1. ARBEITSGRUPPE FÜR BIOMECHANIK / BIOMECHANICS GROUP Institut für Rechtsmedizin / Institute of Legal Medicine Review Positioning and Scaling Tools Preliminary Draft Goteborg, 10th of September, 2013

2. ARBEITSGRUPPE FÜR BIOMECHANIK / BIOMECHANICS GROUP Institut für Rechtsmedizin / Institute of Legal Medicine 22 Outlines 1.Introduction 2.Methodologies a.Positioning b.Scaling 3.Theory a.Kriging b.Delaunay Triangulation c.Homothetic transformation d.Lagrange Multiplier 4.Positioning – existing tools a.DYNAmore / Daimler b.ESI c.Altair d.Others 5.Scaling – existing tools a)DYNAmore / Daimler b)ESI c)Altair 6.References

3. ARBEITSGRUPPE FÜR BIOMECHANIK / BIOMECHANICS GROUP Institut für Rechtsmedizin / Institute of Legal Medicine 3 1. Introduction Review of existing positioning and scaling methods and tools for HBMs was executed within the scope of the TUC. It should provide a basis for the decision for one positioning and scaling tool to be used within the TUC. New challenges are arising, when a HBM is positioned or scaled due to their highly complex structure. It is necessary to define anatomically correct postures and dimensions. Mesh smoothing is required after every positioning or scaling task to preserve an acceptable mesh quality and prevent self-penetrations. Different methods and tools for scaling and positioning of HBMs have been developed in the past years. Most tools are either HBM- specific (exclusively applicable for HUMOS, THUMS etc) or platform specific. Therefore, the challenge for the TUC will be to first identify a positioning and scaling method which fulfils the desired requirements, especially with regard to mesh quality and stability in simulations. After, a generic tool has to be found and further developed which can be used for the TUC Master Model in all 3 codes (DYNA, Pam, Abaqus). Requirements for the positioning / scaling tool Code-independent THUMS specific maintenance of mesh quality stable in following simulations quick easy to use; intuitive applicable for a wide range of positioning and scaling tasks

4. ARBEITSGRUPPE FÜR BIOMECHANIK / BIOMECHANICS GROUP Institut für Rechtsmedizin / Institute of Legal Medicine 4 Positioning using FE simulations (adequate boundary conditions used to move specific body regions into final position) Hybrid approach (combines standard dummy positioning and positioning via FE simulation) AdvantagesDisadvantagesAdvantagesDisadvantages Physical behaviour of materials Prevention of self-penetrations due to defined contact conditions within joint region Time consuming Mesh quality after positioning might be bad due to local oscillations  manual smoothing  time consuming Rigid bodies reduce simulation time Small local oscillations within deformable parts additional mesh correction work Positioning using FE simulations Use of adequate boundary conditions to move specific body regions into final position any transitional part is deformed accordingly Dummy approach model is divided into rigid regions which are connected by rigid joints model can be repositioned by simply changing the joint angles Hybrid approach combination of standard dummy positioning and positioning via FE simulation regions not deforming during the positioning process combined to rigid bodies and connected using rigid body joints (hinges, translational or spherical joints) deformations restricted to deformable parts (reduction of simulation time) 2. Methodologies a.Positioning

5. ARBEITSGRUPPE FÜR BIOMECHANIK / BIOMECHANICS GROUP Institut für Rechtsmedizin / Institute of Legal Medicine 5 2. Methodologies a.Positioning Forward kinematics Every joint rotated individually; equation: x = f(θ) Determination of rotation axes and rotation angle for every joint Tree-structured hierarchy of rigid segments with a transformation matrix used to present the position and orientation of each segment relative to its immediate ancestor in the hierarchy Inverse kinematics Calculation of the required joint angle by solving the equation θ = f -1 (x) Highly non-linear equation θ can be solved by locally linear relationship for velocitieswith J kin = δx/δθ (kinematic map) Equation can be solved for θ and integrated numerically to yield the joint angles for a given end-effector trajectory. Direct optimisation A general non-linear optimisation algorithm is applied to the joint angles of the model, until a local minimum of an objective function is found The global objective function G(x) is defined as weighted sum of a number of individual goal functions g i (x) Several goal functions: position goals, orientation goals, aiming-at goals, half-space goals Each function scalar valued function of the position and/or orientation of one end-effector in Cartesian Space Gradient of the objective function with respect by the joint angles is given by θ and allows an efficient, gradient based optimisation algorithm Contact conditions can be treated with a half-space goal. Simple and direct approach to position a HBM Computationally fast

