{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,10,23]],"date-time":"2026-10-23T19:49:31Z","timestamp":1792784971095,"version":"4.5.0"},"reference-count":50,"publisher":"Springer Science and Business Media LLC","issue":"1","license":[{"start":{"date-parts":[[2021,6,29]],"date-time":"2021-06-29T00:00:00Z","timestamp":1624924800000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"},{"start":{"date-parts":[[2021,6,29]],"date-time":"2021-06-29T00:00:00Z","timestamp":1624924800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"}],"funder":[{"DOI":"10.13039\/501100000781","name":"European Research Council","doi-asserted-by":"publisher","award":["ERC-2016-ADG-741883"],"award-info":[{"award-number":["ERC-2016-ADG-741883"]}],"id":[{"id":"10.13039\/501100000781","id-type":"DOI","asserted-by":"publisher"}]},{"name":"ETH Postdoctoral Fellowship Program","award":["MSCA-COFUND, FEL-25_15-1"],"award-info":[{"award-number":["MSCA-COFUND, FEL-25_15-1"]}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Sci Rep"],"abstract":"<jats:title>Abstract<\/jats:title>\n                  <jats:p>Mechanical loading allows both investigation into the mechano-regulation of fracture healing as well as interventions to improve fracture-healing outcomes such as delayed healing or non-unions. However, loading is seldom individualised or even targeted to an effective mechanical stimulus level within the bone tissue. In this study, we use micro-finite element analysis to demonstrate the result of using a constant loading assumption for all mouse femurs in a given group. We then contrast this with the application of an adaptive loading approach, denoted real time Finite Element adaptation, in which micro-computed tomography images provide the basis for micro-FE based simulations and the resulting strains are manipulated and targeted to a reference distribution. Using this approach, we demonstrate that individualised femoral loading leads to a better-specified strain distribution and lower variance in tissue mechanical stimulus across all mice, both longitudinally and cross-sectionally, while making sure that no overloading is occurring leading to refracture of the femur bones.<\/jats:p>","DOI":"10.1038\/s41598-021-92961-y","type":"journal-article","created":{"date-parts":[[2021,6,29]],"date-time":"2021-06-29T06:07:24Z","timestamp":1624946844000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":18,"title":["Real-time finite element analysis allows homogenization of tissue scale strains and reduces variance in a mouse defect healing model"],"prefix":"10.1038","volume":"11","author":[{"given":"Graeme R.","family":"Paul","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Esther","family":"Wehrle","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Duncan C.","family":"Tourolle","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Gisela A.","family":"Kuhn","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Ralph","family":"M\u00fcller","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"297","published-online":{"date-parts":[[2021,6,29]]},"reference":[{"key":"92961_CR1","doi-asserted-by":"publisher","first-page":"395","DOI":"10.1007\/s11914-018-0448-6","volume":"16","author":"GR Paul","year":"2018","unstructured":"Paul, G. R., Malhotra, A. & Muller, R. Mechanical stimuli in the local in vivo environment in bone: Computational approaches linking organ-scale loads to cellular signals. Curr. Osteoporos. Rep. 16, 395\u2013403. https:\/\/doi.org\/10.1007\/s11914-018-0448-6 (2018).","journal-title":"Curr. Osteoporos. Rep."