Concepts Human movement Sciences
Stability
We define the human body as an inverted pendulum. With stability is: equilibrium
There are always perturbations present, an inverted pendulum is so by definition unstable. By adding
springs to the unstable inverted pendulum we can make it stable again.
We come to an equation: 𝑚 ∙ 𝑔 ∙ ℎ = −𝑑𝑀𝐹𝑠 /𝑑𝛽
This doesn’t say much: −𝑑𝑀𝐹𝑠 /𝑑𝛽, this is also known as the bending stiffness (Kb)
𝑚 ∙ 𝑔 ∙ ℎ = 𝐾𝑏
Now we know that when we add more mass to the Inverted pendulum the system will become more
unstable. We have 2 types of stiffness:
1. Tensile stiffness: when a spring Is pulled out,
2. Compressive stiffness : when a spring is pushed together.
Another important equation would be:
𝑚 ∙ 𝑔 ∙ ℎ = 𝑎2 ∙ 𝐾
With 𝑎 = 𝑀𝑜𝑚𝑒𝑛𝑡 𝑜𝑓 𝑎𝑟𝑚
And 𝐾 = 𝑠pring stiffness
So an increase in moment arm will increase the effect of the spring quadratically!
When trying to make the inverted pendulum as accurate and representable as possible, we need to
add multiple springs to the inverted pendulum. The springs of the inverted pendulum are in the spine
the ligaments and the muscles around the spine. These biological springs are not linear related, a
muscle can pull, but can’t push.
Then the equation becomes a bit different again:
𝑚 ∙ 𝑔 ∙ ℎ < 𝐾𝑏
‘Gain’= the strength of the correction on the output, caused by a perturbation.
Stiffness:
The stiffer the spring the smaller the oscillations become, the more periods/time.
Damping
When no damping is added to the system, the oscillations will continue to exist. With damping the
oscillations will reduce over time.
With more damping the performance gets better! There is a fast return to baseline and the
oscillations are smaller.
State variables:
A state variable is one of the set of variables that are used to describe the mathematical "state" of a
dynamical system
1. Orientation:
Controlled by stiffness
2. Velocity:
Controlled by damping
Robustness:
= describes the biggest perturbation a system can recover from. Higher robustness is accomplished
by higher damping and an increased stiffness.
,So concluded:
One muscle:
𝑚 ∙ 𝑔 ∙ ℎ = 𝑎2 ∙ 𝐾
Multiple muscles:
𝑚 ∙ 𝑔 ∙ ℎ < 𝐾𝑏
The slower the system returns to baseline, the worse the performance of the system. Fast return to
baseline is a good performance.
Biological springs are non-linear springs, with a neutral zone at the beginning, here the ligaments are
still wrinkled and won’t produce any force while there is stretching of the ligaments.
Only ligaments will not be enough to reach stability in the spine.
Muscles are needed to stabilize the spine. There is a linear like relation between muscle stiffness and
Force. When the linear equation is formulated from the data, we get: Km(muscle stiffness) =
(constant* Muscle Force)/ muscle length.
How more muscle Force the stiffer the muscle becomes!
Muscles can provide stability but it does means they have to be active all the time. This has to be so
on both sides of the spine.
= Contraction:
Both agonistic and antagonistic muscles have to be active.
The contribution of the different active muscles are dependent on their moment arm.
We have local muscles structures: connecting all vertebrae to each other
And we have Global muscle structures: connecting only the upper and lower vertebrae.
Resulting in bigger moment arms.
Only the use of global muscle structures is not enough to achieve stability, also the local muscle
structures are needed to stabilize the in-between vertebrae.
When a perturbation is added to a system a reaction from the system to the perturbation is needed.
This is done so by a feedback loop in the system.
Important notes to remember in the feedback loop:
1. Ki = internal stiffness
2. Kr = reflex stiffenss
3. Bi = internal demping
4. Br = reflex damping
5. Tau = delay
Remember that reflex stiffness and damping are delayed in the system while Ki and Bi (internal) are
without delay. So internal is faster than reaction. The delay from the reactional stiffness and damping
are expressed in Tau (s).
Delay plays an important role in the system, a too big of a delay can cause instability of the
pendulum. A solution to this instability is to increase the gain (= damping + stiffness). BUT there is a
downside to this! It has to be considered that the orientation (positive or negative) of the pendulum
and the orientation (negative ) of the delay can work in the same direction, resulting in an increasing
amplitude of the oscillation instead of decreasing it! This happens when the gain is increased too
much, so too stiff muscles can result in a negative moment, while the orientation of the pendulum is
also negative in that moment of time.