6. ARBEITSGRUPPE FÜR BIOMECHANIK / BIOMECHANICS GROUP Institut für Rechtsmedizin / Institute of Legal Medicine 6 2. Methodologies a.Positioning Lagrange Multiplier Method Method based on the first order law of motionF = M with F being the vector of generalised forces, M the mass matrix and q the vector of generalised coordinates which defines the position and orientation of each rigid body in the model Two possibilities of solving the equation of motion for articulated models Joint space description by reduced coordinates: constrained dof corresponding to joints eliminated symbolically from equations of motion Cartesian space description by maximal coordinates: joints implemented by calculating the reaction forces at each joint using Lagrange multiplier constraints Lagrange multiplier method a more general solution whose constraints may be freely mixed and rearranged at run-time; simple to implement and understand Each constraint represented by a constraint function C C equals zero, when it is satisfied:C=0 To remain satisfied, the derivative must be zero: Number of components of the constraint function must be equal to the number of dof removed by the constraint E.g. a ball and socket joint constrains three dof and has three components Equation given by Lagrange multiplier approach is a general method for implementing constraints which can equally well be specified in joint space or in end- effector coordinates Goal functions implemented as external forces (e.g. gravity) High computational costs

7. ARBEITSGRUPPE FÜR BIOMECHANIK / BIOMECHANICS GROUP Institut für Rechtsmedizin / Institute of Legal Medicine 7 Individual 3D Human Model Animation Based on Conformal Geometric Algebra Method obtained from motion analysis of 3D human models Rigid joints and connections between adjacent joints constitute the body’s skeleton Joint points extracted from the 3D grid model of the human body Body model deformation driven by the joint points to extract the model’s key frames Conformal algebra used to describe the 3D human body model and a geometric language implemented to do geometric calculations Hierarchical thinking of the radial basis function deals with grid distortion caused by the mesh transformation around the joints Joints divided into n layers; each layer with a rotation angle of α/n The greater n, the more smooth the joint Mesh deformation caused by the movement of the joint: mesh in the different layers has different angles The more layers the joint has, the better the deformation 2. Methodologies a.Positioning

8. ARBEITSGRUPPE FÜR BIOMECHANIK / BIOMECHANICS GROUP Institut für Rechtsmedizin / Institute of Legal Medicine 8 Premise for each method is a statistical anthropometric study on human body dimensions (external and internal). Based on the dimensions of the human body, proper scaling factors have to be chosen. The scaling parameters should correlate with the parameters to be scaled, and with the outcome parameters. Uniform scaling Whole model scaled by a single scaling factor Inertial and mass parameters can be scaled by the second and third power of scaling factor respectively Intrasegmental uniform scaling Every segment node cloud scaled using a single scaling factor based on a representative segment dimension for that segment Scaling dimensions to be obtained from an anthropometric study Intrasegmental non uniform scaling Scaling matrix defined for every segment node cloud including different scaling factors in different scaling directions Longitudinal and transversal scaling factors 2. Methodologies b.Scaling

