibility of EI measurements MRTA precision (1.07 1.0%) and repeatability (3.1 73.1%) were larger than those of QMT (0.2 70.2% and 1.3þ1.7%, respectively; both p o10 4) (Fig. 3). 3.3. Accuracy of MRTA Measurements The regression line relating MRTA and QMT measurements of EI was indistinguishable from the identity line (R2 ¼0.999). The y-intercept was not significantly different from 0 (p ¼0.44), while the slope was significantly different from 0 (1.001 70.004, p o10 63) but not from 1 (p¼ 0.87). The standard error of the estimate (SEE) was 0.5 Nm2. (See the Supplementary material.) Bland–Altman analysis (Fig. 4) revealed that MRTA measurements of ulna EI were unbiased with respect to QMT (mean EI_MRTA– EI_QMT difference¼ 0.270.8%, p¼0.67). The 95% confidence interval of the mean difference was approximately 71%. The limits of
Fig. 3. Precision and repeatability of ulna EI measurements by QMT (filled circles) and MRTA (open circles).
agreement between (i.e., the 95% confidence interval for) paired measurements of EI by MRTA and QMT in individual ulnas was 75%, and the 95% confidence interval on the limits of agreement ranged from 74% to 76%.
4. Discussion The only previously reported direct comparison of MRTA and QMT measurements (Hutchinson et al., 2001; Roberts et al., 1996) was made in 21 monkey tibias. EI calculations were confounded by differences in end conditions and length between the in vivo and in vitro methods. Axial rotation of the tibias may also have varied, and tibias may have been stiffened in vivo by attachments to other structures in the leg. For whatever reasons, MRTA measurements of EI were 60% higher than QMT measurements, and the 95% confidence interval on paired differences between the two methods was 7 40%. By taking care to avoid such confounding differences in artificial human ulnas, we have shown that MRTA and QMT measurements of EI can be interchangeable within 75%. If such accuracy is achieved on real human ulnas in situ, and if the ulna is representative of the appendicular skeleton, MRTA may prove clinically useful. Our MRTA measurements were less precise and repeatable than QMT measurements, but similar to the 2.0–4.3% precision (Kiebzak et al., 1999; McCabe et al., 1991; Myburgh et al., 1993; Myburgh et al., 1992; Steele et al., 1988) and 3.0–5.3% repeatability (Kiebzak and Ambrose, 2005; Steele et al., 1988) reported in human ulnas in vivo. MRTA measurements of ulna EI in vivo have been reported to range from 12 to 26 Nm2 in older women (McCabe et al., 1991), 16–41 Nm2 in younger women (McCabe et al., 1991) and 25 to 78 Nm2 in men (Myburgh et al., 1992). We have measured ulna EI exceeding 120 Nm2 in young male bodybuilders. Thus, our measurements of EI in artificial ulnas advertised as being modeled on the ulna of a large male fell into the range of older women. This discrepancy can be explained in part by our use of the supported span (245 mm) in the calculation of EI, whereas practitioners of MRTA in vivo have used the entire anatomical length. Adjusting our results for the 272 mm length of the artificial ulnas would raise the range of EI in our artificial ulnas to 16–36 Nm2, within the range of younger women. The rest of the discrepancy may be explained by higher moduli or larger cross-sectional geometries in real human ulnas.
Conflict of interest statement The authors have no financial and personal relationships with other people or organizations that could inappropriately influence (bias) their work.
Acknowledgments
Fig. 4. Bland–Altman analysis of MRTA and QMT measurements of EI in 39 artificial human ulnas. Mean ¼ mean difference; 95% CIMþ and 95% CIM ¼ upper and lower limits of the 95% confidence interval on the mean difference. 95%CI þ and 95%CI ¼limits of agreement¼upper and lower 95% confidence interval on individual differences. 95%CI þ þ and 95%CI þ ¼95% confidence interval on the upper limit of the limits of agreement. 95%CI þ and 95%CI ¼ 95% confidence interval on the lower limit of the limits of agreement.