},{"key":"92961_CR2","doi-asserted-by":"publisher","DOI":"10.1371\/journal.pone.0062172","volume":"8","author":"FA Schulte","year":"2013","unstructured":"Schulte, F. A. et al. Local mechanical stimuli regulate bone formation and resorption in mice at the tissue level. PLoS ONE 8, ARTN e62172. https:\/\/doi.org\/10.1371\/journal.pone.0062172 (2013).","journal-title":"PLoS ONE"},{"key":"92961_CR3","doi-asserted-by":"publisher","first-page":"563","DOI":"10.1016\/0142-9612(93)90171-W","volume":"14","author":"S Goodman","year":"1993","unstructured":"Goodman, S. & Aspenberg, P. Effects of mechanical stimulation on the differentiation of hard tissues. Biomaterials 14, 563\u2013569. https:\/\/doi.org\/10.1016\/0142-9612(93)90171-W (1993).","journal-title":"Biomaterials"},{"key":"92961_CR4","doi-asserted-by":"publisher","first-page":"2418","DOI":"10.1016\/j.jbiomech.2010.04.019","volume":"43","author":"EF Morgan","year":"2010","unstructured":"Morgan, E. F. et al. Correlations between local strains and tissue phenotypes in an experimental model of skeletal healing. J. Biomech. 43, 2418\u20132424. https:\/\/doi.org\/10.1016\/j.jbiomech.2010.04.019 (2010).","journal-title":"J. Biomech."},{"key":"92961_CR5","doi-asserted-by":"publisher","first-page":"405","DOI":"10.1016\/8756-3282(96)00028-2","volume":"18","author":"DB Burr","year":"1996","unstructured":"Burr, D. B. et al. In vivo measurement of human tibial strains during vigorous activity. Bone 18, 405\u2013410. https:\/\/doi.org\/10.1016\/8756-3282(96)00028-2 (1996).","journal-title":"Bone"},{"key":"92961_CR6","doi-asserted-by":"publisher","first-page":"2735","DOI":"10.1098\/rsif.2012.0286","volume":"9","author":"SW Verbruggen","year":"2012","unstructured":"Verbruggen, S. W., Vaughan, T. J. & McNamara, L. M. Strain amplification in bone mechanobiology: A computational investigation of the in vivo mechanics of osteocytes. J. R. Soc. Interface 9, 2735\u20132744. https:\/\/doi.org\/10.1098\/rsif.2012.0286 (2012).","journal-title":"J. R. Soc. Interface"},{"key":"92961_CR7","doi-asserted-by":"publisher","first-page":"1361","DOI":"10.1002\/cnm.2578","volume":"29","author":"TJ Vaughan","year":"2013","unstructured":"Vaughan, T. J., Verbruggen, S. W. & McNamara, L. M. Are all osteocytes equal? Multiscale modelling of cortical bone to characterise the mechanical stimulation of osteocytes. Int. J. Numer. Meth. Bio. 29, 1361\u20131372. https:\/\/doi.org\/10.1002\/cnm.2578 (2013).","journal-title":"Int. J. Numer. Meth. Bio."},{"key":"92961_CR8","doi-asserted-by":"publisher","first-page":"387","DOI":"10.1115\/1.1287161","volume":"122","author":"J You","year":"2000","unstructured":"You, J. et al. Substrate deformation levels associated with routine physical activity are less stimulatory to bone cells relative to loading-induced oscillatory fluid flow. J. Biomech. Eng.-T Asme. 122, 387\u2013393. https:\/\/doi.org\/10.1115\/1.1287161 (2000).","journal-title":"J. Biomech. Eng.-T Asme."},{"key":"92961_CR9","doi-asserted-by":"publisher","first-page":"466","DOI":"10.1016\/j.bone.2005.09.017","volume":"38","author":"T Hoc","year":"2006","unstructured":"Hoc, T. et al. Effect of microstructure on the mechanical properties of Haversian cortical bone. Bone 38, 466\u2013474. https:\/\/doi.org\/10.1016\/j.bone.2005.09.017 (2006).","journal-title":"Bone"},{"key":"92961_CR10","doi-asserted-by":"publisher","first-page":"317","DOI":"10.1016\/S0021-9290(99)00210-9","volume":"33","author":"SP Fritton","year":"2000","unstructured":"Fritton, S. P., McLeod, K. J. & Rubin, C. T. Quantifying the strain history of bone: spatial uniformity and self-similarity of low-magnitude strains. J. Biomech. 