Improving the Process of Adjusting the Parameters of Finite Element Models of Healthy Human Intervertebral Discs by the Multi-Response Surface Method.

The kinematic behavior of models that are based on the finite element method (FEM) for modeling the human body depends greatly on an accurate estimate of the parameters that define such models. This task is complex, and any small difference between the actual biomaterial model and the simulation model based on FEM can be amplified enormously in the presence of nonlinearities. The current paper attempts to demonstrate how a combination of the FEM and the MRS methods with desirability functions can be used to obtain the material parameters that are most appropriate for use in defining the behavior of Finite Element (FE) models of the healthy human lumbar intervertebral disc (IVD). The FE model parameters were adjusted on the basis of experimental data from selected standard tests (compression, flexion, extension, shear, lateral bending, and torsion) and were developed as follows: First, three-dimensional parameterized FE models were generated on the basis of the mentioned standard tests. Then, 11 parameters were selected to define the proposed parameterized FE models. For each of the standard tests, regression models were generated using MRS to model the six stiffness and nine bulges of the healthy IVD models that were created by changing the parameters of the FE models. The optimal combination of the 11 parameters was based on three different adjustment criteria. The latter, in turn, were based on the combination of stiffness and bulges that were obtained from the standard test FE simulations. The first adjustment criteria considered stiffness and bulges to be equally important in the adjustment of FE model parameters. The second adjustment criteria considered stiffness as most important, whereas the third considered the bulges to be most important. The proposed adjustment methods were applied to a medium-sized human IVD that corresponded to the L3-L4 lumbar level with standard dimensions of width = 50 mm, depth = 35 mm, and height = 10 mm. Agreement between the kinematic behavior that was obtained with the optimized parameters and that obtained from the literature demonstrated that the proposed method is a powerful tool with which to adjust healthy IVD FE models when there are many parameters, stiffnesses, and bulges to which the models must adjust.

[1]  Idsart Kingma,et al.  In Vitro Biomechanical Characteristics of the Spine: A Comparison Between Human and Porcine Spinal Segments , 2010, Spine.

[2]  Rubén Lostado-Lorza,et al.  A Proposed Methodology for Setting the Finite Element Models Based on Healthy Human Intervertebral Lumbar Discs , 2016, HAIS.

[3]  Avinash G Patwardhan,et al.  Effect of compressive follower preload on the flexion–extension response of the human lumbar spine , 2003, Journal of orthopaedic research : official publication of the Orthopaedic Research Society.

[4]  Antonius Rohlmann,et al.  Analysis of the influence of disc degeneration on the mechanical behaviour of a lumbar motion segment using the finite element method. , 2006, Journal of biomechanics.

[5]  M. Adams,et al.  The Resistance to Flexion of the Lumbar Intervertebral Joint , 1980, Spine.

[6]  M. Prado,et al.  Calibration of the finite element model of a lumbar functional spinal unit using an optimization technique based on differential evolution. , 2011, Medical engineering & physics.

[7]  A. Nachemson,et al.  Lumbar intradiscal pressure. Experimental studies on post-mortem material. , 1960, Acta orthopaedica Scandinavica. Supplementum.

[8]  A. M. Ahmed,et al.  Stress analysis of the lumbar disc-body unit in compression. A three-dimensional nonlinear finite element study. , 1984, Spine.

[9]  A. Shirazi-Adl Nonlinear stress analysis of the whole lumbar spine in torsion--mechanics of facet articulation. , 1994, Journal of biomechanics.

[10]  Eliseo P. Vergara González,et al.  An Improvement in Biodiesel Production from Waste Cooking Oil by Applying Thought Multi-Response Surface Methodology Using Desirability Functions , 2017 .

[11]  M. Pearcy,et al.  Three-Dimensional X-ray Analysis of Normal Movement in the Lumbar Spine , 1984, Spine.

[12]  A. Schultz,et al.  Bulging of lumbar intervertebral disks. , 1982, Journal of biomechanical engineering.

