{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,25]],"date-time":"2026-03-25T06:05:13Z","timestamp":1774418713783,"version":"3.50.1"},"reference-count":69,"publisher":"Springer Science and Business Media LLC","issue":"4","license":[{"start":{"date-parts":[[2021,9,22]],"date-time":"2021-09-22T00:00:00Z","timestamp":1632268800000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2021,9,22]],"date-time":"2021-09-22T00:00:00Z","timestamp":1632268800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"}],"funder":[{"name":"Funda\u00e7\u00e3o para a Ci\u00eancia e a Tecnologia","award":["UID\/EMS\/50022\/2020"],"award-info":[{"award-number":["UID\/EMS\/50022\/2020"]}]},{"name":"Funda\u00e7\u00e3o para a Ci\u00eancia e a Tecnologia","award":["UIDB\/50021\/2020"],"award-info":[{"award-number":["UIDB\/50021\/2020"]}]},{"name":"fund\u00e7\u00e3ao para a ci\u00eancia e a tecnologia","award":["PTDC\/CCI-BIO\/4180\/2020"],"award-info":[{"award-number":["PTDC\/CCI-BIO\/4180\/2020"]}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["J. Math. Biol."],"published-print":{"date-parts":[[2021,10]]},"DOI":"10.1007\/s00285-021-01666-3","type":"journal-article","created":{"date-parts":[[2021,9,22]],"date-time":"2021-09-22T18:31:17Z","timestamp":1632335477000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["Dynamic modeling of bone remodeling, osteolytic metastasis and PK\/PD therapy: introducing variable order derivatives as a simplification technique"],"prefix":"10.1007","volume":"83","author":[{"given":"Joana Pinheiro","family":"Neto","sequence":"first","affiliation":[]},{"given":"Irina","family":"Alho","sequence":"additional","affiliation":[]},{"given":"Lu\u00eds","family":"Costa","sequence":"additional","affiliation":[]},{"given":"Sandra","family":"Casimiro","sequence":"additional","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0001-9388-4308","authenticated-orcid":false,"given":"Duarte","family":"Val\u00e9rio","sequence":"additional","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0002-1954-5487","authenticated-orcid":false,"given":"Susana","family":"Vinga","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2021,9,22]]},"reference":[{"key":"1666_CR1","doi-asserted-by":"publisher","first-page":"813","DOI":"10.1158\/0008-5472.CAN-13-2652","volume":"74","author":"A Araujo","year":"2014","unstructured":"Araujo A, Cook LM, Lynch CC, Basanta D (2014) An integrated computational model of the bone microenvironment in bone-metastatic prostate cancer. Cancer Res 74:813\u2013817","journal-title":"Cancer Res"},{"issue":"1","key":"1666_CR2","doi-asserted-by":"publisher","first-page":"28","DOI":"10.1186\/1745-6150-5-28","volume":"5","author":"BP Ayati","year":"2010","unstructured":"Ayati BP, Edwards CM, Webb GF, Wikswo JP (2010) A mathematical model of bone remodeling dynamics for normal bone cell populations and myeloma bone disease. Biol Direct 5(1):28","journal-title":"Biol Direct"},{"key":"1666_CR3","doi-asserted-by":"publisher","first-page":"51","DOI":"10.1016\/j.proeng.2015.07.009","volume":"110","author":"J Belinha","year":"2015","unstructured":"Belinha J, Dinis LMJS, Natal Jorge RM (2015) The meshless methods in the bone tissue remodelling analysis. Proc Eng 110:51\u201358","journal-title":"Proc Eng"},{"key":"1666_CR4","doi-asserted-by":"crossref","unstructured":"Bellido T, Plotkin LI, Bruzzaniti A (2014) Chapter 2\u2014bone cells. In: Basic and applied bone biology, chap.