Musculoskeletal Modeling of Smilodon Fatalis for Virtual Functional Performance Testing

1. Musculoskeletal Modeling of Smilodon Fatalis for Virtual Functional Performance Testing Kiran Konakanchi Advisor: Dr. Venkat Krovi Mechanical & Aerospace Engineering State University of New York at Buffalo

2. Agenda Goal : Study the functional and behavioral performance of extinct & extant animals • Our Idea & Introduction • Goal & Issues • Literature Review & Available Tools • Musculoskeletal Modeling in AnyBody • Case Studies • Conclusion & Future Work

3. Why ? Tiger Smilodon + Musculoskeletal Biomechanical Model Engineering Analysis Possible Solution + Idea In our thousands of years of evolution, there are many unanswered questions Why do present members of feline family not have saber teeth? Did the Smilodon use its saber teeth during hunting? Introduction Issues Background Modeling Case studies Conclusion

4. Introduction Virtual Prototyping (VP) “Virtual prototype is a computer simulation of a physical product that can be presented, analyzed, and tested from concerned product life-cycle aspects such as design /engineering, manufacturing, service, and recycling as if on a real physical model. The construction and testing of a virtual prototype is called Virtual Prototyping.” Allows the designer to realistically , accurately and quantitatively test multiple models within virtual environment Introduction Issues Background Modeling Case studies Conclusion

5. Black Box Input Output Introduction Biomechanical modeling Modeling procedure based on the principles of biomechanics Four types of models Conceptual Model Analytical Model CAD Model Musculoskeletal Model Complexity of Modeling Introduction Issues Background Modeling Case studies Conclusion

6. Project Goal Examine various aspects of systematic musculoskeletal model building with the help of detailed examples Explore various issues pertaining to the modeling and analysis of such systems and provide possible solutions Case Studies • Muscle force calculation • Bite force analysis • Determination of optimal muscle location points. Introduction Issues Background Modeling Case studies Conclusion

7. F2 F1 m mg Issues Redundancy The number of actuators (muscles Nm) is greater than the number of degrees (Nd) of freedom of the system Reduction Method: Grouping Muscles until Nm = Nd Addition Method : Adding Constraints Dynamically Determinate One Sided Constrained Method (DDOSC): Problem is divided into series of dynamically determinate problems Optimization Techniques Introduction Issues Background Modeling Case studies Conclusion

8. Neural In MUSCLE Single Muscle Multiple Muscles Velocity or Force Issues Geometric Complexity • Modeling Phase • Analysis Phase Coarse Model Fine Model Group Muscle Model Individual Muscle Model Introduction Issues Background Modeling Case studies Conclusion

9. Background Why Bite force? Bite force: The amount of force that can be exerted by the jaw adductormusculature and realized at the tooth row as a function of jaw geometry. Meers et al.(2003) established prey/predatory relationships among Triceratops horridus, Tyrannosaurus Rex and other dinosaurs. Verwaijan et al.(2002) found that head and body size have considerable impacton bite force magnitude. Introduction Issues Background Modeling Case studies Conclusion

10. Available Tools SIMM • Popularly used musculoskeletal modeling software • Require Bone, Joint, Muscle data in ‘C’ language format • Requires substantial programming knowledge SimMechanics • Good for Mechanical systems • Can define rigid bodies (bones), joints and drivers • Difficult to define mathematical muscle models LifeMod • Can interact with environment • Our data format does not suit the software requirements Introduction Issues Background Modeling Case studies Conclusion

11. Available Tools Visual Nastran Vertebrate Analyzer • Good for mechanical systems simulation • Perform motion and stress analysis • Issue of muscle recruitment pattern • Can not solve the problem of redundancy • Visualize and experiment with accurate biomechanically constrained models • Capability to attach muscles, ligaments, tendons etc. • Proposed future work could be an ideal package for functional performance testing Development of a Computational Toolkit for Biomechanical Analysis and Simulation : The Vertebrate Analyzer Introduction Issues Background Modeling Case studies Conclusion

12. MusculoskeletalModeling in AnyBody What is AnyBody software? What will it do? AnyBody is a musculoskeletal modeling software used for developing detailed multi body biomechanical systems • Applications • Therapy/Medical rehabilitation • Ergonomic Design in the fields of automotives, sports etc. • Functional performance studies • Training tools for surgeons when combined with virtual environment Introduction Issues Background Modeling Case studies Conclusion

13. Software Interface Introduction Issues Background Modeling Case studies Conclusion

14. Modeling Procedure 5 stage process Introduction Issues Background Modeling Case studies Conclusion

15. Analysis Different types of Studies / Analysis Set up Initial Conditions • Kinematic analysis • Main emphasis is on system motion • No forces in the system are calculated. • Obtain position, velocity and acceleration information • Muscle calibration analysis • Adjusts the lengths of tendons • Optimal length is in the middle of simulation • Not required for simple muscle models. Introduction Issues Background Modeling Case studies Conclusion

16. Analysis Inverse Dynamic Analysis (IDA) IDA can be thought as the heart of the software system. • The main requirement for IDA is that, it should be able to cope with • Statically indeterminate problems • Limits on forces in the problem Optimality criteria involving muscle forces Equilibrium equations Unique solution + Body attempts to use its muscles in such a fashion that minimum fatigue condition is obtained. Introduction Issues Background Modeling Case studies Conclusion