This research was funded by the Ohio Space Grant Consortium, the Ohio University Honors Tutorial College, the Ohio University Department of Biological Sciences, and the Ohio Musculoskeletal and Neurological Institute. Neither these sponsors nor Pacific Research Laboratories, Inc. had any role in the study design; in the collection, analysis and interpretation of data; in the writing of the manuscript; or in the decision to submit the manuscript for publication. The Ohio University Russ College of Technology and Engineering fabricated the force probes used for QMT and MRTA testing. Dr. Betty Sindelar of the Ohio University School of Physical Therapy made available her MTS test frame and laboratory for
P.A. Arnold et al. / Journal of Biomechanics 47 (2014) 3580–3583
QMT testing. Peter Czernick of the Department of Orthopedic Surgery at the University of Toledo did the micro-computed tomography of artificial ulnas. Amy Posch of Pacific Research Laboratories/Sawboness oversaw the production of the 4th generation composite human ulnas.
Appendix. Supplementary materials Supplementary data associated with this article can be found in the online version at http://dx.doi.org/10.1016/j.jbiomech.2014.09.005. References Bland, J.M., Altman, D.G., 1986. Statistical methods for assessing agreement between two methods of clinical measurement. Lancet 1, 307–310. Borders, S., Petersen, K.R., Orne, D., 1977. Prediction of bending strength of long bones from measurements of bending stiffness and bone mineral content. J. Biomech. Eng. 99, 40–44. Dunlap, J.T., Chong, A.C., Lucas, G.L., Cooke, F.W., 2008. Structural properties of a novel design of composite analogue humeri models. Ann. Biomed. Eng. 36, 1922–1926. Fyhrie, D.P., Vashishth, D., 2000. Bone stiffness predicts strength similarly for human vertebral cancellous bone in compression and for cortical bone in tension. Bone 26, 169–173. Gardner, M.P., Chong, A.C., Pollock, A.G., Wooley, P.H., 2010. Mechanical evaluation of large-size fourth-generation composite femur and tibia models. Ann. Biomed. Eng. 38, 613–620. Heiner, A.D., 2008. Structural properties of fourth-generation composite femurs and tibias. J. Biomech. 41, 3282–3284. Hutchinson, T.M., Bakulin, A.V., Rakhmanov, A.S., Martin, R.B., Steele, C.R., Arnaud, S. B., 2001. Effects of chair restraint on the strength of the tibia in rhesus monkeys. J. Med. Primatol. 30, 313–321.
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Jurist, J.M., Foltz, A.S., 1977. Human ulnar bending stiffness, mineral content, geometry and strength. J. Biomech. 10, 455–459. Kanis, J.A., Johnell, O., Oden, A., Dawson, A., De Laet, C., Jonsson, B., 2001. Ten year probabilities of osteoporotic fractures according to BMD and diagnostic thresholds. Osteoporos. Int. 12, 989–995. Kiebzak, G.M., Ambrose, C.G., 2005. Relationship among MRTA, DXA, and QUS revisited. J. Clin. Densitom. 8, 396–403. Kiebzak, G.M., Box, J.H., Box, P., 1999. Decreased ulnar bending stiffness in osteoporotic Caucasian women. J. Clin. Densitom. 2, 143–152. McCabe, F., Zhou, L.J., Steele, C.R., Marcus, R., 1991. Noninvasive assessment of ulnar bending stiffness in women. J. Bone Miner. Res. 6, 53–59. Miller, L.E., Ramp, W.K., Steele, C.R., Nickols-Richardson, S.M., Herbert, W.G., 2013. Rationale, design and clinical performance of the mechanical response tissue analyser: a non-invasive technology for measurement of long bone bending stiffness. J. Med. Eng. Technol. 37, 144–149. Myburgh, K.H., Charette, S., Zhou, L., Steele, C.R., Arnaud, S., Marcus, R., 1993. Influence of recreational activity and muscle strength on ulnar bending stiffness in men. Med. Sci. Sports Exerc. 25, 592–596. Myburgh, K.H., Zhou, L.J., Steele, C.R., Arnaud, S., Marcus, R., 1992. In vivo assessment of forearm bone mass and ulnar bending stiffness in healthy men. J. Bone Miner. Res. 7, 1345–1350. National Institutes of Health Consensus Development Panel, 2001. Osteoporosis prevention, diagnosis, and therapy. J. Am. Med. Assoc. 285, 785–795. Roberts, S.G., Hutchinson, T.M., Arnaud, S.B., Kiratli, B.J., Martin, R.B., Steele, C.R., 1996. Noninvasive determination of bone mechanical properties using vibration response: a refined model and validation in vivo. J. Biomech. 29, 91–98. Schousboe, J.T., Shepherd, J.A., Bilezikian, J.P., Baim, S., 2013. Executive summary of the 2013 ISCD Position Development Conference on bone densitometry. J. Clin. Densitom. 16, 455–467. Siris, E.S., Miller, P.D., Barrett-Connor, E., Faulkner, K.G., Wehren, L.E., Abbott, T.A., Berger, M.L., Santora, A.C., Sherwood, L.M., 2001. Identification and fracture outcomes of undiagnosed low bone mineral density in postmenopausal women: results from the National Osteoporosis Risk Assessment. J. Am. Med. Assoc. 286, 2815–2822. Steele, C.R., Zhou, L.J., Guido, D., Marcus, R., Heinrichs, W.L., Cheema, C., 1988. Noninvasive determination of ulnar stiffness from mechanical response—in vivo comparison of stiffness and bone mineral content in humans. J. Biomech. Eng. 110, 87–96.
