A finite element study and mathematical modeling of lumbar pedicle screw along with various design parameters

Published:September 26, 2022DOI:



      Lumbar pedicle screw is one of the most common and important elements in the field of lumbar surgery. It plays a great role in rectifying the spinal alignment and stabilization providing strength and stability to the affected area of spine. In spinal surgery, minimally invasive techniques and minor incisions are made which makes it less painful for the patients than the traditional methods. Moreover, the screws are not needed to be removed after the surgery which is yet another great advantage of the pedicle screw.


      In this study, 3D Finite Element (FE) model of human L4 vertebrae is taken for analysis using image processing tool. Pedicle screw design with varying mechanical and geometrical properties has been carried out at different applied loads on it along with considering the effect of frictional forces between all contact surfaces.


      Mathematical relationship among stress, strain, pitch of the screw and diameter have been developed for different thread profiles which will be beneficial for researchers for further development of pedicle screw implants.


      Results from the different analysis shows that bending stress on the screw for different loads at triangular pitch is higher than the trapezoidal. Hence, trapezoidal thread is efficacious than triangular thread. In case of vertebral bone, the magnitude of stress is less for trapezoidal screw than triangular and stress has a linear relationship with pitch length. In term of strain, triangular thread develops more strain than trapezoidal thread. A set of mathematical relation has been developed for different thread profile based on pitch length, stress and strain which gives the idea about von Mises stress and strain.


      To read this article in full you will need to make a payment

      Purchase one-time access:

      Academic & Personal: 24 hour online accessCorporate R&D Professionals: 24 hour online access
      One-time access price info
      • For academic or personal research use, select 'Academic and Personal'
      • For corporate R&D use, select 'Corporate R&D Professionals'


      Subscribe to Journal of Orthopaedic Science
      Already a print subscriber? Claim online access
      Already an online subscriber? Sign in
      Institutional Access: Sign in to ScienceDirect


