1. Advanced Biomechanics of Physical Activity (KIN 831) Lecture 8 Biomechanical Models and Modeling* * Some of the material included in this presentation is derived from: Nigg, B. M. (1994). In B. M. Nigg & W. Herzog (Eds.), Biomechanics of the Musculo-Skeletal System (pp.365-379). West Sussex, UK:John Wiley & Sons.

2. What is a model?

4. Definitions Model – an object, plan, or theory that represents or imitates many of the features of something else (“an attempt to represent reality”) Deduction – logical reasoning from a known to the unknown, from the general to the specific Induction – logical reasoning from particular facts or individual cases to a general conclusion Validation (of a model) – providing evidence that a model is strong and powerful

5. Definitions (continued) Biomechanical model – a representation (microscopic or macroscopic) of a biological system Free body diagram – simplified drawing of a mechanical system, isolated from its surroundings, showing all force vectors and torques Generalizable – the ability to make broader application of a process or results

6. 1.Working in groups of two, carefully develop a model (drawing) of a inanimate (not a biological structure) mechanical structure which you can show to the class and define its function. [These models should be relatively simple mechanical systems.]

8. Example:

9. 2.Using the example provided, what do you know about the model? List several assumptions that have been made about the model and indicate why these assumptions may have been made.

10. Model Known FactsAssumptions

12. KNOWN FACTS (?): F 1 s 1 = F 2 s 2 or F 1 = F 2 (s 2 /s 1 ) s 1 = ½(s 2 ) ASSUMPTIONS: 1. 2. 3.

13. 3.Refine the model (drawing) in order to remove some of the assumptions about the model. You will be asked to show your revised model and its assumptions.

15. 4.Attempt to simplify the model and redraw it. Be prepared to show and explain your simplified model to the class. Hints: - possibly representing parts of the structures as a point masses and/or lines - possibly representing the parts of the structure by its behavior according to the laws of physics

17. Why are biomechanical models used?

19. 1.to simplify the understanding of the structure and function of a biological system 2.to simply the kinematics and/or kinetics analysis of the biological system 3.to remove the biological system from exposure to potential adverse effects by exposing a representative model and observing its behavior

20. Purposes of models and modeling 1.to increase knowledge and insight about reality 2.to estimate or predict variables of interest [The fact that insight and knowledge are prerequisites for the development of a model, but are also the purpose of using a model, seems contradictory.]

21. Information used to construct a model 1.Knowledge of the system being modeled –Using knowledge of the system being modeled, to move from general principles to specifics, is a deductive process. 2.Experimental data that constitute system inputs and/or outputs –Using experimental data, in an attempt to arrive at a general conclusion that explains the data, is an inductive process.

22. knowledge deduction unique solution experimental data induction no unique solution Information used: Method used: Expected results: Deduction versus Induction Constructing a model – information, method, and results 1.Knowledge may be preliminary assumptions. 2.In deductive model there may be many assumptions. 3.In inductive model there may be many possible answers.

23. Simplification 1.In general, simple is better. 2.Simple may not agree with reality. 3.The key to a model (modeling) is to know what to include and what to eliminate; there is a science and art to creating a model.

24. Validation of a model 1.Validation of a model means that evidence is provided that the model is strong and powerful for the task for which it has been designed (i.e., provision of cases for which the results of the model corresponds to reality). 2.Validation may lead to increased confidence in a model, but it never confirms that the model corresponds to reality.

25. Three ways to validate a model 1.direct measurement – comparison of estimated results from a model with actually measured results (e.g., predicting projectile distances of javelin from information about angle of projection, height of release, and velocity of release and comparing it to actually measured projectile distances)

26. Three ways to validate a model (continued) 2.indirect measurements – measurements of another variable may be made and compared with the value predicted for this variable from the model (e.g., use of IEMG of the hamstring muscles compared with the model’s predicted value of knee flexion force)

27. Three ways to validate a model (continued) 3.trend measurements – the quality of a model depends on how well the trends predicted agree with the trends measured (e.g., if the model predicted that measured girths of the forearm were linearly related to grip strength, validation would require several input variables and subsequent out put values)

28. Types of models 1.Analytical - deductive 2.Semi-analytical – many assumptions are used because there are more unknowns than equations to solve for the unknowns 3.Black box – regression models; functions used to determine relationships between input and output 4.Conceptual – used in hypothesis testing