Contents lists available at ScienceDirect
Journal of Biomechanics journal homepage: www.elsevier.com/locate/jbiomech www.JBiomech.com
Short communication
Accuracy and reproducibility of bending stiffness measurements by mechanical response tissue analysis in artificial human ulnas Patricia A. Arnold, Emily R. Ellerbrock, Lyn Bowman, Anne B. Loucks n Department of Biological Sciences, Ohio University, Athens, OH 45701, USA
art ic l e i nf o
a b s t r a c t
Article history: Accepted 3 September 2014
Osteoporosis is characterized by reduced bone strength, but no FDA-approved medical device measures bone strength. Bone strength is strongly associated with bone stiffness, but no FDA-approved medical device measures bone stiffness either. Mechanical Response Tissue Analysis (MRTA) is a non-significant risk, non-invasive, radiation-free, vibration analysis technique for making immediate, direct functional measurements of the bending stiffness of long bones in humans in vivo. MRTA has been used for research purposes for more than 20 years, but little has been published about its accuracy. To begin to investigate its accuracy, we compared MRTA measurements of bending stiffness in 39 artificial human ulna bones to measurements made by Quasistatic Mechanical Testing (QMT). In the process, we also quantified the reproducibility (i.e., precision and repeatability) of both methods. MRTA precision (1.071.0%) and repeatability (3.1 73.1%) were not as high as those of QMT (0.27 0.2% and 1.3þ1.7%, respectively; both po 10 4). The relationship between MRTA and QMT measurements of ulna bending stiffness was indistinguishable from the identity line (p¼0.44) and paired measurements by the two methods agreed within a 95% confidence interval of 7 5%. If such accuracy can be achieved on real human ulnas in situ, and if the ulna is representative of the appendicular skeleton, MRTA may prove clinically useful. & 2014 Elsevier Ltd. All rights reserved.
Keywords: Mechanical response tissue analysis Quasistatic mechanical testing Bending stiffness Composite ulna
1. Introduction Osteoporosis is a skeletal disorder characterized by reduced bone strength and increased risk of fracture (National Institutes of Health, 2001), but no FDA-approved device measures bone strength. Consequently, osteoporosis is diagnosed by measuring bone mineral density (BMD) (Schousboe et al., 2013), even though BMD does not predict fractures well: among 200,000 postmenopausal women, 96% of those diagnosed with osteoporosis did not fracture, while 81% of fractures occurred in women who did not have osteoporosis (Siris et al., 2001). Bone strength is strongly associated (r40.95) with bone stiffness (Borders et al., 1977; Fyhrie and Vashishth, 2000; Jurist and Foltz, 1977; Roberts et al., 1996), but no FDA-approved device measures bone stiffness either. The reference method for measuring bone stiffness and strength, Quasistatic Mechanical Testing (QMT), can only be employed in vitro. Mechanical Response Tissue Analysis (MRTA) is a non-significant risk, noninvasive, radiation-free, vibration analysis technique for making direct functional measurements of the bending stiffness of long bones in humans in vivo (Steele et al., 1988). Because bending tests are especially sensitive to mid-span mechanical properties, MRTA
n
Corresponding author. Tel.: þ 1 740 593 2286; fax: þ 1 740 593 0300. E-mail address: [email protected] (A.B. Loucks).
