mammothb / BN5205

Scilab codes for BN5205 Computational Biomechanics

BN5205

Contains Scilab codes for BN5205 Computational Biomechanics

Case Studies

• Week 2: Introduction to Scilab
  1. Fizz-Buzz
  2. Plot function
  3. Linear system
  4. Sum of even Fibonacci numbers
• Week 3: Viscoelasticity (Single ODEs, Explicit)
  1. Solving Kelvin-Voigt governing equation using various numerical methods
  • Forward Euler
  • Heun's Method
  • Midpoint Method
  • 4^th order Runge-Kutta method
  2. Comparison between numerical methods and experimental data of the hysteresis loop
• Week 4: Smooth Muscle Contraction (Multiple ODEs, Explicit & Implicit)
  1. Solving Hai & Murphy model using various numerical methods
  • Forward Euler
  • Heun's Method
  • Midpoint Method
  2. Stability of implicit method vs explicit method
  • Backward Euler
  • Midpoint Method
• Week 5: 3-point Bending on Tibia (2^nd order ODE: IVP and BVP)
  1. Solving Euler-Bernoulli beam theory equation (BVP) using two methods
  • Shooting method
  • Equilibrium method
  2. Verifying numerical result against analytical result
• Week 6: Leukocyte Migration (Parabolic PDE)
  1. Solving 1D diffusion-convection model
  • Forward-Time Central-Space Method
  • Method of line with Forward Euler
  • Crank Nicolson method
• Week 7: Cryoablation (Elliptic PDE)

1. Solving 2D steady state heat equation using finite difference
   • Dirichlet BC
   • Neumann BC

• Week 8: Finite element linear basis functions

1. 1D linear basis function and 1D linear Lagrange interpolation
2. 2D bilinear basis functions and 2D linear Lagrange interpolation

• Week 9: 1D steady-state heat conduction

1. Solving 1D steady-state heat equation using finite elements

• Week 11: Gaussian quadrature
• Week 12: Sparse Matrix Operations

Assignments

1. Simulate membrane potential using model of a mesencephalic V neuron developed by Wu et al
   • Solve multiple ODEs using Forward Euler and Heun's Method
2. Simulate 2D diffusion-reaction equation