\u00a02. Academic Press, pp 27\u201345","DOI":"10.1016\/B978-0-12-416015-6.00002-2"},{"key":"1666_CR5","unstructured":"Boyce BF (2012) Bone biology ad pathology. In: Coleman R, Abrahamsson PA, Hadji P (eds) Handbook of cancer-related bone disease, 2nd edn. BioScientifica, pp 5\u20136"},{"key":"1666_CR6","doi-asserted-by":"publisher","first-page":"918","DOI":"10.1016\/j.bone.2010.12.009","volume":"48","author":"PR Buenzli","year":"2011","unstructured":"Buenzli PR, Pivonka P, Smith DW (2011) Spatio-temporal structure of cell distribution in cortical bone multicellular units: a mathematical model. Bone 48:918\u2013926","journal-title":"Bone"},{"issue":"1\u20132","key":"1666_CR7","doi-asserted-by":"publisher","first-page":"497","DOI":"10.1007\/s00285-018-1281-3","volume":"78","author":"A Camacho","year":"2019","unstructured":"Camacho A, Jerez S (2019) Bone metastasis treatment modeling via optimal control. J Math Biol 78(1\u20132):497\u2013526","journal-title":"J Math Biol"},{"key":"1666_CR8","unstructured":"Capacete JDC (2016) Biochemical and biomechanic integrated modeling of bone. Master thesis, Instituto Superior T\u00e9cnico"},{"key":"1666_CR9","doi-asserted-by":"publisher","first-page":"71","DOI":"10.1016\/j.mce.2009.07.004","volume":"310","author":"S Casimiro","year":"2009","unstructured":"Casimiro S, Guise TA, Chirgwin J (2009) Molecular and cellular endocrinology the critical role of the bone microenvironment in cancer metastases. Mol Cellular Endocrinol 310:71\u201381","journal-title":"Mol Cellular Endocrinol"},{"key":"1666_CR10","doi-asserted-by":"publisher","first-page":"E1415","DOI":"10.3390\/ijms17091415","volume":"17","author":"S Casimiro","year":"2016","unstructured":"Casimiro S, Ferreira AR, Mansinho A, Alho I, Costa L (2016) Molecular mechanisms of bone metastasis: which targets came from the bench to the bedside? Int J Mol Sci 17:E1415","journal-title":"Int J Mol Sci"},{"issue":"11","key":"1666_CR11","doi-asserted-by":"publisher","first-page":"1228","DOI":"10.1177\/009127002762491316","volume":"42","author":"T Chen","year":"2002","unstructured":"Chen T, Berenson J, Vescio R, Swift R, Gilchick A, Goodin S, LoRusso P, Ma P, Ravera C, Deckert F, Schran H, Seaman J, Skerjanec A (2002) Pharmacokinetics and pharmacodynamics of zoledronic acid in cancer patients with bone metastases. J Clin Pharmacol 42(11):1228\u20131236","journal-title":"J Clin Pharmacol"},{"issue":"6","key":"1666_CR12","doi-asserted-by":"publisher","first-page":"215","DOI":"10.1186\/bcr2781","volume":"12","author":"YC Chen","year":"2010","unstructured":"Chen YC, Sosnoski DM, Mastro AM (2010) Breast cancer metastasis to the bone: mechanisms of bone loss. Breast Cancer Res BCR 12(6):215","journal-title":"Breast Cancer Res BCR"},{"key":"1666_CR13","unstructured":"Christ F, Val\u00e9rio D, Vinga S (2016) Modelling bone metastases using fractional derivatives (submitted)"},{"key":"1666_CR14","unstructured":"Coelho RM, Vinga S, Val\u00e9rio D (2015) Cancersys\u2014multiscale modeling for personalized therapy of bone metastasis. Tech. rep., Instituto Superior T\u00e9cnico"},{"key":"1666_CR15","doi-asserted-by":"crossref","unstructured":"Coelho RM, Lemos Ja M, Alho I, Val\u00e9rio D, Ferreira AR, Costa L, Vinga S (2016a) Dynamic modeling of bone metastasis, microenvironment and therapy. integrating parathyroid hormone (PTH) effect, anti-resorptive and anti-cancer therapy. J Theor Biol 391:1\u201312","DOI":"10.1016\/j.jtbi.2015.11.024"},{"key":"1666_CR16","doi-asserted-by":"crossref","unstructured":"Coelho RM, Neto JP, Val\u00e9rio D, Vinga S (2016b) Dynamic biochemical and cellular models of bone physiology: integrating remodelling processes, tumor growth and therapy. In: Belinha J, Manzanares-C\u00e9spedes MC, Completo A (eds) The computational mechanics of bone tissue. Springer (2020) (in