http://dx.doi.org/10.1016/j.jbiomech.2014.09.005 0021-9290/& 2014 Elsevier Ltd. All rights reserved.
may be useful for measuring the bending stiffness of cortical bone. About 80% of fractures after age 60 occur at cortical bone sites (Kanis et al., 2001). MRTA has been used for research (Miller et al., 2013), but little has been published about its accuracy. To begin investigating this, we compared MRTA and QMT measurements of the bending stiffness of artificial human ulna bones. The ulna is convenient for MRTA testing in vivo, due to its superficiality and near-ideal biomechanics in bending. We began with artificial bones because they have dimensions and mechanical properties similar to real bones (Dunlap et al., 2008; Gardner et al., 2010; Heiner, 2008), and because they require no special handling, storage or disposal. 2. Methods 2.1. Specimens Custom Sawboness 4th generation composite human ulna bones (N¼ 39, Model #3426, Pacific Research Laboratories, Inc., Vashon, WA) were purchased. These artificial ulnas are comprised of a polyurethane foam core emulating cancellous bone covered by a glass-filled epoxy shell emulating cortical bone. Ulna geometry was standardized within manufacturing tolerances, while the percentage of glass fill in the epoxy was varied to achieve a range of bending stiffness across which to compare MRTA and QMT measurements. Four ulnas were manufactured at each of 9 levels of excess glass fill ( 10%, 7.5%, 5%, 2.5%, 0%, þ 2.5%, þ 5%, þ7.5%, and þ10%), where 0% is the standard proprietary percentage. Two proof-of-concept ulnas with þ 6% excess glass fill
P.A. Arnold et al. / Journal of Biomechanics 47 (2014) 3580–3583 and an anomalous ulna with 0% excess glass fill were also tested and included in the data analysis. Ulnas were received in four batches. 2.2. Data collection For both methods, ulnas were supported and loaded in 3-point bending in a manner similar to that used in MRTA tests of human subjects in vivo. As illustrated in the Supplementary material, ulnas were oriented horizontally, posterior surface up, with the load applied downward at the midpoint of the span between supports. Proximally, the trochlear notch of the ulna was supported by the articulating trochlea at the distal end of a 4th generation composite Sawboness humerus (Model #3404, Pacific Research Laboratories) that was held upright in a bone clamp (Model #1605, Pacific Research Laboratories). Distally, the anterior surface of the distal radioulnar joint was supported by the top of a vertical 50 mm 75 mm 300 mm steel block. To prevent confounding by variations in axial rotation of the ulna, axial rotation was standardized before each test by aligning a mark on the tubercle of the coronoid process on the medial side of the proximal end of each ulna with a mark on the medial side of the trochlea at the distal end of the humerus. 2.2.1. QMT data collection QMT data were collected with a 10 kN load frame (QTest-Elite, MTS Systems Corporation, Eden Prairie, MN) using a 25 N load cell (Model 4501017B, MTS Systems Corporation) to measure applied force. To prevent viscous and inertial effects from confounding elastic force measurements, data (Fig. 1, Top) were collected at a crosshead speed of 0.1608 mm/min (i.e., 1 step of the stepper motor driving the crosshead per data point at 10 Hz) for a strain rate o 0.0001/s. Loading cycles of 0–20 N were repeated until the coefficient of variation (CV ¼ standard deviation/mean) of bending stiffness (KB) in the last five cycles was o 1.0%. This CV was recorded as the index of QMT measurement precision. Ulnas were then dismounted. The mean of three such measurements was taken as the QMT measurement of KB, and the CV of these measurements was recorded as the index of QMT measurement repeatability. 2.2.2. MRTA data collection MRTA data were collected with a custom MRTA system comprised of an impedance head for measuring force and acceleration (Model 288D01, PCB Piezotronics, Inc., Depew, NY), an electromechanical shaker with integrated power amplifier (Model K2007E01, The Modal Shop, Inc., Cincinnati, OH), a dynamic signal analyzer (Photonþ, Brüel & Kjær North America, Inc., Norcross, GA), and a laptop computer with signal processing and waveform source software (RT Pro, Brüel & Kjær North America, Inc.). Rubber tourniquets (x-tourn™ Cat 18679, Avcor Health Care Products, Ft Worth, TX) were used to prevent the coupling of extraneous vibrations of the mechanical structure into the ulna, and to emulate skin between the ulna and the force probe. The applied load was comprised of a 1 N oscillating component randomly spanning a range of frequencies from 40 to 1200 Hz superimposed upon a
3581