[13]  T. Keller,et al.  Mechanical behavior of the human lumbar spine. I. Creep analysis during static compressive loading , 1987, Journal of orthopaedic research : official publication of the Orthopaedic Research Society.

[14]  Mark D. Brown,et al.  Intraoperative Measurement of Lumbar Spine Motion Segment Stiffness , 2002, Spine.

[15]  D. Sengupta Clinical Biomechanics of the Spine. , 2017, Spine.

[16]  M M Panjabi,et al.  Three-Dimensional Movements of the Whole Lumbar Spine and Lumbosacral Joint , 1989, Spine.

[17]  Olivier Palombi,et al.  Construction and Validation of a Hybrid Lumbar Spine Model for the Fast Evaluation of Intradiscal Pressure and Mobility , 2015 .

[18]  G. J. Verkerke,et al.  Biomechanical Characteristics of Different Regions of the Human Spine: An In Vitro Study on Multilevel Spinal Segments , 2009, Spine.

[20]  M. Panjabi The stabilizing system of the spine. Part I. Function, dysfunction, adaptation, and enhancement. , 1992, Journal of spinal disorders.

[21]  Javier Domínguez-Hernández,et al.  The use of response surface methodology to improve the thermal transmittance of lightweight concrete hollow bricks by FEM , 2014 .

[22]  A. M. Ahmed,et al.  Some static mechanical properties of the lumbar intervertebral joint, intact and injured. , 1982, Journal of biomechanical engineering.

[23]  Ruben Lostado,et al.  Optimization of operating conditions for a double-row tapered roller bearing , 2016 .

[24]  H. Wilke,et al.  Numerical Prediction of the Mechanical Failure of the Intervertebral Disc under Complex Loading Conditions , 2017, Materials.

[25]  D S McNally,et al.  'Stress' distributions inside intervertebral discs. The effects of age and degeneration. , 1996, The Journal of bone and joint surgery. British volume.

[26]  Ardeshir Bahreininejad,et al.  Optimum gradient material for a functionally graded dental implant using metaheuristic algorithms. , 2011, Journal of the mechanical behavior of biomedical materials.

[27]  V. Haughton,et al.  Intervertebral disk appearance correlated with stiffness of lumbar spinal motion segments. , 1999, AJNR. American journal of neuroradiology.

[28]  Michael V. Swain,et al.  Surface morphology optimization for osseointegration of coated implants. , 2010, Biomaterials.

[29]  Mohamed Azaouzi,et al.  Optimal design of multi-step stamping tools based on response surface method , 2012, Simul. Model. Pract. Theory.

[30]  G. Bergmann,et al.  Effects of fusion-bone stiffness on the mechanical behavior of the lumbar spine after vertebral body replacement. , 2006, Clinical biomechanics.

[31]  A. Gelman Analysis of variance: Why it is more important than ever? , 2005, math/0504499.

[32]  N. Langrana,et al.  Role of Ligaments and Facets in Lumbar Spinal Stability , 1995, Spine.

[33]  J. I The Design of Experiments , 1936, Nature.

[34]  Alexander Tsouknidas,et al.  A finite element model technique to determine the mechanical response of a lumbar spine segment under complex loads. , 2012, Journal of applied biomechanics.

[35]  M. Panjabi,et al.  Effects of Disc Injury on Mechanical Behavior of the Human Spine , 1984, Spine.

[36]  Volumetric locking in finite elements , 2008 .

[37]  M M Panjabi,et al.  The Basic Kinematics of the Human Spine: A Review of Past and Current Knowledge , 1978, Spine.

[38]  Michael V. Swain,et al.  Design optimization of functionally graded dental implant for bone remodeling , 2009 .

[39]  H. Farfan,et al.  The effects of torsion on the lumbar intervertebral joints: the role of torsion in the production of disc degeneration. , 1970, The Journal of bone and joint surgery. American volume.

[40]  King H. Yang,et al.  Mechanism of facet load transmission as a hypothesis for low-back pain. , 1984, Spine.