press)","DOI":"10.1007\/978-3-030-37541-6_4"},{"key":"1666_CR17","doi-asserted-by":"publisher","first-page":"991","DOI":"10.1242\/jcs.063032","volume":"124","author":"JC Crockett","year":"2011","unstructured":"Crockett JC, Rogers MJ, Coxon FP, Hocking LJ, Helfrich MH (2011) Bone remodelling at a glance. J Cell Science 124:991\u2013998","journal-title":"J Cell Science"},{"key":"1666_CR18","unstructured":"Dhillon S, Gill K (2006) Basic pharmacokinetics. In: Clinical pharmacokinetics, 1st edn, chap 1. Pharmaceutical Press"},{"issue":"4","key":"1666_CR19","doi-asserted-by":"publisher","first-page":"247","DOI":"10.2165\/11598090-000000000-00000","volume":"51","author":"L Gibiansky","year":"2012","unstructured":"Gibiansky L, Sutjandra L, Doshi S, Zheng J, Sohn W, Peterson M, Jang G, Chow A, P\u00e9rez-Ruixo J (2012) Population pharmacokinetic analysis of denosumab in patients with bone metastases from solid tumors. Clin Pharm 51(4):247\u2013260","journal-title":"Clin Pharm"},{"issue":"5","key":"1666_CR20","doi-asserted-by":"publisher","first-page":"E63884","DOI":"10.1371\/journal.pone.0063884","volume":"8","author":"JM Graham","year":"2013","unstructured":"Graham JM, Ayati BP, Holstein SA, Martin JA (2013) The role of osteocytes in targeted bone remodeling: a mathematical model. PLoS ONE 8(5):E63884","journal-title":"PLoS ONE"},{"key":"1666_CR21","unstructured":"Holen I (2012) Pathophysiology of bone metastases. In: Coleman R, Abrahamsson PA, Hadji P (eds) Handbook of cancer-related bone disease, 2nd edn. BioScientifica, p\u00a049"},{"issue":"18","key":"1666_CR22","doi-asserted-by":"publisher","first-page":"10768","DOI":"10.1111\/jcmm.15702","volume":"24","author":"F Huang","year":"2020","unstructured":"Huang F, Cao Y, Wu G, Chen J, Wang C, Lin W, Lan R, Wu B, Xie X, Hong J, Fu L (2020) BMP2 signalling activation enhances bone metastases of non-small cell lung cancer. J Cellular Mol Med 24(18):10768\u201310784","journal-title":"J Cellular Mol Med"},{"key":"1666_CR23","doi-asserted-by":"publisher","first-page":"12","DOI":"10.1016\/j.cam.2018.07.047","volume":"347","author":"S Jerez","year":"2019","unstructured":"Jerez S, Cant\u00f3 JA (2019) A stochastic model for the evolution of bone metastasis: persistence and recovery. J Comput Appl Math 347:12\u201323","journal-title":"J Comput Appl Math"},{"issue":"8","key":"1666_CR24","doi-asserted-by":"publisher","first-page":"3589","DOI":"10.1210\/en.2004-1642","volume":"146","author":"SV Komarova","year":"2005","unstructured":"Komarova SV (2005) Mathematical model of paracrine interactions between osteoclasts and osteoblasts predicts anabolic action of parathyroid hormone on bone. Endocrinology 146(8):3589\u20133595","journal-title":"Endocrinology"},{"issue":"2","key":"1666_CR25","doi-asserted-by":"publisher","first-page":"206","DOI":"10.1016\/S8756-3282(03)00157-1","volume":"33","author":"SV Komarova","year":"2003","unstructured":"Komarova SV, Smith RJ, Dixon SJ, Sims SM, Wahl LM (2003) Mathematical model predicts a critical role for osteoclast autocrine regulation in the control of bone remodeling. Bone 33(2):206\u2013215","journal-title":"Bone"},{"key":"1666_CR26","doi-asserted-by":"publisher","first-page":"293","DOI":"10.1016\/j.jtbi.2004.03.023","volume":"229","author":"V Lemaire","year":"2004","unstructured":"Lemaire V, Tobin FL, Greller LD, Cho CR, Suva LJ (2004) Modeling the interactions between osteoblast and osteoclast activities in bone remodeling. J Theor Biol 229:293\u2013309","journal-title":"J Theor Biol"},{"issue":"5","key":"1666_CR27","doi-asserted-by":"publisher","first-page":"483","DOI":"10.1007\/s10735-019-09842-y","volume":"50","author":"RF