manually adjusted static component of 10–20 N. While observing the imaginary part of the accelerance (i.e., acceleration/force) frequency response function (FRF) (Fig. 1, Bottom), the static component was adjusted to increase the stiffness of the skin and thereby to raise and separate a higher frequency resonance determined primarily by the mechanical properties of the skin from the lower frequency resonance determined primarily by the mechanical properties of the ulna. Frequency response functions were recorded three times at 1 Hz intervals and the CV of the resulting KB measurements was recorded as the index of MRTA measurement precision. Ulnas were then dismounted. The mean of three such measurements was taken as the MRTA measurement of KB, and the CV of these measurements was recorded as the index of MRTA measurement repeatability. 2.3. Data analysis Because the slenderness ratio of the artificial ulna exceeded 20, shear forces were ignored and the ulna was modeled as a simply supported beam in bending with stiffness KB. Then, even though the ulnas were the same length, ulna flexural rigidity (EI) was calculated from Euler beam theory for later comparison to real human ulnas of various lengths: EI ¼ K B L3 =48
ð1Þ
where L ¼0.245 m was the span across which the ulna was supported. 2.3.1. QMT data analysis In QMT bending tests, we derived KB from the steepest slope of the force/ displacement curve over half the 20 N range of applied force, in practice, always the upper half. Within the elastic range of the ulna, this measured stiffness KM reflects the series combination of KB and the stiffness of the test frame (KF ¼ 83.44 N/mm in our case), which was dominated by the most compliant part, i.e., the load cell (Fig. 2, Left) K M ¼ K B K F = ðK B þ K F Þ
ð2Þ
Rearrangement of Eq. (2) yielded KB as K B ¼ K M K F =ðK F –K M Þ
ð3Þ
2.3.2. MRTA data analysis Like previous MRTA practitioners (Steele et al., 1988), we modeled the dynamic behavior of the ulna and overlying skin as a 7-parameter mechanical system (Fig. 2, Right), including the mass, stiffness and damping of the skin (MS, KS, BS) and of the bone (MB, KB, BB) together with an allowance for damping by surrounding soft tissue (Bp). The procedure by which optimum FRF data were selected for model fitting is described in the Supplementary material. Unlike previous practitioners, we fitted the complex, continuous-time transfer functions of both the stiffness and compliance of the skin-bone system to the corresponding FRFs derived from the accelerance FRF of each ulna. Invariably, the coefficient of determination (R2) for fits to stiffness exceeded those for fits to compliance, the lowest of which was 0.977. Then we calculated EI from the average of the two estimates of KB in the two fits. 2.4. Statistical analysis The precision and repeatability of MRTA and QMT measurements were compared by paired Student's t-tests. The association of paired MRTA and QMT measurements was determined by regression analysis. Bland–Altman analysis (Bland and Altman, 1986) was used to quantify the bias and limits of agreement between them.
Fig. 1. Raw force vs displacement data collected by QMT (Top) and raw complex accelerance frequency response function data collected by MRTA (Bottom).
Fig. 2. Mechanical models assumed in the analysis of data from the 3-point bending tests by QMT (Left) and MRTA (Right). F¼ applied force. KF ¼ stiffness of QMT test frame. MS, MB ¼ mass of skin, bone. KS, KB ¼stiffness of skin, bone. DS, DB, DP ¼damping of skin, bone, peripheral tissue.
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3. Results 3.1. Specimen variation Details of variations in artificial ulna mass (48–61 g) and EI (10– 26 Nm2) between and within levels of glass fill in the epoxy emulating cortical bone are reported in the Supplementary material. 3.2. Reproducibility of EI measurements MRTA precision (1.07 1.0%) and repeatability (3.1 73.1%) were larger than those of QMT (0.2 70.2% and 1.3þ1.7%, respectively; both p o10 4) (Fig. 3). 3.3. Accuracy of MRTA Measurements The regression line relating MRTA and QMT measurements of EI was indistinguishable from the identity line (R2 ¼0.999). The y-intercept was not significantly different from 0 (p ¼0.44), while the slope was significantly different from 0 (1.001 70.004, p o10 63) but not from 1 (p¼ 0.87). The standard error of the estimate (SEE) was 0.5 Nm2. (See the Supplementary material.) Bland–Altman analysis (Fig. 4) revealed that MRTA measurements of ulna EI were unbiased with respect to QMT (mean EI_MRTA– EI_QMT difference¼ 0.270.8%, p¼0.67). The 95% confidence interval of the mean difference was approximately 71%. The limits of
Fig. 3. Precision and repeatability of ulna EI measurements by QMT (filled circles) and MRTA (open circles).