33, 317\u2013325. https:\/\/doi.org\/10.1016\/S0021-9290(99)00210-9 (2000).","journal-title":"J. Biomech."},{"key":"92961_CR11","doi-asserted-by":"publisher","DOI":"10.1111\/jmi.12937","author":"A Karali","year":"2020","unstructured":"Karali, A. et al. Full-field strain of regenerated bone tissue in a femoral fracture model. J. Microsc. https:\/\/doi.org\/10.1111\/jmi.12937 (2020).","journal-title":"J. Microsc."},{"key":"92961_CR12","doi-asserted-by":"publisher","first-page":"S36","DOI":"10.1007\/s00198-004-1728-9","volume":"16","author":"P Augat","year":"2005","unstructured":"Augat, P., Simon, U., Liedert, A. & Claes, L. Mechanics and mechano-biology of fracture healing in normal and osteoporotic bone. Osteoporosis Int. 16, S36\u2013S43. https:\/\/doi.org\/10.1007\/s00198-004-1728-9 (2005).","journal-title":"Osteoporosis Int."},{"key":"92961_CR13","doi-asserted-by":"publisher","first-page":"577","DOI":"10.1002\/jor.1100150414","volume":"15","author":"L Claes","year":"1997","unstructured":"Claes, L., Augat, P., Suger, G. & Wilke, H. J. Influence of size and stability of the osteotomy gap on the success of fracture healing. J. Orthop. Res. 15, 577\u2013584. https:\/\/doi.org\/10.1002\/jor.1100150414 (1997).","journal-title":"J. Orthop. Res."},{"key":"92961_CR14","doi-asserted-by":"publisher","first-page":"17445","DOI":"10.1038\/s41598-019-53822-x","volume":"9","author":"E Wehrle","year":"2019","unstructured":"Wehrle, E. et al. Evaluation of longitudinal time-lapsed in vivo micro-CT for monitoring fracture healing in mouse femur defect models. Sci. Rep. 9, 17445. https:\/\/doi.org\/10.1038\/s41598-019-53822-x (2019).","journal-title":"Sci. Rep."},{"key":"92961_CR15","doi-asserted-by":"publisher","first-page":"1456","DOI":"10.1002\/jor.21148","volume":"28","author":"V Rontgen","year":"2010","unstructured":"Rontgen, V. et al. Fracture healing in mice under controlled rigid and flexible conditions using an adjustable external fixator. J. Orthop. Res. 28, 1456\u20131462. https:\/\/doi.org\/10.1002\/jor.21148 (2010).","journal-title":"J. Orthop. Res."},{"key":"92961_CR16","doi-asserted-by":"publisher","first-page":"255","DOI":"10.1016\/S0021-9290(98)00153-5","volume":"32","author":"LE Claes","year":"1999","unstructured":"Claes, L. E. & Heigele, C. A. Magnitudes of local stress and strain along bony surfaces predict the course and type of fracture healing. J. Biomech. 32, 255\u2013266. https:\/\/doi.org\/10.1016\/S0021-9290(98)00153-5 (1999).","journal-title":"J. Biomech."},{"key":"92961_CR17","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1038\/s41598-020-57461-5","volume":"10","author":"DC Tourolle n\u00e9 Betts","year":"2020","unstructured":"Tourolle n\u00e9 Betts, D. C. et al. The association between mineralised tissue formation and the mechanical local in vivo environment: Time-lapsed quantification of a mouse defect healing model. Sci. Rep.-UK 10, 1\u201310. https:\/\/doi.org\/10.1038\/s41598-020-57461-5 (2020).","journal-title":"Sci. Rep.-UK"},{"key":"92961_CR18","doi-asserted-by":"publisher","first-page":"316","DOI":"10.1007\/s00423-003-0396-0","volume":"388","author":"L Claes","year":"2003","unstructured":"Claes, L., Eckert-Hubner, K. & Augat, P. The fracture gap size influences the local vascularization and tissue differentiation in callus healing. Langenbeck. Arch. Surg. 388, 316\u2013322. https:\/\/doi.org\/10.1007\/s00423-003-0396-0 (2003).","journal-title":"Langenbeck. Arch. Surg."