W1&2 Applications of Variability and Complexity Analyses W2 kinda UNFINISHED Flashcards
fractal
geometric shape that has the same appearance when you zoom in - self-similar
example of fractal shape and self-similarity in humans
lungs - have higher surface area than volume should allow
key idea of fractals
really simple rule can produce a really complex output/apperance
fractal dimension
a measure of how complex a self-similar figure is
two types of self-similarity
spatial and temporal
lungs - spatial or temporal self-similarity?
spatial self-similarity
spatial self-similarity
if you zoom in on a shape, you find the same shape at a more zoomed in level
temporal self-similarity
- see similar repeating structures at different levels of inspection in time series
- time series looks the same over 30 minutes as it does over 300 minutes
- nothing systematically changing in what we see at different levels of inspection
white noise
- completely random
- can take on any value at any point
- flat spectrum
- most complex
Brownian noise
- random walk noise
- e.g. staggering home drunk, constrained by where you were the last step but next step can be in any direction
- least complex
1/f noise
- between white and brown noise
- pink noise
- in this time series we see self-similar behaviour
- common in healthy biological systems
- moderately complex
double pendulum
- simple system just behaving based on gravitational laws
- but very quickly you cannot predict it
- simple system with complex and chaotic output
What is a chaotic system?
A system which is seemingly deterministic, but you cannot actually predict where the end point will be.
What is an Improbable system?
A highly ordered system with a structure
Explain the graph from Macklem, 2008?
It highlights how life exists between a very ordered levely of complexity and a very chaotic system. It is chaotic enough to allow for adaptability but we can put energy in to maintain some structure
What is the problem with this balance between stability and adaptability? Give an example
- Small changes in a system can cause such vast changes in the whole system.
- One seemingly minor thing can deviate the whole system from its original purpose or function.
- E.g. a small change in the width of a tube within the lungs can cause a change in the overall respiratory system.
Two types of ways of measuring complexity
- Magnitude - standard deviation/coefficient of variation
-> Takes no account of temporal data order - quantify “variability” or “steadiness” - Temporal pattern: this is what “complexity” usually refers to
How does Approximate Entropy (ApEn) measure complexity?
- Measures the regularity of a time series by searching for patters which repeats themselves.
- It considers noise in the system so matching of repeated patterns in quite loose.
- higher ApEn = more info, less predictable
- ranges from 0 to 2
- 0 = completely predictable
- 2 = white noise (unpredictable)
What is Sample Entropy (SampEn)
- Evaluates the probability that similar sequences will remain similar over subsequent points.
- Unlike ApEN, SampEn incoporates a “self-matching” function that avoids bias introduced by self-matching in the ApEn calculation
How does Detrended fluctuation analysis (DFA) measure complexity?
- You detrend the data by separating it into different boxes with different scales.
- You then fit a line of best fit to each box and subtract the mean associated with that line.
- You can then look at the residual fluctuation.
- You can then complete that process for smaller box sizes.
- You then plot the log of the root mean square error against the log of the corresponding box size.
- You fit a line and that line gives you your alpha (α) exponent.
- An alpha exponent value of 0.5 indicates random, white noise (high complexity).
- An alpha value of 1 indicates pink noise (moderate complexity),
- a value of 1.5 indicates Brownian noise (lower complexity).
How is entropy used in information theory?
entropy increases as freedom of choice increases and decreases as uncertainty decreases
Give an example of ApEn being applied to a biological time series
(Lipsitz & Goldberger, 1992)
* heart rate series from a young and old individual
* If you calculate the mean and SD, they seem to be fairly similiar but the structure is obviously different
* ApEn for the older subject is much lower, while the younger subject has a lot of self-similarity and entropy
* suggests that, as you get older, your system loses complexity and becomes much more structured and predictable
* When you grow older, you lose capacity to adapt
ApEn applied to SIDS (sudden infant death)
(Pincus et al., 1993)
* normal infant vs infant that experience an aborted SIDS event
* SIDS infant had much lower ApEn
* showing a loss of complexity with disease
Give three reasons for why there are fluctuations in Isometric Force Production
- Motor Unit Recruitment
- Motor Unit Firing
- Muscle-Tendon Intercations
Why do we lose complexity with age?
- this process of denervation and reinnervation
- As you age, you lose some of the innervation into your type 2 muscle fibres and they get reinnervated (reattached to) the motor nerve that supply type 1 fibres
- have fewer motor units over time that are larger and slower
- That loss of complexity in the bits making up the motor system leads to reduction in complexity in the motor output
define fatigue
Any exercise-induced decrease in maximal voluntary force of power produced by a muscle or muscle group (Taylor & Gandevia, 2008)
How does isometric muscle force change with fatigue?
- isometric muscle force is complex at rest and loses complexity at task failure
Describe a study that explains how fatigue and entropy relates
(Pethick et al., 2015)
* Participants were required to do a duty cycle; 6 seconds on 4 seconds off. Their ApEn, SampEn, and DFA were measured in the first minute and in the last minute.
* First min: SampEn, ApEn, and DFA were all high, indicating self similarity and 1/F noise.
* Last min: Low ApEn, SampEn, suggesting fatigue causes the system to become more predicable.
* This could be due to their muscles losing oxygen so the participants have to do non-complex movements.
* Complexity is sacrificed to prevent fatigue.
What is critical power?
(Monod & Scherrer, 1965)
* Researchers found an asymptotic point, where you can reporduce the power for a longer time, the critical power.
* It is a maximum rate a muscle can keep up for a very long time without fatigue.
Does the fatigue-induced loss of complexity occur below the critical torque (power)?
(Pethick et al., 2016)
* critical torque is a range not a neat cut-off
* below CP no major loss of compelxity
* above CP loss of complexity over time
