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# BMClab / BMC

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# Introduction to modeling and simulation of human movement

### Time and place

• Tuesdays, 17-19h; Thursdays, 17-19h, lab A2 L003, campus São Bernardo do Campo

## Lecture Schedule

### Lecture 1

Introduction

• Install OpenSim and do the first three tutorials (Help menu).

• TSIANOS, G. A .; LOEB, G. E. Muscle and limb mechanics. Comprehensive Physiology, v. 7, n. 2, p. 429-462, 2017.
• ZAJAC, F. E. Muscle coordination of movement: a perspective. J Biomech, v. 26 Suppl 1, n. SUPPL. 1, p. 109–124, 1993.

### Lecture 2

• Write a Jupyter notebook to compute and plot the acceleration of the particle with displacement data contained in the file pezzack.txt. Additionally, compare the computed acceleration with the true acceleration (contained in the same data).

### Lecture 3

• OpenSim tutorials

### Lecture 4

• Python programming

• Plot the trajectory of a particle during 10 seconds with the gravity force acting on it (gravity acceleration g = -9.81 m/s^2). Consider that the initial velocity of the particle is v0 = 30 m/s and the initial angle with the horizontal plane is 30 degrees.

### Lecture 5

• Discussion about TSIANOS and LOEB (2017) and Zajac (1993)
• Animations about muscle contraction: 1, 2, 3

### Lecture 6

• Write a Jupyter notebook to find the trajectory of a ball considering the air drag proportional to the square root of the ball velocity. Consider that the initial velocity of the particle is v0 = 30 m/s and the initial angle with the horizontal plane is 30 degrees, the gravity acceleration is g = 9.81 m/s^2, the mass of the ball is m = 0.43 kg and the air drag coefficient is \$b= 0.006 kg.m^{1/2}/s^{3/2}\$.

• NIGG, B. M.; HERZOG, W. Modelling. In: Biomechanics of the Musculo-skeletal System. p. 501 - 534.

### Lecture 7

• Discussion about NIGG, B. M.; HERZOG, W. Modelling. In: Biomechanics of the Musculo-skeletal System. p. 501 - 534.

### Lecture 8

• Models of Kelvin, Voigt and Maxwell.

• YAMAGUCHI, Y. T; Dynamic modeling of musculoskeletal motion: A Vectorized Approach for Biomechanical Analysis in Three Dimensions (2001), Sections 2.2.1 and 2.2.2.

• NIGG, B. M.; HERZOG, W. Modelling. In: Biomechanics of the Musculo-skeletal System. p. 631 - 634.

• Implement the Kelvin model. Set the parameters of the model so as to the response of the model is similar to the shown in the Figure 3(a) from VAN LOOCKE, M.; LYONS, C. G.; SIMMS, C. K. Viscoelastic properties of passive skeletal muscle in compression: Stress-relaxation behaviour and constitutive modelling. Journal of Biomechanics, v. 41, n. 7, p. 1555–1566, 2008. You can find this article at the Mendeley group.

In this study the initial length of the fibre is 10 mm. Then the length decreases to 7 mm with different velocities.

### Lecture 9

• Implement muscle model of Nigg and Herzog.

• BEAR, M. F.; W, C. B.; PARADISO, M. A. Neuroscience: Exploring the brain. 4. ed. Philadelphia, PA, USA: Lippincott Williams & Wilkins, 2015. (Chapter 13)

### Lecture 10

Nigg and Herzog model implemented in the class

• Change the derivative of the contractile element length function. The new function must compute the derivative according to the article from Thelen (2003) (Eq. (6) and (7)):

• Thelen D; Adjustment of muscle mechanics model parameters to simulate dynamic contractions in older adults (2003)

### Lecture 11

• Discussion on * BEAR, M. F.; W, C. B.; PARADISO, M. A. Neuroscience: Exploring the brain. 4. ed. Philadelphia, PA, USA: Lippincott Williams & Wilkins, 2015. (Chapter 13)

• Implement the activation dynamics as in Thelen (2003)

### Lecture 12

• Activation Dynamics and Pennation angle

• Implement the Knee simulation of the Nigg and Herzog's book (chapter 4.8.6, knee.m) in Python using the muscle model implemented in class. You can use your own model or the contained on this link.

### Lecture 13

• Knee joint model (adapted from Nigg and Herzog's book)
• Compare the force and vellocity of the active contractile element for the different moment arms
• Ankle joint model
• See Rajagopal et al. (2015) for a list of muscle parameters used in a recent OpenSim model

• Implement a simulation of the ankle joint model using the parameters from Thelen (2003) and Elias (2014)

### Lecture 14

• Write a Python Class to implement the muscle model developed during the course. You can use this notebook and continue the implememtation of the Class.

### Lecture 15

• The muscle function into a Python class

### Lecture 16

• Control of an inverted pendulum model with muscle actuators (using a PID controller) based on ankle angle

### Lecture 17

• Control of an inverted pendulum model with muscle actuators (using a PID controller) based on muscle length

### Lecture 18

• Solve problemas 1 and 2 of the notebook above.

### Lecture 19

• Solve problemas 3 and 4 of the notebook above.

### Lecture 21

• Implement the numerical simulationn of the double pendulum with joint actuators (solve numerically the equation of motion using forward dynamics).