[41]  S. Rolander,et al.  Deformation and fracture of the lumbar vertebral end plate. , 1975, The Orthopedic clinics of North America.

[42]  A B Schultz,et al.  Analog studies of forces in the human spine: mechanical properties and motion segment behavior. , 1973, Journal of biomechanics.

[43]  V C Mow,et al.  Degeneration affects the anisotropic and nonlinear behaviors of human anulus fibrosus in compression. , 1998, Journal of biomechanics.

[44]  María Ángeles Martínez Calvo,et al.  Improvement in the Design of Welded Joints of EN 235JR Low Carbon Steel by Multiple Response Surface Methodology , 2016 .

[45]  J. Nemes,et al.  Load shift of the intervertebral disc after a vertebroplasty: a finite-element study , 2003, European Spine Journal.

[46]  P Brinckmann,et al.  Injury of the Annulus Fibrosus and Disc Protrusions: An In Vitro Investigation on Human Lumbar Discs , 1986, Spine.

[47]  A Shirazi-Adl,et al.  Mechanical Response of a Lumbar Motion Segment in Axial Torque Alone and Combined with Compression , 1986, Spine.

[48]  A B Schultz,et al.  Finite element stress analysis of an intervertebral disc. , 1974, Journal of biomechanics.

[49]  Lutz Claes,et al.  Application of a new calibration method for a three-dimensional finite element model of a human lumbar annulus fibrosus. , 2006, Clinical biomechanics.

[50]  M. Panjabi,et al.  Functional Radiographic Diagnosis of the Lumbar Spine: Flexion—Extension and Lateral Bending , 1991, Spine.

[51]  Tshilidzi Marwala,et al.  Finite-element-model Updating Using Computional Intelligence Techniques , 2010 .

[52]  Adams Ma,et al.  The relevance of torsion to the mechanical derangement of the lumbar spine. , 1981 .

[53]  C. Hirsch,et al.  Anatomical and clinical studies on lumbar disc degeneration. , 1992, Acta orthopaedica Scandinavica.

[54]  A B Schultz,et al.  Mechanical properties of lumbar spine motion segments under large loads. , 1986, Journal of biomechanics.

[55]  M. Shoham,et al.  Morphometric Study of the Human Lumbar Spine for Operation–Workspace Specifications , 2001, Spine.

[56]  N. Broom,et al.  Biomechanics of load-bearing of the intervertebral disc: an experimental and finite element model. , 1997, Medical engineering & physics.

[57]  Jason P. Halloran,et al.  Explicit finite element modeling of total knee replacement mechanics. , 2005, Journal of biomechanics.

[58]  Narayan Yoganandan,et al.  Moment-rotation responses of the human lumbosacral spinal column. , 2007, Journal of biomechanics.

[59]  D. S. Hickey,et al.  Radial bulging of the annulus fibrosus during compression of the intervertebral disc. , 1983, Journal of biomechanics.

[60]  W J VIRGIN,et al.  Experimental investigations into the physical properties of the intervertebral disc. , 1951, The Journal of bone and joint surgery. British volume.

[61]  Russell V. Lenth,et al.  Response-Surface Methods in R, Using rsm , 2009 .

[62]  H S Amonoo-Kuofi,et al.  Morphometric changes in the heights and anteroposterior diameters of the lumbar intervertebral discs with age. , 1991, Journal of anatomy.

[63]  G. Guitiérrez,et al.  Biomechanical study of intervertebral disc degeneration , 2012 .

[64]  M Nissan,et al.  Dimensions of human lumbar vertebrae in the sagittal plane. , 1986, Journal of biomechanics.

[65]  Guilhem Denoziere Numerical Modeling of a Ligamentous Lumbar Motion Segment , 2004 .

[66]  A. Schultz,et al.  Mechanical Properties of Human Lumbar Spine Motion Segments: Influences of Age, Sex, Disc Level, and Degeneration , 1979, Spine.