17. Analysis The muscle recruitment is performed according to the following optimal criteria Minimize (Maximum muscle activity ) + e1*(sum of activities) + e2*(sum of squared activities) Subject to Equilibrium equations are fulfilled Muscles are not allowed to push. Where, e1: RecruitmentLpPenalty e2: RecruitmentQPenalty Weber’s hypothesis: Muscle recruitment is performed in a way such that muscular effort is minimized during routine activities. Introduction Issues Background Modeling Case studies Conclusion

18. Project Implementation Introduction Issues Background Modeling Case studies Conclusion

19. CAD Model from Point data MIMICS (Materialise’s Interactive Medical Image Control System) is used to develop a CAD model from CT/MRI data Introduction Issues Background Modeling Case studies Conclusion

20. CAD Model from Point data Windowing : Adjusting the grey scale values Thresholding : Selection between soft and hard bone Region growing : Reduce noise and separate structures Editing : Remove artifacts Mandible Skull Introduction Issues Background Modeling Case studies Conclusion

21. MATLAB Interface • To provide user friendly easy to use interface • Eliminates the necessity to learn the programming language • Use other MATLAB features and functions for easy analysis of results Introduction Issues Background Modeling Case studies Conclusion

22. Global Reference Frame Introduction Issues Background Modeling Case studies Conclusion

23. Segment(s) addition Tiger Sabertooth tiger Introduction Issues Background Modeling Case studies Conclusion

24. Joints Introduction Issues Background Modeling Case studies Conclusion

25. Drivers Introduction Issues Background Modeling Case studies Conclusion

26. Muscle Models Introduction Issues Background Modeling Case studies Conclusion

27. Muscle Route types Sabertooth tiger Tiger Introduction Issues Background Modeling Case studies Conclusion

28. Process flow of case studies Introduction Issues Background Modeling Case studies Conclusion

29. Revisiting our project flow chart Muscle forces obtained at this point Introduction Issues Background Modeling Case studies Conclusion

30. Muscle force calculation Min/Max criteria is used for muscle force calculation Using bound formulation we can easily solve the min/max problems By choosing artificial variable β and artificial function B(β) such that B(β) = β The min/max criteria can be reformulated as Introduction Issues Background Modeling Case studies Conclusion

31. Case studies • Depending on 3 factors • Specimen (Tiger or Sabertooth tiger) • Muscle route algorithm (Via Point muscle or Shortest Path muscle) • Type of muscle (Simple or Hill muscle) Introduction Issues Background Modeling Case studies Conclusion

32. Case 1: Tiger – VPMuscle - Simple Introduction Issues Background Modeling Case studies Conclusion

33. Case 8: Sabertooth tiger – SPMuscle - Complex Introduction Issues Background Modeling Case studies Conclusion

34. is the line vector matrix that depends on the muscles line of action (calculated from plucker coordinates by knowing the positions of origin and insertion of muscle) is the column vector representing the muscle force (obtained above) is the external force or Bite force Bite force calculation Bite force is calculated from the following equilibrium equation. Where, Introduction Issues Background Modeling Case studies Conclusion

35. Minimize: –Bite force ( ) Subject to: Where, Vector representing design variables i.e. muscle origin and insertion coordinates and represent the lower and upper limits respectively Optimality Criteria Introduction Issues Background Modeling Case studies Conclusion

36. Parametric sweep studies Tiger-SPMuscle-Simple Variation of Masseter origin Variation of Masseter insertion Variation of pterygoid insertion Variation of Temporalis insertion Variation of Temporalis origin Variation of Pterygoid origin Surface plot Line plot Introduction Issues Background Modeling Case studies Conclusion

37. Bite Force graphs Case 1:Tiger – SPMuscle - Simple Introduction Issues Background Modeling Case studies Conclusion

38. Bite Force graphs Case 1:Sabertooth tiger – SPMuscle - Simple Introduction Issues Background Modeling Case studies Conclusion

39. Conclusion Developed a user friendly computational framework for testing hypothesis and various if-then scenarios. Identified the critical issues pertaining to musculoskeletal modeling like redundancy, geometric complexity, muscle recruitment pattern etc. Validated some of the available software packages with regards to available data. Conducted a range of virtual experiments on members of feline family (tiger & sabertooth tiger) with our proposed methodology that can help in the study of functional performance. Finally, we presented the biologist with a novel validated toolbox. Introduction Issues Background Modeling Case studies Conclusion

40. Future work Optimization routine Brute force method has been employed for parametric sweep. More sophisticated algorithm like will be used in future. Limitations of the software: MATLAB interface limitations will be resolved in future versions. Issues pertaining to modeling: We approximated the muscle origin and insertion as points. The future work will include the solution strategy to this issue like proving a curtain of muscles instead of single muscle etc. Task space redundancy: The bite force can be calculated at the tip pf one tooth. Task space redundancy need to be resolved to simultaneously calculate the bite force at the tips of two teeth. Screw theory (delSignore [36]) in order to solve the problem of task space redundancy.

41. Thank You! Questions?