Li","year":"2019","unstructured":"Li RF, Zhang W, Man QW, Zhao YF, Zhao Y (2019) Tunneling nanotubes mediate intercellular communication between endothelial progenitor cells and osteoclast precursors. J Mol Hystol 50(5):483\u2013491","journal-title":"J Mol Hystol"},{"key":"1666_CR28","unstructured":"Lorenzo CF, Hartley TT (2002) Variable fractional order and distributed order operators. Tech. Rep. February, National Aeronautics and Space Administration (NASA)"},{"issue":"5","key":"1666_CR29","doi-asserted-by":"publisher","first-page":"510","DOI":"10.1124\/dmd.31.5.510","volume":"31","author":"DE Mager","year":"2003","unstructured":"Mager DE, Wyska E, Jusko WJ (2003) Minireview on diversity of mechanism based pharmacodynamics models. Drug Metab Dispos 31(5):510\u2013519","journal-title":"Drug Metab Dispos"},{"key":"1666_CR30","unstructured":"Magin RL (2006) Fractional calculus in bioengineering. Begell House Publishers Inc"},{"issue":"1","key":"1666_CR31","first-page":"18","volume":"19","author":"GR Mundy","year":"1998","unstructured":"Mundy GR, Calcium B (1998) Cancer and bone. Endocr Rev 19(1):18\u201354","journal-title":"Endocr Rev"},{"key":"1666_CR32","unstructured":"Neto JP, Coelho RM, Duarte C, Vinga S, Sierociuk D, Malesza W, Macias M, Dzielinski A (2017) Variable order differential models of bone remodelling. In: 20th IFAC world congress. IFAC\u2014International Federation of Automatic Control, Toulouse"},{"key":"1666_CR33","doi-asserted-by":"crossref","unstructured":"Neto JP, Val\u00e9rio D, Vinga S, Sierociuk D, Dzielinski A (2017) Simplifying biochemical tumorous bone remodeling models through variable order derivatives (submitted)","DOI":"10.1016\/j.camwa.2018.01.037"},{"key":"1666_CR34","doi-asserted-by":"crossref","unstructured":"Neto J, Val\u00e9rio D, Vinga S (2019) Variable-order derivatives and bone remodeling in the presence of metastases. In: Baleanu D, Lopes AM (eds) Handbook of fractional calculus with applications, vol 7. Applications in engineering, life and social sciences, part A. De Gruyter, pp 69\u201394","DOI":"10.1515\/9783110571905-005"},{"key":"1666_CR35","doi-asserted-by":"crossref","unstructured":"Ortigueira MD, Machado JT (2019) Fractional derivatives: the perspective of system theory. Mathematics 7(150)","DOI":"10.3390\/math7020150"},{"key":"1666_CR36","doi-asserted-by":"publisher","first-page":"231","DOI":"10.1016\/j.cnsns.2018.12.003","volume":"71","author":"MD Ortigueira","year":"2019","unstructured":"Ortigueira MD, Val\u00e9rio D, Machado JT (2019) Variable order fractional systems. Commun Nonlinear Sci Numer Simul 71:231\u2013243","journal-title":"Commun Nonlinear Sci Numer Simul"},{"key":"1666_CR37","doi-asserted-by":"crossref","unstructured":"Oyajobi B, O Garrett IR, Gupta A, Flores A, Esparza J, Mu\u00f1oz S, Zhao M, Mundy G (2007) Stimulation of new bone formation by the proteasome inhibitor, bortezomib: implications for myeloma bone disease. Br J Haematol 139:434\u2013438","DOI":"10.1111\/j.1365-2141.2007.06829.x"},{"issue":"3","key":"1666_CR38","doi-asserted-by":"publisher","first-page":"273","DOI":"10.1002\/jcb.240550303","volume":"55","author":"AM Parfitt","year":"1994","unstructured":"Parfitt AM (1994) Osteonal and hemi-osteonal remodeling: the spatial and temporal framework for signal traffic in adult human bone. J Cellular Biochem 55(3):273\u201386","journal-title":"J Cellular Biochem"},{"issue":"22","key":"1666_CR39","doi-asserted-by":"publisher","first-page":"4216","DOI":"10.1200\/JCO.2001.19.22.4216","volume":"19","author":"EA Perez","year":"2001","unstructured":"Perez EA, Vogel CL, Irwin DH, Kirshner