},{"key":"92961_CR19","doi-asserted-by":"publisher","unstructured":"Claes, L. E. et al. Effects of mechanical factors on the fracture healing process. Clin. Orthop. Relat. R. S132\u2013S147. https:\/\/doi.org\/10.1097\/00003086-199810001-00015 (1998).","DOI":"10.1097\/00003086-199810001-00015"},{"key":"92961_CR20","doi-asserted-by":"publisher","DOI":"10.1038\/srep34491","volume":"6","author":"RD Brady","year":"2016","unstructured":"Brady, R. D. et al. Closed head experimental traumatic brain injury increases size and bone volume of callus in mice with concomitant tibial fracture. Sci. Rep.-UK 6, ARTN 34491. https:\/\/doi.org\/10.1038\/srep34491 (2016).","journal-title":"Sci. Rep.-UK"},{"key":"92961_CR21","doi-asserted-by":"publisher","first-page":"1299","DOI":"10.1016\/j.bone.2009.11.028","volume":"46","author":"HF Shi","year":"2010","unstructured":"Shi, H. F., Cheung, W. H., Qin, L., Leung, A. H. C. & Leung, K. S. Low-magnitude high-frequency vibration treatment augments fracture healing in ovariectomy-induced osteoporotic bone. Bone 46, 1299\u20131305. https:\/\/doi.org\/10.1016\/j.bone.2009.11.028 (2010).","journal-title":"Bone"},{"key":"92961_CR22","doi-asserted-by":"publisher","first-page":"458","DOI":"10.1002\/jor.20753","volume":"27","author":"KS Leung","year":"2009","unstructured":"Leung, K. S. et al. Low-magnitude high-frequency vibration accelerates callus formation, mineralization, and fracture healing in rats. J. Orthop. Res. 27, 458\u2013465. https:\/\/doi.org\/10.1002\/jor.20753 (2009).","journal-title":"J. Orthop. Res."},{"key":"92961_CR23","doi-asserted-by":"publisher","first-page":"734","DOI":"10.1002\/jor.21299","volume":"29","author":"S Recknagel","year":"2011","unstructured":"Recknagel, S. et al. Experimental blunt chest trauma impairs fracture healing in rats. J. Orthop. Res. 29, 734\u2013739. https:\/\/doi.org\/10.1002\/jor.21299 (2011).","journal-title":"J. Orthop. Res."},{"key":"92961_CR24","doi-asserted-by":"publisher","first-page":"93","DOI":"10.1242\/dmm.018622","volume":"8","author":"E Wehrle","year":"2015","unstructured":"Wehrle, E. et al. The impact of low-magnitude high-frequency vibration on fracture healing is profoundly influenced by the oestrogen status in mice. Dis. Model. Mech. 8, 93\u2013104. https:\/\/doi.org\/10.1242\/dmm.018622 (2015).","journal-title":"Dis. Model. Mech."},{"key":"92961_CR25","doi-asserted-by":"publisher","first-page":"1006","DOI":"10.1002\/jor.22629","volume":"32","author":"E Wehrle","year":"2014","unstructured":"Wehrle, E. et al. Distinct frequency dependent effects of whole-body vibration on non-fractured bone and fracture healing in mice. J. Orthop. Res. 32, 1006\u20131013. https:\/\/doi.org\/10.1002\/jor.22629 (2014).","journal-title":"J. Orthop. Res."},{"key":"92961_CR26","doi-asserted-by":"publisher","DOI":"10.1016\/j.bone.2020.115311","author":"BS Klosterhoff","year":"2020","unstructured":"Klosterhoff, B. S. et al. Wireless sensor enables longitudinal monitoring of regenerative niche mechanics during rehabilitation that enhance bone repair. Bone https:\/\/doi.org\/10.1016\/j.bone.2020.115311 (2020).","journal-title":"Bone"},{"key":"92961_CR27","doi-asserted-by":"publisher","first-page":"543","DOI":"10.1302\/0301-620X.70B4.3403595","volume":"70","author":"H Kojimoto","year":"1988","unstructured":"Kojimoto, H., Yasui, N., Goto, T., Matsuda, S. & Shimomura, Y. Bone lengthening in rabbits by callus distraction\u2014The role of periosteum and endosteum. J. Bone Joint Surg. Br. 70, 543\u2013549 (1988).","journal-title":"J. Bone Joint Surg. Br."