[67]  Luis Gracia,et al.  Development and Kinematic Verification of a Finite Element Model for the Lumbar Spine: Application to Disc Degeneration , 2012, BioMed research international.

[68]  Ming Zhang,et al.  Three-dimensional finite element analysis of the foot during standing--a material sensitivity study. , 2005, Journal of biomechanics.

[69]  V. Goel,et al.  Load-Sharing Between Anterior and Posterior Elements in a Lumbar Motion Segment Implanted With an Artificial Disc , 2001, Spine.

[70]  Ruben Lostado,et al.  Design and optimization of an electromagnetic servo braking system combining finite element analysis and weight-based multi-objective genetic algorithms , 2016, Journal of Mechanical Science and Technology.

[71]  Gerhard A. Holzapfel,et al.  An Anisotropic Model for Annulus Tissue and Enhanced Finite Element Analyses of Intact Lumbar Disc Bodies , 2001 .

[72]  Amonoo-Kuofi Hs,et al.  Morphometric changes in the heights and anteroposterior diameters of the lumbar intervertebral discs with age. , 1991 .

[73]  A. Schultz,et al.  Load-displacement properties of lower cervical spine motion segments. , 1988, Journal of biomechanics.

[74]  K Kedzior,et al.  A Biomechanical Model of the Human Spinal System , 1991, Proceedings of the Institution of Mechanical Engineers. Part H, Journal of engineering in medicine.

[75]  G. diZerega,et al.  Use of Temporary Implantable Biomaterials to Reduce Leg Pain and Back Pain in Patients with Sciatica and Lumbar Disc Herniation , 2010, Materials.

[76]  Michael A. Adams,et al.  'Stress' distributions inside intervertebral discs , 1996 .

[77]  Hutton Wc,et al.  Do bending, twisting, and diurnal fluid changes in the disc affect the propensity to prolapse? A viscoelastic finite element model , 1996 .

[78]  M. F. Eijkelkamp On the development of an artificial intervertebral disc , 2002 .

[79]  Mack Gardner-Morse,et al.  Measurement of a spinal motion segment stiffness matrix. , 2002, Journal of biomechanics.

[80]  A B Schultz,et al.  Nonlinear behavior of the human intervertebral disc under axial load. , 1976, Journal of Biomechanics.

[81]  Albert B. Schultz,et al.  Mechanical Properties of Human Lumbar Spine Motion Segments—Part II: Responses in Compression and Shear; Influence of Gross Morphology , 1979 .

[82]  F Lavaste,et al.  Three-dimensional geometrical and mechanical modelling of the lumbar spine. , 1992, Journal of biomechanics.

[83]  M. Pearcy,et al.  Lumbar Intervertebral Disc Heights in Normal Subjects and Patients with Disc Herniation , 1985, Spine.

[84]  P Brinckmann,et al.  Change of disc height, radial disc bulge, and intradiscal pressure from discectomy. An in vitro investigation on human lumbar discs. , 1991, Spine.

[85]  Lutz Claes,et al.  Stepwise reduction of functional spinal structures increase range of motion and change lordosis angle. , 2007, Journal of biomechanics.

[86]  Ho-Joong Kim,et al.  Finite Element Analysis for Comparison of Spinous Process Osteotomies Technique with Conventional Laminectomy as Lumbar Decompression Procedure , 2014, Yonsei medical journal.

[87]  Farzam Farahmand,et al.  Multi-objective design optimization of functionally graded material for the femoral component of a total knee replacement , 2014 .

[88]  Rubén Lostado-Lorza,et al.  Combining soft computing techniques and the finite element method to design and optimize complex welded products , 2015, Integr. Comput. Aided Eng..

[89]  Ariel Fuerte Hernandez,et al.  CARACTERIZACION DE VERTEBRAS PORCINAS PARA SU USO EN APLICACIONES BIOMECANICAS , 2010 .

[90]  W C Hutton,et al.  Do Bending, Twisting, and Diurnal Fluid Changes in the Disc Affect the Propensity to Prolapse? A Viscoelastic Finite Element Model , 1996, Spine.