JJ, Patel R (2001) Multicenter phase ii trial of weekly paclitaxel in women with metastatic breast cancer. J Clin Oncol 19(22):4216\u20134223","journal-title":"J Clin Oncol"},{"key":"1666_CR40","unstructured":"Petr\u00e1s I (2009) Stability of fractional-order systems with frational orders: a survey. Int J Theory Appl 12(3)"},{"key":"1666_CR41","doi-asserted-by":"crossref","unstructured":"Pinheiro JV, Lemos JM, Vinga S (2011) Nonlinear mpc of hiv-1 infection with periodic inputs.pdf. In: 50th IEEE conference on decision and control and European control conference (CDC-ECC), pp 65\u201370","DOI":"10.1109\/CDC.2011.6160806"},{"issue":"2","key":"1666_CR42","doi-asserted-by":"publisher","first-page":"181","DOI":"10.1016\/j.bone.2010.04.601","volume":"47","author":"P Pivonka","year":"2010","unstructured":"Pivonka P, Komarova SV (2010) Mathematical modeling in bone biology: from intracellular signaling to tissue mechanics. Bone 47(2):181\u2013189","journal-title":"Bone"},{"issue":"2","key":"1666_CR43","doi-asserted-by":"publisher","first-page":"249","DOI":"10.1016\/j.bone.2008.03.025","volume":"43","author":"P Pivonka","year":"2008","unstructured":"Pivonka P, Zimak J, Smith DW, Gardiner BS, Dunstan CR, Sims NA, Martin TJ, Mundy GR (2008) Model structure and control of bone remodeling: a theoretical study. Bone 43(2):249\u2013263","journal-title":"Bone"},{"issue":"2","key":"1666_CR44","doi-asserted-by":"publisher","first-page":"306","DOI":"10.1016\/j.jtbi.2009.09.021","volume":"262","author":"P Pivonka","year":"2010","unstructured":"Pivonka P, Zimak J, Smith D.W, Gardiner B.S, Dunstan C.R, Sims N.A, Martin TJ, Mundy GR (2010) Theoretical investigation of the role of the rank\/rankl\/opg sistem in bone remodeling.pdf. J Theor Biol 262(2):306\u2013316","journal-title":"J Theor Biol"},{"key":"1666_CR45","doi-asserted-by":"publisher","first-page":"134","DOI":"10.1016\/j.engstruct.2012.09.006","volume":"47","author":"P Pivonka","year":"2013","unstructured":"Pivonka P, Buenzli PR, Scheiner S, Hellmich C, Dunstan CR (2013) The influence of bone surface availability in bone remodelling-a mathematical model including coupled geometrical and biomechanical regulations of bone cells. Eng Struct 47:134\u2013147","journal-title":"Eng Struct"},{"issue":"33","key":"1666_CR46","doi-asserted-by":"publisher","first-page":"25103","DOI":"10.1074\/jbc.R109.041087","volume":"285","author":"LJ Raggatt","year":"2010","unstructured":"Raggatt LJ, Partridge NC (2010) Cellular and molecular mechanisms of bone remodeling. J Biol Chem 285(33):25103\u201325108","journal-title":"J Biol Chem"},{"issue":"50","key":"1666_CR47","first-page":"2453","volume":"4","author":"M Rahimy","year":"2010","unstructured":"Rahimy M (2010) Applications of fractional differential equations. Appl Math Sci 4(50):2453\u20132461","journal-title":"Appl Math Sci"},{"issue":"16","key":"1666_CR48","doi-asserted-by":"publisher","first-page":"1655","DOI":"10.1056\/NEJMra030831","volume":"360","author":"GD Roodman","year":"2004","unstructured":"Roodman GD (2004) Mechanisms of bone metastasis. New England J Med 360(16):1655\u20131664","journal-title":"New England J Med"},{"key":"1666_CR49","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1016\/j.gene.2005.10.028","volume":"367","author":"J Rubin","year":"2006","unstructured":"Rubin J, Rubin C, Jacobs CR (2006) Molecular pathways mediating mechanical signaling in bone. Gene 367:1\u201316","journal-title":"Gene"},{"key":"1666_CR50","unstructured":"Ryser MD (2011) Of bones and noises. Ph.D. thesis, McGill University"},{"issue":"5","key":"1666_CR51","doi-asserted-by":"publisher","first-page":"860","DOI":"10.1359\/jbmr.081229","volume":"24","author":"MD