9. ARBEITSGRUPPE FÜR BIOMECHANIK / BIOMECHANICS GROUP Institut für Rechtsmedizin / Institute of Legal Medicine 9 2. Methodologies Scaling by modifying an initial solution First step: initial solution for all coordinates of each point of every isolated part Second step: initial solution modified to best fit measurements predicted in a statistical anthropometric study Some anatomical principles not conserved during the transformation Scaling by using a non-linear equation system Positions each point of a human body part one by one Non-linear equation system including 3 equations and 3 unknowns corresponding to the 3 coordinates X, Y and Z of the point 3 equations provided by the distances predicted in the statistical anthropometric study Some anatomical principles not conserved during the transformation Homothetic transformation Homothetic transformation of each human body part to fit their coordinates with the desired percentile’s dimensions Three scaling factors corresponding to the 3 directions X, Y and Z to be defined in the local frame for each human body part 3 ratios between new percentile part and that of the original model calculated after Anatomical morphology conserved It is necessary to position every body part in the global frame at the end of every the scaling task. 2. Methodologies b.Scaling

10. ARBEITSGRUPPE FÜR BIOMECHANIK / BIOMECHANICS GROUP Institut für Rechtsmedizin / Institute of Legal Medicine 10 a.Kriging Kriging is a geostatistical technique using a “best linear unibiased estimator” (BLUE) of a random function. Its purpose is to interpolate the value of a random field at a specified location from a give set of measurements or samples at control points. A system of linear equations, the Kriging system, is implemented for every control points. The solution of the Kriging systems yields an interpolation value u(x,y). Classical Kriging local interpolation method solution of a new system of equations for each interpolated value Dual Kriging global interpolation method Kriging system evaluated only once for the whole domain by simultaneously using the information provided by all the data points all data points used in interpolation process yielding smooth and more reliable results than usual linear interpolation techniques Kriging used for mesh smoothing in HBMs basic method to create smooth geometric transitions between the parts during the repositioning or scaling process the random field represented by the position or displacement of the finite element nodes initial position is known for all nodes of the model the deformed position only known for a few nodes, e.g. the result of other commands or from directly specified displacements at certain nodes (control points) all other points to be interpolated using the linear mapping u*(x) = Ʃ i=1 wiū(xi)(N=number of control points, wi = weights, ū(x)= known displacement of control points at locations xi) 3. Theory a)b)c) Simple test system (a), geometric rotation of the right part leads to locally deformed elements (b); including a local Kriging process leads to regular deformed elements in adjacent parts (c) (Desai et al, 2012)

11. ARBEITSGRUPPE FÜR BIOMECHANIK / BIOMECHANICS GROUP Institut für Rechtsmedizin / Institute of Legal Medicine 11 b. Delaunay Triangulation 3. Theory Method used in computational geometry Creation of a triangulation out of a point set P in a way that no point in P is inside the circumcircle of any triangle Purpose: maximisation of the minimum angle of all angles of the triangles in the triangulation to avoid skinny triangles Often used to mesh finite element models Angle guarantee Fast triangulation algorithms Delaunay Triangulation c. Homothetic transformation Geometric transformation Leaves the origin of coordinates fixed and multiplies the distance between any two points by the same fixed constant M → S + λ SM Homothetic transformation

12. ARBEITSGRUPPE FÜR BIOMECHANIK / BIOMECHANICS GROUP Institut für Rechtsmedizin / Institute of Legal Medicine 12 d. Lagrange Multiplier 3. Theory Lagrange Multiplier Method used in mathematical optimisation to find the maxima or minima of a scalar function f(x) subject to fixed outside conditions or constraints To maximise the function f(x,y) subject to g(x,y)=c  f and g need continuous first partial derivatives Lagrange function defined by With λ being the Lagrange Multiplier Either added or subtracted If f(x 0,y 0 ) is maximum of f(x,y) for the original constrained problem, then there exists λ 0 such that (x 0, y 0, λ 0 ) is a stationary point for the Lagrange function

13. ARBEITSGRUPPE FÜR BIOMECHANIK / BIOMECHANICS GROUP Institut für Rechtsmedizin / Institute of Legal Medicine 13 4. Positioning – existing tools