Intrinsic stiffness is faster in response but:
1. More energy consuming, muscle are always active
2. It limits joint mobility
, Reflex stiffness in contrary response later, but is less energy consuming, only muscle activation when
needed.
How delays arises:
1. Mechanoreceptors:
Muscle spindles in the muscle are stretch receptors that detect changes in muscle length. A reflex is a
fast feedback loop (but still slower than intrinsic feedback). Reflex feedback goes from the muscle
spindle 1A afferent neuron 1 synapsalpha motor neuron back to the muscle spindle.
Muscle stretches, muscle spindle stretches: 1A afferent nerve starts firing. (=velocity feedback) when
max length is reached of the muscle spindle: the 2 afferent nerve starts firing (=position feedback)
1. 1A afferent nerve:
Velocity feedback
2. 2 afferent nerve:
Position feedback
The delay is caused by a firing threshold of the nerves. Only after reaching the threshold the nerves
starts firing.
2. Nerve conduction
Nerve conductions says something about how fast the signal can travel through the nerve. This
depends on:
Fiber diameter
# synapsis involved
Age (loss of myelin)
When signals travels through only 1 synapse (like reflex loop) than it is called monosynaptic.
3. Electro Mechanical Delay (EMD) in the muscle
This one is not bound to the feedback loop but to the muscle itself. Here a delay arises from the
delay between action potential, CA2+ accumulation and Force production.
There are 2 delays in this process:
1. T-tubule: time between synaptic activation and action potential traveling through T-
tubule.
2. CA2+ build up: it takes time to build up the CA2+ concentration till a level the Force
production comes in.
Time delay is shorter when the tendon (pees) is stiffer or when the muscle is stronger.
The gain of the spindle feedback loop is: O/I
A higher gain is reached when:
The sensor is more sensitive
The alpa-motorneuron is more excitable
The muscle is stronger
Time delay is larger when:
Threshold of muscle spindle is higher
Longer distance to the SC
The # of synapsis increase
The EMD takes longer.
There are besides intrinsic and reaction feedback more feedback loops. Like Km (muscle) and Kv
(visual/vestibular).
Stability
We define the human body as an inverted pendulum. With stability is: equilibrium
There are always perturbations present, an inverted pendulum is so by definition unstable. By adding
springs to the unstable inverted pendulum we can make it stable again.
We come to an equation: 𝑚 ∙ 𝑔 ∙ ℎ = −𝑑𝑀𝐹𝑠 /𝑑𝛽
This doesn’t say much: −𝑑𝑀𝐹𝑠 /𝑑𝛽, this is also known as the bending stiffness (Kb)
𝑚 ∙ 𝑔 ∙ ℎ = 𝐾𝑏
Now we know that when we add more mass to the Inverted pendulum the system will become more
unstable. We have 2 types of stiffness:
1. Tensile stiffness: when a spring Is pulled out,
2. Compressive stiffness : when a spring is pushed together.
Another important equation would be:
𝑚 ∙ 𝑔 ∙ ℎ = 𝑎2 ∙ 𝐾
With 𝑎 = 𝑀𝑜𝑚𝑒𝑛𝑡 𝑜𝑓 𝑎𝑟𝑚
And 𝐾 = 𝑠pring stiffness
So an increase in moment arm will increase the effect of the spring quadratically!
When trying to make the inverted pendulum as accurate and representable as possible, we need to
add multiple springs to the inverted pendulum. The springs of the inverted pendulum are in the spine
the ligaments and the muscles around the spine. These biological springs are not linear related, a
muscle can pull, but can’t push.
Then the equation becomes a bit different again:
𝑚 ∙ 𝑔 ∙ ℎ < 𝐾𝑏
‘Gain’= the strength of the correction on the output, caused by a perturbation.
Stiffness:
The stiffer the spring the smaller the oscillations become, the more periods/time.
Damping
When no damping is added to the system, the oscillations will continue to exist. With damping the
oscillations will reduce over time.
With more damping the performance gets better! There is a fast return to baseline and the
oscillations are smaller.
State variables:
A state variable is one of the set of variables that are used to describe the mathematical "state" of a
dynamical system
1. Orientation:
Controlled by stiffness
2. Velocity:
Controlled by damping
Robustness:
= describes the biggest perturbation a system can recover from. Higher robustness is accomplished
by higher damping and an increased stiffness.