Ryser","year":"2009","unstructured":"Ryser MD, Nigam N, Komarova SV (2009) Mathematical modeling of spatio-temporal dynamics of a single bone multicellular unit. J Bone Mineral Res 24(5):860\u2013870","journal-title":"J Bone Mineral Res"},{"issue":"6","key":"1666_CR52","doi-asserted-by":"publisher","first-page":"1899","DOI":"10.1137\/090746094","volume":"70","author":"MD Ryser","year":"2010","unstructured":"Ryser MD, Komarova SV, Nigam N (2010) The cellular dynamics of bone remodeling: a mathematical model. SIAM J Appl Math 70(6):1899\u20131921","journal-title":"SIAM J Appl Math"},{"issue":"10","key":"1666_CR53","doi-asserted-by":"publisher","first-page":"E1002703","DOI":"10.1371\/journal.pcbi.1002703","volume":"8","author":"MD Ryser","year":"2012","unstructured":"Ryser MD, Qu Y, Komarova SV (2012) Osteoprotegerin in bone metastases: mathematical solution to the puzzle. PLoS Comput Biol 8(10):E1002703","journal-title":"PLoS Comput Biol"},{"issue":"3","key":"1666_CR54","doi-asserted-by":"publisher","first-page":"546","DOI":"10.1016\/0895-7177(88)90553-5","volume":"II","author":"MA Savageau","year":"1988","unstructured":"Savageau MA (1988) Introduction to s-systems and the underlying power-law formalism. Math Comput Modell II(3):546\u2013551","journal-title":"Math Comput Modell"},{"key":"1666_CR55","doi-asserted-by":"publisher","first-page":"181","DOI":"10.1016\/j.cma.2012.10.015","volume":"254","author":"S Scheiner","year":"2013","unstructured":"Scheiner S, Pivonka P, Hellmich C (2013) Coupling systems biology with multiscale mechanics, for computer simulations of bone remodeling. Comput Methods Appl Mech Eng 254:181\u2013196","journal-title":"Comput Methods Appl Mech Eng"},{"key":"1666_CR56","doi-asserted-by":"crossref","unstructured":"Sierociuk D, Dzieli\u0144ski A, Sarwas G, Petras I, Podlubny I, Skovranek T (2013) Modelling heat transfer in heterogeneous media using fractional calculus. Philos Trans Roy Soc 1\u201310","DOI":"10.1098\/rsta.2012.0146"},{"issue":"4","key":"1666_CR57","doi-asserted-by":"publisher","first-page":"1727","DOI":"10.1210\/en.2004-1211","volume":"146","author":"A Schneider","year":"2005","unstructured":"Schneider A, Kalikin LM, Mattos AC, Keller ET, Allen MJ, Pienta KJ, McCauley LK (2005) Bone turnover mediates preferential localization of prostate cancer in the skeleton. Endocrinology 146(4):1727\u201336","journal-title":"Endocrinology"},{"key":"1666_CR58","doi-asserted-by":"crossref","unstructured":"Sierociuk D, Malesza W, Macias M (2015a) Derivation, interpretation, and analog modelling of fractional variable order derivative definition. Appl Math Modell 39(13):3876\u20133888","DOI":"10.1016\/j.apm.2014.12.009"},{"key":"1666_CR59","doi-asserted-by":"crossref","unstructured":"Sierociuk D, Malesza W, Macias M (2015b) Fractional variable order derivative simulink user guide","DOI":"10.1007\/978-3-319-23039-9_3"},{"key":"1666_CR60","doi-asserted-by":"crossref","unstructured":"Sierociuk D, Malesza W, Macias M (2015c) On the recursive fractional variable-order derivative: Equivalent switching strategy, duality, and analog modeling. Circ Syst Sig Process 34(4):1077\u20131113","DOI":"10.1007\/s00034-014-9895-1"},{"key":"1666_CR61","unstructured":"Silbermann R, Roodman GD (2012) Bone health in myeloma. In: Coleman R, Abrahamsson PA, Hadji P (eds) Handbook of cancer-related bone disease, 2nd edn, chap\u00a09. BioScientifica, pp 159\u2013163"},{"key":"1666_CR62","doi-asserted-by":"publisher","first-page":"41","DOI":"10.1016\/j.coph.2015.03.005","volume":"22","author":"B Silva","year":"2015","unstructured":"Silva