29. theoriesdeductionprediction induction description observation facts evaluation “Science must start with facts and end with facts, no matter what theoretical structures it builds in between.” Cyclical interaction between facts and theory in scientific activities 1.Start with observation to build upon what is known. 2.Describe what is known 3.Use the known facts to come to general conclusions; induction) 4.Develop and test the predictions of theories (models); deduction 5.Compare results with actual facts 6.Evaluate the process 7.Seek additional facts 8.Refine theories (models) and possibly repeat the process

30. Why are biomechanical models used? 1.to simplify the understanding of the structure and function of a biological system 2.to simply the kinematics and/or kinetics analysis of the biological system 3.to remove the biological system from exposure to potential adverse effects by exposing a representative model and observing its behavior

31. Why are biomechanical models used? (continued) 4.to obtain information on the structure and function of the biological system 5.to simplify the presentation of a complex biological system

32. General steps in developing a biomechanical model [Prior to developing a biomechanical model the scientist must: a) have a thorough understanding of existing facts, b) make observations of the phenomena to be studied, and c) develop an understanding of the integration of facts and observation.] 1.Define question to be answered 2.Define the system of interest 3.Review existing knowledge (literature review) 4.Select procedure (model) to be applied to solve research question; research methods 5.Make simplifications and assumptions; decide what to include and what not to include based on defendable reasons

33. General steps in developing a biomechanical model [Prior to developing a biomechanical model the scientist must: a) have a thorough understanding of existing facts, b) make observations of the phenomena to be studied, and c) develop an understanding of the integration of facts and observation.] 6.Formulate mathematical approach (e.g., statistical methods) to be applied to data 7.Develop mathematical solution (results) 8.Evaluate the model 9.Discuss, interpret, and apply the results 10.Draw conclusions

34. What are categories of biomechanical models? 1.Static versus dynamic a.static implies constant linear and/or angular velocity (linear and/or angular acceleration = 0) b.dynamic implies changing linear and/or angular velocity (linear and/or angular acceleration  0) 2.Object Dimension a.point-mass (0 dimension) b.line (1 dimension) c.plane (2 dimensions) d.solid (3 dimensions) 3.Space Dimension a.uni-axial b.bi-axial c.tri-axial (three dimensional Cartesian coordinate system)

35. What are categories of biomechanical models? (continued) 4. Kinematic versus kinetic a.kinematic implies a description of position without regard for forces and torques b.kinetic implies the forces and torques that cause linear and/or angular accelerations 5.Uni-segment versus multi-segment a.uni-segment implies internal and external forces and torques b.multi-segment implies reactive forces (joint reaction force) and torques (mutual net muscle moments across joints) between segments

36. Input parameters for biomechanical models 1.Direct measurement – actual measurements of parameters used in the model (e.g., height, weight) 2.Indirect measurement – measures predicted from other sources of information (e.g., location of the center of mass of a segment of the body, segments proportion of total body height, estimate of density of a body segment 3.Inverse dynamics – the use of linear and angular acceleration parameters and information about segmental mass and moment of inertia to determine forces and torques a.mass X acceleration = force (equation of linear motion) b.moment of inertia X angular acceleration = torque or moment (equation of angular motion)

37. What is a free body diagram?

39. Free body diagram [simplified drawing of a mechanical system, isolated from itssurroundings, showing all forces vectors and torques] 1.Particle (or point-mass) free body diagram –assumed that kinematics of object can be represented by its center of mass and its linear movement (e.g., parabolic path of the center of mass of a long jumper in flight) [Note that there is no angular motion associated with a point mass.] = fxfx frfr fyfy mg = wt.

40. Free body diagram (continued) [simplified drawing of a mechanical system, isolated from its surroundings, showing all forces vectors and torques] 2.Segmental - can represent the human body mechanically as a linked system of rigid segments moving about an axes of rotation through joints f yp f xp arar axax mg = wt. dd f xd f yd  ayay pp

41. Assumptions 1.Rules for making assumptions a.assumptions should not adversely or substantially affect the results of the model (e.g., knee joint is pinned) b.assumptions should generally simplify the model (e.g., c.assumptions should be able to be justified (e.g., linear and angular accelerations are small and therefore can be neglected) d.assumptions should usually be made for unknowns (e.g., knee joint is frictionless) 2.Reasons for making assumptions a.remove complexity from model b.simplify computation and/or understanding c.lack of knowledge