modelling and simulation

Question 1

Principle

Answer 1

target system has no clear boundary → model is well defined (only part of target system) → simulation → purpose

Question 2

models of systems

Answer 2

represent a selected part of the world

• models of phenomena: represent all general feautres of the world
• models of data: corrected and idealised raw data

Question 3

models of theory

Answer 3

represent a theory

- interprets law of a theory

Question 4

model types

Answer 4

no accepted categorization of models & broad range of applications

• physical models
• mathematical models: described and solved analytically
• computational models: algorithmic and implemented into computer

Question 5

simulation

Answer 5

• solve equations for which it is not possible to derive results or solve them analytically
  → bone stiffness, blood flow velocity
• used in connection with dynamic models
• aim: solve equation of motion to represent time-evolution of target system

Question 6

purposes of simulations

Answer 6

heuristic purposes
- represent information to ourselves & communicate knowledge to others
predicting purposes
- behaviour of systems under particular set of circumstances
- used for prediction 
understanding purposes
- understand systems and their behaviour
- use existing data, to answer questions

Question 7

computer models

Answer 7

similar to physical models

Question 8

computer simulation definitions

Answer 8

narrow definition: run on a computer, step-by-step methods to explore approximate behaviour of mathematical model
broad definition: comprehensive method to study systems
- choose a model → implementation → calculation output → visualizing; analysing results
alternative definition: any system that is believed or hoped to have dynamical behaviour that is similar enough to some other system, also performed using real physical models

Question 9

equation-based simulation

Answer 9

• based on mathematical model → global differnetial equations describe the system’s behaviour
• most common in physical and other sciences
• associated with physical theories
• can be particle-based (interaction of n-discrete bodies) or field-based (time evolution of a continous medium/field)

Question 10

agent-based simulation

Answer 10

• represent behaviour of discrete agents

- most common in social and behavioural sciences

Question 11

multiscale simualtion

Answer 11

• hybrids of different kinds of modelling methods
• couple together modelling element form different scales of description
  → bone remoddling

Question 12

monte carlo simulation

Answer 12

• use randomness to calculate properties of mathematical model
• random sampling to obtain results
• useful where underlying mechanism are not well understood

Question 13

Verification and Validation definition

Answer 13

addresses correctness of numerical solution → solving chosen equations correctly
- determining wheter output of simulation approximates true solution
principle strategy: compare equations and results

Question 14

solution verification

Answer 14

• verifies that output approximates true solution
• code verification: code carries out intended algorithm
  → comparison of computed output with analytical solutions
  → inadequate: bc simualtions often used where no analytical solution exists
• indirect techniques available: checking discretisation dependency

Question 15

validation

Answer 15

• detemining whether chosen model is good enough to represent real word system
• comparing model output with observable data
  → difficult: data are typically spare
• testing subsystems and comparing results to experiments
  → use simulation to generate missing data

Question 16

simulation and experiments

Answer 16

• accurately mimicking complex phenomenon → what-if experiments = in silico experiments

Question 17

clinically relevant computer simulation

Answer 17

• spatial and temporal resolution very limited in patients
• computer models require input data that is not available
• time-lapse imaging: might be used to at least derive some of these missing model inputs
  → principle: several images taken over time

Question 18

equation-based simulation

example of particle-based and field-based simulation

Answer 18

• particle-based: n discrete elements and a set of differential equations governing their interaction.
• field-based: set of equations governing the time evolution of a continuous medium or field.

Question 19

spatial and temporal limitations

Answer 19

spatial limitations: targeted structures are far away

temporal limitation: measurement with i.e. radiation is not always possible