bmclab / bmc

Notes on Scientific Computing for Biomechanics and Motor Control

Notes on Scientific Computing for Biomechanics and Motor Control

This repository is a collection of lecture notes and code on scientific computing and data analysis for Biomechanics and Motor Control.
These notes (notebooks) are written using Jupyter Notebook, part of the Python ecosystem for scientific computing.

Classic Notebook
JupyterLab

Introduction

• Biomechanics
• The Biomechanics and Motor Control Laboratory @ UFABC

Scientific programming

• Python for scientific computing
• Python tutorial
• Version control with Git and GitHub
• Code structure for data analysis

Numerical data analysis

• Scalar and vector
• Basic trigonometry
• Matrix
• Descriptive statistics
• Bayesian Statistics
• Confidence and prediction intervals
  • One-dimensional intervals
  • Prediction ellipse (2D) and prediction ellipsoid (3D)
• Curve fitting
  • Fundamentals of curve fitting
  • Polynomial fitting
• Propagation of uncertainty
• Frequency analysis
  • Basic properties of signals
  • Fourier series
  • Fourier transform
• Signal processing
  • Data filtering
  • Residual analysis for the optimal cutoff frequency
• Ordinary Differential Equation
• Optimization
• Change detection
  • Detection of peaks
  • Detection of onset
  • Detection of changes using the Cumulative Sum (CUSUM)
  • Detection of sequential data
• Time normalization of data
• Ensemble average
• Select data vectors by similarity using a metric score
• Open files in C3D format
• Camera calibration and point reconstruction based on direct linear transformation (DLT)

Mechanics

Kinematics

• Frame of reference
• Time-varying frame of reference
• Polar and cylindrical frame of reference
• Kinematics of particle
  • One-dimensional motion
  • Projectile motion
  • Spatial and temporal characteristics
  • Minimum jerk hypothesis
• Kinematics of Rigid Body
  • Angular kinematics (2D)
  • Kinematic chain
  • Velocity and Acceleration of a point of a rigid body
  • Rigid-body transformations (2D)
  • Rigid-body transformations (3D)
  • Determining rigid body transformation using the SVD algorithm
  • Angular velocity in three-dimension movements

Kinetics

• Fundamental concepts
• Center of Mass and Moment of Inertia
• Newton Laws for particles
• Newton-Euler Laws
• Free body diagram
  • Free body diagram for particles
  • Free body diagram for rigid bodies
• 3D Rigid body kinetics
• Matrix formalism of the Equations of Motion
• Lagrangian Mechanics

Modeling and simulation of human movement

• Body segment parameters
• Muscle modeling
• Muscle simulation
• Musculoskeletal modeling and simulation
• Multibody dynamics of simple biomechanical models

Biomechanical tasks Analysis

• The inverted pendulum model of the human standing posture
• Measurements in stabilography
• Rambling and Trembling decomposition of the COP
• Biomechanical analysis of vertical jumps
• Gait analysis (2D)
• Force plates
  • Kistler force plate calculation
  • Zebris pressure platform

Electromyography

• Introduction to data analysis in electromyography

How to cite this work

Here is a suggestion to cite this GitHub repository:

Marcos Duarte and Renato Naville Watanabe. (2021). Notes on Scientific Computing for Biomechanics and Motor Control (Version v0.0.2). Zenodo. http://doi.org/10.5281/zenodo.4599319

And a BibTeX entry:

@misc{marcos_duarte_2021_4599319,
  author       = {Marcos Duarte and Renato Naville Watanabe},
  title        = {{Notes on Scientific Computing for Biomechanics and Motor Control}},
  month        = mar,
  year         = 2021,
  publisher    = {Zenodo},
  version      = {v0.0.2},
  doi          = {10.5281/zenodo.4599319},
  url          = {https://doi.org/10.5281/zenodo.4599319}
}