agreement between (i.e., the 95% confidence interval for) paired measurements of EI by MRTA and QMT in individual ulnas was 75%, and the 95% confidence interval on the limits of agreement ranged from 74% to 76%.
4. Discussion The only previously reported direct comparison of MRTA and QMT measurements (Hutchinson et al., 2001; Roberts et al., 1996) was made in 21 monkey tibias. EI calculations were confounded by differences in end conditions and length between the in vivo and in vitro methods. Axial rotation of the tibias may also have varied, and tibias may have been stiffened in vivo by attachments to other structures in the leg. For whatever reasons, MRTA measurements of EI were 60% higher than QMT measurements, and the 95% confidence interval on paired differences between the two methods was 7 40%. By taking care to avoid such confounding differences in artificial human ulnas, we have shown that MRTA and QMT measurements of EI can be interchangeable within 75%. If such accuracy is achieved on real human ulnas in situ, and if the ulna is representative of the appendicular skeleton, MRTA may prove clinically useful. Our MRTA measurements were less precise and repeatable than QMT measurements, but similar to the 2.0–4.3% precision (Kiebzak et al., 1999; McCabe et al., 1991; Myburgh et al., 1993; Myburgh et al., 1992; Steele et al., 1988) and 3.0–5.3% repeatability (Kiebzak and Ambrose, 2005; Steele et al., 1988) reported in human ulnas in vivo. MRTA measurements of ulna EI in vivo have been reported to range from 12 to 26 Nm2 in older women (McCabe et al., 1991), 16–41 Nm2 in younger women (McCabe et al., 1991) and 25 to 78 Nm2 in men (Myburgh et al., 1992). We have measured ulna EI exceeding 120 Nm2 in young male bodybuilders. Thus, our measurements of EI in artificial ulnas advertised as being modeled on the ulna of a large male fell into the range of older women. This discrepancy can be explained in part by our use of the supported span (245 mm) in the calculation of EI, whereas practitioners of MRTA in vivo have used the entire anatomical length. Adjusting our results for the 272 mm length of the artificial ulnas would raise the range of EI in our artificial ulnas to 16–36 Nm2, within the range of younger women. The rest of the discrepancy may be explained by higher moduli or larger cross-sectional geometries in real human ulnas.
Conflict of interest statement The authors have no financial and personal relationships with other people or organizations that could inappropriately influence (bias) their work.
Acknowledgments
Fig. 4. Bland–Altman analysis of MRTA and QMT measurements of EI in 39 artificial human ulnas. Mean ¼ mean difference; 95% CIMþ and 95% CIM ¼ upper and lower limits of the 95% confidence interval on the mean difference. 95%CI þ and 95%CI ¼limits of agreement¼upper and lower 95% confidence interval on individual differences. 95%CI þ þ and 95%CI þ ¼95% confidence interval on the upper limit of the limits of agreement. 95%CI þ and 95%CI ¼ 95% confidence interval on the lower limit of the limits of agreement.
This research was funded by the Ohio Space Grant Consortium, the Ohio University Honors Tutorial College, the Ohio University Department of Biological Sciences, and the Ohio Musculoskeletal and Neurological Institute. Neither these sponsors nor Pacific Research Laboratories, Inc. had any role in the study design; in the collection, analysis and interpretation of data; in the writing of the manuscript; or in the decision to submit the manuscript for publication. The Ohio University Russ College of Technology and Engineering fabricated the force probes used for QMT and MRTA testing. Dr. Betty Sindelar of the Ohio University School of Physical Therapy made available her MTS test frame and laboratory for
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QMT testing. Peter Czernick of the Department of Orthopedic Surgery at the University of Toledo did the micro-computed tomography of artificial ulnas. Amy Posch of Pacific Research Laboratories/Sawboness oversaw the production of the 4th generation composite human ulnas.
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