14. ARBEITSGRUPPE FÜR BIOMECHANIK / BIOMECHANICS GROUP Institut für Rechtsmedizin / Institute of Legal Medicine 14 Platform Developed in LS-DYNA Platform-independent method Input Required angle of rotation Input files: –Model specific files for definition of axes and movements –Task-specific files for achievement of required position –File locking: files can be encrypted (cannot be changed by user) Methods 3 steps: 1.Decomposition of model: –Creation of a rigid body chain –Parts deforming during positioning left deformable 2.Positioning of model: –Positioning commands: rotations, translations, scaling of whole model or single model regions 3.Mesh smoothing by local dual Kriging approach a. DYNAmore / Daimler positioning tool Interface GUI support 3D accelerated visualisation of model geometry, joints, set, contacts Commands: joint-, set- and COS-Sys definition Simplified positioning: user selects single joint and change its position Advanced positioning: different joints definitions with corresponding parameters can be saved in a sequence, which realises a special positioning task Features Generic positioning AND scaling tool Hybrid approach: instead of FE simulations a geometric smoothing process is chosen to circumvent mesh correction problems Local dual Kriging approach for mesh smoothing in transitional regions Joint kinematics knowledge referred from Kinesiology (for anatomically correct postures) –Rotations only –Rotation axes defined for 7 major joints of human body No FE-simulation: repositioning in a few seconds No generation of any kind of strain or force in the repositioned model only one user parameter (reduction of user dependency) Not limited to THUMS model or LS-DYNA No re-meshing necessary: soft tissues in joint region deformed in a realistic manner; model can be directly used for further applications Undo function

15. ARBEITSGRUPPE FÜR BIOMECHANIK / BIOMECHANICS GROUP Institut für Rechtsmedizin / Institute of Legal Medicine 15 Limitations Location of rotational axis cannot be altered during movements as it is for required in knee flexion-extension (no translation) Model positioning limited to small to moderate posture changes, depending on rotation angles and resulting element distortions Need for specific files for Kinesiology (axes and movement definition) At the moment: only implemented to LS DYNA; Pam and Abaqus partly available Some features not yet fully implemented: –Sliding contacts not yet considered: penetrations have to be removed manually –Morphing reflection commands –Command sequence Stable version of GUI available at the end of the year Perspectives Positioning accuracy can be further improved by:  improving Kriging method for large scale meshes  detailed capturing or articulating surfaces geometry in human FE model  introducing instant axis of rotation in the positioning tool Tool has to be adapted to THUMS Master Model a. DYNAmore / Daimler positioning tool Example of the three mutually perpendicular rotational axes passing through humeral head (Desai et al., 2012) Elbow flexion (Desai et al., 2012) The GUI showing main window (incl. tool bars, model explorer: parts, contacts and set view enabled, the graphic canvas and the log window) (User Manual, 2012)

16. ARBEITSGRUPPE FÜR BIOMECHANIK / BIOMECHANICS GROUP Institut für Rechtsmedizin / Institute of Legal Medicine 16 b. ESI positioning tool Platform Developed for PamCrash and HUMOS2 General Based on modelling deformable parts in combination with rigid body rotations Use of a simplified finite element model (SFE model) Input Simplified FE model linked to a classical PamCrash model Required translation or rotation Modelling level of connection, required rotation Methods Real time simulation using rigid body dynamics and joint physics based on joint definitions in the FE model input Small deformations: results can be directly used for further applications Large deformations: generation of motion data which will be replicated during an actual PamCrash safe solber run (pre-simulation) Local intersections to be corrected with the standard pre-processor functionality SFE model Components: –Structure: rigid or deformable –Boundary conditions: damping, contact, pre-stress etc Custom angle: provides value of angle between 2 structures projected in XZ and XY planes respectively Interface SFE model creation and editing Managing of the SFE model Hierarchical structure to organise structures and conditions Features Efficient for small deformations To be coupled with intersection/penetration removal funcionalities of the ESI pre-processor Limitations Need for a individual SFE model SFE model user workflow complex Intersection corrections needed Large deformations: re-meshing necessary Pam specific Information about SimPositioner available soon!