License

The non-software content of this project is licensed under a Creative Commons Attribution 4.0 International License, and the software code is licensed under the MIT license.

bmc's Issues

Inverse Dynamics

I have looked through your notes and they are brilliant. I have skimmed through your notes and have a shallow grasp of some of the concepts. Lets say someone has smart shoes and other wearables that can record the ground contact time, strike angle, left/right foot balance, distance, heart rate, muscle impulses, flight time, stride length, pace, cadence and so on, but not the force applied to the ground nor the ground reaction forces. Can I use inverse dynamics to determine the forces given all the other parameters? If I apply body segmentation and calculate my centre of mass and centre of pressure, can that be converted into a time series ? Does the position of the centre of mass affect posture and form ? When accounting for drag, how big is the difference in the surfaces of a cyclist and a sprinter ? Another question I have would be, if say, someone was on a wind surfing board and could accurately locate their position on a body of water using gps and also using an accelerometer on the sail, how would one apply inverse dynamics to calculate bouyancy forces, forces on an individual, and the propulsion force ?

AMTIbsf.py TypeError

  File "\\#Measurements\\AMTINetForce\AMTIbsf.py", line 171, in loadbsf
    data = np.array(data).reshape((mh.numDatasets, mh.TNC))
TypeError: 'float' object cannot be interpreted as an integer
[Finished in 3.2s with exit code 1]

Example on how to write rich text in issues

Besides the format options in the toolbar when editing an issue,
Latex:

<img src="https://render.githubusercontent.com/render/math?math=\frac{\mathrm d }{\mathrm d t}\left({\frac{\partial\mathcal{L}}{\partial\dot{q}_i }}\right)-\frac{\partial \mathcal{L}}{\partial q_i }=Q_{NCi}\quad i=1,\dotsc,N">
...
Image (drag and drop image file here but use html code to set its size):

<img src="https://user-images.githubusercontent.com/3271581/76967836-b1af5700-6906-11ea-8a26-ef2c89ca1460.png" height="100" >
...

Threshold values for peaks and valleys.

I am trying to detect local maxima (* peaks12* used in the code below) and local minima (* peaks13*) from a vector called nrz. All peaks and valleys should be at above 0.25 and below -0.25 respectively. Since my data is per second, I am using mpd=1. I also want to have a new peak or valley only if the vector value has dropped below 0.1 or rised above -0.1. When I use the code below, it doesn’t seem to work for my case.

peak12 = detect_peaks(nrz, mph=0.25 , mpd=1, threshold=0.25, valley=False)
peak13 = detect_peaks(nrz,mph=-0.25, mpd=1, threshold=-0.25, valley=True)

Should I use another parameter when calling the function?
(I also attached a simple .xlsx file with the peaks and valleys I want to detect.
example.xlsx

Thx for the greate tutorials!

First of all, thank you for writing such a great tutorial. It's both informative and detailed.
I'm very interested in using python to do biomechanics simulation and control.

Is there any plan for adding more tutorials on motor control? I've found it scarce not only in python control but also in biomechanics. I'm mostly interested in using control theory for biomechanics control.

Thx for all you've done!

Issue when specifying ax object for plotting

Thanks for this code, it's been useful so far !

I discovered a small issue in the _plot() method. When specifying an ax object only the first reference would be plot.

The issue can be replicated as:
fig, ax = plt.subplots(ncols=3,nrows=3,figsize=(16,12))
ind1 = detectPeaks.detectPeaks(a1, show=True, ax=ax[2,0], threshold=0, kpsh=True, mpd=2, mph=5e-2)
ind2 = detectPeaks.detectPeaks(a2, show=True, ax=ax[2,1], threshold=0, kpsh=True, mpd=2, mph=5e-2)

The workaround is easy:
if ax is None:
_, ax = plt.subplots(1, 1, figsize=(8, 4))
noAx = True
else:
noAx = False
(...)

if noAx:
plt.show()