},{"key":"92961_CR28","doi-asserted-by":"publisher","first-page":"390","DOI":"10.1007\/s00774-013-0429-x","volume":"31","author":"H Murao","year":"2013","unstructured":"Murao, H., Yamamoto, K., Matsuda, S. & Akiyama, H. Periosteal cells are a major source of soft callus in bone fracture. J. Bone Miner. Metab. 31, 390\u2013398. https:\/\/doi.org\/10.1007\/s00774-013-0429-x (2013).","journal-title":"J. Bone Miner. Metab."},{"key":"92961_CR29","doi-asserted-by":"publisher","first-page":"133","DOI":"10.1038\/nrrheum.2012.1","volume":"8","author":"L Claes","year":"2012","unstructured":"Claes, L., Recknagel, S. & Ignatius, A. Fracture healing under healthy and inflammatory conditions. Nat. Rev. Rheumatol. 8, 133\u2013143. https:\/\/doi.org\/10.1038\/nrrheum.2012.1 (2012).","journal-title":"Nat. Rev. Rheumatol."},{"key":"92961_CR30","doi-asserted-by":"publisher","unstructured":"Wolf, S. et al. Effects of high-frequency, low-magnitude mechanical stimulus on bone healing. Clin. Orthop. Relat. R. 192\u2013198. https:\/\/doi.org\/10.1097\/00003086-200104000-00030 (2001).","DOI":"10.1097\/00003086-200104000-00030"},{"key":"92961_CR31","doi-asserted-by":"publisher","first-page":"1123","DOI":"10.1002\/jor.20863","volume":"27","author":"KTS Palomares","year":"2009","unstructured":"Palomares, K. T. S. et al. Mechanical stimulation alters tissue differentiation and molecular expression during bone healing. J. Orthop. Res. 27, 1123\u20131132. https:\/\/doi.org\/10.1002\/jor.20863 (2009).","journal-title":"J. Orthop. Res."},{"key":"92961_CR32","doi-asserted-by":"publisher","first-page":"1679","DOI":"10.1002\/jor.20230","volume":"24","author":"MJ Gardner","year":"2006","unstructured":"Gardner, M. J. et al. In vivo cyclic axial compression affects bone healing in the mouse tibia. J. Orthop. Res. 24, 1679\u20131686. https:\/\/doi.org\/10.1002\/jor.20230 (2006).","journal-title":"J. Orthop. Res."},{"key":"92961_CR33","doi-asserted-by":"publisher","first-page":"145","DOI":"10.1016\/j.bone.2017.12.027","volume":"108","author":"C Liu","year":"2018","unstructured":"Liu, C. et al. Effects of mechanical loading on cortical defect repair using a novel mechanobiological model of bone healing. Bone 108, 145\u2013155. https:\/\/doi.org\/10.1016\/j.bone.2017.12.027 (2018).","journal-title":"Bone"},{"key":"92961_CR34","doi-asserted-by":"publisher","first-page":"22","DOI":"10.22203\/eCM.v029a02","volume":"29","author":"AE Rapp","year":"2015","unstructured":"Rapp, A. E. et al. Systemic mesenchymal stem cell administration enhances bone formation in fracture repair but not load-induced bone formation. Eur. Cells Mater. 29, 22\u201334. https:\/\/doi.org\/10.22203\/eCM.v029a02 (2015).","journal-title":"Eur. Cells Mater."},{"key":"92961_CR35","doi-asserted-by":"publisher","first-page":"217","DOI":"10.1007\/s00223-017-0275-2","volume":"101","author":"A Morse","year":"2017","unstructured":"Morse, A. et al. Sclerostin antibody increases callus size and strength but does not improve fracture union in a challenged open rat fracture model. Calcified Tissue Int. 101, 217\u2013228. https:\/\/doi.org\/10.1007\/s00223-017-0275-2 (2017).","journal-title":"Calcified Tissue Int."},{"key":"92961_CR36","doi-asserted-by":"publisher","first-page":"15","DOI":"10.1016\/j.bone.2014.05.013","volume":"66","author":"AI Birkhold","year":"2014","unstructured":"Birkhold, A. I. et al. Mineralizing surface is the main target of mechanical stimulation independent of age: 3D dynamic in vivo morphometry. Bone 66, 15\u201325. https:\/\/doi.org\/10.1016\/j.bone.2014.05.013 (2014).","journal-title":"Bone"},{"key":"92961_CR37","doi-asserted-by":"publisher","first-page":"435","DOI":"10.1080\/10255840802078014","volume":"11","author":"DJ Webster","year":"2008","unstructured":"Webster, D. J., Morley, P. L., van Lenthe, G. H. & Muller, R. A novel in vivo mouse model for mechanically stimulated bone adaptation\u2014A combined experimental and computational validation study. Comput. Method Biomec. 