17. ARBEITSGRUPPE FÜR BIOMECHANIK / BIOMECHANICS GROUP Institut für Rechtsmedizin / Institute of Legal Medicine 17 c. Altair positioning tool Platform Developed for HUMOS2 in Hypermesh/Radioss General Using angles defined on a simplified model based on the real articulations of the human body (knee, wrist…) the Positioning tool is able to change the HUMOS2 model position. It combines data of a pre-calculated database to generate the required position. Input Specification of new position by 28 angles Database of recorded articulation positions D00 file of required percentile of HUMOS2 model Positioning tool graphic interface Simplified representation based on the skeleton Interface 3 graphic windows with model in different views (3D, top, side) Positioning and Scaling task in one window Methods Body divided into 16 parts separated by articulations Each articulation set in space by one or two angles given in top and side view Database of recorded articulation positions indexed on the angles of simplified model and used to create intermediaries positions

18. ARBEITSGRUPPE FÜR BIOMECHANIK / BIOMECHANICS GROUP Institut für Rechtsmedizin / Institute of Legal Medicine 18 c. Altair positioning tool (continued) Methods Body divided into 16 parts separated by articulations Each articulation set in space by one or two angles given in top and side view Database of recorded articulation positions indexed on the angles of simplified model and used to create intermediaries positions Features No FE simulation: positioning within seconds Easy to handle Limitations Validity of position setting not checked: penetrations and intersections Geometrical positioning: deformed elements and badly defined interfaces Quality of mesh to be checked before using it in a simulation (local re- meshing might be necessary) Some positions hard to define by top and side angle Radioss / HUMOS specific Database required Angles definition. The first letter indicates Right or Left, the second, Top or Side and the third indicates the angle

19. ARBEITSGRUPPE FÜR BIOMECHANIK / BIOMECHANICS GROUP Institut für Rechtsmedizin / Institute of Legal Medicine 19 Human Body FE Model Repositioning: A step towards posture specific Human Body Models (D Jani, A Chawla, S Mukherjee, 2009, India) d. Others Platform VC++ as programming language and GUI Open GL as graphics platform General Independent of model’s geometry Based on standard computer techniques like morphing and affine transformations Use of Delaunay Triangulation Method Features Not based on FE simulations: fast No precalculated FE model positional data required Minimisation of subjective intervention of user Inclusion of bone and ligament kinematic data Prevention of penetrations Limitations Tool only validated for knee joint Decrease of mesh quality with higher flexion (>75°) Accuracy of anatomy of repositioned parts doubtable (a) Penetrating contours (b) plane rotation to remove penetration of contours (c) corrected position of contours (Jianhua et al. 1994)

20. ARBEITSGRUPPE FÜR BIOMECHANIK / BIOMECHANICS GROUP Institut für Rechtsmedizin / Institute of Legal Medicine 20 5. Scaling – existing tools

21. ARBEITSGRUPPE FÜR BIOMECHANIK / BIOMECHANICS GROUP Institut für Rechtsmedizin / Institute of Legal Medicine 21 a. DYNAmore / Daimler scaling tool Platform Developed in LS-DYNA Generic platform-independent method Input Scaling factors Percentile General Same tool as positioning tool Hybrid approach Local dual Kriging approach for mesh smoothing in transitional regions Interface Same as for positioning tool Limitations No gender anatomy taken into account At the moment: only implemented to LS DYNA; Pam and Abaqus partly available Some features not yet fully implemented; stable version by the end of this year Scaling factor: no information about source

22. ARBEITSGRUPPE FÜR BIOMECHANIK / BIOMECHANICS GROUP Institut für Rechtsmedizin / Institute of Legal Medicine 22 Available soon! b. ESI scaling tool

23. ARBEITSGRUPPE FÜR BIOMECHANIK / BIOMECHANICS GROUP Institut für Rechtsmedizin / Institute of Legal Medicine 23 c. Altair scaling tool Platform Developed for the use of HUMOS2 Available in Hypermesh Input Desired percentile Initial HUMOS mesh HUMOS1 control points General Using a statistical tool based on a human measurement database, the Scaling tool generates the main dimensions of a human body of any desired percentile and modifies the HUMOS2 model according to these dimensions. The software is composed of the statistical and a Kriging tool for mesh smoothing. Control Points Accurate and complete (as far as possible) description of important parts of the human body; based on anatomical details Interface Scaling and Positioning task in one window. Main structure of HUMOS2 Scaling-Tool Homothetic transformation in the local frame Choice of scale factors