B, Bilezikian J (2015) Parathyroid hormone: anabolic and catabolic actions on the skeleton. Curr Opin Pharmacol 22:41\u201350","journal-title":"Curr Opin Pharmacol"},{"issue":"3","key":"1666_CR63","doi-asserted-by":"publisher","first-page":"477","DOI":"10.1111\/bcp.12355","volume":"78","author":"W Sohn","year":"2014","unstructured":"Sohn W, Simiens MA, Jaeger K, Hutton S, Jang G (2014) The pharmacokinetics and pharmacodyamics of denosumab in patients with advanced solid tumors and bone metastases: a systematic review. Br J Clin Pharmacol 78(3):477\u2013487","journal-title":"Br J Clin Pharmacol"},{"issue":"4","key":"1666_CR64","doi-asserted-by":"publisher","first-page":"208","DOI":"10.1038\/nrendo.2010.227","volume":"7","author":"LJ Suva","year":"2011","unstructured":"Suva LJ, Washam C, Nicholas RW, Griffin RJ (2011) Bone metastasis: mechanisms and therapeutic opportunities. Nat Rev Endocrinol 7(4):208\u2013218","journal-title":"Nat Rev Endocrinol"},{"issue":"3","key":"1666_CR65","first-page":"501","volume":"67","author":"D Val\u00e9rio","year":"2019","unstructured":"Val\u00e9rio D, Neto J, Vinga S (2019) Variable order 3D models of bone remodelling. Bull Polish Acad Sci Tech Sci 67(3):501\u2013508","journal-title":"Bull Polish Acad Sci Tech Sci"},{"key":"1666_CR66","doi-asserted-by":"crossref","unstructured":"Val\u00e9rio D, S\u00e1 da Costa J (2013) An introduction to fractional control. Inst Eng Technol","DOI":"10.1049\/PBCE091E"},{"issue":"11","key":"1666_CR67","doi-asserted-by":"publisher","first-page":"E27494","DOI":"10.1371\/journal.pone.0027494","volume":"6","author":"Y Wang","year":"2011","unstructured":"Wang Y, Pivonka P, Buenzli PR, Smith DW, Dunstan CR (2011) Computational modeling of interactions between multiple myeloma and the bone microenvironment. PLoS ONE 6(11):E27494","journal-title":"PLoS ONE"},{"key":"1666_CR68","unstructured":"Zometa\u00ae (2017) Zoledronic acid for injection. Novartis Pharmaceuticals Corporation, East Hanover, NJ"},{"issue":"4","key":"1666_CR69","doi-asserted-by":"publisher","first-page":"910","DOI":"10.1016\/j.bone.2010.12.010","volume":"48","author":"M Zumsande","year":"2011","unstructured":"Zumsande M, Stiefs D, Siegmund S, Gross T (2011) General analysis of mathematical models for bone remodeling. Bone 48(4):910\u2013917","journal-title":"Bone"}],"container-title":["Journal of Mathematical Biology"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s00285-021-01666-3.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s00285-021-01666-3\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s00285-021-01666-3.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,2,6]],"date-time":"2023-02-06T19:03:49Z","timestamp":1675710229000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s00285-021-01666-3"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021,9,22]]},"references-count":69,"journal-issue":{"issue":"4","published-print":{"date-parts":[[2021,10]]}},"alternative-id":["1666"],"URL":"https:\/\/doi.org\/10.1007\/s00285-021-01666-3","relation":{},"ISSN":["0303-6812","1432-1416"],"issn-type":[{"value":"0303-6812","type":"print"},{"value":"1432-1416","type":"electronic"}],"subject":[],"published":{"date-parts":[[2021,9,22]]},"assertion":[{"value":"3 December 2020","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"4 September 2021","order":2,"name":"revised","label":"Revised","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"8 September 2021","order":3,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"22 September 2021","order":4,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}],"article-number":"39"}}