11, 435\u2013441. https:\/\/doi.org\/10.1080\/10255840802078014 (2008).","journal-title":"Comput. Method Biomec."},{"key":"92961_CR38","doi-asserted-by":"publisher","first-page":"301","DOI":"10.1016\/j.actbio.2014.11.021","volume":"13","author":"H Razi","year":"2015","unstructured":"Razi, H. et al. Skeletal maturity leads to a reduction in the strain magnitudes induced within the bone: A murine tibia study. Acta Biomater. 13, 301\u2013310. https:\/\/doi.org\/10.1016\/j.actbio.2014.11.021 (2015).","journal-title":"Acta Biomater."},{"key":"92961_CR39","doi-asserted-by":"publisher","first-page":"480","DOI":"10.1016\/j.bone.2004.11.007","volume":"36","author":"SJ Shefelbine","year":"2005","unstructured":"Shefelbine, S. J. et al. Prediction of fracture callus mechanical properties using micro-CT images and voxel-based finite element analysis. Bone 36, 480\u2013488. https:\/\/doi.org\/10.1016\/j.bone.2004.11.007 (2005).","journal-title":"Bone"},{"key":"92961_CR40","doi-asserted-by":"publisher","first-page":"172","DOI":"10.1016\/j.jmbbm.2018.06.022","volume":"86","author":"S Oliviero","year":"2018","unstructured":"Oliviero, S., Giorgi, M. & Dall\u2019Ara, E. Validation of finite element models of the mouse tibia using digital volume correlation. J. Mech. Behav. Biomed. 86, 172\u2013184. https:\/\/doi.org\/10.1016\/j.jmbbm.2018.06.022 (2018).","journal-title":"J. Mech. Behav. Biomed."},{"key":"92961_CR41","doi-asserted-by":"publisher","first-page":"386","DOI":"10.1038\/bonekey.2013.120","volume":"2","author":"PK Zysset","year":"2013","unstructured":"Zysset, P. K., Dall\u2019ara, E., Varga, P. & Pahr, D. H. Finite element analysis for prediction of bone strength. Bonekey Rep. 2, 386. https:\/\/doi.org\/10.1038\/bonekey.2013.120 (2013).","journal-title":"Bonekey Rep."},{"key":"92961_CR42","doi-asserted-by":"publisher","first-page":"644","DOI":"10.1016\/j.jmbbm.2016.09.014","volume":"65","author":"Y Chen","year":"2017","unstructured":"Chen, Y. et al. Micro-CT based finite element models of cancellous bone predict accurately displacement once the boundary condition is well replicated: A validation study. J. Mech. Behav. Biomed. 65, 644\u2013651. https:\/\/doi.org\/10.1016\/j.jmbbm.2016.09.014 (2017).","journal-title":"J. Mech. Behav. Biomed."},{"key":"92961_CR43","doi-asserted-by":"publisher","unstructured":"Wehrle, E., Paul, G. R., Betts, D. C., Kuhn, G. A. & M\u00fcller, R. Individualized cyclic mechanical loading improves callus properties in novel femur fracture loading model as assessed by time-lapsed in vivo imaging and real-time micro-finite element analysis. BioRxiv. https:\/\/doi.org\/10.1101\/2020.09.15.297861 (2019).","DOI":"10.1101\/2020.09.15.297861"},{"key":"92961_CR44","doi-asserted-by":"publisher","unstructured":"Malhotra, A., Walle, M., Paul, G. R., Kuhn, G. A. & M\u00fcller, R. Subject-specific adaptive mechanical loading improves bone healing in a mouse tail vertebral defect. bioRxiv. https:\/\/doi.org\/10.1038\/s41598-021-81132-8 (2021).","DOI":"10.1038\/s41598-021-81132-8"},{"key":"92961_CR45","doi-asserted-by":"publisher","first-page":"1790","DOI":"10.1002\/jor.23812","volume":"36","author":"P Tufekci","year":"2018","unstructured":"Tufekci, P. et al. Early mechanical stimulation only permits timely bone healing in sheep. J. Orthop. Res. 36, 1790\u20131796. https:\/\/doi.org\/10.1002\/jor.23812 (2018).","journal-title":"J. Orthop. Res."