24. ARBEITSGRUPPE FÜR BIOMECHANIK / BIOMECHANICS GROUP Institut für Rechtsmedizin / Institute of Legal Medicine 24 c. Altair scaling tool (continued) Statistical tool Based on statistical study homothetic transformation of control points to fit their coordinates with the desired percentile’s dimensions predicted by the statistical study Estimation of all scale factors from 8 parameters –Height –Acromion-ground height –Anterior-superior iliac crest-ground height –Sitting height –Thoracic axillary circumference –Head circumference –Greatest forearm circumference –weight Kriging tool Global Kriging method used to interpolate original mesh Interpolation of HUMOS nodes Control points balanced all over the mesh Limitations Predefined control points needed as input Definition of control points by trial and error No gender anatomy taken into account No information of duration of scaling process HUMOS2 Scaling-Tool main window description

25. ARBEITSGRUPPE FÜR BIOMECHANIK / BIOMECHANICS GROUP Institut für Rechtsmedizin / Institute of Legal Medicine 25 G Amos, B Buxton (1999) Positioning Human Body Models with Lagrange Mulitpliers. SAE technical papers 1999-01-1917. S Bertrand et al. (2004) Main parameters defining the external and internal human body geometry. HUMOS2, Deliverable D02 of Task 1.2. M Beaugonin, C Marca (2005) Positioning Tool for PAM HUMOS2 Models. HUMOS2, Deliverable D09c. S Bidal, K Kayvantash (2005) Radioss Positioning Tool. HUMOS2, Deliverable D09a. Carlsson et al. (2012) A 50th Percentile Female Rear Impact Finite Element Dummy Model. IRCOBI conference. R Chaveesuk, A E Smith (2005) Dual Kriging: An Explorary use in Economic Metamodelling. The Engineering Economist, 50, 247-271. Ch Desai, G Sharma, P Shah, Ch Ageorges, Ch Mayer, D Fressmann (2012) A generic Positioning Tool for Human Body FE Models. IRCOBI conference 2012, IRC-12- 09. Dumas et al. (2009) Soft tissue artefact compensation by linear 3D interpolation and approximation methods. Journal of Biomechanics, 42, pp. 2214-2217. DYNAmore GmbH, A THUMS Positioning Tool – Users Manual, 2013. J Hadamard (2008) Lessons in Geometry I. Plane Geometry. American Mathematical Society. Hu et al. (2012) Individual Three-Dimensional Human Model Animation Based on Conformal Geometric Algebra. Software Engineering and Knowledge Engineering, AISC 114, pp. 147-424. D Jani, A Chawla, S Mukherjee (2009) Human Body FE Model Repositioning: a step towards posture specific-Human Body Models (PS-HBM). IRCOBI conference. Jianhua et al. (1994) Human Skin Deformation from Cross Sections. Proc. Computer Graphics International, Melbourne, Australia. Martelli et al. (2007) Scaling of a shoulder musculoskeletal model to individual subject data. Journal of Biomechanics, 40 (S2). A O Ricardo (1991) Geostatistical glossary and multilingual dictionary. Oxford University Press. T Serre, T Bekkour (2005) Scaling of an existing mesh onto personalised geometry. HUMOS2, Deliverable D03. T Serre (2004) Geometry Acquisition. HUMOS2, Deliverable D01. Sigal et al. (2010) Morphing methods to parameterize specimen-specific finite element model geometries. Journal of Biomechanics, 43, pp. 254-262. F Trochu (1993) A Contouring Program based on Dual Kriging Interpolation. Engineering with Computers, 9, 160-177. J Wyatt (2004) Lagrange Multipliers, Constrained Maximisation and the Maximum Entropy Principle. J Zhao, N Badler (1994) Inverse kinematics positioning using non-linear programming for highly articulated figures. ACM Transaction on Graphics, Vol. 13, No. 4, pp 313- 316. 6. References