[91]  Margaret J. Robertson,et al.  Design and Analysis of Experiments , 2006, Handbook of statistics.

[92]  T. Goswami,et al.  Implant material properties and their role in micromotion and failure in total hip arthroplasty , 2012 .

[93]  H. Broman,et al.  Axial stiffness of human lumbar motion segments, force dependence. , 1998, Journal of biomechanics.

[94]  Y K Liu,et al.  The resistance of the lumbar spine to direct shear. , 1975, The Orthopedic clinics of North America.

[95]  A. Mcgregor,et al.  Geometrical dimensions of the lower lumbar vertebrae – analysis of data from digitised CT images , 2000, European Spine Journal.

[96]  M. Adams,et al.  The Relevance of Torsion to the Mechanical Derangement of the Lumbar Spine , 1981, Spine.

[97]  Hans Müller-Storz,et al.  The influence of cancellous bone density on load sharing in human lumbar spine: a comparison between an intact and a surgically altered motion segment , 2001, European Spine Journal.

[98]  G. Derringer,et al.  Simultaneous Optimization of Several Response Variables , 1980 .

[99]  Idsart Kingma,et al.  Contribution of vertebral [corrected] bodies, endplates, and intervertebral discs to the compression creep of spinal motion segments. , 2008, Journal of biomechanics.

[100]  T. C. Howard,et al.  Roentgenographic Evaluation of Lumbar Spine Flexion‐Extension in Asymptomatic Individuals , 1989, Spine.

[101]  P Brinckmann,et al.  The Influence of Vertebral Body Fracture, Intradiscal Injection, and Partial Discectomy on the Radial Bulge and Height of Human Lumbar Discs , 1985, Spine.

[102]  C HIRSCH,et al.  New observations on the mechanical behavior of lumbar discs. , 1954, Acta orthopaedica Scandinavica.

[103]  E Schneider,et al.  Structure and Function of Vertebral Trabecular Bone , 1997, Spine.

[104]  F. J. Martinez-de-Pison,et al.  Combining regression trees and the finite element method to define stress models of highly non-linear mechanical systems , 2009 .

[105]  T. Brown,et al.  Some mechanical tests on the lumbosacral spine with particular reference to the intervertebral discs; a preliminary report. , 1957, The Journal of bone and joint surgery. American volume.

[106]  Shaker A. Meguid,et al.  Three-Dimensional Finite Element Analysis of Prosthetic Finger Joint Implants , 2004 .

[107]  A. Schultz,et al.  Mechanical Properties of Human Lumbar Spine Motion Segments—Part I: Responses in Flexion, Extension, Lateral Bending, and Torsion , 1979 .

[108]  D. Ku,et al.  Biomechanical comparison between fusion of two vertebrae and implantation of an artificial intervertebral disc. , 2006, Journal of biomechanics.

[109]  V. Goel,et al.  Biomechanics of two-level Charité artificial disc placement in comparison to fusion plus single-level disc placement combination. , 2006, The spine journal : official journal of the North American Spine Society.

[110]  I. Stokes,et al.  Structural behavior of human lumbar spinal motion segments. , 2004, Journal of biomechanics.

[111]  G. Box,et al.  On the Experimental Attainment of Optimum Conditions , 1951 .

[112]  G B Andersson,et al.  The influence of lumbar disc height and cross-sectional area on the mechanical response of the disc to physiologic loading. , 1999, Spine.

[113]  Narayan Yoganandan,et al.  Validation of a clinical finite element model of the human lumbosacral spine , 2006, Medical and Biological Engineering and Computing.

[114]  B Weisse,et al.  Determination of the translational and rotational stiffnesses of an L4-L5 functional spinal unit using a specimen-specific finite element model. , 2012, Journal of the mechanical behavior of biomedical materials.

[115]  L. Claes,et al.  Intradiscal Pressure, Shear Strain, and Fiber Strain in the Intervertebral Disc Under Combined Loading , 2007, Spine.