},{"key":"92961_CR46","doi-asserted-by":"publisher","unstructured":"Chao, E. Y. S., Aro, H. T., Lewallen, D. G. & Kelly, P. J. The effect of rigidity on fracture-healing in external fixation. Clin. Orthop. Relat. R, 24\u201335. https:\/\/doi.org\/10.1097\/00003086-198904000-00005 (1989).","DOI":"10.1097\/00003086-198904000-00005"},{"key":"92961_CR47","doi-asserted-by":"publisher","first-page":"539","DOI":"10.1080\/10255842.2012.699526","volume":"17","author":"FA Schulte","year":"2014","unstructured":"Schulte, F. A., Lambers, F. M., Mueller, T. L., Stauber, M. & Muller, R. Image interpolation allows accurate quantitative bone morphometry in registered micro-computed tomography scans. Comput. Methods Biomech. Biomed. Eng. 17, 539\u2013548. https:\/\/doi.org\/10.1080\/10255842.2012.699526 (2014).","journal-title":"Comput. Methods Biomech. Biomed. Eng."},{"key":"92961_CR48","doi-asserted-by":"publisher","first-page":"846","DOI":"10.1016\/j.parco.2011.08.001","volume":"37","author":"C Flaig","year":"2011","unstructured":"Flaig, C. & Arbenz, P. A scalable memory efficient multigrid solver for micro-finite element analyses based on CT images. Parallel Comput. 37, 846\u2013854. https:\/\/doi.org\/10.1016\/j.parco.2011.08.001 (2011).","journal-title":"Parallel Comput."},{"key":"92961_CR49","doi-asserted-by":"publisher","first-page":"842","DOI":"10.1016\/S8756-3282(02)00736-6","volume":"30","author":"W Pistoia","year":"2002","unstructured":"Pistoia, W. et al. Estimation of distal radius failure load with micro-finite element analysis models based on three-dimensional peripheral quantitative computed tomography images. Bone 30, 842\u2013848. https:\/\/doi.org\/10.1016\/S8756-3282(02)00736-6 (2002).","journal-title":"Bone"},{"key":"92961_CR50","doi-asserted-by":"publisher","first-page":"261","DOI":"10.1038\/s41592-019-0686-2","volume":"17","author":"P Virtanen","year":"2020","unstructured":"Virtanen, P. et al. SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nat. Methods 17, 261\u2013272. https:\/\/doi.org\/10.1038\/s41592-019-0686-2 (2020).","journal-title":"Nat. Methods"}],"container-title":["Scientific Reports"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.nature.com\/articles\/s41598-021-92961-y.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.nature.com\/articles\/s41598-021-92961-y","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.nature.com\/articles\/s41598-021-92961-y.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2022,12,3]],"date-time":"2022-12-03T05:42:57Z","timestamp":1670046177000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.nature.com\/articles\/s41598-021-92961-y"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021,6,29]]},"references-count":50,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2021,12]]}},"alternative-id":["92961"],"URL":"https:\/\/doi.org\/10.1038\/s41598-021-92961-y","relation":{"has-preprint":[{"id-type":"doi","id":"10.1101\/2020.09.02.274878","asserted-by":"object"}]},"ISSN":["2045-2322"],"issn-type":[{"value":"2045-2322","type":"electronic"}],"subject":[],"published":{"date-parts":[[2021,6,29]]},"assertion":[{"value":"4 September 2020","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"18 June 2021","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"29 June 2021","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"The authors declare no competing interests.","order":1,"name":"Ethics","group":{"name":"EthicsHeading","label":"Competing interests"}}],"article-number":"13511"}}