,So concluded:
One muscle:
𝑚 ∙ 𝑔 ∙ ℎ = 𝑎2 ∙ 𝐾
Multiple muscles:
𝑚 ∙ 𝑔 ∙ ℎ < 𝐾𝑏
The slower the system returns to baseline, the worse the performance of the system. Fast return to
baseline is a good performance.
Biological springs are non-linear springs, with a neutral zone at the beginning, here the ligaments are
still wrinkled and won’t produce any force while there is stretching of the ligaments.
Only ligaments will not be enough to reach stability in the spine.
Muscles are needed to stabilize the spine. There is a linear like relation between muscle stiffness and
Force. When the linear equation is formulated from the data, we get: Km(muscle stiffness) =
(constant* Muscle Force)/ muscle length.
How more muscle Force the stiffer the muscle becomes!
Muscles can provide stability but it does means they have to be active all the time. This has to be so
on both sides of the spine.
= Contraction:
Both agonistic and antagonistic muscles have to be active.
The contribution of the different active muscles are dependent on their moment arm.
We have local muscles structures: connecting all vertebrae to each other
And we have Global muscle structures: connecting only the upper and lower vertebrae.
Resulting in bigger moment arms.
Only the use of global muscle structures is not enough to achieve stability, also the local muscle
structures are needed to stabilize the in-between vertebrae.
When a perturbation is added to a system a reaction from the system to the perturbation is needed.
This is done so by a feedback loop in the system.
Important notes to remember in the feedback loop:
1. Ki = internal stiffness
2. Kr = reflex stiffenss
3. Bi = internal demping
4. Br = reflex damping
5. Tau = delay
Remember that reflex stiffness and damping are delayed in the system while Ki and Bi (internal) are
without delay. So internal is faster than reaction. The delay from the reactional stiffness and damping
are expressed in Tau (s).
Delay plays an important role in the system, a too big of a delay can cause instability of the
pendulum. A solution to this instability is to increase the gain (= damping + stiffness). BUT there is a
downside to this! It has to be considered that the orientation (positive or negative) of the pendulum
and the orientation (negative ) of the delay can work in the same direction, resulting in an increasing
amplitude of the oscillation instead of decreasing it! This happens when the gain is increased too
much, so too stiff muscles can result in a negative moment, while the orientation of the pendulum is
also negative in that moment of time.
Intrinsic stiffness is faster in response but:
1. More energy consuming, muscle are always active
2. It limits joint mobility
, Reflex stiffness in contrary response later, but is less energy consuming, only muscle activation when
needed.
How delays arises:
1. Mechanoreceptors:
Muscle spindles in the muscle are stretch receptors that detect changes in muscle length. A reflex is a
fast feedback loop (but still slower than intrinsic feedback). Reflex feedback goes from the muscle
spindle 1A afferent neuron 1 synapsalpha motor neuron back to the muscle spindle.
Muscle stretches, muscle spindle stretches: 1A afferent nerve starts firing. (=velocity feedback) when
max length is reached of the muscle spindle: the 2 afferent nerve starts firing (=position feedback)
1. 1A afferent nerve:
Velocity feedback
2. 2 afferent nerve:
Position feedback
The delay is caused by a firing threshold of the nerves. Only after reaching the threshold the nerves
starts firing.
2. Nerve conduction
Nerve conductions says something about how fast the signal can travel through the nerve. This
depends on:
Fiber diameter
# synapsis involved
Age (loss of myelin)
When signals travels through only 1 synapse (like reflex loop) than it is called monosynaptic.
3. Electro Mechanical Delay (EMD) in the muscle
This one is not bound to the feedback loop but to the muscle itself. Here a delay arises from the
delay between action potential, CA2+ accumulation and Force production.
There are 2 delays in this process:
1. T-tubule: time between synaptic activation and action potential traveling through T-
tubule.
2. CA2+ build up: it takes time to build up the CA2+ concentration till a level the Force
production comes in.
Time delay is shorter when the tendon (pees) is stiffer or when the muscle is stronger.
The gain of the spindle feedback loop is: O/I
A higher gain is reached when:
The sensor is more sensitive
The alpa-motorneuron is more excitable
The muscle is stronger
Time delay is larger when:
Threshold of muscle spindle is higher
Longer distance to the SC
The # of synapsis increase
The EMD takes longer.
There are besides intrinsic and reaction feedback more feedback loops. Like Km (muscle) and Kv
(visual/vestibular).