        • Defino H.
        • Galbusera F.
        • Wilke H.J.
        Pedicle Screw Fixation and Design.
        in: Boden Scott D. Lumbar spine online textbook, Section 11, Chapter 9. DT Internet publisher - ISSLS, Wheeless Online, 2020
        • Costa F.
        • Villa T.
        • Anasetti F.
        • Tomei M.
        • Ortolina A.
        • Cardia A.
        • et al.
        Primary stability of pedicle screws depends on the screw positioning and alignment.
        Spine J. 2013 Dec 1; 13: 1934-1939
        • Wegmann K.
        • Gick S.
        • Heidemann C.
        • Pennig D.
        • Neiss W.F.
        • Müller L.P.
        • et al.
        Biomechanical evaluation of the primary stability of pedicle screws after augmentation with an innovative bone stabilizing system.
        Arch Orthop Trauma Surg. 2013 Nov; 133: 1493-1499
        • Schmidt R.
        • Wilke H.J.
        • Claes L.
        • Puhl W.
        • Richter M.
        Pedicle screws enhance primary stability in multilevel cervical corpectomies: biomechanical in vitro comparison of different implants including constrained and nonconstrained posterior instumentations.
        Spine. 2003 Aug 15; 28: 1821-1828
        • Jain P.
        • Rana M.
        • Biswas J.K.
        • Khan M.R.
        Biomechanics of spinal implants—a review.
        Biomed Phys Eng Exp. 2020 Jun 26; 6042002
        • Varghese V.
        • Kumar G.S.
        • Krishnan V.
        Effect of various factors on pull out strength of pedicle screw in normal and osteoporotic cancellous bone models.
        Med Eng Phys. 2017 Feb 1; 40: 28-38
        • Katonis P.
        • Christoforakis J.
        • Aligizakis A.C.
        • Papadopoulos C.
        • Sapkas G.
        • Hadjipavlou A.
        Complications and problems related to pedicle screw fixation of the spine.
        Clin Orthop Relat Res. 2003 Jun 1; 411: 86-94
        • Çetin E.
        • Özkaya M.
        • Güler Ü.Ö.
        • Acaroğlu E.
        • Demir T.
        Evaluation of the effect of fixation angle between polyaxial pedicle screw head and rod on the failure of screw-rod connection.
        App Bion Biomech. 2015 Jan 1; : 1-9
        • Matsukawa K.
        • Yato Y.
        • Imabayashi H.
        Impact of screw diameter and length on pedicle screw fixation strength in osteoporotic vertebrae: a finite element analysis.
        Asian Spine J. 2021 Oct; 15: 566
        • Liu M.Y.
        • Tsai T.T.
        • Lai P.L.
        • Hsieh M.K.
        • Chen L.H.
        • Tai C.L.
        Biomechanical comparison of pedicle screw fixation strength in synthetic bones: effects of screw shape, core/thread profile and cement augmentation.
        PLoS One. 2020 Feb; 15 (e0229328): 1-15
        • Xu M.
        • Yang J.
        • Lieberman I.H.
        • Haddas R.
        Finite element method-based study of pedicle screw–bone connection in pullout test and physiological spinal loads.
        Med Eng Phys. 2019 May 1; 67: 11-21
        • Chevalier Y.
        • Matsuura M.
        • Krüger S.
        • Fleege C.
        • Rickert M.
        • Rauschmann M.
        • et al.
        Micro-CT and micro-FE analysis of pedicle screw fixation under different loading conditions.
        J Biomech. 2018 Mar 21; 70: 204-211
        • Shea T.M.
        • Laun J.
        • Gonzalez-Blohm S.A.
        • Doulgeris J.J.
        • Lee W.E.
        • Aghayev K.
        • et al.
        Designs and techniques that improve the pullout strength of pedicle screws in osteoporotic vertebrae: current status.
        BioMed Res Int. 2014 Oct; 2014
        • Daud R.
        • Nurliyana H.
        • Ayu H.M.
        • Shah A.
        Fatigue analysis of cannulated pedicle screw.
        Int J Eng Trends Technol. 2020 Oct 25; : 87-91
        • Sensale M.
        • Vendeuvre T.
        • Schilling C.
        • Grupp T.
        • Rochette M.
        • Dall'Ara E.
        Patient-specific finite element models of posterior pedicle screw fixation: effect of screw's size and geometry.
        Front Bioeng Biotechnol. 2021 Mar 10; 9: 175
        • Ringel F.
        • Stoffel M.
        • Stüer C.
        • Meyer B.
        Minimally invasive transmuscular pedicle screw fixation of the thoracic and lumbar spine.
        Oper Neurosur. 2006 Jan; 59 (ONS-361)
        • Okuyama K.
        • Abe E.
        • Suzuki T.
        • Tamura Y.
        • Chiba M.
        • Sato K.
        Can insertional torque predict screw loosening and related failures?: an in vivo study of pedicle screw fixation augmenting posterior lumbar interbody fusion.
        Spine. 2000 Apr 1; 25: 858-864
        • Odeh K.
        • Rosinski A.
        • Leasure J.
        • Kondrashov D.
        Pedicle screws challenged: lumbar cortical density and thickness are greater in the posterior elements than in the pedicles.
        Global Spine J. 2021 Jan; 11: 34-43
        • Sandén B.
        • Olerud C.
        • Larsson S.
        • Robinson Y.
        Insertion torque is not a good predictor of pedicle screw loosening after spinal instrumentation: a prospective study in 8 patients.
        Patient Saf Sur. 2010 Dec; 4: 1-5
        • Inoue G.
        • Ueno M.
        • Nakazawa T.
        • Imura T.
        • Saito W.
        • Uchida K.
        • et al.
        Teriparatide increases the insertional torque of pedicle screws during fusion surgery in patients with postmenopausal osteoporosis.
        J Neurosurg Spine. 2014 Sep 1; 21: 425-431
        • Kim K.
        • Park W.M.
        • Kim Y.H.
        • Lee S.
        Stress analysis in a pedicle screw fixation system with flexible rods in the lumbar spine.
        Proc IMechE, Proc Inst Mech Eng H. 2010 Mar 1; 224: 477-485
        • Biswas J.K.
        • Roy S.
        • Pradhan R.
        • Rana M.
        • Majumdar S.
        Effects of cervical disc replacement and anterior fusion for different bone conditions: a finite element study.
        Int J Multiscale Comput Eng. 2019; 17
        • Rana M.
        • Biswas J.K.
        • Roy S.
        • Biswas P.
        • Karmakar S.K.
        • Roychowdhury A.
        Motion analysis of lumbar vertebrae for different rod materials and flexible rod device–An experimental and finite element study.
        Biocybern Biomed Eng. 2020 Jan 1; 40: 415-425
        • Newcomb A.G.
        • Baek S.
        • Kelly B.P.
        • Crawford N.R.
        Effect of screw position on load transfer in lumbar pedicle screws: a non-idealized finite element analysis.
        Comput Methods Biomech Biomed Eng. 2017 Jan 25; 20: 182-192
        • Liu J.M.
        • Zhang Y.
        • Zhou Y.
        • Chen X.Y.
        • Huang S.H.
        • Hua Z.K.
        • et al.
        The effect of screw tunnels on the biomechanical stability of vertebral body after pedicle screws removal: a finite element analysis.
        Int Orthop. 2017 Jun; 41: 1183-1187
        • Matsukawa K.
        • Yato Y.
        • Imabayashi H.
        • Hosogane N.
        • Abe Y.
        • Asazuma T.
        • et al.
        Biomechanical evaluation of fixation strength among different sizes of pedicle screws using the cortical bone trajectory: what is the ideal screw size for optimal fixation?.
        Acta Neurochir. 2016 Mar 1; 158: 465-471
        • Landi A.
        Elastic resistance of the spine: why does motion preservation surgery almost fail?.
        World J Clin Cases: WJCC. 2013 Jul 16; 1: 134
        • Biswas J.K.
        • Rana M.
        • Majumder S.
        • Karmakar S.K.
        • Roychowdhury A.
        Effect of two-level pedicle-screw fixation with different rod materials on lumbar spine: a finite element study.
        J Orthop Sci. 2018 Mar 1; 23: 258-265
        • Chen S.I.
        • Lin R.M.
        • Chang C.H.
        Biomechanical investigation of pedicle screw–vertebrae complex: a finite element approach using bonded and contact interface conditions.
        Med Eng Phys. 2003 May 1; 25: 275-282
        • Rohlmann A.
        • Graichen F.
        • Weber U.
        • Bergmann G.
        Monitoring in vivo implant loads with a telemeterized internal spinal fixation device.
        Spine. 2000 Dec 1; 25: 2981-2986
        • Rohlmann A.
        • Graichen F.
        • Bergmann G.
        Influence of load carrying on loads in internal spinal fixators.
        J Biomech. 2000 Sep 1; 33: 1099-1104


      Major diameter
      Pitch length
      Stress on screw
      Stress on bone
      Strain on bone